U.S. Department of Transportation Publication No. FHWA-NHI-11-032 

Federal Highway Administration GEC No. 3 

August 2011 (Rev. 1) 

NHI Course No. 130094 

LRFD Seismic Analysis and Design of 

Transportation Geotechnical Features and 

Structural Foundations 

Reference Manual 

Developed following:

AASHTO LRFD Bridge Design Specifications 4th Ed., 2007, and 2008 and 2009 Interims 

AASHTO Guide Specifications for LRFD Seismic Bridge Design, 2009 
NOTICE

The contents of this report reflect the views of the authors, who are responsible for the facts and 

accuracy of the data presented herein. The contents do not necessarily reflect policy of the 

Department of Transportation. This report does not constitute a standard, specification, or 

regulation. The United States Government does not endorse products or manufacturers. Trade 

or manufacturer's names appear herein only because they are considered essential to the object of 

this document. 
Technical Report Documentation Page 

1. Report No.

FHWA-NHI-11-032 

2. Government Accession No.

 

3. Recipient’s Catalog No.

4. Title and Subtitle

LRFD SEISMIC ANALYSIS AND DESIGN OF TRANSPORTATION 

GEOTECHNICAL FEATURES AND STRUCTURAL FOUNDATIONS

NHI COURSE NO. 130094 REFERENCE MANUAL

GEOTECHNICAL ENGINEERING CIRCULAR NO. 3 

5. Report Date

 August 2011 (Rev. 1) 

6. Performing Organization Code 

7. Author(s)

Edward Kavazanjian, Jr.1

, PhD, PE, Jaw-Nan Joe Wang, PhD, PE, 

Geoffrey R. Martin2

, PhD, Anoosh Shamsabadi3, PhD, PE, 

Ignatius (Po) Lam2

, PhD, PE, Stephen E. Dickenson4, PhD, PE, and 

C. Jeremy Hung, PE. 

8. Performing Organization Report No.

9. Performing Organization Name and Address 

Parsons Brinckerhoff, Inc. 

One Penn Plaza, New York, NY 10119 

1

Arizona State University, Tempe, AZ 85287 

2 Earth Mechanics Inc., Fountain Valley, CA 92708 

3 California Department of Transportation, Sacramento, CA 95816 4 New Albion Geotechnical, Inc., Corvallis, OR 97333

10. Work Unit No. (TRAIS)

11. Contract or Grant No.

DTFH-61-D-00011/T-07-004 

12. Sponsoring Agency Name and Address

National Highway Institute (NHI) 

U.S. Department of Transportation 

Federal Highway Administration, Washington, D.C. 20590

13. Type of Report and Period Covered

14. Sponsoring Agency Code 

15. Supplementary Notes

FHWA COTR: Louisa Ward 

FHWA Task Manager: Firas I. S. Ibrahim, PhD, PE 

FHWA Technical Reviewers: Silas Nichols, PE; Justice Maswoswe, PhD, PE; Thomas K. Saad, PE; and 

 Jerry A. DiMaggio, P.E.

16. Abstract

This manual serves as a reference manual for use with the 5-day NHI training course 130094 “LRFD Seismic Analysis 

and Design of Transportation Geotechnical Features and Structural Foundations.” Additionally it replaces the previous 

version of Geotechnical Engineering Circular No.3 “Design Guidance: Geotechnical Earthquake Engineering for 

Highways” published in May 1997. This manual is intended to provide a technical resource for bridge and 

geotechnical engineers responsible for seismic analysis and design of transportation geotechnical features and 

structures such as soil and rock slopes, earth embankments, retaining structures and buried structures; and structural 

foundations including shallow and deep foundations and abutments. Topics include earthquake fundamentals and 

engineering seismology, seismic hazard analysis, ground motion characterization, site characterization, site-specific 

seismic site response analysis, geotechnical hazards including liquefaction, slope instability, and seismic settlement, 

and soil-foundation-structure interaction are included. This manual also addresses LRFD analysis and design 

requirements and recommendations of the seismic provisions in AASHTO LRFD Bridge Design Specifications, 

AASHTO Guide Specifications for LRFD Seismic Bridge Design, and the NCHRP Report 611 from NCHRP Project 

12-70 “Seismic Analysis and Design of Retaining Walls, Buried Structures, Slopes, and Embankments.”

17. Key Words

Seismic design, earthquakes, geotechnical hazard, seismic 

hazard analysis, ground motion characterization, liquefaction, 

soil slopes, rock slopes, slope stability, earth embankments, 

earth retaining structures, soil structure interaction, bridge 

structural foundations, seismic settlement. 

18. Distribution Statement

No restrictions. 

19. Security Classif. (of this report) 

UNCLASSIFIED 

20. Security Classif. (of this page)

UNCLASSIFIED 

21. No. of Pages

592 

22. Price

Form DOT F 1700.7(8-72) Reproduction of completed page authorized 
CONVERSION FACTORS

Approximate Conversions to SI Units Approximate Conversions from S

When you know Multiply by To find When you know Multiply by 

(a) Length 

inch 25.4 millimeter millimeter 0.039 

foot 0.305 meter meter 3.28 

yard 0.914 meter meter 1.09 

mile 1.61 kilometer kilometer 0.621 

(b) Area 

square inches 645.2 square millimeters square millimeters 0.0016 

square feet 0.093 square meters square meters 10.764 

acres 0.405 hectares hectares 2.47 

square miles 2.59 square kilometers square kilometers 0.386 

(c) Volume 

fluid ounces 29.57 milliliters milliliters 0.034 

gallons 3.785 liters liters 0.264 

cubic feet 0.028 cubic meters cubic meters 35.32 

cubic yards 0.765 cubic meters cubic meters 1.308 

(d) Mass 

ounces 28.35 grams grams 0.035 

pounds 0.454 kilograms kilograms 2.205 

short tons (2000 lb) 0.907 megagrams (tonne) megagrams (tonne) 1.102 

(e) Force 

pound 4.448 Newton Newton 0.2248 

(f) Pressure, Stress, Modulus of Elasticity 

pounds per square foot 47.88 Pascals Pascals 0.021 p

pounds per square inch 6.895 kiloPascals kiloPascals 0.145 p

(g) Density 

pounds per cubic foot 16.019 kilograms per cubic meter kilograms per cubic meter 0.0624 

(h) Temperature 

Fahrenheit temperature(oF) 5/9(oF- 32) Celsius temperature(oC) Celsius temperature(oC) 9/5(oC)+ 32 Fa

Notes: 1) The primary metric (SI) units used in civil engineering are meter (m), kilogram (kg), second(s), newton (N) and pascal (Pa

 2) In a "soft" conversion, an English measurement is mathematically converted to its exact metric equivalent. 

 3) In a "hard" conversion, a new rounded metric number is created that is convenient to work with and remember.
FHWA-NHI-11-032 

Seismic Design - Geotechnical Features i August 2011

PREFACE

This manual is intended to provide a technical resource for bridge and geotechnical engineers responsible 

for seismic analysis and design of transportation geotechnical features and structures such as soil and rock 

slopes, earth embankments, retaining structures and buried structures; and structural foundations 

including shallow and deep foundations and abutments. This manual includes topics such as earthquake 

fundamentals and engineering seismology, seismic hazard analysis, ground motion characterization, site 

characterization, site-specific seismic site response analysis, geotechnical hazards including liquefaction, 

slope instability, and seismic settlement, and soil-foundation-structure interaction, and addresses the 

requirements and recommendations of the seismic provisions in AASHTO LRFD Bridge Design 

Specifications (2007, 2008, and 2009), AASHTO Guide Specifications for LRFD Seismic Bridge Design

(2009), and the NCHRP Report 611 (2008) from NCHRP Project 12-70 “Seismic Analysis and Design of 

Retaining Walls, Buried Structures, Slopes, and Embankment.” 

Chapters 1 and 2 present LRFD seismic analysis and design principles, and basic concepts of seismic 

geology and engineering seismology. This information is essential background information for

subsequent discussions of seismic hazard analysis, ground motion characterization and structural 

foundation design. 

Chapter 3 presents the details of both probabilistic and deterministic seismic hazard analysis. 

Development of the Uniform Hazard Spectrum for a specified probability and exposure period using 

either the National Seismic Hazard maps developed by the USGS or the ground motion maps developed 

by USGS specifically for AASHTO is presented. Development of the AASHTO truncated acceleration 

response spectra for use in structural analysis from the Uniform Hazard Spectrum is illustrated. The 

process of deaggregation by which a probabilistically-derived uniform hazard spectrum is decomposed 

into magnitude and distance combinations in order to determine a representative magnitude and distance 

for the design earthquake is described. Guidelines for selecting a suite of representative time histories for 

the representative design event are presented.

Chapter 4 described site characterization for seismic analysis. The use of the Standard Penetration Test 

(SPT) and the Cone Penetration Test (CPT) to evaluate site stratigraphy and geotechnical properties is 

explained in detail. Geophysical techniques for site investigation are also addressed. Characterization of 

rock mass behavior and quantification of rock mass strength is described. Correlations between important 

geotechnical properties, including relative density, shear strength, and shear wave velocity, from both in 

situ test results and soil classification and index test data are presented.

In Chapter 5, the process of site specific seismic response analysis is described. Methods addressed in 

this chapter include simplified chart-based methods to adjust the peak ground acceleration for local site 

conditions, equivalent linear one-dimensional site response analysis, non-linear one-dimensional site 

response analysis with pore pressure generation, and advanced two-dimensional site response analysis. 

The development of input parameters for equivalent-linear one-dimensional site response analyses, the 

most common type of advanced analysis performed in practice, are described in detail.

Chapter 6 describes earthquake-induced damage due to the geotechnical seismic hazards of slope 

instability, liquefaction, and seismic settlement. Methods to evaluate seismic slope deformation, 

liquefaction potential, liquefaction-induced ground displacements, and seismic settlement are described in 

detail in this chapter. A method to evaluate the appropriate value of the seismic coefficient for pseudostatic slope stability analyses that accounts for spatial incoherence of ground motions, the local seismic 

environment, local site conditions, and acceptable displacement levels is presented.
FHWA-NHI-11-032 

Seismic Design - Geotechnical Features ii August 2011

Chapter 7 addresses design of earthwork features for transportation facilities, including soil and rock 

slopes and embankments. A performance-based seismic design philosophy that employs the concept of 

allowable displacement is described. Soil and site improvement techniques that can be used when the 

seismic displacement are unacceptable are presented with an emphasis on remediation of slope stability 

and liquefaction. 

Chapter 8 describes the seismic design process and the AASHTO seismic design methodology, including 

capacity design of bridge foundations, the concept of the earthquake resisting system for a bridge, 

guidelines for what types of earthquake resisting elements are allowable and not recommended, and basic 

principles of soil-foundation-structure interaction. The principles of both kinematic and inertial 

interaction are described. 

Chapter 9 describes the seismic design of shallow foundations, including techniques to assess both 

foundation stiffness and foundation capacity. Equations for calculating the stiffness coefficients for the 

six modes of foundation displacement for use in an inertial interaction analysis are presented. Foundation 

capacity analyses discussed in the chapter include bearing, overturning, and sliding.

Chapter 10 addresses deep foundation design. Both p-y/t-z analyses and simple elastic solutions to 

evaluate the stiffness of an individual pile are discussed along with methods to account for group effects 

and to assemble individual pile and pile cap stiffness into a group stiffness. Sophisticated methods and a 

simple approximate method to account for kinematic interaction at soft soil sites are described. Analyses 

to evaluate the response of pile foundations to ground displacement demand from laterally spreading 

induced by liquefaction are discussed.

Chapter 11 presents methods for seismic design of free standing retaining walls. A variety of methods for 

predicting seismic active earth pressures, including the Mononobe-Okabe method, design charts that 

include the influence of a cohesion component to the shear strength, the Coulomb wedge method, and the 

general equilibrium method, are described along with a displacement-based method for evaluating the 

appropriate seismic coefficient for use in design. Charts for evaluating the passive earth pressure 

coefficient, including the effect of cohesion, are also presented in this chapter. Design of gravity and 

semi-gravity retaining walls for sliding, overturning, and bearing modes is discussed in detail. Earth 

pressure diagrams for non-gravity cantilever walls, anchored walls, and MSE walls are described along 

with recommendations for the seismic coefficient for use in design.

Chapter 12 describes bridge abutment design. The characterization of the stiffness of both conventional 

seat-type and integral abutments for inclusion in the global bridge model is presented. The effect of 

skewed abutments on the seismic performance of the bridge is discussed.

Lastly, Chapter 13 presents design considerations for buried structures, including culverts and pipelines. 

Simple closed form solutions are presented for the displacement demand on buried structures subject to 

seismic loading. 
FHWA-NHI-11-032 

Seismic Design - Geotechnical Features iii August 2011

ACKNOWLEDGMENTS

This document serves as a reference manual for use with the National Highway Institute (NHI) Course 

130094 titled LRFD Seismic Analysis and Design of Transportation Geotechnical Features and 

Structural Foundations developed in March 2011 by Parsons Brinckerhoff Inc. (PB) and authored by E. 

Kavazanjian, Jr., J. Wang, G.R. Martin, A. Shamsabadi, I.P. Lam, S.E. Dickenson, and C.J. Hung. It also 

replaces the 1997 version of FHWA Geotechnical Engineering Circular No.3 “Design Guidance: 

Geotechnical Earthquake Engineering for Highways” (FHWA-SA-97-076) developed by GeoSyntec 

Consultants and authored by E. Kavazanjian, Jr., N. Matasovic, T. Hadj-Hamou, and P.J. Sabatini.

This manual addresses in general the requirements and recommendations of the seismic provisions in

AASHTO LRFD Bridge Design Specifications (2007, 2008 and 2009), AASHTO Guide Specifications for 

LRFD Seismic Bridge Design (2009), and the NCHRP Report 611 from NCHRP Project 12-70 “Seismic 

Analysis and Design of Retaining Walls, Buried Structures, Slopes, and Embankments” (2009).

Permission by the FHWA to include some original manuscripts and graphics from the FHWA Reference 

Manual “Geotechnical Earthquake Engineering “(FHWA-HI-99-012) developed by Parsons Brinckerhoff 

Inc. and authored by E. Kavazanjian, Jr., N. Matasovic, T. Hadj-Hamou, and J. Wang, is gratefully 

appreciated. 

The authors would like to especially acknowledge the continuing support of Louisa Ward, NHI Program 

Manager, and Firas Ibrahim, FHWA Task Manger, and the reviews and recommendations provided by the 

following individuals who served on the Technical Working Group for this project:

• Firas I. S. Ibrahim, PhD, P.E. FHWA

• Silas Nichols, P.E. FHWA

• Justice Maswoswe, PhD, P.E. FHWA

• Thomas K. Saad, P.E. FHWA, and

• Jerry A. DiMaggio, P.E. Strategic Highway Research Program/the National Academies

In addition, the authors are grateful for the generous contributions and reviews from Lee Marsh of 

BergerABAM, and from the representatives at South Carolina DOT, Washington DOT, and Illinois DOT.

Lastly, the authors wish to extend their gratitude for the supports provided by a number of professionals 

from Parsons Brinckherhoff (PB), Arizona State University, Tempe, and Earth Mechanics Inc. including 

Matteo Montesi, Vinnie Hung, Lauren Chu and Amy Mengert at PB, and David (Zbigniew) Czupak and

Simon Ghanat at Arizona State University for their support and assistance.
This page is intentionally left blank. 
FHWA-NHI-11-032 Table of Contents

Seismic Design – Geotechnical Features v August 2011

TABLE OF CONTENTS

LIST OF FIGURES ................................................................................................................................. xiii

LIST OF TABLES ................................................................................................................................... xxi

CHAPTER 1 - INTRODUCTION.......................................................................................................... 1-1 

1.1 BACKGROUND........................................................................................................................ 1-1 

1.2 EARTHQUAKE DAMAGE CATEGORIES........................................................................... 1-3 

1.2.1 Primary Damage .................................................................................................................... 1-4 

1.2.2 Secondary Damage ................................................................................................................ 1-5 

1.2.3 Indirect Damage..................................................................................................................... 1-6 

1.3 DAMAGE TO HIGHWAY FACILITIES IN EARTHQUAKES............................................ 1-7 

1.4 AASHTO SEISMIC DESIGN PHILOSOPHY...................................................................... 1-12 

1.5 LOAD AND RESISTANCE FACTOR DESIGN.................................................................. 1-14 

1.5.1 Basic Principles of LRFD .................................................................................................... 1-14 

1.5.2 LRFD versus ASD ............................................................................................................... 1-15 

1.5.3 AASHTO Specifications for Seismic LRFD ....................................................................... 1-15 

1.5.4 AASHTO Limit States and Load and Resistance Factors.................................................... 1-16 

1.6 ORGANIZATION OF THE DOCUMENT ........................................................................... 1-19 

CHAPTER 2 - EARTHQUAKE FUNDAMENTALS AND ENGINEERING SEISMOLOGY....... 2-1 

2.1 INTRODUCTION................................................................................................................... 2-1 

2.2 EARTHQUAKE SOURCES..................................................................................................... 2-1 

2.2.1 General................................................................................................................................... 2-1 

2.2.2 Plate Tectonics....................................................................................................................... 2-2 

2.2.3 Fault Movements ................................................................................................................... 2-6 

2.2.4 Fault Activity ......................................................................................................................... 2-8 

2.3 SEISMIC WAVES ................................................................................................................. 2-11 

2.4 STRONG MOTION RECORDS (TIME HISTORIES)......................................................... 2-12

2.5 PARAMETERS DESCRIBING EARTHQUAKE SIZE AND LOCATION ........................ 2-14

2.5.1 Earthquake Magnitude ......................................................................................................... 2-14

2.5.2 Earthquake Location ............................................................................................................ 2-15

2.5.3 Earthquake Recurrence ........................................................................................................ 2-17

2.6 PARAMETERS DESCRIBING FAULTING........................................................................ 2-19

2.7 PARAMETERS DESCRIBING GROUND SHAKING........................................................ 2-21

2.7.1 Intensity................................................................................................................................ 2-21

2.7.2 Peak Ground Motions.......................................................................................................... 2-23

2.7.3 Energy Content .................................................................................................................... 2-23

2.7.4 Duration ............................................................................................................................... 2-24

2.7.5 Response Spectrum.............................................................................................................. 2-27

2.7.6 Smoothed Uniform Hazard Spectra ..................................................................................... 2-29 
FHWA-NHI-11-032 Table of Contents

Seismic Design – Geotechnical Features vi August 2011

2.7.7 Ground Motion Attenuation Relationships.......................................................................... 2-31 

2.7.8 Predominant Period of the Strong Ground Motions ............................................................ 2-31 

2.7.9 Magnitude-Distance Deaggregation .................................................................................... 2-32 

2.8 SUMMARY ........................................................................................................................... 2-33 

CHAPTER 3 – SEISMIC HAZARD ANALYSIS AND GROUND MOTION 

CHARACTERIZATION ........................................................................................................................ 3-1 

3.1 GENERAL ............................................................................................................................... 3-1 

3.2 SEISMIC HAZARD ANALYSIS ............................................................................................ 3-3 

3.2.1 Seismic Source Identification ................................................................................................ 3-3 

3.2.2 Magnitude-Recurrence Relationships.................................................................................... 3-4 

3.2.3 Strong Motion Attenuation Relationships.............................................................................. 3-9 

3.2.4 Uniform Hazard Spectra ...................................................................................................... 3-19 

3.2.5 Return Period and Seismic Risk........................................................................................... 3-21 

3.2.6 De-aggregation of Design Earthquake, Magnitude and Distance ........................................ 3-23

3.2.7 Deterministic Maximum Magnitude and Ground Motion Evaluation ................................. 3-25 

3.2.8 Probabilistic versus Deterministic Analysis Method ........................................................... 3-26

3.3 HAZARD LEVELS AND RETURN PERIODS FOR FUNCTIONAL AND LIFE SAFETY 

DESIGN .............................................................................................................................................. 3-28 

3.3.1 Performance Levels for Seismi Design................................................................................ 3-28

3.3.2 Return Period for Use in Design .......................................................................................... 3-31

3.3.3 Site Specific Analysis versus USGS National Seismic Hazard Maps................................. 3-32

3.3.4 Ground Motion Characterization ......................................................................................... 3-33

3.3.5 Correlation for Peak Ground Velocity ................................................................................. 3-36

3.3.6 Acceleration Response Spectra versus Displacement Spectra............................................. 3-37

3.3.7 Near-Fault (Near-Field) Directivity Effects......................................................................... 3-37

3.3.8 Local Site Effects................................................................................................................. 3-39

3.3.9 Representative Ground Motion Time Histories................................................................... 3-43

3.3.10 Adjusting Time Histories to a Target Spectrum................................................................... 3-47

3.3.11 Spatially Varying Ground Motions...................................................................................... 3-49

3.3.12 Vertical Ground Motions..................................................................................................... 3-52

3.4 DEVELOPMENT OF AASHTO ACCELERATION RESPONSE SPECTRUM ................. 3-53 

3.4.1 Use of the USGS Website.................................................................................................... 3-54

3.4.2 Use of the USGS/AASHTO CD .......................................................................................... 3-60

3.4.3 Magnitude Deaggregation.................................................................................................... 3-67

3.5 RECENT ADVANCES IN ENGINEERING SEISMOLOGY AND GROUND MOTION 

CHARACTERIZATION ..................................................................................................................... 3-72

3.6 SUMMARY ........................................................................................................................... 3-74

CHAPTER 4 - SITE CHARACTERIZATION ..................................................................................... 4-1 

4.1 INTRODUCTION.................................................................................................................... 4-1 

4.2 SUBSURFACE PROFILE DEVELOPMENT......................................................................... 4-2 

4.2.1 General ................................................................................................................................. 4-2 

4.2.2 Water Level.......................................................................................................................... 4-2 

4.2.3 Soil Stratigraphy................................................................................................................... 4-3 
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Seismic Design – Geotechnical Features vii August 2011

4.2.4 Depth to Bedrock ................................................................................................................. 4-4 

4.2.5 Rock Mass Charcterization .................................................................................................. 4-5 

4.3 REQUIRED SOIL AND ROCK PARAMETERS................................................................... 4-5 

4.3.1 General ................................................................................................................................. 4-5 

4.3.2 Unit Weight and Relative Density ....................................................................................... 4-6 

4.3.3 Shear Wave Velocity............................................................................................................ 4-7 

4.3.4 Cyclic Stress-Strain Behavior .............................................................................................. 4-8 

4.3.5 Peak and Residual Shear Strength...................................................................................... 4-11

4.4 EVALUATION OF SOIL AND ROCK PROPERTIES FOR SEISMIC ANALYSIS.......... 4-12

4.4.1 General ............................................................................................................................... 4-12

4.4.2 In Situ Testing.................................................................................................................... 4-13

4.4.3 Unit Weight and Relative Density ..................................................................................... 4-21

4.4.4 Shear Wave Velocity.......................................................................................................... 4-25

4.4.5 Cyclic Stress-Strain Parameters......................................................................................... 4-28

4.4.6 Peak and Residual Shear Strength...................................................................................... 4-38

4.5 ROCK MASS PROPERTIES................................................................................................. 4-43

4.5.1 Rock Mass Categories........................................................................................................ 4-43

4.5.2 Highly Fractured Rock Masses.......................................................................................... 4-44

4.5.3 Rock Masses with Discrete Discontinuities....................................................................... 4-51 

4.6 SUMMARY ........................................................................................................................... 4-53

CHAPTER 5 - SEISMIC SITE RESPONSE ANALYSIS.................................................................... 5-1 

5.1 GENERAL ............................................................................................................................... 5-1 

5.2 SITE-SPECIFIC SEISMIC RESPONSE ANALYSES............................................................ 5-3 

5.2.1 Types of Site-Specific Analysis........................................................................................... 5-3 

5.2.2 Simple Empirical Relationships........................................................................................... 5-5

5.3 ONE-DIMENSIONAL SITE RESPONSE ANALYSES....................................................... 5-11

5.3.1 Equivalent Linear One-Dimensional Response Analyses.................................................. 5-11

5.3.2 Advanced One-Dimensional Site Response Analysis........................................................ 5-16

5.3.3 Analyses Including Pore Pressure Generation ................................................................... 5-19

5.4 TWO- AND THREE-DIMENSIONAL SEISMIC SITE RESPONSE ANALYSIS ............. 5-21

5.5 SUMMARY ........................................................................................................................... 5-23

CHAPTER 6 - GEOTECHNICAL HAZARDS .................................................................................... 6-1

6.1 GENERAL ............................................................................................................................... 6-1 

6.2 SEISMIC SLOPE INSTABILITY HAZARD.......................................................................... 6-2 

6.2.1 Modes of Slope Instability ..................................................................................................... 6-2 

6.2.2 Limit Equilibrium Pseudo Static Stability Analysis .............................................................. 6-4 

6.2.3 Displacement-Based Seismic Stability Analysis ................................................................. 6-10

6.2.4 Rock Slope Stability Analyses............................................................................................. 6-15

6.3 SOIL LIQUEFACTION HAZARD ....................................................................................... 6-18

6.3.1 Hazard Description and Initial Screening ............................................................................ 6-18

6.3.2 Liquefaction Strengths: Laboratory and In-situ Tests.......................................................... 6-23
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Seismic Design – Geotechnical Features viii August 2011

6.3.3 Empirical and Numerical Evaluation Procedures for Liquefaction Potential...................... 6-26

6.3.4 Evaluation of Liquefaction Potential ................................................................................... 6-28

6.3.5 Use of Site-Specific response Analyses............................................................................... 6-37

6.4 LIQUEFACTION INDUCED GROUND DEFORMATIONS.............................................. 6-38

6.4.1 Post Liquefaction Residual Strength.................................................................................... 6-38

6.4.2 Flow Failures ....................................................................................................................... 6-39

6.4.3 Lateral Spread Displacement Evaluations ........................................................................... 6-40

6.5 SOIL SETTLEMENT HAZARD ........................................................................................... 6-41

6.5.1 Settlement of Unsaturated Cohesionless Soils..................................................................... 6-41

6.5.2 Post Earthquake Settlement of Liquefied Soils.................................................................... 6-46

6.6 SURFACE FAULT RUPTURE HAZARD ........................................................................... 6-47

6.6.1 Fault Types and Field Identification .................................................................................... 6-47

6.6.2 Fault Rupture Characteristics and Displacement Estimates................................................. 6-51

6.7 SUMMARY ........................................................................................................................... 6-54

CHAPTER 7 - GEOTECHNICAL DESIGN OF EARTHWORK FEATURES ............................... 7-1 

7.1 GENERAL ............................................................................................................................... 7-1 

7.2 SEISMIC PERFORMANCE OF SLOPES AND EMBANKMENTS..................................... 7-2 

7.2.1 Natural Slopes...................................................................................................................... 7-2 

7.2.2 Embankment Fills ................................................................................................................ 7-5 

7.2.3 Liquefaction Induced Deformations and Lateral Spreads.................................................... 7-8 

7.3 SLOPE STABILITY DESIGN APPROACHES.................................................................... 7-18

7.3.1 Constructed Fill Slopes and Embankments........................................................................ 7-18

7.3.2 Natural Slopes.................................................................................................................... 7-25

7.3.3 Screening Criteria............................................................................................................... 7-26

7.3.4 Strategies for Developing Acceptable Displacement......................................................... 7-28

7.3.5 Approach for Defining Acceptable Displacements............................................................ 7-30

7.4 SLOPE STABILITY MITIGATION MEASURES ............................................................... 7-31

7.4.1 Introduction........................................................................................................................ 7-31

7.4.2 Soil Slopes.......................................................................................................................... 7-31

7.4.3 Rock Slopes........................................................................................................................ 7-35

7.5 LIQUEFACTION INDUCED LATERAL SPREADS: DESIGN APPROACH AND 

REMEDIATION ................................................................................................................................. 7-42

7.5.1 Background ........................................................................................................................ 7-42

7.5.2 Structural Design to Accommodate Liquefaction-Induced Deformations......................... 7-44

7.5.3 Liquefaction Mitigation Ground Improvement Methods................................................... 7-56

7.6 SUMMARY ........................................................................................................................... 7-66

CHAPTER 8 - GEOTECHNICAL SEISMIC DESIGN FOR TRANSPORTATION STRUCTURES 

AND SOIL-FOUNDATION-STRUCTURE INTERACTION ............................................................ 8-1 

8.1 GENERAL ............................................................................................................................... 8-1 

8.2 INTERACTION BETWEEN STRUCTURAL DESIGNERS AND GEOTECHNICAL 

SPECIALISTS IN THE SEISMIC DESIGN PROCESS ...................................................................... 8-1 
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Seismic Design – Geotechnical Features ix August 2011

8.3 GLOBAL DYNAMIC RESPONSE MODEL.......................................................................... 8-2 

8.4 MEASURES FOR SEISMIC DEMAND IN DESIGN............................................................ 8-4 

8.5 CAPACITY PROTECTED DESIGN FOR FOUNDATIONS ................................................ 8-8 

8.6 FORCE VERSUS DISPLACEMENT BASED SEISMIC DESIGN ..................................... 8-11 

8.7 THE EARTHQUAKE RESISTING SYSTEM...................................................................... 8-12 

8.8 SOIL-FOUNDATION-STRUCTURE INTERACTION ANALYSIS................................... 8-14

8.9 AASHTO SEISMIC DESIGN REQUIREMENTS................................................................ 8-19

8.9.1 Interim Revisions......................................................................................................... 8-19

8.9.2 Guide Specifications.................................................................................................... 8-20 

8.10 COORDINATION BETWEEN STRUCTURAL DESIGNERS AND GEOTECHNICAL 

SPECIALISTS..................................................................................................................................... 8-22 

8.11 TREATMENT OF UNCERTAINTY IN SEISMIC DESIGN............................................... 8-23 

8.12 FOUNDATION DESIGN STRATEGY FOR GOOD SEISMIC PERFORMANCE............ 8-25 

8.13 SUMMARY ........................................................................................................................... 8-27 

CHAPTER 9 - SHALLOW FOUNDATIONS....................................................................................... 9-1 

9.1 GENERAL TYPES OF SHALLOW FOUNDATIONS .......................................................... 9-1 

9.2 SEISMIC PERFORMANCE AND VULNERABILITY OF SHALLOW 

FOUNDATIONS...................................................................................................................... 9-2 

9.3 STATIC VERSUS SEISMIC LOADS ON SHALLOW FOUNDATIONS ............................ 9-3 

9.4 SOIL-FOUNDATION-STRUCTURE INTERACTION ......................................................... 9-4 

9.4.1 Foundation Substructuring............................................................................................. 9-4 

9.4.2 Kinematic and Inertial Interaction ................................................................................. 9-5 

9.5 FOUNDATION STIFFNESS FORMULATION..................................................................... 9-8 

9.5.1 Spring Constants............................................................................................................ 9-8 

9.5.2 Equivalent Stiffness Matrix for Shallow Footing .......................................................... 9-8 

9.5.3 Footing Embedment Effects......................................................................................... 9-10

9.5.4 Soil Modulus for Foundation Stiffness........................................................................ 9-12

9.5.5 Effects of Limited Depth to Hard Layer ...................................................................... 9-13

9.5.6 Advanced Numerical Analysis..................................................................................... 9-13

9.5.7 Incorporation of Foundation Model into Bridge Response Model .............................. 9-14

9.6 GEOTECHNICAL CAPACITY ............................................................................................ 9-15

9.6.1 Pseudo-Static Seismic Loads....................................................................................... 9-15

9.6.2 Effective Footing Dimensions ..................................................................................... 9-16

9.6.3 Overturning .................................................................................................................. 9-17

9.6.4 Bearing Capacity.......................................................................................................... 9-17

9.6.5 Sliding Capacity........................................................................................................... 9-18

9.7 STRUCTURAL CAPACITY................................................................................................. 9-19

9.8 PERMANENT FOUNDATION DISPLACEMENT ............................................................. 9-20

9.8.1 Liquefaction-Induced Lateral Spreading and Settlement............................................. 9-21

9.9 SUMMARY ........................................................................................................................... 9-21
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Seismic Design – Geotechnical Features x August 2011

CHAPTER 10 - DEEP FOUNDATIONS ........................................................................................10-1 

10.1 TYPES OF DEEP FOUNDATIONS .....................................................................................10-1 

10.2 SEISMIC VULNERABILITY OF DEEP FOUNDATIONS .................................................10-1 

10.3 SEISMIC LOADS ON DEEP FOUNDATIONS...................................................................10-8 

10.3.1 Soil-Foundation-Structure Interaction .............................................................................10-8 

10.3.2 Kinematic Loading.........................................................................................................10-10

10.4 EFFECTIVE SUPPORT MOTIONS FOR DEEP FOUNDATIONS AT SOFT SOIL 

SITES ................................................................................................................................................10-10

10.5 SOIL-FOUNDATION INTERACTION SPRINGS.............................................................10-13

10.5.1 Two-Springs-in-Series Model........................................................................................10-13

10.5.2 p-y and t-z Curves for Soil-Pile Interaction Analyses....................................................10-14

10.6 FOUNDATION STIFFNESS EVALUATION....................................................................10-15

10.6.1 Pile Head Stiffness for Lateral Loading.........................................................................10-16

10.6.2 Pile Head Stiffness for Axial Loading ...........................................................................10-25

10.6.3 Lateral Stiffness of Pile Cap ..........................................................................................10-27

10.6.4 Group Effects for Typical Pile Footings........................................................................10-28

10.6.5 Group Effects for Very Large Pile Groups....................................................................10-30

10.6.6 p-y Curves for Liquefied Sand.......................................................................................10-31

10.6.7 Stiffness Matrix of a Pile Group ....................................................................................10-32

10.6.8 Pile Head Rotational Stiffness .......................................................................................10-32 

10.7 MOMENT CAPACITY OF PILE GROUPS .......................................................................10-34 

10.8 DESIGNING FOR UNCERTAINTY ..................................................................................10-36 

10.9 DESIGNING FOR KINEMATIC DISPLACEMENT DEMAND IN LIQUEFIED SOILS10-38

10.10 DESIGN PROCEDURES FOR LARGE DIAMETER DRILLED SHAFTS ......................10-43

10.11 CAISSONS DESIGN ...........................................................................................................10-43 

10.12 SUMMARY .........................................................................................................................10-46

 

CHAPTER 11- EARTH RETAINING STRUCTURES.....................................................................11-1

11.1 INTRODUCTION.....................................................................................................................11-1 

11.1.1 Design Criteria .................................................................................................................11-1 

11.1.2 Types of Earth Retaining Structures................................................................................11-2 

11.1.3 Gravity and Semi-Gravity Walls......................................................................................11-2 

11.1.4 Non-Gravity Cantilevered Walls .....................................................................................11-4 

11.1.5 Non-Gravity Anchored Walls..........................................................................................11-5 

11.1.6 Mechanically Stabilized Earth Walls...............................................................................11-6 

11.1.7 Soil Nail Wall ..................................................................................................................11-7 

11.1.8 Prefabricated Modular Walls...........................................................................................11-8 

11.2 SEISMIC FORCES ON EARTH RETAINING STRUCTURES ..........................................11-9 

11.2.1 Seismic Load and Resistance...........................................................................................11-9 

11.2.2 No Analysis Provisions..................................................................................................11-10

11.3 SEISMIC LATERAL EARTH PRESSURES......................................................................11-11
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Seismic Design – Geotechnical Features xi August 2011

11.3.1 Mononobe-Okabe Seismic Earth Pressure Theory ........................................................11-11

11.3.1.1 Limitations of Mononobe-Okabe Theory................................................................11-12

11.3.2 Trial Wedge Method ......................................................................................................11-13

11.3.2.1 Influence of Cohesion on Seismic Active Earth Pressure .......................................11-15

11.3.3 Log Spiral Earth Pressure Theory..................................................................................11-17

11.3.4 General Limit Equilibrium Method ...............................................................................11-19

11.4 SEISMIC EARTH PRESSURE COEFFICIENT................................................................. 11-20

11.4.1 Maximum Seismic Coefficients for Design...................................................................11-20

11.4.1.1 Wall Height Adjustment Factor...............................................................................11-21

11.4.2 Dsiplacement-Based Seismic Coefficient......................................................................11-22

11.4.2.1 Displacement Ductility Adjustment Factor.............................................................11-23

11.4.3 Walls with Backfill of Limited Extent ..........................................................................11-25

11.5 GRAVITY AND SEMI-GRAVITY EARTH RETAINING STRUCTURE DESIGN........11-25

11.5.1 External Stability for Walls Supported on a Shallow Foundation ................................. 11-27

11.5.2 Internal Stability Assessment of Semi-Gravity Cantilever Retaining Walls .................11-30

11.5.3 Gravity and Semi-Gravity Retaining Walls on Piles .....................................................11-32

11.6 DESIGN OF CANTILEVER AND ANCHORED EARTH RETAINING.......................................

STRUCTURES.........................................................................................................................11-34 

11.6.1 Non-Gravity Cantilevered Earth Retaining System.......................................................11-34

11.6.2 Anchored Walls..............................................................................................................11-37

11.7 MECHANICALLY STABILIZED WALLS .......................................................................11-42

11.8 SUMMARY .........................................................................................................................11-46 

CHAPTER 12 - BRIDGE ABUTMENT.............................................................................................12-1 

12.1 INTRODUCTION..................................................................................................................12-1 

12.1.1 Types of Abutment...........................................................................................................12-2 

12.1.2 Seat Type Abutment.........................................................................................................12-2

12.1.3 Monolithic Abutment.......................................................................................................12-4 

12.1.4 Mechanism of the Abutment Backfill Failure..................................................................12-5 

12.1.5 Typical Backfill Soil Behavior ........................................................................................12-8 

12.1.6 Full Scale Abutment Loading Tests.................................................................................12-9 

12.1.6.1 UCLA Abutment Experiment....................................................................................12-9 

12.1.6.2 UCD Abutment Experiment....................................................................................12-10

12.2 MODELING OF REGULAR (NON-SKEWED) ABUTMENTS .......................................12-13

12.2.1 Bi-linear Model..............................................................................................................12-13

12.2.2 Non-Linear Hyperbolic Abutment Stiffness Relationship.............................................12-15 

12.2.3 Advanced Numerical Analysis.......................................................................................12-17 

12.2.4 Global Backwall-Backfill Longitudinal Response.........................................................12-18 

12.3 MODELING OF SKEWED ABUTMENTS........................................................................12-20 

12.3.1 3-D Finite Element Model of the Abutment Backfill ....................................................12-22

12.3.2 Load-Deformation Relationship ....................................................................................12-23

12.3.3 Effects of Skew Angles on the Bridge Abutment Global Response ..............................12-25

12.4 SUMMARY .........................................................................................................................12-26
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Seismic Design – Geotechnical Features xii August 2011

CHAPTER 13 - BURIED STRUCTURES ..........................................................................................13-1 

13.1 GENERAL .............................................................................................................................13-1 

13.2 SEISMIC PERFORMANCE OF CULVERTS AND PIPELINES ........................................13-1 

13.3 CULVERT/PIPE CHARACTERISTICS ...............................................................................13-2 

13.3.1 Flexible Culverts and Pipes..............................................................................................13-2 

13.3.2 Rigid Culverts and Pipes..................................................................................................13-4 

13.4 GENERAL EFFECTS OF EARTHQUAKES AND POTENTIAL FAILURE MODES......13-4 

13.4.1 Ground Shaking ...............................................................................................................13-5 

13.4.2 Ground Failure .................................................................................................................13-8 

13.5 CURRENT SEISMIC DESIGN PRACTICE FOR BURIED STRUCTURES......................13-8 

13.6 GENERAL METHODOLOGY AND RECOMMENDED PROCEDURES.......................13-11

13.6.1 Ovaling of Circular Conduits.........................................................................................13-11

13.6.2 Lining-Ground Interaction Solutions for Ovaling Response of Circular Lining ...........13-17

13.6.3 Lining-Ground Interaction Solutions for Racking Response of Rectangular Lining.....13-21

13.7 NUMERICAL MODELING METHODS............................................................................13-27

13.8 GENERAL DESIGN METHODOLOGY FOR PERMANENT GROUND ................................

DISPLACEMENT................................................................................................................ 13.29 

13.9 SUMMARY .........................................................................................................................13-30

 
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Seismic Design – Geotechnical Features xiii August 2011

LIST OF FIGURES

Figure 1-1 Peak Ground Acceleration with a 10% Probability of Being Exceeded in a 50 

year Period ....................................................................................................................... 1-2 

Figure 1-2 Areas Impacted by Historic Earthquakes in the United States ........................................ 1-2 

Figure 1-3 Collapse of the Cypress Viaduct in the 1989 Loma Prieta Earthquake ........................... 1-3 

Figure 1-4 Collapse of the I-5, SR-14 Overpass in the 1971 San Fernando Earthquake .................. 1-4 

Figure 1-5 Collapse of the Showa Bridge in the 1964 Niigata, Japan Earthquake............................ 1-5 

Figure 1-6 Fire Following the 1994 Northridge Earthquake due to a Rupture Gas Main ................. 1-6 

Figure 1-7 Damage to the San Francisco-Oakland Bay Bridge East Span due to the 1989 Loma 

Prieta Earthquake............................................................................................................ 1-7 

Figure 1-8 Failure of the Wingwall at the Roxford Street Undercrossing in the 1971 San Fernando 

Earthquake ....................................................................................................................... 1-8 

Figure 1-9 Settlement of Abutment Embankment Fill in the 1971 San Fernando Earthquake ......... 1-9 

Figure 1-10 Collapse of the Bridge over Struve Slough in the 1989 Loma Prieta Earthquake ........ 1-10

Figure 1-11 Shear Failure of the Head of a Pile at the Struve Slough Bridge................................... 1-10

Figure 1-12 Landsliding Along SR-17 in the 1989 Loma Prieta Earthquake ................................... 1-11

Figure 1-13 Collapse of the I-5, SR-14 Interchange in the 1994 Northridge Earthquake ................ 1-12

Figure 1-14 Failure of a Bridge Column – Foundation Connection.................................................. 1-13

Figure 2-1 Major Tectonic Plates and Their Approximate Direction of Movement ........................ 2-3 

Figure 2-2 Worldwide Seismic Activity and Plate Boundaries ........................................................ 2-4 

Figure 2-3 Cross-Section Through a Subduction Zone. .................................................................... 2-4 

Figure 2-4 Southeastern US Seismic Zones and Instrumental Seismicity......................................... 2-7 

Figure 2-5 Blind Thrust Faulting....................................................................................................... 2-8 

Figure 2-6 Deformations Produced by Body Waves: (a) P-waves; (b) SV-Waves......................... 2-11

Figure 2-7 Deformations Produced by Rayleigh Waves................................................................. 2-12

Figure 2-8 Acceleration, Velocity, and Displacement Strong Ground Motion Time Histories ...... 2-13

Figure 2-9 Comparison of Earthquake Magnitude Scales............................................................... 2-15

Figure 2-10 Basic Fault Geometry and Definition ............................................................................ 2-16

Figure 2-11 Various Site-to-Source Distance Measures Used in Earthquake Engineering............... 2-17

Figure 2-12 Truncated Gutenberg Richter and Characteristic Magnitude-Recurrence Models........ 2-18

Figure 2-13 Types of Fault Movement.............................................................................................. 2-20

Figure 2-14 Bracketed Duration of Strong Shaking.......................................................................... 2-25

Figure 2-15 Significant Duration of Strong Shaking......................................................................... 2-26

Figure 2-16 Schematic Representation of Acceleration Response Spectra....................................... 2-28

Figure 2-17 Tripartite Representation of Acceleration, Velocity, and Displacement Response 

Spectra. .......................................................................................................................... 2-29

Figure 2-18 Uniform Hazard Acceleration Response Spectra for Memphis, Tennessee, with a 5% 

 Probability of Exceedance 50-years............................................................................... 2-30

Figure 2-19 Magnitude-Distance Deaggregation for Oceano, California ......................................... 2-33

Figure 3-1 Steps in Probabilistic Seismic Hazard Analysis .............................................................. 3-2 

Figure 3-2 Geometry of Seismic Sources in Seismic Hazard Analysis............................................. 3-3 

Figure 3-3 Truncated Gutenberg Richter and Characteristic Magnitude-Recurrence Models.......... 3-4 

Figure 3-4 Example of Peak Horizontal Ground Acceleration Attenuation Relationship for Strike 

Slip Earthquake and Soil Sites......................................................................................... 3-9 

Figure 3-5 Variation in Definitions on Distance (site to seismic source) in Commonly Used 

Attenuation Relationships; (a) Strike Slip Faulting; (b) Reverse or Normal Faulting, 

Hanging-wall Site; (c) Reverse or Normal Faulting, Foot-wall Site ............................. 3-10

Figure 3-6 Boundary Defining WUS and CEUS Seismic Hazard Regions Based on Change in 

Attenuation Relationship ............................................................................................... 3-11
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Seismic Design – Geotechnical Features xiv August 2011

Figure 3-7 Comparison between Spectral Curve Shapes for the WUS and CEUS Hazard Regions 

(NUREG, 2001); (a) Acceleration Spectra for M=6.5, and R=20 km; (b) Displacement

Spectra for M=6.5, and R=20 km................................................................................... 3-13

Figure 3-8 Acceleration Response Spectra from Abrahamson and Silva (1997)............................ 3-19

Figure 3-9 Seismic Hazard Curves for Site in Southern California: Total Hazard and Individual 

Contributions and Total Hazard from Three Faults....................................................... 3-20

Figure 3-10 Magnitude Deaggregation for Augusta, GA, at 1.0 sec Period for a 2500-year Return 

Period:Predominant Hazard is Charleston M7.3 Characteristic Earthquake ................. 3-25

Figure 3-11 Design Response Spectrum Constructed with the Three-Point Method........................ 3-34

Figure 3-12 Comparison of USGS Spectra to AASHTO Spectra for a Rock Site in Memphis, 

Tennessee (1,000-yr Return Period) .............................................................................. 3-35

Figure 3-13 Influence of Rupture Directivity on Velocity Time Histories Recorded at the Lucerne 

and Joshua Tree Sites During the 1992 Landers Earthquake......................................... 3-38

Figure 3-14 Representative Scaled versus Spectrum-Compatible Adjusted Motion......................... 3-48

Figure 3-15 Coherency Function for Horizontal Component Motion............................................... 3-50

Figure 3-16 Coherency Function for Vertical Component Motion ................................................... 3-51

Figure 3-17 Initiation Screen for the Seismic Design Values for Buildings option .......................... 3-54

Figure 3-18 Initial Screen for Seismic Hazard Curves and Uniform Hazard Response Spectra....... 3-55

Figure 3-19 Input Screen for Seismic Hazard Curves, Response Parameters, and Design

 Parameters...................................................................................................................... 3-56

Figure 3-20 Input Screen for Probabilistic Hazard Curves................................................................ 3-57

Figure 3-21 Screen for PGA for 1000-yr Return Period ................................................................... 3-57

Figure 3-22 Screen for 0.2 sec Spectral Acceleration for 1000-yr Return Period............................. 3-58

Figure 3-23 Screen for 1.0 sec Spectral Acceleration for 1000-yr Return Period............................. 3-58

Figure 3-24 Bay Bridge Site AASHTO Design Spectrum for Site Class C Conditions.................... 3-60

Figure 3-25 Initiation Screen in the USGS/AASHTO Ground Motion CD...................................... 3-61

Figure 3-26 Screen No. 2: Site Location and Design Hazard Level.................................................. 3-61

Figure 3-27 Screen No. 3: Site Factor Table. .................................................................................... 3-62

Figure 3-28 Screen No. 4: Site Class Adjusted Anchoring Points for Design Spectrum. ................. 3-63

Figure 3-29 Screen No. 5: Reference Site Spectrum Values............................................................. 3-64

Figure 3-30 Screen No. 6: Site Class D Spectrum Values................................................................. 3-64

Figure 3-31 Screen No. 7: Options for Viewing Various Spectra ..................................................... 3-66

Figure 3-32 Screen No. 8: Example of “All Sa vs. T Spectra” Option .............................................. 3-66

Figure 3-33 Screen No. 9: Example of “All Sa vs. Sd Spectra” Option ............................................. 3-67

Figure 3-34 Initial Screen from the USGS Web Site for Interactive Deaggregation ........................ 3-68

Figure 3-35 Screen for Specifying Location and PSHA Return Period ............................................ 3-69

Figure 3-36 Available Interactive Deaggregation Results................................................................. 3-70

Figure 3-37 Hazard Deaggregation for Combinations of Magnitude and Distance .......................... 3-71

Figure 3-38 Geographic Hazard Deaggregation................................................................................ 3-71

Figure 4-1 Stresses Induced in a Soil Element by Vertically Propagating Shear Wave.................... 4-9 

Figure 4-2 Hysteretic Stress-Strain Response of Soil Subjected to Cyclic Loading ....................... 4-10

Figure 4-3 Shear Modulus Reduction and Equivalent Viscous Damping Ratio Curves................. 4-11

Figure 4-4 Correction Factor for the Effective Overburden Pressure, CN ..................................... 4-18

Figure 4-5 Soil Classification Chart Based on the CPT .................................................................. 4-20

Figure 4-6 CPT-SPT Correlation Chart........................................................................................... 4-20

Figure 4-7 Correlation between Dry Unit Weight and Normalized Cone Tip Resistance ............. 4-21

Figure 4-8 Correlation among Saturated Weight, Shear Wave Velocity, and Depth...................... 4-22

Figure 4-9 Correlation among Saturated Weight, CPT Sleeve Friction, and Specific Gravity ....... 4-22

Figure 4-10 Correlation among CPT Tip Resistance, Relative Density, and Compressibility 

 for Clean Sands.............................................................................................................. 4-24

Figure 4-11 Field and Laboratory Methods for Evaluating Shear Wave Velocity............................ 4-26
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Seismic Design – Geotechnical Features xv August 2011

Figure 4-12 CPT – Shear Wave Velocity Correlation for Clean Quartz Sands ................................ 4-33

Figure 4-13 CPT – Shear Wave Velocity Correlation for Clay Soils ............................................... 4-34

Figure 4-14 Shear Modulus Reduction Curves for Sands................................................................. 4-35

Figure 4-15 Comparison of Seed et al. (1985) Modulus Reduction and Damping Curves for 

 Sand with Darendeli (2001) Curves for PI = 0. ............................................................. 4-36

Figure 4-16 Darendeli (2001) Confining Pressure Dependent Curves for PI = 30 ........................... 4-37

Figure 4-17 Comparison of Hashash and Park (2001) Modulus Reduction and Damping 

Curves for the Mississippi Embayment with EPRI (1993) curves ............................... 4-38

Figure 4-18 Correlation between the Undrained Residual Strength Ratio, Sr/σ’vo and a) 

Standardized Normalized SPT Blow Count, (N1)60 and b) Normalized CPT Tip 

Resistance, qc1 ................................................................................................................ 4-41

Figure 4-19 Correlation between the Residual Undrained Strength Ratio, Sr/σ’vo and 

Equivalent Clean Sand SPT Blow Count, (N1)60-CS ....................................................... 4-42

Figure 4-20 Void Ratio Redistribution Due to an Overlying Confining Layer................................. 4-43

Figure 4-21 Classes of Rock Mass Discontinuities........................................................................... 4-46 

Figure 4-22 Relationship between Friction Angles and Cohesive Strength Mobilized at 

Failure for Slopes........................................................................................................... 4-46 

Figure 4-23 Relationships between Major and Minor Principal Stresses for Hoek-Brown 

and equivalent Mohr-Coulomb Criteria......................................................................... 4-50

Figure 4-24 Definition of Joint Roughness Coefficient, JRC............................................................ 4-52 

Figure 4-25 Definition of Instantaneous Cohesion ci and Instantaneous Friction Angle φi for 

a Non-Linear Failure Criterion ..................................................................................... 4-53 

Figure 5-1 Refraction of Shear Waves Approaching the Ground Surface ........................................ 5-4 

Figure 5-2 Relationship between PGA on Rock and on Other Local Site Conditions...................... 5-6 

Figure 5-3 PGA Amplification Based Upon NEHRP Site Class....................................................... 5-7 

Figure 5-4 Relationship between PHGA on Rock and on Soft Soil Sites......................................... 5-8 

Figure 5-5 Base and Crest Peak Accelerations Recorded at the Earth Dams.................................... 5-9 

Figure 5-6 1-Dimensional Column for SHAKE Equivalent Linear Seismic Site Response 

Analysis ......................................................................................................................... 5-13

Figure 5-7 Influence of Pressure Dependent Soil Behavior on the Seismic Response of a 3,300 ft

(1,000 m) Thick Soil Column in the Mississippi Embayment....................................... 5-14

Figure 5-8 Equivalent Linear Response Analysis for a Shallow Impedance Contrast Site in 

 Columbia, South Carolina.............................................................................................. 5-16

Figure 5-9 Non-Linear Soil Model for Time-Domain Site Response Analysis .............................. 5-17

Figure 5-10 Comparison of Total Stress Site Response Analysis to Effective Stress Site Response 

 Analyses with Pore Pressure Softening ......................................................................... 5-20

Figure 5-11 Quasi Two-Dimensional Site Response Analysis Using One-Dimensional Column.... 5-21

Figure 6-1 Newmark Sliding Block Concept for Slopes................................................................... 6-3 

Figure 6-2 Pseudo-Static Limit Equilibrium Analysis ...................................................................... 6-5 

Figure 6-3 Simplified Height-Dependent Scaling Factor Recommended for Design ....................... 6-9 

Figure 6-4 Permanent Seismic Deformation Chart ......................................................................... 6-11

Figure 6-5 Comparison between AASHTO (2004) and Recommended Displacement 

Equation 6-5 for PGV = 30kmax (in/sec)...................................................................... 6-13

Figure 6-6 Problem Definition ........................................................................................................ 6-16

Figure 6-7 Representative Analysis Results.................................................................................... 6-16

Figure 6-8 Main Types of Slope Failure and Stereoplots of Structural Conditions Likely to 

Give Rise to these Failures ............................................................................................ 6-17

Figure 6-9 Strength Degradation in Cyclic Torsional Shear tests................................................... 6-24

Figure 6-10 Undrained Cyclic Simple Shear Test Results Nevada Sand, Dr = 40% ........................ 6-24

Figure 6-11 Shear Stress Strain History at the Wildlife Refuge Site during Liquefaction................ 6-25 
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Seismic Design – Geotechnical Features xvi August 2011

Figure 6-12 The CSR Required to Reach Initial Liquefaction (ru=100%) , from Shaking Table

Tests by De Alba et al. (1976)....................................................................................... 6-25

Figure 6-13 Simplified Base Curve Recommended for Determination of CRR from SPT Data for 

Magnitude 7.5 Along with Empirical Liquefaction Data .............................................. 6-30

Figure 6-14 Magnitude Scaling Factors Derived by Various Investigators ...................................... 6-31

Figure 6-15 CPT-Liquefaction Resistance Correlation Chart ........................................................... 6-32

Figure 6-16 CPT Grain Size Characteristic Correction Factor.......................................................... 6-34

Figure 6-17 Shear Wave Velocity – Liquefaction Resistance Correlation Chart.............................. 6-35

Figure 6-18 Soil Flexibility Factor (rd) Versus Depth Curves Developed by Seed and Idriss.......... 6-36

Figure 6-19 Example of a Liquefaction Triggering Analysis for a Single SPT Boring .................... 6-37

Figure 6-20 Newmark Sliding Block Analysis in Liquefied Soil...................................................... 6-41

Figure 6-21 Plot for Determination of Earthquake-induced Shear Strain in Sand Deposits............. 6-43

Figure 6-22 Relationship between Volumetric Strain, Cyclic Shear Strain, and Penetration 

Resistance for Unsaturated Sands.................................................................................. 6-44

Figure 6-23 Computation of Settlement for 50-ft Deep Sand Layer................................................. 6-45

Figure 6-24 Curves for Estimation of Post-liquefaction Volumetric Strain Using SPT Data and 

Cyclic Stress Ratio for Mw 7.5 Earthquakes.................................................................. 6-46

Figure 6-25 Types of Earthquake Faults ........................................................................................... 6-49

Figure 6-26 Relationship between Maximum Surface Fault Displacement and Earthquake 

Moment.......................................................................................................................... 6-53 

Figure 7-1 Ditullio Landslide, Loma Prieta Earthquake.................................................................... 7-3 

Figure 7-2 Route 17 landslide, Loma Prieta Earthquake................................................................... 7-4 

Figure 7-3 Planar Rock Slide in Volcanic Tuff 1989 Armenia Earthquake...................................... 7-4 

Figure 7-4 Slope Failure with Ground Cracking along Mulholland Drive, 1994 Northridge 

Earthquake ....................................................................................................................... 7-5 

Figure 7-5 Differential Settlement Induced by Seismic Compaction at the Easterly Approach to 

 Bridge 53-1991R in I-5 to I-210 Interchange During 1971 San Fernando Earthquake... 7-6 

Figure 7-6 Differential Settlement across Pavement Joints Near Cut-fill Boundary on I-5 north 

of I-405 Separation. The Settlement is due to Seismic Compaction of Fill during the 

1971 San Fernando Earthquake. ...................................................................................... 7-7 

Figure 7-7 Wavy Pavement due to Differential Settlement Enhanced by Liquefaction during the 

1993 Hokkaido-Nansei-Oki, Japan Earthquake............................................................... 7-8 

Figure 7-8 Failure Mechanism for an Embankment Founded Upon Liquefied Soil ......................... 7-9 

Figure 7-9 Segment of Highway 36 Near Carribbean Coast in Costa Rica that Split Longitudinally, 

 Settled and Spread Laterally during 1991 Earthquake by Mechanism............................ 7-9 

Figure 7-10 Disrupted Fill and Pavement due to Liquefaction at the Approach to the Highway 36 

 bridge Over Rio Estrella, Costa Rica, during 1991 Earthquake. ................................... 7-10

Figure 7-11 Rigid pavement on I-5 south of I-5/I-210 interchange that sheared and buckled at two 

 localities during the 1971 San Fernando earthquake due to 6.5 ft (2 m) of lateral spread 

 displacement. ................................................................................................................. 7-11

Figure 7-12 Extensional Fissures in Flexible Pavement Caused by Lateral Spread of Floodplain 

 Deposits Toward Rio Viscaya during the 1991 Costa Rica Earthquake........................ 7-11

Figure 7-13 Liquefaction-induced Flow Failure of Roadway Embankment into Lake Merced 

During 1957 Daly City, California Earthquake ............................................................. 7-12

Figure 7-14 Damage to the Abutments and Piers of Yachiyo Bridge on the Left Bank ................... 7-13

Figure 7-15 Showa Bridge Collapse.................................................................................................. 7-14

Figure 7-16 Deformation of a Steel Pipe pile for the Showa Bridge................................................. 7-14

Figure 7-17 Landing Road Bridge, Whakatane, New Zealand.......................................................... 7-15

Figure 7-18 Schematic of the Raked-pile Foundation at the Landing Road Bridge.......................... 7-16

Figure 7-19 Potential Collapse Mechanism for Landing Load Bridge.............................................. 7-16
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Seismic Design – Geotechnical Features xvii August 2011

Figure 7-20 Site and Damage Characteristics for a Precast Concrete Pile Subjected to Lateral 

 Spread in the Kobe Earthquake ..................................................................................... 7-17

Figure 7-21 Slope Geometry ............................................................................................................. 7-20

Figure 7-22 Procedure to Establish Acceptable Slope Movement .................................................... 7-32

Figure 7-23 Rock Buttress Used to Increase Forces Resisting Slope Failure.................................... 7-33

Figure 7-24 Classification Scheme for Earth Retention Systems...................................................... 7-34

Figure 7-25 Examples of Externally and Internally Stabilized Earth Retention Systems................. 7-34

Figure 7-26 Types of Vertical and Horizontal Drains used to Lower the Groundwater in Natural 

Slopes............................................................................................................................. 7-35

Figure 7-27 Categories of Rock Slope Stabilization Measures......................................................... 7-36

Figure 7-28 Rock Slope Reinforcement Methods............................................................................. 7-37

Figure 7-29 Rock-removal Methods for Slope Stabilization............................................................. 7-38

Figure 7-30 Side View of Rock Fall Restraint Net System with Fully Embedded Posts and

Anchor Support............................................................................................................. 7-39

Figure 7-31 Example of Rock Shed .................................................................................................. 7-40

Figure 7-32 Rock Slope Mitigation Methods Used by Selected States............................................. 7-41

Figure 7-33 Elevation View of a Representative Bridge on a Liquefiable Stratum.......................... 7-42

Figure 7-34 Pseudo-static Stability Analysis..................................................................................... 7-43

Figure 7-35 Design Flowchart........................................................................................................... 7-48

Figure 7-36 Deformation Models for Piles at Lateral Spreading Sites.............................................. 7-49

Figure 7-37 Site profile, Washington Bridge .................................................................................... 7-52

Figure 7-38 Typical Sliding Mechanism for Flow Failure................................................................ 7-53

Figure 7-39 Forces Provided by Bridge and Foundation Piles for Resisting Lateral Spread ............ 7-54

Figure 7-40 Dynamic Deep Compaction........................................................................................... 7-58

Figure 7-41 The Vibro Compaction Process..................................................................................... 7-59

Figure 7-42 Vibro-replacement Equipment and Process................................................................... 7-60

Figure 7-43 Vibro-system (stone column) Treatment at Toe of Approach Embankment................. 7-61

Figure 7-44 Vibro-system (stone column) Treatment Around a Pile-supported Bridge Pier............ 7-61

Figure 7-45 Compaction Grout Bulb Construction ........................................................................... 7-63

Figure 7-46 Dry Method Column Installation................................................................................... 7-63

Figure 7-47 Deep Mixing Column Patterns....................................................................................... 7-64

Figure 7-48 Deep Mixing Applications in Japan............................................................................... 7-65

Figure 7-49 Kobe Hotel Foundation Plan in Japan ........................................................................... 7-65

Figure 8-1 Global Structural Model for Seismic Design................................................................... 8-3 

Figure 8-2 Acceleration and Displacement Design Spectra .............................................................. 8-5 

Figure 8-3 Elastic and Inelastic Force and Displacement Demand and the Ductility Ratio.............. 8-6 

Figure 8-4 Pushover Analysis for Displacement Demand Distribution ............................................ 8-8 

Figure 8-5 Concept for Capacity Protecting the Foundation............................................................. 8-9 

Figure 8-6 Typical Structural Forms for Bridge Foundation Systems ............................................ 8-10

Figure 8-7 Inertial Interaction Models; a) Shallow Foundation Model and b) Deep Foundation 

Model............................................................................................................................. 8-15

Figure 8-8 Direct (or Total) Soil-Structure Kinematic Interaction Model ...................................... 8-16

Figure 8-9 Foundation Substructuring Model for Kinematic Analysis........................................... 8-17

Figure 8-10 Comparison of Kinematic Motion from SSI to Free field Depth Varying Motions...... 8-18

Figure 8-11 Effect of Soil Stiffness on Performance of 24-inch Reinforced Concrete Pile.............. 8-24 

Figure 9-1 Types of Shallow Foundations......................................................................................... 9-2 

Figure 9-2 Two Step Rigorous Inertial Response Solution Incorporating Frequency Dependent 

Foundation Impedance..................................................................................................... 9-6 

Figure 9-3 Frequency Dependent Dynamic Stiffness Factor for a Surface Footing.......................... 9-7 

Figure 9-4 Form of the Shallow Foundation Stiffness Matrix........................................................... 9-9 

Figure 9-5 Stiffnesses for a Rigid Surface Footing on a Semi-Infinite Half Space......................... 9-10
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Seismic Design – Geotechnical Features xviii August 2011

Figure 9-6 Embedment Factors for a Rigid Footing on a Semi-Infinite Half Space ....................... 9-11

Figure 9-7 Embedment Factor in Graphical Format from Lam and Martin (1986) ........................ 9-12

Figure 9-8 Footing Stiffness for a Finite Soil Layer above Rigid Base .......................................... 9-13

Figure 9-9 Implementation of Foundation Submodel in the Global Structural Model.................... 9-14

Figure 9-10 Equivalent Footing Dimensions..................................................................................... 9-16

Figure 10-1 Damage to the Head of Battered Piles at the Port of Oakland.......................................10-2 

Figure 10-2 Shear Failure in the Cap Beam Connection of the Struve Slough Pile Bent .................10-3 

Figure 10-3 Piles Punched-Through the Deck Slab in the Collapsed Struve Slough Bridge ............10-3 

Figure 10-4 Large Lateral Displacements Imposed on Adjacent Piles, Struve Slough Bridge ........10-3 

Figure 10-5 Damage to Excavated Pile from the Niigata Court House.............................................10-5 

Figure 10-6 Pile Damage Observed from S Building; (a) Damage to Foundation Pile; (b) SPT Value;

(c) Photos of Damage ....................................................................................................10-5 

Figure 10-7 Pile Damage Observed from NHK Building ................................................................. 10-6 

Figure 10-8 Pile Damage Observed from Hotel Niigata ...................................................................10-7 

Figure 10-9 Pile Layout of Hokuriku Building .................................................................................10-7 

Figure 10-10 Seismic Design of Pile Foundations..............................................................................10-9 

Figure 10-11 Modeling Approaches to Solve for the Kinematic Interaction ....................................10-11

Figure 10-12 Pile Group Layout and Kinematic Interaction Model, San Francisco East Bay Bridge 

Replacement Structure Skyway ...................................................................................10-12

Figure 10-13 Comparison of Ground Motions from 1-D Site Response Analysis to Kinematic 

Motion..........................................................................................................................10-13

Figure 10-14 Two-Springs-in Series Soil-Pile Interaction Model.....................................................10-14

Figure 10-15 Lateral Translational Diagonal Stiffness Coefficient...................................................10-17

Figure 10-16 Rotational Diagonal Stiffness Coefficient ...................................................................10-18

Figure 10-17 Cross Coupling of Diagonal Stiffness Coefficient.......................................................10-19

Figure 10-18 Lateral Free Head Stiffness Coefficient.......................................................................10-20

Figure 10-19 Lateral Translational Diagonal Stiffness Coefficient for Embedded Pile Head ..........10-21

Figure 10-20 Rotational Diagonal Stiffness Coefficient for Embedded Pile Head...........................10-22

Figure 10-21 Cross Coupling of Diagonal Stiffness Coefficient for Embedded Pile Head ..............10-23

Figure 10-22 Recommended Coefficient of Variation in Subgrade Stiffness with Depth for Sands 10-24

Figure 10-23 Recommended Coefficient of Variation in Subgrade Stiffness with Depth for Clays. 10-24

Figure 10-24 Graphical Solution for Developing Axial Pile Stiffness..............................................10-26

Figure 10-25 Method for Passive Pressure Capacity of Pile Cap......................................................10-28

Figure 10-26 P-Multipliers for Two-Way Seismic Loading .............................................................10-30

Figure 10-27 Scaling Factor to Reese’s static p-y Curves from the 1995 Liu and Dobry 

Centrifuge Test .......................................................................................................... 10-31

Figure 10-28 Measured versus Predicted Pile Head Rotation ...........................................................10-33

Figure 10-29 Shear vs. Moment Load Solution.................................................................................10-34

Figure 10-30 Moment Capacity of a Pile Group ...............................................................................10-35

Figure 10-31 Sensitivity of a 16-inch Drilled Shaft to Variations in p-y Curve Stiffness.................10-37

Figure 10-32 The Two Cases for Pile Design in Lateral Spreading Liquefied Soils ........................10-39

Figure 10-33 p-y Curves Back calculated from Soil Liquefied by Blasting .....................................10-40

Figure 10-34 3-D Finite Element Model of a Pile in Laterally Spreading Ground with a 

Nonliquefied Crust .......................................................................................................10-41

Figure 10-35 Maximum Pile Moment Location................................................................................10-42

Figure 10-36 Maximum Pile Moment Solution.................................................................................10-42

Figure 10-37 Maximum Pile Shear Solution.....................................................................................10-43

Figure 10-38 Various SSI Modeling Approaches for Caissons.........................................................10-45

Figure 11-1 Mass Concrete Gravity Wall..........................................................................................11-2 
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Seismic Design – Geotechnical Features xix August 2011

Figure 11-2 Semi-Gravity Cantilever Retaining Walls......................................................................11-3 

Figure 11-3 Counterfort Retaining Walls ..........................................................................................11-3 

Figure 11-4 Buttressed Retaining Walls............................................................................................11-4 

Figure 11-5 Non-Gravity Cantilever Wall.........................................................................................11-4 

Figure 11-6 Single Tieback System...................................................................................................11-5 

Figure 11-7 MSE Wall with Precast Concrete Face Panels...............................................................11-6 

Figure 11-8 Soil Nail Wall.................................................................................................................11-7 

Figure 11-9 Precast Concrete Crib Walls ..........................................................................................11-8 

Figure 11-10 Seismic Forces on a Semi-gravity Retaining Wall ......................................................11-10

Figure 11-11 Free Body Diagram for Mononobe-Okabe Active Earth Pressure Theory..................11-11

Figure 11-12 Inclination of the Seismic Active Wedge for φ = 35o ..................................................11-13

Figure 11-13 Active Trial Wedge......................................................................................................11-14

Figure 11-14 Effect of cohesion on the seismic active earth pressure coefficient for φ = 35o ..........11-16

Figure 11-15 Critical Log Spiral Surfaces Compared to Planar Critical Surfaces............................11-17

Figure 11-16 Passive Seismic Earth Pressure Coefficient from the Log Spiral Method for 

Cohesionless Soil and δ = 0.67φ..................................................................................11-18

Figure 11-17 General Limit Equilibrium Method for Evaluating the Seismic Active Earth 

Pressure........................................................................................................................11-19

Figure 11-18 Wall height adjustment factor, α, vs. wall height........................................................11-21

Figure 11-19 Modes of Failure for a Semi-Gravity Earth Retaining Structure ................................. 11-26

Figure 11-20 Combined Thrust Loads and Deformed Shape of Cantilever Wall .............................11-31

Figure 11-21 Forces Acting at the Critical Sections of the Wall.......................................................11-32

Figure 11-22 Pile Supported Retaining Wall.....................................................................................11-33

Figure 11-23 Cantilevered and Anchored Earth Retaining Systems.................................................11-34

Figure 11-24 Seismic Load Distribution for Non-Gravity Cantilever Retaining Walls....................11-35

Figure 11-25 Lateral Earth Pressure for Anchored/Braced Walls.....................................................11-37

Figure 11-26 Single Tieback System................................................................................................. 11-39

Figure 11-27 General Pressure Distribution for Tieback Retaining Walls........................................11-40

Figure 11-28 Simple Seismic Pressure Distribution for a Multiple Tieback System........................11-41

Figure 11-29 Hinge Method for Tieback Design ..............................................................................11-42

Figure 11-30 Potential External Failure Mechanisms for MSE Walls..............................................11-43

Figure 11-31 Pressure Diagram for MSE Wall with Seismic Force..................................................11-44

Figure 11-32 Pressure Diagram for MSE Walls with Sloping Backslope.........................................11-45

Figure 12-1 Seat-Type Abutment and Foundation System ...............................................................12-3 

Figure 12-2 Seat Type Abutments; a) Short Seat and b) High Cantilever.........................................12-3 

Figure 12-3 Monolithic Abutment and Foundation System..............................................................12-4 

Figure 12-4 Monolithic Abutment Types; (a) Short Stem and (b) High Stem..................................12-5 

Figure 12-5 Mobilization of Passive Resistance (Shamsabadi, 2007)...............................................12-6 

Figure 12-6 Formations of Mobilized Passive Wedges (Kosa et al., 2001)......................................12-7 

Figure 12-7 Puente Los Banos Bridge...............................................................................................12-8 

Figure 12-8 Full Scale Abutment Experiment with Silty Sand Backfill .........................................12-10

Figure 12-9 UCD Abutment Field Test...........................................................................................12-11

Figure 12-10 UCD Abutment Test Loading Setup............................................................................12-11

Figure 12-11 Failure Mechanism of the UCD Abutment Test ..........................................................12-12

Figure 12-12 Bridge Model for Seat-Type Abutment with an Expansion Gap................................. 12-13

Figure 12-13 Bi-Linear Abutment Force-Deformation Relationship................................................12-14

Figure 12-14 Closed-Form Solution..................................................................................................12-16

Figure 12-15 2-D finite Element Mesh of Bridge Abutment.............................................................12-17

Figure 12-16 Deformed Shape of Abutment Backfill in Simulation by the 2-D FEM Model ..........12-18

Figure 12-17 Bridge and Abutment Model .......................................................................................12-19
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Seismic Design – Geotechnical Features xx August 2011

Figure 12-18 Near-field Ground Motion with High Velocity Pulse..................................................12-19

Figure 12-19 Longitudinal Hysteretic Behavior of a Single-Span Bridge Abutment .......................12-20

Figure 12-20 Deck Rotation in a Bridge with Skewed Abutments During a Seismic Event ............12-21

Figure 12-21 Non-Uniform Passive Wedge behind a Skewed Abutment.........................................12-21

Figure 12-22 Passive Soil Wedge in a Non-Skewed Abutment ........................................................12-22

Figure 12-23 3-D FE Model of Passive Wedge Formation behind a Skewed Abutment..................12-23

Figure 12-24 Nonlinear Normal and Tangential Components of Abutment-Backfill Resistance for

 a 30o Skew ...................................................................................................................12-24

Figure 12-25 Impact of Skew Angles on Nonlinear Abutment Force-Deformation Relationship ....12-24

Figure 12-26 Single Span Bridge 45o Skew Angles..........................................................................12-25

Figure 12-27 Hysteretic Abutment Response Obtuse and Acute Corner of the Single-Span Bridge

 with 45o Skew Angle ...................................................................................................12-26 

Figure 13-1 Longitudinal Axial and Curvature Response to Traveling Waves................................. 13-5 

Figure 13-2 Transverse Ovaling and Racking Response to Vertically Propagating Shear Waves....13-6 

Figure 13-3 Shear Distortion of Ground – Free-Field Condition vs Cavity In-Place Condition.....13-14

Figure 13-4 Lining Response Coefficient, K1 .................................................................................13-18

Figure 13-5 Lining Response Coefficient, K2, for Poisson’s Ratio = 0.2........................................13-19

Figure 13-6 Lining Response Coefficient, K2, for Poisson’s Ratio = 0.35......................................13-19

Figure 13-7 Lining Response Coefficient, K2, for Poisson’s Ratio = 0.5........................................13-20

Figure 13-8 Soil Deformation Profile and Racking Deformation of a Box Structure .....................13-22

Figure 13-9 Racking Coefficient Rr for Rectangular Structures......................................................13-26

Figure 13-10 Simplified Racking Frame Analysis of a Rectangular Structure ................................. 13-26
FHWA-NHI-11-032 Table of Contents

Seismic Design – Geotechnical Features xxi August 2011

LIST OF TABLES

Table 1-1 AASHTO Limit States for Bridge Design ..................................................................... 1-16

Table 1-2 Load Combinations and Load Factors for AASHTO Limit States................................ 1-17

Table 1-3 AASHTO Permanent Load Factors............................................................................... 1-18

Table 1-4 Resistance Factors for Deep Foundations...................................................................... 1-19

Table 2-1 Modified Mercali Intensity Scale................................................................................... 2-22

Table 3-1 Selected Attenuation Relationships Used to Develop USGS Seismic Hazards Maps... 3-15

Table 3-2 Coefficients for the Abrahamson and Silva (1997) Attenuation Model ........................ 3-17

Table 3-3 Magnitude Deaggregation for Bakersfield, California, for a 2500 YR Return Period .. 3-24

Table 3-4 Performance Based Seismic Design Criteria for Transportation Facilities ................... 3-29

Table 3-5 NEHRP Site Classification System ............................................................................... 3-40

Table 3-6 Values of Fpga as a Function of Site Class and the Site Class B Peak Ground

Acceleration................................................................................................................... 3-41

Table 3-7 Values of Fa as Function of Site Class and the Site Class B Short Periods (0.2 Seconds) 

Spectral Acceleration..................................................................................................... 3-42

Table 3-8 Values of Fv as a Function of Site Class and the Site Class B Long Periods (1 Second) 

Spectral Acceleration..................................................................................................... 3-42

Table 4-1 Recommended "Standardized" SPT Equipment............................................................ 4-16

Table 4-2 Correction Factors for Non-Standard SPT Procedure and Equipment .......................... 4-17

Table 4-3 Relative Density of Sandy Soils .................................................................................... 4-24

Table 4-4 Typical Values of Initial Shear Modulus....................................................................... 4-31

Table 4-5 Index Property Correlations for Estimating the Initial (Small Strain) Shear Modulus, 

 Gmax ................................................................................................................................ 4-33

Table 4-6 Blow Count Correction, Ncorr for the Equivalent Clean Sand Blow Count, (N1)60-cs ..... 4-42

Table 4-7 Field Estimates of Uniaxial Compressive Strength of Intact Rock................................ 4-45 

Table 4-8 Geological Strength Index (GSI) for Jointed Rock Masses........................................... 4-47

Table 4-9 Values of mi for Intact Rock by Rock Group................................................................. 4-48

Table 4-10 Estimation of Disturbance Factor, D ............................................................................. 4-49 

Table 5-1 Uses of Site Response Analysis in Seismic Design of Transportation Facilities ............ 5-3 

Table 6-1 Seismic Hazard Level .................................................................................................... 6-20

Table 6-2 Estimated Susceptibility of Sedimentary Deposits to Liquefaction During Strong 

Ground Motion ............................................................................................................. 6-22

Table 6-3 Influence of Earthquake Magnitude on Volumetric Strain Ratio for Dry Sands........... 6-44

Table 6-4 Computation of Settlement for Deposit of Dry Sand..................................................... 6-45

Table 7-1 Site Coordinates and Seismicity Data ........................................................................... 7-21

Table 7-2 Height-Adjusted Seismic Coefficents for Site Class D, Compacted Fill Slope 

Example ......................................................................................................................... 7-22

Table 7-3 Pseudo-Static Stability Analyses Capacity to Demand Ratio (Factor of Safety) for a 

 Seismic Coefficient Equal to 0.5kAV, Compacted Fill Slope Example.......................... 7-23

Table 7-4 Yield Acceleration, kY, for Compacted Fill Slope Example.......................................... 7-23

Table 7-5 Newmark Displacements for Compacted Fill Slope Example ...................................... 7-24

Table 7-6 Seismic Displacement Estimates, Natural Slope Examples........................................... 7-27

Table 7-7 No Seismic Analysis Screening Criterion for Stability of Slopes not Suceptible to 

Liquefaction................................................................................................................... 7-27

Table 7-8 Ground Improvement Methods...................................................................................... 7-57
FHWA-NHI-11-032 Table of Contents

Seismic Design – Geotechnical Features xxii August 2011

Table 8-1 Force Reduction Factors, R, for Bridge Substructures .................................................... 8-6 

Table 8-2 AASHTO Seismic Design Categories........................................................................... 8-19

Table 8-3 Seismic Analysis Requirements for Bridges from the Interim Revisions...................... 8-20

Table 8-4 Seismic Design Requirements for Bridges from the Interim Revisions........................ 8-20

Table 8-5 Seismic Design Requirements from the 2009 AASHTO Guide Specifications............ 8-21

Table 8-6 Foundation Modeling Requirements from the 2009 AASHTO Guide Specifications... 8-21

Table 10-1 p-Multipliers for Piles in a 3 x 3 Group at 3 Diameter Spacing Subject to Monotonic 

 Loading ........................................................................................................................10-29

Table 10-2 Influence of Pile Spacing on p-Multipliers for Pile Subject to Monotonic Loading ...10-29

Table 10-3 p-Multipliers for Large Pile Groups ............................................................................10-30

Table 11-1 Conditions Under which Seismic Analysis is Not Required for a Free Standing Earth 

 Retaining Wall .............................................................................................................11-10

Table 11-2 Maximum Amount of Apparent Cohesion that should be Assumed for Backfill 

Soils .............................................................................................................................11-16

Table 12-1 Presumptive Displacement Factors, FW .......................................................................12-15
 

FHWA-NHI-11-032 1 – Introduction 

Seismic Design – Geotechnical Features 1-1 August 2011 

CHAPTER 1

 INTRODUCTION

1.1 BACKGROUND 

While earthquakes are sometimes considered primarily a California or west coast problem in the 

continental United States (US), damaging earthquakes are not limited to the western US. In fact, some of 

the strongest earthquakes in historical time in the United States occurred in the central and eastern US. 

The Charleston, South Carolina earthquake of 1886 is believed to have been as strong, if not stronger, 

than the 1971 San Fernando and 1994 Northridge earthquakes, and there were three large magnitude 

earthquakes, including at least one believed to have been as strong as the 1906 San Francisco earthquake, 

in the New Madrid seismic zone in the central United States in 1811 and 1812. Furthermore, in many 

areas of the United States bridges and other transportation structures are inadequately designed to resist 

even moderate levels of ground shaking without collapse. 

Figure 1-1 shows the United States Geological Survey (USGS) National Seismic Hazard Map for the 

peak ground acceleration with a 10% probability of being exceeded in 50 Years. The probability level for 

the map in Figure 1-1 corresponds to an annual probability of occurrence of 0.2%, or a return period of 

approximately 500 years, i.e. ground motions that are roughly twice as likely to occur as the design level 

specified in the current AASHTO (American Association of State Highway and Transportation Officials) 

seismic design provisions for bridges in the United States. Data produced by the USGS National Seismic 

Hazard Mapping Program indicates that at least 40 percent of the United States is subject to damaging 

ground shaking levels with 7 percent probability of occurrence in a 75 year period (the AASHTO bridge 

design criterion (corresponding to an approximately 0.1% annual probability of occurrence , or a 1000 

year return period). 

A factor that contributes the seismic hazard in the central and eastern US is that earthquake ground 

motions do not appear to attenuate as rapidly as they do in the western US. Thus, earthquake motions are 

felt over a much larger area in the western US compared to the central and eastern US for similar size 

earthquakes. Figure 1-2 compares the felt areas from the Charleston and New Madrid earthquakes to the 

San Fernando and San Francisco earthquakes. 
 

FHWA-NHI-11-032 1 – Introduction 

Seismic Design – Geotechnical Features 1-2 August 2011 

Figure 1-1 Peak Ground Acceleration with a 10% Probability of Being Exceeded in a 50 year Period 

http://earthquake.usgs.gov/hazards/products/conterminous/2008/maps/) 

Figure 1-2 Areas Impacted by Historic Earthquakes in the United States (ASCE) 
 

FHWA-NHI-11-032 1 – Introduction 

Seismic Design – Geotechnical Features 1-3 August 2011 

The susceptibility of older bridges and highway structures commonly found in the central and eastern US 

to earthquake shaking also contributes to the seismic risk in these areas. The photo in Figure 1-3 shows 

the collapse of the Cypress viaduct in Oakland in the 1989 Loma Prieta earthquake. This type of nonductile concrete construction is common in some parts of the central and eastern US and the level of 

earthquake shaking at the Cypress viaduct was similar to the AASHTO design levels in the many of these 

areas. Essentially, any of the pale green or darker areas on the National Seismic Hazard Map shown in 

Figure 1-1 are subject to ground motions of similar intensity to those experiences by the Cypress 

structure. 

Figure 1-3 Collapse of the Cypress Viaduct in the 1989 Loma Prieta Earthquake (USGS) 

1.2 EARTHQUAKE DAMAGE CATEGORIES

Damage from earthquakes can be subdivided into direct damage and indirect damage. Direct damage is 

the physical damage due to the earthquake. Direct damage includes primary damage due to strong 

shaking and fault rupture and secondary damage due to the effects of strong shaking or fault rupture. 

Indirect damage refers to the socio-economic impacts of an earthquake. The economic component of 

indirect damage often exceeds the economic consequences of direct damage from a major earthquake. 
 

FHWA-NHI-11-032 1 – Introduction 

Seismic Design – Geotechnical Features 1-4 August 2011 

1.2.1 Primary Damage 

Primary damage includes damage due to fault rupture and strong shaking. While fault rupture can cause 

significant damage to facilities built on or across the fault, the extent of the area impacted by fault rupture 

is relatively small as it is limited to the immediate vicinity of the rupture zone. Furthermore, areas 

susceptible to fault rupture in the western United States are often well-defined on geologic maps and 

construction in these areas may be restricted (e.g. Alquist-Priolo special study zones in California). Fault 

rupture is usually not a concern east of the Rocky Mountains, as faults east of the Rocky Mountains tend 

not to have surface expressions when they rupture. 

Primary damage due to strong shaking includes partial or total collapse of structures, landslides, and 

liquefaction. Figure 1-4 shows an example of direct damage to a highway structure due to strong shaking 

in the 1971 San Fernando earthquake. Factors influencing primary damage due to strong shaking include 

the intensity, duration, and frequency characteristics of the strong ground motion. These factors are 

related to distance between the site and the earthquake, the magnitude of the earthquake, and other 

characteristics of the earthquake as well as local site conditions. Primary damage also includes ground 

displacement phenomenon such as landslides and liquefaction induced by strong ground motions 

 

Figure 1-4 Collapse of the I-5, SR-14 Overpass in the 1971 San Fernando Earthquake (USGS) 
 

FHWA-NHI-11-032 1 – Introduction 

Seismic Design – Geotechnical Features 1-5 August 2011 

1.2.2 Secondary Damage 

Secondary damage is damage due to impact of primary damage, i.e., to phenomena induced by strong 

shaking or ground displacement. Secondary damage includes the impacts of landslides (e.g. disrupted 

roadways) and liquefaction (e.g. bearing capacity failure, lateral spreading, and slope instability) as well 

as damage due to seismically-induced settlement and impacts to constructed facilities from seiches and 

tsunamis. Figure 1-5 shows the collapse of the Showa Bridge in the 1964 Niigata, Japan earthquake due 

to liquefaction induced lateral spreading of the bridge piers. Case history data indicates that lateral 

spreading of liquefied soils is one of the major sources of damage to bridge foundations in earthquakes. 

 

Figure 1-5 Collapse of the Showa Bridge in the 1964 Niigata, Japan Earthquake (NGDC) 

Other types of secondary damage include fire following earthquakes and hazardous material spills. Much 

of the damage in San Francisco in 1906 was due to fire following the earthquake. The fire damage was 

exacerbated by ruptures to the water distribution due to earthquake-induced ground failure (e.g. 

liquefaction), which hindered attempts to suppress the fires. More recently, fires following the Coalinga 

(1984) earthquake were a significant source of secondary damage. Figure 1-6 shows fire due to a 

ruptured gas main in the 1994 Northridge earthquake. Gas and oil pipelines and storage facilities are 

often located within or adjacent to highway right-of-ways, creating fire and other secondary earthquake 

hazards (e.g. hazardous material spills) that may impact transportation facilities. 
 

FHWA-NHI-11-032 1 – Introduction 

Seismic Design – Geotechnical Features 1-6 August 2011 

Figure 1-6 Fire Following the 1994 Northridge Earthquake due to a Rupture Gas Main 

1.2.3 Indirect Damage 

There are many sources of indirect damage following an earthquake. Besides the more obvious losses 

due to disruption of business and commerce, disruption of essential services, and decline of property 

values, environmental impacts and mental stress are significant sources of indirect damage. 

Environmental effects can include not only hazardous material spills but also increased air pollution due 

to increased travel distances and congestion from disrupted highways. Mental stress in the aftermath of 

earthquakes often leads to an increase in divorce and suicide rates and other types of emotional problems. 

Indirect damage following the 1989 Loma Prieta earthquake due to closure of the San Francisco-Oakland 

Bay Bridge east span, shown in Figure 1-7, is estimated to have totaled hundreds of millions of dollars of 

economic loss. In total, the economic component of secondary damage due to the Loma Prieta event is 

estimated to have been well over $5 billion dollars. 
 

FHWA-NHI-11-032 1 – Introduction 

Seismic Design – Geotechnical Features 1-7 August 2011 

Figure 1-7 Damage to the San Francisco-Oakland Bay Bridge East Span due to the 1989 Loma 

Prieta Earthquake (USGS) 

1.3 DAMAGE TO HIGHWAY FACILITIES IN EARTHQUAKES 

The record of damage to highway facilities from earthquakes starts with the 1933 Long Beach earthquake 

– primarily because there were few highways before 1933 in areas subject to strong earthquake shaking, 

e.g. in the vicinity of the 1906 San Francisco earthquake. The first scientific studies of bridge damage, 

and liquefaction, commenced after the 1964 earthquakes in Niigata, Japan and Alaska. However, most of 

the bridges damaged in Alaska were railway bridges. The first major study of earthquake-induced 

highway bridge damage in the US followed the 1971 San Fernando earthquake. There have been 

numerous studies of damage to highway facilities in the US and abroad since 1971. Today, almost 

essentially every major earthquake is followed by reconnaissance studies that document both the damage 

to and successful performance of constructed facilities, including transportation systems. 

The 1971 San Fernando event was the first earthquake in the US which caused extensive damage to 

modern highway facilities. The strong motion records collected in the San Fernando event also facilitated 

the first statistical studies of strong ground motions. Observed damage on the San Fernando event 

included structural damage to bridges and retaining walls, cracking and lateral spreading of roadways, and 

slope instability. 
 

FHWA-NHI-11-032 1 – Introduction 

Seismic Design – Geotechnical Features 1-8 August 2011 

Figure 1-4 showed damage to the Interstate 5, State Route 14 interchange in the San Fernando earthquake, 

under construction at the time of the earthquake. These spans fell off their bearings due to inadequate 

seat width. Figure 1-8 shows the failure of an abutment wingwall at the Roxford Street undercrossing for 

SR-101 in the San Fernando event. The wall in Figure 1-8 had inadequate capacity to resist the 

seismically-induced lateral earth pressures. 

Figure 1-8 Failure of the Wingwall at the Roxford Street Undercrossing in the 1971 San Fernando 

Earthquake 

Backfill placed against bridge abutments may be vulnerable to seismic settlement, particularly if the fill is 

cohesionless and poorly compacted. Figure 1-9 shows settlement of an approach fill at an abutment in the 

1971 San Fernando event. The damage shown in Figure 1-8 and Figure 1-9 may be considered acceptable 

under the current AASHTO performance standard for ordinary bridges, as AASHTO allows for damage 

in the design earthquake, even to the point of requiring complete replacement of the structure, as long it is 

not likely to result in structural collapse or loss of life. 
 

FHWA-NHI-11-032 1 – Introduction 

Seismic Design – Geotechnical Features 1-9 August 2011 

Figure 1-9 Settlement of Abutment Embankment Fill in the 1971 San Fernando Earthquake (FHWA, 

2004) 

Several recent earthquakes provide dramatic examples of the types of damage that can occur to highway 

facilities in an earthquake. In addition to the collapse of the Cypress viaduct (Figure 1-3) and the east 

span of the San Francisco-Oakland Bay Bridge (Figure 1-7), another 91 bridges suffered significant 

damage in the 1989 Loma Prieta event. Furthermore, State Route 17, the main highway from the Bay 

Area to Santa Cruz, was blocked by a landslide, hindering emergency response and recovery. Figure 1-10

shows the Struve Slough Bridge following the Loma Prieta event. The pile – cap beam connection failed 

due to strong shaking and ground displacement, the cap beam shifted off the piles, the bridge sat down in 

the slough, and the piles punched through the bridge deck. Figure 1-11 shows the shear failure at the 

head of the piles for the Struve Slough Bridge. Failure at the head of a pile due to inadequate 

confinement or poor connection detailing is one of the most common types of damage to piles in 

earthquakes. 
 

FHWA-NHI-11-032 1 – Introduction 

Seismic Design – Geotechnical Features 1-10 August 2011 

Figure 1-10 Collapse of the Bridge over Struve Slough in the 1989 Loma Prieta Earthquake (USGS) 

Figure 1-11 Shear Failure of the Head of a Pile at the Struve Slough Bridge 
 

FHWA-NHI-11-032 1 – Introduction 

Seismic Design – Geotechnical Features 1-11 August 2011 

Landslides along the route of SR-17, including the one shown in Figure 1-12, closed 12 miles of this the 

highway, the main route between the epicentral region of the Loma Prieta event, including the city of 

Santa Cruz, and the San Francisco Bay Area, for 32 days. Besides hindering emergency response and 

recovery, this closure resulted in substantial economic losses due to loss of commerce, increased traffic 

congestion on alternate routes, and other secondary effects. 

Figure 1-12 Landsliding Along SR-17 in the 1989 Loma Prieta Earthquake (USGS) 

Figure 1-13 shows the collapse of the I-5 / SR-14 overpass in the 1994 Northridge earthquake. This is the 

same overpass that collapsed in the 1971 earthquake (Figure 1-4). The overpass was rebuilt after San 

Fernando earthquake as originally designed, before lessons learned from that earthquake were 

incorporated into practice. The overpass was recognized as being seismically inadequate and was on the 

list of bridges to be seismically retrofit, but funds had not yet been allocated for the retrofit project. About 

10% of the approximately 12,000 miles of the state highway system were impacted by the Northridge 

earthquake, and several major interchanges in the Los Angeles area failed. 
 

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Seismic Design – Geotechnical Features 1-12 August 2011 

Figure 1-13 Collapse of the I-5, SR-14 Interchange in the 1994 Northridge Earthquake (USGS) 

1.4 AASHTO SEISMIC DESIGN PHILOSOPHY 

The seismic design philosophy adopted by AASHTO for ordinary bridges is that they should be able to 

withstand large rare earthquakes without collapse or loss of life (though they may suffer damage that 

requires complete replacement of the structure) and that they should withstand smaller, more frequent 

earthquakes without significant damage. However, only performance in the large, rare earthquake is 

actually analyzed. “Acceptable” performance in smaller events is implicitly assumed, but not quantified, 

and may range from repairable damage to no significant damage. 

The 2009 AASHTO Guide Specifications for LRFD Seismic Bridge Design note that more stringent 

performance requirements are appropriate for critical and essential structures. Bridges are classified by 

the Owner as Critical, Essential, and Other (sometimes called Ordinary) Bridges (in descending order of 

importance), depending on their function. A critical bridge is a bridge that is expected to remain open to 

all traffic, including emergency vehicles, and for defense and security purposes after the design 
 

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Seismic Design – Geotechnical Features 1-13 August 2011 

earthquake. Essential bridges are bridges that are expected to be useable by emergency vehicles and for 

security and defense purposes after the design earthquake. Bridges that don’t fall into either the Critical 

or Essential categories are designated as Other Bridges. Most bridges are classified as Other (or 

Ordinary) Bridges and are designed for significant damage in the design event – the large rare earthquake 

with a 1000-year return period. 

The 2009 AASHTO Guide Specifications define significant damage as conditions that may require 

closure to repair the bridge and/or partial or complete replacement of the structure. Figure 1-8 and Figure 

1-9 provided examples of acceptable damage to bridge abutments in the 1971 San Fernando earthquake. 

After the 1971 San Fernando earthquake, it was evident that many bridge abutments had been subjected 

to large forces and had actually helped dissipate energy by absorbing these forces at the cost of damage to 

the abutment. This type of abutment performance is now recognized as beneficial to the overall seismic 

performance of the bridge. Longitudinal movement of the bridge deck beyond the point at which the 

abutment wall engages the soil takes energy out of the system. While the thrust of the bridge deck on the 

abutment wall may result in damage to the wall, under the AASHTO design philosophy abutment walls 

may be considered sacrificial elements for seismic design of ordinary bridges. 

Figure 1-3, Figure 1-4, Figure 1-7, Figure 1-10, Figure 1-11, and Figure 1-13 show unacceptable damage 

to bridges in earthquakes. Figure 1-14 is another example of unacceptable damage. In this figure, the 

bridge columns have failed at their connection to the foundation. 

Figure 1-14 Failure of a Bridge Column – Foundation Connection 
 

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Seismic Design – Geotechnical Features 1-14 August 2011 

1.5 LOAD AND RESISTANCE FACTOR DESIGN 

1.5.1 Basic Principles of LRFD 

AASHTO has recently moved to a new design philosophy, Load and Resistance Factor Design (LRFD) 

LRFD, from the old Allowable Stress Design (ASD) approach. Ideally, LRFD provides a balanced, 

reliability based design that includes consideration of the various sources of uncertainties that impact 

structural performance. Equation 1-1 shows the basic LRFD design equation: 

iii   RQ ii

1-1

where: 

i = a load modifier to account for ductility, redundancy, and operational importance 

of the bridge or other structure (dimensionless)

i = load factor; a multiplier applied to force effect i

Qi = force effect i 

i = resistance factor for resistance component i

Ri = nominal value of resistance component i 

 

In plain language, Equation 1-1 says that the sum of the factored loads must be less than or equal to the 

sum of the factored resistances. Load combinations and values for load and resistance factors specified in 

AASHTO are discussed below. 

One complication for the geotechnical specialist is that LRFD notation uses several common soil 

mechanics symbols. In standard LRFD notation, load factors are designated by the symbol  and 

resistance factors are represented by the symbol . In soil mechanics, we use these symbols for unit 

weight and the Mohr-Coulomb friction angle, respectively. We therefore need to pay attention to the 

context in which these symbols are used to know which meaning they have in the equations we are using. 

An LRFD related term that will be used in this document is the capacity/demand (C/D) ratio. This is not 

an AASHTO term. The C/D ratio can be calculated using factored or unfactored (nominal) values. In 

accordance with Equation 1-1, the LRFD design criterion is that the (C/D)factored must be equal to or 

greater than 1.0: 

(C/D)factored = 

 QR iiiii

/ 

1-2a
 

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Seismic Design – Geotechnical Features 1-15 August 2011 

(C/D)factored > 1.0 1-2b

 

The unfactored capacity/demand ratio is analogous to the factor of safety (FS). 

(C/D)unfactored = 

 QR ii

/

1-3a

(C/D)unfactored = FS 1-3b

The unfactored C/D, like the factor of safety, must exceed 1, often times by a significant margin, for a 

design to be acceptable. 

1.5.2 LRFD versus ASD 

There is a basic difference how uncertainties in design are accounted for between LRFD and ASD. In 

the ASD approach for geotechnical design, uncertainties are generally lumped together into a single 

safety factor. In the LRFD approach, load and resistance factors are used to account for varying levels of 

uncertainty in the components of the load and the resistance. In LRFD we do not use terms such as 

allowable capacity, allowable load, and ultimate capacity. Instead, we talk about the factored capacity, 

factored load, and nominal resistance 

1.5.3 AASHTO Specifications for Seismic LRFD 

AASHTO specifications for seismic design of bridges using LRFD include the 2007 LRFD Bridge 

Design Specifications (including the 2008 Interim Revisions) and the 2009 Guide Specifications for 

LRFD Seismic Bridge Design. These two sets of specifications use two different approaches to seismic 

design. The LRFD Bridge Design Specifications employ a force-based design approach while the LRFD 

Seismic Bridge Design specifications employ a displacement based design approach. This document 

addresses both approaches for design of foundations and earth retaining structures. Neither of these 

LRFD-based specifications addresses geotechnical aspects of seismic design beyond the design of 

foundations and earth retaining structures. However, NCHRP Project 12-70 (described in NCHRP Report 

611) produced recommendations for LRFD seismic design of free standing retaining walls, slopes, 

embankments, and buried structures. Recommendations from the NCHRP 12-70 project for seismic 

design of these features are included in this document, as appropriate. 
 

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1.5.4 AASHTO Limit States and Load and Resistance Factors 

In AASHTO, LRFD design is based upon four different limit states, including the strength, serviceability, 

extreme loading, and fatigue limit states. The limit state for each of the cases defines the boundary 

between acceptable and unacceptable performance. Table 1-1 defines the limit states considered by 

AASHTO in LRFD for bridges. 

TABLE 1-1 AASHTO LIMIT STATES FOR BRIDGE DESIGN 

Limit State Type Case Load Combination 

Strength 

I Normal vehicular use of the bridge without wind 

II Use of the bridge by Owner-specified special vehicles, evaluation permit 

vehicles, or both, without wind 

III Bridge exposed to wind velocity exceeding 55 mph 

IV Very high dead load to live load force effect ratios 

V Normal vehicular use of the bridge with wind of 55 mph 

Extreme Event 

I Load combination including earthquake 

II

Ice load, collision by vessels and vehicles, and certain hydraulic events 

with a reduced live load other than that which is part of the vehicular 

collision load, CT

Service 

I Normal operational use of the bridge with a 55 mph wind and all loads taken at 

their nominal values 

II Intended to control yielding of steel structures and slip of slip-critical 

connections due to vehicular live load 

III Longitudinal analysis relating to tension in prestressed concrete superstructures 

with the objective of crack control and to principal tension in the webs of 

segmental concrete girders 

IV Tension in prestressed concrete columns with the objective of crack control 

 Fatigue Repetitive gravitational vehicular live load and dynamic responses under the 

effects of a single design truck 

The AASHTO specifications define the load combinations and load factors that must be considered for 

each limit state. More than one load combination may be evaluated for a given limit state. In this 

document, we are only concerned with the Extreme Event I limit state, earthquake loading. 

Table 1-2 shows the load combinations prescribed in AASHTO for each limit state. For Extreme Event 1 

limit state design (earthquake loading) there is only one load combination. Included in the load 

combination for the Extreme Event 1 limit state are the permanent (dead) loads, earthquake live loads, 
 

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Seismic Design – Geotechnical Features 1-17 August 2011 

water and friction loads, and the earthquake load itself. Note that we use a load factor of 1 on the 

earthquake load. 

TABLE 1-2 LOAD COMBINATIONS AND LOAD FACTORS FOR AASHTO LIMIT 

STATES (After AASHTO 2007, Table 3.4.1-1) 

Load 

Combination 

Limit State PL LL WA WS WL FR TCS TG SE

Use one of these at a time 

EQ IC CT CV

Strength I p 1.75 1.00 - - 1.00 0.50/1.20 TG SE - - - - 

Strength II p 1.35 1.00 - - 1.00 0.50/1.20 TG SE - - - - 

Strength III p - 1.00 1.40 - 1.00 0.50/1.20 TG SE - - - - 

Strength IV p - 1.00 - - 1.00 0.50/1.20 - - - - - - 

Strength V p 1.35 1.00 0.40 1.00 1.00 0.50/1.20 TG SE - - - - 

Extreme Event I p EQ 1.00 - - 1.00 - - - 1.00 - - - 

Extreme Event II p 0.50 1.00 - - 1.00 - - - - 1.00 1.00 1.00 

Service I 1.00 1.00 1.00 0.30 1.00 1.00 1.00/1.20 TG SE - - - - 

Service II 1.00 1.30 1.00 - - 1.00 1.00/1.20 - - - - - - 

Service III 1.00 0.80 1.00 - - 1.00 1.00/1.20 TG SE - - - - 

Service IV 1.00 - 1.00 0.70 - 1.00 1.00/1.20 - 1.00 - - - - 

Fatigue - 0.75 - - - - - - - - - - - 

PL permanent load WL wind on live load EQ earthquake 

LL live load FR friction IC ice load 

WA water load and stream pressure TG temperature gradient CT vehicular collision force 

WS wind load on structure SE settlement CV vessel collision force 

 TCS uniform temperature, creep, and shrinkage 

p load factor for permanent loads (see Table 1-3) 

TG load factor for temperature gradient (see AASHTO 2007 Article 3.4.1) 

SE load factor for settlement (see AASHTO 2007 Article 3.4.1) 

Table 1-3 defines the permanent loads and associated load factors considered by AASHTO in LRFD. 

Note that there are maximum and minimum values for each load factor, and the minimum values are less 

than 1. We have maximum and minimum load factors because in some cases loads increase stability and 

in other cases they decrease stability. Both maximum and minimum load combinations need to be 

considered, with the more (or most) critical combination used for design, i.e. when increased load 

increases stability, we use the minimum load factor for design. Furthermore, we generally use load 

factors less than 1 for minimum loads. 
 

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Seismic Design – Geotechnical Features 1-18 August 2011 

TABLE 1-3 AASHTO PERMANENT LOAD FACTORS 

Type of Load 

Load Factor, γp

Maximum Minimum 

DC: Conponents and Attachments 1.25 0.90 

DC: Strength IV Only 1.50 0.90 

DD: Downdrag 1.25 0.35 

DW: Wearing surfaces and utilities 1.50 0.65 

EH: Horizontal earth pressure 

 Active 1.50 0.90 

 At-Rest 1.35 0.90 

EL: Locked-in stresses 1.00 1.00 

EV: Vertical earth pressure 

 Overall Stability 1.00 N/A 

 Retaining walls and abutments 1.35 1.00 

 Rigid buried structure 1.30 0.90 

 Rigid frames 1.35 0.90 

 Flexible buried structures other than metal box culverts 1.95 0.90 

 Flexible metal box culverts 1.50 0.90 

ES: Earth Surcharge 1.50 0.75 

The live load factor for seismic loading, EQ, is not explicitly defined in AASHTO. In the old AASHTO 

ASD specifications, a value of zero was used. The AASHTO LRFD specifications notes that some 

engineers recommend using the average daily truck traffic (ADTT) load for EQ, but suggests that 0.5 

ADTT is a reasonable value. A value of 0.5 ADTT for the maximum load case and 0 for the minimum 

load would thus be consistent with these recommendations. However, for earthquake loads the live load 

is often ignored. Another alternative is to sue the HL-93 load as EQ for the maximum load case. 

At present, the AASHTO Guide Specifications for LRFD Seismic Bridge Design recommends that a 

resistance factor of 1 be used for seismic design for all resistance components of foundation design except 

for deep foundation axial uplift and lateral resistance., wherein a resistance factor of 0.8 is recommended 

Furthermore, the recommendation in NCHRP 12-70 for the bearing resistance of retaining walls on 

spread footings founded upon soil calls for a resistance factor of 0.67 to be applied to the nominal bearing 

capacity. In other words, except for these cases, we should use a resistance factor of 1, reflecting use of 

our best (but reasonably prudent) estimate of resistance parameters. This is described in AASHTO as an 

interim recommendation until more data is available. This, however, does not mean that we are not 

incorporating uncertainty into the seismic resistance parameters. Many geotechnical resistance 

parameters have a reserve capacity for seismic loading that is not quantified (e.g. an increase in the shear 

strength of sand subject to rapid loading). 
 

