Seismic Retrofitting Manual for 

Highway Structures: Part 2 – Retaining 

Structures, Slopes, Tunnels, Culverts, 

and Roadways

PUBLICATION NO. FHWA-HRT-05-067 AUGUST 2004

Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Technical Report Documentation Page 

1. Report No.

FHWA-HRT-05-067 

2. Government Accession No. 

N/A 

3. Recipient’s Catalog No.

N/A 

5. Report Date 

August 2004 

4. Title and Subtitle 

SEISMIC RETROFITTING MANUAL FOR HIGHWAY 

STRUCTURES: PART 2 – RETAINING STRUCTURES, SLOPES, 

TUNNELS, CULVERTS AND ROADWAYS 

6. Performing Organization Code

N/A 

7. Author(s) 

Maurice Power, Kenneth Fishman, Rowland Richards, Faiz Makdisi, 

Samuel Musser and T. Leslie Youd 

8. Performing Organization Report No. 

10. Work Unit No. 

N/A 

9. Performing Organization Name and Address 

Multidisciplinary Center for Earthquake Engineering Research 

University at Buffalo, State University of New York 

Red Jacket Quadrangle 

Buffalo, NY 14261 

11. Contract or Grant No. 

DTFH61-92-C-00106

13. Type of Report and Period Covered 

Final Report 

12. Sponsoring Agency Name and Address 

Office of Infrastructure Research and Development 

Federal Highway Administration 

6300 Georgetown Pike 

McLean, VA 22101-2296 

14. Sponsoring Agency Code 

 

15. Supplementary Notes : Contracting Officer’s Technical Representatives: 

James Cooper, P.E., HRDI-03, Wen-huei (Phillip) Yen, Ph.D., P.E., HRDI-07, John D. O’Fallon, P.E., HRDI-07 

16. Abstract 

This report is the second of a two-part publication entitled: 

Seismic Retrofitting Manual for Highway Structures: 

Part 1: Bridges 

Part 2: Retaining Structures, Slopes, Tunnels, Culverts and Roadways. 

Part 1 of this manual is based on previous Federal Highway Administration (FHWA) publications on this subject including 

Seismic Retrofitting Manual for Highway Bridges, published in 1995 as report FHWA-RD-94-052. Revisions have been made to 

include current advances in earthquake engineering, field experience with retrofitting highway bridges, and the performance of 

bridges in recent earthquakes. It is the result of several years of research with contributions from a multidisciplinary team of 

researchers and practitioners. 

Part 2 includes new procedures for determining the seismic vulnerability of other important highway system structures, 

namely, retaining structures, slopes, tunnels, culverts, and roadways. Guidance is provided on (a) screening for potential seismic 

vulnerabilities; (b) conducting a detailed evaluation; and (c) describing strategies for retrofit design. In addition, discussion is 

provided for classifying each structure by type, construction, or expected performance. This is needed since different types of a 

given structure (e.g., different types of retaining walls) may have different failure modes and will therefore require somewhat

different approaches to seismic vulnerability screening, detailed evaluation, and retrofitting. 

17. Key Words 

Bridges, earthquakes, seismic, retrofitting, prioritization, 

evaluation, classification, retrofit measures, screening, 

guidelines, retaining structures, retaining walls, slopes, 

tunnels, culverts, roadways, pavement 

18. Distribution Statement 

No restrictions. This document is available to the public through 

the National Technical Information Service, Springfield, VA 

22161. 

19. Security Classif. (of this report) 

Unclassified 

20. Security Classif. (of this page) 

Unclassified 

21. No of Pages

370 

22. Price 

 

 Form DOT F 1700.7 (8-72) Reproduction of completed pages authorized 
PREFACE 

This manual is a major revision of the Federal Highway Administration publication Seismic 

Retrofitting Guidelines for Highway Bridges which was published in 1983 as Report FHWA/RD83-007. This original publication was updated in 1994 and an interim revision published as 

Report FHWA-RD-94-052, Seismic Retrofitting Manual for Highway Bridges in May 1995. This 

current edition expands the coverage of the previous publications by including procedures for 

seismically-deficient retaining structures, slopes, tunnels, culverts, and roadways, in addition to 

bridges. It is published in two parts as follows: 

Part I: Bridges 

Part II: Retaining Structures, Slopes, Tunnels, Culverts, and Roadways 

Whereas Part I maintains the basic format of the retrofitting process described in the 1983 

Report, major changes have been made in this revision to include advances in earthquake 

engineering, field experience, and the performance of bridges in recent earthquakes in California 

and elsewhere. 

Part 2 focuses on seismic vulnerability screening, evaluation and retrofitting of the following 

highway system components: retaining structures, slopes, tunnels, culverts, and roadways. It is 

the first known effort to capture, in a formal and consistent manner, the important aspects of 

seismic performance and retrofitting intended to improve performance of highway system 

structural components other than bridges. 