FHWA-NHI-11-032 1 – Introduction 

Seismic Design – Geotechnical Features 1-19 August 2011 

Table 1-4 presents the resistance factors recommended in the NHI training course on LRFD Design for 

Deep Foundations. As noted previously, a resistance factor of 0.8 is recommended for axial uplift and 

lateral resistance. 

TABLE 1-4 RESISTANCE FACTORS FOR DEEP FOUNDTIONS 

Limit State Component of 

Resistance Geomaterial Method Resistance Factor, φ

Extreme Event 

I and II 

Axial geotechnical 

uplift resistance All Geomaterials 

Methods cited 

for strength 

Limit states 

0.80 

Geotechnical lateral 

resistance All Geomaterials 

p-y methods 

pushover 

analysis 

0.80 

All other cases All Geomaterials 

Methods cited 

for strength 

Limit states 

1.00 

1.6 ORGANIZATION OF THE DOCUMENT 

Chapter 2 presents basic concepts of seismic geology and engineering seismology. This information is 

essential background information for subsequent discussions of seismic hazard analysis and ground 

motion characterization. 

Chapter 3 presents the details of both probabilistic and deterministic seismic hazard analysis, including 

seismic source characterization and ground motion attenuation, and the development of design ground 

motions. The advantages and disadvantages of both probabilistic and deterministic seismic hazard 

analysis are discussed. Development of the Uniform Hazard Spectrum for a specified probability and 

exposure period using either the National Seismic Hazard maps developed by the USGS or the ground 

motion maps developed by USGS specifically for AASHTO is presented. Development of the AASHTO 

truncated acceleration response spectra for use in structural analysis from the Uniform Hazard Spectrum, 

including the use of the shear wave velocity in the top 100 ft of the site to account for the influence of 

local site conditions, is illustrated. The process of deaggregation by which a probabilistically-derived 

uniform hazard spectrum is decomposed into magnitude and distance combinations in order to determine 

a representative magnitude and distance for the design earthquake is described. Guidelines for selecting a 

suite of representative time histories for the representative design event are presented. Special topics, 
 

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Seismic Design – Geotechnical Features 1-20 August 2011 

including near field ground motions, spatially varying ground motions, and vertical ground motions, are 

briefly addressed. 

Chapter 4 described site characterization for seismic analysis. The use of the Standard Penetration Test 

(SPT) and the Cone Penetration Test (CPT) to evaluate site stratigraphy and geotechnical properties is 

explained in detail. Geophysical techniques for site investigation are also addressed. Characterization of 

rock mass behavior and quantification of rock mass strength is described. Correlations between important 

geotechnical properties, including relative density, shear strength, and shear wave velocity, from both in 

situ test results and soil classification and index test data are presented. 

In Chapter 5, the process of site specific seismic response analysis is described. Methods addressed in 

this chapter include simplified chart-based methods to adjust the peak ground acceleration for local site 

conditions, equivalent linear one-dimensional site response analysis, non-linear one-dimensional site 

response analysis with pore pressure generation, and advanced two-dimensional site response analysis. 

The development of input parameters for equivalent-linear one-dimensional site response analyses, the 

most common type of advanced analysis performed in practice, are described in detail. 

Chapter 6 describes earthquake-induced damage due to the geotechnical seismic hazards of slope 

instability, liquefaction, and seismic settlement. Methods to evaluate seismic slope deformation, 

liquefaction potential, liquefaction-induced ground displacements, and seismic settlement are described in 

detail in this chapter. A method to evaluate the appropriate value of the seismic coefficient for pseudostatic slope stability analyses that accounts for spatial incoherence of ground motions, the local seismic 

environment, local site conditions, and acceptable displacement levels is presented. 

Chapter 7 addresses design of earthwork features for transportation facilities, including soil and rock 

slopes and embankments. A performance-based seismic design philosophy that employs the concept of 

allowable displacement is described. Soil and site improvement techniques that can be used when the 

seismic displacement are unacceptable are presented with an emphasis on remediation of slope stability 

and liquefaction. 

Chapter 8 describes the seismic design process and the AASHTO seismic design methodology, including 

capacity design of bridge foundations, the concept of the earthquake resisting system for a bridge, 

guidelines for what types of earthquake resisting elements are allowable and not recommended, and basic 
 

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Seismic Design – Geotechnical Features 1-21 August 2011 

principles of soil-foundation-structure interaction. The principles of both kinematic and inertial 

interaction are described. 

Chapter 9 describes the seismic design of shallow foundations, including techniques to assess both 

foundation stiffness and foundation capacity. Equations for calculating the stiffness coefficients for the 

six modes of foundation displacement for use in an inertial interaction analysis are presented. Foundation 

capacity analyses discussed in the chapter include bearing, overturning, and sliding. 

Chapter 10 addresses deep foundation design. Both p-y/t-z analyses and simple elastic solutions to 

evaluate the stiffness of an individual pile are discussed along with methods to account for group effects 

and to assemble individual pile and pile cap stiffness into a group stiffness. Sophisticated methods and a 

simple approximate method to account for kinematic interaction at soft soil sites are described. Analyses 

to evaluate the response of pile foundations to ground displacement demand from laterally spreading 

induced by liquefaction are discussed. 

Chapter 11 presents methods for seismic design of free standing retaining walls. A variety of methods for 

predicting seismic active earth pressures, including the Mononobe-Okabe method, design charts that 

include the influence of a cohesion component to the shear strength, the Coulomb wedge method, and the 

general equilibrium method, are described along with a displacement-based method for evaluating the 

appropriate seismic coefficient for use in design. Charts for evaluating the passive earth pressure 

coefficient, including the effect of cohesion, are also presented in this chapter. Design of gravity and 

semi-gravity retaining walls for sliding, overturning, and bearing modes is discussed in detail. Earth 

pressure diagrams for non-gravity cantilever walls, anchored walls, and MSE walls are described along 

with recommendations for the seismic coefficient for use in design. 

Chapter 12 describes bridge abutment design. The characterization of the stiffness of both conventional 

seat-type and integral abutments for inclusion in the global bridge model is presented. The effect of 

skewed abutments on the seismic performance of the bridge is discussed. 

Chapter 13 presents design considerations for buried structures, including culverts and pipelines. Simple 

closed form solutions are presented for the displacement demand on buried structures subject to seismic 

loading. 
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Seismic Design – Geotechnical Features 2-1 August 2011 

CHAPTER 2

EARTHQUAKE FUNDAMENTALS AND ENGINEERING SEISMOLOGY 

2.1 INTRODUCTION 

Earthquakes are produced by abrupt relative movements on fractures or fracture zones in the earth's crust. 

These fractures or fracture zones are termed earthquake faults. The mechanism of fault movement is the 

sudden release of built-up stress along the fault. The primary source of this built-up stress is the 

accumulated relative movement of large, essentially intact pieces of the earth's crust called tectonic 

plates. This relative movement is restrained by frictional and other forces (e.g. interlocking) along the 

fault, leading to a buildup of stress along the fault and strain (or strain energy) in the rocks adjacent to the 

fault. When the built up stress exceeds the strength of the rock along the fault, relative movement 

between the rocks on either side of the fault, commonly called fault rupture, takes place along the rupture 

zone. When fault rupture occurs, the built up strain energy in the rocks on either side of the fault is 

released as the strained rock rebounds elastically on both sides of the fault. This rebound produces 

vibrations that pass through the earth’s crust and along the earth's surface, generating the ground motions 

that are the source of most damage attributable to earthquakes. If the displacement associated with the 

fault rupture propagates upward to the ground surface, the relative movement may manifest itself as 

surface rupture. Surface ruptures are also a source of earthquake damage to constructed facilities. Fault 

rupture may also cause secondary ground deformations and regional ground deformations (e.g. uplift or 

subsidence) that can be damaging to engineered facilities. Volcanism constitutes a secondary source of 

stress and strain energy accumulation in the earth’s crust. The release of the strain energy associated with 

volcanism may also result in damaging earthquake ground motions. 

2.2 EARTHQUAKE SOURCES 

2.2.1 General 

Faults are ubiquitous in the earth's crust. They exist both at the contacts between tectonic plates (large 

intact pieces of the earth’s crust that tend to move as a coherent unit) and within the tectonic plates 

themselves. In some areas of the western United States, it is practically impossible to perform a site 

investigation and not encounter a fault. However, not all faults are seismogenic (i.e., not all faults are 

capable of producing earthquakes at the present time). Faults that are known to be capable of producing 
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Seismic Design – Geotechnical Features 2-2 August 2011 

earthquakes are termed active faults. Faults for which the potential for producing earthquakes is uncertain 

are termed potentially active faults. Faults that at one time produced earthquakes but are now considered 

dormant are sometimes referred to as inactive faults. However, the term inactive fault is no longer in 

widespread use, as dormant faults can be reactivated under some circumstances. Thus faults that are 

considered to be dormant may also be considered potentially active. 

When a fault is encountered in an area known or suspected to be a source of earthquakes, a careful 

analysis and understanding of the fault is needed to evaluate its potential for generating earthquakes. One 

of the most common means of investigating the potential for a fault to produce earthquakes is through the 

study of surface manifestations of faulting. However, not all active faults have surface manifestations. In 

some cases, faults may be too deep to produce obvious surface manifestations. In other cases, the 

earthquakes generated by a fault may occur so infrequently, or surface geologic processes may be so 

rapid, that surface manifestations of the faulting have been erased. Careful study of geomorphic and 

seismologic information by qualified geo-professionals is required to identify the earthquake faults (or 

seismogenic sources) capable of damaging engineered facilities in a region. 

2.2.2 Plate Tectonics 

Plate tectonics theory has established beyond a reasonable doubt that the earth's crust is a mosaic of 

tectonic plates. These tectonic plates are composed of either oceanic or continental crust and “float” on 

top of a molten rock layer referred to as the upper mantle. Tectonic plates move as relatively intact 

bodies on top of the upper mantle except at their margins, where they may grow due to upwelling of 

molten rock from the mantle or be consumed by crust being drawn down, or subducted, into the mantle. 

The motions of the tectonic plates are driven by convection currents in the molten rock in the earth's 

upper mantle, which cause the upwelling of molten rock at the plate margins where the crust is growing. 

These convection currents are generated by heat sources within the earth (e.g. radioactive decay). The 

zones where tectonic plates grow in size, i.e. where the convection currents send plumes of material from 

the upper mantle to the earth's surface, are referred to spreading zones. The zones where tectonic plates 

are consumed, i.e. are drawn downwards back into the mantle, are referred to as subduction zones. 

Tectonic plates may also override one another and slide past each other. Plate boundaries where two 

tectonic plates slide past each other are referred to as transform boundaries. 

The major tectonic plates of the earth's crust are shown in Figure 2-1. There are also numerous smaller, 

minor tectonic plates not shown in this figure. The motions of these plates are related to the activation of 
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Seismic Design – Geotechnical Features 2-3 August 2011 

faults, the generation of earthquakes, and the presence of volcanism. Most earthquakes occur on or near 

plate boundaries, as illustrated in Figure 2-2. Earthquakes also occur in the interior of the plates, although 

generally with a much lower frequency of occurrence than at plate boundaries. For the continental United 

States, the principal tectonic plate boundary is along the western coast of the continent, where the North 

American Plate and the Pacific Plate are in contact (see Figure 2-1). In California, the boundary between 

these plates is a transform boundary wherein the relative movement is generally (though not exclusively) 

one of lateral (horizontal) slippage of one plate past the other. 

In Washington and Oregon, a smaller plate, the Juan de Fuca plate, is interposed between the North 

American and Pacific plates. The boundary between the North American plate and the Juan de Fuca plate 

is a subduction zone, as is the boundary between the North American plate and the Pacific plate along the 

Aleutian Islands in Alaska. Subduction zones, wherein one plate dives (subducts) beneath the other plate 

(as illustrated in Figure 2-3), are considered capable of very large magnitude earthquakes. Furthermore, 

volcanic activity is generally also associated with subduction, as magma generated by the subducting 

plate rises to the earth’s surface in a zone above the subducting plate (as illustrated in Figure 2-3).

Figure 2-1 Major Tectonic Plates and Their Approximate Direction of Movement (Source: 

www.maps.com)
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Seismic Design – Geotechnical Features 2-4 August 2011 

Figure 2-2 Worldwide Seismic Activity and Plate Boundaries (U.C. Berkeley Museum of 

Paleontology (www.ucmp.berkeley.edu/) 

Figure 2-3 Cross-Section Through a Subduction Zone. (Source: www.platetectonics.com) 

In the western interior of the United States, adjacent to the western edge of the North American plate (e.g. 

in Montana, Utah, Nevada), stresses induced by the complex movements of the North American plate 

(i.e., spreading, translating, and rotating on the surface of the earth) may also result in normal 

(extensional) and thrust (compressional) faulting as well as transform faulting. 
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Seismic Design – Geotechnical Features 2-5 August 2011 

Earthquake source areas in the central and eastern United States are termed intraplate source zones, as 

they lie in the interior of a tectonic plate (the North American plate). The mechanisms generating 

earthquakes in intraplate source zones are poorly understood. Potential mechanisms for intraplate 

earthquakes include relief of locked-in stresses from ancient tectonic movements, crustal rebound from 

the ice ages, and re-adjustment of stress in the interior of the plate due to loads imposed at plate 

boundaries. Earthquakes associated with intraplate volcanism, e.g. earthquakes in Hawaii, are believed to 

be associated with isolated plumes of molten rock rising to the surface from the mantle. These isolated 

plumes of molten rock are sometimes referred to as hot spots. 

The intensity of the ground motions produced by an earthquake at a given site depends upon a variety of 

factors. Primary factors influencing earthquake ground motion intensity include the amount of strain 

energy released by the event (generally quantified as earthquake magnitude), the distance from the 

earthquake to the site in question, the depth of the earthquake, the geologic conditions between the 

earthquake fault and the site, and local ground conditions (e.g. topography and local soil conditions, 

including soil profile and soil properties). Due to significant differences in geologic conditions between 

the source and the site, the intensity of the ground motions from an earthquake of a given magnitude and 

distance may be greater in plate interiors (i.e. an intraplate event) than at active plate boundaries. 

Therefore, while earthquake activity is much greater along the plate boundaries than in the plate interior, 

intraplate events appear to impact a larger area than plate boundary events of the same magnitude because 

the intensity of ground motions (e.g. peak ground acceleration) from intraplate earthquakes appears to 

attenuate, or dissipate, much more slowly than from plate boundary events. 

The depth at which fault rupture occurs is also an important factor influencing the intensity of ground 

motions at a site. This is particularly true for sites close to the surface projection of a fault rupture, where 

the depth of the rupture can contribute significantly to the distance the earthquake waves have to travel 

before arriving at the site. In a subduction zone, such as that along the coast of Oregon and Washington, 

there are both faults that are shallow and located within the over-riding crust (fault depth <12 miles), 

referred to as shallow crustal faults, and faults that are deep within the subducting plate (fault depth >12 

miles). Intraplate faults in the plate interior may also vary from shallow to deep and may be covered by a 

thick mantle of sediments. However, faults along transform boundaries such as along the California coast 

line, where the plates slide laterally past each other are generally relatively shallow (< 12 miles depth) 

crustal faults. 
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Seismic Design – Geotechnical Features 2-6 August 2011 

2.2.3 Fault Movements 

Faults are created when the built up stresses within geologic materials exceed the ability of those 

materials to withstand the stresses. Most faults that exist today are the result of tectonic activity that 

occurred in earlier geological times. These faults are usually non-seismogenic (i.e. incapable of 

generating earthquakes, or inactive). However, faults related to past tectonism may be reactivated by 

present-day tectonism in seismically active areas and can also be activated by anthropogenic (man-made) 

activities such as impoundment of a reservoir by a dam or injection of fluids deep into the subsurface (e.g. 

for geothermal energy development). The maximum size of an earthquake on an anthropogenically 

reactivated fault is a subject of some controversy, but earthquakes as large as moment magnitude 6.5 have 

been attributed to reservoir impoundment. 

Not all faults along which relative movement is occurring are a source of damaging earthquakes. Some 

faults may be surfaces along which relative movement is occurring at a slow, relatively continuous rate, 

with an insufficient stress drop to cause a damaging earthquake. Such movement is called fault creep. 

Fault creep may occur along a shallow fault, where the low overburden stress on the fault results in a 

relatively low threshold stress for initiating displacement along the fault. Alternatively, a creeping fault 

may be at depth in soft and/or ductile materials that deform plastically. Also, there may be a lack of 

frictional resistance or asperities (non-uniformities) along the fault plane, allowing steady creep and the 

associated relatively slow release of the strain energy along the fault. Fault creep may also prevail where 

phenomena such as magma intrusion or growing salt domes activate small shallow faults in soft 

sediments. Faults generated by extraction of fluids (e.g., oil or water in southern California) may cause 

ground settlement and activate faults near the surface, resulting in fault creep. Faults activated by other 

non-tectonic mechanisms, e.g. faults generated by gravity slides that take place in thick, unconsolidated 

sediments, could also produce fault creep. 

Active faults that extend into crystalline bedrock are generally capable of building up the strain energy 

needed to produce, upon rupture, strong ground motions, i.e. ground motions strong enough to damage 

transportation facilities. Fault ruptures in crystalline rock may also propagate from the crystalline 

bedrock to the ground surface and produce ground rupture. Fault ruptures which propagate to the surface 

in a relatively narrow zone of deformation that can be traced back to the causative fault in crystalline rock 

are sometimes referred to as primary fault ruptures. Fault ruptures may also propagate to the surface in 

diffuse, distributed zones of deformation which cannot be traced directly back to the basement rock. In 

this case, the surface deformation may be referred to as secondary fault rupture. 
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In some instances, fault rupture may be confined to the subsurface with no relative displacement at the 

ground surface due to the fault movement. Absence of primary fault rupture at the ground surface is 

believed to be characteristic of all but the largest magnitude earthquakes in the central and eastern United 

States. Furthermore, geological processes may erase surface manifestations of faulting in some areas, 

particularly when the interval between earthquakes with surface manifestations is large. Therefore, 

intraplate seismic source zones often must be evaluated using instrumental seismicity and paleoseismicity 

studies. This is particularly true if the intraplate sources are covered by a thick mantle of sediments, as in 

the New Madrid, Tennessee, and Charleston, South Carolina, intraplate seismic zones. Instrumental 

recording of small magnitude events can be particularly effective in defining seismic source zones. 

Figure 2-4 shows seismic zones in the southeastern US identified using both instrumental seismicity for 

events as small as magnitude 3 and historical records of larger (> M 5) events. 

Figure 2-4 Southeastern US Seismic Zones and Instrumental Seismicity 

Essentially all of the active faults with surface fault traces (i.e. where fault rupture propagates to the 

ground surface) in the United States are shallow crustal faults west of the Rocky Mountains. However, 

not all shallow crustal faults west of the Rocky Mountains have surface fault traces. Several recent 

significant earthquakes along the Pacific Coast plate boundary (e.g., the 1987 Whittier Narrows 
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earthquake, the 1994 Northridge earthquake, and the 2001 Nisqually earthquake) were due to rupture of 

thrust (compressional) faults that did not break the ground surface. Thrust faults that do not break the 

ground surface are termed blind thrust faults. Figure 2-5 illustrates a blind thrust fault in which rupture 

does not propagate to the ground surface. 

Figure 2-5 Blind Thrust Faulting (www.earthsci.org) 

Strong shaking associated with fault rupture may also generate ground deformations such as ridge-top 

shattering, landslides, graben structures (depressions behind large landslide masses), and liquefactioninduced lateral spreads. These types of secondary ground breakage are not considered surface 

manifestations of the fault. 

2.2.4 Fault Activity 

Identifying faults capable of producing damaging ground motions at a project site and assessing the 

potential size (magnitude) and frequency of occurrence (recurrence) of earthquakes on those faults is part 

of a process referred to as a seismic hazard assessment. Whether or not a fault has the potential to 

produce earthquakes is generally categorized by the recency of previous fault movements. Considering 

the slow rate at which geologic processes evolve, if a fault has undergone relative displacement in 

relatively recent geologic time (within the time frame of the current tectonic setting), it is reasonable to 

assume that this fault has the potential to move again. If a fault has propagated up to the ground surface 

in recent geologic time, evidence of faulting is usually found in geomorphic features associated with fault 

rupture (e.g., relative displacement of geologically young sediments). Age dating of the last sediment 
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layer to be displaced by the fault and the first layer not displaced by the fault can be used to bound when 

the fault last moved. For faults that do not propagate all the way to the ground surface, geomorphic 

evidence of previous earthquakes may be more subdued and more difficult to evaluate (e.g., near surface 

folding in sediments or evidence of liquefaction or slumping generated by the earthquakes). Faults that 

have moved in Holocene time (the current geologic epoch, generally the past 11,000 years) are considered 

active. However, faults that have not moved in Holocene time or for which there is no evidence of 

Holocene movement but are located in a tectonic stress regime capable of generating earthquakes may 

still be considered potentially active and incorporated into a seismic hazard assessment. If a fault has 

moved in the distant geologic past but there is no evidence of movement in the current tectonic stress 

regime (i.e. under the current configuration of the earth’s tectonic plates), it will generally not be included 

in a seismic hazard assessment unless there is concern that anthropogenic activities, e.g. reservoir 

impoundment, may trigger fault movement. 

Geomorphic evidence of fault movement cannot always be dated. In practice, if a fault displaces the base 

of unconsolidated alluvium, glacial deposits, or surficial soils, then the fault is generally considered to be 

active. Also, if there is microseismic activity (i.e. small magnitude earthquakes identified using sensitive 

instruments) associated with the fault, the fault is typically judged as active. Microseismic activity is

particularly useful in identifying seismic sources with little to no surface manifestation (e.g. blind thrust 

faults, intraplate faults and other faults at great depth, faults with long recurrence intervals). However, 

shallow microseismic events (i.e. earthquakes of magnitude 3 or less) may sometimes be associated with 

blasting for mining or other non-seismogenic mechanisms. If there is no geomorphic evidence of seismic 

activity and there is no microseismic activity in the area, then faults in the area are unlikely to be capable 

of generating damaging earthquakes. 

Faults are generally of finite length and are subject to certain frictional and geometric constraints that 

cause them to move only after certain threshold levels of accumulated stress (or built up strain) are 

achieved. Thus, a fault may tend to produce earthquakes within a range of magnitudes that are 

characteristic for that particular fault. The maximum potential size of an earthquake on an active or 

potentially active fault is generally related to the size of the fault (i.e., a small fault produces small 

earthquakes and a large fault produces large earthquakes). Fault length is the primary (though not the 

sole) measure of fault size; fault plane surface area is also sometimes used. The average annual 

displacement along a fault, termed the slip rate, is also a measure of the maximum potential size 

earthquake a fault is capable of generating. Field evidence shows that faults that have a larger slip rate 

are generally associated with larger magnitude earthquakes. A long fault, like the San Andreas Fault in 

California or the Wasatch Fault in Utah, will generally not rupture along its entire length in any one 
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earthquake. Such faults typically move in portions (or segments), one segment at a time, although 

sometimes multiple fault segments will rupture simultaneously or sequentially. Earthquake hazard 

scenarios typically consider the possibility of both individual segments rupturing separately and multiple 

segments rupturing simultaneously or sequentially (and generating a larger magnitude event). An 

immobile (or "locked") fault segment, i.e. a fault segment which has remained stationary while the 

adjacent segments of the fault have moved, is a strong candidate for the next episode of movement (i.e. 

the next damaging earthquake) along a given fault. The lengths of fault segments may be interpreted from 

geomorphic evidence of prior movements or from fault geometry and kinematic constraints (e.g., 

segments may be defined by abrupt changes in the orientation of the fault). 

Short, disconnected surface fault traces aligned in a generally parallel manner in sediments at the ground 

surface may well be continuous at depth, with their surface expression modified by the near surface 

geologic structure. Thus, the observed length of a group of such fault traces at the ground surface is often 

shorter than the true length of the causative fault. However, these fault traces may also move in distinct 

segments. The true length of the fault associated with a group of short surface fault traces may be 

identified by the continuity of the geomorphic evidence (e.g. by consistency in the age of the displaced 

features along the fault). 

A variety of correlations between the size of an earthquake (usually expressed in terms of earthquake 

magnitude, using various definitions of magnitude), the length or area of a fault plane, and the amount of 

displacement along the fault are available (e.g. Bonilla, et al., 1984; de Polo and Slemmons, 1990). 

However, evaluation of fault segmentation and magnitude potential is a complex task that is best left to 

qualified geologists and seismologists and should not be attempted by engineers who do not have 

expertise in this area. 

Finally, even in the best of circumstances, with a thorough understanding of local geology, 

geomorphology, and seismicity, one cannot assume that all active faults in a region have been identified. 

Engineering evaluations should be made in such a way that the potential for earthquakes from unknown 

faults is considered. For this purpose, floating or random earthquakes of a characteristic size (magnitude) 

and recurrence rate determined based upon regional geology and seismology are often included in an 

engineering assessment of seismic hazard. These random earthquakes are assumed to occur anywhere 

within a defined earthquake zone. Chapter 3 will have more discussions on this subject. 
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2.3 SEISMIC WAVES 

The elastic rebound of the rock along both sides of a fault that ruptures generates seismic waves that 

radiate away from the fault. These seismic waves are the source of the ground shaking that is 

characteristic of earthquakes. In general, these waves can be separated into two broad categories: body 

waves that travel (propagate) through the interior of the earth and surface waves that travel (propagate) 

along the earth’s surface. Body waves can be further divided into compressional (pressure) waves, or Pwaves, and shear waves, or S-waves. In a P-wave, particle motion is in the same direction as wave 

propagation while in S-waves particle motion is orthogonal (perpendicular) to the direction of wave 

propagation. Shear waves can be sub-divided into SV-waves, or shear waves in which the direction of 

particle motion is in a vertical plane, and SH-wave, or shear waves in which the direction of particle 

motion is in a horizontal plane. Figure 2-6 illustrates the direction of particle motion relative to the 

direction of wave propagation for horizontally propagating P-waves and SV-waves. 

 

Figure 2-6 Deformations Produced by Body Waves: (a) P-waves; (b) SV-Waves (Source: 

Earthquakes, by Bolt, W.H. Freeman and Company, 1993) 

Surface waves are generated when body waves interact with a free surface, e.g. the ground surface. 

Because surface waves attenuate (decay) at a slower rate than body waves, ground motions due to surface 

waves may predominate over body waves at longer distances from the earthquake source. Rayleigh 

waves are the predominant form of surface wave generated in earthquakes. Rayleigh waves are generated 
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by the interaction of P-waves and SV-waves with the ground surface. Particle movement during Rayleigh 

wave propagation tends to follow a retrograde orbital path similar to that in a water wave, as illustrated in 

Figure 2-7. Another type of surface wave is a Love wave. Love waves are generated when SH-waves are 

trapped in a soft surficial layer. Neither Love waves nor Rayleigh waves are generally considered 

explicitly in a seismic hazard analysis. 

Figure 2-7 Deformations Produced by Rayleigh Waves (Source: Earthquakes, by Bolt, W.H. 

Freeman and Company, 1993) 

The propagation velocity of seismic waves depends upon the stiffness of the medium through which they 

are propagating. Because the bulk (compressional) stiffness of geologic media is greater than the shear 

stiffness, P-waves travel faster than S-waves (and surface waves) and thus are generally the first 

earthquake waves to arrive at a site. The P-wave velocity of saturated sediments (particularly in loose or 

soft ground) tends to be governed by the compressibility of water. Thus, it is hard to distinguish among 

the characteristics of saturated sediments based upon P-wave velocity. However, because water has 

essentially no shear stiffness, S-wave velocity in sediments is governed by the shear stiffness of the soil 

skeleton. Thus, S-wave velocity can be used as an indicator of soil characteristics such as stiffness and 

density. 

2.4 STRONG MOTION RECORDS (TIME HISTORIES) 

Earthquake ground motions that are capable of damaging engineered structures are generally referred to 

as strong ground motions. A record of strong ground motion versus time (a strong ground motion time 

history) is called a strong motion record. Strong motion records are captured in an earthquake by a 

strong motion instrument (as opposed to a seismometer, which is used to capture weak motions from 

small or distant earthquakes). Strong motion records can also be generated analytically (numerically) by 

simulation. Strong motion instruments used to capture time histories of ground acceleration, the most 
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Seismic Design – Geotechnical Features 2-13 August 2011 

common type of strong motion record, are sometimes called strong motion accelerometers. 

Acceleration time histories can be integrated to yield time histories of ground velocity and displacement. 

Figure 2-8 shows the recorded time history of acceleration and calculated time histories of velocity and 

displacement for one horizontal component of ground motion at the ground surface during the 1989 Loma 

Prieta earthquake. The time history of ground motions in three orthogonal directions is required to 

completely describe the time history of ground motion at a point. 

Figure 2-8 Acceleration, Velocity, and Displacement Strong Ground Motion Time Histories 

 (FHWA, 1998) 

The acceleration time history, sometimes referred to as an accelerogram, is the form of strong ground 

motion record used most often in engineering practice. However, velocity and displacement time 

histories also have their uses in engineering practice. The processing of recorded time histories of 

acceleration to correct for instrument bias and other sources of error is a complicated process. However, 
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catalogs of numerous (thousands) of processed (corrected) time histories are available on line from a 

variety of different sources. Reputable sources for corrected strong motion records include the Pacific 

Earthquake Engineering Research Center (PEER), the National Geophysical Data Center (NGDC), and 

the Multi-Disciplinary Center for Earthquake Engineering Research (MCEER). 

2.5 PARAMETERS DESCRIBING EARTHQUAKE SIZE AND LOCATION 

2.5.1 Earthquake Magnitude 

In practice, the size of an earthquake is quantified by the earthquake magnitude, M, a measure of the 

energy released by an earthquake. A variety of different earthquake magnitude scales exist. The 

differences among these scales are attributable to the earthquake characteristics used to quantify the 

energy content. Characteristics used to quantify earthquake energy content include the local intensity of 

ground motions, the amplitude of the body waves generated by the earthquake, and the amplitude of the 

surface waves generated by the earthquake. The first earthquake magnitude scale, and the magnitude 

scale most commonly referred to (often incorrectly) in media reports and non-technical publications, is 

the Richter magnitude scale. Richter magnitude is sometimes also referred to as the local magnitude as it 

is based upon the local intensity of the ground motion. Richter magnitude is often designated by the 

symbol ML (for local magnitude). In the eastern United States, earthquake magnitude was often measured 

historically as a short period body wave magnitude, mb. However, the long period body wave magnitude, 

mB, was also sometimes used in the central and eastern United States. In California, earthquake 

magnitude was historically measured as either ML or as surface wave magnitude, Ms. The Japan 

Meteorological Agency Magnitude (MJMA) scale was commonly used in Japan. 

Due to the limited strength of near surface geologic materials, the historical magnitude scales cited above 

tend to reach an asymptotic upper limit (a phenomenon referred to as saturation). To compensate for this 

phenomenon and provide a consistent and logical basis for quantifying the size of earthquakes, the 

moment magnitude, Mw, was defined by Hanks and Kanamori (1979). The moment magnitude of an 

earthquake is a direct measure of the kinetic energy released by the earthquake. Mw is proportional to the 

seismic moment, defined as a product of the material rigidity (i.e. the elastic modulus of the fault), the 

fault rupture area, and the average dislocation (relative displacement, or slip) across the rupture surface. 

Moment magnitude has been adopted by most of the earthquake engineering community as a unifying, 

consistent magnitude measure of earthquake energy content. For this reason, moment magnitude is used 

in this document to describe earthquake magnitude unless it is otherwise noted. Figure 2-9 (Heaton, et 
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al., 1986) provides a comparison of the various other magnitude scales with the moment magnitude scale. 

Note that in the magnitude range of 3 to 6, moment magnitude Mw is approximately equal to the local 

(Richter) magnitude ML, while in the magnitude range of 6 to 7.5, moment magnitude Mw is 

approximately equal to the surface wave magnitude Ms.

Figure 2-9 Comparison of Earthquake Magnitude Scales (Heaton, et al., 1986) 

2.5.2 Earthquake Location 

The location (or origin) of an earthquake is generally described by either the hypocenter or epicenter. The 

hypocenter (focus) of an earthquake is the point from which the seismic waves first emanate. 

Conceptually, it may be considered as the point on a fault plane where the slip responsible for the 

earthquake was initiated. The epicenter is the point on the ground surface directly above the hypocenter. 

The zone of energy release may also be used to describe the location of an earthquake. The zone of 

energy release, sometimes referred to as the zone of seismogenic rupture, is the area on the fault plane 

from which the seismic waves that generate strong ground motions emanate. The zone of energy release 

is typically assumed to be the portion of the fault rupture zone that is within crystalline rock. Therefore, 

even if the fault plane ruptures to the ground surface, the zone of energy release may not extend to the 
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ground surface. Figure 2-10 shows the relationship between the hypocenter, epicenter, fault plane, and 

rupture zone of an earthquake. Figure 2-10 also illustrates the definitions of the strike and dip of the fault 

plane. The strike is the map orientation (in plan) of a horizontal line on the fault plane, e.g. N30oW. The 

dip is the inclination from the horizontal of a line on the fault plane that is perpendicular to the strike. 

Figure 2-10 Basic Fault Geometry and Definition (after FHWA, 1998) 

The distance between the site of engineering interest and the location of the earthquake, generically 

referred to as the site-to-source distance, is used in engineering analyses to estimate the intensity of 

earthquake ground motions at the site if interest. The site-to-source distance depends upon the measure 

used to describe the earthquake location. Figure 2-11 illustrates graphically the definitions of various siteto-source distances commonly used to estimate the intensity of earthquake-induced ground motions in 

engineering analyses. In the eastern United States, epicentral distance, RE, is commonly used. In the 

western United States, the rupture distance, RR, the seismogenic distance, RS, the hypocentral distance, 

RH, and, the so-called Joyner and Boore distance, RJB, are commonly used. Different definitions can 

result in significant differences in site-to-source distance, particularly for sites close to the earthquake 

origin. For instance, if the site is located within the vertical projection of the fault plane, then RJB is equal 

to zero. However, the hypocentral distance to the site can be 10 kilometers or more if the earthquake 

originated at depth. Due to the variety of site-to-source distance definitions used in practice, care must be 

taken to ensure that the correct site-to-source distance is used in any engineering analysis. The site-tosource distance used in an analysis must be consistent with the site-to-source distance employed in 

developing the analytical method or equation. 
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Figure 2-11 Various Site-to-Source Distance Measures Used in Earthquake Engineering 

2.5.3 Earthquake Recurrence 

The rate at which a specific earthquake source (e.g. a fault) generates earthquakes is referred to as the 

recurrence rate. The recurrence rate is usually described in terms of the number of events per year equal 

to or exceeding a specified magnitude. For magnitudes of engineering significance, the average number 

of earthquakes generated each year from a specific source is generally less than one and thus the 

recurrence rate (expressed in the number of events per year) will be less than 1.0. The reciprocal of the 

recurrence rate is sometimes referred to as the recurrence interval, and describes the average number of 

years between events equal to or greater than the specified magnitude. Recurrence rate and recurrence 
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interval are also sometimes used to describe the rate of occurrence of ground motion parameters such as 

the peak ground acceleration. However, the annual probability of exceedance and the return period are 

the terms more properly used to describe the frequency of occurrence of ground motions at a site. 

Recurrence rate depends upon earthquake magnitude. The relationship between recurrence rate and 

earthquake magnitude is referred to the recurrence relationship. The most common type of recurrence 

relationship is an exponential model in which a plot of the logarithm of the recurrence rate versus 

earthquake magnitude forms a straight line. This is the basis for the well-known Gutenberg-Richter 

recurrence model. To account for the fact that the magnitude of earthquake that can be generated by a 

specific fault is limited by the size of the fault, Gutenberg-Richter (or exponential) recurrence models 

used in practice are often truncated at the maximum magnitude for the fault (established based upon 

geological considerations), as illustrated in Figure 2-12. 

Figure 2-12 Truncated Gutenberg Richter and Characteristic Magnitude-Recurrence Models 

(Young and Coopersmith, 1985) 
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Another common earthquake recurrence relationship is a characteristic earthquake recurrence model. The 

characteristic model is used when geologic evidence indicates that the magnitude of earthquake generated 

by a fault falls within a relatively narrow range (typically within a band of 0.5 on the magnitude scale), as 

illustrated in Figure 2-12. In a characteristic recurrence model, the earthquake magnitude is typically 

uniformly distributed across this range and is assigned a recurrence rate, or recurrence rate distribution, 

based upon geologic evidence. The characteristic recurrence model was developed because in some areas 

geologic evidence suggests that the exponential model under-predicts the frequency of large magnitude 

earthquakes, as illustrated in Figure 2-12. Seismic hazard analyses often use a combination of 

exponential and characteristic recurrence models, calculating results using each model separately and then 

combining the results as a weighted average based upon the relative confidence in each model. In some 

cases, a combined recurrence model that employs an exponential relationship for small magnitude 

earthquakes and a characteristic relationship at larger magnitudes has been employed. 

2.6 PARAMETERS DESCRIBING FAULTING 

Faults may be broadly classified according to their mode, or style, of relative movement. The principal 

modes of relative displacement along a fault are illustrated in Figure 2-13 and are described below. 

Strike Slip Faults: Faults along which relative movement is essentially horizontal (i.e., parallel to the 

strike of the fault) are called strike slip faults. Strike slip faults are often expressed as essentially linear 

(or planar) features in the landscape. Strike slip faults that are not fairly linear may produce complex 

surface features. The San Andreas Fault in California is a strike slip fault that is essentially a north-south 

linear feature over most of its length. However, the “Big Bend” in the San Andreas Fault just north of 

Los Angles produces thrusting (compression) that results in mountain building. Strike slip faults may 

sometimes be aligned as individual sub-parallel segments along a linear trend. This type of strike slip 

faulting is sometimes accompanied by step over zones, i.e. zones where the ends of the individual fault 

segments overlap along the linear trend but are separated laterally (perpendicularly to the linear trend) by 

tens to hundreds of feet. Ground rupture patterns within these zones may be particularly complex. 
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Figure 2-13 Types of Fault Movement (FHWA, 1998) 

Dip Slip Faults: Faults in which the deformation is perpendicular to the strike of the fault may occur due 

to either normal (extensional) or reverse (compressional) motion. These faults are sometimes referred to 

as dip slip faults. Reverse (compressional) faults are also referred to as thrust faults. Dip slip faults may 

produce multiple fractures within rather wide and irregular fault zones. Some dip slip faults, e.g. blind 

thrust faults, may produce broad deformational features such as pressure ridges and sags rather than 

clearly defined fault scarps or shear zones (Hart, 1980). 
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Other Special Cases: Faults that show both strike slip and dip slip displacement may be referred to as 

oblique slip faults. In some cases, due to changes in fault alignment, the type of a given fault may be 

mixed. A good example of this is in the vicinity of the so-called "big-bend" in the alignment of the San 

Andreas Fault in California, where the fault, generally north-south trending, bends into a generally eastwest alignment. In the vicinity of the big-bend, the generally strike slip lateral movement along the plate 

boundary is transferred into thrusting and compression, generating deformation perpendicular to the eastwest trending fault plane. 

2.7 PARAMETERS DESCRIBING GROUND SHAKING 

2.7.1 Intensity 

Intensity refers to the local strength and of earthquake ground motions. There are several earthquake 

intensity measures commonly used to describe qualitatively the strength of earthquake shaking at a site. 

These qualitative intensity measures are generally based upon verbal descriptions of the earthquake 

effects, including how humans and animals react to the shaking, observations of damage to structures and 

their contents, and other earthquake-related phenomenon such as ground cracking and sloshing of water 

in lakes and ponds. Qualitative intensity measures are particularly useful in studying historic earthquakes 

for which there are no instrumentally recorded ground motions, as they provide the sole basis for 

estimating the magnitude of such events. However, to be reliable, qualitative intensity information must 

be collected over a broad geographic area in order to average out local site effects, i.e. in order to discount 

local increases or decreases in intensity due to topography or local soil conditions. 

The most commonly used qualitative intensity scale in the United States is the Modified Mercali Intensity 

(MMI) scale. The MMI scale is a twelve point Roman numeral scale that varies from MMI I, 

representing an earthquake that is not felt except by a few people in favorable circumstances to MMI XII, 

representing an earthquake where damage is total, practically all engineered facilities are damaged or 

destroyed. Table 2-1 presents the MMI scale. 

 
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TABLE 2-1 MODIFIED MERCALI INTENSITY SCALE

(Source: http://earthquake.usgs.gov/learning/topics/mercalli.php)

I. Not felt except by a very few under especially favorable conditions. 

II. Felt only by a few persons at rest, especially on upper floors of buildings. 

III. Felt quite noticeably by persons indoors, especially on upper floors of buildings. Many people do not 

recognize it as an earthquake. Standing motor cars may rock slightly. Vibrations similar to the passing of 

a truck. Duration estimated. 

IV. Felt indoors by many, outdoors by few during the day. At night, some awakened. Dishes, windows, 

doors disturbed; walls make cracking sound. Sensation like heavy truck striking building. Standing motor 

cars rocked noticeably. 

V. Felt by nearly everyone; many awakened. Some dishes, windows broken. Unstable objects overturned. 

Pendulum clocks may stop. 

VI. Felt by all, many frightened. Some heavy furniture moved; a few instances of fallen plaster. Damage 

slight. 

VII. Damage negligible in buildings of good design and construction; slight to moderate in well-built 

ordinary structures; considerable damage in poorly built or badly designed structures; some chimneys 

broken. 

VIII. Damage slight in specially designed structures; considerable damage in ordinary substantial 

buildings with partial collapse. Damage great in poorly built structures. Fall of chimneys, factory stacks, 

columns, monuments, walls. Heavy furniture overturned.

IX. Damage considerable in specially designed structures; well-designed frame structures thrown out of 

plumb. Damage great in substantial buildings, with partial collapse. Buildings shifted off foundations.

X. Some well-built wooden structures destroyed; most masonry and frame structures destroyed with 

foundations. Rails bent. 

XI. Few, if any (masonry) structures remain standing. Bridges destroyed. Rails bent greatly. 

XII. Damage total. Lines of sight and level are distorted. Objects thrown into the air. 
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2.7.2 Peak Ground Motions 

The intensity of earthquake-induced ground motion, i.e. the strength of the ground motions at a given site, 

is often described quantitatively by the peak value of the acceleration time history, the peak ground 

acceleration (PGA). Peak ground velocity (PGV) and/or peak ground displacement (PGD) are also 

sometimes used as quantitative indices of earthquake damage potential. Peak ground motions are 

generally specified for the motions in the horizontal plane, as the horizontal ground motions generated by 

an earthquake tend to be the motions that cause the greatest damage. Figure 2-8 illustrates the 

acceleration, velocity, and displacement time histories from the horizontal component of an earthquake. 

The corresponding peak horizontal ground acceleration (PHGA), peak horizontal ground velocity

(PHGV), and peak horizontal ground displacement (PHGD) values are indicated on Figure 2-8 by solid 

dots. 

2.7.3 Energy Content 

The energy content of the acceleration time history provides another means of characterizing 

quantitatively the intensity of strong ground motions. The energy content of a strong ground motion 

record is proportional to the square of the acceleration. In engineering practice, the energy content of the 

motion is typically expressed in terms of either the root-mean-square and duration of the acceleration 

time history or the Arias intensity, IA. The Arias intensity, IA, is proportional to the square of the 

acceleration integrated over the entire acceleration time history: 

[a(t)] dt

g2

I = 

2

t

0

A

f





2-1

where a(t) is the time history of acceleration (the accelerogram), g is the acceleration of gravity and tf is 

the duration of strong shaking. Arias (1969) showed that this integral is a measure of the total energy of 

the accelerogram. 

The root-mean-square of the acceleration time history, or RMSA, is the square root of the square of the 

acceleration integrated over the duration of the motion and divided by the duration: 

[a(t)] dt

t

1

 =RMSA 

2

t

f 0

f



2-2
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where a(t) is the acceleration time history, and tf is the duration of strong ground shaking. The RMSA 

represents an average value of acceleration over the duration of strong shaking. The square of the RMSA 

multiplied by the duration of the motion is directly proportional to the energy content of the motion, i.e. 

Arias intensity is related to the RMSA as follows: 

(RMSA) t

g2

I = f

2

A 



2-3

The value of the Arias Intensity is independent of the duration of strong shaking, while RMSA depends 

upon the definition of the strong shaking duration. However, as the energy content of the motion is fixed, 

the product of the RMSA and the squared duration will remain constant, as suggested by Equation 2-3. 

The definition of the duration of strong shaking for an acceleration time history can be somewhat 

arbitrary (as discussed subsequently), as relatively low intensity motions may persist for a long time 

towards the end of a strong motion record. If the defined duration of strong motion is increased to include 

these low intensity motions, the Arias intensity will remain essentially constant but the RMSA will 

decrease. Therefore, some investigators prefer Arias intensity to RMSA as a measure of energy content, 

as the Arias intensity is essentially a fixed value while the RMSA depends upon the definition of the 

duration of strong ground motion. 

Arias intensity and/or RMSA and duration are useful parameters in selecting time histories for 

geotechnical analysis. This is particularly true if a seismic deformation analysis is to be performed, as the 

deformation potential of a strong motion record is related to the energy content, which can be expressed 

as a function of either Arias intensity or the product of the RMSA and duration of the record. 

2.7.4 Duration 

The duration of shaking is an important factor in determining the damage potential of strong ground 

motions. While duration is often neglected or treated indirectly in some common methods for evaluating 

the dynamic response of structures (e.g. response spectra analysis using modal superposition), duration is 

accounted for either explicitly (e.g. in analyses that use acceleration time histories as input) or implicitly 

based upon magnitude or peak ground velocity (e.g. in geotechnical problems such as liquefaction and 
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slope stability analyses). Duration is an important parameter in selecting representative time histories for 

use in advanced time and frequency domain structural and geotechnical analyses. Common definitions of 

strong ground motion duration include the bracketed duration and the significant duration. The bracketed 

duration of strong motion, Db, as defined by Bolt (1973), is the elapsed time between the first and last 

acceleration excursion of the acceleration time history greater than a specified threshold level. Figure 2-

14 illustrates calculation of bracketed duration for the Saratoga - Aloha Avenue accelerogram from the 

1989 Mw 6.9 Loma Prieta earthquake (the acceleration time history used in Figure 2-8) for a threshold 

acceleration of 0.05 g.

Figure 2-14 Bracketed Duration of Strong Shaking 

While the bracketed duration is intuitively satisfying, it is not a unique property of an accelerogram if 

scaling of the accelerogram is allowed (as often done in engineering practice). If an acceleration time 

history is scaled to a different peak ground acceleration, the bracketed duration will change. Furthermore, 

use of the bracketed duration produces a decrease in the duration of strong shaking with increasing 

distance from the earthquake source, a somewhat counter-intuitive result as earthquake waves are known 

to spread out as they move away from the source, increasing the duration of shaking. 
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Many engineers and seismologists find the significant duration, Ds, proposed by Trifunac and Brady 

(1975) to be the most appropriate duration definition. Trifunac and Brady (1975) defined the significant 

duration as the time interval between 5 and 95 percent of the total Arias intensity on a plot of Arias 

intensity versus time for an accelerogram. This type of plot is known as a Husid plot as it was first 

proposed by Husid (1969) to portray the evolution of energy release for a ground motion record. The 

Trifunac and Brady definition of the significant duration is illustrated on the Husid plot in Figure 2-15 for 

the Saratoga-Aloha Avenue record from the 1989 Mw 6.9 Loma Prieta earthquake (the strong motion 

record for this motion is shown in Figure 2-14). This significant duration is a unique property of the time 

history, independent of any scaling of acceleration. 

Figure 2-15 Significant Duration of Strong Shaking 

For problems related to soil liquefaction, duration is sometimes expressed in terms of the number of 

equivalent uniform cycles (e.g., see Seed, et al., 1975). The number of equivalent uniform cycles is 

typically expressed as a function of earthquake magnitude to reflect the general increase in duration with 

increasing magnitude. Recommendations for the number of equivalent uniform cycles as a function of 

earthquake magnitude for use in liquefaction and seismic settlement analyses are discussed in Chapter 6. 
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2.7.5 Response Spectrum 

The response spectrum of an earthquake record is a plot of the maximum response of a linear single 

degree-of-freedom (SDOF) system versus the natural period of the system for a specified damping ratio. 

Response spectra used in practice include the acceleration (Sa), relative velocity (Sv), and relative 

displacement (Sd) response spectra. The acceleration response spectrum is the sole loading parameter for 

the most common method for seismic analysis of structures (modal superposition). It is also commonly 

used in the selection of representative earthquake time histories for use in analysis. Development of an 

acceleration response spectrum for a single earthquake time history is illustrated on Figure 2-16. A series 

of linear elastic SDOF systems of stiffness k, mass m, and damping c,, each with a different undamped 

resonant (or fundamental) period, T, but the same fraction of critical damping (or damping ratio), , are 

subject to the same earthquake time history. The peak acceleration of each SDOF, amax, also referred to as 

the spectral acceleration, Sa, is plotted versus T to create the acceleration response spectrum for that 

motion. Velocity and displacement spectrum can be generated in the same manner (by potting the peak 

value for each SDOF versus the fundamental period of the SDOF). It should be noted that the spectral 

acceleration for a SDOF with a fundamental period of zero (an infinite stiffness) is equal to the peak 

ground acceleration of ground motion. Also, as illustrated in Figure 2-16, the response spectrum is a 

function of the damping ratio, , of the SDOF. 

The undamped resonant period of the linear SDOF is the square root of its mass, m, divided by its 

stiffness, k, as presented in Equation 2-4: 

k

m

T 

2-4

The damping of the linear SDOF system is represented by the viscous damping coefficient, c. The critical 

damping coefficient for the SDOF system, ccrit, is the damping that results in the quickest approach 

(shortest time) to the at-rest condition for the system during free vibration. With less damping, the system 

reaches the at-rest position faster but oscillates around that position, while with more damping the system 

approaches the at-rest position without oscillation but at a slower rate. The critical damping coefficient, 

ccrit, is the square root of the mass times the stiffness of the SDOF: 

k(2C m) crit 

2-5
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Figure 2-16 Schematic Representation of Acceleration Response Spectra (Reproduced from 

Matasovic, 1993) 

The ratio of the viscous damping coefficient to the critical damping coefficient, c/ccrit, is fraction of 

critical damping, or damping ratio (when expressed as a percent). 

100%

C

C

β

crit



2-6

In the context of a response spectrum,  is sometimes referred to as the spectral damping. In earthquake 

engineering, a spectral damping of 5% is commonly selected for development of response spectra. 
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A tripartite spectral plot is sometimes used to graphically portray response spectra. Figure 2-17 shows an 

example of such a tripartite plot for a smoothed response spectra developed by averaging or enveloping a 

large number of spectra representative of a specified condition. A tripartite plot simultaneously displays 

the spectral acceleration, Sa, as well as the spectral velocity, Sv, and the spectral displacement, Sd, values 

(determined in the same way as Sa as the peak values for the SDOFs in Figure 2-16) for the selected 

spectral damping. For a given fundamental period, T, (or fundamental frequency f = 1/T), Sa, Sv, and Sd

are read from the appropriate ordinates. For example, as indicated on Figure 2-17, for T = 0.7 s (f = 1.4 

Hz), Sa = 0.19 g, Sv = 10 in/s, and Sd = 1.2 in. 

Figure 2-17 Tripartite Representation of Acceleration, Velocity, and Displacement Response Spectra. 

2.7.6 Smoothed Uniform Hazard Spectra 

Seismic hazard analyses often must consider the contributions to seismic risk from a variety of different 

earthquake sources. Furthermore, even when there is only a singular source under consideration, that 

source may be capable of generating earthquakes of different magnitudes at different distances and 

recurrence rates. One method often used to consider the relative contributions of more than one source 
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and/or of multiple events of different magnitude, distance, and recurrence from the same source is a 

probabilistic seismic hazard analysis. In a probabilistic seismic hazard analysis, the probability of 

exceeding a specified level of ground motion for a specified time period is calculated. The specified 

ground motion parameter may be a peak ground motion parameter (e.g. PGA, PGV, or PGD) or a spectral 

parameter (e.g. Sa, Sv, or Sd) at a specified spectral period. One particularly useful output from a 

probabilistic hazard analysis is a plot of a desired spectral parameter (e.g. spectral acceleration, Sa) over 

the entire range of spectral periods of interest for a specified probability of exceedance over a specified 

time period (e.g. for a 7% probability of exceedance in a 75 year period, per the AASHTO seismic design 

specifications). Such a plot is referred to as a uniform hazard spectrum (as each point has the same 

annual probability of being exceeded), or UHS. A UHS typically represents the statistically averaged 

contributions from multiple events on multiple seismic sources, thus the resulting spectra are generally 

represented by a smooth curve. Figure 2-18 presents the uniform hazard acceleration response spectrum 

for a site in Memphis, Tennessee, from the USGS National Seismic Hazard Mapping Program for ground 

motions with a 5 percent probability of being exceeded in a 50-year period (probabilistically equivalent to 

a 7% probability of being exceeded in a 75-year period). More discussions in seismic hazard analysis and 

uniform hazard spectra are presented in Chapter 3. 

Figure 2-18 Uniform Hazard Acceleration Response Spectra for Memphis, Tennessee, with a 5% 

Probability of Exceedance 50-years (USGS National Seismic Hazard Mapping 

Program) 
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2.7.7 Ground Motion Attenuation Relationships 

An attenuation relationship describes the relationship between earthquake magnitude, site-to-source 

distance, and the value of a peak or spectral ground motion parameter (e.g., peak ground acceleration, 

peak ground velocity, peak ground displacement, or spectral parameters Sa, Sv, or Sd at a specified 

spectral period). Attenuation relationships are essential input parameters for seismic hazard analyses. 

Acceleration attenuation relationships (for both peak and spectral values) are the most common form of 

attenuation relationship. Attenuation relationships are usually developed by statistical analysis of ground 

motions recorded in previous earthquakes. The variability in the ground motion parameter of interest for 

a given magnitude and distance is generally characterized by the standard deviation of the statistical data. 

This variability is usually assumed to be log-normally distributed (i.e., the logarithm of the parameter 

value is normally distributed). 

Numerous attenuation relationships can be found in the technical literature. Typical factors included in an 

attenuation relationship are tectonic regime (e.g. shallow crustal earthquakes, subduction zone 

earthquakes, intraplate earthquakes), earthquake magnitude, site-to-source distance, and some measure of 

local ground conditions (e.g. stiff soil, soft soil, or rock or, more recently, shear wave velocity in the 

upper 30 meters of the site). Figure 2-11 identifies the distance measures associated with the most 

common attenuation relationships used in engineering practice. The style of faulting (e.g., slip-strike 

versus normal faulting) and, for normal faulting, the location of the site with respect to the orientation of 

the fault, are also used in some attenuation relationships. 

Attenuation relationships can be particularly sensitive to tectonic setting. Field data indicate that 

attenuation in subduction zone events differs from attenuation in shallow crustal events, which in turn 

differs from attenuation in intraplate events. In particular, intraplate events appear to attenuate at a 

significantly slower rate (decay slower with distance) than shallow crustal events. Hence, strong ground 

motions from an intraplate event is likely to be experienced over a much broader area than strong motions 

from a shallow crustal event of the same magnitude. Attenuation relationships are addressed in more 

detail in Chapter 3 of this document. 

2.7.8 Predominant Period of the Strong Ground Motions 

Earthquake ground motions tend to have a predominant period (or frequency), i.e. a period, or range of 

periods, of vibration where the greatest amount of strong motion energy is concentrated. This 
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predominant period can be identified in an approximate manner as the period, or range of periods, 

corresponding to the peaks of the acceleration response spectrum. Sites with a soil layer (or layers) 

overlying either bedrock or another soil layer that differs significantly in stiffness and density will have a 

resonant period governed by the thickness, density, and stiffness (or shear wave velocity) of the overlying 

soil layer(s). Similarly, an engineered facility is likely to have one or more fundamental (or resonant) 

periods, i.e. a period at which the structural response is the greatest. The damage potential of strong 

ground motions with respect to a specific engineered facility is affected by the fundamental period of the 

base earthquake motion, the resonant period of any soil layer at the site, and the resonant period of the 

engineered facility. When the predominant period of the earthquake motion is close to the resonant 

period of the soil layer, there is a significant potential for amplification of the earthquake motion. In fact, 

the spectral acceleration of the earthquake motion will always be amplified around the resonant period of 

the soil layer. So, the damage potential of an earthquake ground motion increases when the predominant 

period of the earthquake motion is close to the resonant period of the site and when the resonant period of 

the site is close to the fundamental period of the structure. The damage potential of an earthquake ground 

motion will be greatest when all three of these predominant or fundamental periods coincide. 

2.7.9 Magnitude-Distance Deaggregation 

Each point on a uniform hazard spectrum is typically composed of contributions from a family of 

earthquakes of different magnitude and distance. The distribution of magnitude and distance may be 

different for each point on the uniform hazard spectrum. This distribution is referred to as the magnitudedistance deaggregation. The magnitude-distance deaggregation is important as it provides the basis for 

assigning a representative magnitude and distance to a design earthquake ground motion. Figure 2-19

shows the magnitude-distance deaggregation for one point on a uniform hazard spectrum for Oceano, 

California. 

Figure 2-19 indicates that the primary contribution to the seismic hazard at the site is from a M 7.5 event 

at a distance of approximately 3 miles from the site but that there is also a M 8 source about 12.5 miles 

from the site that contributes to the hazard. Magnitude-distance deaggregation is described in more detail 

in Chapter 3. 
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Figure 2-19 Magnitude-Distance Deaggregation for Oceano, California (Source: USGS National 

 Seismic Hazard Mapping Program) 

2.8 SUMMARY 

This chapter presents an overview of the mechanisms of earthquakes and earthquake source zones. It also 

defines the basic parameters describing faults and the recurrence of earthquakes and strong round motions 

generated by earthquakes. The mechanisms of earthquakes are described to provide the reader with a 

physical understanding of earthquake phenomenon. Earthquake sources are discussed within the 

framework of plate tectonics to give the reader an appreciation of the sources of damaging earthquakes 

within the United States. Earthquake source mechanisms are also important because the rate at which 

earthquake motions attenuate is related to source mechanism, with intraplate earthquakes in the central 

and eastern United States attenuating less rapidly with distance compared to earthquakes at transform 

boundaries and other shallow crustal events. 
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Earthquakes are generated by fault rupture. The energy released by an earthquake is quantified by the 

earthquake magnitude. Moment magnitude is presented as a uniform measure of earthquake magnitude. 

The geometric parameters describing the ruptured fault include parameters describing the location of the 

fault such as hypocenter and epicenter, parameters describing its orientation such as strike and dip, and 

the zone of energy release. The measures used to describe the distance of a project site from the 

earthquake source vary depending on the location parameter used in their definition. The rate at which 

earthquakes occur on a given fault is referred to as the recurrence rate. The two models commonly used 

to define the recurrence of earthquakes in a seismic hazard assessment, the truncated exponential 

Gutenberg-Richter model based upon primarily instrumentally recorded earthquakes, and the 

characteristic model developed based upon geologic data, are briefly described. 

The engineering parameters describing strong shaking in earthquakes that are defined in this chapter 

include strong motion time histories, peak ground motion parameters, elastic response spectra, ground 

motion attenuation relationships, uniform hazard spectra and the associated magnitude deaggregation, and 

various energy and duration measures. These parameters are generally related to the return period, or 

annual probability of occurrence, of the ground motion. The evaluation of these strong ground motion 

parameters in accordance with both probabilistic and deterministic earthquake design criteria is discussed 

in Chapters 3 and 5. Chapter 3 further discusses the development of acceleration response spectra that 

satisfies the AASHTO seismic design criteria and modification of the AASHTO response spectra to 

account for local site conditions, while Chapter 5 further discusses modifications to ground motion design 

parameters based upon site-specific site response analysis. Subsequent chapters of this document then 

discuss the use of these design ground motion parameters in geotechnical analysis of the performance of 

transportation facilities in earthquakes including: 

 The use of earthquake magnitude and peak ground acceleration, spectral acceleration, peak ground 

velocity, and/or a suite of representative time histories to evaluate liquefaction potential, 

liquefaction-induced ground displacement, seismic slope stability and deformation, and seismic 

settlement in Chapter 6; 

 The use of representative time histories in soil-structure interaction analyses in Chapter 8; 

 The use of peak ground acceleration, spectral velocity, or representative ground motions to evaluate 

lateral earth pressures and design earth retaining structures in Chapter 12; and 

 The use of representative ground motions to design buried structures for seismic loads in Chapter 

13. 
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CHAPTER 3

SEISMIC HAZARD ANALYSIS AND GROUND MOTION CHARACTERIZATION

3.1 GENERAL 

Seismic hazard analysis is the process by which the appropriate ground motions (or ground motion 

parameters) are established for seismic design. This chapter describes the two basic types of seismic 

hazard analyses (i.e. probabilistic and deterministic analyses) commonly employed in design practice as 

well as characterization of the design ground motions based upon the results of these analyses. AASHTO 

uses a probabilistic approach and has recently adopted a 1,000-year return period as the basis for bridge 

design. The 1000-year return period may also be logically assumed to be appropriate for non-bridge 

highway transportation facilities (e.g., embankments, tunnels, culverts, retaining walls, etc.) for 

consistency. However, occasionally a different return period, or a deterministic analysis, may be 

employed to provide a basis upon which to establish earthquake ground motions for use in design. 

Furthermore, the designer may wish to evaluate performance of a structure or facility for more than one 

return period or to assess the sensitivity of seismic performance to the return period. 

This chapter describes the fundamental principles of seismic hazard analysis and discusses the relative 

merits of, and fundamental differences between, the probabilistic and deterministic approaches to seismic 

hazard analysis. The procedure for obtaining design ground motion parameters in accordance with the

AASHTO criteria for LRFD seismic design, procedures for establishing a suite of representative 

acceleration time histories for use in design, and special considerations is determining design ground 

motions not address by the AASHTO specification, including near-field ground motions, shallow bedrock 

and deep soil basin sites, and spatial variability in ground motions, are also addressed in this chapter. 

Figure 3-1 portrays the four fundamental steps in a probabilistic seismic hazard analysis. In Step 1 

(Seismic Source Identification), the seismic sources capable of generating strong ground motions at the 

project site(s) are identified and the characteristics and geometries of these sources (i.e. their tectonic 

mechanism, style of faulting, location and spatial extent) are defined. In Step 2 (Magnitude-Recurrence), 

a recurrence relationship describing the rate at which various magnitude earthquakes are expected to 

occur, is assigned to each of the identified seismic sources. Together Steps 1 and 2 may be referred to as 

“seismic source characterization”. In Step 3 (Ground Motion Attenuation), an attenuation relationship 
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that describes the link between earthquake magnitude, site-to-source distance, and the ground motion 

parameter of interest is assigned to each seismic source. In Step 4 (Probability of Exceedance), the results 

from the first three steps are combined to produce a curve relating the value of the ground motion

parameter of interest at the site(s) of interest to the probability that it will be exceeded in a specified time 

interval. 

Figure 3-1 Steps in Probabilistic Seismic Hazard Analysis

A deterministic seismic hazard analysis may also be described by the four step process illustrated in

Figure 3-1. However, in a deterministic analysis, Step 2 (Magnitude-Recurrence) is abbreviated by 

assigning a discrete, deterministic magnitude to each seismic source. The magnitude assigned to each 

source is generally some sort of maximum magnitude. Then, Step 4 consists solely of determining which 

source generates the maximum (or most damaging) value of the ground motion parameter of interest

(though it may sometimes be necessary to consider more than one source due to the interrelationship 

between damage potential, intensity, and duration). 
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Each of the steps described above for the probabilistic and deterministic methods of analysis is discussed 

in the following sections. How the deterministic approach differs from the probabilistic approach is also 

addressed herein. Other important subjects that are discussed in the following sections include selection 

of the target ground motion level for use in design, characterization of the design ground motions from 

the results of a probabilistic or deterministic seismic hazard analysis, details of the procedure for 

obtaining design ground motions in accordance with the AASHTO probabilistic seismic hazard design 

criteria, and special topics such as near field (near fault) effects such as directivity and the near field pulse

of ground motion, spatial variation of ground motions, and vertical ground motions. 

3.2 SEISMIC HAZARD ANALYSIS

3.2.1 Seismic Source Identification

The first step in a seismic hazard analysis usually is to identify and characterize the seismic sources 

capable of generating strong ground motions at the project site. The characteristics of seismic sources 

capable of generating strong ground motions at the project site were discussed in Chapter 2. In addition 

to simply identifying the seismic sources impacting a site, the type of seismic source zone (e.g. shallow 

crustal fault zone, subduction zone, or intraplate zone), the style of faulting (e.g. strike-slip, dip-slip, 

oblique)must be identified and a model of the geometry of each seismic source must be developed. There 

are two basic geometries used to model seismic sources in a seismic hazard analysis: area source zones 

(sometimes discretized into a series of point sources), and discrete fault sources (typically modeled as line 

sources). Both types of sources are conceptually illustrated in Figure 3-2. 

Well-defined faults may be modeled as line sources, while area source zones are used to model spatially

distributed seismicity. In the 1970s and early 1980s, seismic source characterization was typically based 

on area sources that were defined using historical seismicity data. In many parts of the world, particularly 

those without well-define active faults, modeling seismic sources using area sources is still the standard of 

practice. However, even in regions with well known faults, area sources are commonly included in the 

source characterization to account for background seismicity and for earthquakes that do not occur on

known faults or fault zones. 
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Figure 3-2 Geometry of Seismic Sources in Seismic Hazard Analysis

In the United States (especially in the western U.S.), faults that have the potential to produce strong 

ground shaking have generally now been well defined by geological and seismological studies and 

therefore discrete fault source modeling can be employed. In state-of-the practice seismic hazard 

analyses, fault sources are usually treated as planes to account for the variable depth of the seismic

activity. Area sources may be treated as volumes to account for uncertainty in the depth of seismic 

activity. Accounting for the depth of seismic source is necessary to properly account for the depthdependence of the site to source in many attenuation relationships. This subject is further discussed in 

Section 3.2.3 in the discussion on ground motion attenuation relationships. 

3.2.2 Magnitude-Recurrence Relationships 

After defining the characteristics and geometry of each seismic source that can contribute to the strong 

ground shaking at the project site, the next is to define the size (i.e. magnitude) and frequency of 

occurrence (recurrence) of the earthquake(s) associated with each seismic source. As noted in Chapter 2, 

Moment Magnitude, Mw, has been generally adopted by seismologists and engineers as the measure of the 

size of an earthquake. Mw was defined by Hanks and Kanamori (1979) using the following equation: 

7.10)M(log 3

2 Mw = o10 − 3-1 
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where Mo is defined as the ‘seismic moment’ (in dyne-cm), given by the following equation: 

o ××μ= DAM 3-2

where μ is the rupture strength (shear modulus) of the crust (dyne/cm2

), 

 A is the area of the fault rupture (cm2

), and 

 D is the average displacement (slip) over the rupture surface (cm).

Mw and Mo both have units of force times length (dyne-cm), or work done, and hence, both are direct 

measures of the energy released by fault rupture during an earthquake.

From Equation 3-1, it can be shown that seismic moment is related to moment magnitude as follows:

7.10M(2/3( ))

o w 10M + = 3-3

From Equations 3-1 and 3-3, it can be seen that the relationship between the energy released by an 

earthquake (Mo) and earthquake magnitude (Mw) is logarithmic, i.e. for each unit increase in moment 

magnitude, Mw, the seismic moment, Mo (energy released by fault rupture), increases by a factor of 31.6. 

Hence, compared to the energy released by a magnitude 5 earthquake, the energy released by magnitude 

6, 7 and 8 earthquakes will be 31.6, 1,000 and 31,623 times greater, respectively. A larger magnitude 

(greater energy release) generally results in stronger and longer shaking from the earthquake. However, 

the additional energy associated with a very large magnitude earthquake may not necessarily induce 

stronger shaking at the site in the near field (i.e. close to the zone of energy release for the earthquake) 

due to the limited strength of near surface soils (which limits the amplitude of the waves they can 

transmit). Even if the amplitude of shaking is limited, a very large magnitude event will still subject a 

much larger area to strong shaking and cause a longer shaking duration. 

In both deterministic and probabilistic seismic hazard analyses, the maximum magnitude earthquake that 

can be generated for each seismic source must be defined. In a deterministic seismic hazard analysis, 

knowledge of the maximum magnitude, or a characteristic magnitude, for each source is generally 

sufficient for seismic source characterization purposes (in addition to the tectonic mechanism, style of 

faulting, source location, and geometry). In a probabilistic seismic hazard analysis, a magnitude-
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recurrence relationship (i.e. the rate of occurrence of various magnitude earthquakes) needs to be defined 

in addition to the maximum earthquake magnitude. As discussed in Chapter 2, the magnitude-recurrence 

relationship relates earthquake magnitude to the number of earthquakes per year equal to or greater than 

that magnitude for a seismic source. The reciprocal of the recurrence rate is the average time period (in 

years) between events equal to or greater than the associated magnitude. (Note that the reciprocal of the

recurrence rate, or recurrence interval, which is the average time period (in years) between occurrences of 

an earthquake of a given magnitude, is generally distinguished from the return period, which is the 

average time period (in years) between occurrences of a specified ground motion level.) 

The need to define the frequency of occurrence of earthquakes in a magnitude-recurrence relationship is 

one of the main distinctions between deterministic and probabilistic seismic hazard analyses. The 

Gutenberg-Richter recurrence model (sometimes referred to as the exponential model) was widely used as 

the sole means of characterizing magnitude-recurrence relationships in the 1970s and early 1980s, and is

given by the following equation (Gutenberg and Richter, 1944): 

10 ×+= Mba)n(Log w 3-4

where n is the annual number of earthquakes with magnitude Mw, and the a and b parameters define the 

recurrence rate based on curve fitting to historical seismicity data. 

One shortcoming of the Gutenberg-Richter model is that it is not limited in magnitude (i.e. there is a 

small but finite frequency of earthquakes of magnitude 9, 10, and greater). To compensate for this 

shortcoming, Gutenberg and Richter proposed truncating the exponential model at a limiting (or 

maximum) magnitude (Gutenberg and Richter, 1954). The truncated Gutenberg-Richter model (i.e. a

truncated exponential model) works well for large regions (e.g. for the worldwide seismicity data base)

but does always fit the observed behavior of finite fault sources (Schwartz and Coppersmith, 1984) or for 

seismicity data measured over smaller regions during the relatively short time frame of instrumental 

seismicity (i.e., since 1933, the start of instrumental seismicity measurements using scientific 

instruments). 

While the use of recorded seismicity data may intuitively seem like the preferred method for development 

of a recurrence relationship, the short history of the instrumental record is insufficient to reflect geologic 

processes in most areas. Therefore, other means, e.g. the use of geologic data, are usually necessary to 
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develop recurrence relationships. Even when representative instrumental data is available for small 

magnitude events, geologic evidence usually is used to anchor the recurrence model at the large 

earthquake end of the magnitude-recurrence relationship, i.e. for the maximum magnitude earthquake, 

Mmax. 

The current preferred approach to account for the recurrence of large magnitude earthquakes on well 

known faults is to complement the instrumental seismicity data for smaller magnitude earthquakes with a 

characteristic magnitude-recurrence model for maximum magnitude events. In the characteristic model, 

the rate at which earthquakes of the characteristic (or maximum) magnitude occur is based on both 

geodetic data (i.e. the tectonic slip rate for the fault) and geologic data (i.e. paleoseismic studies) that can 

cover a much longer history of the earth’s geologic processes than instrumental seismicity. The 

characteristic model assumes that individual faults tend to generate earthquakes of a preferred magnitude 

due to the geometry of the fault and the rate of accumulation of stress due to tectonic forces (i.e. the 

average annual rate of movement, or tectonic slip rate). As a result of this phenomenon, there is a 

‘characteristic’ size (magnitude) of earthquake that a given fault segment tends to generate based on the 

dimension of the fault segment and associated slip rate. 

As discussed in Chapter 2, Figure 2-12 (also shown hereafter as Figure 3-3) shows a composite of the 

Gutenberg-Richter and Characteristic models is often used to describe magnitude-recurrence in seismic 

hazard analysis. The Gutenberg-Richter model is used to describe the recurrence of small magnitude 

events based on instrumental seismicity and the Characteristic model is used to describe magnitude

recurrence in the large magnitude range based upon geologic data such as the fault’s length and/or historic 

slip rate. One such composite model is the Youngs and Coppersmith (1985) model, which is contrasted 

in Figure 3-3 to the truncated exponential model. The Youngs and Coppersmith model employs a 

uniform distribution for the large magnitude characteristic earthquakes. The uniform distribution

illustrated in Figure 3-3 is centered on the mean characteristic magnitude and has a width of 0.5 

magnitude units. 
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Figure 3-3 Truncated Gutenberg Richter and Characteristic Magnitude-Recurrence Models

 (Youngs and Coopersmith, 1985) 

Since a composite model employs two different magnitude distributions, an additional constraint is 

needed to define the relative amplitudes of the two distributions. One commonly adopted constraint is to

set the height of the uniform distribution equal to the value of the exponential distribution at 1.0 

magnitude unit below the lower end of the uniform characteristic distribution (1 magnitude unit less than 

the smallest magnitude of the uniform characteristic magnitude distribution). This additional constraint 

sounds rather arbitrary, but it has a basis in empirical data on earthquake recurrence. A key feature of the 

Young and Coppersmith model is that this constraint results in about 94% of the total energy associated 

with a seismic source being released in characteristic earthquakes and about 6% of the total energy being 

released in the smaller earthquakes that fall within the range of the exponential model. 

An additional consideration in assigning magnitude-recurrence to a seismic source is the distribution of 

the earthquake occurrences over the source, i.e. the locations of the ruptures. In practice, a uniform 

distribution of earthquake occurrence over the seismic source is commonly used. 
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3.2.3 Strong Motion Attenuation Relationships 

The third step in a seismic hazard assessment (after characterizing seismic source geometry and 

magnitude-recurrence) involves defining the appropriate attenuation relationship(s) for the strong ground 

motions. An attenuation relationship relates the design ground motion shaking parameter(s) of interest

(e.g. peak ground acceleration or spectral acceleration as a function of spectral period) to the combination 

of magnitude (M) and distance (D), as shown in Figure 3-4. The preferred method for developing an 

attenuation relationship is to conduct statistical analysis of recorded strong motion data. However, in 

some tectonic regimes there is not sufficient historical strong motion data from which to develop such a 

relationship. Furthermore, there is often a lack of data on attenuation in very large magnitude events for a 

given tectonic regime, particularly in the near field. In these cases, empirical and analytical seismological 

models are employed to supplement the available historical data. 

Historical strong motion data from earthquakes show a wide range of scatter, even after reconciling 

discrepancies due to earthquake magnitude, source mechanism, tectonic regime, and site conditions. This 

variation among recorded data within a single earthquake event is referred to as intra-event variability, 

while the variability among records from different earthquakes is referred to as inter-event variability. It 

is generally recognized that attenuation relationships need to reflect both sources of variability (i.e. the 

total uncertainty) in the strong motion data. Hence, an attenuation relationship is typically presented in 

terms of a median attenuation relationship with the scatter about the median modeled by a statistical 

distribution function. If the functional form of the distribution is known (or assumed), the scatter of the

ground motion about the median can be characterized simply in terms of the standard deviation or 

variance of the distribution. Most current attenuation models assume a log-normal distribution for this 

scatter (i.e., the logarithm of the response parameter has a normal (Gaussian) distribution). Hence, 

modern attenuation relationships are typically defined by an equation for the median value of the ground 

motion parameter as a function of magnitude and distance (and any other parameters included in the 

attenuation model) plus the standard deviation (sigma, or σ, value) for the stated distribution shape. The 

standard deviation may also be a function of magnitude and/or distance. Most current attenuation models 

provide for prediction of both the peak ground acceleration and the spectral acceleration at various 

spectral periods. Attenuation models may also provide values for other ground response parameters of 

interest, e.g. peak ground velocity. 
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Figure 3-4 presents an example of a common attenuation relationship for the peak horizontal ground 

acceleration (PHGA) along with the historical strong motion data used to develop it. The dots in Figure 

3-4 represent the historical data points while the solid lines represent the median values. The dashed lines 

in Figure 3-4 represent the 95% confidence interval from the statistical analysis (i.e. the 2σ bounds 

assuming a log normal distribution). The bell-shaped curves in Figure 3-4 show the assumed statistical 

log normal distribution of the ground motion parameter (the peak ground acceleration) at a distance of 0.6 

miles. 

 

Figure 3-4 Example of Peak Horizontal Ground Acceleration Attenuation Relationship for StrikeSlip Earthquakes and Soil Sites (Boore, Joyner, and Fumal (1997) 

Individual attenuation modelers often have different viewpoints about earthquake mechanisms and hence 

often employ different variables in their attenuation relationship. In particular, the measure of the site-tosource distance, D, which is employed in the attenuation equations varies among common attenuation 

relationships. There are several variations of site-to-source distance used by different attenuation 

modelers, as discussed in Chapter 2 and depicted in Figure 3-5. 
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(a) (b)

(c)

Figure 3-5 Variation in Definitions on Distance (site to seismic source) in Commonly Used 

Attenuation Relationships; (a) Strike Slip Faulting; (b) Reverse or Normal Faulting, 

Hanging-wall Site; (c) Reverse or Normal Faulting, Foot-wall Site

The role the attenuation relationship(s) play in the outcome of both probabilistic and deterministic seismic 

hazard analysis cannot be over-emphasized. Furthermore, the state-of-the-art on this subject is constantly 

evolving: almost every major earthquake has led to a change in attenuation relationships. As the state-ofthe-art progresses, these relationships become more complex and greater expertise may become necessary 

in selecting and implementing the appropriate relationships. For example, attenuation relationships are 

particularly sensitive to tectonic regime. In the United States, the tectonic regimes that may be 

encountered include: 
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1) Shallow crustal earthquakes along active tectonic boundaries, e.g. for the western U.S.

2) Subduction zone earthquakes in Alaska and the northwestern U.S. 

3) Stable continental regions in the central and eastern U.S.

4) Extensional tectonic regions such as those in Nevada and Arizona 

As noted above and in Chapter 2, the current viewpoint among seismologists is that there are fundamental

differences in strong motion attenuation between different tectonic regimes such as between the western 

U.S. (WUS) and the central and eastern U.S. (CEUS), leading to the adoption of different attenuation 

models in different regimes. The boundary between WUS and CEUS tectonic regimes is shown in

Figure 3-6, lying approximately along the Rocky Mountains. West of this boundary is referred to as the 

more seismically active WUS region and east of the boundary is the less active CEUS region. In general, 

probabilistic ground shaking levels are higher in the WUS compared to the CEUS due to higher activity 

rates, especially at longer spectral periods (for example, 0.5 seconds or more). However, ground motions 

appear to attenuate with distance less rapidly in the CEUS compared to the WUS.

USGS Seismic Hazard Regions

Note: Different attenuation relationships used for different regions 

Figure 3-6 Boundary Defining WUS and CEUS Seismic Hazard Regions Based on Change in 

Attenuation Relationship (USGS, 2002) 
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Figure 3-7 compares spectral shapes from WUS and CEUS attenuation models for a typical Magnitude 

6.5 event at a site-to-source distance of 12 miles (20 km). The CEUS curves in Figure 3-7 includes two 

attenuation models to compensate for the lack of sufficient strong motion data plus and a third curve that 

is a weighted average of the first two models. Figure 3-7a presents a comparison of the acceleration

response spectra shapes (i.e. the acceleration response spectra normalized by their respective PGA) and 

Figure 3-7b presents a comparison of displacement response spectra shapes.

(a)

(b) 

Figure 3-7 Comparison between Spectral Curve Shapes for the WUS and CEUS Hazard Regions 

(after NUREG, 2001); (a) Acceleration Spectra for M=6.5, and R=20 km; (b) 

Displacement Spectra for M=6.5, and R=20 km
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The CEUS acceleration response spectra shape in Figure 3-7a has a higher amplitude than the WUS 

spectral curve shape at shorter spectral periods (T < 0.1 sec). The WUS spectral curve shape is higher 

than the CEUS curve shape for spectral periods greater than 0.1 second, the range of periods of 

importance in most structural designs. At a period of one second, the normalized WUS spectral 

acceleration is about twice the normalized CEUS acceleration. The normalized WUS acceleration 

spectral amplitude is over 3 times the normalized amplitude of CEUS spectrum at a period of 3 seconds. 

Furthermore, there may be even more intense, long-period motions associated with forward directivity of 

near-fault ground motions that can be encountered in the WUS (as discussed subsequently). 

Table 3-1 summarizes several of the attenuation relationships used to develop the 2002 USGS National 

Seismic Hazard Maps. The 2002 USGS National Seismic Hazard Maps provide the basis for current 

AASHTO seismic design criteria. There is a more recent 2008 update to these 2002 maps and some 

building codes (but not AASHTO) require the use of ‘the most current version of the USGS National 

Seismic Hazard Maps’. During deliberations on the current seismic design criteria, AASHTO decided 

that, whereas there are good rationales to continuously implement the updated USGS National Seismic 

Hazard Maps, changes to the AASHTO design criteria need to be managed by the AASHTO balloting 

process for technical stability and to control cost impacts. Therefore, it was decided that AASHTO would 

not automatically adopt new USGS maps upon their dissemination and that the 2002 USGS maps would 

remain the basis for seismic design of transportation facilities at the current time. 

There are three general categories of attenuation relationships presented in Table 3-1: one for each of the 

three predominant tectonic regimes associated with the United States. These tectonic regimes are 

categorized as follows: (1) shallow crustal earthquakes in the western U.S. (including extensional and 

volcanic faulting regimes), (2) intra-plate earthquakes in the central and eastern U.S. and (3) subduction 

zone earthquakes in the Pacific Northwest, Alaska, and the Caribbean. Category 1 includes both the 

active tectonic regime along the west coast of the US, the extensional tectonic regime in Arizona and 

Nevada, and earthquakes associated with volcanism in Hawaii and the Pacific northwest. The attenuation 

equations for shallow crustal earthquakes and, to a lesser extent, subduction zone earthquakes are based 

on empirical strong motion recordings. However, there are little strong motion data from significant 

intraplate earthquakes in the central and eastern U.S. (CEUS), or from other analogous tectonic regimes 

around the world, that is suitable for developing intraplate earthquake attenuation equations. 
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TABLE 3-1 SELECTED ATTENUATION RELATIONSHIPS USED TO DEVELOP USGS SEISMIC HAZARD MAPS
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Seismic Design – Geotechnical Features 3-16 August 2011 

Therefore, the CEUS attenuation equations are based largely on analytical and numerical modeling of 

strong motion attenuation in these regions. Toro et al. (1997) discuss the uncertainties associated with 

CEUS attenuation relationships and present another CEUS attenuation relationship commonly used in 

practice. 

The attenuation relationships listed in Table 3-1 provide for prediction not only of the PGA but also of the 

spectral acceleration at various periods. While all of these equations depend upon site-to-source distance, 

each attenuation model uses a different definition for distance. Figure 3-5 illustrates the differences 

among the various distance definitions used in these models. The equations for shallow crustal 

earthquakes presented in Table 3-1 are simplified versions of the complete attenuation equations for these 

models in that they apply solely to strike-slip earthquakes at rock sites. The complete equations include 

additional terms and coefficients to account for style of faulting, site soil conditions, and which side of the 

fault the site is on (for thrust faulting) . The treatment of uncertainty (i.e. values of equations for the 

standard deviation) also varies widely among different attenuation equations. However, all of the 

attenuation relationships in Table 3-1 assume a log normal distribution for the ground motion. Therefore, 

only the standard deviation is required to characterize the uncertainty in the predicted median response 

spectral acceleration values. However, the standard deviation typically depends upon magnitude and 

distance. 

The widely used Abrahamson and Silva (1997) attenuation relationship (one of the relationships used to 

represent attenuation in shallow crustal earthquakes when developing the 2002 USGS maps) can be used 

to illustrate some of the important features of an attenuation relationship. Table 3-2 presents the 

regression coefficients used to predict the median spectral acceleration for the 1997 Abrahamson and 

Silva attenuation equation. These coefficients can be used in the basic equation shown in Table 3-1 to 

compute the spectral acceleration for any combination of magnitude and distance for a scenario 

earthquake. Abrahamson and Silva (1997) tabulated the regression coefficients for 28 spectral periods 

ranging from 0.01 second to 5 second. Note that, because the equations predict the log of the spectral 

acceleration, there is no coefficient for a spectral period of zero, the spectral period corresponding to the 

PGA. Instead, the spectral acceleration at a spectral period of 0.01 is used to represent the PGA. 

To illustrate the use of the Abrahamson and Silva (1997) attenuation equation, consider a site located 10 

kilometers from the fault rupture plane of a moment magnitude 7 strike-slip earthquake (i.e. Mw = 7 and 

Rrup = 10 km). From Table 3-2, at period of 0.01 second (the period used to find the PGA), the regression

coefficients are: a1 = 1.64, a4 = -0.144, c1 = 6.4, a12 = 0, n = 2, a3 = -1.145, a13 = 0.17 and c4 = 5.6. 
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TABLE 3-2 COEFFICIENTS FOR THE ABRAHAMSON AND SILVA (1997) 

ATTENUATION MODEL

Period c4 a1 a2 a3 a4 a5 a6 a9 a10 a11 a12 a13 c1 c5 n

5.00 3.50 -1.460 0.512 -0.7250 -0.144 0.400 -0.200 0.000 0.664 0.040 -0.2150 0.17 6.4 0.03 2 

4.00 3.50 -1.130 0.512 -0.7250 -0.144 0.400 -0.200 0.039 0.640 0.040 -0.1956 0.17 6.4 0.03 2 

3.00 3.50 -0.690 0.512 -0.7250 -0.144 0.400 -0.156 0.089 0.630 0.040 -0.1726 0.17 6.4 0.03 2

2.00 3.50 -0.150 0.512 -0.7250 -0.144 0.400 -0.094 0.160 0.610 0.040 -0.1400 0.17 6.4 0.03 2 

1.50 3.55 0.260 0.512 -0.7721 -0.144 0.438 -0.049 0.210 0.600 0.040 -0.1200 0.17 6.4 0.03 2 

1.00 3.70 0.828 0.512 -0.8383 -0.144 0.490 0.013 0.281 0.423 0.000 -0.1020 0.17 6.4 0.03 2

0.85 3.81 1.020 0.512 -0.8648 -0.144 0.512 0.038 0.309 0.370 -0.026 -0.0927 0.17 6.4 0.03 2 

0.75 3.90 1.160 0.512 -0.8852 -0.144 0.528 0.057 0.331 0.320 -0.500 -0.0862 0.17 6.4 0.03 2 

0.60 4.12 1.428 0.512 -0.9218 -0.144 0.557 0.091 0.370 0.194 -0.890 -0.0740 0.17 6.4 0.03 2

0.50 4.30 1.615 0.512 -0.9515 -0.144 0.581 0.119 0.370 0.085 -0.121 -0.0635 0.17 6.4 0.03 2 

0.46 4.38 1.717 0.512 -0.9652 -0.144 0.592 0.132 0.370 0.200 -0.136 -0.0594 0.17 6.4 0.03 2 

0.40 4.52 1.860 0.512 -0.9880 -0.144 0.610 0.154 0.370 -0.065 -0.160 -0.0518 0.17 6.4 0.03 2 

0.36 4.62 1.955 0.512 -1.0052 -0.144 0.610 0.170 0.370 -0.123 -0.173 -0.0460 0.17 6.4 0.03 2 

0.30 4.80 2.114 0.512 -1.0350 -0.144 0.610 0.198 0.370 -0.219 -0.195 -0.0360 0.17 6.4 0.03 2 

0.24 4.97 2.293 0.512 -1.0790 -0.144 0.610 0.232 0.370 -0.350 -0.223 -0.0238 0.17 6.4 0.03 2 

0.20 5.10 2.406 0.512 -1.1153 -0.144 0.610 0.260 0.370 -0.445 -0.245 -0.0138 0.17 6.4 0.03 2

0.17 5.19 2.430 0.512 -1.1350 -0.144 0.610 0.260 0.370 -0.552 -0.265 -0.0040 0.17 6.4 0.03 2 

0.15 5.27 2.407 0.512 -1.1450 -0.144 0.610 0.260 0.370 -0.557 -0.280 0.0050 0.17 6.4 0.03 2 

0.12 5.39 2.272 0.512 -1.1450 -0.144 0.610 0.260 0.370 -0.591 -0.280 0.0180 0.17 6.4 0.03 2

0.10 5.50 2.160 0.512 -1.1450 -0.144 0.610 0.260 0.370 -0.598 -0.280 0.0280 0.17 6.4 0.03 2 

0.09 5.54 2.100 0.512 -1.1450 -0.144 0.610 0.260 0.370 -0.609 -0.280 0.0300 0.17 6.4 0.03 2 

0.075 5.58 2.037 0.512 -1.1450 -0.144 0.610 0.260 0.370 -0.628 -0.280 0.0300 0.17 6.4 0.03 2 

0.06 5.60 1.940 0.512 -1.1450 -0.144 0.610 0.260 0.370 -0.665 -0.280 0.0300 0.17 6.4 0.03 2

0.05 5.60 1.870 0.512 -1.1450 -0.144 0.610 0.260 0.370 -0.620 -0.267 0.0280 0.17 6.4 0.03 2 

0.04 5.60 1.780 0.512 -1.1450 -0.144 0.610 0.260 0.370 -0.555 -0.251 0.0245 0.17 6.4 0.03 2 

0.03 5.60 1.590 0.512 -1.1450 -0.144 0.610 0.260 0.370 -0.470 -0.230 0.0143 0.17 6.4 0.03 2

0.02 5.60 1.640 0.512 -1.1450 -0.144 0.610 0.260 0.370 -0.417 -0.230 0.0000 0.17 6.4 0.03 2 

0.01 5.60 1.640 0.512 -1.1450 -0.144 0.610 0.260 0.370 -0.417 -0.230 0.0000 0.17 6.4 0.03 2 

For Rrup = 10 kilometer, the distance parameter R in the attenuation equation is calculated as: 

46.116.510cRR 2 2 2

4

2

rup =+=+=

From the basic attenuation equation for the median spectral acceleration at 0.01 second (i.e. the median 

PGA), we get:

ln 133 1 )Rln()]cM(aa[)M5.8(a)cM(aa)g(S n

a 41 121 −++−+−+=

 )46.11ln()]4.68(17.0145.1[)75.8(0)4.67(144.064.1 2 −+−+−+−−=

 =-0.99025. 
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Hence, the median PGA from the Abrahamson and Silva (1997) attenuation equation for Mw=7 and 

Rrup=10 would be e-0.99025, or 0.371 g. 

Abrahamson and Silva (1997) also define a magnitude-dependent standard deviation, σ, in their model. 

For Mw = 7, the standard deviation is given by the following equation. 

43.0)135.0(27.0b2b 65 =−=−=σ

Based upon the assumption of a log normal distribution for the ground motion, the median-minus-sigma 

(84th percentile) PGA would then be: 

exp (-0.99025-0.43) = exp (-1.42025) = 0.242 g 

and the median-plus-sigma (16th percentile) PGA would be: 

exp (-0.99025+0.43) = exp (-0.56035) = 0.571 g. 

Using the regression coefficients tabulated for the other spectral periods in Table 3-2, one can solve for 

the corresponding median, median-minus-sigma, and median-plus-sigma spectral ordinates at other 

periods. This data can then be used to plot the median, median-minus-sigma, and median-plus-sigma 

acceleration response spectra shown in Figure 3-8 for the Mw 7 strike-slip scenario earthquake at a rupture 

distance, Rrup, 10 kilometers from the site. 

As noted above, there are many variations among specific attenuation relationships and these 

relationships are constantly being updated. For instance, a set of Next Generation Attenuation (NGA) 

relationships for shallow crustal earthquake in the western US (discussed briefly in Section 3.5 of this 

chapter) were recently published. Readers are encouraged to refer to the cited publications for complete 

details of these relationships, including the attenuation coefficients and any special conditions or 

constraints considered for specific attenuation models. 
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Figure 3-8 Acceleration Response Spectra from Abrahamson and Silva (1997) 

3.2.4 Uniform Hazard Spectra 

An essential output from a probabilistic seismic hazard analysis is a plot of the ground motion parameter 

of interest, say PGA, versus the annual probability of exceeding that parameter. This plot is called a 

seismic hazard curve. Figure 3-9 shows a plot of PGA versus the annual probability of exceedance (i.e. 

the seismic hazard curve) from the seismic hazard analysis for a port facility in southern California. The 

inverse of the annual probability of exceedance (return period in years, i.e. the average interval between 

earthquake ground motions equal to or greater than the associated value), is shown on the right vertical 

axis. Figure 3-9 shows not only the total probability of exceedance at the site but also the contributions 

from individual seismic sources for this example. The annual probability of exceedance from each source 

is summed to give the total hazard curve as shown in Figure 3-9. 
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Figure 3-9 Seismic Hazard Curves for Site in Southern California: Total Hazard and Individual 

Contributions from Three Major Faults 

A hazard curve such as the one in Figure 3-9 may be used in several ways. For example the level of 

ground motion with a 10% probability of exceedance in 50 years at this site, is 0.55g. (10% exceedance in 

50 years is an annual exceedance of 0.0021, or a return period of 475 years.) This same curve indicates 

that if the return period was doubled to1,000 years the design ground motion would be 0.65g, so it can be 

observed that doubling the return period does not double the design ground motion. Similarly, if a bridge 

at this site has an elastic strength that is exceeded when the design ground motion exceeds 0.2g, the 

elastic capacity of the bridge will be exceeded about once every 15 years (annual probability of 

exceedance for this ground motion = 0.07). 

Similar hazard curves can be generated for the spectral acceleration at selected spectral periods. Then, by 

plotting the spectral acceleration against period for a specified annual probability of exceedance, a 
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uniform hazard acceleration response spectrum for the specified annual probability of exceedance (or 

specified return period) can be extracted from these hazard curves. The resulting spectrum is called a 

uniform hazard spectrum (UHS) because the ground motion parameter at all periods in this spectrum 

represents the same, consistent seismic hazard level, or return period. 

3.2.5 Return Period and Seismic Risk

The return period is a fundamental parameter for quantifying the risk assumed in design. The inverse of 

the return period in years is essentially the annual risk. As noted earlier, AASHTO adopted a 1,000-year 

return period (corresponding to a 0.001 annual risk) in 2007 for the no-collapse design limit state for 

ordinary bridges. Therefore, under the AASHTO criteria for seismic design of ordinary bridges, damage 

may be expected to occur when the bridge is subjected to the 1,000-year ground motions but collapse of 

one or more spans and loss of life is not expected. The annual risk level of 0.001 associated with the 

1,000 year return period ground motion may be compared to that for other natural hazards such as 

extreme weather (floods and high wind) when making decisions regarding the risk level for design. An 

annual risk of 0.001 is lower than the annual risk associated with bridge design for flooding and scour, 

but public acceptance of the risk associated with the widespread loss of life, damage and business 

disruption that may occur in a major earthquake dictates this criterion for seismic design. Furthermore, in 

some circumstances even lower risk levels than that associated with the AASHTO 1,000-year return 

period may be appropriate, such as for particularly important bridges. For example, a 1,500-year return 

period (0.00067 annual risk) was adopted for the design of the new East Bay Spans for the San Francisco 

Oakland Bay Bridge, based upon recommendations from Caltrans’s Seismic Advisory Board. Elsewhere, 

a 2,500-year return period (0.0004 annual risk) has been employed for design of other major critical water 

crossings in the U.S., including the seismic retrofit of several long-span bridges in New York City, and 

the design of the Arthur Ravenal, Jr. (Cooper River) Bridge in Charleston and the Tacoma-Narrows 

Second Crossing in Seattle. 

While the return period (or annual risk) is a convenient way to interpret the risk associated with design 

ground motions, many design engineers prefer to look at the risk over the design life of a facility, 

sometimes referred to as the exposure period. Risk over a specified exposure period is quantified by the 

probability of exceedance over that exposure period. By assuming that earthquakes occur randomly (i.e. 

assuming a Poisson distribution of earthquake in time, e.g. that even if an earthquake occurs today, it has 

the same chance of occurring tomorrow), the following equation can be used to relate the probability of 
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exceedance, P, for an exposure period t to the annual risk γ (i.e. to the annual probability of exceedance, 

which is the inverse of the return period, R):

1P exp( ×γ−−= )t 3-5

At relatively small probabilities of exceedance (e.g. 10% or less), this exponential relationship in 

Equation 3-5 can be replaced by a simple proportional relationship between the annual risk and the 

exposure period, t, or return period, R: 

tP γ×= 3-6

γ= R/P 3-7

So, for example, for a return period of 1,000-year, γ=0.001 and the probability of exceedance during a 50-

year exposure period (t = 50 years) is about 5% in accordance with Equations 3-6 and 3-7. If the 

exposure period becomes 75 years (a common assumption for the design life of highway bridges), the 

probability of exceedance is approximately 7% for a 1,000-year return period. Note, however, that at 

higher probabilities of exceedance (e.g. for a 50% probability of exceedance in 75 years), the exponential 

relationship in Equation 3-5 must be used. 

Care must be exercised in choosing the exposure period, or design life, for an engineered facility. If the 

design life is too short, the design earthquake ground motion can become so low that it has little chance of 

representing the ground motion in a real earthquake. Also, while a design life of 50 years is commonly 

assumed for economic analysis of many engineered structures, this rarely represents the true exposure 

period for a transportation facility, especially for more critical structures. For example, the Manhattan 

Bridge in New York City was opened to traffic in 1909. The bridge has now been in service for about 

100 years. But, it is inconceivable that this bridge would be demolished today and chances are that with 

routine maintenance it will be in service for at least another 50 years. However, if the designer assumes a 

very long design life for a critical structure (e.g. 2500 years), the probabilistic design ground motions may 

become exceedingly high, in some cases significantly greater than the median value of or even median 

plus one standard deviation from the maximum magnitude earthquake for the site (particularly in areas of 

high seismicity). For this reason, some seismic codes and design specifications place a deterministic cap 

on the level of ground motions used in design. 
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3.2.6 De-aggregation of Design Earthquake, Magnitude and Distance 

While the uniform hazard spectrum (UHS) is the most common means of characterizing the seismic 

hazard for use in design, some structural and many geotechnical analyses require additional information 

about the design earthquake that is associated with the UHS, e.g. the earthquake magnitude. Magnitude is 

used, for example, when developing acceleration time histories for structural and geotechnical time 

history analyses. The UHS typically consists of contributions for many different combinations of 

earthquake magnitude and distance. To obtain information on a representative earthquake magnitude, the 

UHS can be decomposed into the contributions from individual seismic sources and the corresponding

magnitude and distance combinations through a process known as deaggregation. This process enables 

the identification of the magnitude and distance combinations that make the most significant contributions 

to the seismic hazard. The deaggregated magnitude information can also be used to determine the 

representative magnitude for magnitude-dependent analyses, including the evaluation of liquefaction 

potential, as well as for selection of representative time histories. 

Selecting a design earthquake magnitude from the deaggregated magnitude data is complicated because 

each spectral period in a UHS will have a different, unique magnitude deaggregation. The dependence of 

magnitude deaggregation on spectral period occurs because the dependence of earthquake ground motion 

attenuation upon magnitude and distance is different for every spectral period. The spectral acceleration 

at short periods (including the zero period, or peak ground acceleration) tends to attenuate faster than at 

longer periods. Furthermore, large magnitude earthquakes tend to have more energy at longer periods 

when compared to smaller magnitude events. Therefore, magnitude deaggregation for shorter spectral 

periods tend to be biased towards smaller magnitude and closer earthquakes compared to the magnitude 

deaggregation for longer spectral periods. Table 3-3 illustrates this effect, presenting the magnitude 

deaggregation for the seismic hazard at a site in Bakersfield, California at periods of 0.0 second (the 

PGA) and 1.0 second (a frequency of 1 Hz) for a 2,500-year return period. For the PGA, almost 70% of 

the hazard is associated with earthquakes of Magnitude 6.5 or less, and almost 92% of the hazard is 

associated with an earthquake of magnitude 7 or less. At a period of 1 second, over 50% of the hazard is 

associated with earthquakes of magnitude 7.5 or greater. Therefore, selection of a single representative 

magnitude for design may still be a subjective decision made of the basis of engineering judgment. This 

judgment should be guided by the engineer’s understanding of the sensitivity of the analysis for which 

magnitude is required to spectral period. 
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TABLE 3-3 MAGNITUDE DEAGGREGATION FOR BAKERSFIELD, CALIFORNIA, 

FOR A 2500 YR RETURN PERIOD

 Deaggregated Seismic Hazard PE = 2% in 50 years pga

 Bakersfield CA 35.373 deg N 119.018 deg W PGA=0.42440 g

 M<= 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0

d<= 25. 0.000 18.239 18.339 32.288 18.484 0.000 0.000 0.000 0.000

 50. 0.000 0.019 0.024 0.086 4.200 7.059 0.000 0.000 0.000

 75. 0.000 0.000 0.001 0.006 0.033 0.019 1.154 0.000 0.000

 100. 0.000 0.000 0.000 0.000 0.015 0.008 0.000 0.000 0.000

 125. 0.000 0.000 0.000 0.000 0.009 0.002 0.000 0.000 0.000

 150. 0.000 0.000 0.000 0.000 0.001 0.003 0.000 0.000 0.000

 175. 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000

 200. 0.000 0.000 0.000 0.000 0.007 0.002 0.000 0.000 0.000

 Deaggregated Seismic Hazard PE = 2% in 50 years 1hz

 Bakersfield CA 35.373 deg N 119.018 deg W SA= 0.38360 g

 M<= 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0

d<= 25. 0.000 0.957 2.329 17.096 16.216 0.000 0.000 0.000 0.000

 50. 0.000 0.004 0.019 0.272 12.374 23.708 0.000 0.000 0.000

 75. 0.000 0.000 0.001 0.019 0.254 0.208 26.228 0.000 0.000

 100. 0.000 0.000 0.000 0.001 0.074 0.097 0.000 0.000 0.000

 125. 0.000 0.000 0.000 0.001 0.037 0.016 0.000 0.000 0.000

 150. 0.000 0.000 0.000 0.000 0.006 0.029 0.008 0.000 0.000

 175. 0.000 0.000 0.000 0.000 0.002 0.006 0.000 0.000 0.000

 200. 0.000 0.000 0.000 0.000 0.015 0.025 0.000 0.000 0.000

Another complicating factor when selecting a design magnitude from deaggregation data is the distributed 

nature of the magnitude data. Sometimes, the magnitude deaggregation falls in a narrow band, as 

illustrated by the bold points in Table 3-3. In this case, selection of the dominant magnitude for a given 

period is relatively straight forward. However, in some cases the magnitude distribution is broadly 

distributed or multi-modal. Figure 3-10 graphically illustrates the bi-modal distribution of the 

deaggregated seismic hazard for Augusta, Georgia, at a period of 1.0 second for a 2,500-year return 

period. The deaggregated magnitude in this case is split between two major seismic sources: the Mw 7.3 

Charleston source and the Mw 8.0 New Madrid source. While the Charleston source contributes a greater 

percentage to the overall hazard (and is thus identified in the figure as the dominant source), the New 

Madrid source is potentially more damaging to certain types of structures. Furthermore, if the site of 

interest is moved closer to New Madrid and away from Charleston, the magnitude distribution would 

become more weighted towards the larger New Madrid event. The choice of dominant magnitude is 

therefore not that straight forward and requires engineering judgment. 
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Figure 3-10 Magnitude Deaggregation for Augusta, GA, at 1.0 sec Period for a 2500-year Return 

Period: Predominant Hazard is Charleston M7.3 Characteristic Earthquake 

3.2.7 Deterministic Maximum Magnitude and Ground Motion Evaluation 

In a deterministic seismic hazard analysis, individual earthquake scenarios (i.e. earthquakes of a specified 

magnitude and location) are developed for each relevant seismic source. The design ground motion 

parameter is then calculated for each earthquake scenario. Typically, either (i) the median (i.e. the zero 

standard deviation), or (ii) the median-plus-one standard deviation (i.e., the 84-percentile confidence 

limit) ground motion attenuation relationship is employed to compute the design ground motion

parameter, depending on the potential consequences of failure. The maximum value of this parameter 

from all of the scenario earthquakes is then employed for design. The approach is ‘deterministic’ in the 

sense that a single value of the design ground motion parameter corresponding to a deterministic 

magnitude and distance is selected for design.

In practice, the scenario earthquake for each seismic source is usually some sort of maximum magnitude 

event, e.g. the maximum magnitude expected in the currently known tectonic framework (sometimes 
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termed the maximum credible earthquake, or MCE) or the maximum magnitude earthquake expected 

during some specified exposure period (for instance, over a 100-year period). Furthermore, this 

maximum magnitude event is usually placed at the closest approach of the seismic source to the site, 

sometimes referred to as the “worst case scenario.” However, if the median ground motion attenuation 

relationship is used, as is the current practice for many transportation facilities that use the deterministic 

approach, the resulting ground motion will not, in fact, be a worst case scenario. When the median 

attenuation relationship is used, 50% of the time an earthquake of the maximum magnitude occurs at the 

specified location the ground shaking will exceed the median value. Furthermore, if the goal of the 

deterministic analysis is to determine the most damaging event, it may be necessary to consider more than 

one scenario event in the design analysis, as damage depends upon both the intensity of shaking and the 

duration of shaking. So, it may not be possible to distinguish a priori whether the most damaging event is 

a nearby relatively small magnitude event or a more distant larger magnitude event with a smaller 

intensity. 

3.2.8 Probabilistic versus Deterministic Analysis Methods 

In the probabilistic seismic hazard approach, the relative likelihood of all possible and relevant 

earthquake scenarios (all possible magnitude and location combinations capable of inflicting damage) are 

considered along with the range of possible ground motion probability levels. Therefore, the probabilistic 

approach incorporates uncertainties with respect to earthquake location, magnitude, and ground motion

attenuation, producing a weighted average of all possibilities that is a best estimate of the hazard 

associated with seismic activity. For this reason, the probabilistic approach is often considered an 

appropriate basis for making rational design decisions about risk versus benefit. The probabilistic 

approach has been widely adopted by the engineering community for use in establishing design ground 

motions. However, even after the probabilistic approach has been embraced, a decision still must be 

made about the appropriate level of hazard to use in design. 