It should be noted that this manual was developed while the U.S. Department of Transportation 

was transitioning to “metric” units. As a consequence, example problems are presented in SI 

units. 

ii
iii

SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol 

LENGTH 

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2 square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m2

yd2 square yard 0.836 square meters m2

ac acres 0.405 hectares ha

mi2 square miles 2.59 square kilometers km2

VOLUME 

fl oz fluid ounces 29.57 milliliters mL 

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m3 

yd3 cubic yards 0.765 cubic meters m3 

NOTE: volumes greater than 1000 L shall be shown in m3

MASS 

oz ounces 28.35 grams g

lb pounds 0.454 kilograms kg

T short tons (2000 lb) 0.907 megagrams (or "metric ton") Mg (or "t") 

TEMPERATURE (exact degrees) o

F Fahrenheit 5 (F-32)/9 Celsius oC 

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2 poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH

mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA mm2

 square millimeters 0.0016 square inches in2 

m2 square meters 10.764 square feet ft2 

m2 square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac

km2 square kilometers 0.386 square miles mi2 

VOLUME 

mL milliliters 0.034 fluid ounces fl oz 

L liters 0.264 gallons gal 

m3 cubic meters 35.314 cubic feet ft3 

m3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T 

TEMPERATURE (exact degrees) o

C Celsius 1.8C+32 Fahrenheit oF 

ILLUMINATION 

lx lux 0.0929 foot-candles fc 

cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2

*SI is the symbol for th International System of Units. Approp e riate rounding should be made to comply with Section 4 of ASTM E380. 

(Revised March 2003)
 
v

TABLE OF CONTENTS 

CHAPTER 1: INTRODUCTION.............................................................................................. 1

 1.1 Scope......................................................................................................................... 1 

 1.1.1 Screening......................................................................................................... 2 

 1.1.2 Detailed Evaluation ........................................................................................2 

 1.1.3 Retrofit Design Strategies .............................................................................. 2 

 1.2 Design Earthquakes, Ground Motions, and Performance 

 Criteria for Seismic Screening, Evaluation and Retrofit Design .............................. 3 

 1.3 Report Outline........................................................................................................... 4

CHAPTER 2: WALLS AND RETAINING STRUCTURES ................................................. 5

 2.1 Introduction............................................................................................................... 5 

 2.2 Classification of Wall Types.....................................................................................5 

 2.2.1 Rigid Gravity and Semi-Gravity Walls ..........................................................6 

 2.2.1.1 Gravity Walls....................................................................................6 

 2.2.1.2 Semi-Gravity Walls ..........................................................................6 

 2.2.2 Prefabricated Modular Gravity Walls ............................................................7 

 2.2.3 Anchored Walls..............................................................................................8 

 2.2.4 Mechanically Stabilized Earth (MSE) Walls .................................................9 

 2.2.5 Other Wall Types .........................................................................................10 

 2.3 Screening................................................................................................................. 10 

 2.3.1 General Screening Criteria ...........................................................................11 

 2.3.1.1 Level 1 ............................................................................................11 

 2.3.1.2 Level 2 ............................................................................................14 

 2.3.1.3 Summary......................................................................................... 14 

 2.3.2 Anchored Walls............................................................................................16 

 2.3.3 MSE Walls ................................................................................................... 16 

 2.4 Evaluation of Retaining Walls................................................................................17 

 2.4.1 Information Required for Detailed Evaluation.............................................17 

 2.4.1.1 Wall Details ....................................................................................17 

 2.4.1.1(a) Gravity Walls.................................................................18 

 2.4.1.1(b) Concrete Cantilever Retaining Walls 

 (Inverted T-Type)..........................................................19 

 2.4.1.1(c) Tied-Back Walls ........................................................... 20 

 2.4.1.1(d) MSE Walls.................................................................... 20 

 2.4.1.2 Soil Properties................................................................................. 20 

 2.4.1.3 Ground Motions.............................................................................. 22 

 2.4.2 Gravity and Semi-Gravity Walls..................................................................22 

 2.4.2.1 External Forces Acting on Gravity or Semi-Gravity 

 Retaining Walls Considering Seismic Loading .............................22 

 2.4.2.1(a) Seismic Lateral Pressure (Thrust) on Walls..................23 

 2.4.2.1(b) Passive Restraint ........................................................... 26 

 2.4.2.1(c) Seismic Bearing Capacity............................................. 27 
vi

TABLE OF CONTENTS (continued) 

 2.4.2.2 External Stability of Gravity or Semi-Gravity Retaining Walls 

 Considering Seismic Loading: Critical Acceleration 

 kh for Loss of Equilibrium .............................................................30 

 2.4.2.2(a) Overturning Stability (Tilting) – 

 Moment Equilibrium.....................................................30 

 2.4.2.2(b) Bearing Capacity Failure - 

 Vertical Equilibrium .....................................................32 

 2.4.2.3 Structural Integrity of Gravity or Semi-Gravity Retaining 

 Walls Considering Seismic Loading............................................... 33 