For critical engineering facilities (e.g. lifeline bridges, hospitals, nuclear power plants, and high hazard 

dams), engineers and other decision makers are sometimes uncomfortable with use of a probabilisticallybased design level. Oftentimes, the decision makers express a desire to design these critical facilities for 

a so called worst case scenario. In such cases, the deterministic approach of employing a Maximum 

Credible Earthquake (maximum magnitude earthquake) is sometimes used. However, as noted above, 

the deterministic approach may not necessarily lead to a worst case ground motion prediction, particularly 
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Seismic Design – Geotechnical Features 3-27 August 2011 

if the median attenuation relationship is used, due to uncertainties regarding ground motion attenuation. 

Use of a median plus one standard deviation (84 percentile) ground motion level, as practiced for some 

critical structures (e.g. high hazard dams and sometimes critical buildings such as hospitals and schools) 

can provide a higher level of certainty regarding the maximum anticipated ground motions. However, 

designing to an 84 percentile attenuation basis is not traditionally done by transportation agencies, as it 

often results in extremely costly seismic design requirements. In fact, the risk associated with either the 

median or 84 percentile ground motions from a deterministic seismic hazard analysis is unknown because 

the analysis only considers uncertainty with respect to ground motion attenuation and does not consider 

uncertainties with respect to earthquake location, magnitude, or rate of occurrence. 

As noted previously, designing to an arbitrarily high probabilistic design level (i.e. a very long return 

period) can also produce unrealistically high ground motions due to compounding of uncertainties at low 

probability levels. One alternative approach that has been used for design of important facilities to 

compensate for the deficiencies in both probabilistic and deterministic analyses is to combine these two 

approaches. For example, Caltran’s seismic peer review panel and the state of California Seismic Safety 

Advisory Board recommended the use of both probabilistic and deterministic ground motion levels 

(including considering both median and median-plus one standard deviation values for the deterministic 

scenario events) when setting the design ground motions for the Toll Bridge Retrofit Program in 

California. 

In summary, fundamentally there is relatively little difference in the basic methodology for deterministic 

and probabilistic seismic hazard approaches. The probabilistic approach can be regarded as an approach 

providing explicitly defined hazard levels in terms of return period or the annual rate of exceedance for 

use in design: information that can then be the basis for design decisions balancing cost versus risk. The 

estimated hazard from a probabilistic assessment can also be compared to the hazard associated with 

other extreme environmental loading conditions to produce a balanced design. A probabilistic approach 

also has the merit of being able to distinguish relative contributions to the hazard from the more active 

versus less active faults. However, a deterministic hazard approach is simpler than a probabilistic 

approach and can be conducted by most engineers (probabilistic analyses should preferably be conducted 

by qualified professionals who specialize in this area). It is very difficult, and sometimes impossible, to 

verify probabilistic solutions by independent checks. Furthermore, as noted previously, the results of 

probabilistic hazard solutions can sometimes be unreasonable, or at least questionable, at very long return 

periods (low probability levels). It is generally believed prudent to, as a minimum, employ deterministic 

solutions as a sanity check on the results of probabilistic analyses for long return periods. To account for 
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Seismic Design – Geotechnical Features 3-28 August 2011 

the large uncertainties associated with low probability levels, a median-plus-one standard deviation 

deterministic hazard solution using maximum magnitudes can be regarded as an upper bound on the 

results of a probabilistic hazard analysis when designing transportation facilities. 

3.3 HAZARD LEVELS AND RETURN PERIODS FOR FUNCTIONAL AND LIFE SAFETY 

DESIGN 

3.3.1 Performance Levels for Seismic Design

The choice of the design ground motion level, whether based upon probabilistic or deterministic analysis, 

cannot be considered separately from performance standard specified for the design event. Sometimes, 

facilities may be designed for multiple performance standards, with a different ground motion level 

assigned to each performance standard. Common performance standards used in design of transportation 

facilities include protection of life safety and maintenance of function after the event. A life safety level 

design earthquake criterion is routinely employed for all types of facilities in seismic design. Keeping a 

facility functional after a large earthquake, a more rigorous requirement than simply maintaining life 

safety, is often also employed for essential and critical facilities. An even more rigorous performance 

standard is a no damage criterion. A no damage seismic performance standard is typically only required 

for critical facilities, e.g. “lifeline” bridges. 

Current AASHTO specifications employ a single seismic performance standard. The AASHTO seismic 

performance standard for conventional (or ordinary) bridges is based upon preventing collapse and 

protecting life safety: an ordinary bridge should not collapse and threaten life safety in the design event, 

though it may suffer significant damage that requires complete replacement of the structure. AASHTO 

seismic design provisions also note that more stringent performance standards may be appropriate for 

critical and essential structures (AASHTO calls for bridges are to be classified by the owner as critical, 

essential, and other (ordinary) bridges, in descending order of importance, depending on their function). 

A critical bridge is a bridge that is expected to remain open to all traffic, including for emergency vehicles 

and defense and security purposes, after the design earthquake. Essential bridges are bridges that are 

expected to be useable by emergency vehicles and for security and defense purposes after the design 

earthquake. Bridges that don’t fall into the categories are designated as ordinary bridges. Table 3-4

presents a two-level, performance-based, set of seismic design criteria for transportation facilities that 

were developed for a proposed revision to the AASHTO LRFD seismic design specifications under the 
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Seismic Design – Geotechnical Features 3-29 August 2011 

sponsorship of the National Cooperative Highway Research Program (NCHRP, 2001). Two levels of 

design ground motions, (a ‘rare’ earthquake and an ‘expected’ earthquake), are specified for two different 

performance standards: ‘life safety’ for ordinary facilities and ‘operational’ for critical facilities. 

Performance criteria are specified for each ground motion level and performance standard. For instance, 

in a ‘rare’ earthquake, an ordinary facility is expected to suffer significant disruption in service and 

significant damage (but not loss of life), while a critical facility is expected to remain in service (for 

emergency vehicles, at a minimum) with minimal damage. In the ‘expected’ earthquake, both ordinary 

and critical facilities are expected to be serviceable after the earthquake, with an ordinary facility

suffering minimal damage while a critical facility should suffer only minimal to no damage. 

TABLE 3-4 PERFORMANCE BASED SEISMIC DESIGN CRITERIA FOR 

TRANSPORTATION FACILITIES (NCHRP, 2001) 

Notes:

(1) Performance Levels

These are defined in terms of their anticipated performance objectives in the upper level earthquake. Life 

safety in the MCE event means that the bridge should not collapse but partial or complete replacement 

may be required. Since a dual level design is required the Life Safety performance level will have 

immediate service and minimal damage for the expected design earthquake. For the operational 

performance level the intent is that there will be immediate service and minimal damage for both the rare and 

expected earthquakes.

(2) Service Levels*

• Immediate – Full access to normal traffic shall be available following an inspection of the bridge.

• Significant Disruption – Limited access (Reduced lanes, light emergency traffic) may be possible after 

shoring, however the bridge may need to be replaced.

In the two-level criteria presented in Table 3-4, the ‘rare’ earthquake was defined as one with a 3% 

probability of exceedance in 75 years (corresponding approximately to a 2,500-year return period), while 

the ‘expected’ earthquake was one with a 50% probability of exceedance in 75 years, corresponding 

approximately to a 100-year return period. The 2006 Edition of the Retrofitting Manual for Highway 

Structures published by the Federal Highway Administration (FHWA 2006) also recommends a dual-
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level performance criterion for use when retrofitting bridges. This Manual uses the terms ‘upper’ and 

‘lower’ level to describe the dual-level ground motions. The upper level motions have a return period of 

1,000 years and the lower level motions have a return period of 100 years. 

AASHTO first adopted a probabilistic approach to seismic design in 1981 with the publication of Guide 

Specifications for Seismic Design of Bridges (AASHTO 1981). These specifications were an approved 

alternative to the seismic provisions in the Standard Specifications for Highway Bridges in use at that 

time and were based on a 500-year return period seismic hazard map prepared by USGS. In developing 

the current AASHTO design criteria (AASHTO 2007, 2009), the two-level design approach proposed in 

the 2001 NCHRP study (NCHRP 2001) was considered to be unjustified for most transportation facilities 

in the US and thus was not adopted. Furthermore, when considering the return period for the ‘design’ 

earthquake (the term used in single-level design), 2,500 years was considered to be too long (too 

inconsistent with the return periods for other natural hazards) and potentially too costly, especially in the 

design of foundations. There was also concern that the cost of retrofitting existing bridges, many of which 

were designed for a 500-year return period, to this new hazard level would be cost prohibitive. 

Nevertheless the arguments for raising the hazard level were persuasive and in 2007 AASHTO elected to 

adopt a 1,000-year hazard level for the design of ordinary bridges. This hazard level is used in both the 

2008 interim of 4th Edition LRFD Specifications (AASHTO 2007) and the LRFD Guide Specifications for 

Seismic Bridge Design (AASHTO 2009). The Guide Specifications were developed under NCHRP 

Project 20-07/193 which showed that the hazard level for the 2,500-year return period corresponds to a 

shaking level at about the median-plus-one standard deviation level in many parts of country. 

Considering Caltrans’ practice, which uses median attenuation models for setting the safety level limit 

state ground motion criteria for ordinary bridges, it can be argued that a 2,500-year hazard level 

(corresponding to the median-plus-one standard deviation ground motion in many areas) is too 

conservative for ordinary (conventional) bridges. Hence, one can infer that the AASHTO’s decision for 

not accepting the 2,500-year return period and adopting a 1,000-year return period is appropriate. The 

NCHRP 20-07/193 study also showed that the return period that best correlated with historical 

earthquakes in various parts of the country varied widely, ranging from less than 500 years for the 

seismically active western U.S. to close to 2,000-years in some parts of central and eastern U.S. Thus 

AASHTO’s selection of a 1,000-year return period is a compromise which can be reconciled against 

many of the historical earthquakes that have occurred in the central and eastern parts of U.S. (on a median 

attenuation basis). 
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AASHTO has no explicit requirements for checking bridge performance for more frequently occurring 

ground motions than those that occur every thousand years, on average. But some owners may wish to 

check that certain important bridges will remain functional in frequently occurring earthquakes such as 

those with return periods of the order of a hundred years or so. In practice, where owners have chosen to 

check functionality, the selected return period has varied from project to project, even within the same 

geographic region. A 72-year return period has been used in California for toll road projects in Orange 

County, CA, and for designing wharf structures in the ports of Los Angeles and Long Beach. A 92-year 

return period has been used for the functional earthquake for the East Bay Spans of the San Francisco 

Oakland Bay Bridge. However, for major bridge structures in less active seismic states, longer return 

periods have been used for the functional earthquake. For example, 500 years has been used as the return 

period for the functional level ground motion for the retrofit of the major water crossing bridges in New 

York City and for design of the new Arthur Ravenal, Jr. (Cooper River) cable-stayed bridge in 

Charleston, South Carolina. The decision on whether or not to design for functionality involves balancing 

the risk of service disruption and the cost of disruption versus the cost associated with additional design 

and construction or retrofit measures. While this decision is the owners’ responsibility, it is the 

engineer’s responsibility to provide the owner with sufficient information with which to make this 

economic decision and, having made the decision to use a functional level earthquake, to set the 

functional level earthquake criteria on a project specific basis. 

3.3.2 Return Period for Use in Design

 

As discussed above, a 1,000-year return period has been adopted by AASHTO for safety level design of 

ordinary bridges. However, owners may choose to deviate from the 1,000-year return period ground 

motion criteria for transportation facilities as the situation warrants it. The following are some of the 

reasons that have been cited for deviation from the AASHTO criteria:

1) A longer return period may be justified for critical structures, when (a) the structure is part of a 

lifeline route for emergency operations, or (b) an extended duration in loss of operation of the 

structure would have an undue cost impact to the community. For these critical structures, 

especially when they are complex structural systems such as long span water crossing structures, 

project-specific ground motions and performance criteria should be developed with the assistance 

of a peer review panel. 
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2) A shorter return period may be justified, if (a) the capital cost for design of the structure to the 

1,000-year return period is deemed too costly, (b) it is required by the owner and regulatory 

agencies, or (c) in retrofit situations the existing facility has limited remaining operating life and the 

facility is expected to be replaced. It is noted that the FHWA retrofit manual (FHWA 2006) does 

not favor a reduction in the return period for older structures. Instead, the minimum level of retrofit 

is adjusted to account for the remaining service life, with little or no retrofit recommended for a 

bridge about to be closed or replaced. 

3) The return period may also be reduced when the 1,000-year return period ground motion is 

excessive, e.g. when it is higher than a median-plus-one standard deviation ground motion from the 

maximum credible earthquake. This situation is may occur in seismically active areas such as some 

parts of California where the faults have relative short rupture recurrence intervals (i.e. rupture 

recurrence intervals on the order of a few hundred years). For such situations, it is common to 

place a deterministic cap on the probabilistic ground motions, e.g. the median-plus-one standard 

deviation MCE ground motions. 

3.3.3 Site Specific Analysis versus USGS National Seismic Hazard Maps

The AASHTO seismic design criterion is based upon the 2002 USGS National Seismic Hazard Maps. 

However, owners can, at their discretion, use more recent versions of the USGS National Seismic Hazard 

maps or commission site-specific seismic hazard analyses to determine design ground motion parameters. 

The USGS hazard mapping efforts are comprehensive, employing state-of-the-art attenuation 

relationships and regional workshops to gather local geological data and to develop consensus within the 

geoscience community on the resultant seismic source models. This level of effort cannot be easily 

duplicated and thus site-specific seismic hazard analyses are generally not justified for small scale 

projects. Furthermore, site specific studies often result in discrepancies with the USGS maps and other 

models for the predicted ground shaking that require investigation and explanation, often leading to 

controversies and delay for the project. Therefore, site-specific seismic hazard studies should only be 

exercised with good justification, conducted by qualified experts, and subject to peer review by experts in 

regional seismicity and seismic hazard evaluation. In general, site specific seismic hazard studies for 

transportation facilities are usually confined to major bridge projects (e.g. major water crossing bridges) 

or regional transportation projects that cover a wide geographic area. Some of the justifications for 

conducting a site specific seismic hazard analysis include:
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1) Failure of a major transportation facility or disruption of a transportation network may have 

tremendous impact on the local economy. Many transportation facilities may be classified as 

important or critical structures, and some may be classified as lifeline structures. Hence, the 

appropriate ground motion and especially the performance criteria may be considered to be 

different from ordinary bridges. Projects that deviate from the 1,000-year return period would 

therefore often be good candidates for site specific studies. For example, many of the water 

crossing bridges in the east coast, including at New York City and the Arthur Ravenal, Jr. bridge in 

Charleston, and the Tacoma Narrows Second Crossing Bridge in Seattle have adopted a 2,500-year 

return period for seismic design. The California State Seismic Advisory Board and the Seismic 

Peer Review Panel recommended a 1,500-year return period for seismic design of the San 

Francisco-Oakland Bay Bridge East Span Replacement project. Due to the potential economical 

impacts of service disruption for such structures, it is common for these projects to employ a site 

specific seismic hazard analysis. 

2) Major bridges and viaducts are complicated structures and therefore often require time history 

analyses. There is a high level of expertise required for generating the appropriate input time 

histories to support design of such bridges. Therefore, such structures would logically be 

candidates for site specific studies due to the requirement for developing input time histories.

A peer review process is recommended for any project that employs a site-specific seismic hazard 

analysis. As major transportation projects of the type that require a site specific seismic hazard analysis 

often involve oversight by a peer review panel, this peer review panel can often also be employed to 

provide the proper review of results from a site specific ground motion hazard study. 

3.3.4 Ground Motion Characterization 

While a response spectrum developed in a probabilistic or deterministic seismic hazard analysis can be 

input directly to a structural response analysis, more often than not a modified version of the spectra from 

the seismic hazard analysis is used for structural design. In general, the acceleration response spectrum 

from a seismic hazard analysis may be modified for use in design in two ways: 1) the shape may be 

modified from the relatively peaked shape typically produced by a seismic hazard analysis to the more 

truncated standard shape typically used in structural analysis; and 2) the amplitude of the spectral 

ordinates may be modified to account for local soil conditions. As noted previously, a deterministic cap 

may also be placed on a probabilistically-derived acceleration spectrum developed from a seismic hazard 
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analysis in areas of high seismicity. This cap limits the amplitude of the spectrum in the short period 

range. Furthermore, the USGS National Seismic Hazard Maps are produced for a site where the average 

shear wave velocity within the upper 100 feet of the site profile ranges from 2,500 to 5,000 feet per 

second (ft/sec). If the shear wave velocity in the upper 100 ft differs from this range of values, the design 

response spectra must be modified to account for the local site conditions. 

Modifications to the response acceleration spectrum developed from the USGS National Seismic Hazard 

maps to develop the acceleration response spectrum for structural design purposes is generally based upon 

the standard spectral shape shown in Figure 3-11. 

Figure 3-11 Design Response Spectrum Constructed with the Three-Point Method 

Three spectral ordinates, the spectral acceleration at 0.0, 0.2 and 1.0 seconds, are used to develop the

modified spectral curve shape from the seismic hazard analysis results. The values for these parameters 

obtained from a seismic hazard analysis for soft rock site conditions, e.g. from the 2002 USGS National 

Seismic Hazard Maps, are modified by site factors Fpga (i.e., FPGA), Fa and Fv that depend upon Vs30, the 

average shear wave velocity in the top 100 ft (30 m) of the site, to account for local site conditions when 
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developing the acceleration response spectrum for structural design (these site factors are discussed in 

detail in Section 3.4.7). This method of modifying the acceleration response spectrum, sometimes 

referred to as the three-point method, was developed as part of the recommended seismic design 

provisions from the National Earthquake Hazard Reduction Program (NEHRP). This three-point method

is employed not only in the AASHTO LRFD and NEHRP seismic design provisions but also in the 

International Building Code (IBC). The primary difference among the NEHRP, AASHTO, and IBC 

seismic design provisions is the return period used to determine the three anchoring spectral accelerations. 

For example, while AASHTO uses the 1,000-year return period, the IBC multiplies the spectral ordinates

for a 2,500-yr return period by a reduction factor of 2/3. One important difference between the current 

AASHTO procedure (described in Section 3.7) and the other versions of this procedure is that the current 

AASHTO procedure uses the PGA to anchor the design spectrum at zero period. Other versions of this 

procedure simply assumed the PGA to be equal to 0.4 times the spectral acceleration at 0.2 second. 

Figure 3-12 compares the UHS acceleration response spectrum developed from the USGS National 

Seismic Hazard mapping program data with the AASHTO truncated structural design spectrum developed 

using the three-point fitting method for a site in Memphis, Tennessee for a 1,000-year return period. 

Figure 3-12 Comparison of USGS Spectra to AASHTO Spectra for a Rock Site in Memphis, 

Tennessee (1,000-yr Return Period) 
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Figure 3-12 clearly illustrates the truncation of the peaked USGS 1000-year return period UHS spectrum 

to develop the spectrum for use in structural design, e.g. in a structural analysis that employs an elastic 

response spectra and the principle of modal superposition to calculate structural response.

3.3.5 Correlation for Peak Ground Velocity 

The Peak Ground Velocity (PGV) is an important parameter in both structural and geotechnical design 

analyses. In structural design, it is generally acknowledged that damage potential is more closely 

correlated to PGV than to any other single earthquake loading parameter. In geotechnical analysis, PGV 

can be used in Newmark displacement analysis for predicting permanent seismically induced 

displacement of slopes and earth retaining structures. USGS (in their national hazard mapping program) 

does not provide maps for PGV. Therefore, it is often necessary to derive PGV for a representative 

deterministic scenario event from an attenuation relationship or by correlation with other earthquake 

parameters.

Several correlations between PGV and ground motion parameters were developed during the NCHRP 12-

70 project. After reviewing the available information, a revised form of a Peak Ground Velocity (PGV) 

correlation suggested by Abrahamson (2005) for the estimation of PGV from the spectral acceleration at 

one second (S1) was recommended in NCHRP 12-70 (NCHRP 2008). This correlation is given as:

C434.0 1 PGV ×= 103937.0 3-8

where PGV is in inches/sec, 

2

1 1V10 V110 += + + ]93.2)FS(log30.2[013.0SFlog16.282.4C 3-9 

and S1 is the spectral acceleration (in g) at a spectral period of 1 second and FV is the site factor for the 

spectral acceleration at a period of 1 second. For design purposes, Equation 3-6 was simplified to the 

following equation: 

SF38 1V

sec

in PGV  ⋅=

 



 3-10 
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It is expected that in the future the USGS will include PGV in their national seismic hazard mapping 

program and will provide map values for a 1,000-year return period. In that case, the S1-PGV correlation 

will be replaced in favor of design PGV values from the USGS maps (unless PGV is available from the 

results of a project-specific seismic hazard analysis).

3.3.6 Acceleration Response Spectra versus Displacement Spectra 

The most common method of seismic design for bridges focuses on providing sufficient strength to resist 

the earthquake force demands. This approach is called a ‘force-based’ approach and it employs 

acceleration response spectra to calculate the earthquake demands. However, there is a growing trend in 

bridge design to move away from ‘force-based’ methods to ‘displacement-based’ methods where the 

focus is on providing sufficient displacement capacity. This approach employs displacement response 

spectra to calculate the earthquake displacement demands. A displacement response spectrum may be 

derived from an acceleration response spectrum using the following equation: 

2 a

2

d S

)2(

T S

π = 3-11 

where Sd is spectral displacement, Sa is spectral acceleration, and T is period.

The spectral displacement demand from the above equation is the relative displacement between the 

center of mass of the structure and the point where ground motion is input to the structure. 

3.3.7 Near-Fault (Near-Field) Directivity Effects

Research over the last 15 years (e.g. Sommerville et al., 1997) has shown that certain combinations of site 

location, the configuration of the seismic source, and the direction of fault rupture can result in a 

significant enhancement to the long period motions at a site that can result in directivity effects that can 

be very damaging to certain structures, particularly in the near field, i.e. when the site is close (within 15 

km) to the fault. Figure 3-13 illustrates the effect of directivity in near-fault ground motions by 

comparing the velocity time histories from two sites subject to the 1992 Mw 7.2 Landers earthquake in 

Southern California at the same distance from the earthquake epicenter but located in different directions 

from the epicenter with respect to the direction of rupture propagation along the fault. It is seen in this 

figure that the ground motion recorded during the earthquake at the station oriented in the direction of 
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fault rupture propagation relative to the earthquake origin, the Lucerne recording station, is significantly

different from that recorded which is in opposite direction of fault rupture, the Joshua Tree station. The 

Lucerne record shows a very large velocity pulse, with a peak ground velocity of 53.5 in/s, compared to 

the Joshua Tree record, which has a much lower amplitude of peak ground velocity of 16.9 in/s, even

though the duration of shaking is longer in the Joshua Tree record. 

Figure 3-13 Influence of Rupture Directivity on Velocity Time Histories Recorded at the Lucerne and 

Joshua Tree Sites During the 1992 Landers Earthquake (Somerville et al., 1997)
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Figure 3-13 shows that if a site is located sufficiently near to a fault and the earthquake fault ruptures 

toward the site, a ground motion with a very large velocity pulse can occur. Because these kinds of 

pulses can be very damaging to long-period bridges, it is necessary to take special design measures in 

these situations. However, the methods used to account for these near-fault directivity effects vary from 

project to project, in part because the subject matter is still under research. In particular, the means for 

quantifying the velocity pulse and relating it to structural response is still a subject of research, although a 

time history analysis using appropriate time histories is one way this can be accomplished. The need to 

consider near fault directivity is, in general, limited to those states with well-defined shallow active faults 

(e.g. California, Washington, and Utah). Furthermore, only project sites within about 10 miles (15 

kilometers) of the rupturing fault subject to relatively large magnitude earthquakes (M > 6.5) need be 

considered for fault directivity effects. 

3.3.8 Local Site Effects 

As noted previously, local site conditions have a significant effect on the characteristics of earthquake 

ground motions. The local site conditions effect needs to be properly taken into account when

establishing design ground motions. There are, in general, three methods that can be used to account for 

the influence of local site conditions on earthquake ground motions: 1) the use of site factors to modify 

the results of the seismic hazard analysis to account for local soil conditions; 2) the use of soil site 

attenuation relationships to directly account for the local soil conditions in the seismic hazard analysis; 

and 3) the use of site-specific site response analysis. Until recently, soil site attenuation relationships were 

generally considered too crude to properly account for local soil conditions, as they tended to group all 

soil sites into one or two site classes. However, a new generation of attenuation relationships that 

discriminates among soil sites on the basis of the shear wave velocity in the upper 100 ft has recently 

been developed for shallow crustal faults in the western United States. This new generation of 

attenuation relationships, termed the Next Generation Attenuation (NGA) relationships, is discussed in 

more detail in Section 3.8. The use of site response analysis to account for local soil conditions is 

discussed in Chapter 5 of this document. 

The use of site factors to account for the influence of local soil conditions on ground motion 

characteristics is illustrated in Figure 3-11. Using the site factor approach, the three anchoring spectral 

accelerations for the design response spectrum are modified by site response factors Fpga (for the PGA, or 

spectral acceleration at a spectral period of 0.0 seconds), Fa (for the spectral acceleration at 0.2 second 

spectral period) and Fv (for the spectral acceleration at 1 second spectral period). Note that on Figure 
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3-11 the site response factor Fpga (for the 0.0 second spectral period) is shown as equal to Fa (for the 0.2 

second period). While this is the case for the NEHRP spectrum, which assumes the PGA is 0.4 times the 

spectral acceleration at 0.2 second spectral period, it may not always be the case for the AASHTO 

spectrum (for which the PGA is evaluated independently). The values of Fpga, Fa and Fv depend upon 

both the local site conditions and the amplitude of the associated spectral accelerations. Local site

conditions are defined on the basis of the average shear wave velocity for the top 100 ft of the site, 

sometimes referred to as Vs30 (the subscript “30” refers to 30 meters, the metric equivalent of 100 ft). Six 

site classes, designated Site Class A through F, have been established on the basis of Vs30. These site 

classes, referred to as the NEHRP site classes because they were initially established under the NEHRP 

program, are shown in Table 3-5. Note that for Site Class F site factors cannot be used and a site-specific 

response analysis must be conducted to evaluate the influence of local site conditions on seismic site 

response. Also note that Site Classes C, D, and E can also be defined on the basis of the average Standard 

Penetration Test blow count, N� , or the average undrained shear strength, Su���. The average blow count, N�, 

is generally defined on the basis of the normalized, standardized blow count (N1)60 discussed in Chapter 

4. 

TABLE 3-5 NEHRP SITE CLASSIFICATION SYSTEM

Table 3-6 provides values for the PGA site factor Fpga, Table 3-7 provides values of the short period (0.2-

second period) site factor, Fa, and Table 3-8 provides values for the long period (1-second) site factor, Fv. 
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These site factors are applied to the PGA, 0.2 second, and 1 second spectral accelerations, respectively. 

The site factor Fpga, which is used to adjust the PGA (i.e. the zero period spectral acceleration), is based 

upon Fa. However, the intensity-dependent categories in the top row of Table 3-7 are divided by 2.5 to 

create the values for Fpga in Table 3-6. For intensity values intermediate to the values at the top of the 

columns in Tables 3-6, 3-7, and 3-8 linear interpolation is used. For intensity values less than the values 

in the first column of these tables, the site factor values in the first column is used and for intensity values 

greater than the values in the last column the values in the last column are used. 

The site factors in Tables 3-6, 3-7, and 3-8 are used to create the three-point truncated design spectrum 

that accounts for local site conditions. In most cases, these site factors are greater than 1.0 (and as great 

as 3.5 in one case), resulting in amplification of the spectral accelerations by local site conditions. But for 

hard, crystalline rock sites (i.e., Site Class A, sites where Vs30 is in excess of 5,000 ft/s) the site factors are 

equal to 0.8, resulting in reduction of the spectral accelerations from the seismic hazard analysis. The 

site factors are also less than 1.0 for short period (0.2 second) spectral accelerations in excess of 1 g (and 

therefore for PGA values in excess of 0.4 g) for Site Class E (Vs30 less than 600 ft/s), where the low shear 

strength of the soil limits the intensity of the ground motions. Note that site factors are not given in Table 

3-6, 3-7, and 3-8 for Site Class F. A site-specific geotechnical investigation and dynamic site response 

analysis is recommended to evaluate the influence of local soil conditions on the site response for Site 

Class F.

TABLE 3-6 VALUES OF Fpga AS A FUNCTION OF SITE CLASS AND THE SITE

CLASS B PEAK GROUND ACCELERATION

Table notes: Use straight interpolation for intermediate values of SS, where SS is the spectral acceleration and 0.2 second obtained from 

 the ground motion maps. 

 a Site-specific geotechnical investigation and dynamic site response analyses shall be performed (Article 3.4.3)
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TABLE 3-7 VALUES OF Fa AS FUNCTION OF SITE CLASS AND THE SITE CLASS B 

SHORT PERIODS (0.2 SECONDS) SPECTRAL ACCELERATION

Table notes: Use straight interpolation for intermediate values of SS, where SS is the spectral acceleration and 0.2 second obtained from 

 the ground motion maps. 

 a Site-specific geotechnical investigation and dynamic site response analyses shall be performed (Article 3.4.3)

TABLE 3-8 VALUES OF Fv AS A FUNCTION OF SITE CLASS AND THE SITE CLASS B 

LONG PERIOD (1 SECOND) SPECTRAL ACCELERATION

Table notes: Use straight interpolation for intermediate values of SS, where SS is the spectral acceleration and 0.2 second obtained from 

 the ground motion maps. 

 a Site-specific geotechnical investigation and dynamic site response analyses shall be performed (Article 3.4.3)
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3.3.9 Representative Ground Motion Time Histories 

While the response spectrum method is the most common method of seismic analysis for conventional 

structural seismic design, many geotechnical analyses and some of the more complex structural analyses 

require the input of representative acceleration time histories for the design earthquake. The process of 

developing appropriate time histories for these analyses generally starts with establishing the target 

response spectra (median and plus and minus one standard deviation spectra). Then, time histories for use 

in the design analyses are developed by first selecting a candidate set of appropriate naturally recorded 

strong motion records (sometimes referred as the startup time histories or seed time histories). These 

candidate time histories are usually based on the peak ground acceleration, earthquake magnitude, and 

other relevant seismic source characteristics (e.g. source mechanism, strong motion duration, arias 

intensity or energy content). The candidate strong motion records are then scaled so that the resultant 

response spectra for the strong motion records best match the target design response spectra. Ideally, the 

suite of candidate time histories should average out to the median spectrum and “fill the envelope” 

between the plus and minus one standard deviation spectra. The accelerations of a candidate records may 

be scaled by a constant factor to meet this criterion. Candidate records may also be modified in the time 

or frequency domain to match the target spectrum, if necessary. Modification of candidate time histories 

to match the intended design response spectrum will be further discussed in the next section. 

There are various approaches to the selection of candidate ground motions for time history design 

analyses. These approaches typically involve selecting the candidate time histories from one of the many 

available catalogs of time histories on the basis of peak ground acceleration, seismic source mechanism, 

earthquake magnitude, and other earthquake parameters. One of the more comprehensive catalogs of 

earthquake ground motions is the one developed by the Nuclear Regulatory Commission for use in design 

of Nuclear Power Plants (NUREG/CR-6728: Technical Basis for Revision of Regulatory Guidance on 

Design Ground Motions: Hazard- and Risk Consistent Ground Motion Spectra Guidelines). NUREG/CR6728 provides a catalog of over 500 sets of three component time history records classified into (1) two 

tectonic regions: the western US (WUS) and the central and eastern U.S. (CEUS), (2) two site classes: 

rock or soil sites, and (3) magnitude (M- 5 to 6, M- 6 to 7, and 7+) and distance (R from 0-6 miles, 6 to 30 

miles, 30 to 60 miles and >60 miles) . The Nureg/CR-6728 report also includes a set of CD-ROMs 

containing the time histories. The NUREG time history records for the WUS are actual recordings while, 

due to lack of actual data, the CEUS NUREG records were developed by modifying WUS records to 

account for differences in seismic source and crustal properties between the two regions based on 

seismological modeling. The Pacific Earthquake Engineering Research Center (PEER) and the State 
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California Department of Conservation (Strong Motion Instrumentation Program-CSMIP) in California 

are other sources of databases for earthquake time histories. However, these two data sets are biased 

toward strong motion records for the WUS The Multidisciplinary Center for Earthquake Engineering 

Research (MCEER) also maintains a catalog of earthquake time histories, providing some strong motion 

records relevant to the CEUS. See http://peer.berkeley.edu/products/strong_ground_motion_db.html for 

the PEER database and http://mceer.buffalo.edu/infoservice/Reference_Services/strongMotionGuide.asp

for the MCEER database. 

After establishing a data set of appropriate strong motion records, subsequent steps in developing a set of 

time histories for use in design involves establishing:

1) The target ground shaking spectra

2) The number of input time histories 

3) The specific time history records to be employed 

The following discussion provides some general guidance on this subject matter.

The uniform hazard spectra from a probabilistic analysis and/or a deterministic scenario earthquake are 

common bases for setting the target response spectra for selection of candidate time histories. The 1,000-

year UHS adopted by AASHTO generally serves as the appropriate target spectrum for most ordinary 

bridges and other transportation facilities within the transportation network for the life safety performance 

goal. Then, a representative magnitude and distance can be selected based upon the magnitude 

deaggregation of the UHS and deterministic median and plus and minus one standard deviation spectra 

for the representative event can be generated using one of the available attenuation relationships. Note 

that if the mean spectrum does not conform to the UHS over the period range of engineering the selection 

of the representative magnitude and distance should be reconsidered. Critical facilities (e.g. major water 

crossing long-span bridges) might involve the use of other project specific ground motion criteria for 

design, as discussed earlier. 

With respect to the number of time histories adopted for design, theoretically the number of time histories 

should be sufficiently large so that the median and variability (standard deviation) of the demand 

predicted by the time history analyses is statistically stable. The number of time histories to achieve this 

objective may depend on the application as well as specifics of the adopted procedures for modifying the 
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startup time history records. The most basic objective in a design analyses, predicting the peak response, 

generally requires a fewer number of input time histories to achieve statistical stability then design 

objectives such as predicting permanent deformation. 

Generally accepted practice is to use a minimum of 3 sets of input time histories for a time-history 

analysis. However, three sets of input motions are generally insufficient to achieve the desired statistical 

stability for the demand. Therefore, it is common practice to employ the maximum response from a set of 

three input motions (rather than the median response) for design purposes. The IBC calls for the use of at 

least seven sets of input motions if the median response from a time-history analysis is to be employed. 

This same criterion for the number of time histories has been used on some recent bridge projects. 

However, for very complex or unusual structures (e.g. for bridges involving isolation devices), the 

designer may chose to design the structure for the maximum response even if a minimum of seven sets of 

input motions are employed.

The use of naturally recorded time histories is generally preferred to the use of modified or synthetic (i.e. 

numerically generated) time histories. To select an appropriate data set of candidate strong motion 

records, the designer usually identifies a set of records from available databases based upon the 

appropriate tectonic conditions, magnitude, site-to-source distance, peak ground acceleration, and site 

class (e.g., rock or soil site). To narrow this data set down further, other strong motion parameters, 

including the duration of strong shaking and Arias intensity, may also be used as a basis for 

discriminating among records for analysis. The response spectra for the reduced set of candidate records 

can then be compared to the target response spectra for the design earthquake. The final suite of time 

histories is selected based upon the goal of conforming, on the average, to the median spectrum for the 

representative event or to the UHS from a probabilistic analysis and filling the envelope between the plus 

and minus one standard deviation spectra from the representative event. If necessary, records can be 

manipulated to meet this goal. However, it is preferable to minimize changes to the selected time history 

records, thus the response spectrum from the selected candidate time histories should be as good a match 

as available to the target spectra over the range of period of design interest. 

If the candidate time histories selected for design must be manipulated, simple constant scaling of the 

acceleration is preferable to other methods of time history manipulation. However, some transportation 

projects may employ spectrum-compatible motions (motions that closely conform to the UHS or median 

spectrum for the scenario earthquake). Development of spectrum compatible motions usually involves 

complex manipulation of a natural time history to fit the smooth UHS target spectrum (or median 
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spectrum from the representative event). A spectrum compatible time history is illustrated in Figure 3-14. 

Some engineers do not approve of the use of spectrum compatible time histories, as they do not, in 

general, simulate real earthquake ground motions. Even if a spectrum compatible time history approach 

is employed, it is desirable to minimize the degree of modification to the original time history record by 

selecting records that have a reasonable initial match to the target spectrum in terms of the amplitude and 

overall spectral shape.

An important step in the process of selecting appropriate time histories for use in design involves 

comparing the response spectrums of the selected records to the target spectrum. There are a variety of 

free computer software tools available for this purpose. SEISMOSIGNAL is a free program for 

processing strong motion records, including plotting response spectra and calculating duration and Arias 

Intensity. SEISMOSIGNAL can be downloaded at www.seismosoft.com. PEER and the California 

Geological Survey have developed an automated program with an associated library of strong motion 

records for selection of design time histories called the Design Ground Motion library, or DGML 

(Powers, 2004; Powers et al., 2004). The trial version of the DGML allows the user to generate target 

spectra from three common WUS attenuation relationships or to input their own project-specific target 

spectrum (e.g. the 1,000-year uniform hazard spectrum for an AASHTO project). The user then specifies 

the range of strong motion parameters that will be employed to screen the DGML database for the 

appropriate time history records. Screening parameters include fault type(s), and ranges for acceptable 

magnitudes, Joyner and Boore distance, the shortest distance to the fault rupture plane, and average shear 

wave velocity in the upper 100-ft at the recording station. Other parameters specified by the user include 

the scaling procedure and the period range of interest. The DGML then generates a list of candidate 

earthquake records which satisfy the defined screening parameters and automatically ranks the seven best 

candidate records based on minimizing the mean square error between the spectral acceleration of a 

record and the target spectrum and a user-defined period weighting scheme. The DGML is still in a 

development stage and its status for public distribution is not clear. Nevertheless, this discussion should 

provide some appreciation of the steps involved in selecting the appropriate time histories for design. 

Other methods for selecting representative time histories do exist. Kottke and Rathje (2008) present a 

semi-automated procedure for selecting scaling factors and ranking input motions for fitting a target 

acceleration response spectrum. The Kottke and Rathje (2008) method represents one of the few studies 

describing a systematic automated algorithm for selecting ground motion time histories and their 

corresponding scaling factors. This method is specific for natural time history records to which a constant 

scaling factor is applied.
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3.3.10 Adjusting Time Histories to a Target Spectrum

Best practice for selection of startup time histories for use in seismic design is to employ actual recorded 

acceleration time histories whenever possible, as opposed to manipulated records or artificially generated 

synthetic records. However, even when actual recorded time histories are used, some modification of 

these time histories is generally required to match the target spectrum. The simplest form of time history 

modification is simple scaling of the accelerations in a record by a constant factor. Scaling of a recorded 

time history by a factor between 0.5 and 2.0 is a non-controversial process that is widely accepted. 

However, scaling by factors outside of this range must be done with caution and is subject to argument. 

Even after it is scaled, a naturally recorded time history will usually fit the target spectrum over only a 

very narrow range of spectral periods. Therefore, a suite of scaled time histories is generally required to 

encompass the entire design spectrum. As noted above, a minimum of three and preferably seven scaled 

time histories are usually employed in a time history analysis. If three time histories are used the 

maximum response is generally used in design, while if seven time histories are used a median response 

can be employed in design. 

Many engineers prefer using only constant scaling to modify time histories for use in design, as opposed 

to modification of records in the time or frequency domain. The preference for constant scaling only is 

based upon the belief that this is the best way to preserve the phasing characteristics of the time history 

record and the correlation among the three orthogonal components of a ground motion. However, the 

computational effort required for a design analysis that employs multiple time histories can be significant, 

particularly if seven sets of three-component time histories are used. This large computational effort may 

present significant practical problems for design applications. To limit the number of time histories 

employed in design for practical reasons, some bridge design analyses employ spectrum-compatible time 

histories. As illustrated in Figure 3-14, a spectrum-compatible time history record is developed by 

modifying the candidate time history in the time and frequency domain so that it closely conforms to the 

design spectrum. Even in a spectrum compatible motion analysis, it is recommended to use 3 (or more in 

some cases) sets of spectrum compatible motions to achieve a statistically stable response result. The 

argument against this type of analysis is that a spectrum compatible time history may not represent a 

realistic earthquake ground motion. The argument in favor of this type of analysis is that it can 

significantly reduce computation effort. 

There are two basic ways to modify naturally recorded startup motions to develop a spectrum-compatible 

motion: (1) time domain adjustment (Lilhanand and Tseng, 1988) and (2) frequency domain adjustment 
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(Silva and Lee, 1987). There are relative merits for both approaches and, ultimately, the best way to 

achieve spectrum-compatibility of the resultant motion would be the one that makes the least changes to 

the original startup motion. Development of spectrum compatible design motions should only be done by 

engineers experienced with these procedures. Further discussion on this topic is provided in Lam and 

Law (2000). 

Figure 3-14 Representative Scaled versus Spectrum-Compatible Adjusted Motion
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3.3.11 Spatially Varying Ground Motions 

Because transportation systems are lineal systems that extend over large distances, it is sometimes 

necessary to consider the effect of the spatial variation of earthquake ground motions across the project 

site. This usually involves analyzing the system (e.g. a long-span bridge, multi-span viaduct, or a tunnel) 

with input motions that differ from support to support. In such circumstances, time histories of both 

acceleration and displacement are required at each support. 

Several factors contribute to spatial variability and these include:

1) Wave Passage Effect. The wave passage effect is due to non-vertical wave propagation and 

produces systematic time shifts in the arrival of the seismic waves at each support. This effect can 

be modeled by applying a time shift to each support time history. Based on field measurements, an 

apparent wave speed of 8,250 ft/s may be used to calculate this time shift. This velocity is toward 

the lower end of the range of measured apparent wave speed, leading to somewhat conservative 

(upper bound) estimates of the time shifts. 

2) Attenuation over Distance. When the seismic source is close to a long structure, the different 

distances to the various support locations can result in different ground motions at each support due 

to the attenuation of the ground motion with distance. Conventional attenuation relationships may 

be used to estimate this difference in the ground motions. 

3) Complex Wave Scattering. Wave propagation can result in spatial incoherency (spatial 

differences) in both the amplitude and phase of the ground motions. These effects are sometimes 

referred to as wave scattering effects and are observed empirically in the recorded data from closely 

spaced strong motion instruments. Empirical models for the coherency function for the horizontal 

and vertical components of ground motion have been developed by Abrahamson (1992) and are 

shown in Figure 3-15 and Figure 3-16. These plots show that the degree of coherency decreases, 

and incoherency increases, at higher frequencies and larger spatial distances. 

4) Variation due to Local Soil Condition. The change in soil profile and soil properties across a site 

can lead to significant variations in ground motions at or near the ground surface. This is perhaps 

the most significant source of spatially-varying input for most cases. Variations in local soil 

conditions are generally accounted for by conducting site response analyses for representative soil 
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columns at each support. Each soil column is subjected to the free-field design ground motion at its 

base and the difference in response of the soil columns is assumed to represent the variation in 

motions due to local soil conditions. 

Figure 3-15 Coherency Function for Horizontal Component Motion (Abrahamson, 1992) 
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Figure 3-16 Coherency Function for Vertical Component Motion (Abrahamson, 1992)

Each of the above phenomena can contribute to differences in the ground motions at the supports of a 

long bridge or tunnel. However, experience has shown that the effect of the first three phenomena is 

usually very small and may be ignored, with the exception of the wave passage effect on long span 

structures. The most important factor contributing to differential ground motion is likely to be variability 

in the soil conditions from support to support. It is most important to include this factor when developing 

spatially varying, multiple support motions for use in time history analyses. Both displacement and 

acceleration time histories may be required to correctly model the response of a bridge, although some 

computer programs will compute one from the other if both are not available. Approximate methods that 

use a modified response spectrum to account for the spatial variability of ground motions, thereby 

avoiding time history analysis, have been proposed but not yet been shown to be reliable. 
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3.3.12 Vertical Ground Motions 

The subject of vertical ground motions sometimes leads to heated debates among academics and 

practicing engineers. An in-depth discussion on this subject is outside the scope of this document. A 

brief discussion of the issues surrounding vertical ground motion is given below. 

1) Few structural design codes and specifications and essentially no geotechnical design provisions 

require consideration of vertical ground motions. 

2) Vertical design spectra are not available from the USGS National Seismic Hazard mapping 

program. If vertical motions are to be considered in design, project-specific generation of vertical 

ground motions and/or spectra will be necessary.

3) The method of most technical merit for the development of a vertical ground motion spectrum 

makes use of the magnitude and distance data from the deaggregation of the hazard curve and an 

appropriate attenuation relationship to develop a period dependent V/H (vertical to horizontal) 

ground motion spectrum ratio. This V/H function can then be applied to the horizontal design 

spectrum to generate a target vertical spectrum for design.

4) In many situations (particularly for the CEUS) an appropriate attenuation relationship for vertical 

ground motions may not exist. In these circumstances, the rule of thumb of scaling the horizontal 

design response spectrum by 2/3 can be used to develop a target vertical spectrum for design 

However, this rule-of-thumb can break down at high frequencies (i.e. at spectral periods less than 

0.15 second), especially where the site to seismic source distance is less than 50 km. Use of the 

2/3rds rule-of-thumb procedure for bridges with short fundamental periods and close to active faults 

is therefore not advised. 

Some investigators have suggested the use of one-dimensional wave propagation theory to account for the 

influence of local soil conditions on vertical ground motions. However, it is not clear that onedimensional wave propagation theory (the most common approach in a site-specific response analysis – 

see Chapter 5 of this report) is the proper approach to account for the impact of local soil conditions on 

vertical ground motions. Experience indicates that modeling the propagation of compressional waves 

using a one-dimensional soil column model usually leads to unrealistic vertical motions, especially at 

high excitation levels. Until further studies are available, it is recommended to rely on empirical 

adjustments for local soil effects (e.g. establishing the spectral period-dependent V/H ratio based on 

attenuation relationships) when developing acceleration spectra for vertical ground motions if they are 

required for analysis. 
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3.4 DEVELOPMENT OF AASHTO ACCELERATION RESPONSE SPECTRUM 

In most situations, the seismic design of a conventional bridge is based on the 1,000-yr return period 

national seismic hazard maps developed by the USGS for AASHTO in 2007. These maps provide the 

spectral acceleration at periods of 0.0, 0.2, and 1.0 seconds for use in constructing the acceleration design 

response spectra shown in Figure 3-11 in accordance with the AASHTO LRFD Specifications (2007, 

2009). The FHWA Retrofitting Manual (2006) uses the same maps and procedure. 

1,000-yr return period maps were not part of the original 2002 National Seismic Hazard mapping project 

but were developed by USGS specifically for AASHTO. Originally only available on a special CD 

provided by AASHTO, the computer program and database developed by USGS for AASHTO to

evaluate the 1000-yr return period ground motions is now available for download from the USGS seismic 

hazard website at http://earthquake.usgs.gov/hazards/designmaps/aashtocd.php . The program provides 

spectral accelerations for the reference AASHTO weak rock site class, Site Class B, along with routines 

for adjusting these reference site values for local site conditions based upon Vs30 using the procedure 

described in Section 3.5.5. Values of spectral accelerations for a 1,000 year return period from the most 

recent National Seismic Hazard map can also be obtained from the USGS website if the owner decides to 

use this data in design. The balance of this section steps through the use of both the USGS website and 

the USGS/AASHTO CD ROM to evaluate the 1,000-yr return period design response spectra and use of 

the USGS website for estimation of the associated magnitude deaggregation.

In some special cases, e.g. for major bridge projects or in regions where there have been significant 

advances in the understanding of the local seismic environment since development of the USGS National 

Seismic Hazard maps, a site-specific seismic hazard analysis may be justified. In such cases, the 

qualified professionals conducting the site-specific analysis can provide the designer with the uniform 

hazard response spectra for any desired return period and the associated magnitude deaggregation for any 

specified spectral period. However, unless an attenuation relationship that accounts for local site 

conditions (e.g. one or more of the Next Generation Attenuation relationships described in Section 3.5) is

employed in the seismic hazard assessment, the results must still be corrected for local site conditions. 

This correction can be accomplished using either the procedure described in the next section to correct the 

spectral acceleration values for Vs30 or a site-specific seismic response analysis as described in Chapter 5. 

Furthermore, if a modal superposition structural analysis is going to be conducted, the AASHTO design 

spectra must still be generated from the site-corrected spectral acceleration values as described in the 

Section 3.3.8 of this chapter. 
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3.4.1 Use of the USGS Website

To obtain the anchoring points for the AASHTO 1,000-yr response spectrum (or for any other desired 

return period) from the USGS website, the Seismic Design Values for Buildings option at 

http://earthquake.usgs.gov/research/hazmaps/design/ must be used. Figure 3-17 shows the initial screen 

for this page of the website. 

 

Figure 3-17 Initiation Screen for the Seismic Design Values for Buildings option 

Clicking on the link for the Java Ground Motion Parameter Calculator – Version 5.0.8 (4.6 MB), circled 

in bold at the bottom of the screen shown in Figure 3-17, will bring up a dialog box for this application. 

Clicking on the OPEN button in the dialog box brings up the screen shown in Figure 3-18 for Seismic 

Hazard Curves, Response Parameters, and Design Parameters. 
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Figure 3-18 Initial Screen for Seismic Hazard Curves and Uniform Hazard Response Spectra 

Clicking the OKAY button on the lower right of Figure 3-18 brings up the basic input screen shown in 

Figure 3-19. The essential information for obtaining the reference site class (Site Class B) peak ground 

acceleration and spectral accelerations for 0.2 second and 1 second periods for the 1,000-yr return period 

(or any other return period desired) is input on this screen. To obtain values for the 1,000-yr return 

period, the “Probabilistic Seismic Hazard Curve” option in the pull-down menu at the top of the screen in 

Figure 3-19 must be selected. This will bring up the screen shown in Figure 3-20. 

The latitude and longitude for the site is entered into the appropriate boxes in the center of the screen in 

Figure 3-20 and a 1,000-year return period is selected in the drop down menu at the bottom of the screen. 

(Note: the search by zip codes option is not recommended, as some zip code areas are excessively large.) 

Then, by clicking on the CALCULATE button at the very bottom of the screen, the screen shown in 

Figure 3-21 will appear. The data points for the PGA seismic hazard curve and the singular value for 

PGA corresponding to a 1,000-yr return period are provided in this screen. For illustration purposes, the 

San Francisco-Oakland Bay Bridge East Span location was arbitrarily chosen as the input location for the 

screen shown in Figure 3-20. The coordinates employed in the demonstration (latitude 37.814o north and 

longitude -122.359o west) corresponds to the far eastern point of the East Span at Yerba Buena Island. As 
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shown in Figure 3-21, the PGA corresponding to a 1,000-yr return period for the Site Class B reference 

condition at this location is 0.571 g. The reference site condition spectral accelerations for periods of 0.2 

and 1 second are then generated by selecting “Hazard Curve for 0.2sec” and “Hazard Curve for 1.0sec” 

from the Seismic Hazard Curve drop down box near the bottom of the screen of the left hand side and 

clicking the calculate button for each of the seismic hazard curves. The resulting screens, shown in 

Figure 3-22 and Figure 3-23, show that for the Site Class B reference condition at this location and a 

1,000-yr return period the spectral acceleration for 0.2 second period is 1.386 g and the spectral 

acceleration for 1.0 second period is 0.608 g. 

Figure 3-19 Input Screen for Seismic Hazard Curves, Response Parameters, and Design Parameters
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Figure 3-20 Input Screen for Probabilistic Hazard Curves

Figure 3-21 Screen for PGA for 1000-yr Return Period 
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Figure 3-22 Screen for 0.2 sec Spectral Acceleration for 1000-yr Return Period 

Figure 3-23 Screen for 1.0 sec Spectral Acceleration for 1000-yr Return Period 
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The PGA and spectral accelerations for the Site Class B reference site condition must still be adjusted for 

site-specific ground conditions using the Site Class factors presented in Tables 3-6, 3-7 and 3-8. 

Assuming Site Class C for illustration purposes, Table 3-6 yields a value for Fpga, the PGA site factor, of 

1.0 for PGA values in excess of 0.5 g. Table 3-7 yields a value for the Fa, the short period site factor, of 

1.0 for short period (0.2 second period) spectral accelerations in excess of 1.25 g. Table 3-8 yields a 

value of Fv, the long period site factor, of 1.3 for spectral accelerations at 1.0 second in excess of 0.5 g. 

To calculate the appropriate spectral values for Site Class C, the PGA is multiplied by Fpga (i.e. multiplied 

by 1.0 for this example) the 0.2 second spectral acceleration is multiplied by Fa (i.e. multiplied by 1.0 for 

this example), and the 1.0 spectral acceleration is multiplied by Fv (1.3 for this example). Applying these 

site factors to the reference site class (Site Class B) values yields a site class-corrected value of 0.571 g

for the PGA, 1.39 g for the spectral acceleration at 0.2 second, and 0.792 g for the spectral acceleration at 

1.0 second for Site Class C at the example site for a 1,000-yr return period. 

The Site Class C PGA and spectral accelerations can then be used to construct the AASHTO design 

spectrum in accordance with Figure 3-11. As shown in this figure, the anchoring periods for the plateau 

of the ASSHTO spectrum, Ts and T0, are calculated as follows: Ts is calculated as the spectral 

acceleration at 1.0 second divided by the spectral acceleration at 0.2 second and T0 is calculated as 0.2 Ts. 

For the example above, this procedure yields Ts = 0.792/1.39 = 0.57 second and T0 = 0.2Ts = 0.11 second. 

The resulting AASHTO design spectrum for the example site for a 1,000-yr return period for Site Class C 

is shown in Figure 3-24. Spectral acceleration values at spectral periods greater than 0.57 second can be 

calculated by assuming that the spectral acceleration decays as 1/T in this range. Based upon this 

assumption and a spectral acceleration of 0.792 at 1 second, the following values can be calculated for the 

spectral acceleration, Sa, at periods greater than 0.57 g: Sa = 1.056 at T = 0.75 sec; Sa = 0.528 at T = 1.5 

sec; Sa = 0.396 at T = 2 sec; Sa = 0.317 at T = 2.5 sec; Sa = 0.264 at T = 3.0 sec; Sa = 0.198 at T = 4.0 sec. 
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Figure 3-24 Bay Bridge Site AASHTO Design Spectrum for Site Class C Conditions 

3.4.2 Use of the USGS/AASHTO CD 

 

The initial screen for the 1,000-Year Ground Motion CD produced by the USGS for AASHTO is shown 

in Figure 3-25. After clicking the “Okay” button on this initial screen, the screen shown in Figure 3-26

appears. As shown in Figure 3-26, the next step after initiation of the ground motion CD program 

involves inputting the site location, either in terms of the geographic coordinates (latitude and longitude) 

or the zip code. As noted before, use of geographic coordinates is more accurate and the use of the zip 

code option is not recommended. In the following example, we use the same location employed to 

illustrate the AASHTO design spectrum in Figure 3-11: a site in Memphis, Tennessee with latitude 35.18o

north and longitude -89.97o west. After inputting the site location, the desired hazard level is selected (in 

this example, a 7% probability of exceedance in 75 yr, corresponding to the 1,000-yr return period). 

Next, upon clicking the “Calculate PGA, SS, and S1” button, the program provides the three design 

spectrum anchoring points, i.e. the spectral accelerations at 0.0, 0.2, and 1.0 seconds, for the reference 

Site Class B site condition of an average shear wave velocity over the top 100 ft of between 2500 and 

5000 ft/s. For the example site location, the three anchoring points provided by the program are 0.388 g 

for the spectral acceleration at 0 seconds (the PGA), 0.725 g for the short period spectral acceleration, Ss

(i.e. the spectral acceleration at 0.2 second), and 0.185 g for the long period spectral acceleration, S1 (i.e. 

the spectral acceleration at 1 second). 
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Figure 3-25 Initiation Screen in the USGS/AASHTO Ground Motion CD 

Figure 3-26 Screen No. 2: Site Location and Design Hazard Level

Following the evaluation of the spectral accelerations associated with the reference Site Class B site 

condition, the site soil factors are calculated by clicking the “Calculate As, SDs, and SD1” box in Screen 
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2 (Figure 3-26). Upon clicking the “Calculate As, SDs and SD1” box, the screen shown in Figure 3-27

appears showing the NEHRP site factors for site classes A, B, C, D, and E. At this point, the user selects 

the appropriate site class from the box on the left hand side of the screen in Figure 3-27. In this example, 

we elected to conduct the analysis for Site Class D. Upon clicking the “Site Class D” box on the left hand 

side of the screen, interpolated site coefficient factors of Fpga = 1.11, Fa = 1.22, and Fv = 2.06 will be used 

to scale the reference site class (Site Class B) values for the PGA (0.388 g), Ss (0.725g) and S1 (0.185g) , 

to the appropriate site specific values for Site Class D. 

Figure 3-27 Screen No. 3: Site Factor Table.

After clicking the “OK” tab at the lower left corner of Screen 3 in Figure 3-27, the program produces the 

screen shown in Figure 3-28 with a tabulation of the spectral accelerations for the three anchoring periods 

for the Class D design spectrum (As = Fpga x PGA = 0.473; SDS = Fa x SS = 0.884; SD1 = Fv x S1 = 0.381) 

along with the values for the initial reference Class B site condition. 

From the screen in Figure 3-28, the user has the option of plotting the spectrum for the reference Class B 

site by clicking the “Map Spectrum” button or the Site Soil Adjusted spectrum (the Class-D Spectrum in 
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this demonstration) by clicking the “Design Spectrum” button. The user can also click both buttons to 

generate both spectra. 

Figure 3-28 Screen No. 4: Site Class Adjusted Anchoring Points for Design Spectrum 

By clicking the “Map Spectrum” tab, the screen shown in Figure 3-29 (Screen 5) is created with a 

tabulation of the AASHTO reference site (Site Class B) acceleration response spectrum. By clicking the 

“Design Spectrum” tab, the screen shown in Figure 3-30 (Screen 6) is created with a tabulation of the 

AASHTO design spectrum for Site Class D.
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Figure 3-29 Screen No. 5: Reference Site Spectrum Values

Figure 3-30 Screen No. 6: Site Class D Spectrum Values
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At this point, the calculations for both the initial reference site condition (the “Map Spectrum”) and the 

site class adjusted spectrum (the “Design Spectrum”) are complete. In the next step, the AASHTO/USGS 

ground motion CD allows graphical display of the various developed spectra. One can initiate the display 

options by clicking the “View Spectra” button at the bottom the prior screen. Then one can click on the 

Select Graph button from the pull down menu in the subsequent screen (Screen 7) which will display the 

various options listed below: 

1) Map Spectrum for Sa vs. T.

2) Map Spectrum for Sa vs. Sd, (plot spectral acceleration versus spectral displacement).

3) Design Spectrum for Sa vs. T.

4) Design Spectrum for Sa vs. Sd. 

5) All Sa vs. T Spectra (for viewing comparison between the mapped spectrum and the Design 

Spectrum), and 

6) All Sa vs. Sd Spectra.

Figure 3-31 (Screen No. 7) presents the screen obtained when selecting Option 1 above for the Map 

Spectrum for Sa vs. T (for Site Class B). Figure 3-32 (Screen No. 8) presents the screen obtained when 

selecting Option 5, the All Sa versus T Spectra option, and shows both the Map Spectrum (for Site Class 

B) and the adjusted Design Spectrum for Site Class D. Figure 3-33 (Screen No. 9) presents the screen 

obtained when selecting Option 6, the All Sa vs. Sd Spectra option, showing spectral acceleration versus 

displacement for both Site Class B and Site Class D. 
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Figure 3-31 Screen No. 7: Options for Viewing Various Spectra 

Figure 3-32 Screen No. 8: Example of “All Sa vs. T Spectra” Option
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Figure 3-33 Screen No. 9: Example of “All Sa vs. Sd Spectra” Option

3.4.3 Magnitude Deaggregation 

The 1,000-year Ground Motion CD distributed by AASHTO/USGS has been designed solely for 

construction of the 1,000-year return period uniform hazard spectra. There is no provision on the Ground 

Motion CD for extracting the deaggregated magnitude and distance information for design. Currently, 

deaggregation of the design earthquake, including for the 1,000-year return period event derived from the 

AASHTO/USGS Ground Motion CD, needs to be conducted through the USGS web site. The following 

link will take the user to the USGS deaggregation web page: http://eqint.cr.usgs.gov/deaggint/. The 

screen associated with this link is shown below in Figure 3-34. 
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Figure 3-34 Initial Screen from the USGS Web Site for Interactive Deaggregation

The deaggregation data for the AASHTO design seismic hazard design event (i.e. for a 100-yr return 

period and the 2002 USGS seismic hazard data) can be obtained by clicking on the “Interactive 

Deaggregation 2002” button on the left hand side of the screen shown in Figure 3-34. Clicking on the 

2002 deaggregation button leads to screen shown in Figure 3-35. On this screen, the user inputs the site 

location and selects the desired hazard level (similar to screen 2 from the USGS/AASHTO CD ROM) as 

well as the spectral frequency (the inverse of the spectral period) for which the deaggregation is desired. 
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Figure 3-35 Screen for Specifying Location and PSHA Return Period

After specifying the ground motion parameters for deaggregation and clicking the Generate Output tab on 

the screen in Figure 3-35, the screen shown in Figure 3-36 appears. The screen shown in Figure 3-36

allows the user to select one of the three types of output files: 

1) Report 

2) Deaggregation

3) Geographic deaggregation 
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Figure 3-36 Available Interactive Deaggregation Results

Figure 3-37 and Figure 3-38 show the screens that will appear following clicking the Deaggregation tab 

and the Geographic Deaggregation tab, respectively. Figure 3-37 is a bar chart of the magnitude/distance 

deaggregation from which the designer can extract magnitude and distance combinations appropriate for 

design. The report tab provides tabular output for this data. Figure 3-38 plots the magnitude distribution 

on a map and can be used to clarify the specific seismic sources contributing to the seismic hazard. Note 

that the plots in Figure 3-37 and Figure 3-38 show a bi-modal hazard, with half the hazard coming from 

an earthquake on the Hayward fault with a characteristic magnitude of 7 and half the seismic hazard 

coming from an event on the San Andreas fault with a characteristic magnitude of 7.9. 
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Figure 3-37 Hazard Deaggregation for Combinations of Magnitude and Distance

Figure 3-38 Geographic Hazard Deaggregation 
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3.5 RECENT ADVANCES IN ENGINEERING SEISMOLOGY AND GROUND MOTION 

CHARACTERIZATION 

One of the most significant recent developments in engineering seismology and ground motion 

characterization is the Next Generation Attenuation (NGA) project sponsored by the National Science 

Foundation, Caltrans, and Pacific Gas and Electric Company. This project has recently completed an 

update of the commonly used attenuation models for shallow crustal earthquakes in active tectonic 

regions (e.g. the WUS). The 2009 USGS National Seismic Hazard Maps have implemented this new 

generation of attenuation relationships. The same consortium has embarked upon a similar update for 

CEUS attenuation relationships. Subsequent phases of the NGA project, hopefully including attenuation 

relationships for subduction zones, will most likely lead to further updates in the USGS ground motion 

hazard maps for U.S. 

The NGA project is being coordinated by the Lifelines Program of the Pacific Earthquake Engineering 

Research Center (PEER), in partnership with the U.S. Geological Survey and the Southern California 

Earthquake Center. In the developing attenuation relationships for the WUS, five sets of ground-motion 

models were developed by teams working independently but interacting with one another throughout the 

development process. The development of these WUS NGA ground motion models was supported by 

other project components, including (1) development of an updated and expanded PEER database of 

recorded ground motions, earthquake sources, travel path, and recording station site conditions (see 

http://peer.berkeley.edu/products/strong_ground_motion_db.html); (2) supporting research projects to 

provide guidance on the selected functional forms of the ground motion models; and (3) a program of 

interactions throughout the development process to provide input and reviews from both the scientific 

research and engineering user communities. A special February, 2008 issue publication of the EERI 

Earthquake Spectra provides documentation of this initial phase of the NGA project (e.g. Abrahamson et 

al., 2008). 

The NGA models have increased the level of sophistication required to apply attenuation equations. Four 

of the five NGA attenuation models (all but the Idriss model) require many more input parameters than 

the traditional parameters of magnitude, distance, and style of faulting in their attenuation equations. The 

average engineer may not have sufficient understanding on what some of these parameters mean and 

there is no easy way to measure some of the required input parameters. With the exception of the Idriss

NGA model, there are as many as 15 parameters involved in the NGA models. An important facet of the 

NGA models is that they account for the influence of local site conditions directly by using Vs30 as one of 
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the input parameters in the attenuation model (as opposed to the use of site factors to modify the reference 

site spectrum). Two of the NGA models also use the depth to a shear wave velocity of 3300 ft/s (1000 

m/s) and another model uses the depth to a shear wave velocity of 8250 ft/s (2500 m/s) as discriminating 

factors that reflect local site conditions. 

Two and three dimensional site response effects and deep soil basin effects are also a subject of much 

current research, as is the response of other types of stratigraphic profiles that do not conform to 

stratigraphy assumed in the development of the NEHRP site factors. Observed multi-dimensional site 

response effects include Basin Edge effects, wherein the ground motions around the edge of a soil basin 

are influenced by the direction of the propagating seismic wave (i.e. from within the basin or from outside 

of the basin). However, there are no simple methods to account for the effects of wave propagating to the 

site from outside the basin edge at the present time. Site response analyses have also shown that response 

of deep soil basins (i.e. basins with over 500 ft of sediments) and of soil sites with a bedrock interface or 

other layer interface across which there is a significant contrast in soil stiffness and density within 150 to 

200 ft of the ground surface is not properly described by the NEHRP soil site factors. These deep soil 

basin and shallow bedrock conditions can be accounted for using appropriate one-dimensional site 

response analysis, as discussed in Chapter 5 of this document. 

The near-fault directivity effect (e.g. Sommerville et al., 1997) discussed previously is another area of 

current research and development. This effect has been included in development of input ground motions 

for seismic retrofit of the long-span bridges in California for over 10 years (starting from about 1995). 

Inclusion of the near field effect using a 1995 Somerville procedure drastically impacted the response of 

several of these bridge structures, leading to a very significant increase in retrofit cost. However, 

subsequent developments, e.g. the Sommerville 1997 near-fault forward directivity adjustment procedure, 

suggest that the 1995 Sommerville near-fault directivity adjustment procedure was overly conservative 

(Abrahamson, 2000). This lesson suggests that one needs to be careful in implementing new state-of-theart procedures in design until these procedures have been properly vetted.
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3.6 SUMMARY

This chapter describes the methods used to assess and characterize strong ground motions for use in 

seismic design. The fundamental steps in a seismic hazard analysis are described, including seismic 

source characterization, strong motion attenuation, and prediction of design ground motion parameters. 

Both probabilistic and deterministic seismic hazard analyses are described and the advantages and 

disadvantages of these two types of analysis are discussed. A detailed discussion of strong ground motion 

attenuation relationships is provided along with examples of common attenuation relationships for the 

tectonic regimes encountered in the United States. Application of a typical attenuation relationship, the 

Abrahamson and Silva (1997) relationship, is illustrated through an example. The essential products of a 

probabilistic seismic hazard analysis, including the development of uniform hazard spectra and the 

associated magnitude-distance deaggregation, are described in detail. Uniform hazard spectra describe 

the intensity of seismic loading. The magnitude-distance deaggregation is used to establish a 

representative magnitude and distance for use in design. Development of acceleration response spectra 

for deterministic scenario earthquakes is also described. The selection of the design earthquake for both 

safety and functionality is discussed. 

The procedure for developing the acceleration response spectra for structural design in accordance with

AASHTO seismic design provisions, including adjustments for local soil conditions, is presented. A 

correlation between spectral acceleration and peak ground velocity and an equation for deriving the 

displacement spectra from the acceleration response spectra are included in the discussion of seismic 

design input parameters. The importance in design of a variety of special considerations, including nearfield fault directivity effects, vertical motions, and the spatial variability of ground motions, is discussed. 

The procedures used to select a suite of representative time histories for use in time-domain analysis is 

presented. Step-by-step procedures are presented for developing the AASHTO 1,000-year return period 

acceleration response spectra for safety-level design of transportation facilities from the USGS web site 

and the special CD prepared by the USGS for AASHTO. Finally, current topics in seismic hazard 

assessment, including the development of the next generation attenuation (NGA) equations under the 

auspices of the Pacific Earthquake Engineering Research (PEER) Center are discussed. 

Design ground motion parameters developed in accordance with the methods described in this chapter, 

are essential input to structural and geotechnical seismic design analyses. These parameters include the 

value of peak parameters (e.g. peak ground acceleration, peak ground velocity), acceleration and 

displacement response spectra, and representative time histories. The most common type of structural 
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analyses for seismic design, described in a companion document on seismic design of bridge structures, 

employs the acceleration response spectra described in this chapter as input. More sophisticated 

structural analyses may require the design earthquake displacement spectra or a suite of representative 

acceleration time histories, developed as described in this chapter, for input. The representative 

acceleration time histories described in this chapter are also essential input for the one-dimensional site 

response analyses described in Chapter 5 and the soil-structure interaction analyses described in Chapter 8 

of this document. Peak ground acceleration, peak ground velocity, and deaggregated magnitude data for 

the design earthquake, developed as described in this chapter, are essential input to the geotechnical 

hazard analyses described in Chapter 6, the earthwork and foundations seismic performance analyses 

described in Chapters 7 through 12, and the buried structure performance analyses described in Chapter 

13. 

 
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CHAPTER 4

SITE CHARACTERIZATION 

4.1 INTRODUCTION 

This chapter describes site characterization for the seismic design of geotechnical transportation features, 

including structural foundations, earth retaining structures, earthworks, and underground structures. The 

relevant soil parameters for seismic site characterization, their importance for seismic analyses, and the 

available evaluation techniques are described in detail. It is assumed that the basic geological, 

geotechnical, and hydrological investigations required for the general design of the structural foundation

or feature under consideration have been (or will be) conducted according to the state of practice. 

Therefore, the emphasis of this chapter is on the supplemental information required for seismic design 

Soil parameters required for seismic analyses include the initial (small strain) dynamic shear modulus, the 

small strain viscous damping ratio, shear modulus reduction and strain-dependent hysteretic damping 

characteristics, dynamic shear strength and liquefaction resistance parameters, and post-liquefaction 

residual shear strength. 

Three broad categories of site investigation activities can be included in a subsurface exploration 

program. The first category is a conventional geotechnical boring program, including laboratory testing 

on undisturbed or remolded samples. The second category is in situ testing, wherein the parameters that 

describe soil properties are estimated in situ using penetrometers and other types of probes and invasive in 

situ testing devices. The third category is geophysical exploration. Conventional geotechnical site 

characterization techniques using all the three categories of site investigations are discussed in detail in 

other FHWA and Transportation Research Board publications (e.g. FHWA 2002, 2002a, 2006; Mayne, 

2007). Only brief discussions of these conventional techniques as they relate to characterization of a site 

for seismic studies are presented herein. However, special attention is paid to the use of the cone 

penetrometer for site investigation due to its utility and reliability and the availability of recentlydeveloped correlations with engineering properties that many geotechnical engineers are still unfamiliar 

with. 
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4.2 SUBSURFACE PROFILE DEVELOPMENT

4.2.1 General

As for all geotechnical engineering analyses, seismic analysis requires knowledge of the subsurface 

profile, or stratigraphy, at the site under study. The required stratigraphic information includes data on 

the water level, soil layering, and the depth to the underlying bedrock. Stratigraphy can be obtained using 

classical investigation techniques (field reconnaissance, geologic mapping, test pits, drilling and 

sampling), in situ tests, or by geophysical means.

As in many other geotechnical problems, identification and quantification of relatively thin, weak layers 

in the soil or rock can be an important part of seismic site characterization. However, the "weak" layer in 

a seismic analysis may differ from the "weak" layer in a static analysis. For instance, a saturated sand 

layer considered a suitable foundation material with respect to static loads may be susceptible to 

liquefaction under earthquake loads and thus becomes a weak layer in a seismic analysis. In other cases, 

such as soft material between beds of rock or stiff soil on a hillside, the same material that is a weak 

material for static analyses may also represent a potential problem under earthquake loads. Therefore, 

attention must be paid to characterize these thin layers in the site exploration program, e.g. through the 

use of continuous sampling or CPT soundings that yield a continuous stratigraphic profile. 

4.2.2 Water Level 

Groundwater may play an important role in seismic analysis, particularly if the soil deposits are 

liquefiable. Therefore, accurate characterization of the groundwater level (or levels) is an essential part of 

seismic site characterization. Furthermore, seasonal variability in the water level should be considered in 

developing the stratigraphic profile and performing liquefaction potential analyses.

Groundwater level information is often obtained by observation of the depth to which water accumulates 

in an open borehole. However, water level observations in boreholes may be unreliable due to a variety 

of factors, including:

• Insufficient time for equilibrium in borings in fine-grained soils;

• Artesian pressures in confined aquifers; and 

• Perched water tables in coarser soils overlying fine-grained deposits. 
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Furthermore, borehole observations do not, in general, permit observations of seasonal fluctuations in 

water levels. Piezometers or observation wells installed in a borehole provide a much more reliable 

means of monitoring water levels in the subsurface. In deposits where layers of fine-grained soils are 

present and multiple water levels are suspected, multiple-point piezometers can be installed in a single 

borehole or multiple boreholes of different depths can be fit with single point piezometers.

A cone penetrometer with pore pressure measuring capabilities, referred to as a piezocone, can also be 

used to estimate water level elevations. By holding the cone at a constant elevation and waiting until the 

pore pressure drops to a constant value, the piezocone can be used to determine the steady state pore 

pressure at a specified elevation at the time of exploration. The potential for perched water tables or 

confined aquifers can be assessed with the piezocone by combining steady-state pore pressure readings at 

several elevations with stratigraphic information developed from the tip and sleeve resistance of the cone.

Geophysical stratigraphic profiling methods used in seismic site investigation are generally not used to 

evaluate the depth to groundwater. Geophysical methods used to evaluate soil stratigraphy and soil 

properties for seismic design are often targeted towards shear wave or Rayleigh wave velocity and thus 

are generally insensitive to the water level. Some resistivity methods (e.g., down hole resistivity surveys) 

can detect the presence of water in the soil pores but cannot measure the pressure in the water. Therefore, 

such methods can neither distinguish between soil above the water table saturated by capillarity and soil 

below the water table in a fine-grained soil nor measure an artesian pressure in a confined aquifer.

4.2.3 Soil Stratigraphy 

The subsurface investigation should provide a detailed description of the soil stratigraphy at the site, 

including the thickness and elevation of the different layers. Potentially liquefiable soils should be clearly 

identified and quantified by one of the methods described later in this chapter. Both conventional boring 

with continuous sampling and in situ testing using the CPT offer the possibility of development of a 

continuous soil profile in which layers as small as 75 mm can be identified. Thin continuous layers of 

weak or potentially liquefiable soil encountered between beds of more competent soil may prove to be the 

critical plane in seismic slope stability analyses. 

Borings offer the advantage of recovery of a physical sample for visual classification and, if desired, 

laboratory testing. In a boring in which continuous Standard Penetration Test (SPT) sampling is 

performed, layers of soil can be visually identified from the sample recovered from the split spoon to 
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develop a stratigraphic profile. However, the SPT blow count, the primary measurement of cohesionless 

soil strength and consistency obtained using the SPT, generally applies only to the gross behavior of a 

relatively large 300 mm interval of the boring and thus cannot be used to characterize the liquefaction 

susceptibility of thin lenses of soil visually identified in the split-spoon sample. 

In the Cone Penetrometer test (CPT) the resistance of the tip and sleeve of the cone to penetration can be 

used to develop continuous profiles of the soil layers and the shear strength of the soil that are applicable 

to layers as thin as 3 in (75 mm). When the CPT is used, soil classification, consistency, shear strength, 

and liquefaction potential are based upon correlation with the tip and sleeve resistance of the cone, as 

discussed subsequently. As discussed previously, a CPT with a pore pressure transducer (a piezocone) 

can also be used to evaluate groundwater conditions. 

Geophysical methods will provide information on the stratigraphy of the soil with respect to the measured 

geophysical property. The measured geophysical property may be a physical property of direct interest in 

a seismic analysis (e.g., shear wave velocity) or may be correlated to a physical property of interest (e.g., 

electrical resistivity and water level). The ability of geophysical methods to resolve layering in the 

ground varies among the available methods. In general, geophysical methods identify contrasts in the 

measured geophysical property. Therefore, if contiguous layers of a stratigraphic profile have the same or 

similar values of the measured geophysical property (e.g. electrical resistivity) they will be characterized 

as a single layer in the geophysical profile. The ability of geophysical methods to delineate stratigraphy, 

in general, decreases with depth unless a down-hole method is used (in which case a boring or in situ 

probe is required).

4.2.4 Depth to Bedrock

Ideally, the soil profile developed for a seismic analysis should extend to competent bedrock, where 

competent bedrock is defined as material with a shear wave velocity of at least 2,500 ft/s (760 m/s) 

(AASHTO Site Class B) and the physical properties of the soil over the entire interval between the ground 

surface and competent bedrock should be defined. However, if competent bedrock is not reachable at a 

reasonable depth, the depth over which the physical properties of the soil for seismic analyses are defined 

should be at least 200 ft (60 m). Furthermore, the depth to which the soil profile is developed should be at 

least as deep as required for conventional geotechnical analyses. However, the results of a seismic 

analysis are generally not sensitive to the properties of the bedrock assuming its shear wave velocity 

exceeds the shear wave velocity of the overlying soil.
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4.2.5 Rock Mass Characterization 

Characterization of the rock mass may be required for seismic stability evaluation of rock slopes and 

seismic design of underground openings. Rock mass characterization may include field mapping, rock 

borings, and geophysical exploration. The most important element in rock mass characterization is 

characterization of the orientation and nature of its discontinuities, including fractures, joints, shear zones, 

and faults. The orientation of discontinuities can be established by field mapping of exposures, logging of 

oriented core, down hole logging of large -diameter boreholes, and borehole geophysical methods such as 

the acoustic televiewer (NCHRP, 2006). The characteristics of the rock mass discontinuities, including 

surface roughness, cementation, and joint filling, are generally evaluated based upon visual examination 

of outcrops and rock core. If fresh rock surfaces are to be exposed by the project, rock durability (e.g. 

slake durability) may also be a concern. Indices of rock quality, including Rock Quality Designation 

(RQD) and the Q-value (Barton, 2002), can be used to quantify rock mass characteristics for engineering 

purposes. 

4.3 REQUIRED SOIL AND ROCK PARAMETERS 

4.3.1 General

At a minimum, a seismic analysis requires the same parameters used to describe soil properties for the 

static analyses of the foundations, earth structures, and underground openings under consideration. 

During the course of a typical geotechnical investigation, the following information is obtained for the 

soil units of interest: 

• Soil classification and index parameters; 

• Unit weight of the soil; and

• Compressibility and shear strength parameters of the soil

For rock units of interest, typical information includes: 

• Unconfined compressive strength

• The orientation and characteristics of the discontinuities

• Durability characteristics (e.g. slake durability)

For seismic design purposes, a series of other soil and rock parameters and properties may need to be 

evaluated. For a seismic analysis, these may include:
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• A measure of the consistency of the soil (e.g. relative density or overconsolidation ratio)

• Shear wave velocity or initial (small strain) shear modulus

• Cyclic stress-strain behavior

• Residual shear strength

4.3.2 Unit Weight and Relative Density

Measures of both the unit weight and relative density of the soil may be required for seismic analysis. 

The unit weight of the soil is used to calculate the total and effective vertical stresses for liquefaction and 

slope stability analyses. Unit weight is also an important parameter in dynamic site response analysis and 

stability analysis, as the inertia force of a soil element is equal to the acceleration times its total weight. 

Total unit weight may be assessed on the basis of measured values from undisturbed samples or from the 

water content and specific gravity of saturated soil.

Relative density is an important parameter with respect to the potential for soil liquefaction and 

seismically-induced settlement of cohesionless soils. The relative density is a measure of the relative 

consistency of the soil. Mathematically, relative density, Dr, is related to the maximum dry density (γd max) 

or minimum void ratio (emin, the densest state to which the material can be compacted) and the minimum 

density (γd min) or maximum void ratio (emax, the loosest state the material can attain) by Equation 4-1: 

%100

1

1

ee

ee D

dmax

dmin

do

dmin

max min

max 0

r





























γ

γ

−

γ

γ −

= −

− = 4-1 

where eo is the in situ void ratio of the material and γdo is the in situ dry unit weight. The relative density 

is an important parameter with respect to liquefaction and seismic settlement potential because it is related 

to the potential for a granular material to decrease in volume when subjected to disturbance.

Relative density is rarely measured directly. Generally, an index of the relative density is measured in 

situ. Commonly used indices of the relative density, or relative consistency, of soil in situ are the SPT 

blow count, N, and the tip and sleeve resistance of the CPT probe, qt, and fs, respectively. 

 
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4.3.3 Shear Wave Velocity

The shear wave velocity of a soil is used to establish the stiffness of the soil at small strains. The small 

strain (initial) shear modulus of a soil, Gmax, is related to the shear wave velocity, Vs, and the mass 

density, ρ, of the soil by Equation 4-2: 

2

max VG S ⋅ρ= 4-2 

 

Mass density of the soil is related to the total unit weight of the soil, γt, by the acceleration of gravity, g, as 

described in Equation 4-3: 

g

t γ =ρ 4-3 

As noted previously, the unit weight of soil or rock can be evaluated from undisturbed samples or, for 

saturated soil, from knowledge of the water content and the specific gravity of the soil solids. The unit 

weight of most soils can also usually be estimated reasonably (+/- 10%) from correlation with CPT 

resistance (as discussed subsequently) or from SPT blow count, soil classification, and location relative to 

the water table. Therefore, measurement of shear wave velocity provides a reliable means for evaluating 

the small strain shear modulus of the soil if the stratigraphic profile is known. 

Small strain (initial) shear modulus is related to small strain Young's modulus, Emax, as a function of 

Poisson's ratio, v, by the theory of elasticity in accordance with Equation 4-4: 

( ) max ν+= G12E max 4-4 

 

For practical purposes, Poisson's ratio of soil can be assumed equal to 0.35 for sands and 0.48 for 

saturated clays. Alternatively, if results of geophysical measurements are available, Equation 4-5 may be 

used to estimate v: 

υ = 1 − 1

2 �1 − �Vs⁄Vp�

2

� 4-5 

 
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where Vs and Vp are shear and compressional wave velocities, respectively. Young's modulus can also be 

evaluated from the compressional wave velocity and mass density of the soil using the analog to Equation 

4-2. Consequently an efficient and reliable means of obtaining the small-strain elastic properties of the 

soil is through the measurement of shear and compressional wave velocities. 

4.3.4 Cyclic Stress-Strain Behavior 

During an earthquake, a soil deposit is subjected to a complex system of stresses and strains resulting 

from the ground motions induced by the earthquake. In general, these stresses and strains will be cyclical 

due to the vibrational nature of the earthquake loading. To evaluate the seismic response of the soil 

deposit, it is necessary to estimate how the soil responds to this cyclic loading.

The earthquake-induced stresses and strains that produce the most damage in soils are generally 

considered to be due to cyclic shearing of the soil. Shear waves propagate primarily upward near the 

ground surface. Therefore, most geotechnical earthquake engineering analyses assume that earthquake 

ground motions are generated by vertically-propagating shear waves.

The cyclic stresses induced on a soil element by a vertically-propagating shear wave, the type of 

earthquake wave most commonly considered in a seismic analysis, are schematically presented in Figure 

4-1. The stress-strain response of soil to this type of cyclic loading is commonly characterized by 

hysteresis. A typical hysteresis loop from uniform cyclic loading of soil is shown on Figure 4-2. Various 

constitutive models have been developed to characterize soil hysteresis loops. The most common model 

used to represent the hysteretic behavior of soil in seismic analysis is the equivalent-linear model (Seed 

and Idriss, 1970). Various non-linear constitutive models (Kondner and Zelasko, 1963; Martin, 1975; 

Matasovic and Vucetic, 1993; Hashash and Park, 2001) have also been developed to represent hysteretic 

soil behavior. Non-linear constitutive models for the hysteretic behavior of soil are discussed in more 

detail in Chapter 5 of this document. 
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Figure 4-1 Stresses Induced in a Soil Element by Vertically Propagating Shear Wave 
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Figure 4-2 Hysteretic Stress-Strain Response of Soil Subjected to Cyclic Loading 

The equivalent-linear model represents non-linear hysteretic soil behavior using an equivalent shear 

modulus, G, equal to the slope of the line connecting the tips of the hysteresis loop and an equivalent 

viscous damping ratio, λ, proportional to the enclosed area of the loop. The equivalent modulus and 

viscous damping ratio depend upon the cyclic shear strain, γc. The shear strain dependence of the 

equivalent modulus and damping ratio are described by the modulus reduction and damping curves shown 

on Figure 4-3. The equivalent viscous damping ratio is evaluated from the area of the hysteresis loop as 

shown on Figure 4-2 and is typically expressed as β, the percentage of the critical damping ratio. 

Modulus reduction and damping curves strictly apply only to uniform cyclic loading. However, these

curves are typically also used to model the soil behavior under irregular (non-uniform) cyclic loading

generated by earthquakes based upon a representative shear strain. 
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Figure 4-3 Shear Modulus Reduction and Equivalent Viscous Damping Ratio Curves 

Cyclic loading can break bonds between soil particles and rearrange the particles into a denser state. In a 

dry soil, this rearrangement will be manifested as compression of the soil and will result in seismic 

settlement. If the soil is saturated, volume change cannot occur instantaneously and the load carried by 

the soil skeleton is transferred to the pore water as the particles are rearranged. If the rearrangement is 

sufficient in magnitude, the soil skeleton can shed its entire load to the pore water, resulting in a pore 

pressure equal to the overburden pressure, complete loss of shear strength, and, consequently, liquefaction 

of the soil.

4.3.5 Peak and Residual Shear Strength

Peak and residual shear strengths are important elements in the evaluation of seismic stability. The peak 

shear strength refers to the maximum shearing resistance an element of soil can sustain during and after 

cyclic loading. The peak shear strength may be used to calculate the yield acceleration of a soil (the 

horizontal acceleration above which permanent seismic deformations begin to accumulate) if buildup of 

seismically-induced pore pressure is not anticipated. Residual shear strength refers to the shear strength 

of the soil after significant static and/or cyclic shearing has occurred. In the context of this document, it is 

also used to represent the shear strength of a soil element after it has liquefied. Residual shear strength 

may be used to evaluate post-liquefaction bearing capacity and stability and to calculate the accumulation 
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of permanent seismic deformation in a post-liquefaction stability and deformation analysis for a 

foundation or earth structure. 

While there is some limited information to indicate that the shear strength of soil increases with increasing 

strain rate, the peak shear strength of soil subjected to cyclic loading is generally assumed to be equal to 

or less than the peak static strength. If the soil is dry, the static drained shear strength may be used. If the 

soil is saturated, even if the soil is relatively free draining, the undrained shear strength should be used for 

seismic analyses because of the rapid nature of earthquake loading. For cohesive soils of low to 

intermediate sensitivity, the static shear strength of the soil may be reduced by 10-15% when subjected to 

large magnitude earthquakes (M > 7) to account for a potential reduction in shear strength due to cyclic 

loading. This potential strength reduction is discussed in more detail in Chapter 6.

The residual shear strength is perhaps the most important parameter with respect to evaluation of the 

impacts of liquefaction. If the static factor of safety against bearing capacity or slope failure is greater 

than 1.0 when evaluated using the residual shear strength, liquefaction-induced deformations may be 

small enough to be acceptable without extensive remediation. If the static factor of safety evaluated using 

the residual shear strength is less than one, large deformations or a flow slide should be anticipated unless 

remedial action is taken. Recent advances in geotechnical earthquake engineering have facilitated much 

more accurate assessment of residual shear strength than possible previously. These recent advances 

allow the residual shear strength to be evaluated as an undrained shear strength that is a fraction of the 

effective overburden pressure. 

4.4 EVALUATION OF SOIL AND ROCK PROPERTIES FOR SEISMIC ANALYSIS

4.4.1 General

The key soil and rock parameters required to perform a seismic analysis are the shear wave velocity, 

modulus reduction and damping curves, peak and residual shear strength, and the soil resistance 

parameters needed to evaluate soil liquefaction potential and seismic settlement. A value for Poisson's 

ratio may also be required. These parameters can either be directly evaluated from laboratory or in situ 

test results or indirectly evaluated by correlation with index properties of soils. Laboratory tests generally 

provide a direct means of evaluating soil parameters for seismic analyses. However, laboratory tests are 

subject to limitations on the recovery and testing of representative samples as well as on the limitations of 

the testing itself. In most cases, in situ testing provides the most reliable and cost effective means of soil 
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and rock property evaluation for seismic analysis. However, in many cases, empirical correlation with 

index parameters is the most practical means of evaluating soil parameters for seismic analyses. 

Sometimes, for particular geographical areas and soils (e.g., Piedmont region residual soils, see Borden, et 

al., 1996) typical dynamic soil parameters have been established.

4.4.2 In Situ Testing 

Standard Penetration Testing (SPT)

Probably the most common in situ test used in geotechnical practice is the SPT. The SPT measures the 

resistance to penetration of a standard split-spoon sampler in a boring. The test method is rapid and yields 

useful data, although there are many factors that affect the results. The procedure used to perform the 

SPT is codified under ASTM Standard D 1586. The SPT consists of driving a standard split barrel 

sampler with a 140 lb hammer dropping 30-in. in a free fall. The sampler is driven 18 inches into the 

bottom of the borehole. The number of hammer blows required to drive the sampler the final 12 inches is 

the uncorrected SPT blow count, N. 

Measurements show that in a typical Standard Penetration Test using a safety hammer and a rope and 

cathead to raise the hammer approximately 60 percent of the theoretical kinetic energy of the free-falling 

hammer is delivered to the drill rods. However, other types of equipment that are allowed within the 

ASTM standard for the SPT typically show a different level of energy efficiency and even for a consistent 

equipment set-up the delivered energy can vary widely not only from site to site but also from blow to 

blow. To compensate for the variability in the average amount of energy delivered by the hammer to the 

drill rod due to the equipment set-up, the uncorrected SPT blow count, N, is generally transformed to N60, 

the SPT blow count standardized to an energy efficiency of 60 percent. Standardization is based either on 

the typical efficiency for the equipment used in a particular test or on the measured delivered energy when 

this information is available. 

SPT blow count also depends on overburden pressure. To provide a basis for comparison of blow counts 

at different depths or overburden pressures, the standardized blow count is sometimes normalized to an 

overburden pressure of 1 ton per square foot, (N1)60 

Although widely recognized as an unsophisticated test, the SPT is performed routinely worldwide and, 

when performed properly, yields useful results. Extensive work has been conducted to understand the 
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limitations of the test and develop reliable correction factors accounting for the influence of vertical 

stress, soil gradation, hammer efficiency, and other factors on test results. Standardized and normalized

SPT blow count values can be used to estimate: 

• The relative density of sand

• Shear strength parameters of cohesionless soils

• Bearing capacity

• Seismic settlement potential of sands

• Liquefaction potential of saturated sands

• Shear wave velocity

Most soil mechanics text books contain correlations relating SPT blow counts to soil shear strength and 

foundation bearing capacity (e.g., Bowles, 1988; Coduto, 2001). SPT blow counts may also be used to 

estimate the relative density of sand and dynamic soil properties (e.g., cyclic resistance against 

liquefaction and residual undrained shear strength) are often correlated to the relative density of the soil. 

The procedure used to account for the effects of energy variations and overburden pressure on the field 

SPT blow counts is presented below. 

Step 1: Evaluate the standardized SPT blow count, N60, i.e. the blow count for a hammer with an energy 

efficiency of 60 percent (60 percent of the theoretical SPT energy is delivered to the drill rod). The 

"standardized" equipment corresponding to an efficiency of 60 percent is specified in Table 4-1. If 

nonstandard equipment is used, N60 is obtained from the equation: 

60 CNN 60 ⋅= 4-6 

 

where C60 is the product of various correction factors. The equation for the global correction factor, C60, 

in Equation 4-6 can be written as:

60 E SS RL CCCHC BD ⋅⋅⋅= 4-7 

where HE is the hammer energy correction factor and CSS, CRL, and CBD are the Sampler Setup, Rod 

Length, and Borehole Diameter factors, respectively. 
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The values for the CSS, CRL, and CBD correction factors recommended by various investigators for some 

common non-standard SPT configurations are provided in Table 4-2 (Richardson, et al., 1995). 

 

The hammer energy correction factor, HE, is a combination of a Non-Standard Hammer Type factor, CHT, 

and a Non-Standard Hammer Weight or Height of Fall factor, CHW: 

 

E HT ⋅= CCH HW 4-8 

Evaluation of CHT and CHW is described in Table 4-2. However, for important projects, HE may be 

calculated directly, by measuring the hammer energy. There are two commercially available methods for 

measuring hammer energy: the Force Squared (F2) method and the Force Velocity (FV) method. 

However, in general the F2 method is not considered as reliable as the FV method and is not 

recommended for correcting SPT blow counts. 

In the FV method, the product of the force times the velocity is integrated over time. The FV method 

requires both load cells to measure the transmitted force to the drill rods and an accelerometer to measure 

the velocity time history of the rods. The equipment for making FV measurements is similar to pile 

driving analyzer equipment for dynamic load testing of driven piles. 

Using the energy measured by the FV method, FVE, the energy correction factor HE may be evaluated as:

max

VE

E F 0.6

F H = 4-9 

 

where Fmax is the theoretical maximum kinetic energy of the SPT hammer (350 ft-lb).
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TABLE 4-1 RECOMMENDED “STANDARDIZED” SPT EQUIPMENT 

(After Seed, et al., 1985 and Riggs, 1986, Reprinted by Permission of ASCE)

Element Standard Specification

Sampler Standard split-spoon sampler with: (a) Outside Diameter, 

O.D. = 2 in (51 mm), and (b) Inside Diameter, I.D. = 1.38 in 

(35 mm) (no room for liners in the barrel)

Drill Rods A or AW-type for depths less than 50 ft (15.2 m); N- or 

NW-type for greater depths

Hammer Standard (safety) hammer with: (a) weight = 140 lbs 

(63.5 kg); (b) drop = 30 in (762 mm) (delivers 60% of 

theoretical free fall energy)

Rope Two wraps of rope around the pulley 

Borehole 4 to 5 in (100 to 130 mm) diameter rotary borehole with 

bentonite mud for borehole stability (hollow stem augers 

where SPT is taken through the stem)

Drill Bit Upward deflection of drilling mud (tricone or baffled drag bit)

Blow Count Rate 30 to 40 blows per minute 

Penetration Resistance Count Measured over range of 6 to 18 in (150 to 460 mm) of 

penetration into the ground 

Notes: (1) If the equipment meets the above specifications, N = N60 and only a correction for overburden is needed.

(2) This specification is essentially the same as the ASTM D 1586 standard.
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TABLE 4-2 CORRECTION FACTORS FOR NON-STANDARD SPT PROCEDURE AND EQUIPMENT

(Richardson, et al., 1995; Youd and Idriss, 1997)

Correction for Correction Factor Reference

Nonstandard Hammer Type and Hammer Release

(DH = doughnut hammer; SH = Safety Hammer;

ER = energy ratio)

CHT=0.75 for DH with rope and pulley

 CHT=1.33 for SH with trip/auto & ER=80

Seed, et al. (1985)

Nonstandard Hammer Weight or Height of Fall 

(H = height of fall in mm; W = hammer weight in kg) 

CHW = 

H · W

63.5 · 762

calculated per Seed, et al. (1985)

Nonstandard Sampler Setup (standard samples with 

room for liners, but used without liners)

CSS = 1.10 for loose sand

 CSS = 1.20 for dense sand 

Seed, et al. (1985)

5 - 13 (Part I)

Nonstandard Sampler Setup (standard samples with 

room for liners, and liners are used) 

CSS = 0.90 for loose sand

 CSS = 0.80 for dense sand 

Skempton (1986)

Short Rod Length CRL = 0.75 for rod length 0 – 13 ft (0-4 m)

 CRL = 0.85 for rod length 13 – 20 ft (4-6 m) 

 CRL = 0.95 for rod length 20 – 33 ft (6-10 m) 

 CRL = 1.0 for rod length 33 – 100 ft (10-30 m) 

 CRL < 1.0 for rod length > 100 ft (30 m) 

Seed, et al. (1983); Youd and Idriss 

(1997) 

Nonstandard Borehole Diameter CBD = 1.05 for 6 in (150 mm) borehole diameter

 CBD = 1.15 for 8 in (200 mm) borehole diameter

Skempton (1986)

Notes: N = Uncorrected SPT blow count.

C60 = CHT ⋅ CHW ⋅ CSS ⋅ CRL ⋅ CBD N60 = N ⋅ C60

CN = Correction factor for overburden pressure. (N1)60 = CN ⋅ N60 = CN ⋅ C60 ⋅ N 
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Step 2: Calculate the normalized and standardized SPT blow count, (N1)60. (N1)60 is the standardized 

blow count normalized to an effective overburden pressure of 1 tsf (96 kPa) in order to eliminate the 

influence of confining pressure. The most commonly used technique for normalizing blow counts is via 

the correction factor, CN, shown in Figure 4-4 (Seed, et al., 1983). However, the closed-form expression 

proposed by Liao and Whitman (1986) may also be used: 

1/2

v

N '

1 9.79C 



 





σ = 4-10 

 

 where σv' equals the vertical effective stress at the sampling point in psf. 

Figure 4-4 Correction Factor for the Effective Overburden Pressure, CN (Seed, et al., 1983, reprinted 

by permission of ASCE) 

 
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As shown in Figure 4-4, the Seed, et al. (1983) effective overburden correction factor curves are 

valid only for depths greater than approximately 10 ft (3 m), or for effective overburden pressures greater 

than approximately 1000 psf (48 kPa). A similar plot presented by Liao and Whitman (1986) suggests 

that CN in Equation 5-10 should be limited to 2.0 at depths greater than 3 m. Once the value of CN is 

estimated, the normalized and standardized blow count is then calculated as:

NC)(N 60N601 ⋅= 4-11 

Other factors, such as grain size distribution, may influence CN (Marcuson and Bieganousky, 1977). 

However, considering the uncertainties involved in the SPT itself, the application of equipment and 

overburden pressure correction factors should be sufficient for engineering purposes. 

Cone Penetration Testing (CPT)

The CPT test involves pushing a standard dimension conical probe into the ground at a standard rate and 

measuring the resistance of the tip of the cone and along the side of the cone to penetration. The cone tip 

resistance, qt, combined with the friction ratio, FR (the ratio between the side resistance, fs, of the cone 

and qt), has been shown to be strongly correlated to soil type and soil strength. In recent years, cone 

penetration testing probes have been fitted with pore pressure cells (piezocones) to measure pore pressure 

during penetrations and pore pressure dissipation after penetration, facilitating in situ measurement of 

consolidation properties and water table depth. The CPT can also be fitted with a geophone for use in 

“down hole” seismic profiling to determine shear wave velocity.

CPT testing is codified as ASTM Standard D 3441. A comprehensive review of CPT equipment, 

procedures, and testing is provided by Mayne (2007). The CPT is relatively easy to perform and provides 

a continuous profile of soil stratigraphy that can be invaluable in identifying the extent of liquefiable soils 

at a site. Figure 4-5 shows the soil classification chart developed by Robertson et al. (1986) based on 

cone penetration resistance readings. Data from the CPT can also be used to establish soil shear strength, 

unit weight, relative density, overconsolidation ratio, shear wave velocity, allowable bearing capacity, and 

for pile design (Mayne, 2007). 
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Figure 4-5 Soil Classification Chart Based on the CPT (Robertson et al., 1986) 

Until recently, correlations between SPT N values and CPT cone resistance were employed to allow for 

the use of CPT data with relationships between SPT values and soil properties (e.g., liquefaction 

potential). Figure 4-6 presents the relationship developed by Robertson et al. (1983) among cone 

resistance, SPT N value, and mean grain size, D50. However, most soil properties, including liquefaction 

potential and shear wave velocity, are now correlated directly with CPT data, eliminating the need for this 

correlation in most situations. 

Figure 4-6 CPT-SPT Correlation Chart (Robertson et al., 1983, reprinted from FHWA-SA-91-043) 
FHWA-NHI-11-032 4-Site Characterization

Seismic Design – Geotechnical Features 4-21 August 2011 

4.4.3 Unit Weight and Relative Density

The total density of soil is usually expressed in terms of total unit weight (total density times the 

acceleration of gravity). Typical values of the total unit weight are often adequate for use in engineering 

analysis. However, a higher degree of accuracy can be obtained by evaluating the unit weight from 

measurements made on undisturbed samples, from the water content and the specific gravity in saturated 

cohesive soils, or from correlations with CPT parameters. Mayne (2007) developed the correlation 

presented in Figure 4-7 between dry unit weight and normalized cone tip resistance, qt1, for uncemented, 

un-aged quartz sands (qt1 is defined in the figure). However, this correlation, developed from the results 

of large-scale calibration chamber tests, has a correlation coefficient, r2

, of only 0.488. The scatter of the 

data in the figure also gives an idea of the accuracy of the correlation.

Figure 4-7 Correlation between Dry Unit Weight and Normalized Cone Tip Resistance (Mayne, 

2007) 

Mayne (2007) developed a more robust correlation for the unit weight of saturated soils as a function of 

shear wave velocity and depth. This correlation, presented in Figure 4-8, includes data from soft to stiff 

clays and silts, loose to dense sands and gravels, and mixed geomaterials. The correlation coefficient for 

the 727 data points in Figure 4-8 is 0.808. By using a correlation between cone penetrometer resistance 

and shear wave velocity (presented subsequently) and assuming a characteristic specific gravity for 
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Seismic Design – Geotechnical Features 4-22 August 2011 

different types of soil, the correlation between cone penetration resistance, saturated unit weight, and 

specific gravity presented in Figure 4-9 was developed. 

Figure 4-8 Correlation among Saturated Weight, Shear Wave Velocity, and Depth (Mayne, 2007) 

Figure 4-9 Correlation among Saturated Weight, CPT Sleeve Friction, and Specific Gravity (Mayne, 

2007) 

Relative density, Dr, is rarely measured directly for geotechnical engineering purposes. Instead, relative 

density is generally derived from correlation with SPT blow count or the CPT resistance. Table 4-4, after 
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Seismic Design – Geotechnical Features 4-23 August 2011 

Terzaghi and Peck (1948), presents a rough correlation between SPT blow count and the relative density 

of sandy soils. 

Kulhawy and Mayne (1990) give the following equation for the relative density, Dr, of cohesionless soil 

as a function of the standardized normalized SPT blow count:

 

%100

CCC

)N( D

5.0

AP OCR

601 ⋅ 



 





⋅⋅ = r 4-12 

where CP is a grain-size correction factor, CA is an aging factor, and COCR is an overconsolidation 

correction factor. These factors may be evaluated as follows:

P D2560C 50 ⋅+= 4-13 





 



 ⋅+=

100

t

A log05.02.1C 4-14 

18.0 COCR = OCR 4-15 

 

where D50 is the grain size, in mm, at which 50 percent of the soil is finer, by weight and t is the time 

since deposition of the soil in years. Coduto (2001) suggest that, in the absence of geologic data, t equal 

to 1000 years and an OCR varying from 1 for loose soils ((N1)60 < 10) to 4 for dense soils ((N1)60 > 50) 

should be sufficient for use with these equations. Alternatively, Mayne (2005) presents the following 

equation, developed using 636 data points from large chamber tests, for the OCR of clean quartz sands as

a function of CPT tip resistance, vertical effective stress (σ’vo), and effective friction angle (φ’):

 

( )





 





− ⋅































































 σ −

































= sinφ 27.0

1

31.0

atm

vo

'

22.0

atm

t

'

e

σ

1 sin 'φ

σ

q 192.0

OCR 4-16 

where σatm is atmospheric pressure. 
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Seismic Design – Geotechnical Features 4-24 August 2011 

TABLE 4-3 RELATIVE DENSITY OF SANDY SOILS (After Terzaghi and Peck, 1948)

Relative Density, Dr

(%)

Penetration Resistance, N

(blows/ft) Descriptive Term

0-15 0-4 Very Loose

15-35 5-10 Loose

35-65 11-30 Medium

65-85 31-50 Dense

85-100 > 50 Very Dense

Figure 4-10 presents the correlation developed by Jamiolkowski et al. (2001) among normalized cone tip 

resistance, relative density, and compressibility for clean sands (less than 15% fines). Carbonate and 

calcareous sands are expected to fall on the high compressibility side of this correlation while silica sands 

should fall on the low compressibility side. 

 

Figure 4-10 Correlation among CPT Tip Resistance, Relative Density, and Compressibility for Clean 

Sands (Jamiolkowski et al., 2001)
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Seismic Design – Geotechnical Features 4-25 August 2011 

4.4.4 Shear Wave Velocity 

General

The initial (small strain) shear modulus, Gmax, required for input to a site response analysis can be 

calculated from the total unit weight and the shear wave velocity of the soil. Shear wave velocity is 

relatively easily and inexpensively measured in the field using geophysical techniques. Therefore, it is 

recommended that shear wave velocity be directly measured in the field. However, for preliminary 

analyses and for projects where the results of the site response analysis are not considered critical, shear 

wave velocity can be estimated based upon soil type and consistency, by using the empirical correlations, 

or from CPT data. Shear wave velocity can also be evaluated in the laboratory using resonant column 

tests. However, field geophysical measurements are generally more reliable and cheaper for estimating 

the in situ shear wave velocity. Thus laboratory testing is rarely used in practice to evaluate shear wave 

velocity on transportation projects. 

Figure 4-11 illustrates the variety of methods commonly used in the field and laboratory to measure shear 

wave velocity. Field measurements of shear wave velocities are typically based on measuring the wave 

travel time along a known propagation path. From knowledge of travel path distance and travel time, the 

velocity is obtained. Wave velocity may be measured using intrusive methods such as boreholes and CPT 

soundings (seismic cone) or non-intrusively using seismic reflection, refraction, and surface wave 

profiling. 

Compressional wave velocity may sometimes be required for seismic analyses. Compressional wave 

velocity can be directly measured in a geophysical test or laboratory test. Alternatively, the 

compressional wave velocity can be calculated from the shear wave velocity and Poisson's ratio using 

Equation 4-5. 

Geophysical Surveys

Geophysical techniques for subsurface exploration are described by Woods (1994) and in FHWA (2002a) 

and FHWA (2006). Geophysical techniques commonly used in geotechnical practice to measure shear 

wave velocity are briefly summarized in the following paragraphs. Two general types of geophysical 

techniques are available to measure shear wave velocities in the field:
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Seismic Design – Geotechnical Features 4-26 August 2011 

• Intrusive techniques whereby measurements are made using probes and sensors that are lowered in 

boreholes or pushed into the ground; and

• Non-intrusive techniques whereby the measurements are made from the ground surface.

Figure 4-11 Field and Laboratory Methods for Evaluating Shear Wave Velocity (FHWA, 2002) 

Borehole Surveys

In a borehole seismic survey, one or more boreholes are drilled into the soil to the desired depth of 

exploration. Wave sources and/or receivers are then lowered into the boreholes to perform the desired 

tests. There are three approaches to borehole seismic surveys:

• Cross Hole Survey: In a cross hole survey, the energy source is located in one boring and the 

detector (or detectors) is placed at the same depth as the energy source in one or more surrounding 

boreholes at a known spacing. Travel time between source and receiver is measured to determine 

the wave velocity. The cross hole survey method is illustrated at the bottom left of Figure 4-11. 
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Seismic Design – Geotechnical Features 4-27 August 2011 

• Down Hole Survey: In a down hole survey, the energy source is located on the surface and the 

detector, or geophone, is placed in the borehole. The travel time is measured with the geophone 

placed at progressively increasing depth to evaluate the wave velocity profile. The down hole 

survey method is illustrated in the left-center of Figure 4-11. Seismic cone penetration testing 

(SCPT) is another form of down hole survey. SCPT surveys can be combined with conventional 

cone penetration testing. SCPT testing is illustrated in the center of Figure 4-11. 

• Up Hole Surveys: Up hole surveys are similar to down hole surveys except that geophones are 

placed on the surface adjacent to the borehole and the source in the borehole. The energy source 

usually is set off within the borehole at successively decreasing depths starting at the bottom of the 

hole. The energy source may be either explosives or a mechanical pulse instrument composed of a 

stationary part and a hammer held against the side of the borehole by a pneumatic or hydraulic 

bladder. 

The cross hole technique generally offers the highest resolution and greatest accuracy among the three 

types of borehole geophysical surveys. However, cross hole measurements require a very precise 

evaluation of the distance between the energy source and the detector. An inclinometer reading is 

generally performed in the boreholes used in a cross hole survey to correct the results for deviation of the 

boreholes from verticality. Cross hole geophysical testing is codified in ASTM Standard D 4428. 

Seismic Refraction and Seismic Reflection Methods

Seismic refraction and reflection exploration surveys are conducted from the surface and do not require 

boreholes. Seismic refraction surveying is illustrated on the right hand side of Figure 4-11. The 

resolution of these methods is relatively poor and decreases with depth. These methods are most suitable 

as a means of identifying the depth to competent rock and the location of prominent soil horizons that 

have a large contrast in density and stiffness compared to the overlying soil as opposed to making precise 

measurements of in situ wave velocities.

Spectral Analysis of Surface Waves (SASW)

Spectral Analysis of Surface Waves (SASW) is a non-intrusive geophysical technique used primarily for 

evaluating subsurface shear wave velocity profiles. SASW testing evaluates shear wave velocity 

indirectly by direct measurement of Rayleigh, or surface wave, velocity. Rayleigh wave velocity is 
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Seismic Design – Geotechnical Features 4-28 August 2011 

related to shear wave velocity by Poisson's ratio. The two velocities are usually within 5 percent of each 

other for most soils. SASW can be a very cost-effective method of investigation. Excitation at the 

ground surface is used to generate the Rayleigh, or surface, waves at various frequencies. By spectral 

analysis of the ground surface response (velocity or acceleration) at two points a known distance apart, 

the Rayleigh wave velocity can be obtained at discrete frequencies. Usually, an inversion process (trial 

and error) is used to determine the velocity profile. The ease and rapidity of field measurements and 

automated algorithms for data processing and inversion allow for evaluation of subsurface conditions at a 

relatively large number of points at a fraction of the cost of conventional intrusive exploration techniques.

Measurements are not affected by the depth to the water table.

The concept of measuring the velocity of Rayleigh waves of different frequencies to determine the profile 

of shear wave velocity with depth was first proposed by Jones (1962), in Great Britain, for pavement 

surveys and by Ballard (1964), at the Waterways Experiment Station in Vicksburg, Mississippi, for 

geotechnical analyses. These investigators used impact loading as the source excitation and developed an 

analysis based upon the assumption of a uniform, homogeneous layer. Stokoe and Nazarian (1985) at the 

University of Texas, Austin, extended the analysis to consider multi-layered media. SASW surveys can 

resolve the shear wave velocity profile to depths in excess of 200 ft when heavy equipment or large 

electro-hydraulic vibrators are used to generate the surface excitation. 

 

4.4.5 Cyclic Stress-Strain Parameters

Laboratory Testing 

Laboratory testing for evaluation of cyclic stress-strain parameters of soil is appealing to many engineers 

because direct measurements are made of the hysteretic stress-strain behavior of soils. However, cyclic 

laboratory testing is subject to a variety of constraints, including:

• Difficulty in reproducing field stresses (and strains);

• Difficulty in recovering and testing undisturbed cohesionless soil samples; and 

• The time and expense associated with cyclic laboratory testing.

A brief summary of the different types of cyclic laboratory tests used in geotechnical practice and their 

advantages and limitations follows. More details on cyclic laboratory testing can be found in Kramer 

(1996). 
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Seismic Design – Geotechnical Features 4-29 August 2011 

Cyclic Direct Simple Shear Test

The cyclic direct simple shear (CyDSS) test may provide the most accurate representation of the stress 

state resulting from a vertically propagating shear wave in a horizontally layered soil deposit of any 

laboratory test (see Figure 4-1). The simple shear device consists either of a rectangle box made of 

hinged plates, a cylindrical specimen confined by a wire-reinforced membrane, or stacked rings which 

surround the sample and restrain it from deforming laterally during the test. The apparatus includes either 

an arrangement for applying a constant vertical load or for maintaining a constant sample height while 

measuring the vertical load and a mechanism for applying a horizontal cyclic shear load. Reconstituted 

samples are usually formed directly in the simple shear device. However, undisturbed samples of 

cohesive soil or frozen sand can be tested in devices that use wire-reinforced membranes.

Cyclic Triaxial Test

The cyclic triaxial test was developed for geotechnical purposes by Seed and his co-workers at the 

University of California at Berkeley in the 1960s and has been used extensively to evaluate cyclic 

behavior of soils. The device consists of a regular triaxial cell and a cyclic, often sinusoidal loading 

machine attached to the loading piston. The sample is isotropically consolidated in the triaxial cell and 

then subjected to a cyclic axial load in extension and compression. The primary drawback of the cyclic 

triaxial tests is that it does not provide a good representation of the stress state induced in the ground by 

an earthquake (see Figure 5-1 in Chapter 5). The main difference in cyclic triaxial test stress conditions 

compared to the field conditions are: (1) the laboratory soil sample is isotropically consolidated, whereas 

the soil is under a Ko condition in the field; (2) in the field there is a continuous reorientation of the 

principal stresses whereas in the triaxial test, the reorientation angle is either 0 or 90 degrees; (3) the 

cyclic shear stress is applied on a horizontal plane in the field but on a 45 degree plane in the triaxial test; 

and (4) the mean normal stress in the field is constant while the mean normal stress in the laboratory 

varies cyclically.

Torsional Simple Shear Test

In order to overcome some of the limitations of the CyDSS and triaxial tests, Ishibashi and Sherif (1974) 

developed a torsional simple shear test. The sample is a hollow cylinder with outer to inner radius and 

outer to inner height ratios of about two. This shape ensures a relatively uniform shear strain on the 
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Seismic Design – Geotechnical Features 4-30 August 2011 

horizontal plane throughout the sample. The torsional simple shear test offers several advantages over 

CyDSS and cyclic triaxial tests, including: 

• Close simulation of the field stress (and strain) conditions (like the CyDSS); 

• The ability to apply vertical and horizontal stresses independently; and 

• The ability to keep the octahedral normal stress constant during the test.

There are also some disadvantages associated with this test, including: 

• Interpretation of the results is rather complicated and the definition of liquefaction (Ishibashi and 

Sherif, 1974) does not permit correlation of torsional simple shear results with those of other tests;

• Mobilization of enough interface shear between the sample and the top and bottom plates to prevent 

slippage may be difficult, however steel pins cast into porous stones will provide good contact 

between the sample and the plates; and 

• The shape of the sample makes the device impractical for use in conventional practice, particularly 

for undisturbed samples.

Resonant Column Test

The resonant column test for determining the dynamic properties of soils is based on the theory of wave 

propagation in rods. Either compression or shear waves can be propagated through the soil specimen in 

resonant column testing. Solid or hollow specimens can be used in the apparatus. Either a sinusoidal 

torque or a vertical compressional load is applied to the top of the sample through the top cap. The 

deformation of the top of the specimen is measured. The excitation frequency is adjusted until the 

specimen resonates. The wave velocity or modulus is computed from the resonant frequency and the 

geometric properties of the sample and driving apparatus. Damping is determined by switching off the 

current to the driving coil at resonance and recording the amplitude of decay of the vibrations. The decay 

of the amplitude with time is used to determine the logarithmic decrement (the percentage decay over one 

log cycle of time), which is directly related to the viscous damping ratio. 

The primary limitation associated with using resonant column tests to measure dynamic soil properties is 

that the test is generally limited to small to intermediate shear strains by the applied force requirements 

and resonant frequencies. Furthermore, at larger strains, hollow samples must be used to maintain a 

relatively constant shear strain across the sample. For these reasons, resonant column testing is primarily 
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Seismic Design – Geotechnical Features 4-31 August 2011 

used to estimate small strain shear modulus and damping. However, resonant column testing can be 

conducted in the same device as torsional shear test in a device known as a Resonant Column Torsional 

Shear (RCTS) device. An RCTS device can be used to determine both the small strain modulus and 

damping of the soil and modulus reduction and hysteretic damping in intermediate strain range.

Use of Empirical Correlations 

Parameters describing the cyclic soil properties required for a dynamic analyses include the initial (small 

strain) damping, λ, the initial (small strain) shear modulus at small shear strain, Gmax, and the modulus 

reduction and damping curves for the soil. Small strain damping is difficult to evaluate. A viscous 

damping ratio of 2 to 5 percent is commonly assumed as the small-strain damping. The small strain shear 

modulus, commonly referred to as the initial shear modulus, Gmax, can be obtained from site-specific 

investigations or by using empirical correlations with index soil properties. Geophysical methods for 

establishing shear wave velocity (VS), from which Gmax may be determined, were previously described. 

Table 4-4 presents the typical range of VS and of Gmax for several generic soil types.

TABLE 4-4 TYPICAL VALUES OF INITIAL SHEAR MODULUS

Type of Soil Small-Strain Shear Wave 

Velocity, VS (ft/s)

Initial Shear Modulus, 

Gmax (tsf)

Soft Clays 130 - 300 30 - 140

Firm Clays 220 - 460 70 - 360

Loose Sands 420 - 900 290 – 1,440

Dense Sands and Gravel 660 – 1,350 720 – 3,600
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Seismic Design – Geotechnical Features 4-32 August 2011 

The parameter Gmax has been empirically related to both the SPT blow count value and CPT 

resistance. Seed, et al. (1984) suggested that Gmax can be related to standardized and normalized 

SPT blow count, (N1)60, by the following equations: 

0.5

max 2 max m = ⋅ )(σ)K(1000G 4-17 

 

[ ] ( ) 33.0

2 max 1 60 = 20)(K N 4-18 

 

where Gmax is in psf and σ’m is the mean effective normal stress (in psf), evaluated as: 

 

v o ' m

' σ

3

K21

σ ⋅ 



 



 + = 4-19 

Seed et al. (1984) also note that (K2)max can vary from 80 to 180 for loose to dense well graded gravels. 

Imai and Tonouchi (1982) present the following equation for Gmax as a function of the standardized blow 

count, N60: 

 

68.0

max 60 = )(N325G 4-20 

Table 4-5 presents the correlations presented in Equations 4-17 and 4-20 in SI units along with several 

additional index correlations for Gmax. Small strain modulus can also be derived from shear wave velocity 

and unit weight using Equations 4-2 and 4-3. 

Figure 4-12 presents a correlation between CPT tip resistance and shear wave velocity developed by Baldi 

et al. (1989) for clean quartz sands. Figure 4-13 presents a correlation between shear wave velocity and 

CPT tip resistance developed by Mayne and Rix (1995) for clay soils.
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TABLE 4-5 INDEX PROPERTY CORRELATIONS FOR ESTIMATING THE INITIAL 

(SMALL STRAIN) SHEAR MODULUS, Gmax

 
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Seismic Design – Geotechnical Features 4-34 August 2011 

Figure 4-12 CPT – Shear Wave Velocity Correlation for Clean Quartz Sands (Baldi et al., 1989) 

Figure 4-13 CPT – Shear Wave Velocity Correlation for Clay Soils (Mayne and Rix, 1989) 

Damping and normalized modulus reduction curves are generally presented as a function of soil type or 

plasticity index, with a PI = 0 representing cohesionless soil. However, since the modulus reduction 

curve is normalized with respect to the small strain, the absolute value of the shear modulus depends not 

only on shear strain but on the factors influencing the small strain modulus. Traditional modulus 

reduction and damping curves are independent of overburden pressure. Traditional curves still widely 

used in practice include the Seed and Idriss (1970) and Seed et al. (1986) sand curves (presented as a band 

of data, with the mean value typically used in practice), the Seed et al. (1984) gravel curves, and families 

of PI-dependent curves for cohesive soils developed by Sun et al. (1988) and Vucetic and Dobry (1991). 

Subsequent work has shown that both modulus reduction and damping depend upon overburden pressure. 

However, these traditional curves can still be used with good confidence for soil layers in the top 50 ft of 

the profile. 

Iwasaki, et al. (1978) found that the mean normal effective stress is a significant factor influencing 

modulus reduction and damping in cohesionless soils. The stress dependent modulus reduction curves 

developed by these investigators are shown in Figure 4-14. 
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Figure 4-14 Shear Modulus Reduction Curves for Sands. (Iwasaki, et al., 1978, reprinted by 

permission of Japanese Society of Soil Mechanics and Foundation Engineering) 

It is now recognized that it is essential to capture the confining pressure dependence of modulus reduction 

in order to properly model the seismic response of deep soil deposits. In particular, the traditional 

confining pressure independent curves have been shown to significantly over-damp site response in soil 

profiles greater than 300 ft thick, filtering out high frequency motions and attenuating peak accelerations. 

Confining pressure dependent curves frequently used in practice today include families of curves 

developed by EPRI (1993), Hashash and Park (2001), and Darendeli (2001). Figure 4-15 compares upper 

bound, average, and lower bound Seed et al. (1986) confining pressure independent modulus reduction 

and damping curves to the confining pressure dependent curves of Darendeli (2001) for PI = 0. 
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Seismic Design – Geotechnical Features 4-36 August 2011 

Figure 4-15 Comparison of Seed et al. (1985) Modulus Reduction and Damping Curves for Sand with 

Darendeli (2001) Curves for PI = 0. (Darendeli, 2001) 

Figure 4-16 presents the Darendeli (2001) confining pressure dependent modulus reduction and damping 

curves for a PI equal to 30. Figure 4-17 compares modulus reduction and damping curves from Hashash 

and Park (2001), used to model seismic response of soil and weak rock columns in the Mississippi 

embayment over 3000 ft thick, with the EPRI (1993) confining pressure dependent modulus reduction and 

damping curves. EPRI (1993) also provides modulus reduction and damping curves for weak rock. Most 

computer programs for seismic site response analysis will have one or more of these confining pressure 

dependent models built into them. 
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Figure 4-16 Darendeli (2001) Confining Pressure Dependent Curves for PI = 30. (Darendeli, 2001) 
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Seismic Design – Geotechnical Features 4-38 August 2011 

 

Figure 4-17 Comparison of Hashash and Park (2001) Modulus Reduction and Damping Curves for 

the Mississippi Embayment with EPRI (1993) curves (after Darendeli, 2001) 

4.4.6 Peak and Residual Shear Strength

The peak shear strength of soil not subject to strength degradation under cyclic loading may be evaluated 

using conventional methods, including laboratory and in situ testing and correlations with soil index 

properties. A key difference in seismic problems compared to static problems is that undrained strength 

parameters are typically used for the strength of saturated soils subjected to cyclic loading, even for 

cohesionless soils (e.g., sands, gravels) because of the relatively rapid rate of earthquake loading.
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Seismic Design – Geotechnical Features 4-39 August 2011 

The undrained shear strength of a soil subject to cyclic loading may be influenced by the amplitude of the 

cyclic deviator stress, the number of applied loading cycles, and the plasticity of the soil. Makdisi and 

Seed (1978) point out that substantial permanent strains may be produced by cyclic loading of clay soils 

to stresses near the yield stress, while essentially elastic behavior is observed for large numbers of (>100) 

cycles of loading at cyclic shear stresses of up to 80 percent of the undrained strength. Therefore, these 

investigators recommend the use of 80 percent of the undrained strength as the “dynamic yield 

strength” for soils that exhibit small increases in pore pressure during cyclic loading, such as clayey 

materials, and partially saturated cohesionless soils. However, the investigators in the NCHRP 12-70 

project found little evidence of cyclic strength loss in cohesive soils during earthquakes and noted that 

cohesive soils also tend to show an increase in undrained shear strength when subject to rapid loading. 

These investigators concluded that, except for earthquakes of greater than magnitude 7 wherein it may be 

prudent to assume a 10-15% strength loss, there was no reason to reduce the undrained shear strength of 

low to intermediate sensitivity cohesive soils to account for cyclic strength loss. 

For saturated cohesionless soils, even relatively modest cyclic shear stresses can lead to pore pressure rise 

and a significant loss of undrained strength. Direct evaluation of the potential for shear strength reduction 

in a saturated or almost saturated cohesionless soil (low plasticity silt, sand, or gravel) subjected to cyclic 

loading would require sophisticated cyclic laboratory testing. Alternatively, a residual strength may be 

assigned to the soil based upon in situ test results. 

The undrained residual shear strength after cyclic loading, Sr, is of critical importance in assessing the 

post-liquefaction stability of a foundation or earth structure. Saturated soils which liquefy typically 

possess some "residual" shear strength even when in the liquefied state. In initially loose soils, this 

residual strength may be very small and of little consequence. In denser soils (particularly in dense 

granular soils which tend to dilate or expand in volume), this residual strength can be high enough to 

render the impact of liquefaction relatively insignificant. For medium dense soils, the residual shear 

strength can be the most important factor in determining whether or not remediation is necessary

Poulos, et al. (1985) proposed a methodology for evaluating Sr based on obtaining high-quality soil 

samples with minimal disturbance. The high-quality samples were tested in the laboratory and the 

laboratory strengths were then adjusted for field conditions using specially developed techniques to 

correct the resulting laboratory Sr values for effects of void ratio changes due to sampling, handling, and 

test set-up. Due to the sensitivity of Sr to even small changes in void ratio, the laboratory techniques 

proposed by Poulos, et al. do not appear to represent a reliable basis for engineering analyses unless very 
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Seismic Design – Geotechnical Features 4-40 August 2011 

conservative assumptions and high factors of safety are employed to account for the considerable 

uncertainties involved. 

Because of the difficulties in measuring steady-state strength in the laboratory, Seed (1987) proposed an 

alternate technique for evaluation of in situ undrained residual shear strength based on the results of SPT 

testing. He back analyzed a number of liquefaction-induced failures from which residual strength could 

be calculated for soil zones in which SPT data was available, and proposed a correlation between residual 

strength, Sr, and (N1)60-cs. (N1)60-cs is a "corrected" normalized standardized SPT blow count, in which the 

normalized standardized (N1)60 value is further adjusted with a correction factor for fines content, Ncorr, is 

applied to generate an equivalent “clean sand” blow count. The original Seed (1987) relationship was 

subsequently updated by Seed and Harder (1990). However, uncertainty due to the large spread of the 

data and the limited number of case studies back analyzed by Seed and Harder (1990) limited the 

usefulness of their work in practice. 

The work of Seed and Harder in back-analyzing case histories of liquefaction flow slides to evaluate Sr

has subsequently been extended by Olsen and his co-workers (Olson and Stark, 2002; Olson and Johnson, 

2008) and Idriss and Boulanger (2007) to develop correlations between the residual undrained strength 

ratio, Sr/σ’vo, and SPT blow count. Olson and Johnson (2008) back analyzed case histories of both lateral 

spreading and liquefaction flow failures to develop relationships between the undrained residual shear 

strength ratio and both the standardized normalized blow count, (N1)60 and the normalized CPT tip 

resistance, qc1. These authors state that they used the average of CPT tip resistance normalization 

procedures suggested by Jamiolkowski et al. (2001) and Tatsuoka et al. (1995) in developing their 

correlation with CPT tip resistance. However, for practical purposes the following normalization 

equation presented in Mayne (2007) can be used: 

( )0.5

vo atm

t

c1 σσ'

q q − = 4-21 

 

The undrained residual shear strength ratio correlations developed by Olson and Johnson (2008) are 

presented in 

Figure 4-18. 
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Seismic Design – Geotechnical Features 4-41 August 2011 

Figure 4-18 Correlation between the Undrained Residual Strength Ratio, Sr/σ’vo and a) standardized 

normalized SPT blow count, (N1)60 and b) normalized CPT tip resistance, qc1 (Olson and 

Johnson, 2008) 

Idriss and Boulanger (2007) also developed correlations between the undrained residual shear strength 

ratio and both SPT and CPT penetration resistance. The SPT correlation developed by Idriss and 

Boulanger (2007) is presented in Figure 4-19. These investigators used the equivalent clean sand blow 

count of Seed and Harder (1990), (N1)60-cs, presented in Equation 4-22, as their SPT resistance parameter: 

 601 −cs 601 += N)(N)(N corr 4-22 

where Ncorr depends upon the percent, by weight, passing the number 200 sieve as presented in Table 4-6. 
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Seismic Design – Geotechnical Features 4-42 August 2011 

TABLE 4-6 BLOW COUNT CORRECTION, Ncorr, FOR THE EQUIVALENT CLEAN SAND 

BLOW COUNT, (N1)60-cs

 

% passing #200 sieve Ncorr

0-9 0

10-24 1

25-49 2

50-74 4

>75 5

 

Idriss and Boulanger (2007) limit the application of their correlations to an effective overburden pressure 

of 8000 psf. In developing their correlations, Idriss and Boulanger (2007) differentiated between cases 

where void ratio redistribution may be anticipated due to the presence of an overlying confining pressure, 

as illustrated in Figure 4-20, and cases where no void ratio redistribution was anticipated. Figure 4-19

shows their suggested correlation for cases where void ratio redistribution is expected. However, this 

portion of their correlation is supported by few data points and therefore should be used with caution. 

Figure 4-19 Correlation between the Residual Undrained Strength Ratio, Sr/σ’vo and equivalent clean 

sand SPT blow count, (N1)60-CS (Idriss and Boulanger, 2007)
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Seismic Design – Geotechnical Features 4-43 August 2011 

Figure 4-20 Void Ratio Redistribution Due to an Overlying Confining Layer (Idriss and Boulanger, 

2007) 

4.5 ROCK MASS PROPERTIES

4.5.1 Rock Mass Categories 

In a seismic analysis, rock may be treated as either a linear elastic material with a constant shear modulus 

and no damping or as an equivalent linear material with an initial small strain modulus, a slight potential 

for modulus degradation, and a small amount of damping. The elastic modulus for the rock mass is 

generally based upon either shear wave velocity measurements or, in cases where the value of the 

modulus is not critical (i.e. when the modulus is merely used to characterize the impedance contrast at the 

bottom of a soil column), using typical properties. Modulus reduction and damping are typically based 

upon generic equivalent linear modulus reduction and damping curves (e.g. the generic curves for soft 

rock from Silva et al. 1997). 

The shear strength of the rock mass is required for seismic stability analyses. The shear strength of a rock 

mass is, in general, less than the shear strength of the intact pieces of rock. However, the shear strength of 

the intact rock may still influence the rock mass shear strength. For the purpose of characterizing rock 

mass shear strength, rock masses may be divided into two broad categories: highly fractured rock masses 

and rock masses with discrete discontinuities. The shear strength characteristics of both categories of 

rock mass are described below. 
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4.5.2 Highly Fractured Rock Masses

The shear strength parameters for highly fractured rock masses may be determined from either of two 

empirical methods (FHWA 1998a, 2002): (i) An empirical method (i.e. Hoek-Brown failure criterion with 

Geological Strength Index) developed by Hoek (1983) and Hoek and Brown (1988, 1997), and updated 

by Hoek et al. (2002); and (ii) back analysis of a failed or failing slope. The applicability of the HoekBrown method is more suitable for intact rock or heavily jointed rock masses such as the Group I and 

Group III rock mass systems shown in Figure 4-21. Representative values of cohesion and friction angle c

and φ from back analysis of rock mass failures are shown in Figure 4-22. 

The generalized Hoek-Brown failure criterion defining the rock mass strength for jointed rock masses is 

expressed as:

a

ci

ci b sm 















+= +

σ'

'σ σ''σ'σ 3

31 4-23 

where 

σ’1 and σ’3 are the maximum and minimum effective stresses at failure,

mb is the value of the Hoek-Brown constant for the rock mass,

s and a are constants which depend upon the rock mass characteristics, and 

 σci is the uniaxial compressive strength of the intact rock pieces.

As shown by Equation 4-23, the strength of a jointed rock mass depends on the uniaxial compressive 

strength (σci) and other properties of the intact rock pieces as well as upon the freedom of these pieces to 

slide and rotate under different stress conditions. This freedom is controlled by the geometrical shape of 

the intact rock pieces as well as the condition of the surfaces separating the pieces. Angular rock pieces 

with clean, rough discontinuity surfaces will result in a much stronger rock mass than one which contains 

rounded particles surrounded by weathered and altered material. Table 4-7 presents typical field 

estimates of uniaxial compressive strength of intact rock. 

The values of mb, s, and a for use in Equation 4-23 have been correlated to the Geological Strength Index 

(GSI) introduced by Hoek (1994) and Hoek, Kaiser and Bawden (1995). The GSI provides a system for 

estimating the reduction in rock mass strength for different geological conditions. This system is 

presented in Table 4-8. 
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 TABLE 4-7 FIELD ESTIMATES OF UNIAXIAL COMPRESSIVE STRENGTH OF

INTACT ROCK (MARINOS AND HOEK, 2000) 

Once the Geological Strength Index has been estimated, the parameters that describe the rock mass 

strength characteristics for use in Equation 4-23 are calculated as follows:

















− = D

GSI

b mm

1428

100-

exp i 4-24 

where mi is the value of the Hoek-Brown constant for the intact rock shear strength which can be 

obtained based upon the typical values shown in Table 4-9. 
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Figure 4-21 Classes of Rock Mass Discontinuities (FHWA 1998)

Figure 4-22 Relationship between Friction Angles and Cohesive Strength Mobilized at Failure for 

Slopes (Hoek and Bray, 1977) 
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TABLE 4-8 GEOLOGICAL STRENGTH INDEX (GSI) 

FOR JOINTED ROCK MASSES (Hoek and Marinos, 2000) 
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TABLE 4-9 VALUES OF mi FOR INTACT ROCK

BY ROCK GROUP (Marinos and Hoek, 2000) 
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Seismic Design – Geotechnical Features 4-49 August 2011 

The values of s and a are constants for the rock mass and can be evaluated as: 















 = D

GSI

s

3-9

100-

exp 4-25 

and 

















−+=

− −

3

20

15

6

1

2

1

eea

GSI

4-26 

D is a factor which depends upon the degree of disturbance to which the rock mass has been subjected by 

blast damage and stress relaxation as shown in Table 4-10 (Hoek et. al, 2002). 

Table 4-10 ESTIMATION OF DISTURBANCE FACTOR, D (Hoek et. al, 2002) 

Appearance Description of Rock Mass Suggested Value 

Excellent quality controlled blasting or excavation by Tunnel 

Boring Machine results in minimal disturbance to the confined 

rock mass surrounding a tunnel. 

D = 0

Mechanical or hand excavation in poor quality rock masses (no 

blasting results in minimal disturbance to the surrounding rock 

mass.

Where squeezing problems result in significant floor heave, 

disturbance can be severe unless a temporary invert, as shown in 

the paragraph, is placed. 

D = 0

D = 0.5 

No invert 

Very poor quality blasting in a hard rock tunnel results in severe 

local damage, extending 2 or 3m, in the surrounding rock mass. D = 0.8 

Small scale blasting in civil engineering slopes results in modest 

rock mass damage, particularly if controlled blasting is used as 

shown on the left hand side of the paragraph. However, stress 

relief results in some disturbance.

D = 0.7 

Good blasting 

D = 1.0 

Poor blasting 

Very large open pit mine slopes suffer significant disturbance due 

to heavy production blasting and also due to stress relief from 

overburden removal. 

In some softer rocks excavation can be carried out by ripping and 

dozing and he degree of damage to the slope is less 

D = 1.0

Production 

blasting 

D = 0.7 

Mechanical 

excavation
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For practical purposes, the Hoek-Brown failure criterion (based on major and minor principal stresses) 

was best-fit to the Mohr-Coulomb criterion with strength parameters c and φ for use in conventional limit 

equilibrium slope stability analyses as shown in Figure 4-23. 

Figure 4-23 Relationships between Major and Minor Principal Stresses for Hoek-Brown and 

equivalent Mohr-Coulomb Criteria (Hoek, 2002) 

The Mohr-Coulomb shear strength (τ ) can be calculated by: 

τ c += 'σ' tanφ' 4-27 

where

4-28 
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Seismic Design – Geotechnical Features 4-51 August 2011 

and 

4-29 

Where 

n max σ/ ci 3

'

3 =σσ 4-30 

Both the Hoek-Brown failure criterion and the GSI classification system have been updated frequently by 

Hoek and various researchers since they were first developed. Readers are referred to Hoek and Marinos 

(2007) for more discussions. 

4.5.3 Rock Masses with Discrete Discontinuities

The stability of rock masses with discrete discontinuities under both static and seismic loading depends on 

the shear strength of the discontinuity surfaces and the slope and wedge geometry. The shear strength of 

the discontinuity surfaces depends on the joint roughness, the strength of the intact rock material and any 

infill materials, and the confining pressure. The roughness of a fracture surface can be defined by a joint 

roughness coefficient, JRC (Barton, 1973). Barton (1976) has shown the strength of a rough rock surface 

may be defined by the equation: 





 



 



 



 ⋅+= ' 'tan log10

σ

φστ JCS JRC 4-31 

where 

JRC = joint roughness coefficient

JCS= compressive strength of the rock at the fracture surface

σ' = effective normal stress
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Values of the parameter JRC may be determined by comparing a fracture surface with standard profiles as 

illustrated in Figure 4-24. Values of JCS may be determined from Schmidt hammer tests in the field. 

(Deere and Miller, 1966).

Figure 4-24 Definition of Joint Roughness Coefficient, JRC (Barton, 1973) 

Equation 4-32 defines a nonlinear failure surface like that shown in Figure 4-25 from which overburden 

pressure-dependent instantaneous cohesion and friction angle values may be determined for stability 

analyses using the Mohr-Coulomb failure criterion. Computer programs for static and seismic stability 

based on wedge analysis are commercially available.
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Figure 4-25 Definition of Instantaneous Cohesion and Instantaneous Friction Angle for a NonLinear Failure Criterion (FHWA 1998) 

i c φi

4.6 SUMMARY

This chapter discusses development of the subsurface profile and evaluation of representative 

geotechnical properties for seismic analysis of transportation facilities, including structural foundations. 

The discussion focuses on the information unique to seismic analysis under the assumption that basic 

geotechnical information for facility design (e.g. soil classification, relative density or unit weight,

moisture content, and shear strength) has already been established. Essential information from which the 

key geotechnical properties required for seismic analysis and design may be determined includes site 

stratigraphy, groundwater conditions, and measures of soil consistency (e.g. SPT blow count or CPT 

resistance). Stratigraphic information should include soil classification, grain size information for 

cohesionless soils, Atterberg limits and in situ water content for cohesive soils, and depth to bedrock.

Key geotechnical properties for seismic analysis and design include the small strain shear stiffness 

(modulus), shear strain-dependent modulus reduction and damping curves, cyclic shear strength, and 

liquefaction resistance and post-liquefaction residual strength of potentially liquefiable soils. Shear 

modulus is generally determined from the shear wave velocity, VS, and total unit weight of the material 

(soil or rock). Shear wave velocity may be measured directly by a variety of geophysical methods, 

including both intrusive and non-intrusive techniques. Alternatively, shear wave velocity may be 

determined by correlation with soil index properties or penetration resistance, including both SPT blow 
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Seismic Design – Geotechnical Features 4-54 August 2011 

count and CPT resistance. Shear strain-dependent modulus reduction and damping curves are generally 

assigned based on index properties and overburden pressure. Use of overburden dependent shear 

modulus reduction and damping curves is essential for soil layers greater than 100 ft thick.

For cohesionless soils, the shear strength for use in a dynamic stability assessment should be the lesser of 

the drained and undrained strengths. For saturated cohesive soils, an undrained shear strength equal to 

85% of the static undrained strength is recommended for seismic stability assessment. Liquefaction 

resistance of liquefiable soil is described by either the normalized standardized SPT blow count, (N1)60, or 

the normalized CPT tip resistance, qc1. Post-liquefaction residual shear strength is expressed as a function 

of the effective overburden pressure using the residual shear strength ratio, Sr/σ’vo. The residual shear 

strength ratio may be determined as a function of either the normalized CPT resistance or the normalized 

standardized SPT blow count and fines content.

For characterization of shear strength, rock masses may be split into two categories: highly fractured rock 

masses and rock masses with discrete discontinuities. The shear strength of highly fractured rock masses 

may be characterized using the Hoek-Brown non-linear shear strength envelope or values of overburdendependent equivalent cohesion and friction angle derived from the Hoek-Brown equation. The shear 

strength of discrete discontinuities can be characterized using Barton’s (1976) equation or values of 

overburden-dependent equivalent cohesion and friction angle derived from the Barton equation. 

The soil profile and soil property information developed in this chapter provides the basis for almost all of 

the geotechnical analyses presented subsequently in this report. The site stratigraphy, small-strain shear 

modulus, and shear strain-dependent modulus reduction and damping curves are the essential input for the 

site specific seismic response analysis presented in Chapter 5. The site stratigraphy, liquefaction 

resistance, and shear strength parameters discussed in this chapter are the fundamental parameters 

required for the geotechnical hazard analysis presented in Chapter 6. The dynamic shear strength 

parameters described in this chapter, including the residual shear strength, are used in slope stability 

analyses presented in Chapter 9, foundation performance analysis (e.g. bearing capacity and lateral 

resistance) presented in Chapters 10 and 11, and retaining wall analysis presented in Chapter 12. Seismic 

analysis of buried structures, presented in Chapter 13, also requires knowledge of the shear stiffness and 

shear strength of the surrounding soils. 
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CHAPTER 5

SEISMIC SITE RESPONSE ANALYSIS

5.1 GENERAL 

The local soil profile at a project site can have a profound effect on earthquake ground motions. Local 

soil conditions can affect the intensity, frequency content, and duration of strong shaking. Amplification 

of peak bedrock accelerations on the order of 0.05 g to 0.10 g by a factor of three or more due to the 

influence of the local soil profile has been documented. Even when the peak ground acceleration is not 

amplified, the local soil profile is likely to alter the frequency content (i.e. the spectral accelerations) of 

the bedrock ground motions. Amplification of the spectral acceleration by a factor of ten or more has 

been observed in the vicinity of the fundamental site period, T0. Embankment and retained earth fills can 

have a similar effect on ground surface motions. 

Conventional seismic hazard analyses typically provide ground motions for a weak rock site, i.e. a site 

with a value of Vs30, the average shear wave velocity over the top 100 ft, equal to 2,500 ft/sec. This 

corresponds to Site Class B in the AASHTO site classification system described in Chapter 3 (see Table 

3-5). The probabilistic ground motions employed by AASHTO as the basis for structural design of 

ordinary bridges correspond to this site classification. The influence of local ground conditions on the 

strong ground motions at a site that differs from a site that is representative of Site Class B can be 

accounted for in several different ways. The peak ground acceleration (PGA) can be modified by 

empirical amplification factors that depend upon soil type or site class. Alternatively, the PGA and 

spectral accelerations at 0.2 second and 1 second can be modified using the site-class dependent PGA, 

short period, and long period site factors, FPGA, Fa and Fv. With the modified values of peak ground 

acceleration and the spectral accelerations at 0.2 second and 1 second, a new response spectrum can be 

constructed, as discussed in Section 3.4.7. Another alternative is to conduct a site-specific seismic hazard 

analysis using one or more of the Next Generation Attenuation (NGA) relationships that explicitly 

accounts for local site conditions. Four of the five NGA relationships discussed in Section 3.6 of Chapter 

3 employ Vs30 as a dependent variable in their formulation and three of these four relationships use an 

additional parameter to capture the influence of local site conditions on ground motions, e.g. the depth to 

a shear wave velocity of 3,300 ft/s. A formal site seismic response analysis can also be used to account 

for the effect of local site conditions on the ground motions. 
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For many engineering analyses, one of the first three methods described above is sufficient to account for 

the effect of local soil conditions on design ground motions. However, if a detailed evaluation of the 

influence of local soil conditions is desired, or when it is not appropriate to use empirical PGA 

amplification relationships or the AASHTO site factors, a formal seismic site response analysis must be 

conducted. Furthermore, for Site Class F, deemed special study sites in the AASHTO seismic design 

provisions, a formal seismic site response analysis is required to evaluate the influence of local site 

conditions on the design ground motions. Sites with significant contrasts in the shear wave velocity 

among layers within 200 ft of the ground surface and sites with deep soil columns, e.g. soil columns in 

excess of 500 ft, are also good candidates for a site-specific seismic response analysis, as the differences 

in the soil profile at these types of sites compared to the profiles used to develop the AASHTO site factors

may create significant differences in site response compared to that predicted using the AASHTO site 

factors. 

There are a variety of design analyses for non-structural features of transportation systems for which site 

response analyses may also be warranted. Site response analyses can be used to determine the seismic 

coefficient for slope stability analyses and retaining wall design. Site response analysis can also be used 

to develop appropriate time histories for use in Newmark-type seismic deformation analyses for slopes, 

embankments, and lateral spreading of liquefied ground. The most accurate means of determining the 

earthquake –induced shear stress, τeq, for liquefaction analysis is through a site response analysis. Site 

response analyses may also be warranted to determine the free field shear strain for evaluation of the 

dynamic stiffness of shallow foundations and the differential shear displacement for seismic design of 

box-shaped underground structures, e.g. culverts and cut and cover tunnels. Furthermore, Chapter 3 

described the use of site response analyses to evaluate the spatial variability of ground motions along a 

linear structure such as a long span bridge or viaduct. Table 5-1 summarizes the different types of design 

analyses where a seismic response analysis may be warranted, along with the chapter in this document 

where these analyses are discussed.
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TABLE 5-1 USES OF SITE RESPONSE ANALYSIS IN SEISMIC DESIGN OF 

TRANSPORTATION FACILITIES

Analysis Response Analysis

Parameter Chapter

• Structural design, including

 spatial incoherence

• Response spectra

• Acceleration time histories

3

• Liquefaction • Peak ground acceleration

• Earthquake-induced shear stress

6

• Slope stability

• Retaining wall design • Seismic coefficient 6, 7, 11

& 12 

• Seismic deformation of slopes and 

embankments • Acceleration time history 6 & 7

• Soil-structure interaction • Acceleration time histories vs. 

depth

8, 9, 10

& 11

• Shallow foundation stiffness • Strain-compatible shear modulus 9

• Racking/Ovaling of underground

structures

• Differential subsurface shear

displacement

13

 

5.2 SITE-SPECIFIC SEISMIC RESPONSE ANALYSES

5.2.1 Types of Site-Specific Analysis

The most common types of site-specific seismic site response analyses are one-dimensional analyses 

based upon the assumption of a vertically propagating shear wave through uniform horizontal soil layers 

of infinite lateral extent. The assumption that shear waves propagate vertically to the ground surface is, in 

general, a valid engineering assumption. Even if the shear wave is not propagating vertically at depth it 

will refract into a near vertical position as it approaches the ground surface. This refraction is due to the 

general increase in shear wave velocity with increasing distance from the ground surface (i.e. increasing 

depth below ground), as illustrated in Figure 5-1. This phenomenon is similar to the refraction of water 

waves at the beach such that they usually approach the shore with their crest aligned parallel to the shore. 

The influence of vertical motions, compressional waves, and laterally non-uniform soil conditions are 

typically not accounted for in conventional seismic site response analyses. There are, however, situations 

where the designer may wish to consider the influence of non-uniform ground conditions on site response. 

In such situations, a two-dimensional site response analysis may be required. 
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Evaluation solely of the impact of vertically propagating shear waves in a site response analysis is 

consistent with current design and code practices. It is also consistent with geotechnical engineering 

analyses for liquefaction potential and seismic slope stability, which usually consider only the horizontal

component of the seismic motions. Three different levels of one-dimensional site-specific seismic site 

response analysis are available to geotechnical specialists: 

• Simplified analysis

• Equivalent-linear one-dimensional site response analyses

• Advanced one-dimensional site response analyses

These three levels of one-dimensional site response analysis are discussed in the remainder of this 

chapter.

Figure 5-1 Refraction of Shear Waves Approaching the Ground Surface
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5.2.2 Simple Empirical Relationships

For screening purposes and preliminary analyses, the influence of local soil conditions on seismic site 

response can be assessed in an approximate manner using simple empirical relationships which correlate 

ground motions at rock sites to those at soil sites. These relationships, developed on the basis of both 

observations of ground motions in earthquakes and equivalent-linear one-dimensional site response 

analyses, provide site response factors that can be used to estimate the free field (i.e., not affected by 

structure and/or topography) ground motion at soil sites from the free field rock site (Site Class B) ground 

motion determined in a seismic hazard analysis. An empirical relationship for the amplification of the 

transverse peak ground acceleration by earthen embankments is also available.

The most common type of simplified site response analysis used in earthquake engineering practice is the 

NEHRP procedure, adopted by AASHTO, for modifying the acceleration response spectra based upon 

Vs30. The NEHRP procedure for modifying the peak ground acceleration (PGA) and the short period 

spectral accelerations (SS) and the spectral acceleration at 1 second (S1) using the site response factors 

Fpga, Fa, and Fv is presented in Sections 3.3.8 and 3.5 in Chapter 3. The values of Fpga, Fa, and Fv, 

presented in Tables 3-6, 3-7, and 3-8, are related to the site class presented in Table 3-5, which depends 

upon Vs30. (Table 3-5 also provides for establishing site class based upon SPT blow count or undrained 

shear strength if Vs30 is not available.) Modified values of the PGA (i.e. As), SS (i.e. SDS), and S1 (i.e. SD1) 

are then used to construct the truncated (three-point) acceleration response spectra for use in structural 

design. However, there are special study sites (Site Class F) where AASHTO specifies that this 

procedure should not be applied. Furthermore, the NEHRP procedure should not be used at sites with 

strong impedance contrasts among layers in the top 200 ft of the soil profile (the impedance is the product 

of the shear wave velocity and mass density of the soil), as these sites do not conform to the model used 

to develop the NEHRP/AASHTO site response factors. The NEHRP/AASHTO site factors should also 

be used with caution for sites with very deep soil columns (e.g. soil columns in excess of 500 ft), as these 

sites are also suspect with respect to conformance to the NEHRP model, as discussed subsequently. 

Whereas structural analyses may require information on the spectral acceleration over a range of spectral 

periods to characterize the design ground motion, geotechnical analyses frequently only require 

knowledge of the peak ground acceleration (in combination with earthquake magnitude). Several 

investigators have developed empirical relationships between the peak ground acceleration at a 

hypothetical bedrock outcrop at the project site and the peak ground acceleration at the site as a function 

of the local soil conditions. Among the first of these relationships, developed by Seed and Idriss (1982), 
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is presented in Figure 5-2. Figure 5-2 (presented solely for historical context) relates the rock site PGA to 

the soil site PGA for stiff soil, deep cohesionless soil, and soft to medium-stiff clay and sand site 

conditions. However, no formal definition of these site conditions was provided. 

While the plot in Figure 5-2 is outdated and should not be used for engineering analysis, the basic pattern 

of behavior illustrated by the plot remains unchanged. At low PGA values, rock site PGAs can be 

amplified at soft soil sites. However, at higher PGAs values the rock site PGA may be attenuated 

(reduced) at these same sites. The reduction in soil site PGA at higher rock site PGA values is due to the 

limited shear strength of the soil, resulting in yielding (shear failure) of the soil near the ground surface. 

Yielding of the soil limits its ability to transmit ground acceleration to overlying soil layers.

Figure 5-2 Relationship between PGA on Rock and on Other Local Site Conditions (After Seed and 

Idriss, 1982, reprinted by permission of EERI) 

A similar plot to Figure 5-2 can be developed using the PGA site factor, Fpga. Figure 5-3 presents a plot 

of the PGA at a weak rock site (Site Class B) versus the corresponding PGA at a soil site based upon 

AASHTO site class (i.e. based upon Vs30). This plot was developed using the PGA amplification factors, 

Fpga, in Table 3-6 with slight modifications for Site Classes C and D for PGA values from 0.4 g to 0.5 g to 
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smooth out the curves and produce a pattern of behavior similar to Figure 5-2. Figure 5-3 can be used to 

modify the PGA as a function of site class (i.e. as a function of Vs30) without going through the entire 

NEHRP procedure. However, as noted previously with respect to the NEHRP procedure, the 

amplification factors in this figure should not be used for Site Class F (special study sites) or for sites with 

a strong impedance contrast in the upper 200 ft of the soil profile. Additionally, Figure 5-3 should be used 

with caution for deep soil sites. 

Figure 5-3 PGA Amplification Based Upon NEHRP Site Class

Figure 5-4 shows a site amplification plot developed by Idriss (1990) for soft soil sites. Figure 5-4

includes both field observations of the amplification of the PGA and the results or numerical response 

analysis using equivalent-linear one-dimensional site response analysis (described subsequently in this 

chapter). The curve in Figure 5-4 may be considered representative of the PGA response at soft soil sites, 

including sites classified as special study sites (Site Class F) by AASHTO because of the plasticity index 

(PI) or thickness of the soft soil layer. 
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Figure 5-4 Relationship between PHGA on Rock and on Soft Soil Sites (Idriss, 1990) 

Figure 5-5 presents a comparison of peak acceleration values recorded at the base (usually bedrock) of 

several earthen dams and the corresponding transverse peak acceleration recorded at the crest (Harder, 

1991). The figure suggests that larger amplification effects may be expected in earthen structures than at 

free field soft soil sites. Note, however, that Figure 5-5 presents an upper bound curve (as opposed to 

Figure 5-4, where a mean curve is presented) and only applies to the transverse acceleration of the 

embankment. For the longitudinal acceleration of embankments (e.g., for end slopes) and for the 

acceleration of cut slopes, amplification effects may be expected to be significantly smaller than indicated 

by Figure 5-5. 
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Figure 5-5 Base and Crest Peak Accelerations Recorded at the Earth Dams (Harder, 1991) 

The free field amplification curves presented in Figure 5-3 and Figure 5-4 may be used in a simplified 

three-step site response analysis procedure to account for the influence of local soil conditions on the peak 

ground acceleration from a conventional seismic hazard analysis (i.e. a seismic hazard analysis for Site 

Class B ground conditions) for PGA values less than or equal to 0.5. The observational data presented in 

Figure 5-5 may be used in a fourth step to account for the influence of an embankment on the transverse 

peak acceleration at the crest of the embankment. The procedure is as follows:

Step 1: Evaluate the free field bedrock acceleration at the site for NEHRP/AASHTO Site Class B. 

Determine the PGA from a conventional seismic hazard analysis for NEHRP/ASHTO Site Class B.

Step 2: Classify the site according to the NEHRP/AASHTO site classification system. Using Table 3-5, 

classify the site on the basis of the average shear wave velocity for the top 100 ft (30 meters) of soil, Vs30. 
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Step 3: Estimate the free field PGA at the site. Estimate the potential amplification of the PGA from Step 

2 from Figure 5-3 for NEHRP/AASHTO Site Classes C through E or from Figure 5-4 for 

NEHRP/AASHTO Site Class F (as appropriate). 

Step 4: Estimate the transverse PGA at the top of the embankment. Estimate the potential amplification 

of the PGA at the top of the embankment, if an embankment is present, using the free field PGA derived 

in Step 3 and the earth dam amplification curve in Figure 5-5. 

Step 4 in the procedure presented above is based upon the simplified “decoupled” assumption that the 

peak acceleration at the base of the embankment is the same as the free field peak acceleration, thereby 

ignoring interaction between the embankment mass and the ground. Analyses of the coupled response of 

embankments and foundation soils indicates that this simplified, decoupled assumption usually provides a 

conservative upper bound estimate of the acceleration at the base of the embankment (Bray, et al., 1995). 

As the amplification curve in Figure 5-5 is already an upper bound curve, the net result of using this four 

step procedure to estimate embankment response may be an extremely conservative assessment of the 

PGA at the top of the embankment. However, in general, this simplified approach is intended only to 

give a rough estimate of amplification effects at a site for screening analyses and preliminary design 

purposes. The simplified approach is not intended for use in final design of transportation facilities. Even 

for screening and preliminary analyses, the design engineer should decide if this approach is appropriate 

for the intended purpose or if it is necessary to perform a more sophisticated analysis.

The peak acceleration at the top of an embankment estimated in Step 4 may also be used in preliminary 

analyses for various highway ancillary structures, including retaining walls, and for structures constructed 

on top of embankment fills. This acceleration is not, however, the appropriate peak acceleration for use 

in seismic stability and deformation analyses for an embankment or bridge abutment or free-standing 

retaining wall. For these calculations, the average acceleration of the assumed failure mass, and not the 

acceleration at the top of the embankment, should be used. The average acceleration is directly 

proportional to the seismically-induced inertia forces and thus is the relevant response quantity. The 

average acceleration is always less than the peak ground acceleration due to spatial averaging. 

Appropriate reduction factors to apply to the PGA to determine the average acceleration for stability and 

deformation analyses of slopes and retaining walls are discussed in Chapter 6. 
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5.3 ONE-DIMENSIONAL SITE RESPONSE ANALYSES

5.3.1 Equivalent Linear One-Dimensional Response Analyses

When an analysis more accurate than the simplified analysis presented above is warranted, a formal 

seismic site response analysis can be performed. In particular, formal seismic response analyses are 

required for Site Class F (Special Study soils). Furthermore, as noted previously, sites with significant 

impedance contrasts within the top 200 ft of the soil profile and sites with thick soil columns (e.g. soil 

columns in excess of 500 ft) do not conform to the site model used to develop the NEHRP site response 

factors and thus are suspect in this respect. Therefore, a formal response analysis may be warranted at 

sites with shallow impedance contrasts and deep soil columns. Formal response analyses may also be 

warranted on important projects, projects with highly variable ground conditions over the span of a 

structure or other transportation facility, and for the other design purposes cited in Table 5-1. 

Equivalent-linear one-dimensional analysis is by far the most common method used in engineering 

practice to analyze site-specific seismic response. In an equivalent-linear one-dimensional site response 

analysis, the soil profile is modeled as a horizontally layered, linear visco-elastic material characterized 

by the shear modulus and damping ratio. To account for the non-linear, strain-dependent behavior of soil, 

the equivalent-linear modulus is evaluated from the initial small strain modulus, Gmax, and the shear strain 

dependent modulus reduction curve. The damping ratio is evaluated from the shear strain dependent 

damping curve. Evaluation of Gmax and the shear strain dependent modulus reduction and damping 

curves were discussed in Chapter 4. 

In an equivalent-linear analysis, strain compatible modulus and damping values are evaluated iteratively 

for each soil layer or sub-layer. An effective shear strain is used to calculate the strain-compatible 

modulus and damping and the analysis iterates until two successive iterations produce the same effective 

shear strain in each layer. The effective shear strain level is usually specified as:

γeff = n γmax 5-1 

where γeff is the effective strain, γmax is maximum value of earthquake-induced shear strain, and n is the 

effective strain factor. Because γeff is not known prior to the start of the analysis, equivalent-linear 

response analyses are performed in an iterative manner, using the effective strain from one iteration of the 

analysis to evaluate the modulus and damping ratio for the next iteration. Initial values are usually 
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assumed based upon experience (although the small strain modulus and damping can also be used as the 

initial values). Usually 5 to 10 iterations are sufficient to achieve convergence of modulus, damping, 

stress and strain values to within a difference of less than one percent between two successive iterations. 

Originally, the value of the effective strain factor, n, used in equivalent linear analysis to determine the 

strain compatible equivalent linear modulus and damping was 0.65. However, based upon back analysis 

of strong motion records obtained at soil sites in earthquakes, the consensus among geotechnical 

earthquake engineers is that the effective strain factor n should be related to the earthquake magnitude. 

Equation 5-2 presents the relationship between earthquake moment magnitude, Mw, and n proposed by 

Idriss and Sun (1992) and commonly used in practice today: 

10

− )1( = MW n 5-2 

The computer program SHAKE, originally developed by Schnabel, et al. (1972) and updated by Idriss

and Sun (1992) as SHAKE91, is perhaps the most commonly used computer program for onedimensional equivalent-linear seismic site response analysis. This program idealizes the site profile as a 

horizontally layered soil deposit overlying a uniform visco-elastic half-space, as illustrated in Figure 5-6. 

SHAKE91 and its derivatives are still reliable platforms for conducting equivalent linear one-dimensional 

site response analyses. A DOS version of SHAKE91 is available from the National Information Service 

for Earthquake Engineering (NISEE) at the University of California at Berkeley for a nominal cost. 

However, the DOS version of SHAKE91 is somewhat cumbersome, requiring a formatted input file and 

direct input of time histories and newer modulus reduction and damping curves by the user. A variety of 

different user-friendly WINDOWS versions of SHAKE91 are now available from commercial software 

vendors. These commercial programs typically have built-in libraries of earthquake time histories and 

modulus reduction and damping curves and menu-driven input and output capabilities. Furthermore, 

there are several other computer programs for equivalent-linear one-dimensional seismic site response 

analysis that are commercially available. Most of these programs are reliable for use in engineering 

design, as visco-elastic response analysis is a fairly simple type of analysis to implement numerically. 

However, the user should carefully check the documentation provided with a program to ensure the 

program’s reliability, as even some commercial versions of SHAKE91 are reported to have been modified 

from the original, validated program. 
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Figure 5-6 1-Dimensional Column for SHAKE Equivalent Linear Seismic Site Response Analysis 

(Schnabel, et al., 1972)

Basic input to an equivalent-linear seismic site response analysis includes the soil profile, soil parameters 

for each layer, and the input acceleration time history. Soil parameters used in the analysis include the 

initial (small strain) shear modulus or shear wave velocity and the total unit weight (or mass density) for 

each soil layer. Also, the shear strain (and sometimes overburden) dependent shear modulus reduction 

and damping ratio curves are required for each soil type. Evaluation of representative values for these 

soil properties is discussed in Chapter 4. As noted in Chapter 4, it is essential to consider the overburden 

dependence of the modulus reduction and damping curves when the soil profile is greater than 50 to 100 

ft thick. Figure 5-7, from Hashash and Park (2001), compares the ground surface acceleration response 

spectrum obtained using a pressure dependent soil model to the ground surface spectrum obtained using a 

pressure-independent model for a 3,300 ft (1,000 m) thick soil column (representative of deep soil 

deposits in the Mississippi embayment). The pressure-independent model (labeled NLPI in the figure) 
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under-predicts spectral accelerations by a factor of 3 to 8 compared to the pressure dependent model 

(labeled NLPD in the figure) in the modal period range of 0.1 second to 1 second. The modulus reduction 

and damping curves provided with early versions of SHAKE and SHAKE 91 may not consider this 

dependence. 

 

Figure 5-7 Influence of Pressure Dependent Soil Behavior on the Seismic Response of a 3,300 ft 

 (1,000-m) Thick Soil Column in the Mississippi Embayment (Hashash and Park, 2001) 

Once the soil profile and material properties have been specified, the principle remaining input to an 

equivalent-linear response analysis is the input earthquake acceleration time history. Selection of 

representative acceleration time histories for the input ground motion is discussed in Chapter 3. The 

acceleration-time history may be input as either the motion at a hypothetical bedrock outcrop at the site 

(the most commonly used option because it is congruent with assumptions embedded in attenuation 

relationships) or as a within profile motion (i.e. a ground motion within the soil profile) at the bedrocksoil interface at the base of the soil column (in general, not recommended and only used if a rigid, noncompliant base is used in the analysis). Results of the analysis provide shear stress-, shear strain-, and 

acceleration-time histories for the ground surface and for each layer within the soil profile. Most 
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programs will also provide response spectra and peak motions at the surface and at designated depths 

along with values for the strain compatible modulus in each soil layer. 

While it is relatively easy to set up and perform an equivalent-linear site response analysis, the results of 

the analysis may be extremely sensitive to the details of the input. Factors such as the thickness and 

number of sub-layers, selection of appropriate input motions, the digitization interval of the input time 

history, the "cut-off" frequency (the highest frequency used in the Fourier transformation of the input 

motion), the shear wave velocity and unit weight of the underlying bedrock “half-space”, and whether the 

input motion is specified as a within profile motion or a bedrock outcrop motion can significantly affect 

program output. Program documentation usually provides recommendations for these parameters. 

However, if the design engineer is not familiar with the program or method of analysis, or if the guidance 

on these parameters is vague or uncertain, a sensitivity analysis and/or a benchmark study may be 

warranted. Furthermore, it is recommended that all formal seismic response analyses should be reviewed 

by a qualified geotechnical specialist familiar with the program being used and the problem being 

analyzed and experienced in seismic site response analysis.

Figure 5-8 illustrates the application of equivalent-linear one-dimensional analysis to predict the seismic 

response of a site in Columbia, South Carolina, with a shallow impedance contrast (Martin, et al., 2008). 

The shear wave velocity profile used in the site response analysis, shown on the left-hand side of the 

figure, has a relatively abrupt change in shear wave velocity at a depth of about 120 ft (36 m). Assuming 

the increase in unit weight from above to below the abrupt change in shear wave velocity is on the order 

of 10 percent, the impedance is more than double below the shear wave velocity contrast compared to 

above the contrast. The site class adjusted PGA from a conventional seismic hazard analysis for NEHRP 

Site Class C was 0.31 g. The right hand side of Figure 5-8 compares the results of equivalent linear site 

response analysis using a suite of 5 representative time histories to the design spectrum from for Site 

Class C developed in accordance with the AASHTO provisions. The formal site response analysis shows 

significantly higher amplifications in the period range from 0.1 to 0.5 seconds compared to the NEHRP 

spectrum. Use of the AASHTO truncated (three-point) spectra at this site to design a structure with a 

resonant period in the short period range (i.e. 0.1 to 0.5 second) could lead to significant underestimation 

of the seismic loads.
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Figure 5-8 Equivalent Linear Response Analysis for a Shallow Impedance Contrast Site in 

Columbia, South Carolina (Martin, et al., 2008) 

5.3.2 Advanced One-Dimensional Site Response Analysis 

Advanced one-dimensional seismic site response analyses refer to truly non-linear response analyses that 

follow the actual hysteretic stress-strain behavior of the soil (rather than simply using a strain-dependent 

equivalent linear modulus and damping). Some of the advanced one-dimensional models site response 

are effective stress analyses that also have the capability of calculating pore pressure generation in the 

saturated soil layers due to cyclic loading and of accounting for the effect of the pore pressure generation 

(and dissipation) on site response. Advanced one-dimensional models must be time-domain models, i.e. 

they must divide the earthquake time history up into small time steps and sequentially calculate the 

response of the soil deposit to each time step, in order to capture non-linear soil behavior. These 

advanced site response models are generally much more computationally intensive than equivalent-linear 

models. (Equivalent-linear models can calculate soil response using a computationally efficient 

frequency domain analysis because, since the soil behavior is linear, the principle of superposition can be 

used). If pore pressure generation is modeled, the analysis may be particularly computationally intensive. 
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The primary difference between non-linear and equivalent-linear site response analyses is that non-linear 

analyses use a more realistic model to represent the behavior of soil subjected to cyclic loads. Essentially, 

a non-linear model traces the evolution of the hysteresis loops generated in a soil by cyclic loading in a 

sequential manner, whereas the equivalent-linear model only approximates soil response using 

representative soil stiffness and damping over the entire sequence of cyclic loads. The more realistic 

representation of the non-linear behavior of cyclically-loaded soils gives non-linear analyses a significant 

advantage over equivalent-linear seismic response analyses at higher levels of seismic shaking where 

non-linear effects tend to dominate.

Non-linear soil models generally describe soil behavior in terms of a backbone curve that describes stressstrain response during initial loading and a set of rules for how the soil behaves during unloading and 

reloading subsequent to initial loading. The backbone curve is the curve that describes the tips of the 

hysteresis loops developed in uniform cyclic loading. The backbone curve is usually described by some 

type of hyperbolic function and is easily related to the small strain modulus, Gmax, and modulus reduction 

curve from the equivalent-linear model. Figure 5-9 illustrates how a typical non-linear soil model 

captures stress-strain behavior during non-uniform cyclic loading. 

Figure 5-9 Non-Linear Soil Model for Time-Domain Site Response Analysis (Hashash and Park,

 2001) 
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Perhaps the most common assumption with respect to unload-reload behavior is the Masing criterion. 

The Masing criterion says the soil stiffness during unloading and reloading is twice the stiffness of the 

soil during initial loading. However, the Masing criterion produces a damping curve that does not 

correspond in shape to a damping curve developed from uniform cyclic loading, i.e. to the equivalent 

linear damping curve. Therefore, many non-linear models use some sort of modified unload-reload rules 

that allow the damping from the non-linear model to correspond closer to the damping observed in 

uniform cyclic laboratory testing, i.e. to equivalent linear damping. Modified damping rules used in 

practice include the extended Masing criterion (Vucetic, 1990) and the Cundall-Pyke hypothesis (Pyke, 

1979, 2000). 

Even with modified damping rules, many non-linear soil models consistently under-predict the damping 

at small strains. In fact, models that use the Masing or extended Masing criterion predict essentially zero 

damping at small strains. Therefore, these models often add a viscous damping to the hysteretic damping 

predicted by the soil model. The viscous damping may be either a constant, frequency independent value 

or a frequency (or rate) dependent damping known as Rayleigh damping. There are simplified, full, and 

extended Rayleigh damping schemes used in practice. Guidelines for evaluating Rayleigh damping 

basically suggest matching it at the fundamental frequency of the soil layer (for simplified Rayleigh 

damping) or at several frequencies that are integer multiples of the fundamental frequency (for extended 

Rayleigh damping). A constant viscous damping value equal to the small strain damping either measured 

in laboratory tests or predicted by correlation for the equivalent linear damping (Kwok et al., 2006) has 

also been used in non-linear analysis. In this manner, close agreement with the damping measured in 

laboratory tests is maintained. 

Equivalent-linear site response analyses are often sufficient for most geotechnical earthquake engineering 

problems that require a site-specific response analysis. However, when the peak ground accelerations are 

high enough to induce yielding (shear failure) in the soil profile, a non-linear site response analysis may 

be warranted. The PGA amplification curve in Figure 5-3, based upon the AASHTO site factors, 

suggests that non-linear site response effects will begin to accumulate at sites classified for Site Class E 

when the PGA for the Site Class B reference condition exceeds about 0.3 g. This is consistent with 

suggestions that equivalent linear analyses may be reliable up to PGA values of 0.4 to 0.5 g (see Ishihara, 

1986) or earthquake-induced shear strains of up to 2 percent. A non-linear one-dimensional seismic site 

response analysis may also be warranted if the project is considered important or critical (e.g., a "lifeline" 

structure) or an analysis more accurate than a one-dimensional equivalent-linear site response analysis is 
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desired. Furthermore, non-linear analyses are generally required if the influence of pore pressure 

generation on site response is to be taken into account. 

Non-linear soil models described in the literature and used in practice include DESRA-2 (Lee and Finn, 

1978), MARDES (Martin, 1975), SUMDES (Li, et al., 1992), D-MOD (Matasovic and Vucetic, 1993), 

TESS (Pyke, 2000), DEEPSOIL (Park and Hashash, 2004), D-MOD_2 (Matasovic, 2006), and a ground 

response module in the OpenSees simulation platform (www.opensees.berkeley.edu). Several of these 

programs have user-friendly input routines that will determine the non-linear parameters that give the best 

fit to specified equivalent-linear modulus reduction and damping curves. Despite this apparent simplicity, 

in general non-linear site response models are significantly more complicated to use than equivalent linear 

models. Issues associated with the use of non-linear site response models are discussed in detail by 

Kwok, et al. (2006). In general, analyses conducted using non-linear soil models should always be 

validated by comparison to the results of equivalent linear models for both low intensity and high 

intensity input motions. For low intensity motions the two types of models should give similar results. 

For high intensity motions, the difference in the response predicted by the two models should be viewed 

with respect to anticipated differences between equivalent-linear and non-linear models, e.g. a progressive 

softening of the soil stiffness and lengthening of the predominant period of the site as the shaking 

intensifies. Furthermore, non-linear site response analyses should always be subject to independent peer 

review by someone experienced with the use of the model.

5.3.3 Analyses Including Pore Pressure Generation

The AASHTO bridge design guide specifications explicitly allow for a reduction in spectral accelerations 

of up to 33% based upon a site specific analysis. Models for computing the reduction in the intensity of 

ground shaking due to pore pressure generation and the consequent softening of soil stiffness have been 

available to researchers for over 15 years. Engineers have been slow to employ these models in practice 

due to the complexity of the computer programs that implement the models and the reluctance of 

regulatory officials to accept these analyses. However, several of the commercially available user 

friendly programs for non-linear site response now have the ability to account for pore pressure 

generation, putting this type of analysis within the reach of practicing engineers. Furthermore, as noted 

above, the AASHTO seismic provisions now allow for up to a 33% reduction in spectral accelerations 

based upon this type of analysis (putting prudent limits on the allowable reduction in shaking intensity 
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due to numerical modeling of pore pressure generation)., making the idea of this type of analysis an 

attractive option in some cases

Figure 5-10, from Matasovic (1993), compares the response spectrum from a total stress analysis to two 

different effective stress site analyses with pore pressure generation; one with pore pressure redistribution 

and dissipation and another without pore pressure redistribution and dissipation. Both effective stress 

analyses show a significant reduction in peak acceleration and in spectral accelerations at periods of less 

than 1 second. However, the pore pressure generation analysis that includes pore pressure redistribution 

and dissipation shows significantly greater spectral accelerations at spectral periods greater than 0.2 

second compared to the analysis without pore pressure redistribution and dissipation. Figure 5-10

highlights both the potential benefits of accounting for pore pressure generation as well as one of the 

complexities of this type of analysis, suggesting that it is essential to consider pore pressure redistribution 

and dissipation as well as generation in this type of analysis. 

Figure 5-10 Comparison of Total Stress Site Response Analysis to Effective Stress Site Response 

Analyses with Pore Pressure Softening (after Matasovic, 1993) 

 
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As noted for non-linear site response analyses in general, analyses that include pore pressure generation 

should always be subject to independent peer review by someone experienced with the use of the model. 

5.4 TWO- AND THREE-DIMENSIONAL SEISMIC SITE RESPONSE ANALYSIS

Occasionally, when the engineer wishes to analyze the influence of irregular geometry in the stratigraphic 

profile or irregular project geometry and for major projects of great importance, a two-dimensional site 

response analysis may be warranted. Three-dimensional site response analyses are rarely employed in 

transportation engineering practice, except as axi-symmetric analyses (even though some commercial 

programs boast of a three-dimensional dynamic capability). The most common type of two-dimensional 

seismic site response analysis conducted in practice is a quasi-two-dimensional analysis that employs 

multiple one-dimensional columns in a two-dimensional cross section. The quasi-two-dimensional site 

response is modeled by analyzing each column using one-dimensional analysis, most commonly with an 

equivalent-linear model. Figure 5-11 compares the results of equivalent-linear one-dimensional site 

response analyses of vertical columns through a two-dimensional cross section, expressed in terms of the 

maximum earthquake-induced shear stress versus depth, to the results of a two-dimensional equivalentlinear analysis. The results from the one-dimensional analysis are generally within 5 to 10 percent of 

results of the two-dimensional analysis, which provides sufficient accuracy for almost all engineering 

applications considering other uncertainties associated with the analysis. 

Figure 5-11 Quasi Two-Dimensional Site Response Analysis Using One-Dimensional Columns 

 (Vrymoed and Calzascia 1978) 
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If a more sophisticated two-dimensional site response analysis is desired or warranted, or a soil-structure 

interaction analysis is to be conducted, a variety of finite element and finite difference computer programs 

for two-dimensional seismic site response and soil-structure interaction analysis are available. The 

computer program QUAD4, originally developed by Idriss and his co-workers (Idriss, et. al., 1973), 

updated as QUAD4M by Hudson, et. al. (1994) is among the most commonly used computer programs 

for two-dimensional site response analysis. One reason for the popularity of QUAD4M is that it uses the 

equivalent-linear soil model employed in the equivalent-linear one-dimensional site response analyses

described in previous sections of this chapter. Therefore, it is relatively easy to establish appropriate 

input parameters for soil layers and to validate the soil model by comparison of results from QUAD4M to 

equivalent-linear one-dimensional analyses. Basic input to QUAD4M includes the two-dimensional soil 

profile, equivalent-linear soil properties, and the acceleration time history of horizontal ground motion. 

QUAD4M solves the equations of motion in the time domain and therefore employs a modified form of 

Rayleigh damping. The QUAD4M damping model requires that the equivalent-linear damping be 

matched to the Rayleigh damping at two frequencies specified by the user. These frequencies are 

generally the fundamental period of the soil layer or earth structure and four times the fundamental 

period. A time history of vertical ground motion may also be applied at the base of the soil profile. The 

base can be modeled as a rigid boundary, with design motions input directly at the base as a within profile 

motion, or as a transmitting boundary which enables application of ground motions as hypothetical rock 

outcrop motions. However, QUAD4M does not have structural elements and thus is not suitable for soilstructure interaction analysis. 

Multi-purpose computer programs like PLAXIS (www.plaxis.com) and FLAC (www.itascacg.com) are 

becoming increasingly popular with practicing geotechnical engineers for all types of analysis, including 

seismic response and soil-structure interaction analyses. These are powerful programs with multiple 

features, including structural elements, energy absorbing boundaries, and sophisticated soil models that 

may include pore pressure generation. These programs should only be used in design by experienced 

professional. Furthermore, problem-specific benchmark studies (comparing program results to 

established solutions for problems that employ the same program features that will be used in the actual 

analysis) and peer review are essential when using these programs. 
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5.5 SUMMARY

This chapter describes the use of seismic response analysis to evaluate the effect of local site conditions 

on earthquake ground motions. Five different levels of site response analysis are described:

• Simplified site response analysis

• One-dimensional equivalent linear site response analysis

• One-dimensional non-linear site response analysis

• One-dimensional non-linear site response analysis with pore pressure generation and dissipation

• Two-dimensional site response analysis

Simplified site response analysis use charts based upon empirical observations of earthquake ground 

motions and the results of one-dimensional site response analysis to relate the ground motion at weak 

rock sites (i.e. AASHTO Site Class B) to the ground motion at the ground surface of the site as a function 

of the AASHTO site class. These analyses include the AASHTO procedure for adjusting the PGA and 

spectral accelerations at 0.2 and 1 second and simple charts for the adjusting just the PGA. The simple 

charts should only be used for screening analyses and preliminary design. Charts are also available for 

evaluating the amplification of the free field PGA by an embankment. 

Equivalent-linear one-dimensional analyses are the most common type of site-specific seismic response 

analysis used in engineering practice. These analyses are required to develop design ground motions for 

AASHTO Site Class F (special study sites) and are recommended for sites with significant impedance 

contrasts within 200 feet of the ground surface and for deep soil sites (basins with soil deposits greater 

than 500 ft in depth). They may also be warranted for major projects and important structures and for the 

design purposes presented in Table 5-1. It is imperative to consider the pressure-dependence of the 

modulus reduction and damping curves for analyses of soil columns greater than 100 ft in thickness. 

One-dimensional non-linear site response analysis are only necessary for sites where the reference site 

PGA exceeds 0.3 g or the cyclic shear strain in the soil exceeds 2 percent or if the engineer wants to take 

into account the influence of pore pressure generation on site response. Non-linear analyses that account 

for pore pressure generation and dissipation can be used to justify reductions in spectral accelerations of 

up to 33%. The most common type of two-dimensional site response analysis used in practice employs 

one-dimensional analysis of multiple columns to represent the two-dimensional response. Formal twodimensional site response analysis is generally only required for soil-structure interaction analysis.
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In addition to evaluating the influence of local soil conditions on the design ground motions discussed in 

Chapter 3 of this report (e.g. on the acceleration response spectra and representative time histories), site 

response analyses are employed in a variety of the other analyses described in this report. Site response 

analyses may also be used to evaluate the seismic coefficient for stability and deformation analysis of 

slopes and embankments (Chapters 6 and 9) and retaining wall structures (Chapter 12), and the 

earthquake induced shear stress for liquefaction analysis (Chapter 6). Time histories from seismic 

response analyses may also be used in the formal Newmark seismic deformation analyses (Chapter 6) and

to evaluate kinematic interaction in soil structure interaction analyses (Chapters 8 and 11). Other uses of 

seismic response analyses include evaluation of the representative free field soil modulus for evaluation 

of the dynamic stiffness coefficients for shallow foundations (Chapter 10) and the free field differential 

soil displacement for analysis of the racking/ovaling displacement induced by seismic loading on

underground structures (Chapter 13). 
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CHAPTER 6

GEOTECHNICAL HAZARDS

6.1 GENERAL 

This chapter describes geotechnical seismic hazards related to slope stability, liquefaction, ground 

settlement and fault rupture. There are numerous documented case histories of slope instability, 

liquefaction, settlement, and fault rupture generated by earthquake ground motions. Earthquake induced 

slope stability and bearing failures may damage bridge foundations or superstructures, block highways, or 

rupture pipelines or culverts. Earthquake induced liquefaction has been a major source of damage to 

bridge structures and non-bridge transportation facilities in past earthquakes. Fault rupture has also been 

a source of significant damage to transportation facilities in earthquakes. 

Section 6.2 of this chapter describes methods that can be used to assess seismically-induced slope 

stability. Section 6.3 discusses procedures to determine the potential for triggering liquefaction, including 

screening procedures to assess the need for such evaluations in regions of low seismicity. Section 6.4 

discusses methods to evaluate flow failure potential and lateral spreading displacements due to 

liquefaction. Analysis methods for post liquefaction settlement of cohesionless soils and for settlement of 

unsaturated cohesionless soils are discussed in Section 6.5. Section 6.6 reviews fault types and their 

associated rupture characteristics.

The methods of analysis presented in this chapter can be used to evaluate potential geotechnical hazards 

that may impact seismic performance of transportation facilities. The methods of analysis presented in 

this chapter are also subsequently employed in Chapter 7 for geotechnical design of earthwork features 

associated with transportation systems. 
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6.2 SEISMIC SLOPE INSTABILITY HAZARD

6.2.1 Modes of Slope Instability

Common modes of instability for soil slopes include rotational (circular) failure surfaces and sliding block 

(planar) failure surfaces. In a seismic analysis, all possible circular and sliding block failure mechanisms 

must be evaluated to find the critical failure surface, i.e. the failure surface with the lowest seismic 

capacity to demand (C/D) ratio or cumulative seismic displacement. However, an experienced 

geotechnical specialist can usually identify a limited number of failure mechanisms that need to be 

evaluated in the stability analysis. In general, circular failure surfaces will govern stability in a 

homogeneous material while sliding block failure modes also need to be evaluated in soil profiles with 

thin, weak layers or for relatively thin soil layers underlain by rock or much stronger soil layers. 

Two important complicating factors when evaluating seismic stability are:

• The critical failure surface with respect to static stability (i.e. the potential failure surface with the 

lowest C/D ratio, or factor of safety, for static loading) is not necessarily the potential failure

surface with the lowest yield acceleration (i.e. with the lowest seismic coefficient that yields a C/D 

ratio of 1.0) for seismic stability: this is particularly true for sliding block failure mechanisms.

• Due to the dependence of the seismic load on the height of the slope, the potential failure surface 

with the lowest yield acceleration is not necessarily the critical surface for seismic slope stability. 

The critical surface for seismic slope stability, i.e. the potential failure surface with the lowest C/D 

ratio or the largest cumulative seismic deformation, may have to be evaluated by analyzing a 

variety of different failure mechanisms to account for this factor.

 

Earthquake-induced ground accelerations can result in significant inertial forces in slopes or 

embankments and these forces may lead to instability or permanent deformation. Current practice for the 

analysis of the performance of slopes and embankments during earthquake loading is to use one of two 

related methods: 

1) Limit Equilibrium using a pseudo-static representation of the seismic forces. In this approach 

induced seismic loads are modeled as a static horizontal force in conventional limit equilibrium 

analysis to either determine that the capacity is greater than the demand or to evaluate the
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Seismic Design – Geotechnical Features 6-3 August 2011

capacity/demand (C/D) ratio (or factor of safety) for comparison to an acceptable value. The 

seismic load is defined by a seismic coefficient, k, that is determined on the basis of the peak 

ground acceleration, the geometry of the mass of soil being loaded, and a performance criterion (i.e. 

the allowable displacement)

2) Displacement-Based Analysis using either the Newmark sliding block concept shown schematically 

in Figure 6-1 or more rigorous numerical modeling methods. As shown in Figure 6-1, when the 

average acceleration of a potential failure mass exceeds its yield acceleration (that is, when the 

acceleration exceeds the acceleration at which the C/D ratio in a limit equilibrium analysis is equal 

to 1.0), deformations accumulate leading to permanent ground displacement. 

Figure 6-1 Newmark Sliding Block Concept for Slopes 

The use of these methods for seismic slope design has been widely adopted both in the United States and 

in international practice. For example, these methods have been described in detail in the 1998 FHWA 

Geotechnical Earthquake Engineering Reference Manual (FHWA, 1998) and in a Southern California 
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Seismic Design – Geotechnical Features 6-4 August 2011

Earthquake Center publication on Guidelines for Analyzing and Mitigating Landslide Hazards in 

California (SCEC, 2002). 

The limit equilibrium approach to seismic slope stability is discussed in Section 6.2.2. The displacement 

based analysis approach is discussed in Section 6.2.3. The selection between the two approaches would 

normally be made on the basis of the complexity of the slope geometry and soil conditions within the 

slope, the level of ground shaking, and the performance based issues for earthworks design, as discussed 

in Chapter 7. 

6.2.2 Limit Equilibrium Pseudo Static Stability Analysis 

The limit equilibrium approach involves introducing a static force representing the inertial force of the 

earthquake and described by a seismic coefficient into a conventional slope stability analysis and 

determining the resulting C/D ratio. This type of analysis is generally referred to as a pseudo static 

stability analysis. As illustrated in Figure 6-2, in current practice the force representing the effect of the 

earthquake in a pseudo static analysis is assumed to be a horizontal force, is applied to the centroid of 

each slide in a “method of slices” limit equilibrium analysis, and is equal to the seismic coefficient times 

the weight of the slice. 

The seismic coefficient is typically assumed to be some function of the site-specific Peak Horizontal 

Ground Acceleration (PGA). The seismic coefficient can range from significantly less than 50 percent of 

the PGA to the full PGA, depending on the slope height, the designer’s views, and performance

requirements. The height-adjusted PGA depends upon the seismic environment, increases with slope 

heigh, and may be as little as 50 percent of the site-specific PHA. The design seismic coefficient and 

associated minimum required C/D ratio are selected such that behavior of the slope, in terms of 

permanent deformation, is within a range considered acceptable. A C/D ratio of less than 1.0 when using 

the height-adjusted PGA as the seismic coefficient implies some permanent movement of the slope. 

However, most slopes can accommodate at least a limited amount of seismically-induced movement. 

Therefore, the seismic coefficient is always equal to less than the height-adjusted PGA and typically is on 

the order of 50% of the height-adjusted PGA for allowable seismic slope deformations on the order of 1-2 

inches. Therefore, the seismic coefficient will never be more than the site-specific PGA, is typically 

equal to or less than 50 percent of the site-specific PGA, and can be equal to or less than 25 percent of the 

site-specific PGA in some cases. 
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Seismic Design – Geotechnical Features 6-5 August 2011

Figure 6-2 Pseudo-Static Limit Equilibrium Analysis

The reason the seismic coefficient can be less than the peak average acceleration within the potential 

failure mass is as follows: Earthquakes produce ground motions that in turn induce inertia forces of an 

alternating nature in slopes or embankments. The alternating inertia forces are of short duration and 

change direction many times. Therefore, even though the C/D ratio during a cycle of earthquake loading 

may fall below one, it will usually remain below one for only a very brief period of time, until the load 

reverses, as shown in Figure 6-1. During the interval when the C/D ratio is below one, permanent 

displacement will accumulate. However, only limited displacements will occur during any one interval 

because of its short duration. Therefore, even though the seismic coefficient is less than the peak average 

acceleration of the failure mass, the cumulative deformation that occurs over the entire earthquake will be 

small provided yield acceleration of the failure mass is not exceeded too many times, i.e. provided that the 

seismic coefficient and C/D ratio are selected appropriately. This concept not only provides a basis for 
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Seismic Design – Geotechnical Features 6-6 August 2011

selection of an appropriate seismic coefficient but also forms the basis of the displacement based analysis 

approach discussed in Section 6.2.3. 

A wide variety of commercially available computer programs are available that can perform the pseudostatic limit equilibrium analyses employed in the seismic coefficient method. Most of these programs 

provide general solutions to slope stability problems with provisions for using the modified Bishop, 

simplified Janbu, and/or Spencer’s method of slices. Potential sliding surfaces, both circular and

polygonal, can usually be pre-specified or randomly generated. Commonly used limit equilibrium slope 

stability programs include PCSTABL (developed at Purdue University), UTEXAS4 (developed at the 

University of Texas at Austin), SLOPE/W (distributed by Geo-Slope International), and SLIDE 

(RocScience).

An important consideration in employing the limit equilibrium approach to seismic slope stability 

analysis is that the rate of loading during the earthquake is relatively fast. For this reason, in most cases 

undrained total stress strength parameters should be used in the seismic stability model if the soil is 

saturated, rather than drained or effective stress parameters. The undrained total stress parameters may be

obtained from static strength tests conducted in the laboratory, from in situ strength testing, or from 

empirical relationships.

Although the rate effects associated with earthquake loading may result in an undrained strength higher 

than the static undrained strength during the first cycle of loading, various studies have shown that in a 

saturated cohesive soil after 10 to 15 cycles of significant loading, as might occur during a seismic event, 

degradation of the undrained strength may occur. In consideration of the potential for strength 

degradation during seismic loading, the static undrained strength is generally considered to be an upper 

bound on the undrained strength that should be used in a seismic stability analysis. For saturated 

cohesive soils of low to intermediate sensitivity, the static strength may be reduced by 10-15% to account 

for cyclic degradation in large magnitude earthquakes (M > 7) to account for the potential for strength 

degradation. Where questionable greater potential for strength degradation is suspected (e.g. in soils of 

high sensitivity), cyclic loading tests can be conducted in the laboratory to obtain a more precise 

definition of the potential for strength degradation during cyclic loading.

As previously discussed, in the limit equilibrium approach a seismic coefficient is used to determine the 

horizontal inertial forces used to represent the forces imposed by the earthquake upon the potential failure 

mass. The vertical acceleration is normally set equal to zero based on studies which have shown that 
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Seismic Design – Geotechnical Features 6-7 August 2011

vertical accelerations have a minor effect on a limit equilibrium seismic stability evaluation. The seismic 

coefficient used in the analysis is based on the peak average acceleration of the failure mass which, in 

turn, is based upon the site-adjusted PGA adjusted for spatial incoherence (wave scattering) effects, as 

discussed below. 

The peak average acceleration of a potential failure mass is the theoretical peak value of the seismic 

coefficient for use in a limit equilibrium stability assessment. A slope with a C/D ratio greater than 1.0 

when subject to this peak seismic coefficient is unconditionally stable (assuming the peak seismic 

coefficient and soil shear strength have been determined appropriately). However, as discussed 

subsequently, unconditional seismic stability is not required for most soil slopes. Most soil slopes can 

accommodate at least a small amount of permanent seismic deformation without threatening life safety or 

adjacent facilities. Under these circumstances, a seismic coefficient less than the peak seismic coefficient 

may be used to evaluate seismic performance of a slope. 

The peak seismic coefficient for use in pseudo-static slope stability analyses can be determined by 

addressing two different factors. The first factor is the maximum acceleration at the ground surface

beneath a fill slope or at the base of a natural slope, i.e. the site-adjusted PGA. As described in the 

NCHRP 12-70 Report (NCHRP 2008) and discussed in Chapter 3, the site-adjusted PGA may be 

estimated as the PGA for reference site conditions from the seismic hazard analysis times the appropriate 

site factor, Fpga (Table 3-6). As the peak average acceleration of the failure mass is at most equal to the 

site-adjusted PGA, the site-adjusted PGA is the maximum possible value of the seismic coefficient, kmax. 

Therefore, kmax is given by the expression: 

max Fk pga ⋅= PGA 6-1 

 

where the PGA is the USGS mapped acceleration coefficient for site class B conditions, and Fpga is the 

AASHTO peak ground acceleration site factor. However, as discussed in NCHRP Report 611 (NCHRP, 

2008), the peak average acceleration of a sliding mass encompassing the full height of the slope will be 

less than the site-adjusted PGA (i.e less than kmax) due to ground motion incoherence (or wave scattering) 

arising from wave propagation effects. Studies conducted in preparation of NCHRP Report 611 (i.e. 

during the NCHRP 12-70 project) led to development of a height dependent reduction in kmax to get the 

peak average acceleration, kav. This adjustment is given by the expression: 
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Seismic Design – Geotechnical Features 6-8 August 2011

av max ⋅α= kk 6-2 

where α = a slope height reduction factor and kav is the average peak acceleration in the potential failure 

mass, taking into account spatial incoherence (or wave scattering).

The following relationship is presented in NCHRP Report 611 for the value of α for slopes and 

embankments of up to 100 ft in height founded upon Site Class C, D, and E soil conditions:

( ) −β⋅⋅⋅+=α 10.5H01.01 6-3 

where H = slope height (feet) and β is a function of the shape of the acceleration response spectrum and 

is given by:

1v max ⋅=β k/SF 6-4 

where Fv = AASHTO site factor for the spectral acceleration at 1 second and S1 = the spectral 

acceleration at 1 second for Site Class B.

For Site Classes A and B (hard and soft rock foundation soils) the value of α from Equation 6-3 is

increased by a factor of 1.2. 

Figure 6-3 shows Equation 6-3 in graphical form. The curved lines in Figure 6-3 are fit to the data points 

developed using numerical analysis while the straight lines in the figure are engineering approximations 

represented by Equation 6-3. Note that the engineering approximations for α remain constant after a 

height of 100 ft. While a smaller value of α may be appropriate for slope heights greater than 100 ft, 

special studies are recommended to justify the use of smaller values of α than the value for H = 100 ft.. 

Similar height adjustment factors are recommended for evaluating the seismic coefficient for design of 

retaining walls, as discussed in Chapter 11. 

Values of β less than 1.0 in Equation 6-3 and in Figure 6-3 would be typically associated with seismic 

conditions in the eastern United States, firm ground conditions, and lower acceleration levels, while 

values of β greater than 1.0 would be associated with the Western U.S., higher accelerations, and Site 

Class C or D site conditions. 
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Seismic Design – Geotechnical Features 6-9 August 2011

Slope Height

Figure 6-3 Simplified Height-Dependent Incoherence Reduction Scaling Factor, α, Recommended 

for Slope Stability Analysis (NCHRP 2008) 

Based upon seismic displacement analyses, NCHRP Report 611 recommends that the average seismic 

coefficient given by Equation 6-2 be reduced by 50% to find the seismic coefficient for a required C/D 

ratio of 1.1, assuming the slope can accommodate 1 to 2 inches of permanent seismic displacement: 

s F5.0k pga ⋅⋅α⋅= PGA 6-5

 

where kS is the seismic coefficient for a required C/D ratio of 1.1 assuming 1 to 2 inches of permanent 

seismic displacement is allowable.

In summary, based upon the recommendations in NCHRP Report 611, the limit equilibrium seismic 

coefficient design approach entails the following steps: 
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Seismic Design – Geotechnical Features 6-10 August 2011

1) Conduct static slope stability analyses using appropriate resistance factors to confirm that slope 

performance meets static loading requirements. 

2) Establish the upper bound value of the seismic coefficient kmax ( = Fpga PGA) and the site-adjusted 

spectral acceleration at one second, FvS1, from the AASHTO ground motions maps for a 1,000-year 

return period and the Site Class-dependent AASHTO site factors.

3) Modify kmax to find the average peak acceleration accounting for slope height effects, kav ( = α kmax), 

in accordance with Equations 6-2 through 6-4. 

4) Reduce kav by a factor of 0.5 to find kS (assuming 1 to 2 inches of permanent displacement are 

permissible). If larger permanent displacements are acceptable, further reductions in kav are 

possible, but these would have to be determined by conducting separate calibrations studies 

between the resulting displacement and the ratio of kS to kav, as discussed in Section 6.2.3. 

5) Conduct a conventional slope stability analysis using kS = 0.5 kav. If the resulting C/D ratio (i.e. the 

resulting FS) is at least 1.1, the slope meets seismic stability requirements.

6.2.3 Displacement-Based Seismic Stability Analysis 

In contrast to the limit equilibrium approach, the displacement-based approach involves the explicit 

calculation of cumulative seismic deformation. The potential failure mass is treated as either a rigid body 

or deformable body, depending on whether a simplified Newmark sliding block approach or more 

advanced numerical modeling is used.

The Newmark sliding block approach treats the potential failure mass as a rigid body on a yielding base, 

as shown on Figure 6-1. The acceleration time history of the rigid body is assumed to correspond to the 

average acceleration time history of the failure mass. Deformation accumulates when the rigid body

acceleration exceeds the yield acceleration of the failure mass, ky, where ky is defined as the seismic 

coefficient (horizontal acceleration) that results in a C/D ratio of 1.0 in a limit equilibrium analysis.

Acceleration pulses in the time history, including accelerations that exceed the yield acceleration and, 

once the block is moving, accelerations below the yield acceleration until the block stops moving are 

double integrated to calculate cumulative seismic displacement. In a Newmark analysis, relative 

displacement is generally assumed to accumulate in only one direction (i.e. the down slope direction). 

With this assumption, the yield acceleration in the other (upslope) direction is implicitly assumed to be 
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Seismic Design – Geotechnical Features 6-11 August 2011

larger than the peak acceleration in that direction for the failure mass being analyzed. Analyses 

conducted by Yan et al. (1996) demonstrate that the influence of the vertical ground motion component in 

a Newmark analysis is generally relatively small for most situations encountered in practice and can be 

ignored. 

The Newmark Analysis approach may be used to calibrate an appropriate pseudo-static seismic 

coefficient reflecting acceptable displacement performance, as discussed in Section 6.2.1. Similar 

discussions on the Newmark approach for slopes are presented in the FHWA publication Geotechnical 

Earthquake Engineering (FHWA, 1998). For example, Figure 6-4 shows results of Newmark seismic 

deformation analyses performed by Hynes and Franklin (1984) using 348 strong motion records (all 

soil/rock conditions; ) and six synthetic records. The Hynes and Franklin “upper bound” 

curve presented in Figure 6-4 suggests that deformations will be less than 12 inches for yield 

accelerations greater than or equal to one-half the peak average acceleration (i.e. for a seismic coefficient 

greater than or equal to 0.5 kav) in all situations. 

Figure 6-4 Permanent Seismic Deformation Chart (Hynes and Franklin, 1984)

M w << 4.75.4
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Seismic Design – Geotechnical Features 6-12 August 2011

As previously discussed, it must be recognized that slope-height effects should be taken into account to 

determine an appropriate seismic coefficient or to estimate permanent seismic displacement. This was 

recognized by Makdisi and Seed (1978), who developed slope displacement design charts for the seismic 

design of earth dams.

Newmark sliding block analyses are also used to evaluate horizontal sliding displacements of gravity 

retaining walls, as described in current AASHTO (2007). The current AASHTO provisions for retaining 

wall design employ the displacement equation of Richard and Elms (1979) in which the permanent 

seismic displacement of a free standing retaining wall (in inches) is given as:

( ) 4

max

y

max

2

k

k

gk

PGV 087.0d

−

















⋅ 



 



 = 6-6 

Newmark sliding block displacement analyses were conducted as part of the NCHRP 12-70 project using 

an extensive database of earthquake records. The end result of these analyses was establishment of 

updated relationships between permanent seismic displacement (d) and the following three terms: the 

ratio ky/kav, kav, and the peak ground velocity (PGV). Noted that NCHRP Report 611 uses the term kmax

in place of kav in these equations but defines kmax in the same manner as kav is defined herein (e.g. as α x 

Fpga PGA). Based on regression analyses, the following simplified relationships for permanent seismic 

displacement were established in the NCHRP 12-70 study and are recommended herein for displacementbased slope stability assessment purposes: 

• For all sites except CEUS rock (Site Class A and B) sites, the displacement (in inches) can be 

estimated by the following equation: 

log(d) = 6-7 

(k max) (PGV )

k k max)

(k kmax)

y

y

log 1.59 log

3.27 log(1 / 0.80

1.51 0.74 log /

+ ⋅

⋅ − −

− − ⋅ +

• For CEUS rock (Site Class A and B) sites, displacement (in inches) can be estimated by:
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Seismic Design – Geotechnical Features 6-13 August 2011

log(d) = 6-8 

(k ) (PGV )

k k max)

(k kmax)

y

y

log 1.12 log

4.52 log (1 / 0.46

1.31 0.93 log /

max + ⋅

⋅ − −

− − ⋅ +

The mean value of PGV is given in NCHRP Report 611 by the approximation: 

PGV SF38 1v ⋅⋅= 6-9 

NCHRP Report 611 actually recommends using the mean plus one standard deviation value for PGV 

(equal to 55FvS1) in Equations 6-7 and 6-8 to provide a margin of conservatism. However, for 

consistency with LRFD principles, the use of the mean value of the PGV is recommended herein. 

The development of the PGV-S1 correlation in Equation 6-9 was based on a simplification of a more 

precise but more complicated equation developed using regression analysis on an extensive database of

recorded and synthetic accelerograms representative of both rock and soil conditions for the WUS and the 

CEUS. It was found that earthquake magnitude need not be explicitly included in the correlation, as its 

influence on PGV is captured by its influence on the value of S1. Figure 6-5 shows a comparison between 

the displacements estimated using the existing AASHTO displacement equation and Equation 6-6. 

Figure 6-5 Comparison between AASHTO (2002) and Recommended Displacement Equation 6-6

for PGV = 30kmax (in/sec)
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Seismic Design – Geotechnical Features 6-14 August 2011

Note that Equations 6-7 and 6-8 represent mean values and, based upon standard deviation from the 

statistical analysis, the resulting displacements can be multiplied by 2 to obtain displacements at the 84 

percent confidence level.

Similar displacement equations to those recommended in Equations 6-7 and 6-8 were developed by 

Martin and Qiu (1994) from a more limited database of earthquake records, and were described in the 

NCHRP 12-49 Project report (NCHRP, 2003). The recommended equations shown above give 

displacements slightly greater than the Martin and Qiu (1994) correlations. In 2000, an approach for 

estimating the displacement of slopes during a seismic event was developed through the Southern 

California Earthquake Center (SCEC, 2002). Displacement comparisons (described in NCHRP Report 

611) between the SCEC approach and the approach recommended above show similar results. 

In summary, the following methodology is recommended for displacement-based seismic stability 

assessment of slopes and embankments: 

1) Conduct static slope stability analyses using appropriate resistance factors to confirm that 

performance meets static loading requirements.

2) Establish the upper bound value of the seismic coefficient kmax ( = Fpga PGA) and the site-adjusted 

spectral acceleration at one second, FvS1, from the AASHTO ground motions maps for a 1,000-year 

return period and the Site Class-dependent AASHTO site factors. 

3) Determine the corresponding peak ground velocity (PGV) from the correlation equation between 

FvS1 and PGV (i.e. PGV = 38 FVS1).

4) When the slope height is greater than 20 ft, modify kmax by multiplying it by the slope height factor, 

α, to get kav, to account for slope height effects.

5) Determine the yield acceleration, ky, using a pseudo-static stability analysis for the slope. Note that 

these stability analyses should normally be conducted using the undrained strength of the soil 

because of the short-term rapid loading from the earthquake. 

6) Establish the earthquake slope displacement potential as a function of ky, kav, and PGV using the 

appropriate Newmark displacement equations.

7) Evaluate the acceptability of the displacement based on performance criteria established by the 

owner for the specific project site.
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Seismic Design – Geotechnical Features 6-15 August 2011

A detailed example demonstrating the application of the NCHRP 12-70 (2008) procedure outlined above 

for the seismic design of embankment slopes is given in Section 7.3 of this document.

6.2.4 Rock Slope Stability Analyses 

Analysis approaches to evaluate rock slope seismic stability follow the same basic principles as the 

approaches used for soil slopes and embankments described above. However, there are unique challenges 

related to the rock mass characterization and the determination of rock mass strength parameters. These 

issues, issues which apply also to static stability evaluations, are briefly reviewed and summarized in 

Chapter 4. A more detailed discussion of these problems is provided in the FHWA NHI course reference 

manual on Rock Slopes (FHWA 1998a) and in FHWA Geotechnical Engineering Circular No. 5 on 

Evaluation of Soil and Rock Properties (FHWA 2002). A summary discussion on rock slope stability 

from these publications is given below. 

With respect to rock slope stability, two distinct cases arise in practice. The first case arises with highly 

fractured rock masses, where the rock may be treated as an isotropic material with equivalent MohrCoulomb strength parameters c and φ. For this case, conventional two dimensional limit equilibrium 

stability analyses are applicable. The second case relates to where distinct bedding planes, 

discontinuities, or joints in the rock mass define potential planes of failure. In these cases, three 

dimensional stability analyses may be required.

One challenge in rock slope stability analyses is that the shear strength envelope for both a fractured rock 

mass and for a discontinuity is often curved. The procedure for using a curved strength envelope in a 

stability analysis is first, to determine the range of effective normal stresses acting along a potential 

rupture surface in the slope, and second to calculate the instantaneous cohesion values and friction angles 

( ) in this stress range. Chapter 4 describes the procedure for evaluating instantaneous values of 

cohesion and friction angle from a curved strength envelope. 

The stability analysis in a highly fractured rock mass is carried out in the same manner as for a soil slope

except that a number of values of and values are used corresponding to the variation in normal 

stress in the ground. Li et al. (2009), have developed seismic rock slope stability charts based on 

conventional limit analysis methods. Figure 6-6 shows that the slope parameter definitions used for the 

charts. Figure 6-7 shows representative results where N is a dimensionless stability number. 

ii c φ','

i c' i φ'
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Seismic Design – Geotechnical Features 6-16 August 2011

Figure 6-6 Problem Definition (Li et al., 2009) 

Figure 6-7 Representative Analysis Results (Li et al., 2009) 

For rock masses with discrete discontinuities, stereo plots of joint systems in a rock mass will often define 

distinct potential failure planes as illustrated in Figure 6-8b and 6-8c and discussed in detail in the Rock 

Slope NHI course manual (FHWA, 1998a). 
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Seismic Design – Geotechnical Features 6-17 August 2011

Figure 6-8 Main Types of Slope Failure and Stereoplots of Structural Conditions Likely to Give Rise 

to these Failures (Hoek and Bray, 1977)
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Seismic Design – Geotechnical Features 6-18 August 2011

6.3 SOIL LIQUEFACTION HAZARD

6.3.1 Hazard Description and Initial Screening

Soil liquefaction is a phenomenon in which a cohesionless soil deposit below the groundwater table loses 

a substantial amount of strength due to pore pressure generation resulting from earthquake strong ground 

shaking. The reason for the generation of pore pressure is that cohesionless soils tend to compact during 

earthquake shaking and this tendency causes the pore water pressures in the soil to increase until the pore 

water has time to drain (dissipate) from the soil skeleton . This pore pressure increase, in turn, causes a 

reduction in effective stress and associated reductions in soil strength and stiffness. Recently deposited 

(i.e., geologically young) and relatively loose natural soils and uncompacted or poorly compacted fill

soils are susceptible to liquefaction. Loose sands and silty sands are particularly susceptible to 

liquefaction. Loose silts and gravels also have a significant potential for liquefaction. Dense natural 

soils, well-compacted fills, and cohesive soils have a relatively low susceptibility to liquefaction. 

Liquefaction has been perhaps the single most significant cause of damage to bridges during past 

earthquakes. Most of the damage has been related to liquefaction-induced lateral movement of soil at 

bridge abutments. However, cases involving the loss of lateral and vertical bearing support of 

foundations for bridge piers due to liquefaction have also occurred. 

The potential consequences of liquefaction can be grouped into the following categories: 

1) Flow slides. Flow failures are the most catastrophic form of ground failure that can occur due to 

liquefaction. These large slides occur when the down slope static (gravity) loads exceed the 

resistance provided by low shear strengths of liquefied soils, (i.e., the static factor of safety drops 

below 1.0 due to liquefaction). These slides can occur even after the ground stops shaking, and 

commonly results in tens of feet of displacement. Further discussion of flow slides is provided in 

Section 6.4.2. 

2) Lateral spreading. Lateral spreading is the most common form of lateral soil movement 

accompanying liquefaction. It can occur on very gently sloping ground or under embankments 

underlain by liquefied soil due to combined static gravity and seismically induced inertia forces in 

the soil mass. In lateral spreading, the static factor of safety of the soil mass is greater than one but 

lateral movements accumulate during the earthquake when the static plus seismically induced shear 
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Seismic Design – Geotechnical Features 6-19 August 2011

stresses exceed the strength of liquefied soil. The resulting lateral movements can range in 

magnitude from inches to several feet and are typically accompanied by ground cracking with 

horizontal and vertical offsets. The potential for lateral movements due to lateral spreading is 

increased if there is a ‘free face’ such as a river bank in the laterally spreading mass. Lateral 

spreading can occur beneath a bridge approach fill or highway embankment if the underlying soil 

liquefies. Further discussion of lateral spreading is provided in Section 6.4.3. 

3) Reduction in foundation bearing capacity. The occurrence of liquefaction beneath, and/or laterally 

adjacent to, bridge foundations can greatly reduce foundation vertical and/or lateral capacity, 

resulting in unacceptable foundation settlements and or lateral movements. The bearing capacity

of a shallow foundation in liquefied soil can be evaluated using conventional bearing capacity 

theory and the residual undrained shear strength of the liquefied soil discussed in Section 4.4.6. 

The lateral resistance of deep foundations in liquefied soil is discussed in Section 10.6.6.

4) Ground settlement. Even in the absence of flow sliding, lateral spreading, or reduction in 

foundation bearing capacity due to liquefaction, ground settlements due to soil consolidation can 

occur as liquefaction-induced, excess pore water pressures in the soil dissipate. In some cases, this 

consolidation may take a substantial period of time to occur, perhaps hours or, in extreme cases,

days after the earthquake, and may result in unacceptable total and/or differential settlement of 

foundations located above the liquefied layer. Furthermore, deep foundations extending through 

liquefied strata may be subject to downdrag as soils overlying the liquefied layers settle relative to 

the piles. However, the magnitude of total and differential ground settlement is typically less than 

that associated with flow slides, lateral spreading, or reduction in foundation bearing capacity. 

Further discussion of the settlement of liquefied soil is provided in Section 6.5.2. 

5) Increased pressure on retaining walls. Liquefaction in the backfill behind a retaining wall, such as 

an abutment backwall or wingwall, will increase lateral earth pressures on the wall, potentially 

leading to wall failure or excessive deformations. 

Table 6-1 presents recommendations concerning the seismic hazard level at which a liquefaction analysis 

is necessary from the FHWA Seismic Retrofitting Manual for Highway Structures (FHWA, 2006). In 

these recommendations, the need to conduct an evaluation of liquefaction is described as a function of the 

Seismic Hazard Level for the bridge, which depend upon the value of the Site Class-adjusted spectral 

acceleration at both 1 second (SD1) and 0.2 second (SDS). For Seismic Hazard Levels I and II, the 

potential for liquefaction is generally low as peak ground accelerations are likely to be less than 0.14g and 
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Seismic Design – Geotechnical Features 6-20 August 2011

earthquake magnitudes are generally less than 6.0. In addition, little potential exists for permanent 

movement of the ground because of the small size and limited duration of seismic events at these levels.