 2.4.2.3(a) Analysis of Wall Stem ..................................................33 

 2.4.2.3(b) Analysis of Footing....................................................... 34 

 2.4.2.4 Loss of Service of Essential Facilities ............................................35 

 2.4.2.4(a) Secondary Screening Procedure for Assessing 

 Vulnerability to Seismically Induced 

 Permanent Deformation................................................36 

 2.4.2.4(b) Determination of Threshold Acceleration ....................37 

 2.4.2.4(c) Estimation of Seismically Induced Deformation..........40 

 2.4.3 Concrete Cantilever Walls (Inverted T Walls).............................................43 

 2.4.4 Anchored Walls............................................................................................44 

 2.4.4.1 Secondary Screening Procedure for Anchored Walls.....................44 

 2.4.4.2 Evaluation Procedure for Anchored Walls .....................................47 

 2.4.4.2(a) Passive Toe Failure-Rotation About the Top................49 

 2.4.4.2(b) Anchor Failure - Rotation of Base................................ 49 

 2.4.5 MSE Walls ................................................................................................... 50 

 2.4.5.1 Evaluation Procedure for MSE Walls for Collapse ........................54 

 2.4.5.1(a) Tension in Reinforcements ...........................................54 

 2.4.5.1(b) Connection Details........................................................56 

 2.4.5.1(c) Seismic Analysis of Segmental Reinforced 

 Walls and Toppling of the Wall Face ...........................57 

 2.4.5.2 Proximity of Structures to MSE Walls ...........................................58 

 2.4.5.2(a) External Sliding Stability.............................................. 59 

 2.4.5.2(b) Pullout........................................................................... 59 

 2.4.5.2(c) Internal Sliding Stability (for SRWs and MCUs)......... 60 

 2.4.5.2(d) Bulging Shear Failure ................................................... 60 

 2.5 Design of Seismic Retrofit for Earth Retaining Structures.....................................62 

 2.5.1 Gravity and Semi-Gravity Walls..................................................................62 

 2.5.2 Concrete Cantilever Walls - Structural Failure of the Wall .........................65 

 2.5.3 Anchored Walls............................................................................................66 

 2.5.4 MSE Walls ................................................................................................... 67 

2.6 Screening, Seismic Evaluation and Design of Seismic Retrofit for a 

 Retaining Wall ........................................................................................................67 
vii

TABLE OF CONTENTS (continued) 

CHAPTER 3: SLOPES, EMBANKMENTS, AND ROCKFALLS ..................................... 97

 3.1 Introduction ......................................................................................................... 97 

 3.2 Classification ......................................................................................................... 97

 3.3 Screening Procedures............................................................................................106 

 3.3.1 Preliminary Screening Procedures .............................................................106 

 3.3.2 Supplemental Screening Criteria for Rockfalls..........................................107 

 3.3.3 Supplemental Criteria for Category III Liquefaction-Induced 

 Landslides................................................................................................... 113 

 3.4 Evaluation Procedures ..........................................................................................113 

 3.4.1 Evaluation of Category I Landslides .......................................................... 113 

 3.4.2 Evaluation of Category II Landslides......................................................... 113 

 3.4.2.1 Pseudo-Static Slope Stability Analysis Procedure........................114 

 3.4.2.1(a) Necessary Data for Analysis .......................................114 

 3.4.2.1(b) Analysis Procedure .....................................................115 

 3.4.2.1(c) Special Considerations for Rock Slopes.....................117 

 3.4.2.2 Deformation Analysis Procedures ................................................118 

 3.4.2.2(a) Yield Acceleration, ky................................................. 119 

 3.4.2.2(b) Peak Acceleration Induced Within the 

 Sliding Mass, kmax ....................................................... 119 

 3.4.2.2(c) Estimating Deformation, D.........................................119 

 3.4.3 Evaluation of Category III Landslides ....................................................... 124 

 3.5 Retrofitting Procedures .....................................................................................124 

 3.5.1 Rock Slopes................................................................................................ 125 

 3.5.2 Soil Slopes..................................................................................................131 

3.6 Example Problems ................................................................................................136 

CHAPTER 4: TUNNELS....................................................................................................... 145 

 4.1 Introduction...........................................................................................................145

 4.2 Tunnel Classification ............................................................................................145 

 4.2.1 Bored Tunnels ............................................................................................145 

 4.2.1.1 Bored Tunnels in Soft Ground ...................................................... 146 

 4.2.1.2 Bored Tunnels in Rock .................................................................146 

 4.2.2 Cut-and-Cover Tunnels ..............................................................................146 

 4.2.3 Submerged Tubes .......................................................................................146 

 4.3 Screening Guidelines ............................................................................................147 

 4.3.1 Objective of Screening Stage .....................................................................147 

 4.3.2 Factors Influencing Tunnel Seismic Performance .....................................148 

 4.3.2.1 Seismic Hazard .............................................................................148 

 4.3.2.2 Geological Conditions ..................................................................149 

 4.3.2.3 Tunnel Design, Construction and Condition ................................149 

 4.3.3 Screening Guidelines..................................................................................149 

 4.3.3.1 Screening Guidelines Applicable to All 

 Types of Tunnels........................................................................... 149 
viii

TABLE OF CONTENTS (continued) 

 4.3.3.2 Additional Screening Guidelines for Bored Tunnels....................150 

 4.3.3.3 Additional Screening Guidelines for Cut-and-Cover 

 Tunnels.......................................................................................... 153 

 4.3.3.4 Additional Screening Guidelines for Submerged Tubes ..............153 

 4.4 Evaluation Procedures ..........................................................................................153 

 4.4.1 Evaluation for Ground Shaking..................................................................153 

4.4.1.1 General.......................................................................................... 153 

4.4.1.2 Broad Guidelines for Analyses for Ground Shaking ....................155 

 4.4.1.3 Evaluation of Axial and Curvature Deformations 

 Along the Longitudinal Tunnel Axis ............................................156 

 4.4.1.3(a) Simplified Analyses/Closed Form Solutions...............157 

 4.4.1.3(b) Numerical Analysis.....................................................166 

 4.4.1.4 Evaluation of Deformations of Tunnel Cross Section ..................166 

 4.4.1.4(a) Simplified Analyses/Closed-Form Solutions ..............166 

 4.4.1.4(b) Numerical Analysis.....................................................179 

 4.4.2 Evaluation for Fault Rupture......................................................................180 

 4.4.2.1 General.......................................................................................... 180 

 4.4.2.2 Assessing the Amount of Fault Displacement..............................181 

 4.4.2.3 Analyzing Tunnels for Fault Displacement ..................................181 

 4.4.3 Evaluation for Landsliding or Liquefaction ...............................................182 

 4.5 Retrofit Strategies ................................................................................................. 186 

 4.5.1 Ground Shaking-Induced Failure ............................................................... 186 

 4.5.1.1 Bored Tunnels...............................................................................186 

 4.5.1.1(a) Tunnels in Rock...........................................................186 

 4.5.1.1(b) Tunnels in Soil/Soft Ground .......................................188 

 4.5.1.2 Cut-and-Cover Tunnels.................................................................191 

 4.5.1.3 Submerged Tubes..........................................................................191 

 4.5.1.4 Junctions and Transitions.............................................................. 193 

 4.5.2 Fault Displacement-Induced Failure ..........................................................196 

 4.5.3 Landsliding- and Liquefaction-Induced Failure......................................... 203 

 4.6 Examples of Tunnel Screening, Evaluation and Retrofit Strategies.....................203 

CHAPTER 5: CULVERTS.................................................................................................... 243 

5.1 Introduction...........................................................................................................243 

5.2 Classification of Culverts and Background Information ...................................... 244 

5.2.1 Flexible Culverts – Background and Design Philosophies.......................245 

5.2.2 Rigid Culverts – Background and Design Philosophies...........................250 

5.2.3 Culvert Joints ............................................................................................ 252 

5.2.3.1 Bell and Spigot Joints ................................................................ 252 

5.2.3.2 Tongue and Groove, Keyed and Butt Joints ..............................253 

5.2.3.3 Closure Bands and Couplings....................................................255 

5.2.3.4 Continuous Joints.......................................................................256 

5.3 Screening for Potential Seismic Damage..............................................................257 
ix

TABLE OF CONTENTS (continued) 

5.3.1 Theoretical Concepts Related to Seismically Induced 

 Culvert Damage ........................................................................................ 257 

5.3.1.1 Permanent Ground Failure.........................................................258 

5.3.1.2 Transient Ground Motion .......................................................... 259 

5.3.2 Empirical Observations of Seismically Induced Culvert Damage ...........259 

5.3.2.1 Embankment Penetration...........................................................262 

5.3.2.2 Lateral and Embankment Spreading..........................................263 

5.3.2.3 Slumping of Fill and Landslides................................................264 

5.3.2.4 Surface Faulting......................................................................... 265 

5.3.2.5 Ground Shaking ......................................................................... 266 

5.3.3 Summary of Culvert Screening Criteria ...................................................267 

5.3.4 Commentary on Screening Procedure ......................................................270 

5.4 Evaluation Techniques ...........................................................................................273 

5.4.1 Permanent Ground Failure........................................................................273 

 5.4.1.1 Embankment and Penetration ....................................................275 

 5.4.1.2 Lateral and Embankment Spreading..........................................275 

 5.4.1.3 Slumping of Fills and Landslides ..............................................275 

 5.4.1.4 Surface Faulting......................................................................... 276 

5.4.2 Transient Ground Motion........................................................................... 276 

5.4.2.1 Longitudinal Response of Culverts Due to 

 Transient Ground Motion .......................................................... 277 