TABLE 6-1 SEISMIC HAZARD LEVEL

Hazard Level Using SD1 = FvS1 Using SDS = FaSs

I 

II

III

IV

Notes:

1. For the purposes of determining the Seismic Hazard Level for Site Class E soils, the value of Fv and Fa need not be taken larger than 2.4 

and 1.6 respectively, when S1 is less than or equal to 0.10 and Ss is less than 0.25.

2. For the purposes of determining the Seismic Hazard Level for Site Class F soils Fv and Fa values for Site Class E soils may be used with 

the adjustment described in Note 1 above.

The potential for liquefaction at the higher accelerations corresponding to Seismic Hazard Levels III and 

IV is greater than for Seismic Hazard Levels I and II and therefore careful attention is needed to 

determine the potential for, and consequences of, liquefaction at sites with this hazard level. However, 

for Seismic Hazard Level III the following magnitude criterion may also be applied: if the mean 

magnitude contributing to the peak ground acceleration is less than 6.0, or if it is between 6.0 and 6.4 and 

either the normalized Standard Penetration Test (SPT) blow count (N1)60 is greater than 20, or (N1)60 is 

greater than 15 and FaSs is less than 0.35g, a liquefaction analysis is not required. 

In summary, an evaluation of the potential for, and consequences of, liquefaction in soils near the surface 

should be made in accordance with the following requirements:

• Seismic Hazards Levels I and II: Not required.

• Seismic Hazards Levels III: Required, unless one of the following two conditions is met: 

• Mean magnitude for the design event is less than 6.0.

15.0 S D1 ≤ ≤ 15.0 DS S

15.0 25.0  S D1 ≤ 15.0 ≤ 35.0  S Ds

25.0 40.0  S D1 ≤ 35.0 ≤ 60.0 Ds  S

1 40.0 D  S 60.0  S Ds
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Seismic Design – Geotechnical Features 6-21 August 2011

• Mean magnitude for the design event is less than 6.4 and equal to or greater than 6.0, and either the 

normalized Standard Penetration Test (SPT) blow count (N1)60 is greater than 20, or (N1)60 is 

greater than 15 and FaSs is less than 0.35g.

• Seismic Hazard Level IV: Required 

In addition to the above criteria, it can be assumed that a significant liquefaction hazard does not exist for 

Seismic Hazards Levels III and IV if any of the following screening criteria are satisfied:

• The geologic materials underlying the site are either bedrock of have very low liquefaction 

susceptibility according to the relative susceptibility ratings shown in Table 6-2, which are based on 

geologic age and general depositional environments (Youd and Perkins, 1978). Table 6-2 should 

be applied conservatively if there are uncertainties regarding geologic age or depositional 

environment. 

• The soils below the groundwater table at the site are one of the following:

1. Clayey soils which have a clay content (grain size < 0.005 mm) greater than 15 percent, liquid limit 

greater than 35 percent, or natural water content less than 90 percent of the liquid limit (Seed and 

Idriss, 1982). However, clayey soils that are highly sensitive, based on measured soil properties or 

local experience, should not be screened out. A highly sensitive1 soil possesses all of the following 

properties: 

a. Liquid limit less than 40 percent.

b. Water content greater than 0.9 times the liquid limit.

c. Liquidity index greater than 0.6 

d. (N1)60 less than five or normalized cone penetration resistance qc1, less than 20 ksf. 

2. Sand with a minimum corrected Standard Penetration Test resistance, (N1)60 value of 30 blows/foot or 

minimum corrected cone penetration test tip resistance, qC1N, of 160 with a sufficient number of 

tests. 

 1 Areas of the United States known to have highly sensitive soils include some coastal areas of 

Alaska, along the St. Lawrence River, some eastern and western coastal areas with estuarine soils 

deposits, near or within saline lakes in the Great basin and other arid areas, and soils resulting 

from weathering of volcanic ash (Youd, 1998). 
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Seismic Design – Geotechnical Features 6-22 August 2011

3. The water table is deeper than 50 feet below the existing ground surface or proposed finished grade at 

the site, whichever is lower, including considerations for seasonal, historic and possible future rises 

in groundwater level. 

TABLE 6-2 ESTIMATED SUSCEPTIBILITY OF SEDIMENTARY DEPOSITS TO 

LIQUEFACTION DURING STRONG GROUND MOTION (Youd and Perkins, 1978)

 

If the above screening criteria are not satisfied, then more detailed evaluations should be used to evaluate 

a liquefaction hazard and its potential consequences. However, prior to initiating screening procedures for 

soils that are susceptible to liquefaction, a check should be made as to whether liquefaction has previously 
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Seismic Design – Geotechnical Features 6-23 August 2011

occurred at the site (or in the near vicinity of the site in similar geotechnical conditions) during past 

earthquakes. This check may involve review of the earthquake history of an area and review of published 

post-earthquake reconnaissance reports. If there is evidence that liquefaction has previously occurred at 

the site, then it must be given further consideration regardless of what screening criteria indicate.

 

6.3.2 Liquefaction Strengths: Laboratory and In-situ Tests

Undrained cyclic stress controlled triaxial tests on saturated sands to simulate liquefaction were first 

studied by Seed and Lee (1966). Subsequently, to better simulate earthquake induced cyclic stress 

conditions in the field, cyclic simple shear tests were conducted by Finn et al. (1971) and Seed and 

Peacock (1971). Cyclic torsional shear tests (a special case of simple shear testing) have also been 

conducted to simulate earthquake induced cyclic loading of liquefiable soil. Representative strain 

controlled cyclic torsional shear tests showing degradation in stiffness and strength with number of cycles 

are shown in Figure 6-9 (Figueroa et al. (1994)). In denser soils, an increase in post liquefaction stiffness 

of the soil due to dilation may occur, as shown in Figure 6-10. Degradation in stiffness and strength of 

liquefied soil has also been demonstrated by back analysis of acceleration records at sites which have 

liquefied, as illustrated in Figure 6-11. 

Most laboratory liquefaction tests are uniform cyclic loading tests. Typically, when displaying the results 

of uniform cyclic loading liquefaction tests, the cyclic stress ratio (CSR) that causes liquefaction is plotted 

against number of cycles of loading it took to cause liquefaction, as shown in Figure 6-12, where the CSR 

= , = horizontal cyclic shear stress, and is the initial vertical effective stress. The 

resulting curves are sometimes referred to as cyclic strength curves.

While there are procedures to use laboratory test results such as those shown in Figure 6-12 to evaluate 

liquefaction potential, the use of laboratory tests to evaluate liquefaction strengths for design has major 

disadvantages. These disadvantages primarily relate to sample disturbance, simulation of the multidirectional shaking which occurs in the field, and replication of the stress history to which the soil has 

been subjected in the field. Consequently, in the 1980’s, correlations between values of the earthquakeinduced CSR that caused liquefaction in the field (termed the cyclic resistance ratio, or CRR) started to be 

established by studies at sites which had or had not liquefied during past earthquakes. CRR correlations 

based on site characterization using SPT or CPT methods or shear wave velocity are now the standard of 

practice for evaluating liquefaction potential, as described in Section 6.3.3. 

'/στ vc c τ ' σ v
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Seismic Design – Geotechnical Features 6-24 August 2011

Figure 6-9 Strength Degradation in Cyclic Torsional Shear tests (Figueroa et al. 1994) 

 

Figure 6-10 Undrained Cyclic Simple Shear Test Results Nevada Sand, Dr = 40% (Arulmoli et al., 

1992) 
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Seismic Design – Geotechnical Features 6-25 August 2011

Figure 6-11 Shear Stress Strain History at the Wildlife Refuge Site during Liquefaction

(Elgamal and Zeghal 1992, Zeghal and Elgamal 1994) 

Number of Cycles

Figure 6-12 The CSR Required to Reach Initial Liquefaction ( ), from Shaking Table 

Tests by De Alba et al. (1976) 

ru = %100
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Seismic Design – Geotechnical Features 6-26 August 2011

Detailed descriptions of SPT and CPT tests and shear wave velocity measurements for site 

characterization are provided in Chapter 4. The use of the data from such tests to establish liquefaction 

strengths at a given site and the associated liquefaction potential are described in the next section. 

6.3.3 Empirical and Numerical Evaluation Procedures for Liquefaction Potential 

The procedures given below for the evaluation of liquefaction are based on the following source 

documents: 

1. Proceedings of the 1996 NCEER Workshop (now MCEER) on evaluating liquefaction resistance 

 (Youd and Idriss, 1997; Youd et al., 2001). 

2. Recommended LRFD Guidelines for the Seismic Design of Highway Bridges (ATC/MCEER, 

2003), and the AASHTO Guide Specifications for LRFD Seismic Bridge Design (AASHTO, 

 2009) 

3. Seismic Retrofitting Manual for Highway Structures: Part 1- Bridges (FHWA, 2006). 

4. Procedures for Implementing Guidelines for Analyzing and Mitigating Liquefaction in California 

(SCEC, 1999).

A number of factors must be considered during the planning and execution of the field exploration phase 

of a liquefaction investigation. These include:

1. Location of Liquefiable soils. 

2. Location of groundwater level. 

3. Maximum anticipated depth of liquefaction. 

During the field investigation, the limits of unconsolidated deposits with liquefaction potential should be 

mapped within and beyond the footprint of the bridge or transportation structure. Typically, this will 

include an investigation at each bridge pier location and at a sufficient number of locations away from 

approach fills to establish the spatial extent of liquefiable material. The investigation should establish the 
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Seismic Design – Geotechnical Features 6-27 August 2011

thickness and consistency of liquefiable deposits from the ground surface to the depth at which 

liquefaction is not expected to occur. 

The permanent groundwater level should be established during the exploration program. If uncertainty 

exists in the location of the groundwater level, piezometers should be installed during the exploration 

program. The location of the groundwater level should be monitored in the piezometers over a sufficient 

duration to establish seasonal fluctuations that may be due to rainfall, river runoff, or irrigation. If the 

groundwater level fluctuates due to tidal action or seasonal river fluctuations, then the zone of fluctuation 

will often have a lower degree of saturation, making the soil more resistant to liquefaction. Unless the 

high water table elevation due to seasonal fluctuation is expected to remain in place for an extended 

period of time (e.g. on the order of weeks) at the higher level, it is usually acceptable to use a long-term 

groundwater level as a basis for design.

Field exploration should be conducted to the maximum depth of liquefiable soil. A depth of about 15 m 

has often been used as the depth of analysis for the evaluation of liquefaction. However, liquefaction is 

now believed to have occurred to depths in excess of 80 ft during the 1964 Alaska earthquake. For this 

reason it is recommended that a minimum depth of 80 ft below the existing ground surface or lowest 

proposed finished grade (whichever is lower) be investigated for liquefaction potential. For deep 

foundations (e.g. shafts or piles), the depth of investigation should extend to a depth that is a minimum of 

20 ft below the lowest expected foundation level (e.g. shaft bottom or pile tip) or 80 ft below the existing 

ground surface or lowest proposed finished grade, whichever is deeper. However, an investigation need 

not extend below a depth at which geologic deposits that are liquefiable are clearly no longer present.

As discussed in Chapter 4 and Section 6.3.2, three field exploration methods are normally used for 

evaluation of liquefaction potential: the Standard Penetration Test (SPT) method, and the Cone 

Penetrometer Test (CPT) method. Other methods may also be used as required if CPT or SPT testing is 

not feasible. For example, shear wave velocity measurements or the Becker Hammer Test (BHT) method 

may be used for assessments of liquefaction potential in gravelly soils (e.g. where SPT and CPT cannot 

be conducted). A geologic reconnaissance and review of the available geotechnical information for the 

site should supplement any field investigation.

Information presented in Youd and Idriss (1997), Youd et al. (2001) and SCEC (1999) indicate that the 

results of SPT explorations are affected by small changes in measurement method. Primarily because of 

their inherent variability, sensitivity to test procedure, and uncertainty, SPT N-values have the potential to 

provide misleading assessments of liquefaction hazard if the tests are not performed carefully. Beacause 
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Seismic Design – Geotechnical Features 6-28 August 2011

of the sensitivity of SPT results to test procedure, the relative reliability of CPT test results, and the 

continuous soil profile provided by CPT sundings, the CPT method is gaining recognition as the preferred 

method for evaluating liquefaction potential in many locations. Methods for assessing liquefaction 

potential from CPT results are given in Youd and Idriss (1997) and Youd et al. (2001). The primary 

advantages of the CPT method are:

• It provides an almost continuous penetration resistance profile that can be used for stratigraphic 

interpretation, which is particularly important in determining the potential for lateral spreading, 

lateral flow slides, and significant earthquake induced total and differential action settlements.

• The repeatability of the test is very good.

• The test is fast and economical and less sensitive to field procedures compared to either the SPT or 

drilling and laboratory testing of soil samples. 

However, the CPT method does have some limitations. The limitations of the CPT method are: 

• It does not provide soil samples for visual classification or laboratory tests.

• It provides interpreted soil behavior types and not the actual soil type according to ASTM Test 

Methods D 2488 (Visual Classification) or D 2487 (USCS Classification) [ASTM, 1998]. 

• Tests cannot be performed in gravelly soils and sometimes the presence of hard/dense crusts or 

cemented layers at shallow depths makes penetration to desired depths difficult.

In cases where neither the SPT nor the CPT method can be employed (e.g. gravelly soil or soils where a 

hard crust hinders penetration), measurement of shear wave velocity provides an alternative means of 

evaluating liquefaction potential. 

6.3.4 Evaluation of Liquefaction Potential 

Two basic procedures are used to evaluate the potential for liquefaction at a site. These are:

• A simplified procedure that is based on empirical correlations to observations of liquefaction. 

• More rigorous numerical modeling. 
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Seismic Design – Geotechnical Features 6-29 August 2011

For most projects, the simplified procedure will be acceptable. However, for some projects, more 

rigorous numerical modeling using advanced codes may be appropriate. Conditions warranting the use of 

more rigorous numerical methods include:

• Sites where potentially liquefiable soils extend to depths greater than 25 m.

• Sites that have significant interlaying, particularly where interlayers comprise highly permeable 

soils or low permeability layers.

• Sites where the cost of ground improvement methods to mitigate the impact of liquefaction is great. 

One potential benefit of using a rigorous numerical method to evaluate liquefaction potential is that the 

results of these methods generally provide an acceleration response spectrum that includes the effect of 

pore pressure softening. As noted in Chapter 5, considering earthquake induced pore pressure generation

may result in lower estimates for earthquake ground motions at the ground surface (as well as within the 

soil profile) and AASHTO seismic provisions allow the design engineer to take advantage of the 

reductions in spectral acceleration due to pore pressure generation (up to a limiting reduction of 33% from 

the non-liquefaction values). 

The most basic procedure used in engineering practice for assessment of soil liquefaction potential is the 

‘Simplified Procedure’. This procedure, originally developed by Seed and Idriss (1971), compares the 

cyclic resistance ratio (CRR, the cyclic stress ratio required to induce liquefaction at a given depth) to the 

earthquake-induced cyclic stress ratio (CSR) at that depth from the design earthquake (generally defined 

by a peak ground surface acceleration and an associated earthquake magnitude). The CRR and CSR are 

both expressed as a ratio of cyclic shear stress to the initial (pre-earthquake) effective overburden pressure 

on a horizontal plane at the specified depth in the soil deposit. Values of CRR for the Simplified 

Procedure were originally established from data on the normalized SPT value, (N1)60 , at sites that did or 

did not liquefy during past earthquakes, independent of earthquake magnitude and the fines content 

(percent by weight passing the #200 sieve) of the soil. The current version of this baseline chart, defining 

values of CRR as a function of (N1)60 and fines content for magnitude 7.5 earthquakes, is shown in Figure 

6-13. This chart was established by consensus at a 1996 workshop organized by the Multi-Disciplinary 

Center for Earthquake Engineering (MCEER) (Youd and Idriss, 1997; Youd et al., 2001). As suggested 

by the form of this chart, the determination of CRR must consider the fines content of the soil, the 

efficiency (delivered energy) of the SPT hammer, the effective overburden pressure at the depth at which 

the SPT was conducted, and the magnitude of the earthquake (Youd and Idriss, 1997; Youd et al., 2001)

as well as peak ground acceleration at the site due to the earthquake. 
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Seismic Design – Geotechnical Features 6-30 August 2011

Figure 6-13 Simplified Base Curve Recommended for Determination of CRR from SPT Data for 

Magnitude 7.5 Along with Empirical Liquefaction Data (Youd and Idriss, 1997)

The effect of earthquake magnitude on CRR (i.e. the effect of magnitude other than 7.5 on the ordinates 

of Figure 6-13) is generally taken into account using a magnitude scaling factor, MSR, as follows:

CRR MSF⋅= CRR =7.5M

6-10

 

The value of MSF was one of the more contentious issues considered during the 1996 MCEER 

Workshop (Youd and Idriss, 1997; Youd et al., 2001). The range of magnitude scaling factors 

recommended by various investigators is shown in Figure 6-14. The consensus recommendation from the 

workshop was that the magnitude factors defined by the curve at the lower-bound of the recommended 

range (cross-hatched area) in Figure 6-14 should be used unless different factors can be justified. Note

that for magnitudes greater than 7.5, the corresponding recommended curve is the second highest curve 

shown in Figure 6-14. 
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Seismic Design – Geotechnical Features 6-31 August 2011

Figure 6-14 Magnitude Scaling Factors Derived by Various Investigators (Youd and Idriss, 1997) 

Adjustments for changes in water table and overburden condition at the time of investigation may have to 

be made during a simplified analysis. The following guidance is provided for making these adjustments.

• Overburden Corrections for Differing Water Table Conditions To perform analyses of liquefaction 

potential, liquefaction settlement, seismically induced settlement, and lateral spreading, it is 

necessary to develop a profile of SPT blow counts that have been normalized to N1, the blow count 

at an effective overburden pressure of 1 TSF, using the effective overburden pressure at the time of 

the investigation. Normalization factors for N1 are presented in Chapter 4. 

Note that this normalization should always be performed using the effective stress profile that existed at 

the time the SPT testing was performed, as this reflects the condition under which the blow count was 

recorded. These normalized blow count values are then held constant throughout the remainder of the 

analyses, regardless of whether or not the analyses are performed using higher or lower water-table 

conditions. Although in some soils softening soil moistening can influence SPT results if the water table 

fluctuates, this is. In general, not a concern in soils prone to liquefaction it is commonly assumed that the 

only effect that changes in the water table have on the SPT blow count is due to changes in the effective 

overburden stress. 
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Seismic Design – Geotechnical Features 6-32 August 2011

• Overburden Corrections for Differing Fill Conditions Approach fills, and other increases in 

overburden pressure, should be handled similarly to that described above for changes in 

groundwater location. The profile of normalized SPT blow counts that were established in the 

investigation before the fill is placed is held constant throughout the remainder of the analyses, 

regardless of whether or not the analyses are performed using a higher fill condition. 

• Figure 6-15 shows the Robertson and Wride (1998) chart for determining liquefaction strength 

(CRR) for clean sands (fines content, FC, less than or equal to 5 percent) from CPT data. This

chart, which is only valid for magnitude 7.5 earthquakes, shows calculated cyclic stress ratios 

plotted as a function of corrected and normalized CPT resistance qC1N. Similar to the SPT CRR plot 

in Figure 6-13, Figure 6-15 is based upon CPT data obtained at liquefied and non-liquefied sites in 

earthquakes. The solid-line CRR curve separates regions of liquefaction from regions of nonliquefaction. Dashed curves showing approximate cyclic shear strain potential as a function of qC1N

are also shown on this plot to emphasize that the cyclic shear strain and ground deformation 

potential of liquefied soils decrease as penetration resistance increases.

Figure 6-15 CPT-Liquefaction Resistance Correlation Chart (Robertson and Wride, 1998) 
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Seismic Design – Geotechnical Features 6-33 August 2011

As in the SPT method, the determination of CRR using the CPT method must account for the fines 

content of the soil, the effective overburden pressure, and the magnitude of the earthquake. To account 

for these factors, the normalized clean sand CPT resistance, (qc!N)CS, is used with Figure 6-15. According 

to Youd et. al (2001), (qc!N)CS, is calculated as shown in Equation 6-11: 

( ) c

a

c

n

vo

'

a

cIN CS K

p

qp q 













  ⋅ 

 





σ = 6-11 

 

where pa = atmospheric pressure (in the same units as qc), the exponent n is equal to 0.5 for sand, 0.7 for 

silty sand, 0.8 for silt, and 1.0 for clay, and Kc is a CPT grain size correction factor. The value of Kc can 

be evaluated from Figure 6-16 as a function of the soil behavior type index, Ic, which can be calculated 

using Equation 6-12: 

[( ) ( ) ] 5.0 2 2

c = ++ Flog22.1logQ -3.47I 6-12

 

where Q and F are evaluated using Equations 6-13 and 6-14, respectively, as: 

( ) n

vo

'

a

a

voc p

p

q Q 



 





σ

⋅ 



 



 σ− = 6-13 

and 

( ) %100

q

f F

voc

s ⋅ 



 





σ− =

6-14

 

Note that if Ic is greater than 2.6, the soil is considered to be non-liquefiable. 

The comments given in the previous section regarding use of normalized (for effective overburden 

pressure) SPT blow counts in liquefaction analyses (e.g. use the water table depth and total and effective 

overburden pressures at the time of the site investigation to calculate CRR) are also valid for use of 

normalized CPT data. The recommended magnitude scaling factors for the CRR based upon CPT 

resistance are the same as those for the SPT-based CRR and are shown in Figure 6-14. 
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Seismic Design – Geotechnical Features 6-34 August 2011

Figure 6-16 CPT Grain Size Characteristic Correction Factor (Robertson and Wride, 1998) 

Figure 6-17 shows the basic plot from Andrus and Stokoe (2000) for determining the liquefaction strength 

(CRR) of Holocene-aged sands with fines contents of less than 5%, 20%, and greater than 35% in an 

earthquake of Mw 7.5 using shear wave velocity. 

Figure 6-17 uses the shear wave velocity normalized to an overburden pressure of 1 TSF, Vs1, to 

characterize the soil. Vs1 is evaluated as:

25.0

vo

'

a

s1 s

p VV 



 





σ = 6-15 

The CRR can also be obtained Becker Hammer Test (BHT) data, as discussed in Youd and Idriss (1997) 

and Youd et al. (2001). However, the use of the BHT for evaluating liquefaction resistance is not 

considered as reliable as the use of shear wave velocity due to the uncertainties and variability associated 

with Becker Hammer data.
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Figure 6-17 Shear Wave Velocity – Liquefaction Resistance Correlation Chart (Andrus and Stokoe, 

2000) 

To estimate values of the earthquake-induced cyclic shearing stress ratio, CSR, the MCEER workshop 

(Youd and Idriss, 1997; Youd et al., 2001) recommended essentially no change to the original simplified 

procedure developed by Seed and Idriss (1971). In this procedure, a magnitude-independent soil 

flexibility factor, rd, shown in Figure 6-18, is used to define the reduction in CSR with depth (from the 

CRR value at the ground surface). Since the MCEER workshop, several investigators have provided 

alternative recommendations for assessing rd. For instance, Idriss (1999) proposed that rd be expressed as

a function of earthquake magnitude. However, none of these alternative recommendations have achieved 

general acceptance in the geotechnical community. A more rigorous alternative to using rd charts is to 

conduct a site-specific seismic response analysis of the ground motions, as discussed below. 
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 SOIL FLEXIBILITY FACTOR (rd)

Figure 6-18 Soil Flexibility Factor (rd) Versus Depth Curves Developed by Seed and Idriss (1971) 

(with added Mean Value line) 

With the Simplified Procedure, the CSR is calculated using the following equation: 

d vo

'

max vo

vo

'

av

g

a CSR 65.0 γ



 





σ

σ ⋅ 





 





  ⋅=

 





σ

τ = 6-16 

where is the representative earthquake induced cyclic shearing stress divided by the initial 

(pre-earthquake) effective overburden stress, amax is the peak ground acceleration in units of g (the 

acceleration due to gravity), is the ratio of the initial total overburden stress to the initial 

effective overburden stress, and rd is the soil flexibility factor.

av vo στ '/

vovo σσ '/
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Seismic Design – Geotechnical Features 6-37 August 2011

After values of CRR and CSR are established for a soil stratum at a given depth, the C/D ratio for

liquefaction (i.e. the ratio CRR/CSR) can be computed. The C/D ratio should be greater than 1.1 to 

preclude the development of liquefaction. If the C/D ratio drops below 1.1, the potential for liquefaction 

must be considered in assessing the seismic performance of the site. An example of the summary plots 

from a liquefaction triggering analysis for a single SPT boring is shown in Figure 6-19. 

Figure 6-19 Example of a Liquefaction Triggering Analysis for a Single SPT Boring (Idriss and 

Boulanger, 2008) 

6.3.5 Use of Site-Specific response Analyses 

For important projects, the use of site-specific equivalent linear or nonlinear one-dimensional site 

response analyses may be warranted to assess the liquefaction potential at a site. These types of analyses 

were discussed in Chapter 5. The most common approach to site-specific site response analysis for 

liquefaction evaluation is to use an equivalent linear total stress analysis, e.g. a SHAKE analysis, to 
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Seismic Design – Geotechnical Features 6-38 August 2011

determine the maximum earthquake-induced shearing stresses at depth, τmax, for use with the simplified 

procedure described above, in lieu of using Equation 6-16. Note that, as suggested by Equation 6-16, τmax

from a site-specific analysis should be multiplied by a factor of 0.65 to obtain τav for calculating 

representative values of CSR for comparison with CRR values. An alternative numerical modeling 

approach involves the use of nonlinear effective stress site response analyses to directly determine 

developed pore water pressures, as discussed in Chapter 5.

As discussed in Chapter 3, numerical analyses of site response should never be based upon a single 

ground motion time history. A minimum of three time histories should be used in any site response 

analysis and if only three time histories are used the maximum response is to be used in the analysis. 

However, if at least seven time histories are used the average response from the analyses may be used in 

the liquefaction analyses. Furthermore, in general, as ground shaking levels increase to values greater 

than about 0.4 g or where maximum shearing strain amplitudes exceed 1 to 2 percent equivalent linear 

analyses become suspect due to the accumulation of non-linear effects in the soil response. For these 

cases, nonlinear effective stress site response analysis should be considered. Non-linear effective stress 

analysis of site response is discussed in Chapter 5. In the discussion of non-linear analysis in Chapter 5, it 

was recommended that analyses conducted for the purpose of evaluating the effect of pore pressure 

generation on the acceleration response spectrum also consider pore pressure dissipation to mitigate the 

potential for an unconservative result with respect to the resulting response spectra. However, in 

evaluating liquefaction potential, it is recommended to ignore pore pressure dissipation during the 

earthquake, as this is the more conservative approach. 

6.4 LIQUEFACTION INDUCED GROUND DEFORMATIONS

6.4.1 Post Liquefaction Residual Strength

Perhaps the most serious consequence of liquefaction occurs when the post-liquefaction residual 

undrained shear strength of the soil is insufficient to maintain stability of a slope or supported 

embankment under the post-earthquake static load. In this case a flow slide will occur, leading to 

uncontrolled large deformations that will continue until the deformed geometry is statically stable. 

Therefore, establishing the post-earthquake residual shear strength of a liquefied soil is an important 

factor in liquefaction analysis.
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As discussed in Chapter 4, empirical approaches for estimating values of the in situ undrained post 

liquefaction residual strength, Sr, have been developed by back-analyses of liquefaction induced flow 

slides. As discussed in Chapter 4, the two approaches currently used in practice today are the Idriss and 

Boulanger (2007) approach based upon SPT blow count and the Olsen and Johnson approach (2008) 

based on either SPT blow count or CPT tip resistance. 

One question that arises in evaluating the post liquefaction residual strength is whether residual strengths 

mobilized during limited deformation lateral spreading displacements are consistent with residual shear 

strengths mobilized in flow slides. This concern due in part to the observation that in cyclic laboratory 

tests apparent low residual strength values in a liquefied soil may be arrested at larger strains due to 

dilation. However, it can be argued that most of the “ratcheting” incremental permanent deformations 

that lead to the accumulation of displacement during a lateral spread will occur during the time residual 

strength is mobilized. Olsen and Johnson (2008) back analyzed 39 well documented liquefaction induced 

lateral spreading case histories in terms of a mobilized undrained residual strength ratio using 

the Newmark sliding block method. Based on analysis results, they found that the back calculated 

mobilized strength ratios from these lateral spreading cased histories essentially coincided with the 

strength ratios back calculated from flow failures. 

6.4.2 Flow Failures 

Flow failures are the most catastrophic form of ground failure that may be triggered when liquefaction 

occurs. Large translational or rotational flow failures are produced when the average static (gravity) 

shearing stresses on potential failure surfaces exceed the average residual strength of the liquefied soil.

To assess the potential for flow failure, the static strength properties of the soil in liquefied layer are 

replaced with the residual strength (Sr) of the liquefied soil and a conventional limit equilibrium static 

slope stability analysis is conducted. No seismic coefficient is used during this evaluation, thus 

representing conditions after completion of earthquake shaking. The resulting C/D ratio defines the 

potential for flow failures. If the C/D ratio is less than 1.0, a lateral flow failure is predicted.

The estimation of the displacements associated with a lateral flow failure cannot be easily made. The 

deformations can be on the order of tens of feet, depending on the geometry of the flowing ground and the 

types and layering of the soil. In the absence of the reliable methods for predicting deformations, it is 

usually necessary to assume that the soil will undergo unlimited deformations. If the loads imposed by 

'/ S σ vr
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these deformations exceed those that can be tolerated by a structure, some type of ground remediation 

will likely be required. This situation should be brought to the attention of the owner and a strategy for 

dealing with the flow problem agreed upon. 

6.4.3 Lateral Spreading Displacement Evaluations 

The vulnerability of highway bridges to earthquake-induced ground failures arising from liquefaction has 

been clearly demonstrated by the extensive damage observed in past earthquakes. This damage has often 

been associated with translational slides and related embankment deformations due to progressive but 

limited lateral spreading deformations of the order of feet, driven by earthquake ground shaking 

subsequent to liquefaction, with deformations ceasing at the end of the earthquake. Damage modes 

associated with such lateral deformations are related to displacement demands on abutments and piers 

leading to possible pile damage and/or span collapse. Representative damage in the 1964 Alaska and 

Niigata earthquakes and the 1991 Costa Rica earthquake has been documented by Youd (1993). Damage 

of the 1995 Kobe earthquake is described by Tokimatsu and Asaka (1998). Specific examples of lateral 

spreading pile damage are provided in Chapter 7. 

The evaluation of the mode and magnitude of liquefaction induced lateral ground deformations involves 

considerable uncertainty and is the subject of on-going research. Therefore, geotechnical specialist must 

stay apprised of recent developments in this area. The current state of the practice for evaluating lateral 

spreading displacements employs the Newmark sliding block approach on an assumed dominant failure 

plane at the base of a liquefied zone. The liquefaction-induced displacements are defined by the 

estimated lateral displacement on this dominant failure surface, as shown in Figure 6-20. In this type of 

analysis, the yield acceleration of the slide mass is evaluated using the post-earthquake undrained residual 

shear strength of the soil and then the lateral displacement is calculated using this yield acceleration in a 

conventional Newmark analysis (Newmark analysis was discussed previously in this chapter).
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Figure 6-20 Newmark Sliding Block Analysis in Liquefied Soil (NCHRP 12-49, 2003) 

Despite the limitations of applying the Newmark method to calculate the deformations induced by 

liquefaction-induced lateral spreading (e.g. assumptions of a constant yield acceleration based on the 

residual strength, a concentrated sliding surface, and a rigid sliding block), it provides a consistent and 

simple framework for analysis. Further, because lateral spreading occurs at relatively shallow depths and 

due to the base isolation effect created by relatively low undrained residual shear strengths, the dynamic 

effects within the sliding mass are likely to be minimal and can be neglected. Hence the Newmark 

displacement relationships described in Section 6.2.2 may be used directly (without slope height 

adjustments to kmax) to calculate lateral spread displacement values. 

 

6.5 SOIL SETTLEMENT HAZARD

6.5.1 Settlement of Unsaturated Cohesionless Soils 

Observations in past earthquakes have indicated that earthquake induced ground shaking can induce 

significant settlement in dry or unsaturated cohesionless soil deposits. In the 1971 San Fernando 

earthquake for example, settlements of 4 to 6 inches were reported under a building on spread footings on 

a 40 ft. deep sand fill (Seed and Silver, 1972). Laboratory tests to study the settlement of dry sands under 
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cyclic loading were first initiated by Silver and Seed (1971) and led to the widely used design procedure 

developed by Tokimatsu and Seed (1987). This procedure is reproduced below as a series of steps. 

Step 1: From borings and soundings, in situ testing and laboratory index tests, develop a detailed 

understanding of the project site subsurface conditions, including stratigraphy, layer 

geometry, material properties and their variability, and the areal extent of potential problem 

zones. Establish the zones to be analyzed and develop idealized, representative sections 

amenable to analysis. The subsurface data used to develop the representative sections should 

include normalized standardized SPT blow counts, (or results of some other test, e.g., 

the CPT from which (N1)60 can be inferred) and the unit weight of the soil.

Step 2: Evaluate the total vertical stress, and the mean normal total stress, , at 

several layers within the deposit at the time of exploration and for design. The design values 

should include stresses resulting from highway facility construction. Outside of the highway 

facility footprint, the exploration and design values are generally the same.

Step 3: Evaluate the stress reduction factor, , using one of the approaches presented in Section

6.3.3. 

Step 4: Evaluate the normalized effective stress using γeff (Geff / Gmax the Tokimatsu and Seed (1987) 

equation: 

( ) N1 60

σ v σ m σ v 65.0 ⋅≈

dr

















⋅

γ⋅σ⋅α⋅ =γ

max

max dv

max

eff

eff Gg

0.65 ) GG

(

6-17 

2

max VG s ⋅ρ=

where γeff (Geff / Gmax) is a hypothetical effective shear stress factor. Note that Gmax can be 

evaluated from the shear wave velocity (Vs) and the mass density (ρ) of the soil (i.e.

). Alternatively, Gmax (in kPa) can be evaluated from one of the correlations in 

Chapter 4. 

For unsaturated sand, σ’m can be based upon an estimated value of the lateral earth pressure 

coefficient, Ko. However, for most practical purposes, the approximation σ’m = 0.65 σ’v

(which assumes Ko = 0.475) will suffice. 
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Step 5: Evaluate γeff as a function of σ’m and γeff (Geff/Gmax) using the chart reproduced in Figure 6-21. 

Step 6: Assuming that , where is the cyclic shear strain, evaluate the volumetric strain 

due to compaction, , as a function of γc and (N1)60 for an earthquake of magnitude 7.5 (15 

cycles) using the chart reproduced in Figure 6-22. 

Step 7: Correct for earthquake (moment) magnitude other than Mw 7.5 using the correction factors 

reproduced in Table 6-3. 

Step 8: Multiply the volumetric strain due to compaction for each layer by two to correct for the 

multidirectional shaking effect, as recommended by Tokimatsu and Seed (1987), to get the 

representative volumetric strain for each layer.

Step 9: Calculate seismic settlements of each layer by multiplying the layer thickness by the 

representative volumetric strain evaluated in Step 8. Sum up the layer settlements to obtain 

the total seismic settlement for the analyzed profile.

Figure 6-21 Plot for Determination of Earthquake-induced Shear Strain in Sand Deposits (Tokimatsu 

and Seed, 1987) 

eff c ≈ γγ c γ

c ε
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Figure 6-22 Relationship between Volumetric Strain, Cyclic Shear Strain, and Penetration Resistance 

for Unsaturated Sands (Tokimatsu and Seed, 1987) 

TABLE 6-3 INFLUENCE OF EARTHQUAKE MAGNITUDE ON VOLUMETRIC STRAIN 

RATIO FOR DRY SANDS (after Tokimatsu and Seed, 1987) 

Earthquake

Magnitude

Number of Representative 

Cycles at 0.65 τmax

Volumetric Strain Ratio 

8.5 26 1.25

7.5 15 1.0

6.75 10 0.85

6.0 5 0.6

5.25 2-3 0.4

Seed and Silver (1972) computed the settlement in a 50-ft thick deposit of sand with a relative density of 

45%, which was subjected to a maximum surface acceleration of 0.45 g. They concluded that the 

computed settlement of 2.5 in. was in fairly good agreement with the observed settlement during the 1971 

San Fernando earthquake. The same soil profile has been evaluated using the simplified method above. 

The results of the analysis are shown in Table 6-4, and the results are compared with those by Seed and 

Silver (1972) in Figure 6-23. It may be noted that the strain distribution determined by the approximate 

ε C,N / ε C,N = 15
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method is in good agreement with the values computed by Seed and Silver and that the settlement 

estimated by the simplified procedure is in reasonable accordance with that determined previously. 

Figure 6-23 Computation of Settlement for 50-ft Deep Sand Layer (Seed and Silver, 1972) 

TABLE 6-4 COMPUTATION OF SETTLEMENT FOR DEPOSIT OF DRY SAND

Layer 

number 

(1)

Thickness 

(ft) 

(2)

σp = σ′

p

(psf) 

(3)

Dr 

(%) 

(4)

N1

(5)

Gmaxa

(ksf) 

(6)

γeff 

(Geff/Gmax) 

(7)

γeff 

(8)

εC,M=7.5

(%)

(9)

εC,M=6.6b

(%)

(10)

2εC,M=6.6c

(%)

(11)

Settlement 

(in)

(12)

1 5 240 45 9 520 1.3x10-4 5x10-4 0.14 0.11 0.22 0.13

2 5 714 45 9 900 2.3 8 0.23 0.18 0.36 0.22

3 10 1,425 45 9 1,270 3.2 12 0.35 0.28 0.56 0.67

4 10 2,375 45 9 1,630 4 14 0.4 0.32 0.64 0.77

5 10 3,325 45 9 1,930 4.5 15 0.45 0.36 0.72 0.86

6 10 4,275 45 9 2,190 4.6 13 0.38 0.3 0.6 0.72

Total 3.37

a

Gmax = K2 ∙ 1,000(σm

′ )

1

2 = 20N1

1

3(σm

′ )

1

2 × 1,000 b

εC,M=6.6/εC,M=7.5=8.0 c Multidirectional effect
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6.5.2 Post Earthquake Settlement of Liquefied Soils 

Another consequence of earthquake induced liquefaction is the subsequent post earthquake dissipation of 

excess pure-water pressures, leading to settlement. Based on experimental studies, Tokimatsu and Seed 

(1987) developed a simple chart based procedure for estimating post liquefaction settlement at level 

ground sites. The Tokimatsu and Seed (1987) chart for a magnitude 7.5 earthquake is shown in Figure 

6-24. The volumetric strains corresponding to the blow counts (N1)60 and cyclic stress ratios (CSR) for 

each liquefied layer should be multiplied by layer thickness to estimate settlement. Note that these

settlement estimates are valid for level-ground sites that have no potential for lateral spreading. For 

lateral spreading sites, settlement estimates are likely to be larger than those for level ground sites.

Figure 6-24 Curves for Estimation of Post-liquefaction Volumetric Strain Using SPT Data and Cyclic 

Stress Ratio for Mw 7.5 Earthquakes (Tokimatsu and Seed, 1987) 

During the 1995 Kobe (Hyogoken-Nanbu) earthquake, total settlements in liquefied soils in the range of 

0.5m to 0.7m were observed. However, in the case of these observations, the differential settlements 

were small as evidenced from the limited cracks in the paved areas (Bardet et al., 1997). Similar 

observations made during the 1994 Northridge earthquake suggest that the differential settlements due to 

pore pressure increases are only a fraction of the total settlement. Except for liquefaction occurrences 

with lateral spreading, the observed liquefaction-induced settlements during the Northridge earthquake 

were less than those observed in Kobe. In various observations in the San Fernando Valley, particularly 
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in the Woodland Hills area, the ground settlements were found to be relatively uniform. This 

phenomenon may be attributable to the following conditions: (1) presence of deep alluvial sediments; (2) 

relatively horizontal layering; (3) significant fines content in the soils.

Based on the above observations, it can be concluded that the differential settlements at level-ground sites 

with natural soils are expected to be small even if the total settlement is large compared to the total 

settlement for conditions that typically exist in Southern California. However, in the absence of extensive 

site investigation, it is suggested that the minimum differential settlement on the order of one-half of the 

total settlement be used in the design. The actual differential settlement value used is dependent upon 

factors such as the type of structure, bearing elevation of the foundation, subsurface conditions (relatively 

uniform versus highly variable laterally), number of borings/CPTs, etc. 

6.6 SURFACE FAULT RUPTURE HAZARD 

6.6.1 Fault Types and Field Identification 

Surface fault rupture refers to the ground displacements that occur along an active fault trace when 

movement on the fault extends to the ground surface, or to the depth of a bridge foundation. 

Displacements can range from inches to tens of feet, depending on the magnitude of the earthquake. 

Because surface fault displacements tend to occur abruptly, often across a narrow zone, fault rupture can 

be very damaging to a bridge, particularly if it occurs directly below the structure. It is also difficult and 

often cost-prohibitive to mitigate. In the central and eastern United States, east of the Rocky Mountains, 

very few active faults with surface traces have been identified and the hazard of surface fault rupture is 

generally low in comparison to the western United States. 

Surface fault ruptures generally are expected to occur along existing traces of active faults. Therefore, it 

can be assumed that a significant hazard of surface fault rupture does not exist if it can be established that 

either:

• There is no evidence of a fault trace traversing the bridge site, or

• If a fault trace does cross the bridge site but it has been established that the fault is not an active 

fault. Faults are generally considered to be active faults with a significant potential for future 
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earthquakes and displacements if they have experienced displacement during the past 

approximately 11,000 years (Holocene time). 

Hazard screening for fault rupture should involve, as a minimum, the following steps: 

1) Review of geologic maps as well as discussions with geologists in government agencies who are 

knowledgeable about the geology of the area, and 

2) Site reconnaissance and review of aerial photographs, looking for geomorphic expression of 

faulting. If there is uncertainty in the fault location or its activity, the screening criteria should be 

applied conservatively.

If a surface fault rupture hazard cannot be screened out, the owner may decide to accept the risk or 

evaluate the hazard and consequences in detail. If detailed evaluations are carried out, they should be 

oriented toward: 

1) Establishing the fault or fault zone location relative to a bridge site if it is not clearly established in 

the screening stage,

2) Establishing the activity of the fault if it traverses a bridge, and

3) Evaluating fault rupture characteristics; i.e., amount of fault displacement, width of zone of 

displacement, and distribution of slip across the zone for horizontal and vertical components of 

displacement. A probabilistic assessment of the likelihood of different magnitudes of fault 

displacement during the life of the bridge may also be useful in decision-making.

After a site has been evaluated by the screening criteria presented above and either there is insufficient 

information to rule out a surface fault rupture hazard or there is seismic, geomorphic, and/or geologic data 

that suggests an active fault(s) might be present at or near the site, the following information is required to 

define the fault rupture hazard: 

1) The location of fault traces (if any) with respect to the site.

2) The timing of most recent slip activity on the fault.

3) The ground rupture characteristics for a design earthquake on the fault (e.g. type of faulting from

Figure 6-25), amount of slip and distribution into strike-slip and dip-slip components, and width of 

the zone of ground deformation. 
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Figure 6-25 Types of Earthquake Faults

There are several steps that can be taken to confirm and define the location of active faults. Further 

assessments are not required if it can be shown, on the basis of the procedures outlined below, that there 

are no faults passing beneath the site.

1) Interpretation of Aerial Photographs 

Aerial photographs can be an excellent supplementary resource to geologic and topographic maps of the 

site and vicinity for identifying faults. Older photographs are particularly useful if they depict the site and 

/or its environs prior to development activities that would have altered or destroyed landforms that 

indicate the presence of faults. For many parts of the country, stereo photographic coverage is available 

as far back as the 1920s or 1930s. Aerial photographs are usually available from several sources 

including private companies and from various governmental agencies including the U.S. Geological 
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Survey (USGS), U.S. Department of Agriculture (Natural Resources Conservation Service), Bureau of 

Land Management, and the Forest Service. The USGS maintains the repository for federal photographic 

resources at its EROS Data Center, Sioux Falls, South Dakota 57198. 

2) Contacting Knowledgeable Geologists

Geologists and other earth scientists familiar with geologic and tectonic conditions in the site vicinity may 

be willing to share their knowledge. These geologists might work for governmental agencies (federal, 

state, and local), teach and conduct research at nearby colleges and universities, or practice as consultants.

3) Ground Reconnaissance of Site and Vicinity

A walk-down of the site and its vicinity should be conducted to observe unusual topographic conditions 

and evaluate any geologic relationships visible in cuts, channels, or other exposures. Features requiring a 

field assessment might have been previously identified during the geologic and topographic map review, 

aerial photography interpretation, and/or during conversations with geologists. 

4) Surface Exploration 

Faults obscured by overburden soils, site grading, and/or structures can potentially be located by one or 

more techniques. Geophysical techniques such as seismic refraction surveying provide a remote means of 

identifying the location of steps in a buried bedrock surface and the juxtaposition of earth materials with 

different elastic properties. Geophysical surveys require specialized equipment and expertise, and their 

results may sometimes be difficult to interpret. Trenching investigations are commonly used to expose 

subsurface conditions to a depth of 4.5 to 6 m. While expensive, trenches have the potential to locate 

faults precisely and provide exposures for assessing their slip geometry and slip history. Borings can also 

be used to assess the nature of subsurface materials and to identify discontinuities in material type or 

elevation that might indicate the presence of faults.

If it is determined that faults pass beneath the site, it is essential to assess their activity by determining the 

timing of the most recent slip(s) as discussed below. If it is determined, based on the procedures outlined 

below, that the faults are not active faults, further assessments are not required.
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1) Assess Fault Relationship to Young Deposits/Surfaces

The most definitive assessment of the recent history of fault slip can be made in natural or artificial 

exposures of the fault where it is in contact with earth materials and/or surfaces of Quaternary age (last 

1.8 million years). Candidate deposits might include native soils, glacial sediments like till and loess, 

alluvium, colluvium, beach and dune sands, and other poorly consolidated surficial materials. Quaternary 

age surfaces might include marine, lake, and stream terraces, and other erosional and depositional 

surfaces. A variety of age-dating techniques, including radiocarbon analysis and soil profile development, 

can be used to estimate the timing of the most recent fault slip.

2) Evaluate Local Seismicity

If stratigraphic data are not available for assessment of fault activity, historical seismicity patterns might 

provide useful information. Maps and up-to-date plots depicting historical seismicity surrounding the site 

and vicinity can be obtained from the USGS at its National Earthquake Information Center in Golden, 

Colorado. Additional seismicity information may be obtained from state geologic agencies and from 

colleges and universities that maintain a network of seismographs (e.g. California Institute of Technology, 

University of California, Berkeley, University of Nevada, Reno, University of Washington, and the 

Multidisciplinary Center for Earthquake Engineering Research, Buffalo, New York). If the fault(s) that 

pass beneath the site are spatially associated with historical seismicity, and particularly if the seismicity 

and fault trends are coincident, the faults should probably be considered active. 

3) Evaluate Structural Relationships

In the absence of both stratigraphic and seismological data, an assessment of the geometric/structural 

relationships between faults at the site and faults of known activity in the region could be useful. 

Although less definitive than the two prior criteria, the probability that the site fault is active increases if it 

is structurally associated with another active fault, and if it is favorably oriented relative to stresses in the 

current tectonic environment.
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6.6.2 Fault Rupture Characteristics and Displacement Estimates 

If the fault activity evaluation indicates one or more active faults are present beneath the site, the 

characteristics of future slip on the faults must be estimated. Several methods can be used to estimate the 

size of future displacements. These methods include: 

1) Observations of the amount of displacement during past surface-faulting earthquakes.

2) Empirical relationships between fault displacement and earthquake magnitude or fault rupture 

length. 

3) Calculated values based on the assumed recurrence rate for earthquakes along the fault and 

cumulative fault displacement over a long period of time encompassing numerous fault ruptures 

(i.e. fault slip rate). 

The most reliable displacement assessments are based on the displacement in past events. Observations 

of historical surface ruptures and geologic evidence of paleoseismic events provide the most useful 

indication of the location, nature, and size of the future events. Where the geologic conditions do not 

permit a direct assessment of the size of past fault ruptures, the amount of displacement must be estimated 

using indirect methods. Empirical relations between displacement and earthquake magnitude based on 

historical surface-faulting earthquakes (e.g. Wells and Coppersmith, 1994) provide a convenient means 

for assessing the amount of fault displacement. An example of such a relationship is shown in Figure 

6-26. 

In Figure 6-26, the maximum displacement along the length of a fault rupture is correlated with 

earthquake magnitude. Maximum displacement typically occurs along a very limited section of the fault 

rupture length. Relationships are also available for the average displacement along the rupture length. 

Data from well-documented historical earthquakes indicate that the ratio of the average displacement to 

the maximum displacement ranges between 0.2 and 0.8 and averages 0.5 (Wells and Copppersmith, 

1994). Other methods for calculating the average size of past displacements include dividing the 

cumulative displacement by the number of events that produced the displacement, and multiplying the 

geologic slip rate by the recurrence interval.
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Figure 6-26 Relationship between Maximum Surface Fault Displacement and Earthquake Moment 

 Magnitude for Strike-Slip Faulting (after Wells and Coppersmith, 1994)

Predicting the width of the zone and the distribution of slip across the zone of surface deformation 

associated with a surface faulting event is more difficult than predicting the total displacement. The best 

means for assessing the width of faulting is site-specific trenching that crosses the entire zone. Historical 

records indicate that the width of the zone of deformation is highly variable along the length of a fault. 

No empirical relationships having general applicability have been developed that relate the size of the 

earthquake or the amount of displacement on the primary fault trace to the width of the zone or to the 

amount of secondary deformation. The historical record indicates, and fault modeling shows that the 

width of the zone of deformation and the amount of secondary deformation tend to vary as a function of 

the dip of the fault and the sense of slip. Steeply dipping faults, such as vertical strike-slip faults, tend to 

have narrower zones of surface deformation than shallow-dipping faults. For dipping faults, the zone of 

deformation is generally much wider on the hanging wall side than on the foot wall side. Low-angle 

reverse faults (thrust faults) tend to have the widest zones of deformation.
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Probabilistic methods for assessing the hazard of fault rupture have been developed that are similar to the 

probabilistic seismic hazard analysis (PSHA) methods used to assess earthquake ground motions (e.g. 

Coppersmith and Youngs, 1990, 2000). A PSHA for fault rupture defines the likelihood that various 

amounts of displacement will be exceeded at a site during a specified time period. For critical bridges, 

such analyses could be considered to assess whether the likelihood of surface fault rupture is high enough 

to warrant design for hazard and to aid in quantifying design values of displacement. 

6.7 SUMMARY

This chapter presents an overview of geotechnical seismic hazards related to slope stability, liquefaction, 

seismic settlement and fault rupture. In the case of slope stability hazards, both pseudo-static limit 

equilibrium and displacement based slope stability are described for both soil and rock slopes. 

Development of the seismic coefficient for pseudo-static analyses is discussed in light on recent findings 

from the NCHRP 12-70 project. Newmark displacement based stability analyses are presented in the 

form of displacement design equations, which have been developed using the results of parametric time 

history analyses. 

Liquefaction hazard or the potential for seismically generated pore pressure leading to reduced soil shear 

strength, slope failures and associated ground deformations, is discussed in detail. Laboratory and site 

investigation methods to determine the liquefaction strength of site soils (including SPT and CPT 

methods) are discussed leading to empirical evaluation procedures commonly used to determine the 

potential for triggering liquefaction. Screening approaches to assess the need for such evaluations in 

regions of low seismicity are also described. Liquefaction induced ground deformations are a significant 

source of damage in earthquakes. The various methods for the determination of post liquefaction residual 

undrained strength are reviewed. 

The potential for post liquefaction flow failure under static loads is addressed along with a discussion of 

earthquake induced lateral spreading displacement. Both empirical and numerical methods for 

determining lateral spreading displacement potential are reviewed with particular emphasis on Newmark 

sliding block approaches. The soil settlement hazard includes both the post-liquefaction settlement of 

saturated cohesionless soil and the settlement of unsaturated cohesionless soil subject to seismic loading. 

Emphasis is placed on the commonly used Tokimatsu and Seed analysis approach for evaluating these 
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settlements. The final section of the Chapter briefly reviews fault types and field identification 

approaches, together with rupture characteristics and estimates of fault displacement.

The methods for analyzing the slope stability, liquefaction, and seismic settlement hazards presented in 

this chapter provide the basis for Chapter 7, Geotechnical Design of Earthwork Features, including

discussions on performance based design concepts for slopes and embankments. The liquefaction hazard 

evaluation techniques for lateral spread deformations and post liquefaction settlement provide the basis 

for the discussion on mitigation measures in Chapter 7. The liquefaction hazard concepts will also be an 

issue in discussions on Shallow Foundation and Deep Foundation design presented in Chapters 10 and 11, 

respectively. 
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Seismic Design – Geotechnical Features 7-1 August 2011 

CHAPTER 7

GEOTECHNICAL DESIGN OF EARTHWORK FEATURES 

7.1 GENERAL 

This chapter describes the seismic analysis and geotechnical design of earthwork features associated with 

transportation systems. These features include embankment fills supporting a roadway or for a bridge 

approach and natural or cut slopes associated with a highway or bridge, including very gentle slopes of 

just a few degrees that may be subject to lateral spreading or flow failure in earthquakes. Evaluation of 

the performance of these features when subject to strong ground motions, including overall stability and 

permanent seismic deformation including liquefaction induced deformations, is discussed in this chapter. 

Permanent seismic displacement analyses including slope deformation, lateral spreading, and seismic 

settlement are presented. Performance based design criteria are discussed for each type of analysis, 

together with mitigation measures. 

Section 7.2 presents selected case histories of earthquake induced landslides and slope or embankment 

deformations that have resulted in extensive damage to highway systems in past earthquakes. These case 

histories are presented to illustrate typical earthquake-induced damage modes and the need for seismic 

design. The case histories highlight the need for displacement (or performance) based design methods 

that address the development of unacceptable slope deformations in unstable slopes. 

Section 7.3 describes performance based design criteria for the two most commonly used seismic slope 

stability design procedures (pseudo static limit equilibrium analysis and displacement based design) for 

both constructed embankments and natural or cut slopes. Screening criteria to identify when slopes 

designed using accepted static analysis procedures do not require seismic design checks are also 

presented. Strategies for establishing owner-approved criteria for acceptable seismic displacements of 

slopes and embankments are described based on the NCHRP 12-70 study (NCHRP 2008). 

Section 7.4 summarizes mitigation measures that may be employed where a slope stability evaluation (for 

both soil and rock slopes) does not meet established seismic performance criteria. Methods described 

include the use of toe buttress structures, piles, ground anchors, and retaining structures. Lastly, Section 

7.5 addresses performance based design concepts related to liquefaction induced embankment lateral 

spreading deformations and lateral spreading interaction with pile foundations. Design procedures for 
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Seismic Design – Geotechnical Features 7-2 August 2011 

accommodating lateral spreading effects are discussed. Liquefaction mitigation ground improvement 

techniques that can be employed when the liquefaction hazard is unacceptable are presented. Ground 

improvement techniques discussed in this section include densification methods such as dynamic 

compaction and stone column installation and deep soil mixing methods that are finding increasing 

application in the United States. 

7.2 SEISMIC PERFORMANCE OF SLOPES AND EMBANKMENTS 

Earthquake induced slope instability in the form of slope or embankment fill deformations and 

liquefaction induced deformations or lateral spreading have caused extensive damage to highways in past 

earthquakes. This section describes selected case histories of slope instability to illustrate damage modes 

and associated displacement potential. The case histories are divided into three groups (1.) natural slopes, 

(2.) embankment fills and (3.) liquefaction induced deformations and lateral spreads. These case histories 

illustrate that, from a highway geotechnical design standpoint, the potential for such instability needs to 

be evaluated when assessing the seismic design of cut slopes, embankments, and approach fills. The two 

seismic stability design procedures most commonly used in practice, pseudo static limit equilibrium and 

displacement based design, were introduced in Chapter 6 and are discussed more detail in Section 7.3. 

7.2.1 Natural Slopes 

Ground instability in major earthquakes is often characterized by significant landslides or rockfalls in 

natural slopes. The instability can take the form of catastrophic ground displacements (for slopes with 

marginal static stability or where strain softening leads to low residual strength as in the case of ancient 

landslides) or limited ground movements (of the order of inches) that are still potentially disruptive to 

associated highways or bridge foundations. Selected illustrative case histories of ground instability in 

earthquakes are described in the subsequent paragraphs of this section. 

In the 1989 Loma Prieta Earthquake in California (Mw 7.1), over 1000 landslides and rockfalls were 

documented in the Santa Cruz Mountains (EERI 1990). Many of the landslides were associated with 

reactivation of old landslides (USGS 1998b), including the Ditullio landslide shown in Figure 7-1. The 

Ditullio landslide had a cumulative displacement of the order of about 20 in. As described in Section 7.3, 

Newmark displacement analyses may be applied to evaluate the potential for such displacements. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-3 August 2011 

Figure 7-1 Ditullio Landslide, Loma Prieta Earthquake (after USGS, 1998c) 

An example of a rockfall during the same earthquake is shown in Figure 7-2. This rockfall occurred on 

State Highway 17 in the Santa Cruz Mountains. 

Figure 7-2 Route 17 landslide, Loma Prieta Earthquake (after USGS, 1998a) 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-4 August 2011 

Similar rockfalls closed the Rt 17 highway, the primary transportation corridor from the San Francisco 

Bay area into the epicentral region of the earthquake, for 12 miles over a period of 32 days (USGS 

1998a). 

Hundreds of landslides were also caused by the 1988 Spitak Earthquake (Mw 6.8) in Armenia, mostly 

occurring as rockfalls. Figure 7-3 shows a rock slide that occurred in this event along the main road near 

Spitak. This is an example of a planar failure which occurred along joint sets, striking parallel to and 

dipping 50° toward the road. 

Figure 7-3 Planar Rock Slide in Volcanic Tuff 1989 Armenia Earthquake (after EERI, 1989) 

In many cases, slope instability is reflected simply as ground cracks in sloping ground. Such cracks are 

associated with cumulative slope displacements of the order of inches, as illustrated in the 1994 

Northridge Earthquake, California (Mw 6.8) case history shown in Figure 7-4. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-5 August 2011 

Figure 7-4 Slope Failure with Ground Cracking along Mulholland Drive, 1994 Northridge 

Earthquake (after EERI, 1995) 

7.2.2 Embankment Fills 

In the absence of deformation or displacement of foundation soils or poorly compacted embankment 

materials, even the most intense seismic shaking has not caused significant damage to roads on properly 

compacted embankment fills. For example, numerous stable Interstate, primary arterial, and secondary 

roadways were strongly shaken during the 1971 San Fernando, 1989 Loma Prieta and 1994 Northridge 

earthquake without damage. Damage occurred only at localities susceptible to some form of permanent 

foundation deformation or displacement or where embankment soils did not meet current standards of 

practice for compaction. Based on past performance, pavements supported by embankments and 

foundations not susceptible to ground deformation or failure have also performed well, although some 

cases of buckling of pavement have been observed in epicentral regions of major earthquakes. 

Embankment and foundation failure modes that have caused damage to highway pavements are 

summarized in the FHWA Seismic Retrofitting Manual for Highway Structures (MCEER 2006) and are 

described below. The special case of embankment fills on liquefiable soils which has resulted in the most 

significant earthquake-induced damage to highway fills is discussed in Section 7.2.3. 

Differential settlements induced by seismic compaction of embankment and/or foundation soils may be 

disruptive to pavements. The breadth of the zone across which the differential settlement occurs is 

generally as important to pavement damage as the amount of settlement. Where settlements are small, 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-6 August 2011 

uniform, or distributed across wide zones, little damage occurs. Rigid pavements are generally able to 

bridge areas of small differential settlement and flexible pavements are usually sufficiently ductile to 

absorb small differential movements without significant damage. Where large differential settlements 

have occurred across narrow zones, both rigid and flexible pavements have fractured and separated, 

disrupting traffic operations and requiring repairs. 

Seismic compaction of approach fills adjacent to bridge abutments has been a major cause of damaging 

differential settlement in earthquakes. The stronger and longer the earthquake shaking, the thicker the fill, 

and the poorer the state of compaction, the greater the amount of seismically-induced differential 

settlement and pavement damage. Figure 7-5 shows about 600 mm of differential settlement that offset 

the paved surface and blocked traffic at the easterly approach to Bridge 53-199R during the 1971 San 

Fernando Earthquake (Mw 6.6). That bridge was part of a connector from northbound I-5 to eastbound I210 in Sylmar, California. The highway was still under construction at the time of the earthquake. This 

settlement was caused by seismic compaction and perhaps some lateral spreading of the approach 

embankment. 

Figure 7-5 Differential Settlement Induced by Seismic Compaction at the Easterly Approach to 

Bridge 53-1991R in I-5 to I-210 Interchange During 1971 San Fernando Earthquake 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-7 August 2011 

Backfills placed against bridge abutments have been particularly vulnerable to seismic settlement due to 

poor compaction. The difficulty in operating mechanized compaction equipment near walls is one reason 

for the poor compaction at these localities. The rigidity of the abutment wall also tends to concentrate 

and accentuate differential settlement. 

Contacts between cuts and fills are also locations where differential settlements commonly occur. 

Materials in the cut section are usually more rigid and less compressible than material in the fill. Also, 

the cut-fill contact may impede the maneuvering of compaction equipment, leaving a poorly compacted 

section adjacent to the cut-full line. For example, Figure 7-6 shows pavement disruption due to 100 mm 

to 200 mm of differential settlement and offset between pavement slabs at a cut-fill contact. This damage 

occurred on I-5 east of Van Norman Lake and about 1650 ft (500 m) north of the junction of I-5 and I-405 

during the 1971 San Fernando Earthquake. 

Pavements supported by poorly compacted embankment materials and/or loose or collapsible foundation 

soils are also vulnerable to large settlements. Such conditions are more likely to occur beneath sections of 

older highways than under highways built in accordance with modern codes and construction practices. 

Figure 7-6 Differential Settlement across Pavement Joints Near Cut-fill Boundary on I-5 north of I405 Separation. The Settlement is due to Seismic Compaction of Fill during the 1971 

San Fernando Earthquake. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-8 August 2011 

7.2.3 Liquefaction Induced Deformations and Lateral Spreading

As described in the FHWA Seismic Retrofitting Manual for Highway Structures (MCEER 2006), 

liquefaction of soils has been a major cause of highway embankment damage. Liquefaction may lead to a 

variety of types of ground deformation or ground failure, as discussed below, depending on geometric and 

soil conditions at the site. The types and amounts of displacement accompanying liquefaction depends on 

several factors including the height and steepness of embankments, the ground slope, and the depth, 

thickness and continuity of liquefiable layers. The following descriptions are extracted from the 

Retrofitting Manual cited above. 

Where highways are underlain by low embankments and flat terrain, liquefaction induced ground 

settlement commonly mimics the thickness of underlying liquefiable layers in the foundation soils. 

Figure 7-7 shows a section of Highway 5 south of Oshamanbe, Japan that settled differentially during the 

1993 Hokkaido-Nansei-Oki Earthquake (Mw 7.8). In this instance, differential settlement generated 

waves in the highway that gave the flexible pavement a roller coaster appearance. Differential vertical 

displacements were as great as 2 ft (0.6 m) between crests and troughs of the induced waves (Youd, 

1995). 

Figure 7-7 Wavy Pavement due to Differential Settlement Enhanced by Liquefaction during the 

1993 Hokkaido-Nansei-Oki, Japan Earthquake. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-9 August 2011 

Liquefaction of soils beneath embankments may also lead to penetration of the embankment into the 

liquefied soil, creating a bearing capacity type of failure as illustrated in Figure 7-8. During penetration, 

the embankment usually fractures longitudinally and may spread laterally, generating long open fissures 

oriented roughly along the centerline of the embankment. In some instances, one or both sides of the 

embankment may subside and rotate forming a rotational slump. For example, Figure 7-9 shows a 

segment of Highway 36, along the Caribbean coast in eastern Costa Rica that split longitudinally during 

the 1991 Limon Province Costa Rica Earthquake (Mw 7.5). 

Figure 7-8 Failure Mechanism for an Embankment Founded Upon Liquefied Soil 

Figure 7-9 Segment of Highway 36 Near Caribbean Coast in Costa Rica that Split Longitudinally, 

Settled and Spread Laterally during 1991 Earthquake by Mechanism 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-10 August 2011 

Embankment penetration and disruption due to liquefaction of the underlying soil is also illustrated in 

Figure 7-10 for the Highway 36 approach to the Rio Estrella Bridge in eastern Costa Rica. This approach 

fill subsided about 6.5 ft (2 m) and spread laterally due to a combination of soil compaction within the 

embankment, embankment penetration into the liquefied foundation soil, and embankment spreading. 

These actions severely disrupted the embankment and paved surface. In total, about 30 percent of all 

highways pavements in the lowlands of eastern Costa Rica were disrupted by the effects of liquefaction, 

primarily embankment penetration and spreading, during the 1991 earthquake. 

Figure 7-10 Disrupted Fill and Pavement due to Liquefaction at the Approach to the Highway 36 

bridge Over Rio Estrella, Costa Rica, during 1991 Earthquake. 

Where lateral spreading occurs, the surface of the mobilized ground is commonly disturbed by a variety 

of ground deformation features, including open fissures, differential settlement, scarps, lateral shear 

zones, and pressure ridges. Structures built over or within lateral spreading zones, including highways, 

are commonly disrupted and displaced along with the underlying ground. Lateral spreading soil generally 

moves down gentle slopes or toward a free face such as an incised river channel. Horizontal 

displacements of laterally spreading soil commonly range up to a few meters in large earthquakes, but 

where shaking is particularly intense or of long duration and ground conditions are extremely vulnerable 

larger displacements have occurred. Figure 7-11 shows a section of the Golden State Freeway (I-5) that 

translated laterally by as much as 6.5 ft (2 m) due to a large lateral spread (called the Juvenile Hall slide) 

during the 1971 San Fernando Earthquake. Sheared and buckled pavement marked both margins of the 

failure zone. Between these margins, the highway shifted as much as 6.5 ft (2 m) westward. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-11 August 2011 

Figure 7-11 Rigid pavement on I-5 south of I-5/I-210 interchange that sheared and buckled at two 

localities during the 1971 San Fernando earthquake due to 6.5 ft (2 m) of lateral spread 

displacement. 

Where a highway is aligned parallel to the direction of lateral spreading movement, lateral spreading 

usually induces extensional features such as open fissures and pulled apart pavement slabs at the head of 

the slide and compressional features such as pressure ridges and buckled pavement at the toe. Figure 7-12

shows a section of Highway 36 in Costa Rica that crossed the head of a lateral spread and shifted toward 

the Rio Viscaya. The spreading movement generated deep open fissures in the ground and overlying 

highway embankment and pavement. Extensional movement at the head of the spread was compensated 

for by compression at the toe, beneath the Rio Viscaya Bridge. The displacement beneath the bridge 

sheared bearings and connections, causing the superstructure to collapse into the river. 

Figure 7-12 Extensional Fissures in Flexible Pavement Caused by Lateral Spread of Floodplain 

Deposits Toward Rio Viscaya during the 1991 Costa Rica Earthquake 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-12 August 2011 

Flow failure is the most catastrophic form of ground dislocation associated with liquefaction. Flow 

failures occur on relatively steep (typically greater than 6 percent) slopes or embankments that are 

underlain by loose saturated granular materials. Under these adverse conditions, seismic shaking 

generates large reductions in soil strength within the liquefied layers (causing static factors of safety 

against slope failure to drop below 1.0 because of the low residual shear strength) and resulting in 

massive ground displacements deformations. Substantial internal deformation usually occurs within the 

mobilized soil mass and overlaying structures. Pavements on such failures are nearly always displaced 

and destroyed. Figure 7-13 shows a flow failure that occurred in a highway fill along the western edge of 

Lake Merced in San Francisco during the 1957 Daly City, California Earthquake (Mw 5.2). This failure 

dislodged a section of the highway embankment that flowed into the lake, severing the roadway and 

blocking traffic. 

Figure 7-13 Liquefaction-induced Flow Failure of Roadway Embankment into Lake Merced during 

1957 Daly City, California Earthquake 

The vulnerability of highway bridges to earthquake-induced ground failures arising from liquefaction is

clearly evidenced by the extensive damage observed in past earthquakes. Damage has been primarily 

associated with large translational flow slides and related embankment deformations (when static factors 

of safety against slope failure drop below 1.0 due to low residual undrained strengths of liquefied soil 

layers) or progressive but limited lateral spread embankment deformations of the order of feet, driven by 

earthquake ground shaking subsequent to liquefaction, with deformations ceasing at the end of the 

earthquake. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-13 August 2011 

Damage modes associated with such lateral deformations are related to displacement demands on 

abutments and piers leading to possible pile damage and/or span collapse. Representative damage in the 

1964 Alaska and Niigata Earthquakes and the 1991 Costa Rica Earthquake has been documented by 

Youd, (1993). Damage in the 1995 Kobe Earthquake is described by Tokimatsu and Asaka (1998). 

Specific examples of lateral spread pile damage are described below. 

Hamada (1992) summarized the destructive effect of lateral spreading on two bridges during the 1964 

Niigata Earthquake in Japan, an event that caused extensive damage due to soil liquefaction. Figure 7-14

illustrates the damage to the abutment and piers of the Yachiyo Bridge. The foundations of the abutments 

and piers were reinforced concrete piles, 1 ft (30 cm) in diameter and about 33 ft (10 m) in length. Pier 

No. 2 broke at the ground surface level and displayed a permanent deformation of 1.2 ft (1.1 m) between 

top and bottom. Once extracted, the piles showed severe damage in locations corresponding to the 

bottom of the liquefied layer, damage that was clearly caused by the 6.5 – 16.5 ft (2-5 m) of free field 

lateral spreading toward the river. 

Figure 7-14 Damage to the Abutments and Piers of Yachiyo Bridge on the Left Bank (Hamada, 1992) 

Figure 7-15 shows the collapse of the Showa Bridge during the 1964 Niigata Earthquake. Lateral 

spreading pushed the piers toward the river, causing five simply supported spans to fall off of their seats. 

The bridge was founded on 2 ft (60 cm) diameter steel piles driven through a 33 ft (10 m) layer of loose to 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-14 August 2011 

medium sand and 20 ft (6 m) into an underlying layer of dense fine sand. The 33 ft (10 m) layer is 

believed to have liquefied from the level of the riverbed down through its full depth. Figure 7-16

schematically illustrates a pile for this bridge that was extracted after the earthquake, evidencing a 

permanent lateral displacement of approximately 3 ft (1 m) and a maximum curvature close to the depth 

at which the strata made a transition from loose to medium dense sand. 

Figure 7-15 Showa Bridge Collapse (Hamada, 1992) 

Figure 7-16 Deformation of a Steel Pipe pile for the Showa Bridge (Hamada, 1992) 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-15 August 2011 

An important case history of shallow non-liquefied soil layers riding on top of spreading liquefied soils is 

the lateral spreading that occurred at the site of the Landing Road Bridge during the 1987 Mw 6.3 

Edgecumbe (New Zealand) Earthquake, shown in Figure 7-17. A liquefied 13 ft (4 m) thick loose sand 

layer moved about 6.5 ft (2 m) toward the river, carrying along a non-liquefied 5 ft (1.5 m) thick clayey 

silt layer. The movement was resisted by the five piers of the on-land spans of the bridge, which 

consisted on eight 16 in. (400 mm) square battered pre-stressed concrete piles connected by a pile cap and 

slab pier, as shown in Figure 7-18. After the earthquake, soil was mounded up behind the piers in what 

was apparently a passive failure. Subsequent trenching found failure surfaces and disturbed failure 

masses of soil confirming the occurrence of passive failure in the non-liquefied crust as it was driven 

against the buried piers and pile cap. The passive forces were found to be of the order of 10 times the 

estimated drag force exerted on the pile group by the liquefied sand (Berrill et al., 1997). Observations 

from the excavations and back analyses indicated that the piles successfully resisted the passive pressures 

mobilized against the piers. Cracks in the piles suggested plastic hinges in the piles were on the verge of 

forming, as shown schematically in Figure 7-19. 

In the 1995 Kobe earthquake, field investigations using borehole cameras and slope indicators showed 

that failures of piles in lateral spreading zones concentrated at the interfaces between liquefied and nonliquefied layers as well as near pile heads. Also lateral pile analyses using p-y interface springs subject to 

the estimated ground displacement profiles were consistent with observed pile performance in this 

earthquake, as shown in Figure 7-20 from Tokimatsu and Asaka (1998). 

Figure 7-17 Landing Road Bridge, Whakatane, New Zealand (Keenan, 1996) 
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Seismic Design – Geotechnical Features 7-16 August 2011 

Figure 7-18 Schematic of the Raked-pile Foundation at the Landing Road Bridge (Berrill and Yasuda, 

2002)

 

Figure 7-19 Potential Collapse Mechanism for Landing Load Bridge (Keenan, 1996) 
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Seismic Design – Geotechnical Features 7-17 August 2011 

Figure 7-20 Site and Damage Characteristics for a Precast Concrete Pile Subjected to Lateral Spread 

in the Kobe Earthquake (after Tokimatsu and Asaka, 1998) 

The above case histories illustrate important aspects of pile foundation response to lateral spreading. 

While in some cases the top of the pile foundation displaced laterally a distance similar to that in the free 

field, in other cases it moved much less due to the lateral stiffness of the foundation and/or constraining 

effect of the superstructure. Foundations may be exposed to large lateral soil pressures due to lateral 

spreading, including passive pressures from non-liquefied soil layers riding on top of the liquefied soil. 

In some cases the soil fails before the foundation, with negligible pile bending distress and small 

deformation of the piles. In other cases, foundations fail first, experiencing large permanent deformation 

and rotation. The observed damage and cracking of piles is often concentrated at the upper and lower 

boundaries of the liquefied soil layer where there is a sudden change in soil properties. More damage 

tends to occur to piles when the lateral movement is forced by a strong non-liquefied soil. 

The above observations are reflected in the simplified design concepts discussed in Section 7.5, wherein 

the lateral resistance provided by piles and the associated foundations is incorporated into a lateral 

spreading analysis. These observations are also reflected in the analysis procedures for deep foundations 

in liquefied soils presented in Chapter 10. Clearly, lateral spreading deformations of the order of several 

feet can cause significant pile damage. However, analyses described in Section 7.5 suggest damage 
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Seismic Design – Geotechnical Features 7-18 August 2011 

related to plastic hinge formation could be acceptable if displacements are less than about 1 ft, depending 

on pile type or liquefied layer thickness. 

7.3 SLOPE STABILITY DESIGN APPROACHES 

The two basic analysis methods for evaluating seismic stability of slopes, the pseudo static analysis 

approach and the displacement based analysis approach, were described in detail in Chapter 6. In this 

section emphasis is placed on illustrating the displacement based approach and the basis for developing 

performance based criteria for evaluating slope stability using this approach. Screening criteria to identify 

situations in regions of low or moderate seismic exposure where seismic analysis would not be required 

are also presented in this chapter. Strategies for developing performance criteria that depend on the 

facilities or structures associated with the slope are discussed in detail. Mitigation measures for cases 

where the calculated seismic displacement exceeds the allowable value are presented in Section 7.4. 

Design issues related to liquefaction problems are addressed in Section 7.5. 

In developing slope stability design approaches, two general classes of slopes need to be considered: 

constructed or engineered slopes and natural slopes. The general characteristics of these two categories of 

slopes vary significantly in terms of geometry, material properties, and groundwater conditions. In most 

cases constructed fill and embankment slopes will be relatively uniform in soil conditions, though the 

constructed material can vary from sands and gravels to fill that has a high fines content (that is, cohesive 

soil). Furthermore, the groundwater level will generally be below the base of the fill or embankment. On 

the other hand natural slopes, including soil slopes and jointed or weathered rock slopes, will usually be 

highly variable (e.g. with layers in soil slopes that range from gravels to clays) and often groundwater will 

be located within the slope. 

7.3.1 Constructed Fill Slopes and Embankments 

Fill and embankment slopes generally will be constructed from an imported material. Depending on the 

geographic area, the imported materials can be predominantly sands or gravels or they can have a high 

percentage of cohesive soil. These slopes are generally well compacted and will usually exhibit good 

strength characteristics. Slope angles often will range from 2H:1V (horizontal to vertical) to flatter than 

3H:1V. The height of the slope can vary from a few feet to over 50 feet. A common example of these 
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Seismic Design – Geotechnical Features 7-19 August 2011 

slopes would be the approach fill used at either end of a bridge. These approach fill slopes are often on 

the order of 30 feet in height. 

 

Constructed fill and embankment slopes are perhaps the easiest to evaluate from the standpoint that the 

soil type and density of the fill is generally well defined and therefore determination of material properties 

is generally straight-forward. If the fill is cohesionless, the friction angle will normally be on the order of 

35 degrees or higher. If the fill has appreciable fines content, the compacted shear strength often will be in 

excess of 2,000 psf. The groundwater location for most of these slopes will be at some distance below the 

base of the fill. However, the design of these slopes become problematic if the embankment fill is being 

placed on a soft or liquefiable foundation material. In these cases the determination of the strength of the 

foundation material under static and seismic loading becomes a key consideration during the analysis, as 

discussed in Section 7.5 for liquefiable foundation soils. 

 

The geotechnical investigation for an engineered fill will often be limited to investigating the 

characteristics of the foundation material. Exploration typically is conducted to a depth equal to twice the 

slope height to define the strength and compressibility of the soil layers upon which the embankment is, 

or will be, constructed. The geometry and properties of the fill is constrained by right-of-way widths and 

the cost of importing fill material. 

 

From a seismic design perspective these types of slopes are routinely encountered in design of new 

roadways or where existing roadways are modified. Performance of well compacted fill or embankment 

slopes during seismic loading generally has been very good, even when subject to sever earthquake 

loading (as illustrated in the example below), except where liquefaction of the foundation material occurs. 

The following example demonstrates the application of the NCHRP 12-70 (TRB 2008) procedure 

outlined in Chapter 6 for the seismic design of embankment slopes. The example considers embankments 

constructed with three slope heights (15, 30 and 45 feet) at two slope angles: 2:1 and 1.5:1 (typical of 

constructed embankment slopes). The two angles and three slope heights examined as shown on Figure 

7-21. 

 

The foundation soil below the embankment fill is assumed to be cohesive soil with a friction angle of 10° 

and cohesion of 4,000 psf. Therefore, deep failure planes through the foundation material were not a 

design consideration. 
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Seismic Design – Geotechnical Features 7-20 August 2011 

Figure 7-21 Slope Geometry 

Three different fill materials were considered in the analysis. The properties for these fills are as follows: 

 Fill 1: = 33° and c = 500 psf (silty sand borrow) 

 Fill 2: = 23° and c = 2,000 psf (clayey sand borrow) 

 Fill 3: = 40° and c = 50 psf (gravel borrow) 

The above fill properties represent a range of conditions that can be expected in different areas of 

the country. In areas with wet climates, the fill would likely be primarily cohesionless and 

exhibit low cohesion values. Embankment construction in areas with drier climates often will 

use soils with higher fines content and a higher cohesion value. The effects of the cohesion 

component of the shear strength (whether it be true cohesion or apparent cohesion due to 

capillarity acting at the time of the earthquake) are significant during seismic loading. Apparent 

cohesion due to capillarity may well be part of the reason compacted fill slopes have performed 

so well during seismic events. 

Three sites with different levels of seismic activity were considered in the analysis. Two of the sites are 

located in the Western United States (WUS), one in the Los Angeles area and the other one in Seattle. 

The third site is located in Central and Eastern United State region (CEUS), in Charleston, South 

Carolina. The Peak Ground Acceleration (PGA) for each site was determined in accordance with the 

AASHTO seismic design specifications for 7.5% probability of being exceeded in 75 years 

(approximately a 1000 year return period). PGA values were initially determined for bedrock (Soil Type 






B) and modified for Site Class D foundation soil. A summary of the site locations and seismicity data for 

this example is given in Table 7-1. 

TABLE 7-1 SITE COORDINATES AND SEISMICITY DATA

Site Coordinates 

Region 

Soil Type B (Bedrock) Soil Type D 

Longitude Latitude PGA S1

1 FpgaPGA FVS11

-117.9750 34.0500 WUS (Los Angeles) 0.60 0.52 0.60 0.78 

-122.2500 47.2700 WUS (Seattle) 0.40 0.30 0.46 0.54 

-79.2370 33.1000 CEUS (Charleston) 0.20 0.10 0.30 0.24 

1. Spectral acceleration coefficient at 1.0 second period 

A common commercial lint equilibrium computer program was used in the analyses. Only circular failure 

planes were examined through the fill. The PGA was adjusted for slope-height effects when the 

maximum depth of the failure plane below the ground surface was greater than 20 feet (as discussed in 

Section 6). As the critical circular failure surfaces all were tangential to the underlying foundation soil, 

the height factor used to adjust the PGA was taken as the slope height H. Based on the NCHRP 12-70 

procedure, the seismic acceleration was adjusted using Equation 6-2: 

av max  kk

The height correction factor 



was calculated from Equation 6-3: 

.01 01    10.5H

where H is the slope height in feet and is calculated from Equation 6-4: 



k/SF max1v

vSF 1

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Seismic Design – Geotechnical Features 7-21 August 2011 

where is the spectral acceleration coefficient of a period at one second adjusted for site conditions. 

A seismic coefficient equal to kav/2 was used in pseudo-static seismic slope stability analyses, consistent 

with an acceptable seismic slope deformation of 1-2 inches, as described in Section 6. The values of kav

used in the analyses are shown in Table 7-2. 
TABLE 7-2 HEIGHT-ADJUSTED SEISMIC COEFFICENTS FOR SITE CLASS D, 

COMPACTED FILL SLOPE EXAMPLE 

Longitude Latitude Region FpgaPGA FVS1 β H 

[ft] α kav

-117.9750 34.0500 WUS 

 (Los Angeles) 0.60 0.78 1.30 

15 0.95 0.569 

30 0.90 0.537 

45 0.84 0.506 

-122.2500 47.2700 WUS (Seattle) 0.46 0.54 1.16 

15 0.94 0.431 

30 0.87 0.402 

45 0.81 0.373 

-79.2370 33.1000 CEUS 

(Charleston) 0.30 0.24 0.80 

15 0.91 0.271 

30 0.82 0.244 

45 0.73 0.217 

The Newmark displacement correlation equations from the NCHRP 12-70 study were used to estimate the 

slope movement during seismic loading for those cases where the Capacity to Demand (C/D) ratio (i.e., 

factor of safety) using a seismic coefficient equal to kav/2 was less than 1.0. The seismic slope 

deformation was estimated from Equation 6-6: 

FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-22 August 2011 d .1)log( 51 .0 74 y

kk a v .3)/(log 27 ykk a v kmax .1)(log8.0)/1(log 50 log PGV

where the PGV was estimated as the value at the mean plus one standard deviation, given by PGV = 

55FVS1. The yield acceleration (ky) for each case was calculated using the limit equilibrium computer 

program (the yield acceleration is the horizontal seismic coefficient that results in a C/D ratio, or factor of 

safety, of 1.0). Note that in this manual, use of the mean value of the PGV, given by PGV = 38FVS1, and 

not the mean plus one standard deviation value as used in this example, is recommended for consistency 

with LRFD principles. Use of the mean value for the PGV instead of the mean plus one standard 

deviation value reduces the calculated displacement value by approximately 30 percent. 

The pseudo static C/D ratios for each analysis using 0.5 kav are reported in Table 7-3. Yield acceleration 

values are shown in Table 7-4. Permanent displacements are only expected for cases where kav is larger 

than the yield acceleration (ky). As discussed in Chapter 6, the NCHRP 12-70 design approach involves 

using half the kav value and confirming that the C/D is greater than 1.0, assuming that some amount of 

deformation (1 to 2 inches) is acceptable. As shown in Table 7-3, the C/D ratios are less than 1.0 only for 

the steepest slopes and for the higher values of PGA. Newmark displacement estimates were made for 

these cases. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-23 August 2011 

TABLE 7-3 PSEUDO-STATIC STABILITY ANALYSES CAPACITY TO DEMAND RATIO 

(FACTOR OF SAFETY) FOR A SEISMIC COEFFICIENT EQUAL TO 0.5 KAV, COMPACTED 

FILL SLOPE EXAMPLE 

Site 1: Soil Type D (kmax = 0.6) 

Slope 

Angles 

[H:V] 

Slope 

Height 

 [ft] 

C/D Ratio (Spencer) 

c = 500 psf / φ = 33o c = 2000 psf / φ = 23o c = 500 psf / φ = 40o 

2:1 

15 2.40 5.59 1.28 

30 1.73 3.31 1.17 

45 1.53 2.55 1.16 

1.5:1 

15 2.19 5.28 1.09 

30 1.58 3.09 0.98 

45 1.36 2.44 0.94 

Site 2: Soil Type D (kmax = 0.46) 

Slope 

Angles 

[H:V] 

Slope 

Height 

[ft] 

C/D Ratio (Spencer) 

c = 500 psf / φ = 33o c = 2000 psf / φ = 23o c = 500 psf / φ = 40o 

2:1 

15 2.68 6.39 1.43 

30 1.94 3.76 1.32 

45 1.72 2.89 1.31 

1.5:1 

15 2.43 5.96 1.21 

30 1.75 3.48 1.10 

45 1.50 2.72 1.05 

Site 3: Soil Type D (kmax = 0.298) 

Slope 

Angles 

[H:V] 

Slope 

Height 

[ft] 

C/D Ratio (Spencer) 

c = 500 psf / φ = 33o c = 2000 psf / φ = 23o c = 500 psf / φ = 40o 

2:1 

15 3.10 7.55 1.66 

30 2.26 4.43 1.54 

45 1.99 3.39 1.52 

1.5:1 

15 2.78 6.91 1.38 

30 1.97 4.01 1.26 

45 1.71 3.14 1.21 

TABLE 7-4 YIELD ACCELERATION, KY, FOR COMPACTED FILL SLOPE EXAMPLE 

Slope 

Angles 

[H:V] 

Slope 

Height [ft] 

Yield Acceleration 

c = 500 psf / φ = 

33o

c = 2000 psf / φ = 

23o

c = 500 psf / φ = 

40o

2:1 

15 > 0.6 > 0.6 0.44 

30 > 0.6 > 0.6 0.37 

45 0.55 > 0.6 0.34 

1.5:1 

15 > 0.6 > 0.6 0.34 

30 > 0.6 > 0.6 0.26 

45 0.48 > 0.6 0.22 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-24 August 2011 

Results of the analyses are summarized in Table 7-5. These results show that embankments constructed 

at slopes varying from 2:1 to 1.5:1 using common types of embankment fill will perform very well during 

ground motions that might be encountered in seismically active areas of southern California, the Pacific 

Northwest, and the central and southeastern United States. Another conclusion that can be reached from 

these results is that the level at which seismic analyses are required will be relatively high for engineered 

slopes as long as some permanent slope displacement is acceptable. 

TABLE 7-5 NEWMARK DISPLACEMENTS FOR COMPACTED FILL SLOPE EXAMPLE 

Site 1: Soil Type D (kmax = 0.60) 

Slope 

Angles 

[H:V] 

Slope 

Height 

[ft] 

Newmark Displacement [in] 

c = 500 psf / φ = 33o c = 2000 psf / φ = 23o c = 500 psf / φ = 40o 

2:1 

15 0 0 < 1 

30 0 0 < 1 

45 0 0 < 1 

1.5:1 

15 0 0 1-2 

30 0 0 4 

45 0 0 6 

Site 2: Soil Type D (kmax = 0.46) 

Slope 

Angles 

[H:V] 

Slope 

Height 

[ft] 

Newmark Displacement [in] 

c = 500 psf / φ = 33o c = 2000 psf / φ = 23o c = 500 psf / φ = 40o 

2:1 

15 0 0 0 

30 0 0 0 

45 0 0 0 

1.5:1 

15 0 0 < 1 

30 0 0 1 

45 0 0 1 

Site 3: Soil Type D (kmax = 0.298) 

Slope 

Angles 

[H:V] 

Slope 

Height 

[ft] 

Newmark Displacement [in] 

c = 500 psf / φ = 33o c = 2000 psf / φ = 23o c = 500 psf / φ = 40o 

2:1 

15 0 0 0 

30 0 0 0 

45 0 0 0 

1.5:1 

15 0 0 0 

30 0 0 0 

45 0 0 0 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-25 August 2011 

7.3.2 Natural Slopes 

Natural slopes present more difficulties than fill slopes because of the wide range of conditions that occur 

within these slopes, ranging from soil to weathered rocks to jointed rocks. While relatively uniform 

conditions can sometimes exist within a natural slope, most often a natural slope involves layers of 

different geologic materials and these materials often change from cohesionless to cohesive in 

characteristics. Groundwater often is found within the slope, and sometimes the water is intermittently 

perched on less permeable layers within the slope. 

Further complicating the evaluation of a natural soil slope is the geometry. In areas where soils have been 

overconsolidated from glaciation stable natural slope angles can be steeper than 1H:1V, even where the 

fines content is minimal. In some areas the natural slopes can be marginally stable in their existing state. 

In other areas natural slopes that are relatively flat can have thin bedding planes characterized by very low 

friction angles for long-term loading. Where located adversely to a planned slope cut, the removal of 

materials buttressing these slopes can initiate large slides under gravity loading and reactivate slides 

during seismic events 

 

Natural slopes are often the most difficult to characterize in terms of layering and material characteristics. 

Access to conduct site exploration can be difficult, particularly where steep slopes exist. The variability of 

natural deposits forming the slope often makes it difficult to locate or adequately model soil layers critical 

to the evaluation of slope stability, either under gravity or seismic loading. 

 

From a seismic perspective, natural slopes are where most slope failures have been observed. Although 

there is no single cause of these past seismic failures, many of these failures have occurred where slopes 

are over steepened, i.e. where the slope is barely stable under gravity loading. The size of the failure can 

range from small slides of a few yards of soil or rock to movements involving thousands of yards of 

material. In highly seismic areas of the western US, the potential for seismic instability becomes a key 

consideration in some areas, particularly where critical lifeline transportation routes pass over mountain 

terrain. 

The displacement-based slope design methodology applied to natural slopes is illustrated by considering 

the following slope conditions representative of glacial till slopes found in the State of Washington. The 

example is discussed in more detail in the NCHRP Report 611 (TRB 2008) 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-26 August 2011 

The glacial till at the site is primary silty sand with gravels. Blow counts from Standard Penetration Tests 

(SPTs) are generally very high, indicating a dense condition. With some slopes standing as steep as 1H to 

1V, the friction angle of the granular soil could be as high as 45 degrees. However, common practice in 

the area is to assign the glacial till one of two strengths: (1) = 42 degrees and c = 0 pounds per square 

foot, or (2)  = 38 degrees and c = 200 pounds per square foot. A lower bound till strength of  = 36 

degrees and c = 0 pounds per square foot has also been used. Natural slope angles in the area ranged 

from 2H to 1V up to 1H to 1V. The firm-ground (Site Class B) values of PGA, Ss, and S1, for the site 

were determined to be 0.41g, 0.92 g, and 0.30g, respectively, for the 1,000-year return period design 

earthquake based on the AASHTO seismic hazard maps. Soil conditions at the site were representative of 

Site Class C. The objective of the seismic stability study was to evaluate the displacements that would be 

expected for the design earthquake. The owner was also interested in the risk of widening the roadway 

facility on the slope and therefore stability also was evaluated for a 10 percent probability of exceedance 

in 50 years (a 475-year event) and for a 2 percent probability of exceedance in 50 years (a 2,475-year 

event). Each of the common alternatives for the strength of the glacial till was evaluated in the analysis. 

A commercially available limit equilibrium computer program was used to determine the static factor of 

safety and the yield accelerations for the various cases involved in this example. The yield acceleration, 

site-adjusted PGV, and site-and slope height-adjusted PGA were employed with the equations from 

Chapter 6 to estimate permanent seismic displacement. The estimated displacements from the analyses 

are summarized in Table 7-6. The summary indicates that the calculated displacements ranged from zero 

to a maximum of 44 inches, depending on assumptions made for soil properties and the design 

earthquake. 

7.3.3 Screening Criteria 

From the previous examples and based on additional examples from design practice, it is clear that from a 

displacement based perspective simple screening criteria can be established for slopes not requiring 

seismic analysis at sites not susceptible to liquefaction or that are not compromised by sensitive soil 

conditions. The screening criteria in Table 7-7 were established in the NCHRP 12-70 project (NCHRP, 

2008. Seismic analysis of a cut or fill is not required if the site adjusted peak ground acceleration 

coefficient (i.e., Fpga PGA) at the ground surface for the site is less than the values listed in Table 7-7, 

unless allowed or required otherwise by the Owner. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-27 August 2011 

TABLE 7-6 SEISMIC DISPLACEMENT ESTIMATES, NATURAL SLOPE EXAMPLE

Parameter Slope Angle

Static 

C/D 

Ratio

Yield 

Acceleration

ky

Ground Motion Displacement (inches)

7% in 75 

Years

10% in 50 

Years

2% in 50 

Years

Upper Bound Till (φ = 42 degrees)

Case 1 1H to 1V 0.9 NA NA NA NA

Case 2 1.5H to 1V 1.3 0.13 6-9 3-5 14-18

Case 3 2H to 1V 1.7 0.25 < 1 < 1 3-4

Upper Bound Till (φ = 38 degrees, c = 200 psf)

Case 1 1H to 1V 1.2 0.09 12-19 7-11 26-32

Case 2 1.5H to 1V 1.6 0.26 < 1 0 3

Case 3 2H to 1V 2 0.32 0 0 < 1

Upper Bound Till (φ = 36 degrees)

Case 1 1H to 1V 0.8 NA NA NA NA

Case 2 1.5H to 1V 1.2 0.07 18-27 11-17 36-44

Case 3 2H to 1V 1.5 0.17 3-5 1-2 8-11

Note: (1) NA indicates no analysis conducted. Static factor of safety was less than 1.0 

 (2) Upper bound of range based on 84% confidence interval. 

TABLE 7-7 NO SEISMIC ANALYSIS SCREENING CRITERION FOR STABILITY OF 

SLOPES NOT SUSCEPTIBLE TO LIQUEFACTION

Slope Angle Fpga PGA

3H:1V 0.3

2H:1V 0.2

If liquefiable or sensitive soils exist within or support the slope, the minimum acceptable acceleration 

without requiring a stability analysis shall be 0.15g, as long as the SPT blow count measured in the field 

at an efficiency of 60% (N60) is greater than 5 blows per foot (bpf). The slope angle used in screening 

criteria refers to the average angle of the slope above the retaining wall. If the slope is characterized by a 

non-uniform slope condition, the average angle of the slope should be used. Linear interpolation can be 

used when determining the need for a seismic analysis for slopes between those given in the table. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-28 August 2011 

7.3.4 Strategies for Developing Acceptable Displacement 

In many practical situations some small-to-moderate amount of permanent displacement is acceptable 

after the design seismic event. The Specifications and Commentaries prepared for the NCHRP 12-70 

Project include provisions that allow for seismically-induced permanent displacements of slopes and 

embankments. These permanent displacements are generally associated with global stability, where the 

entire soil mass moves. Small permanent displacements are not likely to be life threatening and can be 

repaired by removing or placing earth. However, there are locations where even small slope or 

embankment movements may affect nearby structures or present a risk to public safety. In such cases, 

even a few inches of movement may not be acceptable. 

If permanent movement of the slope is acceptable, there are significant benefits to the Owner: 

 The seismic coefficient used in design may be reduced by 50% if 1 to 2 inches of permanent 

movement are acceptable. 

 In many cases the slope or embankment can undergo more than 1-2 inches of displacement and not 

affect the function of the adjacent roadway, facilities, or public safety. In these cases a reduction in 

the seismic coefficient of greater than 50% may be acceptable. 

Chapter 6 provided a methodology for estimating the amount of deformation in situations where 

deformations larger than the 1-2 inches associated with the 50% reduction in seismic coefficient are 

acceptable and where the capacity-to-demand (C/D) ratio does not meet the target of 1.0 with the 50% 

reduction. Rather than regrading the slope or introducing expensive mitigation measures to achieve a C/D 

ratio of 1.0 or more, the amount of permanent displacement can be calculated. If the amount of 

displacement is within reasonable limits, the seismic performance of the slope may be acceptable even 

though the C/D ratio is less than desired. 

An overriding question in any approach that involves permanent deformations is the amount of 

deformation that is acceptable. Ultimately, that decision belongs to the Owner, who must weigh a number 

of factors in reaching this decision. Factors that should be considered when deciding on acceptable levels 

of permanent displacement include the implications of the movement and the likely mode of slope 

movement. When considering these factors, the Owner should evaluate both the relative consequences of 

movement and, as appropriate, the cost of designing to avoid the movement. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-29 August 2011 

One of the main factors for deciding on the acceptable level of movement involves the location and 

function of the slope. The considerations associated with this factor can be summarized as follows: 

 Slopes located in urban locations usually can tolerate less movement than slopes located in the 

countryside. Part of this relates to effects of slope movement on utilities and other nearby facilities, 

and part relates to aesthetics. After a design seismic event a slope that has moved 24 inches or more 

in the countryside may be completely functional and acceptable, but this same level of slope 

deformation may not be acceptable in an urban environment. 

 Slopes that support a heavily traveled roadway should usually be designed for smaller 

displacements than slopes that are part of a less traveled roadway. This relates to loss of function if 

there is damage associated with slope movement. Generally, less traveled roadways can remain 

unusable for a longer period of time and, therefore, large amounts of permanent movement are 

acceptable. On the other hand, damage to roadways with heavy use may result in significant traffic 

and economic disruption if the roadways are out of service for even a few hours. For this situation 

it may be very important to limit displacement to levels that will have minimal disruption to 

service. 

 Slopes the movement of which may pose a large risk to public safety should be designed for less 

movement than slopes the movement of which poses a low risk. Generally, the risk to the public 

increases as the amount of soil movement increases. The volume and rate of movement can also 

become considerations in this assessment. If there is a large risk associated with soil-mass 

movement, then the Owner is obligated to take a more conservative approach to design, which often 

will mean minimizing acceptable movements. 

The type of soil at a site also should be considered when establishing displacement limits. This 

consideration is related to both the type of failure mechanism and the response of the slope to loads. 

 Seismically-induced slope failures in some slopes will be primarily surface sloughing, while other 

slopes may undergo deep rotational failures. The former type of failure often involves simply a 

maintenance cleanup, while the latter can involve a significant rebuilding effort. The form of the 

failure usually is controlled by the types of soil making up the slope – with granular soils being 

involved in more surficial failures while cohesive soils are more often involved in deeper rotational 

failures. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-30 August 2011 

 Displacement of slopes that are characterized by brittle soils or soils that decrease in strength with 

deformation will have a lower acceptable displacement threshold than soils that do not soften with 

strain. It is usually very hard to estimate how much cyclic strain will result in strength softening 

during the earthquake, making the prediction of deformations difficult and requiring more 

conservatism in establishing acceptable displacement limits. 

 Finer-grained granular soils (e.g. fine sands) may often have some apparent cohesion due to 

capillarity. If this apparent cohesion has not been considered in design, it provides an unquantified 

inherent level of conservatism to the displacement estimates. 

 The confidence in displacement predictions for liquefiable soils is often relatively low. If liquefaction 

is predicted at a slope location, it is generally better to mitigate the liquefaction condition. While it is 

possible to make estimates of slope displacement using residual strengths, the possibility of 

performance being different than expected increases for this situation. 

Perhaps the easiest consideration to understand is the effects that slope movement will have on other 

facilities in proximity to the slope. Examples of these effects are summarized below. 

 Utilities, sidewalks, and pavements located in front of, within, or behind the slope could be affected 

by permanent movement of the soil. The amount of displacement of the utility, sidewalk, or 

pavement can be approximated by the amount of permanent displacement being estimated. 

 

 Slope aesthetics may also be affected by permanent displacements, as noted previously. Generally, 

as the amount of movement increases, the amount of distortion becomes more noticeable to the 

public. The slope movement can also alter drainage within the slope and adversely affect the 

vegetation growing on the slope. 

7.3.5 Approach for Defining Acceptable Displacements 

As summarized above, there are many factors that must be considered when deciding on the acceptable 

level of displacement for slopes and embankments. These factors make the development of a simple 

strategy for establishing the permanent displacement difficult. If displacements of more than 1 to 2 

inches are being considered, a rigorous review of the possible consequences of movement of the slope or 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-31 August 2011 

embankment should be conducted. Figure 7-22 shows the steps that the Owner might use to define an 

acceptable limit to permanent displacement. 

7.4 SLOPE STABILITY MITIGATION MEASURES 

7.4.1 Introduction 

Where stability evaluations for slope or embankment design do not meet seismic performance criteria, 

mitigation measures are required. Detailed procedures for stabilizing soil and rock slopes are presented in 

the Transportation Research Board Special Report 247, Landslides Investigation and Mitigation (TRB, 

1996). Procedures are best categorized by whether the slope needing stabilization is composed of rock or 

soil. Procedures for stabilizing rock slopes are presented by TRB (1996) and FHWA Rock Slope 

Training Course (FHWA, 1998a); stabilization procedures for soil slopes are presented by Holtz and 

Schuster (1996). Many of these procedures are summarized in a report for the FHWA (FHWA, 2004). 

The subsequent descriptions have largely been extracted from the latter report. The specific case of 

mitigation measure for liquefaction induced lateral spreads, is addressed in Section 7.5. 

7.4.2 Soil Slopes 

Approaches to the design of remediation measures for landslides, potential slope failures, and design of 

stable slopes can be categorized as follows (Holtz and Schuster, 1996): 

 Avoidance of Problem 

Adverse conditions affecting stability of slopes, such as poor surface drainage, seepage on existing 

natural slopes, hillside creep, existing landslides, and soft foundations should have been revealed by 

geologic and geotechnical reconnaissance studies. If relocation or realignment of a proposed 

facility is not practical, partial or complete removal of the unstable material may be considered. 

 Reduction of Driving Forces 

A simple approach to increasing slope stability is to reduce the mass of soil involved in potential 

sliding. Methods that have been successfully used to improve slope stability include flattening 

slopes, benching slopes, excavation of material at the top of a landslide, surface and subsurface 

drainage, and the use of lightweight fills. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-32 August 2011 

Figure 7-22 Procedure to Establish Acceptable Slope Movement 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-33 August 2011 

Drainage of surface water and groundwater is a widely used method for slope stabilization. Proper 

drainage will both reduce the weight of the sliding mass and increase the strength of the material in 

the slope. Lightweight backfill materials have been used in embankment construction to reduce 

driving forces tending to cause instability. 

 Increase in Resisting Forces 

Increasing the resisting forces on a potential or existing landslide can be achieved by applying an 

external load or a resisting force at the toe of the landslide, or increasing the internal strength of the 

soils in the failure zone so that the slope would remain stable. 

Procedures that have been used to increase the resisting force at the toe of a potential sliding mass include 

buttress fills and structural retention systems. Buttresses are often constructed of quarry rock, boulders, 

cobbles, and coarse gravel fill. An example of a rock fill buttress is shown in Figure 7-23. Notice in this 

figure that a toe drain was installed to further stabilize the slope by facilitating drainage. 

Figure 7-23 Rock Buttress Used to Increase Forces Resisting Slope Failure 

In situations where buttress fills are not feasible because of geometry, cost, or space limitations, 

conventional retaining structures, piles, and mechanically stabilized earth slopes and walls may be used as 

for stabilization. These methods are summarized in Figure 7-24. The methods are divided into two 

groups, depending on whether they provide external or internal support. Both types of systems are 

illustrated in Figure 7-25. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-34 August 2011 

Figure 7-24 Classification Scheme for Earth Retention Systems 

Figure 7-25 Examples of Externally and Internally Stabilized Earth Retention Systems 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-35 August 2011 

Techniques that are commonly used to increase the internal strength of potentially unstable soil include 

subsurface drainage and soil reinforcing systems. Subsurface drainage is used to lower the groundwater 

table and usually consists of the following procedures: (a) drainage blankets and trenches; (b) drainage 

wells, galleries, and tunnels; and (c) horizontal and vertical drains. Types of vertical and horizontal 

drainage methods used in natural slopes are shown in Figure 7-26. 

Figure 7-26 Types of Vertical and Horizontal Drains used to Lower the Groundwater in Natural 

Slopes 

Geosynthetic products such as reinforcing geotextile and drainage geocomposites have been used for 

slope stabilization in several of the situations described above. Geotextiles have also been used as 

replacements of graded granular filters. Geocomposites are commonly installed for drainage in areas 

where access is difficult, behind retaining structures, and in other places where interception of seepage is 

desired. 

7.4.3 Rock Slopes 

Wyllie and Norrish (1996) describe three categories of stabilization and protection of rock slopes: (1) 

reinforcement; (2) rock removal; and (3) protection. Engineering measures in these three categories are 

listed in Figure 7-27. Selecting the appropriate stabilization system is dependent on several issues that are 

usually site-specific. These issues include service life, importance of the highway structure, 

environmental concerns, construction time, economics and others. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-36 August 2011 

Figure 7-27 Categories of Rock Slope Stabilization Measures (FHWA 1998a) 

A number of different techniques are used for rock slope reinforcement. These techniques are shown 

schematically in Figure 7-28. These methods include reinforced concrete dowels, tensioned rock anchors, 

tie-back walls to prevent sliding on potential fault zones, shotcrete to prevent raveling of fractured rock, 

drain holes for reduction of pore pressures; and concrete buttresses to fill rock cavities. Potential rock 

toppling failures also may be stabilized through rock reinforcement. A feature common to many of these 

methods is that they minimize the relaxation and loosening of the rock mass that may take place as a 

result of excavation and/or seismic loading. 