5.4.2.2 Transverse Response of Culvert Due to 

 Transient Ground Motion .......................................................... 278 

5.4.2.3 Examples of Culvert Evaluation Under 

 Transient Ground Motion .......................................................... 278 

5.5 Retrofitting Strategies.............................................................................................280 

5.5.1 Ground Remediation.................................................................................280 

5.5.2 Remove and Replace................................................................................. 281 

5.5.3 Culvert Liners ........................................................................................... 281 

 5.5.3.1 Cast-in-Place Liners...................................................................283 

 5.5.3.2 Field Erected Metallic Liners.....................................................284 

 5.5.3.3 Sliplining.................................................................................... 284 

 5.5.4 Joint Retrofit ............................................................................................. 287 

CHAPTER 6: ROADWAYS.................................................................................................. 289

 6.1 Introduction...........................................................................................................289

 6.2 Classification......................................................................................................... 289

 6.3 Screening and Evaluation Guidelines ................................................................... 290 

 6.3.1 Stable Embankments and Foundations....................................................... 290 

 6.3.1.1 Hazard ........................................................................................... 290 

 6.3.1.2 Screen............................................................................................290 

 6.3.2 Compaction of Embankment and Foundation Materials............................290 

 6.3.2.1 Hazard........................................................................................... 290 
x

TABLE OF CONTENTS (continued) 

 6.3.2.2 Screen............................................................................................292 

 6.3.2.3 Evaluation ..................................................................................... 292 

 6.3.3 Liquefiable or Soft Embankment and Foundation Materials .....................295 

 6.3.3.1 Hazard........................................................................................... 295 

 6.3.3.2 Screens for Liquefaction Hazard ..................................................300 

 6.3.3.3 Evaluation ..................................................................................... 301 

 6.3.4 Potentially Unstable Embankments, Foundations or Slopes......................302 

 6.3.4.1 Hazard........................................................................................... 302 

 6.3.4.2 Preliminary Screening and Detailed Evaluation of 

 Slope Instability ............................................................................ 306 

 6.3.5 Active Faults............................................................................................... 306 

 6.3.5.1 Screens for Fault Rupture Hazard.................................................308 

 6.3.5.2 Evaluation Procedures ..................................................................308 

 6.4 Retrofit Strategies ................................................................................................. 309 

 6.4.1 Passive Strategies ....................................................................................... 309 

 6.4.2 Active Strategies.........................................................................................309 

 6.4.2.1 Structural Approach Slabs (SAS) .................................................309 

 6.4.2.2 Use of Easily Repairable Pavement Sections ...............................310 

 6.4.2.3 Replacement of Inferior Pavement Structures ..............................310 

 6.4.2.4 Strengthen Foundations Beneath Roadway Grades......................310 

 6.4.2.5 Clear and Strengthen Side or Cut Slopes......................................310 

APPENDIX A: CHARACTERISTICS OF SURFACE WAVES....................................... 311 

 A.1 Introduction ................................................................................................ 311 

 A.2 Examples of Prominent Rayleigh Waves During 

 Earthquakes ................................................................................................ 311 

 A.3 Summary .................................................................................................... 313 

ACKNOWLEDGMENTS ....................................................................................................... 315 

REFERENCES......................................................................................................................... 317 
xi

LIST OF FIGURES 

2-1 Mass concrete gravity wall ............................................................................................6 

2-2 Inverted T-type cantilever wall......................................................................................7 

2-3 Crib wall.........................................................................................................................7 

2-4 Anchored wall................................................................................................................8 

2-5 Generic cross section of MSE structure.........................................................................9 

2-6 Seismically induced distress of retaining walls ...........................................................12 

2-7 Structure loaded within zone of active failure wedge..................................................13 

2-8 Flowchart summarizing the general procedure for screening, evaluation 

 and retrofit of retaining walls.......................................................................................15 

2-9 Backfill geometry considering construction of the retaining wall...............................18 

2-10 Approximate dimensions for various components of a retaining wall ........................19 

2-11 Forces acting on coherent gravity structure.................................................................23 

2-12 Effect of horizontal and vertical seismic coefficients on active and passive 

 pressure coefficients.....................................................................................................27 

2-13 Ratio of seismic to static bearing capacity factors.......................................................29 

2-14 Assumed distribution of dynamic earth pressure.........................................................34 

2-15 Relationship between static factor of safety and threshold acceleration, s k , for sliding..............................................................................................................36 h

2-16 Incremental failure by base sliding..............................................................................41 

2-17 Incremental bearing capacity failure by Coulomb sliding wedge 

 mechanism ...................................................................................................................42

2-18 Chart for seismic screening of anchored walls ............................................................44 

2-19 Definition of the effective anchor index: EAI=d/H .....................................................45 