Cement grout anchors are commonly used for rock reinforcement because they provide a long service life 

at a reasonable cost. The grout usually contains non-shrink cement and/or admixtures for high strength, 

maximum viscosity, and reducing shrinkage. Rock removal is an effective method for stabilization of 

potentially unstable rock slopes because it eliminates the hazard, without the requirement of future 

maintenance. Rock removal includes resloping zones of unstable rock, trimming overhangs, and scaling 

of loose individual blocks of shattered rock. Examples of these methods are illustrated in Figure 7-29. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-37 August 2011 

Figure 7-28 Rock Slope Reinforcement Methods (FHWA 1998a) 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-38 August 2011 

Figure 7-29 Rock-removal Methods for Slope Stabilization (FHWA 1998a) 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-39 August 2011 

Another effective method of protection against the hazards of rockfalls is to let the rockfalls occur and 

control the distance and direction of travel of the falling rock. These methods include catchment ditches 

and barriers, wire mesh fences, mesh lining on the face of the slope, and rock sheds. All these methods 

rely on the energy-absorbing characteristics of the rockfall barrier, which is designed to either stop the 

rockfall over some distance or deflect it away from the facility being protected. 

Details of various types of rockfall barriers are provided by Willie and Norrish (1996). Examples of these 

types of barriers include gabions and concrete blocks and geofabric-reinforced soil barriers. Flexible rock 

catch fences and attenuators also are commonly used for rockfall protection. These types of barriers 

include woven wire-rope nets, flex-post rockfall fences, and draped wire mesh. Figure 7-30 details the 

main components of a rockfall retaining net system used by the California Department of Transportation 

(Smith and Duffy, 1990). 

Figure 7-30 Side View of Rock Fall Restraint Net System with Fully Embedded Posts and Anchor 

Support 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-40 August 2011 

In areas of extreme rockfall hazards where stabilization work may be very costly, construction of rock 

sheds may be used to protect the highway. The sheds are built with roofs that are inclined at a shallow 

angle to direct the falling rocks over the highway rather than to withstand a direct impact. Figure 7-31, 

from McCauley et al. (1985) illustrates the rock shed concept. Design of such structures is based on 

the energy required to redirect the falling rocks and boulders. 

Figure 7-31 Example of a Rock Shed 

The California Department of Transportation (Caltrans) report on rockfall mitigation (McCauley et al., 

1985) provides a summary of the mitigation methods used by 14 selected states that responded to a 

survey. The results of the survey are summarized in Figure 7-32. Based upon this survey, mesh fences, 

catch ditches, rock bolts and dowels, controlled blasting, and flattening and scaling slope are the most 

widely applied rock slope mitigation methods. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-41 August 2011 

Figure 7-32 Rock Slope Mitigation Methods Used by Selected States 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-42 August 2011 

7.5 LIQUEFACTION INDUCED LATERAL SPREADS: DESIGN APPROACH AND 

REMEDIATION 

7.5.1 Background 

As noted in Chapter 6 and illustrated by the case histories in Section 7.2, the vulnerability of 

transportation facilities to liquefaction-induced ground failure has been clearly demonstrated in past 

earthquakes (e.g. 1964 Niigata, 1964 Alaska, 1990 Luzon, 1991 Costa Rica, 1995 Kobe). 

Based on past experience, three liquefaction-related hazards need to be considered in highway design: 

1. Flow slides (large translational or rotational movements) mobilized by existing static stresses. 

2. Limited lateral spreads (displacements) triggered and sustained by the earthquake’s ground motion. 

3. Post-liquefaction ground settlement. 

Each of these hazards can cause major damage and should be considered during the development of 

bridge design or retrofit as well as in highway design. Damage modes for a typical highway structure 

such as the one illustrated in Figure 7-23 include: 

 Lateral deformation of abutments and piers due to liquefaction-induced flow or lateral spreads, 

leading to pile damage and potential span collapse. 

 Differential settlement of footings and abutments leading to damage in continuous superstructures 

and pile damage due to downdrag. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-43 August 2011 

Figure 7-33 Elevation View of a Representative Bridge on a Liquefiable Stratum 

Liquefaction-induced lateral spreading, flow sliding, and differential settlement of the running length of 

the highway must also be considered. 

Methods to assess the potential for liquefaction are discussed in Chapter 6 together with recommended 

procedures to estimate post-liquefaction settlement. The calculation of the amount of lateral spreading 

ground deformation to be expected in the free-field is also described in Chapter 6. The calculation of 

liquefaction-induced ground displacements, which uses the Newmark sliding block approach on an 

assumed dominant failure plane within the liquefied zone, involves considerable uncertainty and is the 

subject of ongoing research. The free-field displacements calculated in this manner are defined by an 

estimated lateral displacement on a failure surface, with the displacement linearly distributed over the 

failure zone, as shown in Figure 7-34 and discussed in Chapter 6. 

Figure 7-34 Pseudo-static Stability Analysis 

Mitigation methods can be considered when damaging liquefaction-induced ground displacements are 

likely to occur. Aside from relocating the highway (or bridge) to a less vulnerable site, two basic 

mitigation options are available: 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-44 August 2011 

1) Structural design or retrofit to accommodate liquefaction and related ground displacement 

demands. This could entail construction of a bridge or viaduct to span over liquefiable ground or, if 

a structure on deep foundations is involved, an analysis of soil-foundation-structure interaction to 

determine if the deformation and load capacity of the foundation system can accommodate the 

ground deformation demands without collapse, or can meet other prescribed performance criteria. 

Evaluation methods that may be used in this approach are discussed briefly in paragraph 7.5.2 and 

in detail with respect to deep foundation performance in Chapter 10. 

2) Site remediation to stabilize the soil and prevent or inhibit liquefaction and thereby minimize 

ground displacement demand. Remediation methods that can reduce ground deformations to 

tolerable levels include: 

 In-situ densification of liquefiable soils in zones surrounding bridge piers and underneath 

the highway and the toe of approach fills; 

 Deep soil mixing using cement, which creates stabilizing zones in the soil similar to those 

developed by ground densification techniques; and 

 Dewatering, installation of gravel drains or permeation grouting, and similar techniques. 

Site remediation methods are discussed in detail in Section 7.5.3. 

7.5.2 Structural Design to Accommodate Liquefaction-Induced Deformations 

Structural design to accommodate liquefaction-induced ground deformations is a complex soilfoundation-structure interaction design problem. While in many cases the geotechnical specialist merely 

passes the displacement demand on to the structural specialist, design if deep foundations to resist lateral 

spreading and seismic settlement is a geotechnical problem and is the subject of ongoing research. 

Analysis of the performance of deep foundations in liquefied ground is discussed in detail in Chapter 10. 

However, besides consideration of the impact of foundation performance on the overlying structure, deep 

foundations may also mitigate lateral spreading. Simplified concepts to address this the impact of deep 

foundations on lateral spreading were addressed in the NCHRP 12-49 project (NCHRP, 2003 and 

ATC/MCEER, 2003) and are described in the FHWA Seismic Retrofitting Manual (FHWA, 2006). 

These concepts are summarized below. 

Initial design of pile foundations would normally be based on the LRFD design procedures for static 

loading, using both of the following configurations: 
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Seismic Design – Geotechnical Features 7-45 August 2011 

1) Non-liquefied configuration – using the appropriate acceleration response spectrum for the nonliquefied site soil conditions. 

2) Liquefied configuration – using a softened pile-foundation stiffness within the liquefied layer and 

the non-liquefied site soil spectrum (unless special studies are undertaken). 

If liquefaction-induced lateral flow sliding or spreading of the ground is predicted during a seismic event, 

structures that would be loaded by the deforming ground need to be checked and possibly re-designed to 

withstand the loads from the moving soil. The recommended approach for evaluating this condition 

involves the following four basic steps: 

1) Slope stability analyses are conducted for the liquefied state using the residual shear strength to 

determine the post-liquefaction yield acceleration and the associated failure surface (normally 

associated with the deepest soil layer showing liquefaction potential). This step may include 

consideration of the pinning effects of the piles and/or the increased resistance of soil that has 

provided by some type of ground improvement method. 

2) Newmark sliding block analyses are performed using the post-liquefaction yield acceleration to 

estimate the post-liquefaction displacements of the soil-pile system. 

3) Forces on the structure and its foundation due to the lateral spreading movements are calculated. 

4) Plastic hinge mechanisms that are likely to develop in foundation elements are determined. 

In the above procedures, it is assumed that the effects of ground displacement can be decoupled from the 

effects of structural inertial loading. In most cases, this is a reasonable assumption, as peak vibration 

response is likely to occur in advance of the maximum ground displacement and displacement-induced 

maximum moment and shear on a foundation element will generally occur at deeper depths than those 

from inertial loading. The rationale behind the proposed procedure is to assess the ability of the structure 

to both accommodate the anticipated movement and/or potentially limit the movement. 

The concept of considering a plastic mechanism in the foundation under the action of the lateral spreading 

forces is tantamount to accepting damage in the foundation. The justification for this is that it is unlikely 

that the formation of a hinge mechanism in the foundation will lead to structure collapse. The reasoning 

behind this is that lateral spreading is essentially a displacement-controlled process. Thus the estimated 

soil displacement represents a limit on the structure displacement excluding the phenomenon of buckling 

of the piles or shafts below grade and the continued displacement that could be produced by large P-Δ 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-46 August 2011 

effects. This is an important concept, as analyses suggest that the moments induced in a deep foundation 

element for a structure subject to significant liquefaction-induced displacement demand can be very large 

at the interface between the liquefied zone and an underlying non-liquefied layer. Buckling should be 

also be checked using methods that include the residual soil resistance. O’Rourke et al. (1994) provides a 

method for checking buckling of deep foundation elements in liquefied soil. 

The magnitudes of the moment and shear induced in pile foundations by ground displacements may be 

computed using soil-pile interaction programs. The assumed displacement field is as a support 

displacement to soil springs whose properties are represented by p-y curves. In the liquefied zone, these 

p-y curves must be adjusted for liquefaction effects. Examples of such analysis are given by O’Rourke et 

al. (1994), Soydemir et al. (1997), and Ishihara and Cubrinovski (1998). In the liquefied zone, the soil is 

can be treated as a soft cohesive soil with p-y curves computed using the undrained residual strength of 

liquefied soil as the cohesion. 

The largest loads on foundations at sites where lateral spreading or flow sliding is expected occurs in 

cases where a non-liquefied crust slides on a liquefied layer. In such case, the ground deformations may 

exert full passive pressures on the foundation in the non-liquefied zone. The loads in these cases may be 

very large, as the passive pressure will typically be generated over a width equal to 2 times the width of 

the foundation element in cohesive soil and 3 times the width of the foundation element in cohesionless 

soil. The passive pressure against a pile cap in a laterally spreading non-liquefied crust may be assumed 

to be applied over the width of the pile cap plus twice the depth of the base of the cap below grade. In the 

liquefied zone, the passive pressure calculated using the residual shear strength may be assumed to apply 

over the width of the foundation element or pile cap. An analysis conducted using these assumptions will 

generally result in extremely large forces on the foundation and the formation of plastic hinges in the 

foundation elements. However, the foundations may still remain intact without failure in a state of 

limiting equilibrium, as in the case history of the Landing Road Bridge described in Section 7.2.3. 

The reinforcing or pinning effects a piles or pile group has on the lateral displacements may then be 

considered by representing the pile shear forces at the location of the failure plane as an equivalent shear 

strength in the calculation of the yield acceleration of the sliding mass, which is subsequently used in the 

displacement analysis. This requires an iterative approach, as shear forces are a function of displacements 

which, in turn, are reduced as shear forces increase. 
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Seismic Design – Geotechnical Features 7-47 August 2011 

In the event that the pile foundations cannot accommodate the displacement demands from spreading 

ground, one option is to install additional foundation piles (using a pile cap overlay in a retrofit case) to 

increase the pinning action and, hence, reduce the displacement demands. Another option is the use 

passive piles driven through the liquefiable layer and failure surface to provide additional pinning action 

without physically attaching the piles to the bridge structure (such piles are sometimes referred to as 

“pinch” piles). Installing additional foundation piles may be particularly relevant if additional piles are 

also required to accommodate high overturning moments or to minimize down drag effects. Where 

additional piles are required, the costs of mitigation should be compared with the costs of ground 

remediation to reduce lateral spreading displacements. 

The framework of the simplified approach to design for the impact of soil liquefaction on a bridge 

structure using the above concepts and presented in the NCHRP 12-49 Guidelines is outlined in the flow 

chart shown in Figure 7-35. The steps involved are described as follows: 

Step 1: Identify the soil layers that are likely to liquefy 

Step 2: Assign residual undrained strengths to layers that liquefy. Conduct pseudo-static seismic 

stability analyses to determine the minimum yield acceleration ky. This defines the depth of soil 

likely to spread laterally and the extent of the likely-soil failure block. If the yield acceleration 

is equal to (or less than) zero, the site is subject to uncontrolled flow failures and unlimited 

deformation in the liquefied zone must be assumed. 

Step 3: Estimate the maximum lateral spreading displacement of the soil. This may be accomplished 

using the displacement equations presented in Chapter 6 or a site-specific Newmark time 

history analysis. 

Step 4: Assess whether the soil will continue to displace or flow around a stable foundation or whether 

movement of the foundation will occur in concert with the soil. This assessment requires a 

comparison between the estimated passive soil forces that can be exerted on the foundation and 

the ultimate structural resistance that can be developed by the structure. In cases where a crust 

of non-liquefied material may exist at the ground surface, the full structural resistance may be 

less than the displacement-induced passive forces and the foundation is likely to continue to 

move with the soil. In many cases, it may be immediately obvious which condition is more 

likely to occur. Schematic illustrations of the two cases are shown in Figure 7-36. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-48 August 2011 

Figure 7-35 Design Flowchart 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-49 August 2011 

Figure 7-36 Deformation Models for Piles at Lateral Spreading Sites 

Step 5: If the soil continues to displace around a stable foundation, the foundation is designed to 

withstand the passive pressures created by the flowing soil. The induced forces are effectively 

the largest forces that the structure will experience and, for this reason, it is conservative to 

design a structure for such forces. 

Step 6: If the assessment indicates that movement of the foundations is likely to occur in concert with 

the soil, then the structure must be evaluated for adequacy at the maximum expected 

displacement. The implication of this assessment is that for relatively large ground movements, 

soil displacements are likely to induce similar magnitude movements of the foundation. In this 

context, “large” is taken relative to the structural yield resistance. The resulting induced 

movements of the foundations may produce substantial plasticity or hinge zones in the 

foundations, and may induce relatively large reactions in the superstructure. For an upper level 

event, a maximum plastic rotation of 0.05 radians is the recommended acceptance criteria, 

although values determined by rational cross section analyses are also acceptable and preferred 

in many cases. 

Step 7: If the deformations determined in Step 6 are not acceptable, two ways to restrict the foundation 

and substructure forces to values less than yield can be considered. The first method is to 

design or retrofit the foundations to resist the forces that would accompany passive flow of the 

soil around the foundations. The second method would be to limit the ground movement by 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-50 August 2011 

providing either ground or structural remediation. It is the structural option that provides a 

potential first path, and this makes use of the “pinning” or dowel action that pile or shaft 

foundations contribute as they cross the potential failure plane of the moving soil mass. This 

can effectively reduce the magnitude of lateral displacement. 

Step 8: Determine the plastic mechanism that is likely to occur in the presence of lateral spreading. 

This should be done in a reasonable manner. Due to the range of inherent uncertainties, great 

precision in the determination may not produce more accuracy. Simple estimates of the 

mechanism and its corresponding lateral resistance capability may be adequate. Such estimates 

could be based on hinge development in stable or firm soil zones above and below (by say 2 

pile diameters) the liquefiable layer. Maximum “pinning” shear could then be assumed equal 

to 2Mp/L, where Mp is the plastic moment and L is the distance between hinges – this assumes 

that the load transfer in the liquefied zone is negligible. The lateral shear that produces the 

plastic mechanism can be adjusted downward to account for the driving influence of the P-Δ 

effect. A more precise method of determining the plastic mechanism would be to use an 

approach that ensures compatibility of deformations between the soil and piles (e.g., one that 

uses a p-y analysis) and which accounts for plastic deformations in the piles themselves. 

Step 9: Assess the system for the calculated displacement field from the lateral spreading analysis. 

From this analysis, an estimate of the likely shear resistance that the foundation will provide is 

determined, which can then be incorporated back into the stability analysis. 

Step 10: If substantial resistance is provided by the foundation system, then its effect on limiting the 

instability driven movement of the soil block should be accounted for. 

Step 11: Recalculate the overall displacement on the basis the revised resistance levels. 

Step 12: Once a realistic displacement is calculated, the foundation and structural system can be 

assessed for this movement. It is at this point that more permissive displacements than those 

allowed for substructure design can be relied upon. This implies that plastic and potentially 

large rotations may be allowed to occur in the foundation under such conditions. 

Step 13: If the structure’s behavior is acceptable, then the liquefaction design is complete. If not, assess 

whether or not adequate behavior can be achieved by providing ground remediation or 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-51 August 2011 

additional piles or shafts. Note that additional piles or shafts may not need to connect to the 

foundation (passive piles) or the cap. Ground improvement approaches may be considered 

include stone columns, deep soil mixing, and grouting. The selection of a preferred structural 

or geotechnical method is based on the relative economies of the systems being considered. 

An example of the application of this procedure is provided by the analysis of a Washington State 

Department of Transportation (WSDOT) bridge site (Site Class E) at the site whose abutment fill 

subsurface profile is shown in Figure 7-37. Seismic hazard analyses for the site (assumed located near 

Olympia) generated a site-specific peak horizontal ground acceleration of 0.42 g for a 2475 year return 

period and a 6.5 mean magnitude for the design event. For a 475 year return period. The design 

magnitude was still 6.5 and the peak horizontal ground acceleration was 0.24 g. 

The 500 ft long box girder bridge structure at the site is continuous between the overhanging stub 

abutments. The intermediate piers are two column bents supported on pile caps and concrete-filled 24 in. 

steel pipe piles, embedded in till at elevation -200 ft. Soils between elevations of 0 to -100 ft comprise 

interlayered medium-dense sands and soft clays (shear strength 1000 psf). Stiff clays (shear strength 

2000 psf) were assumed between elevations -100 to -200 ft. 

Evaluations of liquefaction potential (step 1 of the design procedure) for the 2475 year event, show 

liquefaction in all sands without overlying fill, and with overlying fill for layers at elevations -10 to -15 ft, 

-30 to -35 ft and 045 to -50 ft and below. For the 475 year event, liquefaction occurs in sands at 

elevations -30 to -35 ft and -45 to -50 with overlying fill, but does not occur for sands below the fill. 

One dimensional nonlinear effective stress site response analyses were also conducted to evaluate the 

time history of pore pressure increase and site liquefaction characteristics. Acceleration time histories 

were developed from records consistent with the hazard levels and site conditions and modified to match 

design response spectra. The results of the nonlinear effective stress site response analysis were generally 

consistent with the liquefaction calculations. However, a key conclusion from these studies was the 

strong likelihood that lateral spreading deformations would be controlled by a failure zone in the layer at 

elevations of between -45 ft to -55 ft. In general, the effective stress site response analyses showed that 

the post-liquefaction shear strains focused on the deepest layer susceptible to liquefaction. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-52 August 2011 

Figure 7-37 Site profile, Washington Bridge 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-53 August 2011 

Once it was established that liquefaction and lateral spreading was likely to occur, a post-liquefaction 

stability analysis of the abutment fill was performed as indicated in Step 2 of the design procedure. Preliquefaction analyses indicated static C/D values for the embankment slopes were greater than 1.5. 

However, when post liquefaction residual undrained strengths of 300 psf were assigned to the sand layer 

at elevations -45 to -55 ft, C/D values dropped to a minimum of approximately 0.8. as shown in Figure 

7-38, indicating the potential for an unconstrained flow failure. 

Figure 7-38 Typical Sliding Mechanism for Flow Failure 

Given the potential for large unconstrained lateral spreading, the next step (step 7) was to evaluate the 

beneficial pinning action of the pile foundations. The deep failure mechanism for lateral spreading at the 

right abutment shown in Figure 7-39 is example f this step of the analysis. Given the high passive 

pressure forces which could be generated by the embankment moving against the abutment and piles, it 

was clear in this case that a limiting equilibrium condition associated with flow around the foundations 

would not develop and that the foundation would move with the soil. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-54 August 2011 

Figure 7-39 Forces Provided by Bridge and Foundation Piles for Resisting Lateral Spread 

The maximum pinning forces that could be developed were then considered to see if they were sufficient 

to provide post-earthquake static stability. Figure 7-39 illustrates the pinning forces acting on a soil block 

sliding on the lower liquefiable layer. In this case, the abutment itself provides about 400 kips of shear 

resistance (through passive resistance provided by backfill acting against end diaphragm), and the 

columns at Pier 5 provide about 420 kips of shear resistance. The total abutment pile resistance is 1080 

kips and the total resistance of the Pier 5 piles is 1440 kips. The pile resistance corresponds to the 

approximate plastic mechanism shear force with 30 ft between points of assumed fixity in piles. The 30 ft 

between points of fixity is comprised of 10 feet of liquefiable material and a conservatively assumed 

distance of 5D (D = pile diameter) to the point of fixity above and below that layer. This conservatism 

allows for softening in adjacent layers. The upper portion of the soil block is assumed to move essentially 

as a rigid body, and therefore the piles are assumed to be restrained by the integrity of this upper block. 

The sum of these forces (3360 kips total) represents the maximum shear resistance provided by the bridge 

foundation system and occurs only after significant plasticity develops. In the case of Pier 5, the 

approximate displacement limit is 22 in., which is comprised of 4 inches to yield and 18 inches of plastic 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-55 August 2011 

drift. The plastic drift limit for this case was taken as 0.05 radians, which is reasonable for well detailed 

ductile piles. Because the abutment piles (Pier 6) are the same as the piles at Pier 5, their displacement 

limit was also 22 in. 

The total 3360 kip resistance calculated above represents 70 kips/ft of width of the abutment and was 

introduced into the slope stability analysis as an equivalent shear strength (530 psf) along the shear plane 

in the liquefied zone. This increase in shear resistance was sufficient to increase the post-earthquake C/D 

ratio to greater than 1.0, hence negating the potential for an uncontrolled flow failure. Similar pinning 

analyses for the upper failure surface led to a C/D ratio of 1.0, indicating the potential for an uncontrolled 

flow failure was still a concern. 

For the lower failure surface, the lateral spreading displacement due to inertial forces imposed during the 

earthquake remained to be evaluated (step 3). These displacements were evaluated by calculating the 

yield acceleration and estimating the resulting lateral displacements using the Newmark sliding block 

method. For the calculated yield acceleration of 0.02g, a displacement of about 22 in. was calculated for 

the 475 year event and a displacement of 36 in. was calculated for the 2475 year event. The 22 in. 

displacement is within the plastic capacity of the piles, whereas for the 2475 year event, either additional 

“pinch” piles could be added or ground remediation could be implemented. Subsequent analyses showed 

that the installation of a 30 ft wide stone column toe buttress extending through the liquefied zones to an 

elevation of -55 ft leads to a yield acceleration of 0.12g and reduced the estimated lateral displacement to 

less than 5 in. for the 475 year event and 8 in. for the 2475 year event. The 30 ft wide stone column 

buttress was estimated to cost about $120,000 for both sides of the embankment, or about 4% of the likely 

bridge cost. 

The case history above shows that the beneficial effects of considering the resistance that the bridge 

substructure offers to lateral displacements of soil via “pinning” action can be significant and should be 

considered in predictions of lateral soil movements. In addition, the benefit of allowing inelastic behavior 

of pile foundations under the action of lateral ground spreading is that relatively large displacements of 

the ground may be accommodated by the structure without collapse. If pile foundations cannot tolerate 

the predicted displacements (including pile pinning effects), then either structural or ground improvement 

remediation options should be used. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-56 August 2011 

7.5.3 Liquefaction Mitigation Ground Improvement Methods 

To prevent or inhibit liquefaction and reduce lateral ground deformations and settlements to acceptable 

performance levels, site remediation using one or more ground improvement options may be deployed. 

Remediation methods include: 

 In-situ densification of liquefiable soils in zones beneath embankments, underneath the toe of 

approach fills or surrounding bridge piers; this will reduce ground deformations to tolerable levels. 

 Deep soil mixing using cement, which creates stabilizing zones in the soil similar to those 

developed by ground densification techniques. 

 Dewatering or installation of gravel drains to prevent pore water pressure build up. 

 Grouting techniques. 

Such remediation methods are also applicable to embankments on liquefiable soils in the absence of 

bridge abutments, where lateral spread deformations are not acceptable. 

Overviews of the state-of-practice for site remediation are documented in several publications (ASCE, 

1997; Andrus and Chung, 1995, Elias et al., 2006). A comprehensive report on ground remediation 

measures for liquefaction at existing bridge sites was published by Cooke and Mitchell (1999). A 

summary of several ground improvement methods for liquefaction remediation is given in Table 7-8, 

extracted from the Cooke and Mitchell (1999) report. Brief summaries of several of the remediation 

methods are given below. 
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Seismic Design – Geotechnical Features 7-57 August 2011 

TABLE 7-8 GROUND IMPROVEMENT METHODS (after Cooke and Mitchell, 1999) 

Method Principle Suitable

Soil Types

Treated Soil

Properties

Relative

Costs

Compaction

Grout

Highly viscous grout acts as 

spherical hydraulic jack 

when pumped under high

pressure resulting in

densification.

Compressible

soils with some 

fines

Increased Dr

SPT: (N1)60

25 to 30

CPT: qcl=80

To 150 tsf

(Kg/cm2)

Low material cost; 

high injection

cost.

Particulate

Grouting

Penetration grouting: fill soil 

pores with cement, soil 

and/or

clay.

Clean, medium 

to

coarse sand

and gravel

Cementgrouted soil:

high strength

Lowest of grouting

systems

Chemical

Grouting

Solutions of two or more 

chemicals react in soil pores 

to form a gel or solid

precipitate.

Silts and sands Low to high

strength High to very high

Jet Grouting

High speed jets at depth 

excavate, inject and mix

stabilizer with soil to form 

column or panels

Sands, silts

and clays

Solidified

columns and

walls 

High

VibroCompaction

Densification by

vibration and 

compaction of

backfill at depth.

Sand

(<20% passing 

No. 200 sieve)

Dr: up to 85+%

SPT: (N1)60

25 to 30

CPT: qcl=80

To 150 tsf

(Kg/cm2)

Moderate

Vibroreplacement/

Stone

Columns

Densely compacted

gravel columns provide 

densification, reinforcement, 

and drainage

Sands and 

silts

Increased Dr

SPT: (N1)60

25 to 30

CPT: qcl=80

To 150 tsf

(Kg/cm2)

Moderate

to high

Drains:

Gravel

Sand

Wick

Relief if excess pore water 

pressure to prevent 

liquefaction. Intercept and

dissipate excess pore water 

pressure plumes from

adjacent liquefied soil.

Sands, Silts Improved 

drainage

Low to

moderate

Mini-Piles Provide piles to carry loads 

through liquefiable soils to

firm stratum.

All soils - High
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Seismic Design – Geotechnical Features 7-58 August 2011 

For new construction, particularly in open areas some distance from existing structures, in situ 

densification using vibratory techniques or dynamic compaction are the most commonly deployed 

methods for improving the density, and hence strength and stiffness, of loose cohesionless soils. For 

saturated cohesionless soils, vibratory methods have been widely used to increase liquefaction resistance 

under earthquake loading. However, these methods would in most cases, not be suitable for use in 

improving soils around existing foundations, embankments, or roadways. Each method has its own 

technology, effectiveness and suitability for different soil types. Experience indicates that vibratory 

techniques can increase relative densities to values greater than 80%. 

Deep dynamic compaction (shown schematically in Figure 7-40) entails dropping weights of 10-40 tons 

from heights of 50-100 feet over impact grids ranging from 7x7 feet to 25x25 feet. The depth that can be 

effectively improved is a function of the size of weight, height of drop, and the soil type. The effective 

depth of improvement is limited to about 35 feet using conventional equipment and is controlled by the 

soil type, degree of saturation, permeability, and initial relative density. Levels of ground vibration are an 

important environmental constraint with this method, and areas treated using this method will probably 

need to be a minimum of 100 feet from existing structures. A detailed description of applications of 

dynamic compaction and associated ground response is given by Mayne et al. (1984), ASCE (1994), 

ASCE (1997), and FHWA (2004). 

Figure 7-40 Dynamic Deep Compaction 

Vibro-compaction methods, the most common of which is known as vibroflotation (shown schematically 

in Figure 7-41), involves the repeated insertion and withdrawal of a large vibrating probe to the desired 

depth of densification. In some cases granular backfill soil is added and densified during withdrawal of 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-59 August 2011 

the probe. The procedure is repeated over the site using a grid spacing ranging between 6 and 11 feet 

with typical depths of improvement ranging from 10 to 50 ft. The method is more suited to clean sands. 

For silty sands, the vibro-replacement method described below is more widely used. The effectiveness of 

vibro-compaction in saturated cohesionless soils depends on the initiation of localized liquefaction 

followed by pore pressure dissipation and settlement. Brown (1977) provides general background 

information on the technique. Dobson (1987) describes several case histories where vibro-systems have 

been used to minimize liquefaction. 

Figure 7-41 The Vibro Compaction Process 

The most widely used densification method is the vibro-replacement technique, which has been shown to 

be effective in remediating potentially liquefiable soil in past earthquakes (Mitchell et al., 1995). This 

method involves the replacement or displacement of the liquefiable soil with a column of dense granular 

soil formed by repeated insertion and withdrawal of a large vibrating probe into the soil to the desired 

depth of improvement, as shown in Figure 7-42. As the vibrating probe is plunged up and down, crushed 

stone backfill is placed around the vibrator, leading to the development of a dense stone column that is 

approximately 1 m (3 ft) in diameter. The procedure is repeated at a grid spacing of 2.4 to 3.7 m (8 to 12 

ft) to form an improved zone. 

Vibro-replacement includes wet methods where the insertion of the probe is aided by jetting and dry 

methods where the probe is penetrated into the ground typically using a vibrating hammer of some sort. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-60 August 2011 

The wet methods rely more on replacement then displacement and are more suitable for ground 

improvement at non-liquefiable soft soil sites. Dry methods displace the soil, densifying the adjacent 

soil and providing liquefaction mitigation by densification as well as through reinforcement and enhanced 

drainage. 

Figure 7-42 Vibro-replacement Equipment and Process 

Vibro-replacement is effective if the sands to be densified contain less than 15 to 20 percent fines. 

A representative application of vibro-replacement is shown in Figure 7-43, where a densified stone 

column buttress has been constructed at the toe of an embankment. The buttress increases the yield 

acceleration through the reinforcement provided by the columns and the densification of the soil in 

between the columns. This, in turn, reduces lateral spreading. The enhanced drainage provided by the 

stone columns is an unquantified additional benefit of the buttress. An example of this approach is 

described by Egan et al. (1992). 

Another example of the application of stone columns for liquefaction remediation is shown in Figure 

7-44, where a densified soil zone has been placed around a pile-supported bridge pier. The placement of 

such a zone (normally within a radius of 150 to 200 percent of the thickness of the liquefiable layer) 

would be designed to eliminate post-liquefaction downdrag on the piles as well as to reduce the potential 

for liquefaction induced lurching or lateral spreading of the ground.. 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-61 August 2011 

Figure 7-43 Vibro-system (stone column) Treatment at Toe of Approach Embankment 

Figure 7-44 Vibro-system (stone column) Treatment Around a Pile-supported Bridge Pier 
FHWA-NHI-11-032 7 –Earthwork Features 

Seismic Design – Geotechnical Features 7-62 August 2011 

For sites where vibratory techniques may be impractical, compaction grouting can be used. Shown 

schematically in Figure 7-45, compaction grouting involves pumping a stiff mix of soil, cement, and 

water into the ground under high pressure to compress or densify the soil. A very stiff soil-cement and 

water mixture is injected into the soil forming a grout bulb, which displaces and potentially densifies the 

surrounding ground, without penetrating the soil pores. A grid or network of grout columns that is 

formed by grouting from the bottom up results in improved liquefaction resistance over the required 

surface area, similar to a network of stone columns (Boulanger and Hayden 1995). A theoretical study of 

the mechanics of ground improvement in sands (Mace and Martin, 2000) has shown that increased 

liquefaction resistance arises primarily from increased lateral stresses rather than from densification. 

Consequently, increases in liquefaction strength are best measured using cone penetration test (CPT) 

correlations (Salgado et al., 1997). However, there are uncertainties as to the permanence of increases in 

the lateral stress. Furthermore, compaction grouting is one of the more expensive liquefaction ground 

remediation options. 

The deep soil mixing method encompasses a group of technologies where cementitious material (usually 

cement or lime) is introduced and blended into the soil through a hollow rotating shaft or shafts equipped 

with cutting tools and mixing paddles or augers. The materials may be injected under pressure in either 

slurry (wet) or dry form. 

Figure 7-46 shows a typical rig used for the dry mixing method with a schematic diagram of the mixing 

process. The process leads to vertical stabilized columns of about 1 m diameter. Multiple augers are 

often used in the wet methods. For dry methods (used beneath the water table or in high moisture content 
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clays), typically 50-150 lb (100-300 kg) of cementitious material is injected per cubic meter of soil, while 

for wet methods, 50-250 lb (100-500 kg) is injected. The strength gain of the soil depends on the physical 

properties of the soil and the quantity of cementitious material injected. Typically, values of unconfined 

compressive strengths of 5-50 tsf are achieved in treated granular soils and 2-20 tsf in cohesive soils

Figure 7-45 Compaction Grout Bulb Construction 
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Seismic Design – Geotechnical Features 7-64 August 2011 

Figure 7-46 Dry Method Column Installation 

The versatility of the deep mixing construction technique allows columns to overlap to form blocks, 

walls, or lattice configurations, as shown in Figure 7-47. The choice of pattern depends on the specific 

application as illustrated in Figure 7-48. Structural walls are typically used for resisting lateral earth 

pressures in construction of deep excavations while solid blocks may be used to strengthen large volumes 

of weak soil. Lattice or cellular structures may be used to support lightly loaded structures or to control 

embankment stability. 

Figure 7-47 Deep Mixing Column Patterns (after Porbaha et al., 1999) 
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Seismic Design – Geotechnical Features 7-65 August 2011 

An example of the use of a lattice type deep mixing columns to mitigate liquefaction is illustrated by a 

Kobe earthquake case history. The lattice-type deep mixing method was applied to enhance the lateral 

resistance of the pile foundation of a fourteen story hotel building on the foreshore of the Port of Kobe as 

shown in Figure 7-49. The building was supported on concrete piles 2.5 m in diameter and 33 m long. 

The deep mixed walls were installed to encapsulate the piles to a depth of 15.8 m to mitigate liquefaction 

in the liquefiable fill and prevent lateral spread. During the great Hanshin earthquake (January 17, 1995, 

magnitude of 7.2 Richter), the quay walls on the west, south and east of the building moved horizontally 

by 1 m, 2 m, and 0.5-0.6 m, settling by 0.4-0.6 m, 0.5-0.7 m, and 0.2-0.3 m, respectively. This building, 

nevertheless, survived without damage to its pile foundation. Excavation of the foundation after the 

earthquake indicated no sign of liquefaction or lateral spread. In concept, the cellular wall structure 

reduced levels of shear strain in the fill be absorbing the shear loading, thereby mitigating the liquefaction 

potential.

Figure 7-48 Deep Mixing Applications in Japan (after Terashi and Juran, 2000) 
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Figure 7-49 Kobe Hotel Foundation Plan 

7.6 SUMMARY 

This chapter presents an overview of approaches to the seismic analysis and geotechnical design of 

earthwork features associated with transportation systems. These features are primarily associated with 

embankment fill and natural and/or cut slopes, where seismic design issues of concern include slope 

stability and/or earthquake induced deformations, settlement, and liquefaction induced lateral spreads. 

Case histories of damages to highways from the above failure modes in past earthquakes are reviewed to 

illustrate the need for design methods to address deformation performance criteria. Both pseudo-static 

and displacement based design procedures for slope stability analyses are described and illustrated 

leading to screening procedures to define conditions where deformation based design checks are not 

needed. Criteria for establishing acceptable slope displacements are discussed, and mitigation measures 

to employ where slopes do not meet performance criteria are reviewed. Such measures include toe 

buttresses, piles, ground anchors, and retaining structures. 
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The special case of liquefaction included embankment lateral spread deformations are discussed in detail 

including analysis and design procedures, and illustrative examples. Liquefaction mitigation ground 

improvement techniques are described including dynamic compaction, stone column installation and deep 

soil mixing. 
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CHAPTER 8

GEOTECHNICAL SEISMIC DESIGN FOR TRANSPRTATION STRUCTURES AND 

SOIL-FOUNDATION-STRUCTURE INTERACTION 

8.1 GENERAL 

This chapter discusses geotechnical aspects of seismic design for transportation structures, including the 

importance of interaction between the structural designers and geotechnical specialists, the principles of 

capacity design, and soil-structure interaction. The following topics are discussed in this chapter: 

 The need for collaboration between structural designers and geotechnical specialists in seismic 

design of transportation structures. 

 The seismic design process, including the need for interaction between structural designers and 

geotechnical specialists in this process. 

 How seismic design demand is established for both force-based design and displacement-based 

design and the principle of capacity protection of foundation elements. 

 The desired characteristics of earthquake resisting systems for transportation structures; 

 The unintended and potentially adverse consequences on the seismic performance of the overall 

structure of the intentional incorporation of what is often perceived as conservatism to 

accommodate uncertainties in soil properties. 

 The proper way to account for uncertainties in geotechnical earthquake engineering, including 

uncertainties associated with the earthquake motion characteristics and soil properties in a practical 

manner. 

 General aspects of geotechnical design for good seismic performance. 

 Inertial and kinematic soil-structure-foundation interaction analyses. 

8.2 INTERACTION BETWEEN STRUCTURAL DESIGNERS AND GEOTECHNICAL 

SPECIALISTS IN THE SEISMIC DESIGN PROCESS 

Interaction between structural designers and geotechnical specialists during the design of transportation 

structures is essential, particularly in the context of seismic design, in order to ensure that the resultant 

design functions as intended when subjected to the design loads. Reasons why interaction between 

structural designers and geotechnical specialists is necessary in the seismic design process include: 
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 There are many complexities involved in defining the design earthquake load. The characteristics 

of the earthquake load (e.g. amplitude, frequency content, duration) depends on three major 

parameters: (1) the ground motion characteristics, (2) the inertial mass of the structural system, and 

(3) the overall stiffness of the superstructure and the foundation system. The characteristics of the 

earthquake ground motion are generally the purview of the geotechnical specialist and the inertial 

mass of the structure is generally controlled by the structural engineer. However, design decisions 

from both the structural designer and geotechnical specialist can affect the overall stiffness of the 

structure. 

 Complexities in establishing the earthquake demand often necessitate further interaction between 

the structural designers and geotechnical specialists. Complexities in the interpretation of the 

design load associated with the earthquake load include the use of force reduction factors (reduction 

factors applied to forces established from an elastic response modal analysis in the force based 

seismic design method). Furthermore, it is often necessary and appropriate to treat the earthquake 

load as a displacement demand (i.e. to employ the displacement based seismic method) and design 

strategies for providing force based capacity (which often result in a stiffer system) can be counterproductive to the need for providing displacement capacity (i.e. ductility) to the overall system. 

These complexities associated with earthquake resistant design require a high degree of interaction 

between structural designers and geotechnical specialists so that design decisions from either party 

are not counter-productive to the desired performance of the resultant structure. 

 Since some of the required soil properties are difficult to assess and can change significantly during 

the earthquake, there is a high degree of uncertainty in soil properties as well as an inherent 

uncertainty in the earthquake loading condition. As such, there is a greater need to properly 

account for basic uncertainties in the design process for earthquake design than in non-seismic 

design. This increased uncertainty requires a higher degree of interaction between the structural 

designers and geotechnical specialists in the earthquake design process. 

8.3 GLOBAL DYNAMIC RESPONSE MODEL 

Development of a global structural model is usually the first step in the seismic design process for a 

transportation structure. Typically, a dynamic response analysis using a global structural model is used to

develop the seismic demand (load) on individual components of the structure. The dynamic response 
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analysis is then followed by the determination of the capacity of the structure (e.g., using a pushover 

analysis to determine the displacement capacity of the structure in the displacement based method). 

Integrity of the structural system is then established by comparing the capacity to the demand. The three 

fundamental parameters in the dynamic response analysis of the global structural model, depicted in an 

idealized manner in Figure 8-1, include: 

1) Design ground motion characteristics are usually provided by the geotechnical specialist. Chapter 3 

in this report provides further details on ground motion characterization. Either a response 

spectrum or a suite of acceleration time histories usually form the basis for ground motion 

characterization. In most design applications the design ground motion is characterized by an 

acceleration response spectrum. 

2) The inertial mass of the structure. The inertial mass is usually defined by the structural designer. 

3) The overall stiffness of the structural system. Both the structural designer (who defines the 

stiffness of the superstructure) and the geotechnical specialist (who defines the stiffness of the 

foundation) affect the resultant overall stiffness. 

Figure 8-1 Global Structural Model for Seismic Design 

Upon developing the global dynamic response model of the structural system, the fundamental period of 

the structure, T, can be estimated. The earthquake load demand can then be determined from the response 

spectrum for the fundamental period of the structure. The fundamental period of the structure T is related 

to the ratio of the overall (lumped) mass and stiffness of the structural system as shown in Equation 8-1: 
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K

M 2T 

8-1

where M is the inertial mass of the structure and K is the overall stiffness (the structure and the 

foundation) of the system. 

Equation 8-1 described the fundamental period, or first mode of vibration, of the structure. In many 

cases, higher modes of response are also considered in design. 

8.4 MEASURES FOR SEISMIC DEMAND IN DESIGN 

Figure 8-2 presents a typical generic elastic acceleration response spectrum for use in seismic design. For 

an analysis where only the first mode of vibration is considered, the fundamental period of the structural 

system, T, is used along with the design response spectrum to estimate the peak force-based seismic 

design load, F, in accordance with Newton’s second law of motion, F = MA, where A is the spectral 

acceleration from the design response spectrum corresponding to the fundamental period T. In addition to 

the force-based design defined by the peak inertial load F (subject to force modification via the use of 

response modification factor), the system also has a displacement demand defined by the spectral 

displacement corresponding to the fundamental period, T. The spectral displacement, D, is defined by 

Equation 8-2: 

 2

2

2

AT

D







8-2

Therefore, in addition to the conventional acceleration response spectrum established for design, there is a 

corresponding displacement response spectrum defined by Equation 8-2. 

Figure 8-2 shows both the acceleration and the displacement response spectra. The acceleration response 

spectra are denoted by the solid line and the displacement response spectra are shown by the dashed line 

in this figure. 
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Figure 8-2 Acceleration and Displacement Design Spectra 

Figure 8-2 can be used to establish the seismic demand in terms of both the force demand (proportional to 

the spectral acceleration) and the displacement demand (proportional to the spectral displacement) on the 

structure for the specified damping ratio (usually assumed to be at 5% in most common design 

applications). The relationship between spectral acceleration and spectral displacement shown in 

Figure 8-2 is valid as long as the structure behaves within the linear elastic range. However, in most 

situations, it would be uneconomical to design a structure for elastic response (implying no damage) in a 

major earthquake (except in some geographic locations where the seismicity may be low enough that 

elastic response is all that is expected and required). Modern seismic design in the U.S. is often 

predicated upon a structure responding inelastically to the design earthquake, provided that life safety is 

not threatened. When a structure performs inelastically, a force reduction factor, R, is applied to the force 

demand based upon the elastic response spectrum to determine the actual force level for design. 

Figure 8-3 illustrates some of the assumptions implicit in applying a force reduction factor to the peak 

load based upon the elastic response spectrum to account for inelastic behavior in seismic design. The 

force demand developed from the elastic design response spectrum. The corresponding elastic 

displacement demand (from the elastic displacement spectrum) is designated as u. The force level VD in 

Figure 8-3 corresponds to the force at which the member is expected to yield corresponds to an elastic 

displacement y. 
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Figure 8-3 Elastic and Inelastic Force and Displacement Demand and the Ductility Ratio 

Table 8-1 presents the force reduction factors for bridge substructures from the AASHTO LRFD Bridge 

Design Specifications. Note that the value of the force reduction factor depends upon the importance 

category of the bridge. Critical and essential bridges are designed using smaller force reduction factors 

and thus higher loads (loads closer to the force demand form an elastic response spectra analysis). 

TABLE 8-1 FORCE REDUCTION FACTORS, R, FOR BRIDGE SUBSTRUCTURES 

(Table 3.10.7.1-1, AASHTO LRFD Bridge Design Specifications, 2008 Interim Revisions) 
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A common assumption in seismic design is the “equal displacement principle” which states that, whereas 

the actual force demand on the structural system will be much lower than the elastic force demand (VD is 

much lower than VE in Figure 8-3), the displacement demand for the yielding structural system can be 

approximated by the elastic displacement demand ( u in the Figure 8-3). The ratio of u (the elastic 

displacement demand, assumed equal to the displacement demand for the yielding structure) to y (the 

displacement at yield) is defined as the ductility demand, , from the design earthquake (i.e.  = u/y) 

and is used as an indicator of the anticipated performance of the structure. The ductility ratio  is related 

to the degree of damage expected for the structure for various limit states. A ductility ratio 1 might 

represent minimal damage for the serviceability limit state while a larger ductility ratio 2 would 

represent repairable damage for the controlled damage limit state and an even larger ductility ratio 3

would represent the non-collapse but significant damage for the life safety limit state. 

Once the seismic demand has been established, the next step in the design process is the capacity analysis. 

The structure capacity may also be force based or displacement based. The capacity analysis in the 

displacement based method typically consists of a pushover analysis in which the lateral load on the 

structure is increasing until the lateral displacement from the demand analysis is reached, as illustrated in 

Figure 8-4. As the structure is displaced laterally the overall displacement demand is distributed into the 

various components within the structural system. Part of the displacement demand is accommodated by 

the deformation of the superstructure (e.g. by deformation of the column) and part of the displacement 

demand is distributed to the foundation system. Theoretically the portion of the displacement demand 

distributed to the foundation corresponds to the seismic demand on the foundation and the foundation 

should be checked for the stress corresponding to this demand (superimposed on top of the initial static 

load). However, very often the foundation is designed to a higher level of performance than the load 

induced by the superstructure in a pushover analysis (i.e. to keep the behavior of the foundation in the 

elastic range even when subject to the forces from yielding of the superstructure). This technique, 

intended protect the foundation from yielding, is referred to as capacity protecting the foundation system 

(described further in the next section). 

An appreciation of the concept of displacement demand in seismic design, as opposed to a conventional 

force based demand, is important when furnishing geotechnical recommendations to the structural 

designer. The conventional notion that a lower soil stiffness and foundation capacity is conservative is 

invalid in a displacement based design framework. Projecting a lower soil stiffness and foundation 

capacity into the global seismic response model may be counter-productive with respect to the seismic 

performance of the overall structure due to the following reasons: 
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 An overly soft soil stiffness may lead to lower stresses in the structural components of both the 

superstructure and the foundation in a displacement based capacity pushover analysis. 

 An overly soft foundation capacity will lead to distribution of a larger proportion of the 

displacement deformation to the foundation, and hence can lead to an unconservative proportion of 

the displacement demand being assigned to the superstructure (usually at the bridge column). 

Depending on the response characteristics (global stiffness) of the structure and the frequency content of 

the ground motion, a lower stiffness may also move the overall response of the structure towards 

resonance (towards the peak or the acceleration response spectrum), thereby increasing the seismic 

demand. Additional discussions on this topic will be presented in later sections of this chapter when 

recommendations on accounting for uncertainties in design and on design practice for good seismic 

performances are provided. 

Stages: 1 – First Plastic Hinges Form; 2 – Second Hinges Form; 3 – Deformation Capacity Reached. 

 Figure 8-4 Pushover Analysis for Displacement Demand Distribution 

8.5 CAPACITY PROTECTED DESIGN FOR FOUNDATIONS 

The previous section summarized the steps in developing the earthquake force and displacement demand 

of the overall structure. In a force-based analysis, the force-based demand is compared to the elastic 
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capacity (capacity at yield) of the structural element. However, displacement based design analysis has 

increasingly become the general practice for seismic design in areas of high seismicity, especially in the 

design of the bridge columns. In displacement based design, design of foundation systems can be more 

complicated than simply providing adequate displacement capacity. In addition to accommodating the 

portion of the overall displacement demand distributed to the foundation system from the pushover 

analysis, modern seismic design usually also calls for capacity protection of the foundation. Under 

capacity protected design, the foundation is provided with an elastic capacity greater than the capacity 

required to accommodate the applied displacement in order to force inelastic behavior into the bridge 

columns, where it can be detected and repaired. Figure 8-5 illustrates the concept of capacity protecting 

the foundation for earthquake loading. 

 

Figure 8-5 Concept for Capacity Protecting the Foundation 

Because it is difficult to inspect damage below ground and because there are large inherent uncertainties 

in the geotechnical elements of the design, capacity protection of the foundation calls for confining 

potential damage to above ground elements of the structure, typically at the bridge column. For instance, 

a typical seismic design strategy would be to allow a plastic hinge to form at the base of the column, as 

illustrated in Figure 8-5. The capacity of the plastic hinge limits the moment and shear that can be 

transferred to the foundation and the foundation is designed to perform elastically under these limiting 
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loads (i.e. after the plastic hinge formed). Because the plastic hinge limits the transmission of lateral load 

to the foundation, it is often referred to a load fuse. In general, the foundation is designed with forces that 

are greater than the forces required to form the plastic hinge in the column. The AASHTO seismic design 

procedures are, in general, intended to ensure that yielding is confined above the foundation. 

 

In many situations, capacity protection may not be achievable due to economic constraints and structural 

forms. Figure 8-6 presents various deep foundation structural forms. 

Pile Footing Single Column 

on Drilled Shaft Pile Bent Large Caissons

Figure 8-6 Typical Structural Forms for Bridge Foundation Systems 

Among the various foundation systems depicted in Figure 8-6, only the classical case of a pile group 

supported on a column footing readily lends itself to design of a capacity protected foundation. For all 

the other cases, including for pier walls (in transverse direction), there are practical difficulties in 

implementing a capacity protected foundation strategy. These difficulties include: 

1) It is difficult to detail a pier wall for satisfactory ductility behavior in the transverse direction. 

Hence, it is difficult to ensure for a load fuse above ground for the transverse loading direction. 

2) For single column drilled shafts, and especially for the multiple column pile extensions, it is 

difficult to enforce a plastic hinge zone above ground because the maximum moment will usually 

be below ground. In some cases, structural designers might have the option of enlarging the portion 

of the shaft or pile extension below ground (relative to the section above ground) to achieve a 

plastic hinge zone above ground. However, such an approach may complicate construction and 

lead to a more costly design. Therefore, this approach is employed only in special situations 

(usually only in seismically active states for important structures). 
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3) It is difficult to achieve capacity protection for large caissons (often used for support of major water 

crossing structures). For such foundations, most of the inertial mass occurs in the caissons 

themselves, which are normally very rigid and difficult to detail for ductile behavior. For large 

caissons, the weak link is often in the soil-caisson interface below the caisson, even though it is 

possible to design for plastic hinges in the tower leg above the caisson. 

In addition to the inherent difficulties in designing various structural forms to achieve a capacity protected 

foundation system, there are other difficulties in applying this strategy. The concept of foundation 

capacity protection is a relatively new concept, introduced after the 1971 San Fernando earthquake. 

Therefore, it is usually very costly to retrofit the older vintage designs often encountered on seismic 

retrofit projects. On these retrofit projects, the foundations are generally not capacity protected. Instead, 

there is an emphasis on evaluating the actual performance of the foundation subject to the displacement 

demand for the design earthquake. 

Capacity protection may be extended to elements of the structural system beyond the foundation. The 

process of applying capacity protection to the entire structure may be generically referred to as capacity 

design. Capacity design may be summarized by the following three principles: 

1) Select the locations where damage to the structure is preferred. 

2) Design those elements of the structure to be ductile. 

3) Suppress the failure in all other elements. 

In force-based design, capacity protection is implicit (based upon the variations in the R factors applied to 

the elastic demand forces) while in displacement-based design capacity protection is an explicit 

component of the design process in areas of high seismicity. 

8.6 FORCE VERSUS DISPLACEMENT BASED SEISMIC DESIGN 

While the trend in practice is towards use of the displacement based method, particularly in areas of high 

seismicity, force-based design is still used in some jurisdictions and, even if a displacement-based design 

methodology is used the design of foundations (and some other structural components) may need to be 

based on force-based criteria to achieve capacity protection. In general, designing the foundation using 

the capacity protection method implies a higher performance goal, and hence implies an additional cost 

for the foundation compared to a foundation designed using displacement-based capacity criteria. The 
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cost differential between force and displacement based design may be especially significant in the less 

seismically active states, where column sizes are normally dictated by conventional gravity load cases. 

It should be recognized that design analysis using a force-based capacity approach implies designing the 

structural system to resist the peak earthquake load. Such criteria is generally very conservative as it does 

not consider the transient nature of the earthquake force and the limited amount of time the peak load is 

applied to the structure compared to sustained gravity load cases (the exception being for very brittle 

designs). In reality, there can generally be substantial yielding in a ductile structure subject to extreme 

loads. Yielding will generally modify the dynamic behavior of the structural system such that a reduction 

in force demand from the assumed elastic response will occur. 

One of the consequences of yielding behavior is an increase in the fundamental period of the structure. As 

the fundamental period lengthens, the forces in the structure will usually be reduced and the displacement 

will progressively increase. Figure 8-2 can be used to illustrate this point. Assume that the initial period 

estimated for the structure is equal to T1. From the elastic response spectrum depicted in Figure 8-2, the 

force demand would correspond to spectral acceleration coefficient A1 and the displacement demand 

would be 1. However, as yielding occurs, the initial stiffness would decrease. Assuming the stiffness 

decreased progressively to a stiffness corresponding to fundamental periods T2, T3, and T4, the force 

demand would initially increase to correspond to spectral acceleration A2 but then would decrease to 

values corresponding to spectral accelerations A3 and A4. At the same time, the displacement demand on 

the structure will progressively increases to values corresponding to 2, 3, and 4. 

8.7 THE EARTHQUAKE RESISTING SYSTEM 

One of the beneficial requirements of displacement-based design is that, in areas of high seismicity, the 

earthquake resisting system of the structure must be explicitly defined, facilitating rational and economic 

seismic design. Although it is not required, the earthquake resisting system can also be explicitly defined 

in a displacement based design, and probably should be as a matter of good design practice. The 

earthquake resisting system defines the path through which the lateral inertial force from the earthquake is 

transmitted from the superstructure to the foundation. The earthquake resisting system is a “building 

block” approach for organizing the earthquake load path – it is a tool that focuses the designer on 

providing a rational load path. The basic requirements for the earthquake resisting system include: 
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 Simplicity: the load path should be clear and designable; 

 Symmetry: the design should provide balanced stiffness, mass, and strength; and 

 Integrity: there should be adequate connectivity between elements along the load path. 

With respect to design of the foundation, the general principles employed in developing the earthquake 

resisting system for a displacement-based design include: 

 Preventing damage, if possible, by allowing yielding in the structure above the foundation and 

designing the foundation to withstand forces from the yielding structure times an overstrength 

factor; and 

 If foundation damage is unavoidable, avoid brittle failure modes and limit ductility demands on the 

foundation elements. 

Bridge abutments do not necessarily need to be included in the earthquake resisting system for a bridge. 

However, abutment design must consider the forces mobilized during the earthquake, should protect 

damage intolerant parts of the abutment, and prevent brittle modes of failure and limit ductility demands 

where damage is allowed. 

Section 3.3 of the 2009 AASHTO Guide Specifications for LRFD Seismic Bridge Design defines three 

classes of earthquake resisting system elements: elements that are unconditionally permissible, elements 

that are permissible with the owner’s approval, and elements that are not recommended. With respect to 

bridge foundations, permissible earthquake resisting system elements include: 

 Capacity protected footings, pile caps, and piles that behave elastically; 

 Piles or footings with pinned head connections; 

 Plastic hinges below cap beams; 

 Spread footings that meet eccentricity criteria; and 

 Abutment walls that rely on no more than 70% of the presumptive seismic passive earth pressure. 

Earthquake resisting elements in the foundation that are permissible with the owner’s approval include: 

 Batter piles that fail geotechnically (as opposed to structurally); 

 Spread footings that slide and rock; 

 Pile groups in which more than the outer piles plunge or uplift; and 

 Abutment walls that mobilize the full seismic passive resistance. 
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8.8 SOIL-FOUNDATION-STRUCTURE INTERACTION ANALYSIS 

The presence of a constructed facility alters the motion at the base of the structure in a manner that 

usually tends to reduce it compared to the free field ground motion. The source of the modification of the 

free field ground motion by the presence of a structure is referred to as soil-structure interaction (SSI). 

Considering that the structure interacts with the foundation and the foundation interacts with the ground, 

this phenomenon is perhaps more properly referred to as Soil-Foundation-Structure interaction. There are 

two sources of soil-foundation-structure interaction: 

 Modification of the support motion due to the compliance (stiffness) of the foundation, referred to 

as inertial interaction; and 

 Modification of the free-field ground motions by the presence of the foundations, referred to as 

kinematic interaction. 

Inertial interaction effects depend upon the fundamental period of the structure and the frequency content 

of the ground motions. Kinematic interaction is generally negligible for shallow foundations and for 

flexible piles in competent soils and tends to reduce the support motion for stiff piles. 

There are various approaches for solving a SSI problem. The most comprehensive approach involves 

using the finite element or finite difference method to discretize the foundation soils and the structure, 

including the superstructure, embedded elements of the foundation system, and the surrounding soils. 

Input motions are applied to the boundary of the model and then propagated through the discretized 

model. However, such an approach generally leads to extremely large numerical models and is not 

feasible for most practical applications. If kinematic interaction can be ignored or can be accommodated 

using an approximation to adjust the free-field ground motion for kinematic interaction effects (which is 

the case for most situations encountered in practice), simplified approaches such as an equivalent 

cantilever or the spring and dashpot model shown in Figure 8-7 are often used in practice to model SSI 

effects. In the simplest case, SSI can be ignored and the free-field motions can be applied to the base of 

the structure as the design input motions. Such a model ignores the tendency for ground shaking to 

decrease with depth and hence will generally be conservative and in some cases overly conservative. 

The spring and dashpot models illustrated in Figure 8-7 can employ uncoupled or coupled springs. The 

uncoupled spring models are simple and easy to use but cannot represent the cross-coupling of moment 

and shear (e.g.. coupled rocking and sliding) in foundation behavior. Uncoupled models are generally 

adequate for shallow foundations and can also be used to model pile groups if proper care is taken to 
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account of connection details. They are, however, inappropriate for single-column drilled shaft 

foundations. Coupled springs, including p-y and t-z deep foundation models, can, in general, rigorously 

account for all types of foundation and abutment systems. However, more parameters are required to 

describe foundation response and they require more work to develop. Equivalent cantilever models are 

simple and generally accepted by all bridge design computer codes. They allow for some degree of crosscoupling and may be used to model the dynamic response of single-column drilled shafts foundations. 

However, they cannot account for the moment distribution in the deep foundation element and the 

equivalent cantilever may have a different length for each of the five relevant degrees of freedom (3 

translational and 2 rotational degrees of freedom) of the foundation 

. 

 spring-dashpot model

 

 (a) (b)

 p-y springs

 equivalent spring-dashpot

 cantilever model

Figure 8-7 Inertial Interaction Models; a) Shallow Foundation Model and b) Deep Foundation 

Model 

The kinematic interaction of a deep foundation system can be modeled using the approach illustrated in 

Figure 8-8. This model makes use of linear or nonlinear spring elements to model the soil and beam 

column elements to model the structural components. Depth-varying free field motions from a site 

response analyses are input at the free ends of the soil spring elements. This type of soil-structure 

interaction model, representing the entire pile foundation all the way to the pile tips, is referred to as a 

direct (or total) soil-structure interaction model. 
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Figure 8-8 Direct (or Total) Soil-Structure Kinematic Interaction Model 

The degree of conservatism implicit in designing for the free field ground surface motion, i.e. in ignoring 

kinematic interaction, depends on several factors, including the stiffness of the soil profile. Using the free 

field ground surface shaking motion as the design motion is particularly conservative for soft soil sites, 

where there is generally a significant decrease in ground shaking intensity at depth, even for a moderate 

depth below ground surface. For such soft soil sites, there may be a significant benefit for conducting 

more advanced kinematic soil-structure interaction analyses to minimize the conservatism associated with 

using the free field ground surface motion as the input motion. In these cases, the SSI analysis can be 

conducted employing the direct SSI model shown in Figure 8-8. However, on many projects a more 

economical substructuring analysis technique is used to reduce the size of the foundation model. A 

common way to develop a foundation substructure would be to statically condense the pile foundation 

and the depth-varying free field motions to the pile cap node. In this manner, the many degrees of 

freedom of a pile group foundation can be reduced to a six degree of freedom system (3 translational and 

3 rotational degrees of freedom) at the pile cap node, as shown in Figure 8-9. Static condensation of the 

depth-varying input motion is accomplished by taking the dot product of the input ground displacement 

and the soil spring stiffnesses. The resulting kinematic motion time history can be used as the input 
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motion for a time history response analysis of the structural substructure or to develop a response 

spectrum for a response spectrum analysis of the bridge. This methodology has been discussed in detail 

by Lam and Law (2000). 

Figure 8-9 Foundation Substructuring Model for Kinematic Analysis 

Kinematic interaction can also be addressed in an approximate manner by empirically adjusting the freefield ground motion to account for kinematic interaction effects. Figure 8-10 presents ground shaking 

versus depth (in terms of acceleration and displacement response spectra) from a site response analysis 

conducted for the San Francisco-Oakland Bay Bridge East Span Replacement Project. A response 

spectrum developed from the kinematic pile cap motion (shown as the thick dark green spectrum) from 

substructure static condensation has also been presented in this figure for comparison. Comparison of the 

kinematic pile cap response spectrum to the free field ground surface response spectrum (shown in red) 

shows that the intensity of the kinematic motion is about 50% of the intensity of the free field ground 

surface motion. However, as shown in the figure, the kinematic pile cap spectrum corresponds roughly to 

the free field motion at about 46 ft depth (between 5.5 and 6 times pile diameter). 
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Figure 8-10 Comparison of Kinematic Motion from SSI to Free field Depth Varying Motions 

From the Bay Bridge example, it can be deduced that, for soft soil sites and large diameter pile 

foundations (8 ft diameter piles were used for the Bay Bridge project), soil-structure interaction analyses 

can lead to a significant cost saving by minimizing undue conservatism associated with the use of the free 

field ground surface motion as the input motion for structural design. Developing a mathematically 

rigorous substructure model for the kinematic pile cap motion may be beyond the scope of many projects. 

However, experience with SSI analysis suggests that a pile foundation may be designed for the ground 

motion at equal to approximately 4 to 6 times pile diameter beneath the pile cap. The validity of this 
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approximate method to account for kinematic interaction has been verified by independent checks 

conducted by structural designers on numerous projects (e.g. by Ingham et al.1999). 

8.9 AASHTO SEISMIC DESIGN REQUIREMENTS 

AASHTO bridge design specifications include provisions for both force-based design and displacementbased design. The 2008 Interim Revisions to the 2007 LRFD Bridge Design Specifications (the Interim 

Revisions) address force-based design. The 2009 Guide Specification for LRFD Seismic Bridge Design 

(the Guide Specifications) addresses displacement-based design. In both the force- and displacementbased design provisions of AASHTO, bridge seismic design requirements depend upon the value of SD1, 

the site class-adjusted value of the design spectral acceleration coefficient at 1 second. AASHTO defines 

four seismic design levels, referred to as Seismic Zones in the Interim Revisions and Seismic Design 

Categories in the Guide Specifications, based upon, SD1. Table 8-2 presents the four AASHTO Seismic 

Zones (Table 3.10.6-1 in the Interim Revisions) and Seismic Design Categories (Table 3.5-1 in the Guide 

Specifications). 

TABLE 8-2 AASHTO SEISMIC DESIGN CATEGORIES 

Value of SD1=FvS1

Seismic 

Zone SDC

SD1 < 0.15 1 A

0.15 ≤ SD1 < 0.30 2 B

0.30 ≤ SD1 < 0.50 3 C

0.50 ≤ SD1 4 D

Both seismic design requirements and foundation modeling requirements in AASHTO depend upon the 

seismic design zone or category. 

8.9.1 Interim Revisions 

The AASHTO Interim Revisions employ force based design. Design requirements are based upon the 

Seismic Zone as briefly outlined in Table 8-2. Table 8-3 (Table 4.7.4.3.1-1 from the Interim Revisions) 

presents a summary of the minimum analysis requirements for seismic design of bridges in accordance 

with the Interim Revisions. Table 8-4 summarizes seismic design requirements from Section 3.10 of the 

Interim Specifications. 
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TABLE 8-3 SEISMIC ANALYSIS REQUIREMENTS FOR BRIDGES FROM THE INTERIM 

REVISIONS 

UL = uniform load elastic 

SM = single-mode elastic 

MM = multimode elastic 

TH = time history method 

TABLE 8-4 SEISMIC DESIGN REQUIREMENTS FOR BRIDGES FROM THE INTERIM 

REVISIONS 

Seismic 

Zone

Summary of Seismic Design Requirements

1 Horizontal connection forces based upon prescribed horizontal force coefficient and 

minimum support lengths

2 Design for elastic seismic forces divided by R-factors except for foundation elements other 

than pile bents and retaining wall, where R/2 (but not less than R=1) shall be used.

Prescriptive detailing and minimum support lengths are also required.

3 and 4 Design for the lesser of:

Elastic seismic forces divided by R-factors, with R = 1 for foundation elements; or

The force effects resulting from inelastic hinging with prescribed overstrength factors for 

columns and piers

Prescriptive detailing and minimum support lengths are also required.

8.9.2 Guide Specifications 

Table 8-5 presents a summary of the minimum seismic design requirements from Section 2.5 of the 2009 

AASHTO Guide Specifications for LRFD Seismic Bridge Design. For SDC A, explicit identification of 

the Earthquake Resisting System is not required, no demand analysis or capacity check is needed, and 

capacity design is not required. Furthermore, in the AASHTO Guide Specifications a liquefaction 

analysis is not required for SDC A. The only seismic design requirements for SDC A are minimum 

detailing, connection force, and support length requirements. 

For SDC B, identification of the ERS is optional, a demand analysis is required, a capacity check is 

performed using implicit formulae. The ERS should be identified to avoid weak links in the ERS, 

capacity design should be considered for column shear, and a liquefaction check should be considered. 

For SDC C, identification of the ERS, demand analysis, capacity design, and liquefaction evaluation are 
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required. For SDC D, in addition to the requirements for SDC C, a displacement capacity evaluation 

using a pushover analysis is required as is a member ductility demand limit check. In SDC D, the 

implicit displacement capacity check may be used in lieu of the pushover analysis, but the limits provided 

by that check are conservative. There are also specific detailing requirements for each SDC. 

TABLE 8-5 SEISMIC DESIGN REQUIREMENTS FROM THE 2009 AASHTO GUIDE 

SPECIFICATIONS 

SDC ERS Demand 

Analysis

Capacity 

Check

Capacity 

Design

A No No No No

B Optional Yes Implicit Optional

C Yes Yes Implicit Yes

D Yes Yes Yes Yes

Table 8-6 presents the AASHTO requirements for foundation modeling from Section 5.3.1 of the 2009 

AASHTO Guide Specifications for LRFD Seismic Bridge Design. Modeling methods are divided into 

two categories for each of three foundation types. The recommended modeling method depends upon 

both Seismic Design Category and Site Class. Modeling Method 1 includes modeling foundations as 

rigid supports and modeling foundations using an equivalent depth to fixity. Method II includes rigid 

modeling for rock-supported foundations and modeling using foundation springs and p-y curves for soilsupported foundations. For SDC A, no modeling is required. For SDC B and C, foundations for bridges 

in Site Class A through D may be modeled as rigid foundations or using the depth of fixity, i.e., using 

Method 1. For SDC B and C and Site Classes E and F, Modeling Method II is required. For SDC D, 

Modeling Method II is required for all site classes. 

TABLE 8-6 FOUNDATION MODELING REQUIREMENTS FROM THE 2009 AASHTO 

GUIDE SPECIFICATIONS 

Foundation Type

Modeling 

Method I Modeling Method II

Spread Footing Rigid Rigid for Site Classes A and B. For other soil 

types, foundations springs required if footing 

flexibility contributes more than 20% to pier 

displacement.

Pile Footing with 

Pile Cap

Rigid Foundation springs required if footing flexibility 

contributes more than 20% to pier displacement.

Pile Bent/Drilled 

Shaft

Estimated depth 

to fixity

Estimated depth to fixity or soil springs based on 

P-y curves.
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8.10 COORDINATION BETWEEN STRUCTURAL DESIGNERS AND GEOTECHNICAL 

SPECIALISTS 

There are a variety of design issues on which coordination is required between geotechnical specialists 

and structural designers. These issues include: 

1) How do the structural designers intend to use the foundation stiffness parameters (e.g. soil springs) 

provided by the geotechnical specialists. Are the foundation stiffness parameters to be used solely 

for determining the fundamental period of the overall structure, or will they also be used for 

determining the seismic demand of the overall structural system? Is the primary measure of seismic 

demand for the overall structure to be measured in terms of the displacement or force demand? 

2) Are the foundation springs to be used in capacity pushover analyses for assessing the integrity of 

the superstructure (e.g. at the column)? Will the drift of the column be reduced by the foundation 

displacement, in which case an overly soft foundation stiffness could result in under-estimating the 

column demand and hence be unconservative for designing the superstructure (e.g. the bridge 

columns)? 

3) Following the integrity evaluation of the superstructure (e.g. bridge columns), how will the 

foundation integrity evaluation be conducted? Is the measure of foundation demand in terms of 

displacement (e.g. the displacement demand distributed to the foundation in a pushover analysis), 

or is it a force based demand from a plastic hinge in the column? Clarifying this issue is important 

in recommending soil spring stiffness parameters so as not to mislead the structural designers in a 

manner counter-productive to good design. If the foundation demand is displacement based (e.g. in 

terms of pile cap displacement demand), an overly soft soil spring can lead to an unconservative 

pile stress in addition to an unconservative column drift. 

4) Is the project a new design as opposed to a retrofit design? It is generally economically feasible to 

design a new foundation system based on the capacity protected foundation approach because one 

can design the column based on more modern ductility design procedures. However, in a retrofit 

project, it may not be economically feasible to achieve a capacity protected foundation system. In 

such cases, it is usually necessary to evaluate the actual performance of the structure, including the 

foundation system, based on a displacement based procedure. 
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5) Realizing that there are significant uncertainties in the soil properties used in seismic design, it is 

generally desirable to evaluate the design considering some degree of variation in the soil 

parameters. Additional comments on incorporation of uncertainties in soil properties into the 

design are presented in the next section. 

8.11 TREATMENT OF UNCERTAINTY IN SEISMIC DESIGN

As discussed in the preceding section, good seismic design practice often requires consideration of a 

range of soil parameters to account for uncertainty in their values. Consideration of soil property 

uncertainty is particularly important due to the difficulty in determining the impact of soil spring stiffness 

on design. The impact of soil spring stiffness on design depends upon (1) the specific structural 

component being designed (e.g. the column in the superstructure or the foundation element), (2) whether 

the demand is measured in terms of force or displacement, and (3) where the fundamental period of the 

structure lies with respect to the predominant period of the design ground motion 

Experience shows that a large degree of uncertainty can be accommodated in soil stiffness with only a 

very modest cost impact on the designed structure. One of the most important aspects in considering the 

impact of soil spring stiffness on seismic design is the need to be consistent in the assumed soil stiffness 

throughout the design analysis process. Seismic design is usually conducted in a two step procedure, 

starting with a response analysis using a linear elastic model for establishing the seismic demand and then 

employing a capacity analysis involving a nonlinear structural model (when displacement based method 

is adopted). Due to a different analytical frameworks in the two step procedure, an incompatible soil 

spring representation is often introduced into the two models. This practice usually leads to undue 

conservatism in the design process. 

Figure 8-11 illustrates the need for consistency in analysis and the potential for undue conservatism if 

inconsistent soil spring stiffness is adopted between the demand analysis and the capacity assessment. 

This figure presents the results of a sensitivity study that employed three soil spring stiffness scenarios: 

(1) the best estimate case, (2) a stiffer case in which the soil stiffness is multiplied by 2.0, and (3) a softer 

case in which the soil stiffness is reduced by a factor of 0.3. The figure presents the pile load versus 

deflection and corresponding pile load versus pile moment curves for the three different soil stiffness 

cases for a 24-inch reinforced concrete pile. The load-deflection plots for the 660% in soil stiffness show 

about a 300% difference in the overall pile stiffness. 
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Figure 8-11 Effect of Soil Stiffness on Performance of 24-inch Reinforced Concrete Pile 

The variation in pile stiffness leads to a change in the fundamental period for the bridge from 0.7 second 

for the best-estimate stiffness to 0.53 second for the stiffer case and 0.93 second for the softer case. 

The bridge that employed the piles modeled in Figure 8-11 was designed using the response spectra 

shown at the top of Figure 8-11. The variation in the fundamental period for the three cases of soil 

stiffness led to a displacement demand varying from 3.1 to 6.6 inches. Thus the 660% variation in soil 

stiffness led to a 300% variation in overall pile stiffness and a 210% variation in the corresponding 

displacement demand. However, the associated pile maximum moment changes from 21,240 in-kip to 

24,520 in-kip over this displacement demand range, a variation of only about 15%! The 15% variation in 

pile moment will have a relatively modest impact on the reinforcing requirement for the pile foundation 

and therefore will impact the cost of the constructed structure by a very modest amount. The 210% 

variation in the displacement demand may only affect the design of the expansion joints and therefore 

would also have a modest cost impact on the constructed bridge. It is also interesting to note that the 

governing pile moment arises from the best-estimate soil stiffness, illustrating the difficulty in 

predetermining which design scenario would be most conservative in seismic design. This sensitivity 
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study suggests that even if one employs a 660% variation in soil stiffness to account for uncertainty, it 

may not have a significant cost impact to the design. This is consistent with feedback from experienced 

structural designers on past projects. 

Figure 8-11 can also be used to illustrate the impact of designing the bridge using inconsistent soil 

stiffness between the demand and the capacity models. For example, if the seismic demand is developed 

based on the stiffer soil stiffness, it would imply a shear load of 320 kips per pile. If this shear load is 

then used in a separate laterally loaded pile analysis based on the softer stiffness, the pile moment would 

become 39,500 in-kip, which is much higher than the 24,520 in-kip maximum obtained when consistent 

in soil stiffness is used in the demand and capacity model, even when this stiffness is allowed to vary by 

660%. 

 

8.12 FOUNDATION DESIGN STRATEGY FOR GOOD SEISMIC PERFORMANCE 

Keys to good seismic performance include simplicity, integrity and symmetry in the structural system. 

AASHTO strongly encourages balanced stiffness among various frames in a bridge system. Design 

guidelines suggest the difference in stiffness between any two bents within a frame or between any two 

columns in a bent should be no more than 50 percent. Furthermore, the variation in stiffness between 

adjacent bents within a frame or between adjacent columns within a bent should not differ by more than 

25 percent. Balanced frame geometry provisions strongly encourage that adjacent frames (i.e. structural 

units on either side of an articulation joint, such as an in-span hinge) have fundamental vibration periods 

that are within 30 percent of one another. 

The concept of minimizing the variation in the overall structural stiffness may also be extended to the 

foundation system. The foundation designer should strive to minimize the variation in foundation 

stiffness from bent to bent and from footing to footing where feasible. One of the primary contributors to 

the variation in foundation stiffness, especially between adjacent bents, is the variation in soil conditions. 

Variable soil stiffness is particularly important in the surficial soil layers. Surficial soil layers tend to 

have the greatest impact on the lateral stiffness of the foundation as well as a tendency for a larger degree 

of variation than soil layers at depth. The structural stiffness of a deep foundation element (i.e. the 

bending stiffness EI) also influences the overall stiffness of the foundation. Employing a pile with a 

larger EI can therefore reduce the degree of variation in foundation stiffness due to variations in surficial 

soil stiffness at the site. Also, because the variation in surficial soil stiffness has a more profound 

influence on the lateral foundation stiffness than the axial pile stiffness, the use of battered piles to carry 
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the lateral load can sometimes be an effective strategy for reducing the degree in variation in the lateral 

stiffness among bents. However battered pile systems can introduce additional complexity in design 

(especially when there is significant potential for kinematic earth pressure loading on the pile due to 

permanent ground movements), as discussed in the next paragraph. 

The preceding paragraphs have concentrated on designing for seismic inertial loads. However, there is 

another seismic load case, the kinematic ground displacement load case. The kinematic ground 

displacement load case refers to the loads due to seismically induced permanent ground displacement on 

the foundation, and was discussed in detail in Chapter 7. The kinematic ground displacement load case is 

important at sites prone to liquefaction induced lateral spreading ground displacement as well as sites 

where there is downslope movement due to embankment instability (e.g. at banks of river crossings). 

These permanent ground displacements can induce passive earth pressures on the foundation system, 

resulting in distress to the structural elements of the foundation, or cause excessive movement of the 

bridge resulting in the bridge deck falling off the bridge seats (and other forms of structural distress). 

These forms of bridge damage have been the cause for a significant proportion of the recorded bridge 

damage during earthquakes, e.g. in the 1964 Alaskan earthquake and the 1964 Niigata earthquake in 

Japan. These forms of damage also have been the prevalent form of earthquake induced damage to pile 

supported wharf structures at port facilities. 

Kinematic ground displacement loading tends to involve massive movement of the ground and hence it is 

generally not feasible to resist this movement with foundation elements on a brute force basis. A better 

option in case of kinematic loading is to employ a compliant foundation system that can move and deform 

with the ground. Because they are relatively non-compliant, battered pile groups have performed poorly 

when subject to kinematic loading (e.g. battered concrete pile damage beneath Port of Oakland wharf 

structures during the 1989 Loma Prieta earthquake). Either steel piles, due to their ductility, or specially 

fabricated concrete piles or drilled shafts that are designed to accommodate ground deformation would be 

the preferred foundation system for cases of kinematic loading. 

Kinematic loading due to permanent ground displacement may also be important for embedded structures 

(including retaining walls, culverts and tunnels). For an embedded structure, the kinematic ground 

deformation induced earth pressure may far exceed the magnitude of loading due to inertial effects. 

Hence, a good strategy in seismic design of an embedded structure is to provide the structure with an 

ability to deform with the ground movement, as oppose to hardening the structure to resist it. 
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8.13 SUMMARY 

In summary, this chapter presents a discussion of several seismic design issues, including the need for 

collaboration between structural designers and geotechnical specialists, force- and displacement-based 

methods for seismic demand and capacity evaluation, the principles of capacity protection and earthquake 

resisting system design, and soil-structure interaction. Interaction between structural designers and 

geotechnical specialists is needed to deal with conflicting requirements for earthquake design. Seismic 

design of foundation systems may employ both displacement-based and force-based design procedures. 

The displacement-based design procedure is particularly useful in areas of high seismicity as it has the 

capacity to account for the inelastic response of modern structures in the design earthquake. The force 

based approach, especially the use of capacity protected foundation systems, is designed to provide 

adequate seismic performance of the structural system but is not necessarily expected to predict its actual 

performance. The force based approach is generally a more conservative approach suitable for designing 

new structures where one can implement an appropriate ductility mechanism in the intended locations. 

The displacement based approach, however, would generally be more appropriate in the context of 

retrofitting existing structural systems. It is generally too costly to retrofit existing structures to achieve 

the goal of a capacity protected foundation system. The geotechnical specialist should discuss with the 

structural designer the appropriate foundation evaluation approach in order to develop a workable overall 

design approach. 

A description of advanced soil-structure interaction topics was also presented in this chapter. The need 

for revision of the free-field ground surface motion to account for kinematic interaction effects was 

discussed. Previous project experience showed that significant reduction in free field ground surface 

motion may be realized in soft soil sites when proper SSI effects are taken into consideration. 

This chapter also provides a discussion on practical ways to treat uncertainty in the seismic design 

process. It was demonstrated that, when properly handled, the foundation design can account for a very 

large degree of uncertainty in soil properties with only very modest impact on the cost of the structural 

system. It was also demonstrated that it is dangerous to design based on the conventional assumption that 

a softer soil stiffness and lower soil strength is conservative. 

Strategies for selecting the appropriate foundation system for good seismic performance of the overall 

structure were also presented in this chapter. In addition to the basic inertial load case, the issue of 

seismic loads due to kinematic ground displacement (deformation) was discussed. 
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Seismic Design – Geotechnical Features 9-1 August 2011

CHAPTER 9

SHALLOW FOUNDATIONS 

9.1 GENERAL TYPES OF SHALLOW FOUNDATIONS

This section outlines seismic analysis and design procedures for shallow foundations. As the name 

implies, in a shallow foundation the base of the foundation where the loads from the structure are 

transferred to the underlying soil is at relatively shallow depth, close to the ground surface. This 

geometric configuration lends itself to modeling as a rigid footing resting on the surface of an infinite soil 

mass. Classical solutions for rigid surface footings, including solutions for capacity and stiffness, can be 

evaluated independent of the coupling between moment and shear loads. This is fundamentally different 

from deep foundations, where it is important to account for the coupling effects between the moment and 

shear load. 

The assumption of a rigid footing at a shallow depth is implicit for most design equations and charts in 

the literature for shallow foundations (spread footings). When analyzing the performance of a shallow 

foundation, the engineer should examine the validity of the two parts of this implicit assumption (rigidity 

and shallow depth), as foundations that do not conform to these two conditions may require special 

treatment. Further comments regarding the validity of these conditions will be provided subsequent 

sections of this Chapter. 

Figure 9-1 presents typical configurations employed for shallow foundations. The most common types of 

shallow foundations for transportation facilities are rectangular footings (for circular or rectangular 

columns) and strip footings for pier walls. Mat foundations are relatively rare for transportation facilities. 

Shallow foundations are suitable at rock sites or when firm soils are found at shallow depth provided the 

potential for landslide induced displacements is fairly low and the risk of liquefaction is very low or nonexistent. In areas where deposits of compressible, expansive, or collapsible soils are found at depth below 

the ground surface, shallow foundations may not be suitable. Where soil conditions are not suitable for 

the use of shallow foundations, deep foundations are used. 
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Figure 9-1 Types of Shallow Foundations

9.2 SEISMIC PERFORMANCE AND VULNERABILITY OF SHALLOW FOUNDATIONS 

Iwasaki et al. (1972) provided a comprehensive review of the seismic performance of highway bridges. 

Although their review was triggered by the 1971 San Fernando Earthquake, these investigators compiled 

observations of damage to highway bridges from 14 major earthquakes around the world, including 

earthquakes in U.S., Japan and in South America. The report documented a wide range of bridge damage, 

including the role played by foundation in the observed damage. These investigators observed apparent 

distinct differences in case histories for highway bridge damage as far as foundation behavior was 

concerned. For example, bridge damage from the 1964 Alaskan earthquake and many of the Japanese 

earthquakes, including the 1964 Niigata Earthquake, were typically due to foundation failure triggered by 

ground failure (often from liquefaction). There is little evidence in those case histories that excessive 

inertial force from dynamic bridge response led to the observed damage of the bridge. The bridge deck 

commonly remained intact for such case histories, but the excessive foundation movement often led to the 

bridge deck falling off its seat support. 
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Bridge damage observed in the 1971 San Fernando Earthquake was very different from the damage 

observed in Japan and Alaska in 1964. The most common type of bridge damage observed in the 1971 

San Fernando Earthquake, as well as in other more recent California earthquakes (including the 1989 

Loma Prieta Earthquake and the 1994 Northridge Earthquake), was associated with excessive inertial 

loading induced by the earthquake. However, most of the damage in these case histories was confined to 

the structural components of the bridge. There is relatively little evidence of seismically-induced damage 

to bridges on shallow foundations due to inadequate geotechnical foundation capacity that does not 

involve liquefaction ground failure. Shallow foundations generally perform satisfactorily when subject 

to earthquake-induced inertial loads in the absence of liquefaction largely because a relatively large 

margin of safety is provided for the bearing capacity under static loads. Therefore, vertical bearing failure 

under seismic loads is unlikely. The primary impacts of seismic loads on a shallow foundation are likely 

to be limited lateral and vertical displacements and perhaps yielding of structural components of the 

footing, impacts that are not likely to threaten life safety or lead to collapse. 

The inertial loading on the bridge structure (including the loading on the foundation elements) is 

dependent upon is the response characteristics (stiffness) of the foundation due to soil-foundationstructure interaction effects, as discussed in Chapter 8. Thus, characterizing the stiffness of a shallow 

foundation subject to earthquake loading is an important seismic design consideration. Despite the 

paucity of case histories of earthquake-induced damage due to exceeding the geotechnical capacity of a 

shallow foundation, geotechnical capacity evaluation of a shallow foundation is also an important design 

task, along with evaluation of the structural capacity of the foundation elements. 

9.3 STATIC VERSUS SEISMIC LOADS ON SHALLOW FOUNDATIONS 

The most common seismic analysis procedure in bridge design is the response spectrum method, in which 

evaluation of the seismic loads are based upon the assumption that the bridge structure behaves in a linear 

elastic manner. Non-linear behavior, including yielding of structural components, yielding of the soil, 

and geometric nonlinearity such as rocking or uplifting of the footing, tends to reduce the calculated 

earthquake load for most bridge structures. Hence, relatively large load reduction factors (2 to 4) are 

commonly applied to the force calculated from a response spectrum analysis. Actually, as discussed in 

Chapter 8, earthquake design analyses are progressively trending toward the displacement based 

approach, leading to the need to design bridge components to accommodate the displacement demands 

from the earthquake (described by the displacement response spectrum) as opposed to the force demand 
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(from the acceleration response spectrum). In a displacement-based capacity analysis, a pushover 

analysis is conducted to model various forms of nonlinearity in the bridge system and to evaluate the 

force levels for design. Forces determined from these nonlinear structural pushover analyses are, in 

general, more realistic than the elastic forces from an elastic response spectrum analysis reduced by gross 

force reduction factors in a bridge designed to yield but not collapse. Furthermore, as discussed in 

Chapter 8, in areas of high seismicity foundations are often capacity protected, with force demands 

controlled by fuses in the system such as a plastic hinge at the base of the column. The designer of the 

foundation should be clear about the design approach being used by the structural designer to determine 

the foundation demand in order to provide appropriate recommendations for design. 

9.4 SOIL-FOUNDATION-STRUCTURE INTERACTION 

9.4.1 Foundation Substructuring 

Foundation design often employs the concept of substructuring the overall bridge structure-foundationand soil mass system so that the foundation can be considered independently of the superstructure. A 

global bridge model generally involves a very large number of elements in order to model the entire 

superstructure, all of the piers or columns, and the foundation supports at each pier or bent along the 

alignment. Because of the size of the overall model, generally it is not feasible to analyze the overall 

bridge structure-foundation-soil mass system as a total complete model in a single step solution. Hence, 

substructuring is generally employed to condense each of the foundation supports and its supporting soil 

mass into a foundation substructure to reduce the resultant global bridge model to a manageable size. 

Available methods for substructuring foundation systems are discussed by Lam and Law (2000). One of 

the most common ways involves substructuring the foundation to a single node at the base of each pier. 

One of the limitations of the substructuring approach is that in a response spectrum analysis it invokes the 

principal of superposition and therefore cannot explicitly model nonlinearity in the foundation 

substructure system. However, if the dynamic (inertial) response analysis of the bridge superstructure 

model is conducted in the time domain, nonlinearity in the superstructure can be treated in the inertial 

interaction problem. State-of-the-art dynamic response analyses for seismic design have been moving 

toward time- domain solution approaches (particularly for major long-span bridge projects). The need for 

substructuring to reduce the size of the global bridge model has also been progressively relaxed in favor 

of the superior complete total model (i.e. incorporating the foundation into the global structural model 
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Seismic Design – Geotechnical Features 9-5 August 2011

without the need of substructuring) as computational capabilities increase. However, for a shallow 

foundation the substructuring approach can generally adequately capture the dynamic response 

characteristics of the foundation and their impact on the seismic performance of the bridge system. 

9.4.2 Kinematic and Inertial Interaction 

As discussed in Chapter 8, soil-foundation-structure interaction effects include kinematic interaction 

(modification of the foundation support motion by the presence of the foundation) and inertial interaction 

(modification of the structure motion due to the compliance of the foundation). Lam and Law (2000) 

concluded that, even for very large foundations (caisson foundations for long-span bridge), as long as the 

site soil is competent the free field outcrop motion will be modified by kinematic interaction only in the 

high frequency range (spectral periods less than 0.5 second period). Furthermore, it has been shown that 

ignoring the effect of kinematic interaction and designing for the free field outcrop motion tends to be 

conservative, especially for high frequency motions. Kinematic interaction effects can be significant at 

very soft soil sites, but these sites typically require the use of deep foundations. Therefore, for spread 

footings (i.e. for foundations in competent soil conditions) kinematic interaction is not important for 

practical problems and only inertial interaction needs to be considered for seismic design of the 

foundation and superstructure. 

Figure 9-2 outlines the two steps involved in a rigorous inertial interaction analysis. The first step 

involves conducting a forced vibration analysis of the foundation-soil mass system (Figure 9-2a) to solve 

for the frequency dependent foundation impedance (stiffness and damping) function. The second step 

involves inputting the frequency dependent foundation impedance function developed in Step-1 to the 

global structural model and conducting the inertial response analysis of the structure (Figure 9-2b). As 

shown in Figure 9-2, the impedance function can be visualized as a dynamic spring of stiffness K in 

parallel with a viscous dashpot with a damping coefficient C. When this impedance function is used in

the inertial response analysis, it accounts for both the soil mass stiffness and the energy dissipation 

mechanism referred to as radiation damping (the dissipation of energy due to seismic waves radiating 

away from the foundation). 
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Seismic Design – Geotechnical Features 9-6 August 2011

Figure 9-2 Two Step Rigorous Inertial Response Solution Incorporating Frequency Dependent 

Foundation Impedance 

Figure 9-3, from Mylonakis and Gazetas (2002), shows the dynamic stiffness factor (the ratio of the 

dynamic stiffness to the static stiffness) for the impedance function for the rocking mode of a rigid 

rectangular footing on the ground surface (assuming an elastic semi-infinite half space). Figure 9-3

shows that the dynamic stiffness approaches the static foundation stiffness (i.e. the dynamic stiffness 

factor becomes unity) when the normalized frequency of loading (B/VS) approaches zero (i.e. at long 

periods) and when the length, L, of the footing divided by its width, B, is equal to or less than 4. In fact, 

for the range of spectral periods and L/B ratios generally applicable to the seismic design of bridges, the 

dynamic stiffness factor is close to 1. Therefore, for response spectrum analysis (the analysis most often 

used for ordinary highway bridges), the static foundation stiffness is generally employed in design, The 

frequency dependent stiffness only becomes important for problems involving high frequency response 

such as foundation vibration problems and nuclear power plant containment structures. 

Even in a major bridge project employing time history response analyses, it is not possible to implement 

the frequency dependent foundation impedance function. Instead, the engineer can select one 

characteristic frequency relevant to the overall response of the global structural system. However, in 

virtually all cases where this has been done, the period of interest was sufficiently long that the foundation 

stiffness was based on the static stiffness 
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Seismic Design – Geotechnical Features 9-7 August 2011

Figure 9-3 Frequency Dependent Dynamic Stiffness Factor for a Surface Footing (Gazetas, 2002) 

It also should be noted that there is a lack of experimental data to support the validity of the frequency 

dependent solution. In fact, data presented by Gadre and Dobry (1998) showed that footing stiffness and 

damping exhibit very strong displacement amplitude dependent tendencies, as opposed to being 

frequency dependent. The trend of softening in stiffness and an increase in energy dissipation with 

increasing amplitude of footing displacement observed by Gadre and Dobry suggests nonlinear material 

governs footing response behavior rather than frequency dependent behavior of a rigid footing on an 

elastic medium. 

Gadre and Dobry also conducted forced vibration experiments at frequencies ranging from 0.5 to 0.0167 

hertz and concluded that radiation damping was negligible and that the observed damping can be largely 

attributable to internal (material) damping. Gadre and Dobry also compared the shear modulus back 

calculated from the response measured in their experiments with the small strain shear modulus, Gmax, for 

their foundation material (75% relative density dry Nevada sand). The shear modulus deduced from their 

testing was approximately 1.73 MPa (36,200 psf) at the smallest displacement level that could be 

measured in their experiments. This shear modulus is much lower than small strain modulus for the 

Nevada sand. In fact, the modulus reduction factor, G/Gmax, implied by the experiment for the foundation 

soil is smaller than 0.05. This observation emphasizes the need to be focused on the near field large strain 
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behavior as opposed to the far field smaller strain behavior relevant to a free field wave propagation 

problem. 

9.5 FOUNDATION STIFFNESS FORMULATION 

9.5.1 Spring Constants 

Procedures for evaluating soil-footing-structure interaction problems have evolved over time from the 

theory of continuum mechanics. As noted above, frequency dependent stiffness and damping (or 

foundation impedance functions) applicable to low amplitude, high frequency machine vibration 

problems and very rigid site nuclear power plant containment buildings founded on very competent soil 

are not applicable to earthquake soil-foundation-structure interaction problems for bridges. The 

frequency dependence of the dynamic stiffness of the foundation can be ignored and it is adequate to 

employ the static foundation stiffness for seismic design of bridges. 

9.5.2 Equivalent Stiffness Matrix for Shallow Footing 

The general form of the 6 x 6 shallow footing stiffness matrix is shown in Figure 9-4. As shown in the 

figure, off diagonal terms in the stiffness matrix for shallow footings are generally assumed to be zero 

(i.e. the cross-coupling terms are ignored). However, this assumption may become invalid when the 

depth of embedment becomes large. Additional discussion is provided in Section 9.5.3 on this point. 

The uncoupled stiffness coefficients (i.e. the diagonal terms) in the 6 x 6 stiffness matrix may be based 

upon theoretical solutions from elasticity theory. Solutions for the stiffness of a rectangular rigid plate of 

dimensions L and B resting on the surface of an elastic half space from Gazetas (1991) are presented in 

Figure 9-5. The stiffness matrix coefficients shown in Figure 9-5 can be adjusted to account for 

embedment, as discussed in the next section. 

In some cases, when the size of the footing becomes large the rigid footing assumption may no longer be 

valid and the footing stiffness developed from Figure 9-5 and Figure 9-6 may over estimate the stiffness 

of the foundation. Hytenyi (1946) used beam on elastic subgrade theory to check whether a large footing 

can be assumed to be rigid. Hytenyi classified beam and subgrade combinations into (1) short beam, (2) 

intermediate beam and (3) infinitely long beam problems. A rigid footing assumption must satisfy the 

short beam classification. 
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Hytenyi defined a short beam in terms of the following condition: 

L < 6 for  = 4

s

4EI

E

9-1

where Es is the subgrade modulus (dimension of FL-2); and EI is the bending stiffness of the footing 

(dimension of FL2).

Figure 9-4 Form of the Shallow Foundation Stiffness Matrix 
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Seismic Design – Geotechnical Features 9-10 August 2011

9.5.3 Footing Embedment Effects 

The surface footing stiffness terms discussed above can be modified for embedment effects by 

multiplying the stiffness coefficients for the surface footing shown in Figure 9-5 by the embedment 

factors ei presented in Figure 9-6. However, the assumption that the off-diagonal stiffness terms are small 

and can be ignored becomes questionable when the thickness of the footing, d, becomes large with respect 

to the footing width. The embedment factors in Figure 9-5 should not be used when d > B (i.e. when the 

footing thickness is greater than the smaller plan dimension of the footing). 

Figure 9-5 Stiffnesses for a Rigid Surface Footing on a Semi-Infinite Half Space 
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Seismic Design – Geotechnical Features 9-11 August 2011

Figure 9-6 Embedment Factors for a Rigid Footing on a Semi-Infinite Half Space 

Design charts for adjusting for the embedment effect for rectangular footings, developed by Lam et al. 

(1986), are presented in Figure 9-7. The advantage of these charts is that they employ a single parameter, 

D, to characterize the embedment effect instead of the two parameters, D and d, employed in Figure 9-6. 

It should be noted that the embedment adjustment factor appears to become unrealistically large at large 

embedment, possibly due to the idealistic no slippage at the interface and the no soil failure assumption 

inherent to the elastic half space solution. 
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Seismic Design – Geotechnical Features 9-12 August 2011

Figure 9-7 Embedment Factor in Graphical Format from Lam and Martin (1986) 

9.5.4 Soil Modulus for Foundation Stiffness 

As noted previously, soil modulus values based upon the shear wave velocity of the soil (i.e. the small 

strain modulus of the soil) must be reduced to account for softening at the strain levels relevant to 

foundation response. For practical purposes, modulus softening can be related to the intensity of the 

earthquake ground motions. In NCHRP 12-49 (NCHRP 2002), modulus softening was related to the site 

class-adjusted spectral acceleration at a period of 1 second for the free field motion. For relatively strong 

motions, e.g. FvS1 > 0.5g, it was recommended that the small strain modulus be reduced by a factor of 

0.25. For weak motions, e.g. FvS1 < 0.3g, it was recommended that the shear modulus be reduced to 50 

percent of the small strain value. For in between values of ground motions, interpolation was 

recommended. However, is also recommended that the sensitivity of the results of the seismic analysis to 
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Seismic Design – Geotechnical Features 9-13 August 2011

the foundation stiffness be evaluated using stiffness values varied from half of the best estimate value to 

twice the best estimate value. 

9.5.5 Effects of Limited Depth to Hard Layer 

Natural soil deposits are frequently underlain by stiffer soil layers or bedrock. If the stiffer or bedrock 

layer is at a sufficiently shallow depth, it may be appropriate to adjust the foundation stiffness for the 

effect of the underlying stiffer layer. Figure 9-8, from Mylonakis and Gazetas (2002), presents the 

solution for the stiffness coefficients for a finite soil layer overlying a rigid base for use in design. 

Figure 9-8 Footing Stiffness for a Finite Soil Layer above Rigid Base 

9.5.6 Advanced Numerical Analysis 

As noted above, the stiffness coefficients for the 6 x 6 stiffness matrix, i.e. stiffness coefficients 

developed using Figure 9-6 though Figure 9-8, represent the static elastic stiffness of the footing. 

Therefore, another way to develop these stiffness coefficients is to conduct a linear elastic analysis using 

a finite element method or other advanced numerical model. This type of analysis could be used to model 

irregular foundation geometry and complex soil profiles that cannot be accounted for using the closed 

form solutions discussed above. 
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9.5.7 Incorporation of Foundation Model into Bridge Response Model 

The stiffness matrix developed using Figure 9-6 through Figure 9-8 implicitly represents the stiffness 

matrix for a point at the centroid of the bottom of the footing. However, very often the superstructure 

model stops at the bottom of the bridge pier or the column, i.e. at the top of the footing, as illustrated in 

Figure 9-9. In addition to the difference in elevation of the interface nodes between the foundation and 

superstructure models, the column may not always be positioned at the centroid of the footing and the 

local axes of the footing (i.e. its long and short directions) may not be aligned with the column axes (i.e. 

the longitudinal and transverse axes of the bridge pier) or the longitudinal and transverse axes of the 

superstructure. All these geometric aspects must be reconciled in order to properly implement the 

foundation stiffness matrix defined in the prior section in the global bridge model. This aspect of 

foundation modeling is often neglected and can lead to significant error in the design analysis. For 

instance, if the centroid of the footing is not aligned with the point of structural loading (e.g. the bottom 

bridge column), the stiffness matrix must be transformed to a different loading position (the point of 

structural loading) and, will become more complex, including off-diagonal stiffness terms. 

Figure 9-9 Implementation of Foundation Submodel in the Global Structural Model 

There are two ways to reconcile the difference in the nodal positions between the two models (the 

foundation model for the bottom of the footing and a superstructure model that ends at the bottom of the 

column or pier). The foundation stiffness matrix can be transformed to a different position. As noted 

above, this normally will lead to a more complex form for the stiffness matrix and will generally involve 

the use of a computer program. A simpler approach to reconcile the difference is to define two nodes at
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the base of the superstructure model: one node at the point of structural loading application point (e.g. the 

base of the column) and another node at the foundation stiffness reaction point (i.e., at the centroid of the 

bottom of the footing). The foundation stiffness matrix can be input to this superstructure model in terms 

of the local axes of the footing (which can be different from both the global coordinate system and the 

local axes of the pier or the column). After defining the two nodes, a rigid link element between the two 

nodes can be assigned to the model, as illustrated in Figure 9-9. This rigid link element will essentially 

take care of the proper transformation of the foundation stiffness matrix to other loading application 

points and will also reconcile the transformation of different coordinate axes (i.e. transforming the 

stiffness matrix for the footing to the appropriate global coordinate system). 

If an advanced numerical model (e.g. a finite element model) is used to develop the stiffness matrix for 

the foundation system, the footing can be explicitly included in the model and the stiffness coefficient can 

be developed for the point of load application at the top of the footing. 

9.6 GEOTECHNICAL CAPACITY 

Geotechnical capacity analyses for shallow foundations subject to seismic loading include overturning, 

bearing capacity, and sliding resistance. These analyses are essentially the same as the analyses 

employed for static design of the foundation except that the Extreme Event 1 load combinations are 

employed in the analysis. The complete details of these analyses are covered elsewhere (e.g. NHI Course 

132037 on Shallow Foundations). This section only addresses those aspects of evaluation of the 

geotechnical capacity of shallow foundations that is unique or particularly relevant to seismic design. 

9.6.1 Pseudo-Static Seismic Loads 

As in the case of retaining wall design and slope stability, the geotechnical capacity analysis of a shallow 

foundation is a pseudo-static analysis. The effect of the earthquake is modeled by applying static loads to 

the foundation that represent the inertial loads applied to the foundation by the superstructure. However, 

unlike slope stability and retaining wall design, vertical and moment loads induced by the earthquake 

must be considered in the geotechnical capacity evaluation of the foundation. 

The loads employed in the geotechnical capacity evaluation are based upon the peak loads from the 

inertial response analysis of the superstructure. However, similar to slope stability and retaining wall 
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design, consideration should be given to reducing these loads to account for permissible displacements of 

the foundation. Furthermore, the appropriate combination of loads must be considered, as it would be 

overly conservative to superimpose the peak moment on top of the peak vertical load if they did not occur 

at the same time. With respect to load combinations, it is suggested that load cases include peak loads for 

each type of load (e.g. moment, vertical force, horizontal force) in combination with the other loads that 

occur at the same time as the peak load. However, in the case of the vertical load it may be necessary to 

include both the upwards and downwards vertical load if it not be clear a priori which load case is 

critical. 

Load reductions may be applied due to acceptable lateral (sliding) displacement based upon the logic 

employed in retaining wall and slope design. Using this logic, a reduction factor of 0.5 may be applied to 

the loads if sliding displacements on the order of 1-2 inches are acceptable. However, criteria for 

overturning and bearing capacity implicitly account for acceptable displacements and thus no reduction 

factor should be applied to these loads. 

9.6.2 Effective Footing Dimensions 

Geotechnical capacity analyses for shallow foundation do not, in general, explicitly consider moment 

loading of the footing. Instead, the bearing capacity and overturning analyses consider the performance 

of a footing with reduced dimensions subject to only the applied normal and shear forces. These reduced, 

or effective, dimensions are based upon the eccentricity induced by the moment load, as illustrated in 

Figure 9-10 and as discussed in Section 10.1.6.3 of the AASHTO LRFD Bridge Design Specifications 

(AASHTO 2007). 

Figure 9-10 Equivalent Footing Dimensions (FHWA 1998) 
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9.6.3 Overturning 

The overturning capacity of a shallow foundation subject to seismic loading is based upon the eccentricity 

of the applied load. The AASHTO Guide Specifications for LRFD Seismic Bridge Design allow for an 

eccentricity of B/4 for a shallow foundation on soil and 3B/4 for a shallow foundation on rock without the 

owner’s approval. Larger values of eccentricity are allowed with the owner’s approval and, in fact, there 

can be substantial benefit to allowing larger eccentricity, as this can limit the load transferred to the 

footing from the bridge structure. There is little evidence of bridge foundation failure due to overturning 

(rocking) under seismic loads and some owners (e.g. Caltrans) allow for complete uplift (eccentricity 

equal to B/2) under the peak seismic load. Appendix A of the AASHTO Guide Specifications for LRFD 

Seismic Bridge Design provides a detailed discussion on rocking limits for shallow foundations. 

9.6.4 Bearing Capacity 

For foundations on soil, bearing capacity is evaluated using the effective footing width (the footing width 

adjusted for eccentricity per Figure 9-10) and the equivalent uniform load (the vertical load divided by the 

effective footing width). For foundations on soil designed for loads from an elastic response analysis, 

bearing capacity is evaluated by comparing the bearing stress from the linear elastic seismic response 

analysis to the nominal bearing resistance (i.e. using load and resistance factors of 1.0). Nominal bearing 

resistance is evaluated using the effective footing dimensions and the general bearing capacity equation 

given in Section 10.6.3 of the AASHTO LRFD Bridge Design Specifications. For footings on loose sand, 

the a resistance factor of 0.67 should be applied to the strength parameter (c’ and tan’) to account for 

general shear failure, as described in AASHTO. 

In displacement-based design, capacity-protected shallow foundations are evaluated based upon the 

plastic moment capacity and associated shear demand of the column or pier wall using the following 

equation: 

Mpo + Vpo Hf <  Pu [(L-a)/2] 9-2

where: Mpo = overstrength plastic moment capacity of footing

Vpo = overstrength plastic shear demand

Pu = axial force in column (including force from overstrength plastic hinging) 

a = Pu / (qnB) where qn = nominal bearing capacity
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Hf = depth of footing 

L = length of the footing in the direction of loading 

B = width of footing 

 = resistance factor for overturning of the footing = 1.0 

The overstrength plastic moment, Mpo, in Equation 9-2 is 1.2 times the idealized plastic moment if ASTM 

A 706 reinforcement is used in the column and 1.4 times the plastic moment if ASTM A 615 grade 

reinforcing steel is used. Nominal bearing capacity is evaluated as described previously. 