2-20 Ratio of active and passive earth pressure coefficients as a decreasing 

 function of ke................................................................................................................46 

2-21 Forces on an anchored wall..........................................................................................47 

2-22 Seismic effects on anchored walls ...............................................................................48 

2-23 Modes of failure for MSE walls...................................................................................52 

2-24 Forces acting on MSE wall for external stability analysis...........................................52 

2-25 Assumed failure surface within the reinforced wall fill...............................................53 

2-26 Influence of seismic coefficients, kh and kv and normalized depth 

 below crest of wall, z/H, on dynamic force amplification factor, rF............................55 

2-27 Tensile load in a reinforcement layer due to seismic lateral earth 

 pressure and wall inertia ..............................................................................................56 

2-28 Overturning moment at an interface within the wall facing of an SRW 

 due to seismic lateral earth pressure and wall inertia ..................................................58 

2-29 Shear force at an interface within the wall facing of an SRW due to 

 seismic lateral earth pressure and wall inertia .............................................................61 

2-30 Retrofit strategies for gravity and semi-gravity walls..................................................63 

2-31 Retrofitting by increasing the width of the base ..........................................................64 

2-32 Seismic effects and retrofit for tied-back walls ...........................................................66 
xii

LIST OF FIGURES (continued) 

3-1 Flowchart for screening, evaluating, and retrofitting embankments and 

 slopes adjacent to highway structures..........................................................................98 

3-2 Rock fall mechanism and resulting hazard ................................................................101 

3-3 Rock falls along the Pacific Coast highway caused by the 1973 Point 

 Mugu earthquake .......................................................................................................101 

3-4 Examples of toppling failures ....................................................................................102 

3-5 Aerial view of coalescing disrupted soil slides caused by the 1976 

 Guatemala earthquake. Slides stripped away vegetation and sheets of 

 sandy residual soil, generally less than 0.6 m thick, exposing white pumice 

 bedrock. Slopes in the foreground are approximately 30 m high.............................103 

3-6 Examples of landslides with discrete basal shear surfaces ........................................103 

3-7 Aerial view of the Native Hospital slide, a large soil block slide in 

 Anchorage, Alaska, caused by the 1964 earthquake..................................................104 

3-8 Rock slump failure mechanism..................................................................................104 

3-9 Soil slump failure mechanism....................................................................................104 

3-10 Lateral spread failure mechanism ..............................................................................105 

3-11 Relationship between corrected “clean sand” blowcount (N1)60-cs and 

 underdrained residual strength (Sr) from case studies ...............................................115 

3-12 Horizontal and vertical seismic coefficients for pseudo-static analysis 

 of rock slopes .............................................................................................................118

3-13 Integration of acceleration time history to determine velocities and 

 displacements.............................................................................................................120 

3-14 Variations of normalized permanent displacement with yield 

 acceleration – summary of all data ............................................................................121 

3-15 Variations of average normalized displacement with yield acceleration...................121 

3-16 Upper bound envelope curves of permanent displacements for all 

 natural and synthetic records analyzed ......................................................................122 

3-17 Variation of normalized permanent deformation with yield acceleration .................123 

3-18 Categories of rock slope stabilization measures ........................................................125 

3-19 Rock slope reinforcement methods............................................................................126 

3-20 Rock-removal methods for slope stabilization ..........................................................127 

3-21 General design criteria for shaped ditches.................................................................128 

3-22 Side view of rock fall restraint net system with fully embedded posts 

 and anchor support.....................................................................................................129 

3-23 Example of rock shed.................................................................................................129 

3-24 Rock slope mitigation methods used by selected states.............................................130 

3-25 Rock buttress used to increase forces resisting slope failure.....................................134 

3-26 Classification scheme for earth retention systems.....................................................135 

3-27 Examples of externally and internally stabilized earth retention systems .................135 

3-28 Types of vertical and horizontal drains used to lower the groundwater in 

 natural slopes .............................................................................................................136
xiii

LIST OF FIGURES (continued) 

4-1 Cross sections of submerged tubes ............................................................................147 

4-2 Summary of empirical observations of seismic ground shaking induced 

 damage to bored tunnels ............................................................................................150 

4-3 Tunnel response to seismic waves .............................................................................154 

4-4 Approaches for analyzing a tunnel for longitudinal axial and curvature 

 deformations ..............................................................................................................157 

4-5 Example of maximum relative displacements associated with seismic 

 wave propagation. The effects of wave passage and incoherency are 

 shown separately and combined. The dashed lines correspond to constant 

 strains of 10 −3and 10 −4 ..............................................................................................158 

4-6 Seismic waves causing longitudinal axial and bending strains .................................158 

4-7 Induced forces and moments caused by seismic waves propagating 

 along the longitudinal tunnel axis..............................................................................160 

4-8 Approaches for seismic analysis of tunnel cross section...........................................167 