For footings on rock, the maximum bearing stress on the base of the footing is compared to the 

unconfined compressive strength of the rock. The maximum bearing stress is evaluated using either a 

trapezoidal or triangular distribution, depending upon the magnitude of the applied moment, in 

accordance with Section 10.6.1.4 of the AASHTO LRFD Bridge Design Specifications. 

9.6.5 Sliding Capacity 

The capacity check for sliding of a shallow foundation subject to seismic loading, like bearing capacity, 

depends upon whether the foundation has been designed using a force-based approach or a displacementbased approach as follows. 

If the forces on the foundation are from a linear elastic analysis (force-based design):

 Ph > t Rt + ep Rep 

9-3

If the forces on the foundation are based upon the plastic moment analysis (displacement-based design):

Vpo <  Rn 

9-4

where: Ph = shear demand from linear elastic response analysis 

Rt = nominal shear resistance 

Rep = nominal passive resistance 

Vpo = overstrength plastic shear demand of column or wall

Rn = nominal shear resistance against sliding = Rt + Rep
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t, ep = resistance factors for sliding and earth pressure = 1.0 

 = load factor for seismic loading = 1 

Components of the sliding capacity of a shallow foundation in Equation 9-4 include both the frictional 

resistance to sliding and the lateral earth pressure. If evaluating the friction sliding resistance, the shear 

strength parameters for the soil-concrete interface (cB and tanB) are typically assumed to be 70% of the 

shear strength parameters for the underlying soil (c’ and tan’). In evaluating the earth pressure, the 

active thrust on the back for the footing should be subtracted from the passive resistance against the face 

of the footing. 

9.7 STRUCTURAL CAPACITY 

Shallow foundation design must also consider the structural capacity of the footing. Structural capacity 

checks include checks for flexure, shear, and, for Seismic Design Categories C and D, joint shear. The 

flexure capacity check may be conducted in accordance with Equation 9-5: 

 Mn > Mu 

9-5

where: Mu = factored ultimate moment demand in footing

  = resistance factor for concrete in bending 

Mn = nominal moment capacity of the footing at the critical section based upon effective 

width, beff , = Bc + 2Hf < B, 

Bc = diameter or width of column or wall normal to direction of loading. 

The capacity check for shear may be done in accordance with Equation 9-6: 

 Vn > Vu 9-6 

where: Vu = factored ultimate shear demand in footing at the face of the column or wall

f = resistance factor for concrete in shear 

Vn = nominal shear capacity of the footing at the face of the column or wall
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The capacity check for joint shear may be done by checking the principal stress ratio in accordance with 

Equation 9-7: 

 pc < 0.25 fc’ (Compression) 9-7 

│pt │< 0.38 (fc’)0.5 (Tension) 9-8 

where: pc = principal compression stress 

│pt│ = principal tensile stress 

fc’ = uniaxial compressive strength of concrete 

The principal compression stress, pc, and the principal tensile stress, pt, are evaluated in accordance with 

the provisions of Section 6.4.5 of the AASHTO Guide Specifications for LRFD Seismic Bridge Design. 

9.8 PERMANENT FOUNDATION DISPLACEMENT 

Assuming that the structural components of the bridge system have been designed to perform 

satisfactorily when subject to the peak earthquake load (in terms of either force or displacement basis), 

then it is relevant to consider the capacity of the foundation to accommodate permanent foundation 

displacements induced by the earthquake. Permanent foundation displacement may place a displacement 

demand on the superstructure or on the foundation itself. Damage to the foundation caused by permanent 

displacement may be difficult, or impractical, to repair. The desire to avoid foundation damage leads to 

the concept of capacity protecting the foundation system, as discussed in Chapter 8. However, as 

discussed in Chapter 8, capacity protection of the foundation may not always be possible due to economic 

considerations (especially at poor soil sites) or limitation on structural forms (e.g. limitations on 

implementing a structural load fuse), particularly on retrofit projects. Experience has shown that it can be 

both difficult and costly in a retrofit project to capacity protect the foundation system. Because of these 

difficulties, the permissible permanent foundation displacements for a bridge subject to seismic loading 

must sometimes be addressed (Lam, 1994; Fenves and Chung, 1996 and Martin and Lam, 2000).
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The impact of permanent ground displacement on foundation and bridge performance is generally 

considered on a project-specific basis. In the recent Washington State Tacoma Narrows Bridge Second 

Crossing design-build contract, WSDOT’s specifications for designing the caisson foundation called for 

the permanent displacement of the caisson at the end of the earthquake to be less than 2-ft at the top of the 

caisson. The Bay Bridge East Span replacement design scope of work also included analyses of the 

amplitude of permanent pile footing settlement after the design earthquake and its impact on bridge 

performance. 

Experience shows that the permanent displacement of the foundation can be highly sensitive to the 

earthquake time history characteristics. Near-field earthquake ground motion records with high velocity 

pulses, which can be highly directional, may be particularly problematic. Lam (1994) and Martin and 

Lam (2000) showed that unacceptable permanent foundation displacements (especially permanent 

settlement) generally occur under seismic loading when there is inadequate reserve capacity for static 

loading. Therefore, a practical way to mitigate the potential for permanent foundation displacement 

(especially for settlement) in a seismic event may be to provide an adequate static capacity. Martin and 

Lam concluded that, in the absence of liquefaction, if the static factor safety (capacity/demand ratio) for 

the foundation is higher than 2.5, permanent seismic settlement will be minimal, even in major 

earthquake. 

9.8.1 Liquefaction-Induced Lateral Spreading and Settlement 

In general, shallow foundations are not a viable foundation type for sites that are prone to liquefaction 

unless ground improvement is employed to mitigate liquefaction potential. However, occasionally an 

existing bridge may have a shallow foundation that is located on top of a liquefiable soil layer. In this 

case, the methods presented in Chapter 6 may be used to evaluate the seismic settlement and lateral 

spreading associated with the design earthquake. The ground deformations calculated in these analyses 

may then be applied to the bridge structure as a displacement demand. Seismic settlement of dry 

cohesionless soils beneath the foundation may also be addressed in this manner. 
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9.9 SUMMARY 

This section outlines seismic analysis and design procedures for shallow foundations. Shallow 

foundations are suitable at rock sites or when firm soils are found at shallow depth provided the potential 

for landslide induced displacements is fairly low and the risk of liquefaction is very low or non-existent. 

There is relatively little evidence of seismically-induced damage to bridges on shallow foundations due to 

inadequate geotechnical foundation capacity that does not involve liquefaction ground failure. The 

primary impacts of seismic loads on a shallow foundation are likely to be limited lateral and vertical 

displacements and perhaps yielding of structural components of the footing, impacts that are not likely to 

threaten life safety or lead to collapse. Classical solutions for the capacity and stiffness of rigid surface 

footings at a shallow depth are employed in shallow foundation design independent of any coupling 

between moment and shear loads. 

The most common seismic analysis procedure in bridge design is the response spectrum method, in which 

evaluation of the seismic loads are based upon the assumption that the bridge structure behaves in a linear 

elastic manner. As the inertial loading on the bridge structure (including the loading on the foundation 

elements) is dependent upon is the response characteristics (stiffness) of the foundation due to soilfoundation-structure interaction effects, characterizing the stiffness of a shallow foundation subject to 

earthquake loading is an important seismic design consideration. In areas of high seismicity, shallow 

foundations are often capacity protected, with force demands controlled by fuses in the system such as a 

plastic hinge at the base of the column. 

For shallow foundations, kinematic interaction is not important for practical problems and only inertial 

interaction needs to be considered for seismic design. It is common to represent the foundation as a 

single node at the base of each pier. Linear springs are then attached to this node to represent foundation 

compliance for each degree of freedom included in the response analysis, with the spring stiffness based 

upon the static stiffness of the foundation. These stiffness values may be based upon theoretical solutions 

from elasticity theory or may be derived using numerical methods, e.g. finite element analysis. Soil 

modulus values based upon the small strain modulus of the soil must be reduced to account for softening 

at the strain levels relevant to foundation response. For relatively strong motions, e.g. FvS1 > 0.5g, it is 

recommended that the small strain modulus be reduced by a factor of 0.25. For weak motions, e.g. FvS1 < 

0.3g, it is recommended that the shear modulus be reduced to 50 percent of the small strain value. 

However, is also recommended that the sensitivity of the results of the seismic analysis to the foundation 
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stiffness be evaluated using stiffness values varied from half of the best estimate value to twice the best 

estimate value. 

Geotechnical capacity analyses for shallow foundations subject to seismic loading include overturning, 

bearing capacity, and sliding resistance. These analyses are essentially the same as the analyses 

employed for static design of the foundation except that the Extreme Event 1 load combinations are 

employed in the analysis. The loads employed in the geotechnical capacity evaluation are based upon the 

peak loads from the inertial response analysis of the superstructure. However, a reduction factor of 0.5 

may be applied to the loads if sliding displacements on the order of 1-2 inches are acceptable. The 

bearing capacity and overturning analyses consider the performance of a footing with reduced dimensions 

based upon the eccentricity induced by the moment load. Structural capacity may be evaluated using 

either force of displacement based design methods.
FHWA-NHI-11-032 10 – Deep Foundations 

Seismic Design – Geotechnical Features 10-1 August 2011 

CHAPTER 10

 DEEP FOUNDATIONS 

10.1 TYPES OF DEEP FOUNDATIONS 

Compared to shallow foundations, deep foundations are usually more costly and therefore are generally 

used when soil conditions are not suitable for shallow foundations, e.g. at site with compressible soils in 

order to minimize potential settlement problems. Deep foundations can be categorized into pile 

foundations (including drilled shafts in the context of this document) and caisson foundations. Pile 

foundations can be subdivided into various sub categories in terms of the pile sizes (i.e. pile diameters), 

number of piles in a group (large groups, small groups), types (e.g. reinforced concrete, steel, timber), 

installation method (e.g. drilled, driven), and how they are connected to the superstructure (e.g. embedded 

pile footings, pile extensions, pile footings cantilevered above the mudline). 

One main difference between modeling caissons and pile foundation is that caissons are relatively rigid 

and they can be regarding as a rigid foundation. However, piles are relatively flexible and it is necessary 

to account for the deformability of piles. Furthermore, as opposed to shallow foundations, a deep 

embedment configuration for a pile foundation and caisson design require consideration of the coupling 

of moment and shear loads when modeling the stiffness of these foundations. 

10.2 SEISMIC VULNERABILITY OF DEEP FOUNDATIONS 

There have been numerous reports of damage to deep foundations in earthquakes. Perhaps the most 

recognized case history of pile damage from earthquakes in the United States is the extensive damage to 

battered piles at the Seventh Street Pier at the Port of Oakland from the 1989 Loma Prieta Earthquake 

(Serventi et al., 2004). Lateral spreading of a rockfill dike on top of the liquefied soil at Seventh Street 

placed large demands upon battered piles driven through the dike. Figure 10-1 shows damage to the head 

of one of the battered piles at Seventh Street. Gerwick and Fotinos (1990) reported that “Almost all the 

inshore-leading batter piles of the 6 marginal wharves on the Seventh Street Pier were broken. Piles 

crushed and sheared near their top, and in many cases pulled out from the bottom of the deck slab. The 

failure appeared to be due to a combination of high compression, shear and bending at the top of the pile, 
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Seismic Design – Geotechnical Features 10-2 August 2011 

caused not only by the lateral forces imparted to the deck slab and its overlying fill and pavement, but by 

the subsidence of the rock dike around the pile. Several marginal wharves have been constructed recently 

in Oakland, using all-vertical piles. The inner row (or rows) of piles is given additional ductility through 

incorporation of additional unstressed reinforcement along with very heavy confining spiral. These 

structures all performed well with no damage.” This case history suggests that battered piles are 

particularly vulnerable to liquefaction-induced lateral spreading but that well designed pile foundations 

can perform satisfactorily, even at liquefied sites. 

Figure 10-1 Damage to the head of battered piles at the Port of Oakland (after Serventi, 2004) 

Most of the case histories of pile damage from earthquakes in the United States have involved damage to 

the pile head, as shown in Figure 10-1. Other modes of earthquake-induced damage to pile foundations 

includes shear failure and punching shear failure of the deck or pile cap at the pile head connection point, 

as shown in Figure 10-2 through Figure 10-4 for the Struve Slough Bridge following the Loma Prieta 

Earthquake. As observed in Figure 10-1 through Figure 10-4, pile head damage in earthquakes is often 

due to deficiencies in confinement (spiral reinforcement) or inadequacies in detailing for ductile behavior 

at the pile head. Furthermore, in both the Port of Oakland and the Struve Slough Bridge case histories, 

the observed damage appeared to have been induced by liquefaction-induced permanent lateral ground 

displacement, as opposed to the inertial loading. 
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Seismic Design – Geotechnical Features 10-3 August 2011 

Figure 10-2 Shear Failure in the Cap Beam Connection of the Struve Slough Pile Bent (EERI, 1990) 

Figure 10-3 Piles Punched-Through the Deck Slab in the Collapsed Struve Slough Bridge (EERI, 

1990) 

Figure 10-4 Large Lateral Displacements Imposed on Adjacent Piles, Struve Slough Bridge (EERI, 

1990) 
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Seismic Design – Geotechnical Features 10-4 August 2011 

Pile head damage similar to that shown in Figure 10-1 through Figure 10-4 has been observed in 

earthquakes around the world, including to piles supporting bridges in several earthquakes in Japan and 

New Zealand and piles supporting harbor structures in India in the recent 2004 Sumatra earthquake 

(Current Science, 2006). These case histories clearly illustrate the need for attention to the design of the 

vulnerable pile head connection. 

Piles in liquefied ground have also been found to be damaged at depth, typically at the interfaces between 

liquefied and non-liquefied soil layers. Hamada and O’Rourke (1992) compiled case histories of 

liquefaction and lifeline performance during earthquakes from a number of Japanese earthquakes. 

Several of these case histories clearly showed that permanent displacements induced by liquefaction can 

lead to significant pile damage at depth at the boundaries of liquefied soil layers (in addition to damage at 

the pile head location). A noteworthy aspect of these case histories is that in many cases the damaged 

piles continued to adequately support the overlying structure. The damage to the piles in these cases was 

not uncovered until many years after the earthquake, when the piles were excavated during building 

reconstruction. Figures 10-5 through 10-8 illustrates the phenomenon of liquefaction-induced pile 

damage below the ground surface from the case histories of Hamada and O’Rourke (1992), as discussed 

in the following paragraphs. 

The Niigata Court House The Niigata Family Court House, a four-story reinforced concrete building, 

was located in the Hakusan area on the left bank of the Shinano River. It was founded upon concrete pile 

foundations, each with a diameter of 35 cm and a length of 6 to 9 m. After the earthquake, the building 

inclined about 1 degree due to the differential settlement of the ground. There was some conjecture 

following the earthquake that the foundation piles were damaged. However, after minor repairs were 

made to the inclined floors, the building was used without additional modifications for 25 years. When 

the building was reconstructed, two foundation piles were excavated. Figure 10-5 illustrates observed 

damage in the excavated piles. 
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Seismic Design – Geotechnical Features 10-5 August 2011 

Figure 10-5 Damage to Excavated Pile from the Niigata Court House (Hamada and O’Rourke, 1992) 

S-Building The S-building was a three-story reinforced concrete building constructed on reinforcedconcrete friction piles with a 25 cm outer diameter and a 13 cm inner diameter. Three piles were 

extracted during reconstruction of the building 24 years after the earthquake. Figure 10-6 shows the a 

photo of the extracted piles and a sketch of the crack patterns in these piles 

 (a) (b) (c) 

Figure 10-6 Pile Damage Observed from S Building (Hamanda and O’Rourke, 1992); (a) Damage to 

Foundation Pile; (b) SPT Value; (c) Photos of Damage 
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Seismic Design – Geotechnical Features 10-6 August 2011 

NHK Building. The NHK Building was a four-story reinforced concrete building founded upon 

reinforced concrete piles 35 cm in diameter and 11 to 12 m in length. When the foundations of the 

building was excavated for reconstruction in 1985, about twenty years after the earthquake, the reinforced 

concrete piles were found to be completely fractured, as shown in Figure 10-7. This building had been 

return to use after the earthquake following basic repairs to the floors without any awareness of damage to 

the pile. From the observed pile damage suggested horizontal ground displacement on the order of about 

1.0 to 1.2 m beneath the building compared to about 2 m lateral displacement away from the building. 

Hotel Niigata. Figure 10-8 shows damage to the 35 cm diameter reinforced concrete piles of the Hotel 

Niigata. The damage was discovered during reconstruction of the building 23 years after the earthquake. 

Hokuriku Building. The 10-storey Hokuriku building is in the same neighborhood as the NHK building. 

The Hokuriku building was founded on reinforced concrete piles 40 cm in diameter and 12 m long. No 

damage was reported to the superstructure after the earthquake. The number of piles supporting the 10-

story Hokuriku-Building was significantly greater than for the four-story NHK building. There was little 

evidence of lateral spreading beneath the Hokuriku building, despite evidence of 2-m ground 

displacement close to the building. It has been suggested that densification of the soil due to the large 

number of driven piles beneath contributed to limiting the lateral displacement beneath the building. 

Figure 10-7 Pile Damage Observed from NHK Building (Hamanda and O’Rourke, 1992) 
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Seismic Design – Geotechnical Features 10-7 August 2011 

Figure 10-8 Pile Damage Observed from Hotel Niigata (Hamanda and O’Rourke, 1992) 

Figure 10-9 Pile Layout of Hokuriku Building (Hamanda and O’Rourke, 1992) 
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Seismic Design – Geotechnical Features 10-8 August 2011 

In addition to the case histories presented above, there are many other cases of damage to bridges due to 

large ground displacements at liquefied soil sites. In particular, these are several notable cases of bridge 

decks falling off their bearings (seats) due to lateral spreading of the bridge piers. 

The case histories reported above all damage involve liquefaction-induced lateral spreading. Piles at sites 

that have not liquefied have generally been reported to have performed well in earthquakes. However, as 

evidenced by the case histories from O’Rourke and Hamada, the lack of reported pile damage might be 

due to the fact that the damage was hidden below the ground surface. 

10.3 SEISMIC LOADS ON DEEP FOUNDATIONS 

Many structures on piles that have performed well in earthquakes were designed either without 

consideration of earthquake loads or based on very low lateral design loads (e.g. 10% of the gravity load) 

by today’s standards. What the foundations for these structures have in common is that they generally 

had an adequate static factor of safety (capacity). Therefore, the static capacity of the foundation remains 

an important benchmark, as it affects the reserve capacity available to accommodate extreme loads, e.g. 

the design earthquake load. 

10.3.1 Soil-Foundation-Structure Interaction 

Figure 10-10, from Gazetas et al. (1992), provides an overview of the earthquake design process for a pile 

foundation from a rigorous theoretical perspective. Similar to the seismic design of shallow foundations, 

the overall design uses the substructuring technique to separate the foundation response from the response 

of the superstructure. The foundation response can then be separated into two problems: (1) the 

kinematic response problem, with the objective of developing the appropriate earthquake ground motion 

for design of the superstructure, and (2) the inertial structure response problem, for evaluating the 

performance of the structural system, including the foundation elements, subject to the design ground 

motion. 
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Seismic Design – Geotechnical Features 10-9 August 2011 

Figure 10-10 Seismic Design of Pile Foundations (Gazetas et al., 1992) 

In Chapter 9 it was established that kinematic interaction can be ignored for shallow foundations built 

upon competent soils. However, pile foundations are often used at soft soil sites with low shear wave 

velocity. At soft soil sites, kinematic interaction can create a ground motion at the base of the structure 

that differs significantly from the free field ground surface motion and that should be accounted for in 

design. 
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Seismic Design – Geotechnical Features 10-10 August 2011 

Similar to the design of shallow foundations, the inertial response problem involves developing the 

impedance function for the pile foundation and then applying this impedance function in the global 

structural model to calculate the seismic response of the superstructure. In a manner also similar to 

shallow foundation design, the frequency dependent impedance function can be simplified by adopting 

the static foundation stiffness and ignoring the radiation damping radiation damping in the foundation 

model. It is common practice to develop the pile foundation stiffness based on p-y and t-z solutions for 

pile response, which directly the near field nonlinear soil-structure interaction behavior of the piles. 

The displacement of the foundation interface node can then be used as input back into the p-y and t-z 

analyses to evaluate the stresses and displacements of the piles. 

Detailed discussions of the theory of substructuring techniques for bridge foundations are presented by 

Lam and Law (2000). The transformation of the original problem into an inertial response structural 

system involving only the superstructure and the foundation interface pile-cap node and can be developed 

based on classical static condensation techniques (e.g., Cook, et al., 1989). Reduction of the pile 

foundation pile group and its supporting soil mass into a 6 x 6 condensed stiffness matrix is well 

understood and accepted in design practice. The design ground motion is input to the superstructure 

model through a foundation node that is represented by the stiffness matrix. 

10.3.2 Kinematic Loading 

As observed from the case histories of damage to pile foundations in earthquakes, permanent ground 

displacement is an important load case. The response of a pile foundation to permanent ground 

deformation is unrelated to the mechanism of inertial loading. Therefore, it is necessary to formulate an 

additional load case for design of pile foundations subject to earthquake-induced permanent ground 

displacement. This load case is generally referred as kinematic loading. However, this kinematic load 

case should not be confused with the classical kinematic interaction problem shown in Figure 10-10. 

10.4 EFFECTIVE SUPPORT MOTIONS FOR DEEP FOUNDATIONS IN SOFT SOIL SITES 

In cases where the foundation is located in soft soil, the designer may wish to take advantage of kinematic 

interaction, as it usually reduces the amplitude of the input motion. A rigorous kinematic interaction 

analysis would require very large and complex three-dimensional numerical models (even without 
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Seismic Design – Geotechnical Features 10-11 August 2011 

modeling of the superstructure). Hence, the simplified (but not necessarily simple) modeling approach 

illustrated in Figure 10-11(b) is often used. The simplified modeling approach involves conducting wave 

propagation site response analyses to develop the depth-dependent free field motions. Then, the free field 

input motions are applied to the support nodes of the horizontal soil springs attached below the ground 

surface to the pile, as shown in Figure 10-11b. The wave propagation analysis may be conducted using 

any of the site response analysis methods described in Chapter 5, including the equivalent linear method. 

The soil springs may be developed using conventional p-y analyses. The resultant displacement time 

history at the defined foundation substructure interface node may then be used as the kinematic input 

motion for the inertial response problem. 

Figure 10-11 Modeling Approaches to Solve for the Kinematic Interaction 

For many practical problems, the simplified kinematic interaction analysis described above is still overly 

complex. An even more simplified approach is needed to account for kinematic interaction effects for 

these problems. Figure 10-12 presents a typical bent from the skyway for the San Francisco-Oakland Bay 

Bridge East Span replacement structure along with the soil condition. The simplified kinematic soilstructure interaction method described above was employed to derive the kinematic motion to be used in 

the global model response analysis. The site response analyses were conducted using conventional 1-D 
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Seismic Design – Geotechnical Features 10-12 August 2011 

equivalent linear site response analyses. Figure 10-13 presents the acceleration response spectra 

developed from the free field motions from the site response analysis at various depths. The acceleration 

response from the kinematic interaction analysis is also shown in this figure by the thick green line. 

Comparison of the kinematic motion with free field motions shown in Figure 10-13 suggests that the 

kinematic motion corresponds reasonably with the free field motion at a depth of about 14-m, or 5.6 pile 

diameters, below the mudline, especially in the long period range of the response. The comparison also 

shows that designing for the ground surface outcrop motion is rather conservative for this site. Therefore, 

this example suggests that the engineer can use the free field motion at a depth of between 5 and 6 pile 

diameters as the input motion for an inertial interaction analysis in order to account for the effect of 

kinematic interaction. This simple approach can be easily be implemented within the context of a site 

specific response analysis. 

Figure 10-12 Pile Group Layout and Kinematic Interaction Model, San Francisco East Bay Bridge 

Replacement Structure Skyway 
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Seismic Design – Geotechnical Features 10-13 August 2011 

Figure 10-13 Comparison of Ground Motions from 1-D Site Response Analysis to Kinematic Motion 

10.5 SOIL-FOUNDATION INTERACTION SPRINGS 

10.5.1 Two-Springs-in-Series Model 

Traditionally, p-y and t-z analyses are used to develop the soil springs for a soil-foundation-structure 

interaction analysis. Recently, some investigators have suggested modifications to this approach to 

account for the rate of dynamic loading and other earthquake related response issues (e.g. liquefaction 

effects). Wang et al. (1998) showed that, while analyses based upon traditional p-y and t-z curves gave 

reasonable agreement with the results of centrifuge tests of dynamic loading of pile groups, enhanced 

accuracy could be obtained by using two horizontal springs in series at each node on the pile: a near-field 

spring modeled using the conventional p-y approach and a much stiffer spring representing the far-field 

soil response. Figure 10-14 illustrates this model. In such a model, the far-field spring (based on soil 

modulus at smaller strain amplitude at far-field associated with wave propagation loading) will usually be 

over 10 times the stiffness of the near-field spring (as the near field motions involve a much higher degree 

of soil nonlinearity due to the large strains adjacent to the pile). Due to the significantly greater stiffness 
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Seismic Design – Geotechnical Features 10-14 August 2011 

of the far-field spring, the resultant overall behavior of the composite element is dominated by the near 

field spring response. Hence, for practical purposes, the far-field spring can be ignored without 

significantly altering the resultant behavior. Furthermore, as the global model for a major bridge is 

inherently complicated due to the need to model many bents and many structural components, the added 

complexity of the two-springs-in-series approach does not appear to be warranted even on major bridge 

projects. 

Figure 10-14 Two-Springs-in Series Soil-Pile Interaction Model (Wang et al., 1998) 

10.5.2 p-y and t-z Curves for Soil-Pile Interaction Analyses 

The state-of-practice for design of piles subject to lateral loading is a beam-column model employing 

nonlinear discrete Winkler spring foundations. This approach, commonly referred to as a p-y analysis, is 

widely accepted by both structural and geotechnical specialists and the nonlinear support curves 

characterizing the lateral soil reaction are usually referred to as p-y curves. For analysis of a pile subject 
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Seismic Design – Geotechnical Features 10-15 August 2011 

to vertical loading, the corresponding nonlinear curves for the soil reaction on the side of the pile are 

usually referred to as t-z curves. Recommendations for p-y, t-z and Q-z curves are generally embedded 

in the computer programs used to conduct the soil-pile interaction analyses and will not be covered 

herein. Lam and Martin (1986), Lam (1994), Lam and Cheang (1995), Lam and Law (1996), and Lam et 

al. (1998) provide a thorough discussion on p-y curves for earthquake design applications. 

10.6 FOUNDATION STIFFNESS EVALUATION

Development of the stiffness matrix for an inertial response analysis is generally accomplished by first 

evaluating the stiffness of a single pile and then, if necessary, adjusting that stiffness for pile group 

effects. Evaluation of the stiffness of an individual pile must consider the response of the pile head to 

vertical and lateral loads and to moments applied about a horizontal axis. The stiffness of an individual 

pile subject to moment loading about a vertical axis is generally assume equal to the structural torsional 

stiffness of the pile, with no contribution from the surrounding soil. As noted above, evaluation of pile 

stiffness due to lateral loads and moments applied about a horizontal axis are often accomplished suing py computer programs. Evaluation of pile response to vertical loads may be accomplished using t-z/Q-z 

computer programs. The non-linear load-deformation response provided by these programs must be 

linearized to develop the stiffness coefficients for the 6 x6 stiffness matrix. Ideally, the stiffness matrix 

coefficients should be developed in an iterative manner, with initial stiffness based upon assumed 

deformation levels adjusted in subsequent iterations based upon foundation displacements obtained from 

the inertial interaction model. However, as the foundation response can be relatively linear up to the 

point where a plastic moment forms in the pile and as results of the global analysis may be relatively 

insensitive to foundation stiffness for many problems, sensitivity analyses may be used instead of an 

iterative procedure as a practical way to develop a robust design while minimizing the need for overly 

complex analysis procedures. Furthermore, estimates of the stiffness coefficients for a single pile can be 

obtained from simple design charts based upon linear elasticity that employ the pile stiffness and the 

coefficient of subgrade reaction for the near-surface soil. 

Both the more sophisticated p-y approach to developing pile lateral stiffness and the simple chart 

solutions assume typically assume either that the pile head is free to rotate or is fixed against rotation, 

though a rotational stiffness can be input to the p-y solutions. However, the free-head and fixed-head 

conditions represent end cases for pile head restraint and the lateral stiffness of most piles can be 

reasonably modeled using one of these assumptions. 
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10.6.1 Pile Head Stiffness for Lateral Loading 

Various authors have developed recommendations for p-y curves for piles in sand and clays based on 

small-diameter pile load tests that can be used in a p-y program to estimate the lateral stiffness of the head 

of a pile subjected to seismic loading. The most commonly used p-y curves are those by Reese et al. 

(1974) and O’Neill et al. (1983) for sands and by Matlock (1970) and O’Neil et al. (1984) for clays. A 

variety of commercially available p-y programs have these relationships built in to them. 

Given the many uncertainties in site conditions, a simplified procedure to develop a linear stiffness for a 

laterally loaded pile based on typical working loads can be used to eliminate the need for iteration to find 

appropriate p-y stiffness. Lam and Martin (1986) found that lateral load-deflection characteristics 

representing the overall stiffness of the soil-pile system is only mildly nonlinear because the relatively 

stiff elastic response of the pile usually dominates pile response. Furthermore, the significant soil-pile 

interaction zone for lateral loading is usually confined to a depth equal to 5 to 10 pile diameters. 

Therefore, simplified single-layer pile-head stiffness design charts are appropriate practical design 

applications provided that sensitivity studies are conducted to ensure that the designed foundation is 

sufficiently robust to allow for uncertainty in soil stiffness. 

Single-layer linear design charts for the lateral and rotational stiffness of fixed head and free head piles 

with the pile head at the ground surface are presented in Figure 10-15 to Figure 10-18 (FHWA, 2006). 

These charts assume a soil stiffness which increases linearly with depth, starting from zero at grade. 

Figure 10-19 through Figure 10-21 give stiffness coefficients for piles with their head embedded to depths 

of 1.5 m and 3 m (5 and 10 ft), also based on a subgrade modulus that increases linearly with depth. 

The soil stiffness in these solutions is defined by a subgrade modulus, Es, and the coefficient of variation 

of the subgrade modulus, f, with depth, z, in accordance with Equation 10-1: 

z

E

f

s



10-1

Values of the coefficient f, which has units of force/unit volume, are provided for sands in Figure 10-22

as a function of the friction angle or relative density and in Figure 10-23 for clays as a function of 

cohesion (undrained shear strength) or normalized and standardized Standard Penetration Test blow 
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Seismic Design – Geotechnical Features 10-17 August 2011 

count, (N1)60. Average soil conditions for the upper five pile diameters should be used when using these 

charts, which are strictly applicable only for piles up to 0.6 m (24 in) in diameter. 

Figure 10-15 Lateral Translational Diagonal Stiffness Coefficient (Same as Fixed Head Stiffness)
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Figure 10-16 Rotational Diagonal Stiffness Coefficient
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Figure 10-17 Cross Coupling of Diagonal Stiffness Coefficient 
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Figure 10-18 Lateral Free Head Stiffness Coefficient 
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Figure 10-19 Lateral Translational Diagonal Stiffness Coefficient (Same as Fixed Head Stiffness) for 

Embedded Pile Head 
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Figure 10-20 Rotational Diagonal Stiffness Coefficient for Embedded Pile Head 
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Figure 10-21 Cross Coupling of Diagonal Stiffness Coefficient for Embedded Pile Head 
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Figure 10-22 Recommended Coefficient of Variation in Subgrade Stiffness with Depth for Sands 

Figure 10-23 Recommended Coefficient of Variation in Subgrade Stiffness with Depth for Clays 
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Seismic Design – Geotechnical Features 10-25 August 2011 

10.6.2 Pile Head Stiffness for Axial Loading 

The axial stiffness of a pile head is generally assumed to be uncoupled from the stiffnesses in the lateral 

and rotational directions. One reason why axial load-displacement characteristics may be assumed to be 

uncoupled from the lateral load-displacement behavior is because much of the soil resistance to axial 

loading comes from relatively deep depths. A realistic determination of axial pile stiffness should 

account for heterogeneous soil layering as well as slippage along the sides of the pile. Therefore, linear, 

homogeneous analytical solutions should not be used for axial stiffness calculations. Instead, methods that 

account for both soil layering and plastic slippage at the soil-pile interface should be used. 

A graphical procedure that gives the axial stiffness coefficient for a single pile and includes layering and 

slippage at the pile soil interface proposed by Lam and Martin (1986) is illustrated in Figure 10-24 and 

described as follows: 

Step 1: Ultimate compressive capacity. Calculate the ultimate pile capacity from a site-specific pile 

capacity analysis using conventional procedures for skin-friction and end-bearing capacities 

for the different soil layers. When assigning values to the skin-friction and end-bearing 

capacities, make allowances for the construction method (e.g., pre-drilling, driving), special 

conditions (e.g., consolidation due to surcharging, corrosion), and dynamic soil behavior 

(e.g., cyclic strength degradation, soil liquefaction). 

Step 2: Rigid pile load-displacement curve. Develop the pile load-displacement curve based on the 

estimated ultimate capacity and published skin-friction and end-bearing pile displacement 

relationships (e.g. the relationships in Section 10.8.2.2.2 of the AASHTO LRFD Bridge 

Design Specifications (AASHTO 2007). The resulting load-displacement curve, illustrated in 

Figure 10-24, is obtained from the sum of the skin friction and end-bearing capacities at each 

axial displacement, provides a pile-head load-displacement relationship for a pile that is 

axially-rigid. This curve is a lower bound on the actual pile displacements.
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Figure 10-24 Graphical Solution for Developing Axial Pile Stiffness 

Step 3: Flexible pile load-displacement curve. Calculate the axial displacement at the pile head due to 

the compression of the pile under axial load but neglecting the surrounding soil. This 

displacement is given by: 

AE

QL  c



10-2

where Q is the axial load, L is the length, and AE is the axial rigidity of pile. 

Obtain the flexible pile solution by adding the displacement from Equation 10-2 to the rigid-pile loaddisplacement curve in Figure 10-24 at pile loads that correspond to the rigid pile load- displacement 

curve. This curve is an upper bound on the actual pile displacements. 

Step 4: Actual load-displacement curve. As a first approximation, obtain the actual axial loaddisplacement curve by averaging the curves from steps 2 and 3. The actual solution is 

bounded by the rigid and flexible load-displacement solutions derived in steps 2 and 3 and 

depends on the nature of the soil-pile system. Averaging the results is a good place to start. 
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For an end-bearing pile, the actual curve may be closer to the flexible-pile solution. For a 

friction pile at small load levels, the upper portion of the pile is compressed first and thus the 

load-displacement curve will be closer to the rigid- pile curve. At higher loads, slippage 

occurs along most of the pile and the solution moves towards the flexible-pile curve. 

Step 5: Axial pile stiffness. Calculate a value for the pile secant stiffness from the load- displacement 

curve over the range of expected displacements and use it to find the equivalent axial stiffness 

coefficient for inclusion in the pile stiffness matrix. Expected displacements may be found 

from the expected range of axial loads, which for a regular highway bridge foundation would 

be in the range of 50 to 70 percent of the ultimate pile capacity. 

The above procedure may be used to obtain the corresponding uplift load-displacement curve by ignoring 

end-bearing and using only skin-friction to evaluate capacity. 

10.6.3 Lateral Stiffness of Pile Cap 

Because most pile footings are embedded, the pile cap stiffness should be superimposed on the pile 

stiffness to develop the pile footing stiffness. The centrifuge tests conducted by Gadre and Dobry (1998) 

confirmed the concept that the stiffness of the piles and the pile cap are additive as well as that the passive 

pressure acting on the pile cap constitutes the bulk of the pile cap stiffness. Because of the possibility of 

soil settlement and the uncertainties concerning the interaction between the footing and the piles, 

contributions to the pile cap stiffness as well as to foundation capacity from the footing’s base and from 

side shear are neglected. Hence the primary source of lateral resistance is the mobilization of passive 

pressure on the vertical face of the pile cap. Maximum passive pressures can be computed using the 

approach illustrated in Figure 10-25 (FHWA, 2006) or the approach used for earth retaining structure 

design (discussed in Chapter 11). The mobilized passive pressure and the associated deformation depend 

upon the displacement of the pile cap and may be calculated using the method described for calculating 

the stiffness of bridge abutments in Chapter 12.
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Seismic Design – Geotechnical Features 10-28 August 2011 

Figure 10-25 Method for Passive Pressure Capacity of Pile Cap (FHWA, 2006) 

10.6.4 Group Effects for Typical Pile Footings 

The single pile stiffness must be adjusted for group effects if the foundation is supported by a pile group. 

In general, if the center to center spacing of the piles in a group is less than five pile diameters, 

interactions between the piles (i.e. pile group effects) must be considered in evaluating pile stiffness. In 

the p-y approach, this interaction is defined using what is referred to as a p-multiplier, a factor by which 

the p ordinate of the p-y curve is multiplied to account for group effects. However, as group effects 

reduce pile stiffness the p-multiplier is always less than 1. Experimental data on p-y curves for closely 

spaced piles show that the load distribution varies depending on the position of the pile. Table 10-1

presents recommendations for the p-multiplier for piles in a 3 x 3 group spaced at 3 diameters subject to 
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Seismic Design – Geotechnical Features 10-29 August 2011 

monotonic unidirectional loading. Table 10-2 shows the effect of pile spacing on the p-multiplier of piles 

subjected to monotonic unidirectional loading. 

TABLE 10-1 P-MULTIPLIERS FOR PILES IN A 3 X 3 GROUP AT 3 DIAMETER SPACING 

SUBJECT TO MONOTONIC LOADING 

Pile Test, Soil Description, Reference

p-multiplier on single-pile p-y curves

Front Row Middle Row Back Row

Free-Head, Medium Dense Sand, Dr = 50% Brown et al. 

(1988) 0.8 0.4 0.3

Fixed-Head, Medium Dense Sand, Dr = 55% McVay 

Centrifuge (1995) 0.8 0.45 0.3

Fixed-Head, Medium Dense Sand, Dr = 33% McVay 

Centrifuge (1995) 0.65 0.45 0.35

Free-Head, Soft to Medium Clays and Silts Rollins et al. 

(1997) 0.6 0.38 0.43

TABLE 10-2 INFLUENCE OF PILE SPACING ON P-MULTIPLIERS FOR PILE SUBJECT 

TO MONOTONIC LOADING 

Row Spacing Front Row 2nd Row 3rd & More 

Rows

3D 0.8 0.45 0.35

4D 0.9 0.65 0.55

5D 1 0.85 0.75

Piles subjected to earthquake loading are generally subjected to reversing (cyclic) loads, as opposed to the 

monotonic loading used to develop Table 10-1 and Table 10-2. Under cyclic loading condition, the front 

row pile will become the back row pile when the load direction reverses. For simplicity, Lam et al. 

(1998) recommend use a 0.5 p-multiplier on all the piles for design analyses. This recommendation is 

supported by full scale pile load test data reported by Matlock et al. (1980) that shows that the load tends 

to become uniformly distributed among all the piles in a pile group during cyclic loading. The value of 

0.5 is approximately the mean value for the p-multiplier of piles a 3-diameter spacing subject to 

monotonic loads. If we assume that under two way loading a constant p-multiplier equal to the mean pmultiplier for one-way loading should be used, the p-multiplier values in Figure 10-26 can be derived. 
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Seismic Design – Geotechnical Features 10-30 August 2011 

Figure 10-26 P-Multipliers for Two-Way Seismic Loading 

10.6.5 Group Effects for Very Large Pile Groups 

The pile group effects discussed above are from pile load tests on relatively small pile groups involving 

either 9 or 16 piles in the pile groups. Foundations for major water crossings may involve extremely large 

piers supported by several hundred piles. In these cases, the horizontal dimension of the footing can 

easily be greater than the length of the piles, in contrast to small groups where the pile length is usually 

several times the size of the pile cap. The pile-soil system in these configurations may be thought of as a 

reinforced soil mass. A full-scale experiment for such a huge pile group would be impossible. Therefore, 

engineers must rely upon numerical analyses to evaluate group effects for this problem. Dodds (2005) 

developed the recommendations shown in Table 10-3 for the p-multiplier for piles in large groups as a 

function of pile spacing. 

TABLE 10-3 P-MULTIPLIERS FOR LARGE PILE GROUPS (DODDS 2005) 

Soil Condition 3D Spacing 6D Spacing

Soft Clay 0.1 0.5

Medium Dense Sand 0.2 0.7
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10.6.6 p-y Curves for Liquefied Sand 

Liu and Dobry (1995) conducted centrifuge tests to evaluate the reduction in the p-y resistance of a soil as 

a function of the cyclically generated excess pore pressure in sandy soils. Figure 10-27 presents a plot 

obtained from these experiments showing the reduction in pile resistance (i.e. the p-multiplier), termed Cu 

in this figure, versus the excess pore pressure ratio. Note that at a pore pressure ratio of 1, representative 

of liquefaction, the p-multiplier is approximately 0.1, so the lateral resistance of the liquefied soil is 

approximately 10% of its initial value. However, it may not be appropriate to assign this reduced p-y 

resistance to the pile during shaking, as pore pressure generally builds up gradually during the earthquake 

and the reduction in p-y resistance does not exceed 0.5 until the pore pressure ratio equals 70%. 

The centrifuge experiment discussed above was conducted on loose, clean Nevada sand with a relative 

density Dr of 40%. Evidence of a higher residual strength of liquefied soil has been observed in parallel 

centrifuge experiments conducted at the University of California at Davis in which p-multipliers for 

liquefied soil as high as 0.25 have been reported. 

Figure 10-27 Scaling Factor to Reese’s static p-y Curves from the 1995 Liu and Dobry Centrifuge Test 
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Seismic Design – Geotechnical Features 10-32 August 2011 

Another approach to characterizing the lateral resistance of a pile in liquefied soil is to assign the 

liquefied soil a representative undrained shear strength, Su. Based upon back analysis of centrifuge test 

results, Abdoun (1997) found that the lateral resistance of a pile in liquefied loose sand could be 

represented by assigning an undrained shear strength of 21 psf to the liquefied soil. The ultimate passive 

pressure on the side of a pile in cohesive soil (i.e. the p in a p-y curve) was been found to increase from 

3SuD at mudline to 9SuD at depth (Matlock, 1970). Therefore, the p value corresponding to an undrained 

shear strength of 21 psf could vary from 63 psf to 189 psf depending on the depth along the pile. 

10.6.7 Stiffness Matrix of a Pile Group 

The stiffness of the individual piles must be integrated with the stiffness of the pile cap to develop the 

stiffness matrix for a pile group. For complex pile group configurations, and particularly for pile groups 

that include battered piles, developing a linear 6 x 6 pile group stiffness matrix involves the use of a 

computer program (see Lam and Martin 1986). However, many pile groups encountered in practice have 

relatively simple configurations and involve only plumb (vertical) piles. For such situations, it is practical 

to develop the pile group stiffness matrix by hand calculations. The vertical and translational stiffness are 

simply the sum of the stiffness of the individual piles (plus the stiffness of the cap for the translational 

mode). The rotational stiffness for moment loading about a horizontal axis (rocking) is coupled to the 

vertical stiffness of the piles in the group as follows: 

(kq)cap = Skqi + S(kdi Ri

2

) 10-3

 

where (kq)cap = rotational stiffness of cap 

 kqi = rotational stiffness of pile i 

 kdi = translation stiffness of pile i 

 Ri = distance from pile i to center of group 

The torsional stiffness is evaluated in a similar manner using the vertical stiffness of the piles and the 

passive resistance against the pile cap. 

10.6.8 Pile Head Rotational Stiffness 

A fixed head (or rigid) pile-pile cap connection is probably the most widely adopted assumption in pile 

design analysis. This assumption is adopted for convenience, as it is difficult to characterize the 
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Seismic Design – Geotechnical Features 10-33 August 2011 

rotational stiffness of a pile embedded in a pile cap. However, as real pile-pile cap connections generally 

do allow some rotation, the assumption of a rigid connection can have a profound impact on design. The 

assumption of a rigid connection can result in significant under-estimation of the shear capacity of the pile 

due to exaggeration of the bending moment at the pile head. 

The impact of the rotational stiffness of the pile-pile cap connection on the performance of a pile was 

investigated as part of the Pier 400 Project for the Port of Los Angeles. The performance of a pile 

supported wharf structure subject to seismic loading using a bi-linear rotational spring to model the pilepile cap connection. The bi-linear pile rotational spring was developed based on a full-scale pile load in 

which the pile head moment-rotational characteristics were evaluated. Figure 10-28 compares the 

observed pile head rotational behavior (Blandon, 2007) to the behavior predicted using the pile head 

rotational spring. 

POLA Pile Head Connection Test and Design

0

100

200

300

400

500

600

700

800

0.00 0.02 0.04 0.06 0.08 0.10

Rotation (Radian)

Moment (ft-kip)

'Seismic Pile Test Data'

Prior Recommendations

Alternate Idealization

Figure 10-28 Measured versus Predicted Pile Head Rotation 

Figure 10-29 presents the results of pile pushover analyses that illustrate the benefit of modeling the pile 

head with the rotational spring as opposed to employing the traditional assumption of a fixed head. The 

moment capacity for the pile at the pile-pile deck connection point was found to be 6,692 in-kips. At this 

moment capacity, the pile would have a displacement capacity of only about 0.7 inch for the conventional 

fixed-head assumption. However, the displacement capacity of the pile increased to almost 10 inches for 
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Seismic Design – Geotechnical Features 10-34 August 2011 

the recommended safety level criterion of 0.0855 radian rotation when the bi-linear moment-rotation 

spring was employed. Even under a no damage criterion (no inelastic action at the pile head), the 

displacement capacity using the bi-linear moment-rotation spring increased to approximately 1.4, 

essentially twice the 0.7 inch capacity from the fixed head assumption. 

Figure 10-29 Shear vs. Moment Load Solution 

The rotational spring also increased the shear capacity of the pile head connection. With the bi-linear 

spring, a lateral shear load capacity of 264 kips mobilized at the 11.17 inch limiting deflection compared 

to the 132 kips shear load capacity for the fixed head assumption. The rotational spring also resulted in a 

more evenly distributed moment along the entire pile at failure, as the pile becomes more efficient in 

mobilizing soil capacity at deeper depths without overstressing the pile top region. 

10.7 MOMENT CAPACITY OF PILE GROUPS 

Moment capacity of a pile group is typically governed by the axial pile uplift and compression capacities. 

The ultimate moment capacity of a pile group is often evaluated based upon first yield of any pile in the 

group. However, unrestrained deformation cannot occur until multiple piles in the group (typically all but 
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Seismic Design – Geotechnical Features 10-35 August 2011 

one pile or row of piles, about which the group will rotate) yield. Figure 10-30 shows calculations of the 

moment capacity of a 4 x 3 pile group using both assumptions. The ultimate compression and uplift 

capacity of the piles are 180 kips and 90 kips, respectively. If the cap is assumed to fail upon first yield of 

one of the outer piles in the group, the moment capacity of the group is 2,700 ft-kips. However, if it is 

assumed the cap does not fail until three of the four piles yield geotechnically (as required for 

unrestrained rotation of the cap), the moment capacity of the cap is 4,050 ft-kips. Note that the pile cap 

must be designed to sustain a tension load equal to the uplift capacity of the pile to realize this capacity. 

Figure 10-30 Moment Capacity of a Pile Group 

It is recommended that the pile head connection be designed so that its capacity in tension exceeds the 

geotechnical uplift capacity of the pile, forcing the failure of the system under moment loading into the 

soil, rather than at the connection. Again, using this design philosophy it can be counter-productive if 

geotechnical engineer is overly conservative in evaluating the uplift capacity of the pile, as 

underestimating the uplift capacity could be counter-productive to the goal of forcing the failure into the 

soil. 
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Seismic Design – Geotechnical Features 10-36 August 2011 

Following the 1989 Loma Prieta earthquake, Caltrans embarked on a very aggressive program to retrofit 

existing bridges in California. Many of the foundations were concluded to be inadequate in terms of their 

capacity to resist the earthquake loading. A particular concern was the lack of moment capacity due to 

exceeding the uplift capacity of the piles in conventional force-based demand analyses. However, it was 

also recognized that there was a lack of any evidence of inadequate moment capacity in past earthquakes 

(e.g. from overturning failure of bridge piers). A series of research projects were organized under the 

auspices of MCEER to investigate this apparent discrepancy. The following paragraphs summarize the 

overall conclusions from the studies conducted by Fenves (1998) as part of this effort: 

 In terms of the moment-rotation ductility demand on the column, an overly strong footing results in 

a higher potential for damage to the column. A softer foundation (i.e. lower moment capacity of 

the footing), especially where there are good connection details to enforce the energy dissipation 

mechanism in the soil, results in lower inelastic demand on the column. 

 A lower static factor of safety implies a higher degree of peak and permanent footing rotation. A 

higher static factor of safety leads to significantly lower peak and residual rotations. 

 In the case of a connection detail failure (zero uplift pile capacity), the inelastic demand on the 

column is actually reduced significantly. As connection detail failure takes place, the superstructure 

becomes isolated from the earthquake ground motion and hence a lower amount of earthquake 

force is transmitted to the superstructure. However, connection detail failure implies a higher 

degree of global instability. 

 The force-based design approach is an extremely conservative approach with respect to global 

stability. 

10.8 DESIGNING FOR UNCERTAINTY 

Figure 10-31 presents the results of a series of pushover analyses for a 16-inch drilled shaft at a medium 

dense sand site. The pile is represented as a linear elastic material and the pile head is modeled using the 

typical fixed head pile top boundary condition. The figure presents the results of a sensitivity study using 

three p-y curves (1) benchmark p-y curves developed based on a 35-degree friction angle, (2) a set of 
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Seismic Design – Geotechnical Features 10-37 August 2011 

stiffer p-y curves developed by using a p-multiplier of 2 on the benchmark p-y curves, and (3) a set of 

softer p-y curves developed using a p-multiplier of 0.5 on the benchmark p-y curves. 

Figure 10-31 Sensitivity of a 16-inch Drilled Shaft to Variations in p-y Curve Stiffness 

For the variation of a factor of 4 in the p-y curve stiffness, the mobilized pile resistance at 0.5-inch 

deflection changes from 18.5 to 39.9 kips, or a variation by a factor of approximately 2. The right side of 

Figure 10-31 presents the moment versus pile shear relationship, which is often of more importance than 

the pile load-deflection relationship shown on the left side. For a pile head load of 26.64 kips, the pile 

moment varies from 957 to 1,553 in-kips, or a variation by a factor of 1.6, which is even smaller than the 

variation in the pile stiffness. Furthermore, from the right side of Figure 10-31 it can be seen that for a 

moment of 1,235 in-kips the shear load on the pile varies from 22.2 to 32.8 kips, a variation by a factor of 

approximately 1.5 times. In summary, a 4 times variation in the stiffness of the p-y curve implies about a 

2 times variation in the foundation stiffness, about a 1.62 times variation in the pile moment for a 

specified shear load, and a 1.5 variation in the shear load for a specified moment capacity. This example 

highlights the fact that the behavior of pile foundations is usually relatively insensitive to relative small 

variations in p-y curve stiffnesses, especially when designing for displacement capacity. 

If the earthquake demand is assumed to be a displacement based demand, at a moment capacity of 1,235 

in-kips the corresponding displacement capacity of the foundation would be 0.72 inch and 0.36 inch, 
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Seismic Design – Geotechnical Features 10-38 August 2011 

respectively, for the soft p-y and stiff p-y cases. Therefore, the softer p-y curve results in a higher 

displacement capacity for the foundation. This notion is supported by case histories that show that stiffer 

structural components are actually more vulnerable to earthquake damage than softer components. 

Actually, it is difficult to predetermine whether softer or stiffer p-y curves would be conservative in the 

overall design of the structure. Therefore, good design practice calls for analyzing the foundation and the 

structural system for a wide range of p-y curve stiffness assumptions to account for the basic uncertainty 

in p-y curve characterization. In addition to varying p-y curve stiffness, the designer often needs to allow 

for uncertainty in other aspects of the design, including the assumed pile cap embedment depth and pile 

head fixity assumptions. Often, these issues are of more significance to the design than p-y curve 

stiffness. Designing the foundation for large variations in p-y curve stiffness is also a practical way to 

deal with design issues such as pile group effects and the stiffness of piles in liquefiable ground. 

10.9 DESIGNING FOR KINEMATIC DISPLACEMENT DEMAND IN LIQUEFIED SOILS 

Analysis of ability of a deep foundation to withstand the kinematic displacement demand from laterally 

spreading soil can be into two categories: (1) cases where the liquefied soil layer extends all the way to 

the ground surface; and (2) cases where the liquefied soil layer is overlain by a nonliquefied layer. These 

two categories of the lateral spreading problem are shown schematically in Figure 10-32. 

Conceptually, cases where the liquefied soil extends all the way to the ground surface can be analyzed 

simply by applying the appropriate p-y curves to the liquefied soil. Recommendations for liquefied soil 

p-multipliers are on the order of 0.1 to 0.25, as previously discussed. However, p-y curves back 

calculated from the performance of laterally loaded piles in soil liquefied by blasting reported by Rollins 

et al (2005) and presented in Figure 10-33 show stiffening at large deflections as well as a different 

backbone curve shape than conventionally assumed for p-y curves. At the present time there is no 

consensus on the proper approach to modeling the p-y behavior of liquefied soils, suggesting a need for 

sensitivity studies to account for this uncertainty, as discussed above. 
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Seismic Design – Geotechnical Features 10-39 August 2011 

Figure 10-32 The Two Cases for Pile Design in Lateral Spreading Liquefied Soils
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Seismic Design – Geotechnical Features 10-40 August 2011 

Figure 10-33 p-y Curves Back calculated from Soil Liquefied by Blasting (Rollins et al 2005) 

A review of the case histories of piles damaged by lateral spreading of liquefied ground suggests that all 

of the cases in which pile damage is reported are associated with a non-liquefiable crust sliding on a 

liquefied layer. This loading mechanism is generally considered to be unrelated to the inertial response of 

the foundation. 

In an attempt to address the problem of a non-liquefied soil layer sliding on liquefied soil, Lam et al. 

(2007) conducted a series of 3-dimensional finite element analyses, illustrated in Figure 10-34. The 

studies included analyses for a large range of pile types and pile diameters with a large range of EI values, 

three sets of liquefied layer thicknesses, and also a sufficiently large range of soil properties. The 

resultant solutions were used to develop a set of non-dimensional charts for simplified design analysis. 

The pile is modeled using linear elastic properties and therefore the design charts will only be valid prior 

to pile yielding. Furthermore, the solution is for the basic single solitary pile problem (i.e. without pile 

group effect). 

The steps involved in the simplified pile design analyses are outlined below: 

Step-1: Estimating the Relative Slippage Displacement Amplitude, D, between the upper crust and the 

lower stable nonliquefied layer: Any of the commonly used approaches for evaluating the 
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Seismic Design – Geotechnical Features 10-41 August 2011 

magnitude of lateral spreading, including the Newmark sliding block approach discussed in 

Chapter 6, can be used to estimate the basic displacement amplitude demand value for design. 

Figure 10-34 3-D Finite Element Model of a Pile in Laterally Spreading Ground with a Nonliquefied 

Crust 

Step-2: Estimating the Locations of the Maximum Pile Moment Above and Below the Liquefied Soil 

layer: Lam et al (2007) found a rational non-dimensional parameter encompassing a very wide 

range of pile types, liquefied layer thickness and soil properties (the solution is only sensitive to 

the soil modulus, Es of the nonliquefied upper and lower crust adjacent to the liquefied soil 

layer) to accomplish this task. This dimensionless characteristic parameter β, referred to as the 

soil-pile-liquefied thickness interaction parameter, is defined by the equation shown below. 

EI

DTE

22

s 

10-4

where: Esis the modulus of elasticity of the stiff soil layer 

 EI the bending stiffness of the pile 

 T is the thickness of the liquefiable layer 

 D is the (outer) diameter of the pile. 

After determining the β parameter, Figure 10-35 can be used to establish the location of the maximum 

pile moment, Figure 10-36 can be used to estimate the maximum moment, Figure 10-37 can be used to 

estimate the maximum shear. 
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Seismic Design – Geotechnical Features 10-42 August 2011 

Figure 10-35 Maximum Pile Moment Location 

Figure 10-36 Maximum Pile Moment Solution 
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Seismic Design – Geotechnical Features 10-43 August 2011 

Figure 10-37 Maximum Pile Shear Solution 

10.10 DESIGN PROCEDURES FOR LARGE DIAMETER DRILLED SHAFTS 

The question of whether p-y curves should be diameter dependent has been debated for a long time and 

there have been various proposals for adjustments to the Reese and Matlock p-y curve procedures to 

better account for diameter effects (Stevens and Audibert, 1979 and Penders 1993, and Ling, 1988). 

Ashford and Juirnarongrit (2003) presented evidence that the initial tangent modulus of the p-y curves 

appeared to be independent of pile diameters, confirming the hypothesis of Terzaghi (1955) that p-y 

resistance should be independent of pile diameter. This is still a subject of active research. But, at the 

present time there is no reason to consider p-y curves as being diameter dependent. 

10.11 CAISSONS DESIGN 

Caissons foundations are typically used for over-water bridges. They are typically sunk to significant 

depths (varying from tens of feet to over 100 feet) and hence are classified as deep foundations. Because 

of their large embedment depth, the coupling effects between the lateral shear and overturning moment 

can be an important consideration in caisson design. However, caissons such as the caissons for the west 

span of the San Francisco-Oakland Bay Bridge that rest directly on rock can be treated as shallow 

foundations without consideration of coupling. 
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Seismic Design – Geotechnical Features 10-44 August 2011 

Because of the large dimensions involved in typical caissons (usually over 50-ft for the shorter 

dimensions), elastic charts are rarely applicable because of the need to account for the inhomogeneous 

soil profile over the embedment depth. Also, because caissons are used for major bridges, there is usually 

room in the design process to conduct more complex finite element analyses for developing the 

appropriate soil springs for caisson design. Figure 10-38 depicts the various soil-foundation-structure 

interaction modeling approaches for caissons. The nonlinear lumped springs approach is shown in Figure 

10-38 (b), where uncoupled nonlinear springs are assigned to some appropriate point of support (e.g. the 

base of the caisson) for various modes of displacements. Nonlinear soil springs are usually necessary for 

caisson design, even if the caisson is resting on stiff soils (such as the west span of the San FranciscoOakland Bay Bridge), because of the likelihood of uplift of the base under moment loading. Due to the 

potential for base uplift, a nonlinear moment-rotational spring will be necessary to capture this geometric 

nonlinearity, as shown in Figure 10-38b. However, it needs to be recognized that under cyclic loading a 

geometric nonlinearity will behave very different from a material nonlinearity. For geometric 

nonlinearity, even though the moment-rotation backbone curve is nonlinear, there is little or no material 

yielding and the hysteretic behavior should be modeled as nonlinear but elastic for both the loading and 

unloading paths (i.e. loading and unloading will follow the same backbone curve). The conventional 

Masing type of hysteretic cyclic load-displacement loading and unloading rules can over-exaggerate the 

damping effect when modeling caisson type foundations using the lumped springs approach. 

Because of the potential for geometric nonlinearity (i.e. base separation and gapping) interacting with 

material nonlinearity, present day caisson modeling normally employs nonlinear distributed springs, as 

depicted in Figure 10-38d (MCEER,2007). This approach entails the use of Winkler springs distributed 

over the bottom and the sides of the embedded portion of the caisson foundation. The soil springs are 

normally modeled as nonlinear and hysteretic springs for consideration of yielding of the adjacent soils. 

However, gapping elements are usually implemented in series with the nonlinear hysteretic soil springs to 

allow for the base uplift and gapping behavior. These springs are included as part of the global bridge 

model. 
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Figure 10-38 Various SSI Modeling Approaches for Caissons 
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Seismic Design – Geotechnical Features 10-46 August 2011 

Establishment of the proper distributed soil springs is a key to successful modeling of the caisson using 

the distributed spring approach. A pushover analysis of the caisson using the finite element method can 

be conducted to extract the appropriate soil springs for use in the global bridge model. It should be noted 

that the load-displacement solution from the finite element analysis will be dependent on the loading 

condition employed in the analysis. Therefore, the appropriate pushover loading condition needs to be 

carefully considered, especially the proportion of the shear versus moment load. 

Input seismic excitation to the distributed spring model is accomplished by applying multiple ground 

motions at each layer of the soil strata. This provides a mechanism that could potentially be used to 

consider incoherent motions that occur as a result of wave scattering. However, Lam et al. (2007) showed 

that wave scattering generally will alter only the high frequency motions, and these motions are not 

particularly important with respect to caisson response. Therefore, it is generally valid to use the free 

field motions for input to caisson analyses. 

10.12 SUMMARY 

This chapter presents approaches to the design of deep foundations. Case histories of pile foundation 

damage in earthquakes are reviewed. Lessons from these case histories formed the basis for emphasis in 

the recommended procedures and design approaches (e.g. characterization of the pile head connections 

and design against liquefaction). 

Experience with design of deep foundations shows that, similar to the design of shallow foundations, 

frequency dependent stiffness models are not required and the static stiffness can be used in seismic 

analysis to assemble the 6 x 6 stiffness matrix. However, unlike shallow foundations, there are situations 

where kinematic interaction must be considered in seismic design of deep foundations. 

Both rigorous and simplified (but not simple) procedures for conducting a kinematic interaction analysis 

are described. The benefit of considering kinematic interaction at soft soil sites is illustrated and an 

approximate method to consider the effects of kinematic interaction suing the results of a one-dimensional 

site response analysis is presented. 

The use of both p-/t-z analyses and simple design charts to evaluate the stiffness coefficients for a single 

pile are described. Considerations in the analysis of pile groups, including pile interaction effects, 
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Seismic Design – Geotechnical Features 10-47 August 2011 

evaluation of the contribution of the pile cap to group stiffness, and calculating the group stiffness 

coefficients are presented. The impact of pile stiffness on design is discussed and illustrated with an 

example. In the context of moment capacity of the pile group, the importance in designing the pile 

connection to prevent uplift pull out at the pile head is discussed. 

The importance and benefits of conducting sensitivity analyses by varying the p-y stiffness of the piles is 

illustrated with an example. Results from pushover analyses are presented to provide an appreciation of 

how p-y curves affect the pile foundation in various aspects, including foundation stiffness, pile moment 

and shear load capacity as well as displacement capacity of the pile foundation. 

Recommendations for developing p-y curves in liquefied soils are reviewed. A new procedure to analyze 

the piles subject to lateral spreading in soils with a nonliquefied surface layer is presented. 

The issue of the diameter-dependence of p-y curves is briefly addressed, with the conclusion that no 

adjustment is warranted at this time. Design methodologies for large caissons are presented. 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-1 August 2011 

CHAPTER 11

EARTH RETAINING STRUCTURES

11.1 INTRODUCTION 

11.1.1 Design Criteria 

This chapter describes the seismic design procedure for earth retaining systems (as opposed to bridge 

abutments, which are addressed in the next Chapter). The current AASHTO LRFD specifications do 

discuss the seismic design of earth retaining structures., Furthermore, additional information and 

recommendations on design of earth retaining structures is provided in FHWA-NHI-07-071, Earth 

Retaining Structures. However, NCHRP Report 611 (NCHRP, 2008), developed under NCHRP Project 

12-70, provides enhanced recommendations for LRFD seismic design of these types of structures and 

forms the basis of the recommendations provided herein. 

In accordance with the AASHTO LRFD specifications for bridge design, seismic LRFD design 

requirements for earth retaining structures should be done in general compliance with requirements for 

Extreme Event I. Under these requirements, presented in Table 1.1, seismic LRFD design of free 

standing retaining walls shall include the earthquake load, the friction load, and the water and stream 

pressure load with a load factor of 1.0, and the factored permanent (dead) load and live load. AASHTO 

LRFD permanent load factors, presented in Table 1.2, provide maximum and minimum values for 

components, wearing surfaces, vertical earth pressures, and earth surcharge loads and call for using the 

values that produce the most critical design load combination for design. However, as discussed in 

Chapter 1 and consistent with the recommendations in NCHRP Report 611, it is recommended herein to 

use a load factor of 1.0 for all permanent loads for LRFD seismic design of free standing earth retaining 

structures. Furthermore, as discussed in Chapter 1, a load factor of 0.5 applied to the average daily truck 

traffic (ADTT) load is recommended for the earthquake live load. However, no inertial component of the 

live load is considered in seismic design. 

In addition to the above considerations, seismic design of earth retaining systems requires consideration 

of the tolerable lateral deformation of the wall system. Displacement-based seismic design of earth 

retaining structures is addressed in this chapter. However, criteria for the tolerable level of lateral wall 

deformations are controlled by the surrounding facilities and are set by the owner (though often based 
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Seismic Design – Geotechnical Features 11-2 August 2011 

upon input from the engineer). An Appendix in Volume 2 of NCHRP Report 611 discusses the 

considerations involved in establishing such criteria. 

11.1.2 Types of Earth Retaining Structures 

Retaining walls can be broadly classified as walls that retain fills and walls that retain cuts. Walls that 

retain fill include gravity, semi-gravity, prefabricated modular, and mechanically stabilized earth (MSE) 

walls. The gravity, semi-gravity, and prefabricated modular walls are considered to be externally 

stabilized walls while MSE walls are considered to be internally stabilized walls. Walls that retain cuts 

include non-gravity cantilever, anchored, soil nail, and micro-pile walls. Non-gravity cantilever and 

anchored walls are considered to be externally stabilized while soil nail and micro-pile walls are 

considered to be internally stabilized. 

11.1.3 Gravity and Semi-Gravity Walls 

Gravity walls derive their capacity to resist lateral loads through dead weight of the wall. Semi-gravity 

walls are similar to gravity walls, except they rely on their structural components to mobilize the dead 

weight of backfill to derive their capacity to resist lateral loads. While gravity and semi-gravity walls are 

classified as fill walls, they can also be used in cut applications. 

Gravity walls may be constructed of stone masonry, un-reinforced concrete, or reinforced concrete as 

shown in Figure 11-1. However, reinforcement in these walls is usually nominal and is provided 

primarily to resist temperature loads. They have relatively narrow base widths. They are generally not 

used when deep foundations are required and are most economical at low wall heights. 

Figure 11-1 Mass Concrete Gravity Wall 
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Seismic Design – Geotechnical Features 11-3 August 2011 

Semi-gravity walls are sometimes referred to as stem walls. As shown in Figure 11-2, semi-gravity walls 

may be supported on deep or shallow foundations. Semi-gravity cantilever walls include counterfort and 

buttress walls, as shown in Figure 11-3, and Figure 11-4. Semi-gravity cantilever walls are constructed of 

reinforced concrete. Classified as fill walls, they can also be used in cut applications. They have 

relatively narrow base widths. The position of the wall stem relative to the footing can be varied to 

accommodate right-of-way constraints. These walls can support soundwalls, sign structures, and other 

highway features. They are most economical at low to medium wall heights. 

Figure 11-2 Semi-Gravity Cantilever Retaining Walls 

Figure 11-3 Counterfort Retaining Walls 
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Seismic Design – Geotechnical Features 11-4 August 2011 

Figure 11-4 Buttressed Retaining Walls 

11.1.4 Non-Gravity Cantilevered Walls 

Non-gravity cantilevered walls are constructed of vertical structural members consisting of partially 

embedded soldier piles or continuous sheet piles, as shown in Figure 11-5. Non-gravity cantilevered 

walls rely on the structural components of the wall that are embedded in the foundation material to resist 

lateral loads. 

Figure 11-5 Non-Gravity Cantilever Wall 
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Seismic Design – Geotechnical Features 11-5 August 2011 

Soldier piles may be constructed with driven steel piles, treated timber, precast concrete or steel piles 

placed in drilled holes and backfilled with concrete or cast-in-place reinforced concrete. Continuous sheet 

piles are typically driven steel sheet piles but precast prestressed concrete sheet piles may also be used. 

Soldier piles may be faced with treated-timber, reinforced shotcrete, reinforced cast-in-place concrete, 

precast concrete or metal elements. This type wall depends on both the resistance of the foundation 

material and the moment resisting capacity of the vertical structural members for stability, therefore its 

maximum height is limited by the competence of the foundation material and the moment resisting 

capacity of the vertical structural members. The economical height of this type wall is generally limited to 

a maximum value of around 18 feet. 

11.1.5 Non-Gravity Anchored Walls 

Non-gravity anchored walls derive their capacity to resist lateral loads by their structural components, 

including tension elements connected to anchors and sometimes by embedment of their structural 

components into foundation material. Non-gravity anchored walls are typically composed of the same 

elements as non-gravity cantilevered walls plus one or more levels of anchors as shown in Figure 11-6. 

The additional lateral resistance provided by the anchors allows these walls to overcome the height 

limitations of non-gravity cantilever walls. For transportation applications, the anchors are typically 

ground anchors (tiebacks) consisting of drilled holes with grouted prestressing steel tendons extending 

from the wall face to an anchor zone located behind potential failure planes in the retained soil or rock 

mass. Anchored walls are typically constructed in cut situations. Anchored walls may be used to 

stabilize unstable slopes. Provided adequate foundation material exists at the site for the anchors, wall 

heights up to 80 feet are feasible for anchored walls. 
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Seismic Design – Geotechnical Features 11-6 August 2011 

Figure 11-6 Single Tieback System 

11.1.6 Mechanically Stabilized Earth Walls 

Mechanically stabilized earth (MSE) walls use either metallic (inextensible) or geosynthetic (extensible) 

soil reinforcement embedded within the wall backfill and attached to vertical or near vertical facing 

elements, as shown in Figure 11-7, to mobilize the shear strength of the soil for support of the wall 

system. MSE walls behave as a gravity wall in that they derive their lateral resistance through the dead 

weight of the mechanically stabilized backfill. MSE walls are typically used for fill walls and are 

employed in the same types of situations where conventional gravity and semi-gravity retaining walls are 

employed. The practical height of an MSE wall may be limited only the competence of the foundation 

material at a given site: tiered MSW walls with stepped-back faces have been used for wall height of over 

100 ft. MSE walls are particularly well suited for sites where substantial total and differential settlements 

are anticipated. The allowable differential settlement is limited by the deformability of the wall facing 

elements within the plane of the wall face. 

Figure 11-7 MSE Wall with Precast Concrete Face Panels 
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Seismic Design – Geotechnical Features 11-7 August 2011 

11.1.7 Soil Nail Wall 

Soil nailing is an economical technique for stabilizing cut slopes and for constructing retaining walls in 

cuts from the top down. Soil nail walls are similar to MSE walls in that they rely on reinforcing elements 

that extend into the soil or rock behind the wall to mobilize the shear strength of the ground to support the 

wall. The reinforcing elements in a soil nail wall are generally steel tendons which are drilled and 

grouted into the soil or rock, as shown in Figure 11-8. The soil nails are typically spaced about 4 to 6 feet 

apart in both the horizontal and vertical direction, and usually vary in length from 0.7 to 1.2 times the wall 

height. In permanent soil nail walls, the soil nail bars have an additional layer of corrosion protection 

(usually epoxy coating). A wire mesh and shotcrete facing is typically employed for soil nail walls, 

though many architectural options such as precast panels or "green" vegetated cells are available for 

permanent wall facings. Prefabricated drainage panels are often placed against the cut slope behind the 

facing before the shotcrete is applied. 

Figure 11-8 Soil Nail Wall 
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Seismic Design – Geotechnical Features 11-8 August 2011 

11.1.8 Prefabricated Modular Walls 

Prefabricated modular walls use stacked or interconnected structural elements filled with soil or rock to 

resist lateral earth pressures, as shown in Figure 11-9, acting essentially as gravity retaining walls. 

Prefabricated modular block walls include crib walls, bin walls, gabion walls, and modular block walls. 

Structural elements consisting of treated timber, or precast reinforced concrete may be used to from a 

cellular system which is filled with the backfill material to construct a crib wall. Steel modules bolted 

together in similar manner are also used to construct a bin wall. Rock filled wire gabion baskets may be 

used to construct a gabion wall. Solid precast concrete units or segmental concrete masonry units are 

stacked to form a modular block wall. The aesthetic appearance of some of these type walls is governed 

by the nature of the structural elements used. Those elements consisting of precast concrete may 

incorporate various aesthetic treatments. This type wall is most economical for low to medium height 

walls. 

 

Figure 11-9 Precast Concrete Crib Walls 
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Seismic Design – Geotechnical Features 11-9 August 2011 

11.2 SEISMIC FORCES ON EARTH RETAINING STRUCTURES 

11.2.1 Seismic Load and Resistance 

The seismic demand on retaining walls includes the seismic active thrust from the soil behind the wall 

and the inertial loading on the wall itself. Surcharge loads may also contribute to the demand. Sources of 

resistance for retaining wall systems include seismic passive resistance in front of the wall, the frictional 

sliding resistance of the base of the wall and the bearing resistance of the foundation soil for walls that 

rely on the base to serve as a spread footing, e.g. gravity, semi-gravity, and MSE walls, the axial and 

lateral geotechnical capacity of the deep foundation elements for retaining walls supported on deep 

foundations, and the structural resistance of the wall system. 

Figure 11-10 shows the forces acting on a semi-gravity cast-in-place retaining wall during a seismic 

event. As described subsequently, the active seismic thrust, PAE, and the seismic passive earth pressure, 

PPE, are functions of backfill properties, the wall and backfill geometry, and the seismic coefficient, kh, 

which in turn depends upon the site adjusted peak ground acceleration, FPGAPGA. In the absence of other 

information, PAE and PPE may be assumed to act at the midpoint of the wall height (NCHRP Report 611). 

Note that the NCHRP Report recommends that the total active pressure under seismic loading PAE may be 

assumed uniformly distributed. The procedures described to determine PAE in subsequent sections are 

detailed in the NCHRP 2008 Report, and are recommended to replace the current AASHTO procedures. 

The inertia loads acting on the wall, kh x Wc, and the inertia force acting on the soil above the heel of the 

wall, kh x Ws, are also a function of seismic coefficient, kh. The resistance force of the base of the wall, 

HR, is a function of total normal load on the base of the wall, N, and the frictional coefficient between the 

base of the wall and the underlying foundation, . In the absence of adhesion between the wall and the 

foundation soil,  is equal to tanw, where w is the interface friction angle between the wall foundation 

and the soil underneath the foundation. 
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Seismic Design – Geotechnical Features 11-10 August 2011 

HR =  N

d

PA E

Ws

khWs

khWc

Wc

h

/2

N

h

d

PPE

D

Surcharge

Figure 11-10 Seismic Forces on a Semi-gravity Retaining Wall 

11.2.2 No Analysis Provisions 

Not all walls need be analyzed for seismic loading. The NCHRP Project 12-70 recommendations indicate 

that the site-adjusted peak ground acceleration, FPGAPGA, is less than 0.3 g and the backfill behind the 

wall is flat, no seismic analysis is necessary unless the foundation is susceptible to liquefaction. 

Similarly, no analysis is necessary if the site-adjusted PGA is less than 0.2 g and the backfill slope is 

flatter than 3H:1V or if the site adjusted PGA is less than 0.1 g and the backfill slope is flatter than 2H:1 

V and liquefaction is not anticipated. Table 11-1 (NCHRP, 2008) summarizes these conditions under 

which no seismic analysis is necessary for free standing earth retaining structures. 

TABLE 11-1 CONDITIONS UNDER WHICH SEISMIC ANALYSIS IS NOT REQUIRED FOR 

A FREE STANDING EARTH RETAINING WALL (NCHRP, 2008) 

Slope Angle Above

Wall

 FPGAPGA

Flat 0.3 g

3H:1V 0.2 g

2H:1V 0.1 g
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Seismic Design – Geotechnical Features 11-11 August 2011 

11.3 SEISMIC LATERAL EARTH PRESSURES 

11.3.1 Mononobe-Okabe Seismic Earth Pressure Theory 

The most common means of calculating seismic active thrust used in practice today is Mononobe-Okabe 

earth pressure theory. Mononobe-Okabe theory is an extension of basic Coulomb earth pressure theory to 

include a lateral force on the backfill soil to represent the effect of seismic loading. The forces acting on 

a Coulomb wedge due to horizontal and vertical ground acceleration are shown in Figure 11-11. 

khW

(1-kv) W

R



b

PAE aae

d

w

h

Figure 11-11 Free Body Diagram for Mononobe-Okabe Active Earth Pressure Theory 

In practice, the effect of the vertical acceleration on the seismic earth pressure is usually ignored. 

Reasons for ignoring the vertical acceleration include that: 

 the vertical acceleration is generally out of phase with and has different frequency characteristics 

than the horizontal acceleration, and thus is as likely to be acting in a manner that reduces the 

earth pressure (upwards) as it is to be acting in a manner that increases the earth pressure 

(downwards); 

 the peak vertical acceleration generally does not occur at the same time as the peak horizontal 

acceleration, thus it does not make sense to superimpose a vertical seismic coefficient on top of a 

horizontal seismic coefficient that is based upon the peak ground acceleration; and 
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Seismic Design – Geotechnical Features 11-12 August 2011 

 the tendency of a downward vertical acceleration to increase the seismic earth pressure is 

counteracted by the associated increase in the sliding and overturning resistance due to a 

downward vertical acceleration. 

Ignoring the vertical acceleration, in a uniform soil the seismic active earth pressure on a wall of height H 

is given by: 

AE AE P k

2 H 

2

1

 

11-1

where kAE is the seismic active earth pressure coefficient. In Mononobe-Okabe theory, kAE can be 

expressed as a function of the friction angle of the backfill, , the wall batter, w, the backfill slope, b, the 

wall-backfill interface friction angle, d, and the seismic coefficient, kh, by the following equation: 

 

     

   

2

2

2

cos cos

sin sin

coscoscos 1

cos



























wbwd

wd

bww

w

AE k

11-2

where  is the seismic inertial angle and is given by: 

  h

k

1

tan

 

11-3

Mononobe-Okabe theory can also be used to calculate a seismic passive earth pressure coefficient. 

However, as discussed subsequently, the use of Mononobe-Okabe theory to predict seismic passive earth 

pressure is not recommended. Hence, the Mononobe-Okabe equation for seismic passive earth pressures 

is not presented herein. 

11.3.1.1 Limitations of Mononobe-Okabe Theory 

The use of the Mononobe-Okabe theory to evaluate seismic earth pressures is subject to a number of 

significant limitations. As noted above, Mononobe-Okabe theory should not be used to calculate seismic 

passive earth pressure under any conditions. The use of the Mononobe-Okabe theory to evaluate seismic 

active earth pressure assumes that the soil within the seismic active wedge is a uniform free draining 
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Seismic Design – Geotechnical Features 11-13 August 2011 

cohesionless material and that the backfill slope is uniform. However, the seismic active wedge can be 

significantly flatter than the active wedge for static conditions, particularly at high values for the seismic 

coefficient, kh. Figure 11-12 presents the inclination (to horizontal) of the seismic active wedge, aAE, 

versus seismic coefficient, kh, for backslope inclinations varying from horizontal to 2H:1V for a friction 

angle of 35o. 

Figure 11-12 Inclination of the Seismic Active Wedge for  = 35o (NCHRP, 2008) 

In practice the soil within the active wedge under seismic conditions is unlikely to be cohesionless or 

even uniform, except for small values of H and/or kh. In fact, the Mononobe-Okabe equation tends to 

“blow up” (give very large values of kh) for soils with steep backslope angles and/or high seismic 

coefficients. Furthermore, the backslope within the seismic active zone may not be uniform (even if the 

backfill composition is uniform) and the soil behind the wall may often have some cohesion (even if it is 

apparent cohesion). In these instances, earthquake-induced active pressure should be determined using 

either the Coulomb wedge method or the general equilibrium method as described subsequently. 

11.3.2 Trial Wedge Method 

The trial wedge method provides an alternate means of calculating seismic active earth pressures in cases 

where the Mononobe-Okabe equation does not apply. This includes cases where the soil within the active 

wedge is non-uniform or contains some cohesion or where the backslope angle is not uniform. The trial 
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Seismic Design – Geotechnical Features 11-14 August 2011 

wedge method is essentially the Coulomb active wedge method with a horizontal force equal to kh x Ws, 

where Ws is the weight of the soil within the wedge, applied at the centroid of the wedge to simulate the 

effect of seismic loading. For the conditions assumed by the Mononobe-Okabe method (uniform 

cohesionless soil with a constant backslope), the trial wedge method gives the same result as the 

Mononobe-Okabe equation. Trial wedge method solutions can be used for any wall adhesion and 

interface friction angle regardless of irregularity of the backfill and surcharges. Figure 11-13 shows the 

generalized geometry employed in the trial wedge method. 

Figure 11-13 Active Trial Wedge 

In Equation 11-4, the equations of force equilibrium have been solved for the trial wedge geometry shown 

in Figure 11-13 to develop an equation for PAE as a function of the angle of the trail wedge, an. The soil 

in Figure 11-13 is assumed to have a shear strength characterized by a friction angle  and a cohesion c 

and interface shear strength between the wall and the backfill is characterized by a wall-backfill interface 

friction angle d and an adhesion ca

. 
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Seismic Design – Geotechnical Features 11-15 August 2011 

        wdawd





tan1 tan cos

WT COH ADH PAE

11-4

where WT is the seismic earth pressure due to the weight of the wedge, COH is the reduction in seismic 

earth pressure due to soil cohesion, and ADH is the reduction in seismic earth pressure due to wallbackfill adhesion. WT is given by: 

    W a  kh WT tan

 

11-5

where W is the weight of the soil in the wedge. COH is given by: 

L c    cosaaa  COH 

n

tansin 

 

11-6

where Ln is the length of the surface upon which the cohesion acts (chord DE in Figure 11-13). ADH is 

given by: 

 tan    cos  sinwwa  ADH Lc aa

11-7

where La is the length of the surface upon which the adhesion acts (chord DB in Figure 11-13). For a 

vertical wall face without adhesion, Equation 11-4 reduces to: 

11-8

The trial wedge method is an iterative process. The failure plane angle, an, for the trial wedge is varied 

until the maximum value of the active earth pressure is computed using Equation 11-4 or 11-8. 

11.3.2.1 Influence of Cohesion on Seismic Active Earth Pressure 

   

 

P

AE = 

W k

h

tan( ) c L tan( ) sin cos

tan tan( ) * cos

 a  a a a

d  a d

     

1  

 
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Seismic Design – Geotechnical Features 11-16 August 2011 

One of the primary shortcomings of the Mononobe-Okabe method is that it cannot consider the effect of 

cohesion in the backfill on the seismic active earth pressure. Even relatively small amounts of cohesion 

in the backfill can significantly reduce the seismic active earth pressure. Sources of cohesion in backfill 

soils include both true cohesion due to inter-particle bonding and apparent cohesion due to capillary 

forces in the backfill. The influence of cohesion on the seismic active earth pressure is a function of the 

normalizing parameter c/H, where  is the unit weight of the backfill soil. Figure 11-14 presents a plot 

of the seismic active earth pressure coefficient, kAE, as a function of the normalizing parameter c/H and 

the seismic coefficient, kh, for a friction angle of 35o and for a uniform level backfill. An Appendix in 

NCHRP Report 611 presents additional plots for friction angles of 30o and 40o. 

Figure 11-14 Effect of cohesion on the seismic active earth pressure coefficient for  = 35o (NCHRP, 

2008) 

NCHRP Report 611 provides recommendations for the maximum amount of apparent cohesion that 

should be assumed for backfill soil as a function of the fines content of the soil. These recommendations 

are presented in Table 11-2.

TABLE 11-2 MAXIMUM AMOUNT OF APPARENT COHESION THAT SHOULD BE 

ASSUMED FOR BACKFILL SOILS (NCHRP, 2008) 

% (by weight) passing #200 sieve maximum apparent cohesion
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5 - 15 50 psf

15 - 25 100 psf

25-50 200 psf

11.3.3 Log Spiral Earth Pressure Theory 

The Mononobe-Okabe and Trial Wedge methods for calculating earth pressure assume that the failure 

surface in the backfill is planar. It has been long recognized that when there is a significant soil-wall 

friction angle, the assumption of the planar failure surface is incorrect. Instead, in a homogeneous soil a 

logarithmic surface gives the critical values for the active and passive earth pressure in a limit equilibrium 

analysis. Note, however, that when there is no wall friction the logarithmic surface degenerates to a 

planar surface. As illustrated in Figure 11-15, or the active case the difference between the critical log 

spiral surface and the critical planar surface is small enough that it can be ignored, even when there is 

wall friction. However, as illustrated in Figure 11-15, the critical log spiral surface for the passive case 

differs significantly from the critical planar surface when the wall friction angle is more than one-third the 

value of the backfill friction angle. In these cases it is essential to consider the logarithmic surface: 

failure to do so can result in an unconservative assessment of the seismic passive earth pressure. 

Figure 11-15 Critical Log Spiral Surfaces Compared to Planar Critical Surfaces 

The log spiral method can be used to evaluate seismic passive earth pressures accounting for backfill 

friction and cohesion, soil-wall interface friction angle, and backslope angle. Shamsabadi et al. (2007) 

describe the general method that can be used to do this. The soil-wall interface friction angle is a key 

parameter in this approach. The soil-wall interface friction angle for static loading is often assumed to 
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Seismic Design – Geotechnical Features 11-18 August 2011 

range from 50% to 80% of the soil friction angle. In the absence of any specific guidance or research 

results for seismic loading, NCHRP Report 611 suggests that a wall interface friction equal to 2/3rds of the 

soil friction angle be used to evaluate the seismic passive earth pressure. 

Figure 11-16 presents a plot of the seismic passive earth pressure coefficient versus seismic coefficient 

derived using the log spiral method for friction angles from 20o to 40o

for cohesionless soil and a wall 

friction angle (d) equal to 2/3rds of the friction angle of the soil in the passive wedge. 

Figure 11-16 Passive Seismic Earth Pressure Coefficient from the Log Spiral Method for Cohesionless 

Soil and d = 0.67 (NCHRP, 2008) 

Like the seismic active earth pressure, the effect of cohesion on the seismic passive earth pressure can be 

described using the normalizing parameter c/H. The Appendix of NCHRP Report 611 presents charts 

similar to Figure 11-16 for values of c/H equal to 0.05 through 0.25. 

Another important consideration when using the seismic passive earth pressure is the amount of 

deformation required to mobilize this force. The deformation required to mobilize the passive earth 

pressure during static loading is usually assumed to be 3% to 10% of the wall height (Shamsabadi et al 

2007). Similar guidance is not available for seismic loading and therefore the normal approach during 

design for seismic passive earth pressures is to assume that the displacement required to mobilize the 
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Seismic Design – Geotechnical Features 11-19 August 2011 

seismic passive earth pressure is the same as for static loading. Shamsabadi et al. (2007) suggest that 5% 

of the wall height to be used for granular backfill and 10% of the wall height to be used for cohesive 

backfill. 

11.3.4 General Limit Equilibrium Method 

Another alternative for evaluating seismic earth pressure is to use the general limit equilibrium (GLE) 

method. Any conventional slope stability program can be used to evaluate the seismic active earth 

pressure using this type of analysis. As illustrated in Figure 11-17, to evaluate the seismic active earth 

pressure for a specified seismic coefficient, the seismic coefficient is assigned to the backfill and an 

external force is applied at mid-height of the face of the backfill at an angle equal to the wall/backfill 

interface friction angle. The value of the external force is then increased until the factor of safety is equal 

to 1 to find the seismic active thrust. The method is described in more detail in NCHRP Report 611 

(NCHRP, 2008). 

Figure 11-17 General Limit Equilibrium Method for Evaluating the Seismic Active Earth Pressure 

(Chugh, et. al, 1995) 

In applying the GLE method, the engineer must make sure the geometry of the problem is set up 

appropriately, as some programs have a preferred direction in which failure is assumed to occur. In 

Figure 11-17, the failure is assumed to occur from right to left. 

The seismic passive earth pressure may also be evaluated using the GLE method. However, in applying 

this method, the engineer must make sure the geometry of the problem is set up appropriately to force a 
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Seismic Design – Geotechnical Features 11-20 August 2011 

passive failure in the soil. To determine the passive resistance for the slope shown in Figure 11-17, the 

slope geometry would have to be turned around so that the backfill was on the left hand side of the wall 

and the force applied to the face of the backfill was oriented from right to left. Again, the seismic 

coefficient is assigned as a pseudo-static load on the backfill and an external force is applied to the face of 

the backfill at an angle equal to the wall/backfill interface friction angle. The value of the external force is 

increased until the factor of safety is equal to 1, to find the seismic passive thrust, PPE. The height of the 

external force is varied between 0.3H and 0.6H from the base of the wall. The minimum value of PPE for 

the different application heights is used for design. 

11.4 SEISMIC EARTH PRESSURE COEFFICIENT 

11.4.1 Maximum Seismic Coefficients for Design 

The maximum seismic coefficient (kmax) for computation of seismic earth pressure shall be determined on 

the basis of the site class adjusted peak acceleration at the ground surface, FPGAPGA, as shown in 

Equation 11-9: 

PGAFkmax PGA 

11-9

where Fpga is the site factor for the PGA, discussed in Chapter 4. 

For the walls founded on AASHTO Site Class A and B, kmax shall be based on 1.2 times the site-adjusted 

peak ground acceleration coefficient as shown in Equation 11-10. 

kmax 2.1 PGA  PGAF

11-10

However, the values of kmax in Equations 11-9 and 11-10 are the maximum possible values and only apply 

to walls of less than 20 ft in height that cannot accommodate lateral displacement on the order of 1-2 

inches in the design earthquake. For walls 20 ft tall or higher, the value of kmax can be reduced to account 

for spatial incoherence (also referred to as wave scattering), or averaging of the ground acceleration over 

the active (or passive) wedge. For walls that can accommodate at least 1-2 inches of lateral displacement 

in the design earthquake, another reduction for system ductility (allowable lateral displacement) can be 
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Seismic Design – Geotechnical Features 11-21 August 2011 

applied. These adjustments can be applied to the maximum seismic coefficient to evaluate the design 

seismic coefficient, kh, in accordance with Equation 11-11: 

h Max

*a  krk

11-11

where r is the ductility (allowable lateral displacement) reduction factor and a is the height adjustment 

factor. 

11.4.1.1 Wall Height Adjustment Factor 

For values of H greater than 20 feet but less than 70 feet, the value of height adjustment factor, a, can be 

determined from Figure 11-18 for walls founded upon AASHTO Site Class C, D, and E soils. For 

retaining walls with AASHTO Site Class A and B foundations (rock sites), values from Figure 11-18

must be multiplied by 1.2. Figure 11-18 is essentially the same figure used to develop the heightdependent seismic coefficient for slope stability analysis discussed in Chapter 6. b is a parameter related 

to the seismic environment and is related to the site adjusted values of the peak ground acceleration and 

spectral acceleration at 1 second. Values of β less than 1.0 would be typically associated with seismic 

conditions in the East, firm ground conditions and lower acceleration levels, while values of β greater 

than 1.0 would be associated with the Western U.S., higher accelerations, and C or D site conditions. The 

curved lines in Figure 11-18 represent the results of numerical analyses while the straight lines represent 

engineering simplifications. 
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Figure 11-18 Wall height adjustment factor, a, vs. wall height (NCHRP, 2008) 

As reported in Chapter 6, the straight line simplifications for the wall height adjustment factor can be 

represented by the following equations: or site Category C, D, and E 

a  .01 01H  b 15.0

11-12

where H = slope height (feet) 

max1

11-13

b 

v

/ kSF

where Fv = site adjustment factor for 1 second spectral ordinates 

 S1 = USGS mapped 1 second spectral ordinate for site class B. 

For site categories A and B (hard and soft rock foundation soils) the values of α from Equation 11-12 

should be increased by a factor of 1.2. 
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11.4.2 Displacement-Based Seismic Coefficient 

If the earth retention system can be allowed to translate laterally, the seismic coefficient can be reduced to 

account for the ductility of the wall system. In the current AASHTO specifications, the allowable 

reduction is based upon the 1979 Richard and Elms displacement equation. This equation was based 

upon a rather limited number of model tests and numerical analyses. As discussed in Chapter 6 with 

respect to seismically-induced slope displacements, in NCHRP project 12-70 (as described in NCHRP 

Report 611) a pair of new seismic displacement equations were developed using a large database of 

strong motion records. These two equations (one for rock sites in the Eastern and Central US and one for 

the rest of the US) were developed using the Newmark method to calculate the permanent seismic 

displacement for each record and regression analyses. As discussed in Chapter 6, in the Newmark 

method permanent seismic displacement is a function of the yield acceleration, the acceleration at which 

seismic displacement is initiated. For a retaining wall, the yield acceleration is the seismic coefficient at 

which the horizontal forces (the demand) on the wall system equal the lateral resisting forces (its 

capacity). For instance, for the semi-gravity wall in Figure 11-12 the horizontal forces include the 

horizontal component of the seismic active earth pressure (PAEcosd) and the inertia forces on the wall 

itself (khWc) and the backfill over the heel of the wall (khWs), while the resisting forces include the 

frictional sliding resistance of the wall (HR) and the horizontal component of the seismic passive pressure 

on the toe of the wall (PPEcosd). The yield acceleration would be the seismic coefficient at which 

(PAEcosd + khWc + khWs) was equal to (HR + PPEcosd).

The NCHRP 12-70 displacement equations reported in Chapter 6 are repeated here for the sake of 

completeness. For all sites except Central and Eastern United State (CEUS) rock sites (i.e. except for 

CEUS Site Class A and B), displacement (in inches) can be estimated by:

    k PGV

k

k

k

k

d

y y

.1)log( 5 1 .0 7 4 log .3 2 7 1log log8.0 .1 5 9 log max

max max

 

















 



















11-14

For CEUS rock sites (i.e. for CEUS Site Class A and B), displacement (in inches) can be estimated by: 

    k PGV

k

k

k

k

d

y y

.1)log( 3 1 .0 9 3 log .4 5 2 1log .0 4 6 .1log 1 2log max

max max

 

















 



















11-15

 where: 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-24 August 2011 

 ky = Yield acceleration

PGV = Peak ground velocity 

When using Equation 11-14 or 11-15, it is necessary to estimate the peak ground velocity (PGV). Values 

of PGV in inch per second may be estimated using the following correlation between the PGV and 

spectral ordinates at one second (S1) for Site Class B. 

PGV  38 SF 1V

11-16

Note that the above displacement equations represent mean values and can be multiplied by 2 to obtain an 

84 percent confidence level. 

11.4.2.1 Displacement Ductility Adjustment Factor 

For rigid retaining wall systems that are not able to accommodate any lateral displacement in the design 

earthquake, and for wall systems in which critical displacement-sensitive facilities are located within the 

active wedge, no reduction in the seismic coefficient for wall displacement ductility is recommended (i.e. 

r = 1). However, many free standing retaining wall systems can accommodate lateral displacements in 

the design earthquake on the order of several inches, particularly if the performance standard is life safety. 

Extensive analyses conducted for the NCHRP 12-70 project using Equation 11-14 and 11-15 show that 

when the seismic coefficient is greater than or equal to 50% of kmax, the calculated seismic displacement 

is less than 1 inch. Therefore, for earth retention systems that are able to accommodate 1-2 inch of lateral 

displacement, it is recommended that the ductility reduction factor, r, be set equal to 0.5. For retaining 

wall systems that can accommodate more than 2 inches of lateral displacement in the design earthquake, a 

ductility reduction factor less than 0.5 may be used. To summarize these recommendations: 

 For rigid retaining wall systems that cannot accommodate any lateral displacement in the design 

earthquake and for retaining walls in which critical displacement facilities are located in the active 

wedge: 

max kkh a 

11-17
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-25 August 2011 

 For retaining wall systems able to accommodate 1-2 inches of lateral 

displacement in the design earthquake:

*5.0 max k k h a 

11-18

 For retaining wall systems able to accommodate more than 2 inches of lateral displacement in the 

design earthquake, the recommended approach is to evaluate the yield acceleration for a design that 

meets all static design requirements and then calculate the seismic displacement using Equation 

11-14 or 11-15. If this calculated seismic displacement is less than the established acceptable value 

(i.e. to the design criterion): 

*

max krkh a 

11-19

and 

max / kkr y

11-20

For cases where the retaining wall system can accommodate more than 2 inches of lateral displacement in 

the design earthquake (Equations 11-19), if the calculated displacement is significantly less than the 

acceptable value, the ductility reduction factor may be even greater than calculated using Equation 11-20. 

In this case, the engineer may wish to iteratively reduce the value of r until the calculated displacement 

equals the acceptable displacement. 

11.4.3 Walls with Backfill of Limited Extent 

There are many situations such as walls constructed in front of natural slopes where the existing ground is 

stable and stands without sliding and/ or caving where the backfill for a gravity or semi-gravity retaining 

wall is limited to a zone of lesser extent than the seismic active wedge. In these cases, either the trial 

wedge method or Equations 11-4 through 11-7, with an (the inclination of the trial wedge) equal to the 

angle between the stable natural slope and the horizontal, may be used to estimate the seismic active earth 

pressure imposed from the limited backfill zone on the wall. Further discussion of these cases is provided 

in NHCRP Report 611 (NCRHP, 2008). 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-26 August 2011 

11.5 GRAVITY AND SEMI-GRAVITY EARTH RETAINING STRUCTURE DESIGN 

Design of gravity walls must satisfy both external stability as well as internal stability. External stability 

modes include sliding, overturning (eccentricity), and bearing capacity. Internal and external stability 

modes of the failure for a semi-gravity earth retaining wall supported on a shallow foundation are shown 

in Figure 11-19. 

Sliding of the wall is simply due to the lateral thrust exceeding the lateral resistance. Most gravity and 

semi-gravity retaining structures can withstand substantial amounts of sliding displacement unless there 

are displacement-sensitive facilities (e.g. structures, utilities) located within the seismic active wedge 

behind or the seismic passive wedge in front of the wall. Overturning is of particular concern for tall 

walls with narrow footings. Excessive lateral thrust loads can induce unacceptable tilting and or rotation 

of the wall during a seismic event. 

Sliding

Overturning (Eccentricity)
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-27 August 2011 

Bearing Structural

Figure 11-19 Modes of Failure for a Semi-Gravity Earth Retaining Structure 

Bearing capacity failure is due excessive vertical loads but can be exacerbated by the increase is vertical 

stress at the toe of the wall due to the overturning moment induced by the lateral thrust on the wall. Loss 

of bearing capacity can also lead to overturning and or excessive tilting and settlement of the wall. 

Internal failure is generally not a concern with a gravity wall. Internal failure of a semi-gravity wall is 

due overstressing of the structural components of either the stem or base of the wall. Seismic loading has 

a twofold effect on the lateral earth pressure applied to the stem and foundation of the earth retaining 

system. In addition to the seismic load, the height above the base of the lateral earth pressure resultant 

(the lateral thrust) increases with respect to the base of the wall. This increase in the height of the 

resultant can lead to significant increases in bending moments within the stem of the wall and the toe and 

heel of the wall foundation. 

11.5.1 External Stability for Walls Supported on a Shallow Foundation 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-28 August 2011 

The procedure for external stability evaluation is essentially the same for gravity and semi-gravity 

retaining walls. The only difference between these two wall types with respect to external stability is that 

the soil above the heel of a semi-gravity wall is considered to be part of the wall for external stability 

evaluation purposes. The procedure for external stability evaluation of gravity and semi-gravity walls is 

as follows: 

1) Calculate seismic load and resistance as a function of backfill properties, PGA, and AASHTO Site 

Class (for the foundation material). 

2) Evaluate sliding. 

3) Evaluate eccentricity. 

4) Evaluate bearing capacity. 

5) Evaluate global stability. 

6) Evaluate maximum wall displacement and settlement. 

Sliding of the wall is due to excessive horizontal driving horizontal forces. The driving force is a result of 

horizontal seismic thrust load from the backfill (PAEcosd) and the horizontal seismic inertial loads from 

the wall itself (khWc) and, for a semi-gravity wall, from the soil above the heel of the wall (khWs). The 

resisting force is provided by the passive pressure in front of the wall (PPEcosd) and the shear resistance 

between the foundation base and foundation soil (HR). The seismic active thrust and passive resistance 

and the wall and soil inertial forces are a function of kh, which, in turn, depends upon the acceptable 

lateral displacement, as discussed in the previous section. For the wall to be stable, the summation of the 

factored driving force must be less than summation of factored resisting forces as shown in Equation 11-

21: 

  RQ n

11-21

 

where   Load Factors 

Q = Driving Forces

 

Rn =

Resistance Factors

Nominal Resisting Forces

The resistance against sliding can be written as: 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-29 August 2011 

R n RRRH epep  

 

11-22

 Where Rn = nominal sliding resistance against failure by sliding 

 = resistance factor for shear resistance between soil and foundation

Rτ = nominal sliding resistance between soil and foundation

 ep

= resistance factor for passive resistance 

 Rep = nominal passive resistance of soil in front of the toe (equal to PPEcosd)

For seismic loading, the load and resistance factors for sliding evaluation are all 1.0. If the soil beneath 

the footing is cohesionless, the nominal sliding resistance between soil and foundation is given as: 

b 

 NR tan

11-23

where   Summation of the normal forces acting on the base of the footing, including the vertical 

 components of PAE and PPE; and 

 b = Interface friction angle between the footing and soil 

For a wall system in which there is adhesion between the base and the foundation, an adhesion term must 

be added to Equation 11-23 for the nominal sliding resistance between the soil and the foundation. 

Furthermore, when the lateral thrust load on the wall is large, a shear key may be added to stabilize the 

wall against sliding, adding additional active thrust and passive resistance terms to the equation. 

However, the passive resistance in front of the wall may be neglected unless the wall extends well below 

the depth of frost penetration, scour or other types of disturbance. 

Eccentricity (wall rotation) is a particular concern for tall walls with narrow footings. The rotational 

stability of the wall depends upon the driving moment, MD, that tends to rotate the earth retaining system 

and the resisting moment, MR, that tends to resist wall rotation. MD is a function primarily of the driving 

seismic thrust and its line of action while MR depends to a large extent upon wall geometry. Whether or 

not the eccentricity of the wall system is acceptable is evaluated based upon the location of the resultant 

force, N, at the base of the footing (which depends upon both MD and MR). For the seismic case, the 

location of the resultant force, N, should be within B/4 of the foundation centroid for foundations on soil, 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-30 August 2011 

and within 3B/8 of the foundation centroid for foundations on rock. Equation 11-24 may be used to 

calculated wall eccentricity. 

N

B MM

e

 RR



2

11-24

For a wall founded on soil, bearing capacity is evaluated by comparing the factored maximum bearing 

stress at the toe of the wall to the factored nominal foundation material bearing resistance. The procedure 

for evaluating the nominal bearing resistance, qn, is given in AASHTO (2007) Section 10.6.3.1 and 

10.6.3.2. 

The maximum bearing stress shall be calculated assuming a linearly distributed pressure over an effective 

base area. If e < B/6, the resultant vertical force is within the middle one-third of the wall base and the 

bearing stress distribution on the bottom of the footing is trapezoidal. In this case, the maximum bearing 

stress v max can be found as: 















B

e

B

N

v

6

 max 1

11-25

If e > B/6, the resultant vertical force is outside the middle one-third of the wall base and the bearing 

stress distribution is triangular. In this case, the maximum bearing stress v max can be found as: 

  eB

N

v

23

4

max



 

11-26

Equation 11-21 is also the governing equation for bearing capacity evaluation, except that the seismic 

load, Q, is the maximum bearing stress, v max, the load factor for bearing stress is 0.67, and the nominal 

seismic resistance, Rn, is the nominal bearing resistance, qn. Therefore, employing a load factor of 1 for 

the seismic case, the bearing capacity criterion can be written as: 

 0.67 qn > v max 11-27 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-31 August 2011 

The use of a resistance factor of 0.67 for the nominal bearing stress, recommended in NCHRP Report 

611, is intended to provide reserve resistance against permanent rotation or tilt of the wall in the design 

earthquake. 

Global stability refers to the stability of the entire earth retaining wall system, including the soil behind 

the wall and below wall footing. Global stability analysis is typically performed using a commercially 

available slope stability computer program. 

The lateral displacement limits for the retaining wall system is implicit in the selection of the seismic 

coefficient, kh. For most gravity and semi-gravity walls, a ductility factor, r, equal to 0.5 can be used as 

this type of wall can easily accommodate 1-2 inches of lateral displacement. However, if critical facilities 

are located in front of or behind the wall it may be prudent to use a ductility factor of 1.0 and ductility 

factors of less than 0.5 may be appropriate for wall systems that can accommodate more than 2 inches of 

lateral displacement. Vertical settlement of both the backfill and the foundation soil due to seismic 

loading must be evaluated using the methods discussed in Chapter 6 and compared to allowable values to 

complete the external stability assessment. 

11.5.2 Internal Stability Assessment of Semi-Gravity Cantilever Retaining Walls 

Semi-gravity cantilever retaining walls must also be designed to satisfy two internal failure criteria. This 

type of wall consists of two structural elements: the stem and the footing. The footing must be wide and 

thick enough to provide adequate external and internal stability for the wall. The thickness of the stem 

and footing must be sufficient to resist the shears and moments due to the seismic loads. 