4-9 Pseudo-static stability analysis for weak zone adjacent to tunnel .............................168 

4-10 Forces and moments in tunnel lining due to ovaling .................................................169 

4-11 Area and moment of inertia for ovaling analysis of circular tunnel ..........................169 

4-12 Definition of terms for Wang (1993) procedure for analysis of racking 

 of a rectangular tunnel ...............................................................................................173 

4-13 Racking coefficients for rectangular tunnels .............................................................176 

4-14 Simplified frame analysis models for analysis of racking of a rectangular tunnel....177 

4-15 Lateral earth pressures acting on the walls of a cut-and-cover rectangular 

 tunnel..........................................................................................................................178 

4-16 Discrete element model of tunnel ..............................................................................180 

4-17 Relationship between maximum surface fault displacement (MD) and 

 earthquake moment magnitude, Mw, for strike-slip faulting .....................................181 

4-18 Analytical model of tunnel structure at fault crossing...............................................183 

4-19 Schematic illustration of soil-structure model of tunnel at fault crossing .................184 

4-20 Analytical model of soil restraint for tunnel at fault crossing ...................................185 

4-21 Rock bolt stabilization of rock wedge .......................................................................187 

4-22 Rock bolt reinforcement in soft or fractured rock .....................................................187 

4-23 Precast concrete segmental liner................................................................................189 

4-24 Example of flexible circumferential joint detail in tunnel lining with 

 seismic isolation washer ............................................................................................190 

4-25 Example of a flexible circumferential joint detail in tunnel lining............................190 

4-26 Corner reinforcing details for seismic design of box-type tunnel..............................192 

4-27 Typical stone column placement around Webster tube .............................................194 

4-28 Typical jet grout column around Posey tube .............................................................194 

4-29 Redesigned joint preventing tension and allowing compression and 

 shear forces between segments of Posey tube ...........................................................195 

4-30 Seismic joint for transbay tube ..................................................................................196 

4-31 Seismic joint for North Point tunnel ..........................................................................197 

4-32 Enlarged tunnel at fault crossing, plan view, strike-slip faulting ..............................198 
xiv

LIST OF FIGURES (continued) 

4-33 Design of LA Metro tunnel across Hollywood fault zone.........................................199 

4-34 Enlarged tunnel section with final liner and frangible backpacking to 

 accommodate fault displacement...............................................................................200 

4-35 Segment reinforcing and circumferential joint detail, precast concrete 

 segmental liner used in Rose Canyon fault zone for South Bay Tunnel 

 Ocean Outfall Project, San Diego..............................................................................201 

4-36 Flexible joint proposed for segmented tunnel lining in fault zone ............................202 

4-37 Flexible joint detail for Coyote Dam outlet tunnel ....................................................203 

5-1 Available types and sizes of flexible culverts............................................................246 

5-2 Available types and sizes of rigid culverts ................................................................247 

5-3 Corrugated metal culvert wall profiles ......................................................................248 

5-4 Spiral rib metal culvert wall profiles .........................................................................248 

5-5 Selected examples of thermoplastic culvert wall profiles..........................................249 

5-6 Selected examples of bell and spigot culvert joints...................................................253 

5-7 Tongue and groove, keyed and butt joints in reinforced concrete culverts ...............254 

5-8 Selected types of closure bands for corrugated metal culverts..................................255 

5-9 Typical coupling for plain end thermoplastic culverts ..............................................256 

5-10 Penetration of embankment and culvert into liquefied foundation strata..................262 

5-11 Embankment slump (similar effect on culverts as landslide) ....................................265 

5-12 Flowchart of screening procedure for culverts under (a) permanent 

 ground deformation and (b) transient ground deformation........................................268 

5-13 Cast-in-place culvert liner..........................................................................................283 

5-14 Two-flange steel culvert liner plate (top) and four-flange steel culvert 

 liner plate (bottom) ....................................................................................................285 

5-15 Push and pull techniques for installing HDPE sliplining...........................................286 

5-16 Internal corrugated sleeve for joining CMP...............................................................287 

6-1 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...........................................................................................291 

6-2 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.......................................................292 

6-3 Wavy pavement due to differential settlement enhanced by liquefaction 

 during the 1993 Hokkaido-Nansei-Oki, Japan earthquake. The site is on 

 Highway 5 south of Oshamanbe................................................................................296 

6-4 Failure mechanism beneath embankments that split, settle, and spread 

 due to liquefaction of foundation soils.......................................................................297 

6-5 Segment of Highway 36 near Caribbean coast in Costa Rica that split 

 longitudinally, settled and spread laterally during 1991 earthquake by 

 mechanism illustrated in figure 6-4 ...........................................................................297 
xv

LIST OF FIGURES (continued) 

6-6 Disrupted fill and pavement at approach to collapsed Highway 36 bridge 

 over Rio Estrella, Costa Rica. The disruption was due to liquefaction of 

 foundation soils during 1991 earthquake...................................................................297 