The lateral thrust load on the stem can create a tensile force on the back face of the stem and a 

compressive force on the front of the stem, causing the stem to bend away from the backfill. The 

exaggerated deformed shape of the wall as a result of thrust loads is shown in Figure 11-20. The heel of 

the footing supports a large amount of backfill weight as well as the vertical component of the thrust 

loads, while the soil bearing pressure acting at the bottom of the heel is very small due to the eccentricity 

of the normal force on the base induced by the seismic thrust. This will cause the footing to bend concave 

downward, creating a tensile stress at the top surface and a compressive stress at the bottom surface of the 

heel. The bearing pressure at the bottom surface of the toe is relatively large compared to the weight of 

the soil resting at the top surface of the toe. This causes the toe to bend concave upward, creating a tensile 

stress at the bottom surface of the toe and a compressive stress at the top surface of the toe. 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-32 August 2011 

Since the concrete has low tensile strength, reinforcement is required on the tension sides of all the wall 

components. Thus, reinforcement is required at the backfill face of the stem, the top of the heel and 

bottom face of the toe. In wall design, it is assumed that the stem, the heel and the toe all behave like a 

cantilever beam with fixed ends located at sections ac, ab and cd in Figure 11-20. 

The thickness and the required reinforcement of the stem, the heel and the toe is controlled by the induced 

shear and moment from the lateral thrust loads, the backfill vertical weight and vertical component of the 

lateral thrust loads and the bearing pressure, respectively. 

Passive

Active

Water 

Pressure

Bearing Pressure

Ws

Fs

Wc

Fc

a

b

c

d

Fs and Fc -Seismic Inertial Loads

Passive

Active

Water 

Pressure

Bearing Pressure

Ws

Fs

Wc

Fc

a

b

c

d

Fs and Fc -Seismic Inertial Loads

Figure 11-20 Combined Thrust Loads and Deformed Shape of Cantilever Wall 

In structural design of the wall, the factored seismically induced shear forces and bending moments 

computed at the critical sections of the wall are compared to the factored seismic resistance of these 

elements. The seismically induced inertia forces applied to the stem, footing and the soil above the heel 

must be included in the calculation of maximum shear forces and moment. The critical sections for a castin-place concrete wall are shown in Figure 11-21. 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-33 August 2011 

Since the horizontal inertia load, Fs, of the soil above the heel reduces the moment at section cd of the 

heel, it is generally not considered in the heel design. 

The reinforcement for a semi-gravity retaining wall is generally detailed by a structural specialist. 

Mh

d g

c

V

Pah

P’ah

P’av

Pav

Ms

Mt

Mh

a c

b d

V Mt



f

a

b

c

d

f

g



P’ah

P’av

Ws

Fs

Wc

Fc

Ws

Fs

Mh

d g

c

V

Pah

P’ah

P’av

Pav

Ms

Mt

Mh

a c

b d

Ms

Mt

Mh

a c

b d

V Mt



f

a

b

c

d

f

g



P’ah

P’av

Ws

Fs

Wc

Fc

Ws

Fs

Figure 11-21 Forces Acting at the Critical Sections of the Wall 

11.5.3 Gravity and Semi-Gravity Retaining Walls on Piles 

Retaining structures may be constructed on pile foundations when the soil for a considerable depth 

beneath the base of the wall is too weak or compressible to provide adequate support for the wall. A pilesupported retaining wall is illustrated in Figure 11-22. Note that for the wall illustrated in Figure 11-22, 

the piles in the front two rows are battered to resist the horizontal components of the lateral earth 

pressure. If batter piles are employed to support the wall, most of the lateral loads are carried as axial 

loads in the batter piles (due to the much greater stiffness of batter piles in axial loading compared to 

vertical piles subject to a lateral load). However, the heads of the batter piles still must be designed to 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-34 August 2011 

resist the moments induced in these piles by lateral loading. The moment induced on the footing by 

seismic loading is also assumed to be carried by the foundation piles as axial loads. 

Figure 11-22 Pile Supported Retaining Wall 

Because of the rigidity of pile supported foundations, a ductility factor of 1.0 is recommended for design 

of gravity retaining walls supported on piles unless a deformation analysis is conducted to determine the 

associated seismic displacement of the system. If a displacement analysis is conducted, an iterative 

analysis: seismic loads based upon an initial estimated ductility factor of 0.5 are applied to the wall 

system and the resulting lateral displacement of the pile-supported wall system is calculated. If this 

displacement is not between 1- 2 inches, the ductility reduction factor should be changed (increased if the 

calculated displacement is less than 1 inch, decreased if it is greater than 2 inch) and the seismic loads and 

displacements re-calculated. The new displacement should be compared to a displacement calculated 

using Equation 11-14 or 11-15 a yield acceleration ky equal to (r x FPGAPGA) for compatibility with the 

displacement calculated based upon the seismic forces. This process continues until convergence. 

11.6 DESIGN OF CANTILEVER AND ANCHORED EARTH RETAINING STRUCTURES 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-35 August 2011 

Cantilevered and anchored earth retaining systems are constructed of vertical structural members with an 

above-ground height, H and an embedded depth D. The vertical support members may be soldier piles 

spaced at a distance, S, or continuous sheet piles. Both types of systems are illustrated in Figure 11-23. 

Figure 11-23 Cantilevered and Anchored Earth Retaining Systems 

11.6.1 Non-Gravity Cantilevered Earth Retaining System 

Non-gravity cantilevered walls include both soldier pile and sheet pile wall systems. Soldier piles may be 

constructed with driven steel piles, cast-in-place reinforced concrete drilled piers, or treated timber, 

precast concrete, or steel piles placed in drilled holes and backfilled with concrete. Soldier pile walls are 

faced with either treated-timber, reinforced shotcrete, reinforced cast-in-place concrete, precast concrete 

panels, or metal panels. Continuous sheet pile walls may be constructed with driven precast pre-stressed 

concrete sheet piles or steel sheet piles. Non-gravity cantilevered walls depend on the passive resistance 

of the foundation material against the embedded potion of the wall and the moment resisting capacity of 

the vertical structural members for stability. Therefore, the maximum height of these walls is limited by 

the competence of the foundation material and the moment resisting capacity of the vertical structural 

members. The economical height of this type wall is generally limited to a maximum height of 18 feet. 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-36 August 2011 

The simplified seismic lateral earth pressure distribution shown in Figure 11-24 may be used for design of 

cantilever earth retaining systems (NCHRP Report 611). The seismic active earth pressure is distributed 

uniformly above the excavation line (NCHRP Report 611). The hydrostatic water pressure is assumed to 

be zero. Furthermore, the active lateral earth pressure acting over the wall height (H) shall not be less 

than 0.25 times the effective overburden pressure at any depth, or 0.035 KSF/FT of wall height, 

whichever is greater. 

PAE1 Psur

PAE2

PAE3 PPE1

ae

a1 ssur

p1 a2

D H

Figure 11-24 Seismic Load Distribution for Non-Gravity Cantilever Retaining Walls 

For a sheet pile wall, the load distribution shown in Figure 11-24 can be used directly to design the wall. 

For a solider pile wall, the load diagram must take into account the spacing between the soldier piles and 

the effective width of the embedded soldier piles. For the above-ground section of the soldier pile, the 

earth pressure and water pressure diagrams are multiplied by the soldier pile spacing, S, to get the load on 

each soldier pile. Below grade, the active soil pressure acts only on the width of the soldier pile but the 

passive pressure is assumed to act on an effective width that is greater than the actual soldier pile width. 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-37 August 2011 

The width of the soldier pile maybe taken as the diameter of the drilled-hole when structural concrete is 

used. 

Arching of the soil between soldier piles can increase the effective width of a soldier pile to as much as 3 

times the width of the element (AASHTO, 3.11.5.6). In competent cohesionless soil, a factor of three is 

used to calculate the effective width in the passive zone as long as the center-to-center spacing of the 

solider piles exceeds 3.75 feet (for spacing less than 3.75 feet, the factor is 0.8 times the spacing). 

However, if the soldier pile is embedded in stiff clay, the factor used to develop the effective width is 2 

and for soft clay (clay in which the undrained shear strength greater than 3 times the in situ vertical 

normal stress), soil arching will not occur and the actual width shall be used as the effective width for 

passive resistance. Where a vertical element is embedded in rock (AASHTO, Figure 3.11.5.6-2) the 

passive resistance of the rock is assumed to develop through the shear failure of a rock wedge equal in 

width to the vertical element, b, and defined by a plane extending upward from the base of the element at 

an angle of 45°. 

A ductility reduction factor of 1.0 is recommended for design of non-gravity cantilever walls unless a 

demonstration of the ability of the wall to sustain displacement is provided and the owners’ permission is 

obtained. With a demonstration of the ability to sustain displacement and the owner’s permission, a 

displacement-based ductility reduction factor may be used for the seismic active pressure above the 

ground surface in front of the wall. Furthermore, due to the deformation required to mobilize the passive 

resistance, it is recommended that a passive resistance equal to PPE/1.5 be used in design. 

The following procedure is used for the seismic design of a cantilever retaining wall: 

1) Calculate the surcharge loads above the excavation line and the Active/Passive earth pressures to 

some arbitrary point depth below the excavation line. 

2) Find the embedment depth DO at which the moment due to the seismic passive earth pressure on the 

left hand side of the wall (PPE1) is balanced by the moments due to the seismic active earth 

pressures and surcharge pressures on the left hand side of the wall (PAE1, PAE2, PAE3, and PSUR), i.e. 

where the sum of the moments due to the earth pressures is zero.. 

3) Increase DO by 20 percent (D = 1.2DO) 

4) Calculate the resultant force on the wall, R, by summation of all of the forces in horizontal 

direction: if R is larger than zero, increase D until R = 0. 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-38 August 2011 

5) Use the resulting pressure diagram to calculate the Maximum Bending Moment (MMAX) and 

Maximum Shear Force (VMAX) for design of the vertical structural member and lagging. 

11.6.2 Anchored Walls 

Anchored walls are typically composed of the same elements as non-gravity cantilevered walls but derive 

additional lateral resistance from one or more levels of anchors. The anchors are typically ground 

anchors (tiebacks) consisting of drilled holes with prestressing steel tendons extending from the wall face 

to an anchor zone located behind potential failure plane (i.e. behind the active wedge) in the retained soil 

or rock mass, as illustrated in Figure 11-25. The tendons are typically grouted over the section of the hole 

in the active zone (the bonded length), then prestressed, and then grouted over the balance of the hole for 

corrosion protection (the unbonded length). Other support systems include deadman anchors and, in rare 

instances for permanent walls, external bracing. An anchored wall includes an exposed design height (H) 

over which the soil is retained, as well as, an embedded depth (D) which provides vertical and lateral 

support. 

ACTIVE ZONE

L1 L2



D

H

d

ACTIVE ZONE

L1 L2



D

H

d

Failure 

Surface

Figure 11-25 Lateral Earth Pressure for Anchored/Braced Walls 

where L1 = Unbonded Length

L2 = Bonded Length

d = Diameter of Drill Hole

D = Wall Embedment Depth

H = Wall Height
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-39 August 2011 

 = Tieback Inclination Angle

The lateral earth pressure distribution for seismic design of a single level braced/tieback wall, developed 

in accordance with the recommendations in NCHRP Report 611, is shown in Figure 11-26. The 

maximum ordinate (a) of the trapezoidal seismic pressure diagram is determined as follows: 

H

P

a

3

2

 

11-28

where the total active earth pressure, P, is found as: 

PP AE  3.1

11-29

The active earth pressure PAE above the excavation line is best determined using the generalized 

equilibrium method as soil conditions are likely to be c - phi materials and stratified. 

A ductility reduction factor of 1.0 is recommended for design of single anchor walls. Use of a 

displacement-based ductility reduction factor is not recommended. As recommended for non-gravity 

cantilever walls, due to the deformation required to mobilize the passive resistance, it is recommended 

that a passive resistance equal to PPE/1.5 be used in design. The following procedure can be used for the 

design of a Single Tieback/Brace System wall: 

1) Determine the seismic active and passive earth pressure coefficients using the methods described in 

Section 11.3. Reduce the passive coefficient by 1.5 to account for the large displacement required 

to fully mobilize passive resistance. 

2) Convert the seismic active earth pressure above the excavation line to a trapezoidal pressure 

distribution 

3) Take a moment about the tieback to calculate embedment depth, D. 

4) Apply force equilibrium in the horizontal direction (set the sum of the horizontal forces equal to 

zero) to calculate tieback/brace force, T.

5) Calculate Maximum Bending Moment (MMAX) and Maximum Shear Force (VMAX) for design of the 

vertical structural member and lagging. 

The bonded length of the tieback should be located behind the actual failure surface. 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-40 August 2011 

Figure 11-26 Single Tieback System 

The lateral active horizontal earth pressure for a multilevel anchored wall, developed in accordance with 

the recommendations in NCHRP Report 611, is shown in Figure 11-27. The maximum ordinate of the 

trapezoidal seismic pressure distribution for a multiple tieback wall may be calculated as follows. 

 















1 1

3

1

n

a

HHH

P



11-30

where P is again evaluated in accordance with Equation 11-29 as 1.3 times the seismic active earth 

pressure. 
FHWA-NHI-11-032 11-Earth Retaining Structures 

Seismic Design – Geotechnical Features 11-41 August 2011 

Figure 11-27 General Pressure Distribution for Tieback Retaining Walls 

Similar to single anchor walls, a ductility reduction factor of 1.0 is recommended for design of multiple 

anchor walls. Use of a displacement-based ductility reduction factor is not recommended. As 

recommended for non-gravity cantilever and single anchor walls, due to the deformation required to 

mobilize the passive resistance, it is recommended that a passive resistance equal to PPE/1.5 be used in 

design. 

Figure 11-28 shows a simple trapezoidal pressure diagram for a multiple tieback system. The vertical wall 

element is divided into three types of spans. 

 Starting Cantilever Span S1

 Interior Spans Sn

 Embedment Span SD
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Seismic Design – Geotechnical Features 11-42 August 2011 

Figure 11-28 Simple Seismic Pressure Distribution for a Multiple Tieback System 

The hinge method illustrated in Figure 11-29 is used to design multiple Tieback/Brace wall systems. The 

procedure may be described as follows: 

1. Take a moment M1 about the upper level tieback due to cantilever action of the soil pressure above 

the upper tieback 

2. Use combination of the moment, M1, and tributary area to calculate the remaining tieback loads 

except the last tieback load 

3. Take a moment about the last tieback to calculate embedment depth, D using a factor of safety of 

1.0 

4. Set summation of forces equal to zero in horizontal direction to calculate the last tieback force, Tn+1

5. Calculate Maximum Bending Moment (MMAX) and Maximum Shear Force (VMAX) for structural 

design of the vertical structural member and lagging. 
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Seismic Design – Geotechnical Features 11-43 August 2011 

Figure 11-29 Hinge Method for Tieback Design 

11.7 MECHANICALLY STABILIZED WALLS 

Mechanically stabilized earth (MSE) walls are composed of either metallic (inextensible) or geosynthetic 

(extensible) soil reinforcement in the soil mass and vertical or near vertical discrete modular precast 

concrete facing elements. Various aesthetic treatments can be incorporated in the precast concrete face 

panels. MSE walls behave as a gravity wall, deriving their lateral resistance through the dead weight of 

the reinforced soil mass behind the facing. 

MSE walls are typically used where conventional reinforced concrete retaining walls are considered, and 

are particularly well suited for sites where substantial total and differential settlements are anticipated. 

MSE walls can be used in both cut and fill applications. Because their base width is greater than that of 

conventional reinforced concrete walls they are most cost effective in fill applications. The practical 

height of MSE walls is limited by the competence of the foundation material at a given site. Due to the 

inherent flexibility of MSE walls they have performed exceptionally well during past earthquakes. 
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Seismic Design – Geotechnical Features 11-44 August 2011 

MSE walls are designed for both external stability and internal stability of the reinforced soil mass. 

Structural design of the wall facing may also be required. However, only external stability of MSE walls 

is addressed in this manual. Internal stability and facing design are discussed in a separate NHI document 

dedicated entirely to MSE wall design. 

The current method for seismic design of MSE walls in the AASHTO LRFD Bridge Design 

Specifications is based on pseudo-static analysis procedures. Relevant modes of external failure for MSE 

wall are shown in Figure 11-30. These modes of failure include: 

 Sliding 

 Eccentricity 

 Bearing Capacity 

 Global Stability 

The global stability of the wall, including vertical settlement, will not be discussed in this manual. 

 (a) Sliding (b) Overturning (eccentricity)

 (c) Bearing capacity (d) Global (Deep seated rotational) stability
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Figure 11-30 Potential External Failure Mechanisms for MSE Walls 

The design procedure for external stability of MSE walls may be described as follows: 

1) Calculate seismic loads 

2) Evaluate Sliding 

3) Evaluate Eccentricity 

4) Evaluate Bearing Capacity 

5) Evaluate Wall Displacement 

The design height of the MSE wall (for external stability computations) is the sum of the wall embedment 

depth and the wall height. Similar to the gravity retaining walls, for the design and analysis of MSE walls 

lateral seismic earth pressure, as well as, lateral inertial load of the reinforced soil mass must be 

considered. Figure 11-31 shows the forces acting on a MSE wall during a seismic event. 

5.0 H

H

`

H

SUR PAE P

q

B

HR

N

W

KhW

Figure 11-31 Pressure Diagram for MSE wall with Seismic Force 

Figure 11-32 shows the seismic active earth pressure acting on the back of the reinforced zone for the 

case of a sloping backslope. The procedures described in Section 11.3 are recommended to be used to 

determine the seismic active earth pressure on the backfill of a MSE wall, in place of the current 

AASHTO procedure. As MSE walls are inherently ductile structures, a ductility reduction factor of 0.5 

(for acceptable lateral displacements of 1-2 inches) or less (for acceptable displacements greater than 2 

inches) may be used to calculate the seismic coefficient for MSE wall design unless critical structures or 

facilities are located in front of or behind the wall. 
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Seismic Design – Geotechnical Features 11-46 August 2011 b

PAE H/2

h b

H

HR

N

Figure 11-32 Pressure Diagram for MSE Walls with Sloping Backslope 

The sliding resistance of a MSE wall is evaluated in the same way as it is evaluated for a gravity earth 

retaining structure. 

The eccentricity, eb, of an MSE wall can be calculated as shown in the equation below: 

b Xo

B

e 

2

11-31

where 

B = base width (length of reinforcement elements) and 

Xo = location of the resultant from the toe of the wall.

The parameter Xo is calculated as: 

 

N

MM

X

RE DR

o





11-32

where MRE= resisting moment due to vertical component earth pressure calculated about the toe of 

the wall; 

MDR = driving moment due to seismic horizontal earth pressure from ground and from live 

load surcharge calculated about the toe of the wall;

N = vertical weight of the reinforced soil mass and vertical component of the seismic 

earth pressure
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Seismic Design – Geotechnical Features 11-47 August 2011 

It should be noted that the effect of external loadings on the MSE mass, which increases sliding 

resistance, should only be included if the loadings are permanent (with the exception of traffic live loads, 

where a surcharge equal to 0.5 times the average daily truck traffic load is recommended (as discussed in 

Chapter 1). For eccentricity to be considered acceptable, the calculated location of the resultant vertical 

force should be within the middle half of the base (i.e., eb max = B/4).

Due to the flexibility of MSE walls and the inability of the flexible reinforcement to transmit moment, a 

uniform base pressure distribution is generally assumed beneath the base of the MSE wall over an 

equivalent footing width, B’, equal to the actual footing width, B, minus twice the eccentricity, eb (i.e. 

B’= B – 2eb).

 

Assuming a load factor of 1 for seismic loading, the design criterion for the bearing resistance (

R q

) for an 

MSE wall is given as: 

uniform qq n

11-33

 

 

where: 

φ = resistance factor = 0.67 per recommendations in NCHRP Report 611

qn =

quniform

nominal bearing resistance

uniform bearing pressure

 

11.8 SUMMARY 

This chapter describes the seismic design procedure for earth retaining systems. NCHRP Report 611 

(NCHRP, 2008) forms the basis of the recommendations provided herein. Seismic LRFD design for earth 

retaining structures should be done in general compliance with requirements for Extreme Event I. 

However, it is recommended herein to use a load factor of 1.0 for all permanent loads for LRFD seismic 

design of free standing earth retaining structures. Furthermore, it is recommended that a load factor of 0.5 

be applied to the average daily truck traffic (ADTT) load the earthquake live load but that no inertial 

component of the live load is considered in seismic design. 
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The seismic demand on retaining walls includes the seismic active thrust from the soil behind the wall 

and the inertial loading on the wall itself. Surcharge loads may also contribute to the demand. Sources of 

seismic resistance for retaining wall systems include seismic passive resistance in front of the wall, the 

frictional sliding resistance of the base of the wall, and the bearing resistance of the foundation soil for 

walls that rely on the base to serve as a spread footing, the axial and lateral geotechnical capacity of the 

deep foundation elements for retaining walls supported on deep foundations, and the structural resistance 

of the wall system. the active seismic thrust, PAE, and the seismic passive earth pressure, PPE, are 

functions of backfill properties, the wall and backfill geometry, and the seismic coefficient, kh, which in 

turn depends upon the site adjusted peak ground acceleration, FPGAPGA. In the absence of other 

information, PAE and PPE may be assumed to act at the midpoint of the wall height (NCHRP Report 611). 

The inertia loads acting on the wall, kh x Wc, and the inertia force acting on the soil above the heel of the 

wall, kh x Ws, are also a function of seismic coefficient, kh. Not all walls need be analyzed for seismic 

loading. Table 11-1 summarizes these conditions under which no seismic analysis is necessary for free 

standing earth retaining structures. 

The most common means of calculating seismic active thrust used in practice today is Mononobe-Okabe 

earth pressure theory. While Mononobe-Okabe theory can sometimes be used to calculate the seismic 

active pressure coefficient, the use of Mononobe-Okabe theory to predict seismic passive earth pressure is 

not recommended. Shortcomings of the Mononobe-Okabe method for calculating the seismic active earth 

pressure coefficient include inability to consider cases where the soil within the active wedge is nonuniform or contains some cohesion or where the backslope angle is not uniform. The trial wedge method 

provides an alternate means of calculating seismic active earth pressures in cases where the MononobeOkabe equation does not apply, including 

Even relatively small amounts of cohesion in the backfill can significantly reduce the seismic active earth 

pressure. Sources of cohesion in backfill soils include both true cohesion due to inter-particle bonding 

and apparent cohesion due to capillary forces in the backfill. Charts are available for a uniform backfill 

that include the influence of cohesion on the seismic active earth pressure as a function of the normalizing 

parameter c/H, where c is the backfill cohesion, H is the wall height, and  is the unit weight of the 

backfill soil, for values of c/H equal to 0.05 through 0.25. Recommendations are provided in Table 11-2

for the maximum amount of apparent cohesion that should be assumed for backfill soil as a function of 

the fines content of the soil. There are many situations such as walls constructed in front of natural slopes 

where the existing ground is stable and stands without sliding and/ or caving where the backfill for a 

gravity or semi-gravity retaining wall is limited to a zone of lesser extent than the seismic active wedge. 
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Seismic Design – Geotechnical Features 11-49 August 2011 

In these cases, either the trial wedge method or Equations 11-4 through 11-7, with an (the inclination of 

the trial wedge) equal to the angle between the stable natural slope and the horizontal, may be used to 

estimate the seismic active earth pressure. 

The log spiral method can be used to evaluate seismic passive earth. The soil-wall interface friction angle 

is a key parameter in this approach. Charts are available for a uniform backfill to evaluate the seismic 

passive earth pressure coefficient for a wall interface friction equal to 2/3rds of the soil friction for values 

of c/H equal to 0.05 through 0.25. 

Another alternative for evaluating seismic earth pressure is to use the general limit equilibrium (GLE) 

method. Any conventional slope stability program can be used to evaluate the seismic active and passive 

earth pressure using this type of analysis. 

The maximum possible seismic coefficient (kmax) for computation of seismic earth pressure is equal to the 

site class adjusted peak acceleration at the ground surface, FPGAPGA, For walls 20 ft tall or higher, the 

value of kmax can be reduced to account for spatial incoherence (also referred to as wave scattering), or 

averaging of the ground acceleration over the active (or passive) wedge and for walls that can 

accommodate at least 1-2 inches of lateral displacement in the design earthquake another reduction for 

system ductility (allowable lateral displacement) can be applied to evaluate the design seismic coefficient, 

kh. The same pair of seismic displacement equations used in seismic slope deformation analysis, one for 

rock sites in the Eastern and Central US and one all other cases, can be used to calculate the permanent 

seismic displacement is a function of the yield acceleration of the all system, the acceleration at which 

seismic displacement is initiated. Based upon these equations, a ductility reduction factor, r, equal to 0.5 

is recommended for earth retention systems that are able to accommodate 1-2 inch of lateral 

displacement. For retaining wall systems that can accommodate more than 2 inches of lateral 

displacement in the design earthquake, a ductility reduction factor less than 0.5 may be used 

Design of retaining walls must satisfy both external and internal stability criteria. Global stability of the 

wall system must also be considered. External stability modes include sliding, overturning (eccentricity), 

and bearing capacity. Internal stability includes consideration of shear and moment capacity of the 

structural elements of the wall system. While it is generally recommended to use load and resistance 

factors of 1.0 in seismic design, the use of a resistance factor of 0.67 for the nominal bearing stress and of 

0.8 for the lateral and uplift resistance of piles is recommended for LRFD seismic design. 
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Seismic Design – Geotechnical Features 11-50 August 2011 

Gravity and semi-gravity retaining walls and non-gravity cantilever walls may often be able to 

accommodate more than 1-2 inch of lateral displacement and thus may be designed using ductility 

reduction factors smaller than 0.5. However, anchored wall systems are relatively rigid and should be 

designed for a ductility reduction factor of 1.0 unless it can be demonstrated that the wall system 

(including the anchors) can tolerate displacements of 1-2 inch, in which case a ductility reduction factor 

of 0.5 may be used. While the seismic active earth pressure behind a gravity, semi-gravity wall, on nongravity cantilever wall may be taken as uniformly distributed over the wall height, the seismic earth 

pressure above the excavation line behind an anchored wall should be distributed in the same manner as 

the static active earth pressure. 
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Seismic Design – Geotechnical Features 12-1 August 2011 

CHAPTER 12

BRIDGE ABUTMENTS 

12.1 INTRODUCTION 

In current practice, LRFD seismic design of bridge abutments is often based on a displacement 

performance philosophy. This type of design necessitates that the geotechnical engineer predict the 

resistance of the abutment backfill soils to large displacements. Characterization of the inherently nonlinear stiffness of the abutment-backfill system is also necessary if the designer wishes to consider the 

interaction between the bridge superstructure and the abutments in the global bridge model. Note that the 

abutment wingwalls are usually designed as conventional retaining walls to retain the abutment backfills 

and are expected to yield or fail during a major seismic event (i.e. they do not contribute to the capacity of 

the bridge structure). The transverse capacity of the abutment is provided by the abutment shear keys. 

The displacement-based design philosophy in the AASHTO Guide Specifications for LRFD Seismic 

Bridge Design (AASHTO 2009) involves the design of ductile bridge structures that will resist 

earthquake loads in a predictable and quantifiable manner. While force-based design also generally 

involves the design of ductile bridge structures, ductility demand is not explicitly quantified in the forcebased approach. Bridge designs with ductile columns will impose large displacements on abutments and 

this may cause more damage to the abutments than the damage levels that have been observed in the past 

earthquakes. Furthermore, in many cases, bridge engineers ignore the contributions of the abutment 

resistance in seismic design of bridge structures due to the complexity of the abutment soil-structure 

interaction problem. However, proper evaluation and design of the contribution of the bridge abutments 

to the global response of the bridge can reduce the column displacement demand during earthquake 

shaking, thus leading to a more efficient and economical design. 

Measurements from instrumented bridges and results of large-scale field tests have demonstrated that the 

stiffness of the abutment-backfill system is a function of the mobilized displacement of the abutment wall. 

The abutment-backfill can not only provide significant lateral resistance but is also a good source of 

energy dissipation during large deformations due to nonlinear hysteretic behavior of the abutment-soil 

system. The abutment force-displacement relationship exhibits significant stiffness degradation at large 

displacements. Therefore, it is important for practicing engineers to realistically represent the relationship 
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Seismic Design – Geotechnical Features 12-2 August 2011 

between the mobilized passive resistance (force) of the backfill on the abutment wall and the abutment 

wall movement (displacement) for dynamic analysis of bridge structures. 

For modern highway bridges, backfill soils behind bridge abutments usually satisfy AASHTO (or State) 

specifications with regard to compaction and soil type. Therefore, abutment-backfill force-displacement 

models can be developed based upon typical backfill materials and material properties. AASHTO seismic 

design provisions provide simple bi-linear models for the abutment-backfill force-displacement 

relationship for typical backfill soils. Furthermore, data from recent field tests on bridge abutments with 

typical backfill soils discussed below provide an enhanced understanding of the characteristics of the 

force-displacement behavior of bridge abutment-backfill systems. This field data provides a basis for the 

development of a closed-form expression for the non-linear force-displacement behavior of bridge 

abutments. 

12.1.1 Types of Abutment 

A bridge abutment system consists of stem walls to support the bridge deck, wingwalls to retain the 

abutment-backfill, and footings or piles to support the stem wall and wingwalls. Abutments are basically 

classified into two types: (1) seat-type-abutments, and (2) monolithic abutments. A seat-type abutment is 

constructed separately from the bridge deck while a monolithic abutment is cast integrally with the 

superstructure. The bridge engineer is responsible for the selection of the bridge abutment type, taking 

into account the requirements for the service, strength, and extreme event limit states. 

12.1.2 Seat Type Abutment 

Seat-type-abutments are located at or near the top of approach fills and may be supported on piles or 

spread footings. As shown in Figure 12-1, seat-type abutments have a backwall with a depth sufficient to 

accommodate the bridge deck depth and the bridge deck rests on the abutment seat through bearings pads. 

Seat-type abutments may be classified as a short seat abutment (stemwall height less than 8 feet) or as a 

high cantilever abutment (stemwall height greater than 8 feet), as shown in Figure 12-2. 

During a seismic event, a bridge deck moves longitudinally and may collide with the abutment backwall. 

In an ordinary bridge designed to a life safety standard, the backwall may be designed to break off in the 

design earthquake in order to protect the foundation from inelastic action as a result of backwall 
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Seismic Design – Geotechnical Features 12-3 August 2011 

displacement. This type of abutment design allows the bridge engineers to control the amount force that 

is transferred to the abutment foundation (i.e. to capacity-protect the foundation). 

Figure 12-1 Seat-Type Abutment and Foundation System 

 (a) (b) 

Figure 12-2 Seat Type Abutments; a) Short Seat and b) High Cantilever 
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Seismic Design – Geotechnical Features 12-4 August 2011 

 

Abutment capacity is provided by the passive resistance of the abutment backfill. A typical highway 

bridge usually has a moderate back wall height in comparison to its width. This height to width 

relationship makes the earth pressure problem a plane strain problem and two-dimensional passive earth 

pressure solutions such as those discussed in Chapter 9 are generally sufficient to characterize the 

abutment-backfill capacity. 

12.1.3 Monolithic Abutment 

Monolithic abutments are cast integrally with the superstructure and are supported on either spread 

footings or pile foundations. A pile-supported monolithic abutment is shown in Figure 12-3. For 

monolithic abutments, the backwall engages the backfill immediately when the bridge is displaced 

longitudinally. Monolithic bridge abutments are classified as either short stem (H less than 14 feet) or 

high stem (H greater than 14 feet) abutments, as shown in Figure 12-4. 

Figure 12-3 Monolithic Abutment and Foundation System 
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Seismic Design – Geotechnical Features 12-5 August 2011 

 (a) (b) 

Figure 12-4 Monolithic Abutment Types; (a) Short Stem and (b) High Stem 

There is no relative displacement allowed between the superstructure and abutment. All the superstructure 

forces at the bridge ends are transferred to the abutment backwall and then to the abutment backfill and 

foundations. The lateral force-deformation capacity of a monolithic abutment is a function of abutment 

backfill properties as well as the foundation and structural capacity of the abutment backwall. As opposed 

to a seat-type abutment, a monolithic abutment wall may have to sustain large forces during a major 

seismic event if the backwall capacity is greater than the passive resistance of the backwall. However, if 

the backwall has been designed to be weaker than the passive earth pressure exerted by the abutment 

backfill, the effective abutment height is limited to the depth of the bridge deck and the resistance of the 

abutment is controlled by the passive resistance associated with this effective backfill height. 

12.1.4 Mechanism of Abutment Backfill Failure 

When an abutment wall is loaded by a horizontal force, F, the wall movement is resisted by the mobilized 

passive resistance of the abutment backfill. This mobilized passive resistance is a function of relative 

displacement  between the wall and the backfill, as illustrated in Figure 12-5. When the displacement 

becomes large enough (ult), the shear strength of the backfill will be fully mobilized and the ultimate 

passive backfill capacity Fult develops. For intermediate levels of displacement (<ult), the shear 

strength of the backfill is not be fully mobilized and therefore an intermediate passive resistance force F is 

developed. 
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Seismic Design – Geotechnical Features 12-6 August 2011 

(a) Force-Displacement Relationship 

(b) Stress-Strain Relationship 

Figure 12-5 Mobilization of Passive Resistance (Shamsabadi, 2007) 
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Seismic Design – Geotechnical Features 12-7 August 2011 

Post earthquake investigations and full scale field experiments have shown that during a major seismic 

event mobilized passive wedges will form within the abutment backfill. The effect of an actual 

earthquake pushing a bridge deck into the abutment-backfill is shown in Figure 12-6. Figure 12-6 shows 

surface cracks that developed in the roadway pavement behind the northern (77-feet wide, near-normal 5o

skew) abutment of the Shiwei Bridge in Taiwan during the Chi-Chi earthquake (Kosa et al., 2001). This is 

an example of the mobilized passive wedge formation when a bridge superstructure has been pushed into 

the abutment-backfill due to longitudinal seismic excitation 

Figure 12-7 shows another example of formations of mobilized passive wedges and the associated 

abutment damage from the June 2001 Attica earthquake in Peru. The north abutment of the Puente Los 

Banos Bridge (a three-span continuous RC box girder structure supported on two-column bents and seattype abutments) experienced significant displacement and rotation in this event. The top of the abutment 

was pushed back by the impact from the superstructure. Since there was not sufficient lateral embankment 

resistance, the bottom of the abutment moved forward, pushing out the slope paving and imposing high 

flexural and shear demand on the abutment piles. 

.

Figure 12-6 Formations of Mobilized Passive Wedges (Kosa et al., 2001) 
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Seismic Design – Geotechnical Features 12-8 August 2011 

Figure 12-7 Puente Los Banos Bridge 

12.1.5 Typical Backfill Soil Behavior 

As part of the California Department of Transportation (Caltrans) seismic safety research program, a 

state-wide research study on abutment backfill characterization was performed in 2004 (Kapuskar et al. 

2005). The purpose of this study was to develop typical soil properties for bridge abutment backfills in 

California, with the ultimate goal of developing soil-specific abutment load-deformation relationships that 

could be used for improved bridge design. The study involved a review of 115 sets of bridge plans statewide and geotechnical investigation of the abutment backfill at 11 typical bridges sites. The field 

investigations consisted of soil borings with sampling, CPT soundings with shear wave velocity 

measurement, pressuremeter testing, and data analysis. 

Laboratory testing was conducted on soil samples from the 11 bridge sites and on samples provided by 

Caltrans from four additional bridge sites. Testing included in-place moisture and density, gradation, 

plasticity index, expansion potential, sand equivalent, modified Proctor compaction, direct shear, and 

cyclic triaxial testing. The data was grouped into 4 characteristic backfill soil types: clean sands, silty 

sands, clayey sands, and cohesive soils (the majority of backfills were found to be silty sands with 

gravels). Representative geotechnical properties were assigned to each soil type. Results from laboratory 

cyclic triaxial tests indicated that the stress-strain behavior was nonlinear from the very early stages of the 

loading and that stiffness decreased and irreversible plastic strain increased with increasing load 

amplitude for all the backfill soil types. 
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Seismic Design – Geotechnical Features 12-9 August 2011 

12.1.6 Full Scale Abutment Loading Tests 

The behavior of typical bridge abutment-backfill systems have been studied experimentally on full-scale 

bridge abutments field tests conducted by the University of California at Los Angeles (UCLA) and the 

University of California at Davis (UCD) as part of the Caltrans seismic safety research program. These 

field tests provide insight on the performance of abutment-backfill systems as well as data for 

development of backfill-abutment force-displacement models. 

12.1.6.1 UCLA Abutment Experiment 

A University of California, Los Angeles (UCLA) research team performed a full-scale cyclic load test on 

a 15 foot-wide seat-type abutment wall with a height of 5.5 feet and a silty sand backfill (Stewart et. al., 

2007). The backfill was placed in layers and compacted to over 95% Modified Proctor dry density. The 

compacted backfill extended longitudinally about 3 times the backwall height. Before loading the 

abutment, 3-inch diameter vertical holes were drilled along the longitudinal centerline of abutment 

backfill and filled with the gypsum columns, as shown in and Figure 12-8. The abutment wingwalls were 

constructed using smooth plywood and plastic sheeting was placed at the interior face of the wingwalls to 

minimize friction and thereby simulate a plane strain condition. 

In the load test, the backwall was pushed horizontally in between the abutment wingwalls without any 

vertical component. After the completion of the test, a longitudinal trench was excavated and the failure 

mechanism of the backfill was carefully mapped using the gypsum columns and cracks in the compacted 

soil to identify the local passive wedges mobilized along the abutment backfill. The observed crack 

patterns in within the abutment backfill are highlighted in Figure 12-8b. En echelon passive wedges start 

from near the top of the abutment wall and progress down to the base of the wall, breaking the ground 

surface progressively further away from the top. The final failure surface extended from the bottom of 

the abutment backwall and intersected the backfill surface at about 3 times the height of the backwall. The 

width of the surface rupture zone and displacement of the gypsum columns indicated that the final failure 

surface was manifested as a shear band, or zone of intense shearing, which formed a log spiral failure 

surface, as shown in Figure 12-8b. The ultimate capacity of the abutment backfill was measured to be 

approximately 480 kips at a lateral displacement of about 2.5 inches followed by a residual capacity of 

about 475 kips at a lateral displacement of about 3.5 inches (Stewart et. al 2007). 
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Seismic Design – Geotechnical Features 12-10 August 2011 

Figure 12-8 Full Scale Abutment Experiment with Silty Sand Backfill 

12.1.6.2 UCD Abutment Experiment 

A full-scale abutment load test was conducted on a monolithic abutment at the University of California, 

Davis (UCD). Cyclic longitudinal loading of increasing amplitude was applied to the 5.5 foot-high pile –

supported abutment wall until failure. Figure 12-9 shows the test abutment configuration and Figure 12-

10 shows the loading ram (Romstad et al., 1995, Maroney et al., 1994). The backfill for this test consisted 

of compacted Yolo Loam clay. 
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Seismic Design – Geotechnical Features 12-11 August 2011 

Figure 12-9 UCD Abutment Field Test 

Figure 12-10 UCD Abutment Test Loading Setup 

Before the loading the test abutment, 3-inch diameter vertical holes were drilled along the longitudinal 

centerline of the abutment backfill and filled with liquid Styrofoam, as illustrated in Figure 12-11. After 

the completion of the test, a longitudinal trench was excavated through the backfill and the backfill failure 

mechanism was carefully mapped using the displacement of the styrofoam columns as a guide (Romstad 
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Seismic Design – Geotechnical Features 12-12 August 2011 

et al., 1995). The approximate idealized failure surface mapped using the Styrofoam columns as a guide is 

shown in Figure 12-11. Maroney (1995) reported that the failure surface extended from the bottom of the 

abutment backwall at initially a zero slope upward to the embankment surface with increasing slope, 

intercepting embankment surface at a distance behind the wall approximately equal to twice the height of 

the backwall. 

(a) Plan 

(b) A-A Section 

Figure 12-11 Failure Mechanism of the UCD Abutment Test 
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Seismic Design – Geotechnical Features 12-13 August 2011 

12.2 MODELING OF REGULAR (NON-SKEWED) ABUTMENTS 

The complex nonlinear force-displacement response of bridge abutments subject to seismic loading is 

usually idealized using a simple, bi-linear relationship. Furthermore, presumptive values are often used to 

calculate this bi-linear relationship. The bi-linear relationship is then used to model the nonlinear 

behavior of the backfill as a set of independent horizontal springs, as illustrated in Figure 12-12. Various 

numerical simulations have been developed and calibrated using full-scale abutment experiments to 

develop simplified procedures for seismic analysis of bridge abutments. However, more realistic nonlinear force-displacement models have recently been developed to better characterize the seismic 

performance of abutment-backfill systems. Furthermore, advanced two- and three-dimensional models 

that employ the Finite Element (FE) method have been employed to investigate the mechanisms of 

backfill failure. Brief descriptions of each model are presented in the following sections. 

Figure 12-12 Bridge Model for Seat-Type Abutment with an Expansion Gap 

12.2.1 Bi-linear Model 

The bi-linear abutment force-deformation relationship assumes linear elastic stiffness, KAbut, for all stress 

states below the backfill capacity (i.e. the passive resistance of the backfill). Once the backfill capacity, 

FUlt, is reached, the abutment resistance remains constant with increasing displacement, d, as shown in 

Figure 12-13. For a seat-type abutment, an initial displacement equal to the gap between the bridge deck 

and the backwall, gap in Figure 12-13, is required to mobilize the backfill resistance. For design 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-14 August 2011 

purposes, the stiffness of seat-type abutment is then characterized by the effective abutment stiffness, Keff, 

as illustrated in Figure 12-13. 

 

KAbut

Keff

FUlt

eff

gap

F

d

KAbut

Keff

FUlt

eff

gap

F

d

KAbut

Keff

FUlt

eff

gap

F

d

Figure 12-13 Bi-Linear Abutment Force-Deformation Relationship 

The abutment passive capacity may be calculated using the methods for evaluating the passive resistance 

discussed in Chapter 9 (subject to certain limitations discussed subsequently). However, in bridge 

engineering practice, it is common to use a presumptive value to calculate the abutment capacity for 

seismic analysis and design. Section 5.2.3 of the AASHTO LRFD Guide Specification (AASHTO 2009) 

provides the following recommendations for the passive soil pressure, pp, for backfill compacted to at 

least 95% of the modified Proctor maximum dry density: 

 for cohesionless soil with less than 30%, by weight, passing the #200 sieve: 

pp = 2H/3 ksf 12-1a

 

where H is the wall height in feet; and 

 for cohesive soil with greater than 15% clay-sized particles and an undrained shear strength of at 

least 4 ksf: 

pp = 5 ksf 12-1b
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-15 August 2011 

Note that pp is the passive earth pressure and must be multiplied by the wall area to get the passive 

resistance, PP. Also note that the AASHTO LRFD Guide Specifications state that owner’s approval 

should be obtained if the engineer is going to rely upon a passive resistance greater than 70% of the 

presumptive passive resistance in seismic design (AASHTO 2009). 

 

The abutment-backfill stiffness, KAbut, is calculated by assuming that the passive resistance is mobilized at 

a deformation equal to the wall height, H, times the presumptive displacement factor FW presented in 

Table 12-1. The abutment stiffness is therefore given by the following equation: 

KAbut = PP/[H x FW] 12-2

TABLE 12-1 PRESUMPTIVE DISPLACEMENT FACTORS, FW (AASHTO 2009) 

Soil Type Dense Sand Medium 

Dense Sand

Compacted 

Silt Loose Sand Compacted Clay

FW 0.01 0.02 0.04 0.05 0.05

12.2.2 Non-Linear Hyperbolic Abutment Stiffness Relationship 

Shamsabadi et al. (2007) summarized load-deflection test data from model tests and full-scale tests for a 

variety of structural backfills and concluded that the abutment- backfill load-displacement curve is 

approximately hyperbolic in shape, as shown in Figure 12-14. In the Shamsabadi et al. (2007) hyperbolic 

model illustrated in Figure 12-14, Fult, the maximum abutment capacity, is developed at a maximum 

displacement ymax. The average soil stiffness, K, is defined at yave , the displacement corresponding to half 

of the maximum abutment force, 1/2Fult, by Equation 12-3: 

ave

ult

y

F

K

2

1



12-3

The hyperbolic force-displacement relationship shown in Figure 12-14 can then be expressed as: 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-16 August 2011  

By

Ay yF





1

x H

n

12-4

0

K

y

max y

ave

Fult

2

Fult y

F y

Ay

B y

( ) 

1 

0

K

y

max y

ave

Fult

2

Fult y

F y

Ay

B y

( ) 

1 

Figure 12-14 Closed-Form Solution 

The constants A and B can be related to the key parameters (K, Fult, ymax, yave) as follows: 



















max

2

y

F

KA

ult

12-5



















max

1

2

yF

K

B

ult

12-6

The maximum wall displacement ymax in Equation 12-6 can be estimated from: 

y ForH Granular Backfill

y ForH Granular Backfill

.0 10

.0 05

max

max





12-7

where H is the wall height. Based on experimental data and parametric studies, the exponent n can be 

assumed equal to 1.5 and the hyperbolic force-displacement relationships per foot of abutment-backwall 

for cohesionless and cohesive backfills, respectively, can be expressed as: 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-17 August 2011   5.1

31

8

H

y

y

yF





(y in inches, F in kips per ft of wall) 12-8

  5.1

3.11

8

H

y

y

yF





(y in inches, F in kips per ft of wall) 12-9

12.2.3 Advanced Numerical Analysis 

The most common numerical method used in the geotechnical engineering to solve complicated soilstructure interaction problems is the finite element method (FEM). Numerical simulations for the fullscale Caltrans-UCLA abutment test were carried out using the FEM model to calculate the nonlinear back 

bone force-displacement curves and to investigate the failure mechanism of the abutment backfill 

(Shamsabadi et. al., 2009). The 2-D finite element mesh used in this analysis is shown in Figure 12-15. 

-Nodes

-Interface Interface Element

Triangular Element

H

6H

-Nodes

-Interface Interface Element

Triangular Element

H

6H

Figure 12-15 2-D finite Element Mesh of Bridge Abutment 

The abutment backwall-backfill interaction was modeled in the FE analysis with interface elements. The 

shear strength of the interface was established by applying a suitable reduction factor to the shear strength 

of the backfill. The deformed mesh after loading of the wall to failure is presented in Figure 12-16. 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-18 August 2011 

Figure 12-16 clearly shows that the failure surface for the passive wedge behind the wall is a logarithmic 

spiral in shape. 

Before After

Figure 12-16 Deformed Shape of Abutment Backfill in Simulation by the 2-D FEM Model 

12.2.4 Global Backwall-Backfill Longitudinal Response 

To evaluate the interaction behavior of an abutment with the bridge superstructure, a global threedimensional nonlinear dynamic analysis of the concrete box-girder bridge shown in Figure 12-17 was 

performed using a zero skew angle (Shamsabadi, 2007). The interaction between abutments and backfill 

was modeled by four nonlinear soil springs, denoted A, B, C and D, oriented normal to the backwall at 

each abutment. Each spring was modeled by a nonlinear plasticity link element. The model was excited 

by the near-field earthquake motion with a high-velocity pulse shown in Figure 12-18. 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-19 August 2011 

Figure 12-17 Bridge and Abutment Model 

Figure 12-18 Near-field Ground Motion with High Velocity Pulse 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-20 August 2011 

Figure 12-19 shows the hysteretic abutment-backfill force-displacement response due to the input 

acceleration time history shown in Figure 12-18. It can observed that the ultimate abutment passive force 

is fully developed at both abutments. 

Figure 12-19 Longitudinal Hysteretic Behavior of a Single-Span Bridge Abutment 

12.3 MODELING OF SKEWED ABUTMENTS 

Due in part to the complexities of modeling skewed abutments, AASHTO recommends avoiding skewed 

abutments or minimizing the skew when it cannot be avoided. During seismic events, the bridge deck in 

a skewed abutment may experience significant rotational motions about its vertical axis, as illustrated in 

Figure 12-20. As a result, the opposite corners of the deck first “collide” with the abutment and then 

rotate away from the abutment, resulting in the separation of the deck from the abutment (for a seat-type 

abutment). 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-21 August 2011 

Figure 12-20 Deck Rotation in a Bridge with Skewed Abutments During a Seismic Event 

Inspection of skewed abutments after recent earthquakes indicates that the passive wedges that form 

behind the skewed walls tend to be asymmetric along the abutment backwall due to deck rotation. Such 

behavior was observed at the northern abutment of the skewed Wushi highway bridge in Taiwan that was 

severely damaged during the recent Chi-Chi earthquake, as shown in Figure 12-21. 

Figure 12-21 Non-Uniform Passive Wedge behind a Skewed Abutment 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-22 August 2011 

12.3.1 3-D Finite Element Model of the Abutment Backfill 

A set of 3-D FE analyses was performed to evaluate the development of passive resistance behind a 75-

feet wide abutment with a 5.5-feet high backwall of varying skew angles (Shamsabadi, 2007). First, a 

non-skewed abutment was loaded. The formation of a uniform mobilized passive wedge behind the 

abutment wall and the associated displacement contours are shown in Figure 12-22. 

Figure 12-22 Passive Soil Wedge in a Non-Skewed Abutment 

The same 3-D FE model was then used to investigate the failure mechanism of skewed-abutments with 

various skew angles. Figure 12-23 shows the shape of the 3-D passive wedge formed between the 

wingwalls of an abutment with 45o skew. The FE analyses showed that, as a result of deck clockwise 

rotation, the abutment backwalls tend to be pushed primarily into the obtuse corners of the deck, causing 

asymmetric passive wedges to form behind the abutment backwall. Furthermore, the non-uniform 

loading of the skewed abutment backwall can result in a reduced mobilized soil capacity compared to an 

ordinary non-skewed abutment. The ground heave at the far side of the wall in Figure 12-23 illustrates the 

overstress and breakdown of the passive wedge in a skewed abutment, resulting in reduction of soil 

resistance normal to the abutment backwall. 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-23 August 2011 

Figure 12-23 3-D FE Model of Passive Wedge Formation behind a Skewed Abutment 

12.3.2 Load-Deformation Relationship 

Due to the in-plane motions and compressive pounding forces of the bridge deck in a skewed abutment 

system, the abutment-backfill response consists of both normal and tangential passive resistance. Figure 

12-24 shows an example of the nonlinear tangential and normal components of 30o skewed-abutmentbackfill backbone curves. Therefore, in the global seismic analysis of the skew bridges both the tangential 

and normal components of the abutment backfill force should be considered. The tangential component of 

passive resistance for the abutment with 30o skewed-angle in this example was about one third of the 

normal component. 

The normal components of the abutment passive resistance for various skew angles are shown in Figure 

12-25. These results indicate that the mobilized passive capacity might decrease as a function of skew 

angles at large displacement levels. 

From the computer simulations described above, it was found that the skewed abutment develop an 

asymmetric passive soil wedge that is less wide and generates less soil resistance than the passive wedge 

that forms behind a non-skewed abutment. The size (width) and capacity of the skew-affected passive 

wedge depends on abutment’s backwall width and the skew angle, which influence the interaction of the 

bridge deck with the abutment. Soil resistance is not seen to increase with higher skew angles, as might be 

expected from a combination of passive resistance normal to the wall and the additional soil traction 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-24 August 2011 

developed along the back face of the abutment wall. These analyses indicate that the width and total 

resistance of the mobilized passive wedge is a maximum for zero skew and decreases as the magnitude of 

skew angles is increased. Full-scale field experiments at UCLA are planned by Caltrans to investigate the 

formation and force-displacement capacity of the soil backfill behind a skewed abutment wall. 

Figure 12-24 Nonlinear Normal and Tangential Components of Abutment-Backfill Resistance for a 30o

Skew 

Figure 12-25 Impact of Skew Angles on Nonlinear Abutment Force-Deformation Relationship 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-25 August 2011 

12.3.3 Effects of Skew Angles on the Bridge Abutment Global Response 

It has been long recognized that ground motions with asymmetrical and high amplitude velocity pulse 

characteristics have a tendency to produce a biased, one-sided response of the bridge structure. This 

tendency is exacerbated in a bridge with a skewed abutment, as the asymmetrical impulsive loading 

generates large displacements in one direction, leading to significant rotation and residual displacement of 

the bridge. To evaluate the interaction behavior of a skewed bridge deck with a skewed abutment, a 

global three-dimensional nonlinear dynamic model of the single span bridge shown in Figure 12-26 was 

performed using a 45 degree skew angle (Shamsabadi, 2007). The interaction between abutments and 

backfill was modeled by rows of four nonlinear soil springs, denoted A, B, C and D, oriented normal to 

the backwall at each abutment. The model was excited by the two horizontal components of the 

earthquake motion with a high-velocity pulse. 

Figure 12-26 Single Span Bridge 45o Skew Angles 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-26 August 2011 

Figure 12-27 shows the hysteretic behavior of the abutment backfill at the obtuse corner (south west) and 

acute corner (south east) of the 45 degree skewed-bridge abutment due to the input motion. As the result 

of bridge rotation, the obtuse corners of the bridge deck have been pushed into the abutment backfill and 

the passive force is fully mobilized, while the acute corners have moved away from the abutment backfill 

and the passive wedge has been mobilized only partially. 

-8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0

 Displacement (inches)

0

40

80

120

160

Force (Kips)

Motion #3

West Abut.

East Abut.

Obtuse Corner Acute Corner

-8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0

 Displacement (inches)

0

40

80

120

160

Force (Kips)

Motion #3

West Abut.

East Abut.

Figure 12-27 Hysteretic Abutment Response Obtuse and Acute Corner of the Single-Span Bridge with 

45oSkew Angle 

12.4 SUMMARY 

LRFD seismic design of bridge abutments is often based on a displacement performance philosophy. This 

type of design necessitates that the geotechnical engineer predict the resistance of the abutment backfill 

soils to large displacements. Characterization of the inherently non-linear stiffness of the abutmentbackfill system is also necessary if the designer wishes to consider the interaction between the bridge 

superstructure and the abutments in the global bridge model. The abutment-backfill can not only provide 

significant lateral resistance but is also a good source of energy dissipation at large deformation due to 

nonlinear hysteretic behavior of the abutment-soil system. 

Abutment capacity is provided by the passive resistance of the abutment backfill. Seat-type abutments 

have a backwall with a depth sufficient to accommodate the bridge deck depth and the bridge deck rests 

on the abutment seat through bearings pads. In an ordinary bridge designed to a life safety standard, the 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-27 August 2011 

backwall may be designed to break off in the design earthquake in order to protect the foundation from 

inelastic action as a result of backwall displacement. Monolithic abutments are cast integrally with the 

superstructure and are supported on either spread footings or pile foundations. For monolithic abutments, 

the backwall engages the backfill immediately when the bridge is displaced longitudinally. The lateral 

force-deformation capacity of the monolithic abutment is a function of abutment backfill properties as 

well as foundation and structural capacity of the abutment backwall. Contrary to the seat-type abutment, 

a monolithic abutment wall may have to sustain large forces during a major seismic event if the backwall 

capacity is greater than the passive resistance of the backwall. However, if the backwall has been 

designed to be weaker than the passive earth pressure exerted by the abutment backfill, the effective 

abutment height is limited to the depth of the bridge deck and the resistance of the abutment is controlled 

by the passive resistance associated with this effective backfill height. 

Post earthquake investigations and full scale field experiments have shown that during a major seismic 

event mobilized passive wedges will form within the abutment backfill. The force-displacement response 

of bridge abutments subject to seismic loading is usually idealized using a simple, bi-linear relationship. 

The bi-linear relationship is then used to model the nonlinear behavior of the backfill as a set of 

independent horizontal springs. The bi-linear abutment force-deformation relationship assumes linear 

elastic stiffness, KAbut, for all stress states below the backfill capacity (i.e. the passive resistance of the 

backfill). Once the backfill capacity is reached, the abutment resistance remains constant with increasing 

displacement. For a seat-type abutment, an initial displacement equal to the gap between the bridge deck 

and the backwall is required to mobilize the backfill resistance. For design purposes, the stiffness of seattype abutment is then characterized by the effective abutment stiffness, Keff. The abutment passive 

capacity may be calculated using the methods for evaluating the passive resistance discussed in Chapter 9 

(subject to certain limitations discussed subsequently). However, in bridge engineering practice, it is 

common to use a presumptive value to calculate the abutment capacity for seismic analysis and design. 

Field data has provided a basis for the development of more realistic hyperbolic force-displacement 

models to better characterize the seismic performance of abutment-backfill systems. Furthermore, 

advanced two- and three-dimensional models that employ the Finite Element (FE) method have been 

employed to investigate the mechanisms of backfill failure. 

Due in part to the complexities of modeling skewed abutments, skewed abutments should be avoided or 

the skew minimized when it cannot be avoided. Inspection of skewed abutments after recent earthquakes 

indicates that the passive wedges that form behind the skewed walls tend to be asymmetric along the 
FHWA-NHI-11-032 12 - Bridge Abutment 

Seismic Design – Geotechnical Features 12-28 August 2011 

abutment backwall due to deck rotation. Furthermore, both the tangential and normal components of the 

abutment backfill force should be considered. For example, the tangential component of passive 

resistance for an abutment with 30o skewed-angle was about one third of the normal component in the 

example presented at the end of this chapter. 


FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-1 August 2011

CHAPTER 13

BURIED STRUCTURES 

13.1 GENERAL 

This chapter presents rational procedures for seismic evaluation of buried structures that are used as part 

of highway facilities, including culverts and pipelines. Buried structures, in general, have performed 

better during earthquakes than have above ground structures such as bridges and buildings. Buried 

structures are constrained by the surrounding ground and, in general, cannot be excited independent of the 

ground or be subject to strong vibratory amplification, such as the inertial response of a bridge structure 

during earthquakes. Adequate design and construction of seismic resistant culvert/pipeline structures, 

however, should never be overlooked, as moderate to major damage has been experienced by many 

buried structures during earthquakes. 

The general procedure for seismic design and analysis of buried structures should be based primarily on 

the ground deformation approach (as opposed to the inertial force approach); i.e., the structures should be 

designed to accommodate the deformations imposed by the ground. This chapter presents the 

deformation-based procedure for seismic design and analysis of buried structures. The following general 

subjects are discussed in this chapter: (1) seismic performance and vulnerability of buried structures, (2) 

general characteristics and properties of these structures, (3) potential failure modes when subject to 

seismic loading, (4) seismic loads on buried structures, (5) simplified procedure for ovaling of circular 

buried structures and racking of rectangular buried structures, (6) numerical modeling, and (7) a general 

design approach to permanent ground displacement (PGD). 

13.2 SEISMIC PERFORMANCE OF CULVERTS AND PIPELINES 

Damage to buried culverts and pipelines during earthquakes has been observed and documented by 

previous investigators (Davis and Bardet, 1999 and 2000; NCEER, 1996; O’Rourke, 1999; Youd and 

Beckman, 2003). In general, buried structures have performed better in past earthquakes than aboveground structures. Seismic performance records for culverts and pipelines have been very favorable, 

particularly when compared to reported damages to other highway/transportation structures such as 

bridges. 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-2 August 2011

The main reason for the good performance of buried structures has been that buried structures are 

constrained by the surrounding ground. It is unlikely that they could move to any significant extent 

independent of the surrounding ground or be subjected to vibration amplification/resonance. Compared to 

surface structures, which are generally unsupported above their foundations, buried structures can be 

considered to display significantly greater degrees of redundancy thanks to the support from the ground. 

The good performance may also be partly associated with the design procedures used to construct the 

embankment and backfill specifications for the culverts and pipes. Typical specifications require close 

control on backfill placement to assure acceptable performance of the culvert or pipe under gravity loads 

and to avoid settlement of fill located above the pipe or culvert, and these strict requirements for static 

design lead to good seismic performance. 

It is important that the ground surrounding the buried structure remains stable. If the ground is not stable 

and large permanent ground deformation (PGD) occur (for example, resulting from liquefaction, 

settlement, uplift, lateral spread, or slope instability/landslide) then significant damage to the culvert or 

pipe structures can be expected. Although transient ground deformation (TGD) due to shaking can also 

damage buried structures, compared to the effects of PGD, the damage is typically of a more limited 

extent. 

13.3 CULVERT/PIPE CHARACTERISTICS

Culvert/pipe products are available over a large range in terms of material properties, geometric wall 

sections, sizes, and shapes. Pipe sizes as small as 1 foot and as large as culverts that span 40 feet and 

larger are used in highway applications. They can be composed of concrete, steel, aluminum, plastic, and 

other materials. Detailed information about their shapes, range of sizes, and common uses for each type of 

culvert or pipe are summarized by Ballinger and Drake (1995). 

13.3.1 Flexible Culverts and Pipes 

In general, culverts and pipes are divided into two major classes from the static design standpoints: 

flexible and rigid. Flexible culverts and pipes typically are composed of either metal (for example, 

corrugated metal pipe, CMP, made of steel or aluminum) or thermoplastic materials (for example, HDPE 

or PVC). Flexible culverts and pipes respond to loads differently than rigid culverts/pipes. Because their 

ovaling stiffness is small relative to the adjacent soil, flexible culverts and pipes rely on firm soil support 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-3 August 2011

and depend upon a large strain capacity to interact with the surrounding soil to hold their shape while 

supporting the external pressures imposed upon them. 

For static design, current AASHTO LRFD Bridge Design Specifications require as a minimum the 

following main design considerations (in addition to the seam failure) for flexible culverts and pipes: (1) 

buckling (general cross sectional collapse as well as local bucking of thin-walled section), and (2) 

flexibility limit for construction. Except for large box structures or other large spans with shapes other 

than circular (NCHRP Report No. 473, 2002), the flexural strength consideration (i.e., bending moment 

demand) is generally not required for flexible culverts and pipes. 

Neither current AASHTO LRFD Bridge Design Specifications nor the NCHRP (2002) study has 

addressed seismic design concerns for culvert structures. From the seismic design standpoint, there are 

two main factors that should be considered: 

1) Seismic loading is in general non-symmetric in nature and therefore may result in sizable bending 

in the culvert structures (even for circular shape culverts). Furthermore, the behavior of thin-walled 

conduits (such as for the flexible culverts and pipes) is vulnerable to buckling. This behavior differs 

somewhat from that of a rigid concrete culvert structure, for which bending moments are often the 

key factor by which to judge structural performance. For buckling, thrust (that is, hoop force) is the 

key factor and seismically induced thrust can be significant, particularly if the interface between the 

culvert or pipe structure and the surrounding soil is considered a non-slip condition (Wang, 1993). 

Therefore, it is important that both seismically induced bending and thrust be evaluated using 

published solutions for circular tube (Moore, 1989; Janson, 2003) as failure criteria for evaluating 

the seismic performance of CMP and polymeric conduits (for example, corrugated HDPE pipes). 

2) Implicit in the current AASHTO design assumptions for flexible culverts is the existence of 

adequate soil support. This may happen to be the weakness of flexible culverts in case of 

earthquakes in that the soil support can be reduced or lost during liquefaction or other permanent 

ground failure mechanisms associated with seismic events. Significant distortion or collapse of the 

culvert cross section is likely if soil support is reduced or lost. 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-4 August 2011

13.3.2 Rigid Culverts and Pipes 

Rigid highway culverts and pipes consist primarily of reinforced concreted shapes that are either precast 

or cast-in-place. Unreinforced concrete culverts and pipe structures are not recommended for use in 

seismic regions. The sizes of reinforced concrete pipe (RCP) range (in diameter) from about 1 foot to 12 

feet. Larger RCP can be precast on the site or constructed cast-in-place. Rectangular four-sided box 

culverts can be furnished precast in spans ranging from 3 feet to 12 feet. Larger spans can be constructed 

cast-in-place. Three-sided precast box culverts can be furnished in spans up to 40 feet. 

Unlike the flexible culverts and pipes, the strain capacity of rigid culverts and pipes is much lower. 

Therefore, rigid culverts must develop significant ring stiffness and strength to support external pressures. 

Hence, they are not as dependent upon soil support as flexible culverts. 

For static design the primary design methods used for precast concrete pipe, either reinforced or 

unreinforced, include: (1) the Indirect Design Method, based on the laboratory three-edge bearing 

strength test, (2) a more direct design procedure that accounts for bending moment, shear, thrust/tension, 

and crack width (bucking is generally not an issue with rigid converts/pipes) around the periphery of the 

culvert wall, and (3) methods employing computerized numerical models accounting for the soil-structure 

interaction effects. 

For box culverts the static design uses the same criteria as other reinforced concrete structures (for 

example, beams and columns). In general, the effect of surrounding soils is accounted for by applying the 

soil pressures (active or at-rest) directly against the wall in the model, instead of fully taking advantage of 

the soil-structure interaction effect. Most current commercially available computer software can perform 

the structural analysis required for this design. For other structural shapes, consideration of soil-structure 

interaction becomes important and therefore is generally accounted for by using computerized numerical 

models. 

13.4 GENERAL EFFECTS OF EARTHQUAKES AND POTENTIAL FAILURE MODES

The general effects of earthquakes on culverts and pipe structures can be grouped into two broad 

categories – ground shaking and ground failure. The following sections discuss each of these categories. 

As it will be demonstrated, soil-structure interaction plays a critical role in the evaluation of the effect of 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-5 August 2011

seismic loading for both flexible and rigid culverts and pipes. A unified evaluation procedure is developed 

in this chapter to provide a rational and reliable means for seismic evaluations as well as realistic design 

for buried culvert and pipe structures. 

13.4.1 Ground Shaking 

Ground shaking refers to the vibration of the ground produced by seismic waves propagating through the 

earth’s crust. The area experiencing this shaking may cover hundreds of square miles in the vicinity of the 

fault rupture. The intensity of the shaking attenuates with distance from the fault rupture. 

Ground shaking motions are composed of two different types of seismic waves, each with two subtypes: 

 Body waves travel within the earth’s material. They may be either longitudinal compressional (P-) 

waves or transverse shear (S-) waves, and they can travel in any direction in the ground. 

 Surface waves travel along the earth’s surface. They may be either Rayleigh waves or Love waves. 

As a stable ground is deformed by the traveling waves, any culverts or pipelines in the ground will also be 

deformed. The shaking or wave traveling induced ground deformations are called transient ground 

deformations (TGD). 

When subject to TGD, the response of a buried linear culvert or pipe structure can be described in terms 

of three principal types of deformations: (1) axial deformations, (2) curvature deformations (refer to 

Figure 13-1), and (3) ovaling (for circular cross section) or racking (for rectangular cross section) 

deformations (refer to Figure 13-2).

Figure 13-1 Longitudinal Axial and Curvature Response to Traveling Waves 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-6 August 2011

Figure 13-2 Transverse Ovaling and Racking Response to Vertically Propagating Shear Waves 

The axial and curvature deformations are induced by components of seismic waves that propagate along 

the culvert or pipeline axis. Figure 13-1 shows the idealized representations of axial and curvature 

deformations. The general behavior of the linear structure is similar to that of an elastic beam subject to 

deformations or strains imposed by the surrounding ground. 

Current design and analysis methodology for pipeline systems was developed typically for long, linear 

structures. The principal failure modes for long, continuous pipeline structures consist of (1) rupture due 

to axial tension (or pull out for jointed segmented pipelines), and (2) local bucking (wrinkling) due to 

axial compression and flexural failure. If the pipelines are buried at shallow depth, continuous pipelines in 

compression can also exhibit beam-buckling behavior (that is, global bucking with upward buckling 

deflections). If the axial stiffness of the structures is large (such as that for a large sectional concrete 

pipe), then the buckling potential in the longitudinal direction is small (for both local buckling and global 

buckling). The general failure criteria for the above-mentioned potential failure modes have been 

documented by previous studies (O’Rourke and Liu, 1996). 

It should be noted, however, that typical culvert structures for transportation applications are generally of 

limited length. Therefore this condition is unlikely to develop significant transient axial/curvature 

deformations along the culvert structures. The potential failure modes mentioned above are not likely to 

take place during the earthquake. Important pipeline structures with a long length, such as gas, sewer, or 
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Seismic Design of Geotechnical Features 13-7 August 2011

water pipeline, are generally not designed as a part of the highway facility. The main focus of this 

chapter therefore will not be on the effects of axial/curvature deformations. Instead, the scope of this 

chapter will concentrate on transverse deformations of culverts and pipes, as discussed below. 

The ovaling or racking deformations of a buried culvert or pipe structure may develop when waves 

propagate in a direction perpendicular or nearly perpendicular to the longitudinal axis of the culvert or 

pipe, resulting in a distortion of the transverse cross-sectional shape of the structure. Figure 13-2 shows 

the ovaling distortion and racking deformation associated with a circular culvert or pipe and a rectangular 

culvert, respectively. In this figure, vertically propagating shear waves (with soil particles moving 

horizontally in back-and-forth motions) from the base of a soil column caused shear displacement in the 

ground which in turns caused the ovaling/racking displacements in the structure lining. The general 

behavior of the structure may be simulated as a buried structure subject to ground deformations under a 

two-dimensional, plane-strain condition. 

Ovaling and racking deformations may be caused by vertically, horizontally, or obliquely propagating 

seismic waves of any type. Many previous studies have suggested, however, that the vertically 

propagating shear wave is the predominant form of earthquake loading that governs the ovaling/racking 

behavior for the following reason: (1) except possibly in the very near-source areas, ground motion in the 

vertical direction is generally considered less severe than its horizontal component, (2) vertical ground 

strains are generally much smaller than shearing strain because the value of confined modulus of 

compressibility is much higher than that of the shear modulus, and (3) the amplification of vertically 

propagating shear wave, particularly in the soft/weak soils, is much higher than vertically propagating 

compressional wave and any other type of waves traveling in the horizontal direction. Therefore the 

analysis and methodology presented in this chapter addresses mainly the effects of vertically propagating 

shear waves on ovaling/racking behavior of the buried culverts or pipes. 

When subject to ovaling/racking deformations, a flexural type failure mode due to the combined effects of 

bending moment and thrust force must be checked. The flexural failure mode is typically the main 

concern for rigid culverts and pipes, such as those constructed with reinforced concrete. For flexible 

culverts and pipes (typically, thin-walled conduits constructed with steel, aluminum, or thermoplastic 

such as HDPE or PVC), they are likely to be controlled by buckling, which can occur in the elastic range 

of stresses. For buckling, thrust is the key factor and conservative assumption must be made regarding 

interface condition (slip or non-slip) between the exterior surface of the conduit and the surrounding 
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Seismic Design of Geotechnical Features 13-8 August 2011

ground. An elastic buckling criterion for circular conduits in uniform soil was proposed by Moore (1989) 

and may be used for buckling potential evaluation purpose. 

13.4.2 Ground Failure 

Ground failure broadly includes various types of ground instability such as faulting, landslides, 

liquefaction (including liquefaction-induced lateral spread, settlement, floatation, etc.), and tectonic uplift 

and subsidence. These types of ground deformations are called Permanent Ground Deformations (PGD). 

Each of these PGDs may be potentially catastrophic to culvert or pipeline structures, although the 

damages are usually localized. To avoid such damage some sort of ground improvement is generally 

required, unless the design approach to this situation is to accept the displacement, localize the damage, 

and provide means to facilitate repairs. 

The characteristics of PGD and its effects on culvert and pipes are extremely complex and must be dealt 

with on a case-by-case basis. It is unlikely that simple design procedures or solutions can be developed 

due to the complex nature of the problem. In this chapter, detailed study of problems associated with PGD 

will not be conducted. Instead, only general guidelines and recommendations on methodology for seismic 

evaluation under the effects of PGD will be provided. 

13.5 CURRENT SEISMIC DESIGN PRACTICE FOR BURIED STRUCTURES 

Currently there is no standard seismic design methodology or guidelines for the design of culvert 

structures, including Section 12 within the current AASHTO LRFD Bridge Design Specifications. The 

NCHRP Report 473 Recommended Specifications for Large-Span Culverts, (NCHRP, 2002) does not 

address issues related to seismic evaluation of long-span culverts. 

In the past, design and analysis procedures have been proposed by some researchers and design engineers 

for pipelines (for example, gas and water) or tunnel (that is, transportation or water) systems. While some 

of these procedures can be used for the design and analysis of culvert and pipes (for example, the 

transverse ovaling/racking deformation of the section, Figure 13-2), others cannot be directly applied 

because they are only applicable for buried structures with a long length, or with a deep burial depth. 

Furthermore, significant disparity exists among engineers regarding the appropriate design philosophy 

and methods of analysis that is applicable to various types of culvert structures. The following paragraphs 
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Seismic Design of Geotechnical Features 13-9 August 2011

provide a brief description of some procedures and methodologies proposed in the past for seismic 

evaluation of buried structures in general. 

O’Rourke (1998) provides a general overview of lifeline earthquake engineering, including the treatment 

of seismic evaluation of pipelines. O’Rourke and Liu (1996) present a detailed methodology for 

evaluating response of buried pipelines subject to earthquake effects. Pipelines response to both TGD and 

PGD were addressed in these two studies. However, the focus of these studies was on pipeline behavior in 

the longitudinal direction which is more suitable for a long continuous buried pipeline structure. Although 

failure criteria for axial tension and axial compression (local buckling/wrinkling and beam buckling) were 

developed, there were no discussions related to the procedure for evaluating the transverse ovaling 

deformation of the pipe’s cross-sectional behavior. 

Based on the field performance of 61 corrugated metal pipes (CMP) that were shaken by the 1994 

Northridge Earthquake, Davis and Bardet (2000) provided an updated approach to evaluating the seismic 

performance of CMP conduits. The focus of their study was on the ovaling and buckling (of the thin 

metal wall) of the transverse section behavior of the CMP. This approach involves the following general 

steps: 

1) Estimating the initial condition of compressive strain in the conduit, which is related to depth of 

burial. 

2) Estimating the compressive ground strain induced by a vertically propagating shear wave, which 

was calculated from the closed-form solution for transient shearing strain, as max = Vs/Cse, in which 

max is the maximum transient shearing strain of the ground, Vs is the horizontal peak particle 

velocity transverse to the conduit, and Cse is the average effective shear wave velocity of the 

surrounding ground. 

3) Adding the static and transient compressive strains. 

4) Comparing the strain so determined with the critical compressive strain that would cause the 

dynamic buckling (due to hoop force) of the CMP pipe. The critical buckling strain (or strength) 

was assumed to be dependent on the stiffness of the surrounding soil (Moore, 1989). 

The methodology derived by Davis and Bardet, although more rational than most of the other procedures, 

has some drawbacks, including: 
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 The procedure is applicable for thin-walled pipes only. The failure mode considered by using this 

procedure is primarily for buckling and does not include flexural (that is, bending) demand and 

capacity evaluation. The latter is a very important failure mode that must be considered for rigid 

culvers and pipes (such as those constructed with reinforced concrete). 

 The soil-structure interaction effect was considered in evaluating the buckling capacity, but not in 

the evaluation of the demand (that is, earthquake-induced ground strains). 

 The method assumed that the strains in the pipe coincide with those in the surrounding ground (that 

is, pipe deforms in accordance with the ground deformation in the free-field), on the basis of the 

assumption that there is no slippage at the soil-pipe interface. This assumption was incorrect, as 

Wang (1993) pointed out in his study that the strains/deformations of a buried conduit can be 

greater, equal, or smaller than those of the surrounding ground in the free-field, depending on the 

relative stiffness of the conduit to the surrounding ground. 

To account for the effects of TGD on tunnel structures, Wang (1993) developed closed-form and 

analytical solutions for the determination of seismically induced ovaling/racking deformations and the 

corresponding internal forces (such as moments and thrusts) for bored as well as cut-and-cover tunnel 

structures. The procedure presented by Wang for the bored tunnels was developed from a theory that is 

familiar to most mining/underground engineers (Peck et al., 1972). Simple and easy-to-use seismic design 

charts were presented. The design charts are expressed primarily as a function of relative stiffness 

between the structure and the ground. Solutions for both full-slip and no-slip conditions at the interface 

between soil and the exterior surface of the tunnel lining were developed. These solutions fully account 

for the interaction of the tunnel lining with the surrounding ground. The results were validated through a 

series of finite element/difference soil-structure interaction analyses. 

For the cut-and-cover tunnels (with a rectangular shape), the design solutions were derived from an 

extensive study using dynamic finite-element, soil-structure interaction analyses. A wide range of 

structural, geotechnical, and ground motion parameters were considered by Wang in his study. 

Specifically, five different types of cut-and-cover tunnel geometry were studied, including one-barrel, 

one-over-one two-barrel, and one-by-one twin-barrel configurations. To quantify the effect of relative 

stiffness on tunnel lining response, varying ground profiles and soil properties were used in the parametric 

analyses. Based on the results of the parametric analyses, a deformation-based design chart was 

developed for cut-and-cover tunnels. 
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Seismic Design of Geotechnical Features 13-11 August 2011

Although these solutions were intended originally for tunnel structures (considered a fairly rigid type of 

structure), the methodology is rational and comprehensive and provides a consistent and unified approach 

to solving the problem of buried conduits subject to ground shaking regardless of whether they are rigid 

or flexible structures. With some adjustments this approach is also applicable to the culvert and pipe 

structures typically used for highway construction. Therefore, a more detailed discussion of Wang’s 

approach is given in the following section. 

13.6 GENERAL METHODOLOGY AND RECOMMENDED PROCEDURES 

The general methodology and recommended procedures are presented in the following sections for the 

ovaling of circular conduits and the racking of rectangular conduits. 

13.6.1 Ovaling of Circular Conduits 

This section provides methods for quantifying the seismic ovaling effect on circular conduits. The 

conventionally used simplified free-field deformation method, discussed first, ignores the soil-structure 

interaction effects. Therefore its use is limited to conditions where the buried structures can be 

reasonably assumed to deform according to the free-field displacements during earthquakes. 

A refined method is then presented in Section 13.6.2 that is equally simple but capable of eliminating the 

drawbacks associated with the free-field deformation method. This refined method - built from a theory that is 

familiar to most mining/underground engineers - considers the soil-structure interaction effects. Based on this 

method, a series of design charts are developed to facilitate the design process. 

Ovaling Effect: As mentioned earlier, ovaling of a circular lining is primarily caused by seismic waves 

propagating in planes perpendicular to the axis of the buried structure. The results are cycles of additional stress 

concentrations with alternating compressive and tensile stresses in the lining. These dynamic stresses are 

superimposed on the existing static state of stress in the lining. 

Free-Field Shear Deformations: As mentioned previously, the shear distortion of ground caused by 

vertically propagating shear waves is probably the most critical and predominant mode of seismic 

motions. It causes a circular buried structure to oval and a rectangular buried structure to rack (sideways 

motion), as shown in Figure 13-2. Analytical procedures by numerical methods are often required to 
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Seismic Design of Geotechnical Features 13-12 August 2011

arrive at a reasonable estimate of the free-field shear distortion, particularly for a soil site with variable 

stratigraphy. Many computer codes with variable degree of sophistication are available (e.g., SHAKE, 

FLUSH, FLAC, PLAXIS, et al.). The most widely used approach is to simplify the site geology into a 

horizontally layered system and to derive a solution using one-dimensional wave propagation theory 

(Schnabel, Lysmer, and Seed, 1972). The resulting free-field shear distortion of the ground from this type 

of analysis can be expressed as a shear strain distribution or shear deformation profile versus depth. 

For a deep buried structure located in relatively homogeneous soil or rock and in the absence of detailed 

site response analyses, the simplified procedure by Newmark (1965) may provide a reasonable estimate, 

noting, however, that this method tends to produce more conservative results particularly when the effect 

of ground motion attenuation with depth is ignored. Here, the maximum free-field shear strain, γmax, can 

be expressed as 

se

S

max C

V



13-1

 

where VS

= Peak particle velocity 

 Cse = Effective shear wave propagation velocity 

The effective shear wave velocity of the vertically propagating shear wave, Cse, should be compatible with the 

level of the shear strain that may develop in the ground at the elevation of the buried structure under the design 

earthquake shaking. The values of Cse can be estimated by making proper reduction (to account for the strainlevel dependent effect) from the small-strain shear wave velocity, Cs

, obtained from in-situ testing (such as 

using the cross-hole, down-hole, and P-S logging techniques). For rock, the ratio of Cse/Cs can be assumed 

equal to 1.0. For stiff to very stiff soil, Cse/Cs may range from 0.6 to 0.9. Alternatively, site specific response 

analyses can be performed for estimating Cse. 

 

An equation relating the effective propagation velocity of shear waves to effective shear modulus, Gm, is 

expressed as: 





m

se

G

C

13-2
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Seismic Design of Geotechnical Features 13-13 August 2011

where ρ = Mass density of the ground 

An alternative simplified method for calculating the free-field ground shear strain, γmax, is by dividing the 

earthquake-induced shear stresses (τmax) by the shear stiffness (i.e., the strain-compatible effective shear 

modulus, Gm). This method is especially suitable for buried structures with shallow burial depths. 

In this simplified method the maximum free-field ground shear strain is calculated using the following 

equation: 

m

max

max G





13-3

max Rdv g

PGA 









 

13-4

tv

   DH

13-5

 

where Gm = Effective strain-compatible shear modulus of ground surrounding the 

buried structure (ksf) 

τmax = Maximum earthquake-induced shear stress (ksf) 

σv = Total vertical soil overburden pressure at invert elevation of buried structure (ksf) 

γt = Total soil unit weight (kcf) 

H = Soil cover thickness measured from ground surface to structure crown (ft) 

 D = Height of structure (or diameter of circular structure) (ft) 

 Rd = Depth dependent stress reduction factor; can be estimated using the following 

 relationships: 

Rd = 1.0 - 0.00233z for z < 30 ft 

Rd = 1.174 - 0.00814z for 30 ft < z < 75 ft 

Rd = 0.744 - 0.00244z for 75 ft < z < 100 ft 

Rd = 0.5 for z > 100 ft 

where z = the depth (ft) from ground surface to the invert elevation of the structure and 

 is represented by z = (H+D). 
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Seismic Design of Geotechnical Features 13-14 August 2011

Lining Conforming to Free-Field Shear Deformations: When a circular lining is assumed to oval in accordance 

with the deformations imposed by the surrounding ground (e.g., shear), the lining’s transverse sectional stiffness 

is completely ignored. This assumption is probably reasonable for most circular structures in rock and in very 

stiff/hard ground, because the lining stiffness against distortion is low compared with that of the surrounding 

ground. Depending on the definition of “ground deformation of surrounding ground,” however, a design based 

on this assumption may be overly conservative in some cases and non-conservative in others. This will be 

discussed further below. 

Shear distortion of the surrounding ground, for this discussion, can be defined in two ways. If the nonperforated ground in the free-field is used to derive the shear distortion surrounding the structural lining, 

the lining is to be designed to conform to the maximum diameter change, ΔDfree-field, shown in the top of 

Figure 13-3. 

Figure 13-3 Shear Distortion of Ground – Free-Field Condition vs. Cavity In-Place Condition 
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Seismic Design of Geotechnical Features 13-15 August 2011

The maximum diametric change of the lining for this case can be derived as: 

D D)2/( max  fieldfree 

13-6

 

where 

D = the diameter of the structure 

γmax

= the maximum free-field shear strain 

On the other hand, if the ground deformation is derived by assuming the presence of a cavity due to the 

excavation of the structure (bottom of Figure 13-3, for perforated ground), then the lining is to be 

designed according to the diametric strain expressed as: 

cavity max  m D)1(2D

13-7

where νm

 = the Poisson’s Ratio of the surrounding ground 

Equations 13-6 and 13-7 both assume the absence of the lining. In other words, lining-ground interaction 

is ignored. 

Comparison between Equations 13-6 and 13-7 shows that the perforated ground deformation would yield 

a much greater distortion than the free-field case (non-perforated ground). For a typical ground medium, 

the difference could be as much as three times. Based on the assumptions made, some preliminary 

conclusions can be drawn as follows: 

 Equation 13-7, for the perforated ground deformation, should provide a reasonable estimate for the 

deformation of a lining that has little stiffness (against distortion) in comparison to that of the 

surrounding ground. 

 Equation 13-6, for the free-field ground deformation, on the other hand, should provide a reasonable 

result for a lining with a distortion stiffness close or equal to the surrounding ground. 
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Seismic Design of Geotechnical Features 13-16 August 2011

Based on the discussions above, it can be further suggested that a lining with a greater distortion stiffness 

than the surrounding ground should experience a lining distortion even less than the free-field 

deformation. This latest case may occur when a structure is built in soft to very soft soils. It is therefore 

clear that the relative stiffness between the structure and the surrounding ground (i.e., soil-structure 

interaction effect) plays an important role in quantifying the response of a buried structure during the 

seismic loading condition. This effect will be discussed next. 

Importance of Lining Stiffness- Compressibility and Flexibility Ratios: To quantify the relative stiffness 

between a circular lining and the surrounding ground, two ratios designated as the compressibility ratio, C, and 

the flexibility ratio, F (Hoeg, 1968, and Peck et al., 1972) are defined by the following equations: 

Compressibility Ratio: 

1(tE )( )21

R)1(E

C

ll m m

l

2

m l







13-8

Flexibility Ratio: 

 

)1(IE6

R)1(E

F

1,ll m

3

l

2

m l







13-9

Where: 

Em

 = Strain-compatible elastic modulus of the surrounding ground 

m 

 = Poisson’s ratio of the surrounding ground 

Rl

 = Nominal radius of the structure lining 

l 

 = Poisson’s ratio of the structure lining 

1,l

I

 = Moment of inertia of lining per unit width of structure along the buried 

 conduit axis. 

 

l

t

 = The thickness of the lining 
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Seismic Design of Geotechnical Features 13-17 August 2011

Of these two ratios, it often has been suggested that the flexibility ratio is the more important because it is 

related to the ability of the lining to resist distortion imposed by the ground. As will be discussed later, the 

compressibility ratio also has a significant effect on the lining thrust response, particularly in the case 

where buckling potential may be of concern for flexible culverts/pipes. 

In the following section a refined procedure taking into account the lining-ground interaction effect is 

presented to provide a more accurate assessment of the seismic ovaling effect on a circular lining. 

13.6.2 Lining-Ground Interaction Solutions for Ovaling Response of Circular Lining 

Closed form analytical solutions have been proposed (Wang, 1993) for estimating ground-structure 

interaction for circular lining under the seismic loading conditions. These solutions are generally based 

on the assumptions that: 

 The ground is an infinite, elastic, homogeneous, isotropic medium. 

 The circular lining is generally an elastic, thin walled tube under plane strain conditions. 

 Full-slip or no-slip conditions exist along the interface between the ground and the lining. 

The expressions of these lining responses are functions of flexibility ratio and compressibility ratio as 

presented previously in Equations 13-8 and 13-9. The expressions for maximum thrust, Tmax, bending 

moment, Mmax, and diametric strain, ΔD/D, can be presented in the following forms: 

max

2

l

m

m

max 1 R

)1(

E

K

6

1 M 





13-10

 

maxl

m

m

max 2 R

)1(2

E

KT 





13-11

 

3 max1

1

max FKD/D 

13-12

 
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Seismic Design of Geotechnical Features 13-18 August 2011

m

m

1

65F2

12 )1(

K







13-13

m

2

2 m m

5

m m

2

2 m

1

m m

2

F[( 86]68[C]C)21()23

F[( 2C)21(]C)21()21

1K







13-14

K1 and K2 are defined herein as lining response coefficients. The earthquake loading parameter is 

represented by the maximum shear strain induced in the ground (free-field), γmax, which may be obtained 

through a simplified approach (such as Equations 13-1 or 13-3), or by performing a site-response 

analysis. 

 

To ease the design process, Figure 13-4 shows the lining response coefficient, K1, as a function of 

flexibility ratio and Poisson’s Ratio of the ground. The design charts showing the lining coefficient K2, 

primarily used for the thrust response evaluation, are presented in Figure 13-5, Figure 13-6 and Figure 

13-7 for Poisson’s Ratio values of 0.2, 0.35 and 0.5, respectively. 

0

0.5

1

1.5

2

2.5

3

0 1 2 3 4 5 6 7 8 9 10

Flexibility Ratio, F

Response Coefficient, K1

Poisson's Ratio

0.1

0.2

0.3

0.4

0.5

Figure 13-4 Lining Response Coefficient, K1 (Full-Slip Interface Condition) 
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Seismic Design of Geotechnical Features 13-19 August 2011

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Compressibility Ratio, C

Thrust Response Coefficient, K2 

Poisson's Ratio = 0.2

Flexibility Ratio 50

10

4

2

1

0.5

Figure 13-5 Lining Response Coefficient, K2, for Poisson’s Ratio = 0.2 (No-Slip Interface Condition) 

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Compressibility Ratio, C

Thrust Response Coefficient, K2 

Poisson's Ratio = 0.35

Flexibility Ratio

50

10

4

2

1

0.5

Figure 13-6 Lining Response Coefficient, K2, for Poisson’s Ratio = 0.35 (No-Slip Interface 

Condition) 
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Seismic Design of Geotechnical Features 13-20 August 2011

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Compressibility Ratio, C

Thrust Response Coefficient, K2 

Poisson's Ratio = 0.5

Flexibility Ratio

50

10

4

2

1

0.5

Figure 13-7 Lining Response Coefficient, K2, for Poisson’s Ratio = 0.5 (No-Slip Interface Condition) 

It should be noted that the solutions in terms of Mmax, ΔDmax, and εm provided herein are based on the fullslip interface assumption. For the maximum thrust response Tmax the interface conditions is assumed to be 

no-slip. These assumptions were adopted because full-slip condition produces more conservative results 

for Mmax and ΔDmax, while no-slip condition is more conservative for Tmax. During an earthquake, in 

general, slip at interface is a possibility only for structures in soft soils, or when seismic loading intensity 

is severe. For most buried structures, the condition at the interface is between full-slip and no-slip. In 

computing the forces and deformations in the lining, it is prudent to investigate both cases and the more 

critical one should be used in design. 

The conservatism described above is desirable to offset the potential underestimation of lining forces 

resulting from the use of equivalent static model in lieu of the dynamic loading condition. Therefore, the 

full-slip model is recommended in evaluating the moment and deflection response (i.e., Figure 13-4 and 

Equations 13-10, 13-12 and 13-14) of a circular lining. 
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Using the full-slip condition, however, would significantly underestimate the maximum thrust, Tmax, 

under the seismic simple shear condition. Therefore, it is recommended that the no-slip interface 

assumption be used in assessing the lining thrust response (Equations 13-11 and 13-14). 

13.6.3 Lining-Ground Interaction Solutions for Racking Response of Rectangular Lining 

During earthquakes a rectangular box structure in soil or in rock will experience transverse racking 

deformations (sideways motion) due to the shear distortions of the ground, in a manner similar to the 

ovaling of a circular structure discussed in Section 13.6.1. The racking effect on the structure is similar to 

that of an unbalanced loading condition. 

The external forces the structure is subjected to are in the form of shear stresses and normal pressures all 

around the exterior surfaces of the box. The magnitude and distribution of these external earth forces are 

complex and difficult to assess. The end results, however, are cycles of additional internal forces and 

stresses with alternating direction in the structure members. These dynamic forces and stresses are 

superimposed on the existing static state of stress in the structure members. For rigid frame box 

structures, the most critical mode of potential damage due to the racking effect is the distress at the top 

and bottom joints. 

Realizing that the overall effect of the seismically induced external earth loading is to cause the structure 

to rack, it is more reasonable to approach the problem by specifying the loading in terms of deformations. 

The structure design goal, therefore, is to ensure that the structure can adequately absorb the imposed 

racking deformation (i.e., the deformation method), rather than using a criterion of resisting a specified 

dynamic earth pressure (i.e., the force method). 

Free-Field Racking Deformation Method It has been proposed in the past that a rectangular buried 

structure be designed by assuming that the amount of racking imposed on the structure is equal to the 

“free-field” shear distortions of the surrounding ground, as illustrated in Figure 13-8 (i.e., Δfree-field = Δs). 

The racking stiffness of the structure is ignored with this assumption. 
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Figure 13-8 Soil Deformation Profile and Racking Deformation of a Box Structure 

The free-field deformation method serves as a simple and effective design tool when the seismically 

induced ground distortion is small, for example when the shaking intensity is low or the ground is very 

stiff. Given these conditions, most practical structural configurations can easily absorb the ground 

distortion without being distressed. The method is also a realistic one when the racking stiffness of the 

structure is comparable to that of its surrounding medium. 

It has been reported (Wang, 1993), however, that this simple procedure could lead to overly conservative design 

(i.e., when Δfree-field > Δs) or un-conservative design (i.e., when Δfree-field < Δs), depending on the relative stiffness 

between the ground and the structure. The overly conservative cases generally occur in soft soils. Seismically 

induced free-field ground distortions are generally large in soft soils, particularly when they are subjected to 

amplification effects. Ironically, rectangular box structures in soft soils are generally designed with stiff 

configurations to resist the static loads, making them less tolerant to racking distortions. Imposing free-field 

deformations on a structure in this situation is likely to result in unnecessary conservatism, as the stiff structure 

may deform less than the soft ground. 

On the other hand, the un-conservative cases arise when the shear stiffness of the ground is greater than 

the racking stiffness of the structures – a behavior similar to that described for the ovaling of circular 

structures (Section 13.6.1). To more accurately quantify the racking response of rectangular structures a 

rational procedure accounting for the structure-ground interaction effect is presented in the following 

section. 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-23 August 2011

Structure-Ground Interaction Analysis: Although closed-form solutions accounting for soil-structure interaction, 

such as those presented in Section 13.6.2, are available for circular lining, they are not readily available for 

rectangular structures due primarily to the highly variable geometrical characteristics typically associated with 

rectangular structures. 

To develop a simple and practical design procedure, Wang (1993) performed a series of dynamic soilstructure interaction finite element analyses. In this study, the main factors that may potentially affect the 

dynamic racking response of rectangular structures were investigated. Additional parametric studies and 

evaluations were also conducted specifically for buried structures with properties and characteristics that 

are typical of culverts in the NCHRP 12-70 study (NCHRP Report No. 611, 2008). Based on the results 

of the analyses, a simplified procedure incorporating soil-structure interaction for the racking analysis of 

rectangular buried structures was developed. The step-by-step procedure is outlined below. 

Step 1: Estimate the free-field ground strains 

max 

(at the structure elevation) caused by the vertically 

propagating shear waves of the design earthquakes, see Section 13.6.1 in deriving the freefield ground strain using various methods. Determine 



free-field, the differential free-field 

relative displacements corresponding to the top and the bottom elevations of the box structure 

(see Figure 13-10) by using the following expression:

fieldfree H max 



13-15

 

Where: H = height of the box structure 

Alternatively site-specific site response analysis may be performed to provide a more accurate assessment 

of 



free-field. 

Step 2: Determine the racking stiffness, Ks, of the box structure from a structural frame analysis. The 

racking stiffness should be computed using the displacement of the roof subjected to a unit 

lateral force applied at the roof level, while the base of the structure is restrained against 

translation, but with the joints free to rotate. The ratio of the applied force to the resulting 

lateral displacement yields Ks. In performing the structural frame analysis, appropriate 

moment of inertia values, taking into account the potential development of cracked section, 

should be used. 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-24 August 2011

Step 3: Determine the flexibility ratio, Fr, of the box structure using the following equation: 

































H

W

K

G

F

s

m

r

13-16

 

Where: W = Width of the box structure 

H = Height of the box structure 

Gm = Average strain-compatible shear modulus of the surrounding ground between 

the top and bottom elevation of the structure 

Ks

 = Racking Stiffness of the box structure 

The strain-compatible shear modulus can be derived from the strain-compatible effective shear wave 

velocity, Cse, see Equation 13-2).

Detailed derivation of the flexibility ratio, Fr, is given by Wang (1993). 

Step 4: Based on the flexibility ratio obtained from Step 3 above, determine the racking coefficient, 

Rr, for the proposed structure. The racking coefficient, Rr, is the ratio of the racking 

distortion of the structure embedded in the soil, Δs, to that of the free-field soil, Δfree-field, over 

the height of the structure (see Figure 13-9):

fieldfree

s Rr

 





13-17

 

From a series of dynamic finite element analyses, Wang (1993) presented results showing the relationship 

between the structure racking and the flexibility ratio, Fr. The values of Rr vs. Fr obtained from the 

dynamic finite element analyses are shown in Figure 13-9a and Figure 13-9b. Also shown in these figures 

are curves from closed-form static solutions for circular lining (refer to Section 13.6.2). The solutions 

shown in the figures are from the full-slip solution presented by Wang (1993) and Penzien (2000) and the 

no-slip solution presented by Penzien (2000). As can be seen in the figures, the curves from the closedform solutions provide a good approximation of the finite element analysis results. These curves can 

therefore be used to provide a good estimate of the racking of a rectangular structure as a function of the 

flexibility ratio defined by Equation 13-17. The analytical expressions for the curves in Figure 13-9 are: 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-25 August 2011

For no-slip interface condition: 

rm

rm

r

F43

F)1(4

R







13-18

 

For full-slip interface condition: 

 

rm

rm

r

F35.2

F)1(4

R







13-19

Several observations can be made from Figure 13-9. When Fr is equal to zero, the structure is perfectly 

rigid, no racking distortion is induced, and the structure moves as a rigid body during earthquake loading. 

When Fr is equal to 1, the racking distortion of the structure is approximately the same as that of the 

surrounding soil (exactly equal to that of the soil for the no-slip interface condition). For a structure that is 

flexible relative to the surrounding ground, (Fr > 1), racking distortion of the structure is greater than that 

of the free-field. As noted by Penzien (2000), if the structure has no stiffness (i.e., Fr → ∞), Rr is 

approximately equal to 4(1- νm ), which is the case of an unlined cavity. 

Step 5: Determine the racking deformation of the structure, Δs, using the following relationship: 

R  fieldfreers

13-20

 

Step 6: The seismic demand in terms of internal forces as well as material strains are calculated 

by imposing Δs upon the structure in a frame analysis as depicted in Figure 13-10. Results 

of the analysis can also be used to determine the detailing requirements. 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-26 August 2011

Figure 13-9 Racking Coefficient Rr for Rectangular Structures (MCEER-06-SP11, Modified from 

Wang, 1993, and Penzien, 2000) 

Figure 13-10 Simplified Racking Frame Analysis of a Rectangular Structure 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-27 August 2011

It should be noted that the methodology developed above was intended to address the incremental effects 

due to earthquake-induced TGD only. The seismic effects of transient racking/ovaling deformations on 

culverts and pipes must be considered additional to the normal load effects from surcharge, pavement, 

and wheel loads, and then compared to the various failure criteria considered relevant for the type of 

culvert structure in question. 

A load factor of 1.0 shall be used in conjunction with the methodology given in this chapter to determine 

the seismic loading effects discussed above. The current AASHTO LRFD Bridge Design Specifications

require that the load factor for live load in combination with the seismic load should be determined on a 

project-specific basis. On a heavily traveled roadway where the buried structure is likely to be subjected 

to the live load on a nearly continuous basis, the load factor for live load shall be taken at least equal to 

0.5. 

13.7 NUMERICAL MODELING METHODS 

In situations where the simplified methods for estimating seismic forces are inadequate, more rigorous 2-

dimensional soil-structure interaction continuum numerical modeling methods should be used. There are 

a number of situations that may warrant the use of numerical modeling, including where (1) the geometry 

is too complex to be represented by a circular or box-type structure, (2) long-span culverts that may be 

sensitive to seismic loads are being used, (3) critical (important) structures are identified, (4) highly 

variable subsurface conditions occur, and (5) in high seismic areas. 

For transverse ovaling/racking analysis, the model needs to be developed with the capability of capturing 

SSI effects as well as appropriate depth-variable representations of the earth medium and the associated 

free-field motions (or ground deformations) obtained from site-response analyses of representative soil 

profiles. 

Two types of two-dimensional finite element (or finite difference) continuum numerical modeling 

methods have been used in practice and they are described in the following sections. 

Pseudo-Static Seismic Coefficient Deformation Method: The pseudo-static seismic coefficient induced 

deformation method (the simpler of the two methods) is a generally accepted method of analysis for 

underground structures buried at shallow depths and is particularly suited for conventional highway 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-28 August 2011

culverts/pipes where the burial depths are generally shallow (i.e., within 75 feet from ground surface). In 

this analysis it is assumed that ground stability is not of concern. The general procedure in using this 

method is outlined below: 

 Perform one-dimensional free-field site response analysis (e.g., using SHAKE program). From the 

results of the analysis derive the maximum ground acceleration profile expressed as a function of 

depth from the ground surface. 

 Develop the two-dimensional finite element (or finite difference) continuum model incorporating the 

entire excavation and soil-structure system, making sure the lateral extent of the domain (i.e., the 

horizontal distance to the side boundaries) is sufficiently far to avoid boundary effects. The side 

boundary conditions should be in such a manner that all horizontal displacements at the side 

boundaries are free to move and vertical displacements are prevented (i.e., fixed boundary condition 

in the vertical direction and free boundary condition in the horizontal direction). These side boundary 

conditions are considered adequate for a site with reasonably leveled ground surface subject to 

lateral shearing displacements due to horizontal excitations. 

 The strain-compatible shear moduli of the soil strata computed from the one-dimensional site 

response analysis (e.g., using the SHAKE program) should be used in the two-dimensional 

continuum model. 

 The maximum ground acceleration profile (expressed as a function of depth from the ground 

surface) derived from the one-dimensional site response analysis is applied to the entire soil-structure 

system in the horizontal direction in a pseudo-static manner. 

 The analysis is executed with the culvert structure in place using the prescribed horizontal maximum 

acceleration profile and the strain-compatible shear moduli in the soil mass. It should be noted that 

this pseudo-static seismic coefficient approach is not a dynamic analysis and therefore does not 

involve displacement, velocity, or acceleration histories. Instead, it imposes ground shearing 

displacements throughout the entire soil-structure system (i.e., the two-dimensional continuum 

model) by applying pseudo-static horizontal shearing stresses in the ground. The pseudo-static 

horizontal shearing stresses increase with depth and are computed by analysis as the product of the 

total soil overburden pressures (representing the soil mass) and the horizontal seismic coefficients. 

The seismic coefficients represent the peak horizontal acceleration profile derived from the onedimensional free-field site response analysis. As discussed above the lateral extent of the domain in 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-29 August 2011

the two-dimension analysis system should be sufficiently far to avoid boundary effects. In this 

manner, the displacement profiles at the two side boundaries are expected to be very similar to that 

derived from the one-dimensional free-field site response analysis. However, in the focus area near 

the culvert construction the displacement distribution will be different from that of the free field, 

reflecting the effects of (1) soil-structure interaction, and (2) the earth mass removed for constructing 

the culvert. 

Dynamic Time History Analysis: In a dynamic time history analysis, the entire soil-structure system is 

subject to dynamic excitations using ground motion time histories as input at the base of the soil-structure 

system. The ground motion time histories used for this purpose should be developed to match the target 

design response spectra and have characteristics that are representative of the seismic environment of the 

site and the site conditions. 

13.8 GENERAL DESIGN METHODOLOGY FOR PERMANENT GROUND 

DISPLACEMENTS

As mentioned earlier, the greatest risk to buried structures is the potential for large ground movements as 

a result of unstable ground conditions (e.g., liquefaction and landslides) or fault displacements. In 

general, it is not feasible to design a buried structure to withstand large ground displacements. The proper 

design measures in dealing with the unstable ground conditions may consist of: 

 Ground stabilization 

 Removal and replacement of the problem soils 

 Re-route to bypass the problem zone 

With regard to the fault displacements, the best strategy is to avoid any potential crossing of active faults. 

If this is not possible, then the general design philosophy is to accept and accommodate the displacements 

by either employing an oversized excavation, perhaps backfilled with compressible/collapsible material, 

or using ductile lining to minimize the instability potential of the lining. In cases where the magnitude of 

the fault displacement is limited or the width of the sheared fault zone is considerable such that the 

displacement is dissipated gradually over a distance, design of a strong lining to resist the displacement 

may be technically feasible. The structures, however, may be subject to large axial, shear and bending 

forces. Many factors need to be considered in the evaluation, including the stiffness of the lining and the 

ground, the angle of the fault plane intersecting the structure, the width of the fault, the magnitude as well 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-30 August 2011

as orientation of the fault movement. Analytical procedures are generally used for evaluating the effects 

of fault displacement on lining response. Some of these procedures were originally developed for buried 

pipelines (ASCE Committee on Gas and Liquid Fuel Lifelines, 1984). Continuum finite-element or 

finite-difference methods have also been used effectively for evaluating the structure-ground-faulting 

interaction effects. 

The effects of liquefaction and liquefaction-induced ground deformations on buried structures should be 

evaluated and considered in the seismic design. These effects include the following: (1) uplift, buoyancy, 

and floatation of the buried structures, (2) large lateral displacement, and (3) post-liquefaction settlements 

and deformations, total as well as differential. 

An initial screening study (NCEER, 1996) should be carried out, followed by more refined analyses and 

evaluations of the impact on the proposed structures, to assess the risk of liquefaction-related permanent 

ground displacement. If the liquefaction impact analyses yield unacceptable performance of the 

structures, mitigation measures should be incorporated into the design. 

The evaluation for seismically induced landslides and slope instability, if identified, should also be 

conducted in accordance with the procedures discussed in Chapter 6, followed by an impact study. If the 

impact analyses yield unacceptable performance of the structures, mitigation measures should be 

incorporated into the design. 

13.9 SUMMARY 

Simplified seismic analysis procedures for evaluating culvert and pipe structures against ground shaking 

induced transient ground deformations (TGD) were discussed in this chapter. The analysis procedures use 

a deformation-based methodology that can provide a more reliable prediction of culvert/pipe 

performance. The approach focuses on the deformations in the transverse section of the structure (that is, 

ovaling/racking deformations) instead of the longitudinal axial/curvature deformations, due primarily to 

the general condition that typical culvert structures for transportation applications are of limited length, 

and as such it is in general unlikely to develop significant transient axial/curvature deformations along the 

longitudinal direction of the culvert structures. 
FHWA-NHI-11-032 13 - Buried Structures 

Seismic Design of Geotechnical Features 13-31 August 2011

For PGD, such as occurs with slope failures and liquefaction, a general deformation-based methodology 

for evaluating the impacts of PGD on culverts and pipe structures are briefly described. In this case 

conventional methods for assessing liquefaction potential (including spreads, settlement, and floatation) 

and the seismic stability of the slope, with or without liquefaction, can be used to derive the magnitude 

and distributions of the PGD, and where appropriate ground improvement can be implemented to mitigate 

the ground movement. 
FHWA-NHI-11-032 14-References 

Seismic Design – Geotechnical Features 14-1 August 2011

CHAPTER 14 

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