6-7 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 

 2 m of lateral spread displacement.............................................................................298 

6-8 Extensional fissures in flexible pavement caused by lateral spread of 

 floodplain deposits toward Rio Viscaya during the 1991 Costa Rica 

 earthquake..................................................................................................................299 

6-9 Fractured and overlapped flexible pavement on Highway 229 near 

 northern edge of Assabu River valley. The disruption was due to liquefaction and 

ground oscillation during 1993 Hokkaido-Nansei-Oki, Japan earthquake; 

 note extensional separation between curb blocks at same locality............................300 

6-10 Liquefaction-induced flow failure of roadway embankment into Lake 

 Merced during 1957 Daly City, California earthquake .............................................301 

6-11 Slump failure in Highway 5 embankment north of Oshamanbe, Japan 

 during the 1993 Hokkaido-Nansei-Oki earthquake. Failure was due to 

 weakening of soft foundation soils ............................................................................302 

6-12 Rigid and flexible pavements disrupted by slump failure of Blucher 

 Avenue near Lower Van Norman reservoir during the 1971 San Fernando 

 earthquake..................................................................................................................303 

6-13 Slump of Highway S22 fill east of Salton Sea during the 1968 Borrego 

 Mountain, California earthquake ...............................................................................304 

6-14 Sinuous scarp in Summit Road caused by apparent movement of a deep- 

 seated landslide during the 1989 Loma Prieta, California earthquake ......................305 

6-15 Disruption to 4th Street, Anchorage, Alaska, caused by deep slump 

 during 1964 Alaska earthquake; headscarp is about 2.8 m high................................305 

6-16 Steep slopes along western shore of Okashiri Island from which 

 numerous rock falls descended onto roadway pavement during the 1993 

 Hokkaido-Nansei-Oki, Japan earthquake. The debris pitted pavement and 

 blocked highway ........................................................................................................306 

6-17 Rigid and flexible pavements buckled and overlapped by thrust faulting 

 on I-405 south of separation from I-5 during 1971 San Fernando 

 earthquake..................................................................................................................307 
xvi

LIST OF TABLES 

2-1 Results from application of seismic evaluation procedure for anchored 

 walls (described in Example 2-1) ..................................................................................50 

3-1 Characteristics of earthquake-induced landslides..........................................................99 

3-2 Geologic environments likely to produce earthquake-induced landslides 

 in the Los Angeles region ............................................................................................108 

3-3 Description and ratings for the parameters RQD, Jn and Jr..........................................111 

3-4 Description and ratings for the parameter Ja ................................................................112 

3-5 Description and ratings for AF ....................................................................................112 

3-6 Comparison of deformation analysis methods.............................................................124 

3-7 Allowable bond stresses in cement-grout anchors.......................................................126 

3-8 Summary of approaches to potential stability problems..............................................132 

4-1 Assessment of need for seismic evaluations of bored tunnels as related 

 to tunnel lining/support system, geologic conditions, and level of ground 

 shaking .........................................................................................................................152 

4-2 Strains and curvature induced by seismic wave propagating along a 

 tunnel............................................................................................................................159 

4-3 Ratios of ground motion at tunnel depth to motion at ground surface ........................162 

4-4 Ratios of peak ground velocity to peak ground acceleration in rock 

 and soil.........................................................................................................................163 

5-1 Summary of highway culvert performance..................................................................261 

6-1 Expected maximum volumetric strains in dry to moist soils due to seismic 

 shaking .........................................................................................................................293 

6-2 Relative density of sands estimated from standard (SPT) and cone (CPT) 

 penetration test data .....................................................................................................294 
xvii

LIST OF ABBREVIATIONS AND SYMBOLS 

ABBREVIATIONS 

AASHTO American Association of State Highway and Transportation Officials 

ACI American Concrete Institute 

ACP Asphaltic Concrete 

ACPA American Concrete Pipe Association 

AFTES Association Francaise des Travaux en Souterrain 

AISI American Iron and Steel Institute 

ASCE American Society of Civil Engineers 

ASTM American Society for Testing and Materials 

ATC Applied Technology Council 

BART Bay Area Rapid Transit 

BSSC Building Seismic Safety Council 

CMBC Corrugated Metal Box Culvert 

CMLS Corrugated Metal Long Span 

CMP Corrugated Metal Pipe 

CPT Cone Penetration Test 

EAI Effective Anchor Index 

EP Embankment Penetration 

EPI Embedment Participation Index 

FEMA Federal Emergency Management Agency 

FHWA Federal Highway Administration 

FR Fault Rupture 
xviii

FRP Fiber Reinforced Plastic 

GEC Geotechnical Engineering Circular 

GS Ground Shaking 

H/B Height/Base width 

HDPE High Density Polyethylene 

LA Landslide 

LO Lateral Overpressures 

LQ Liquefaction 

LS Lateral Spread 

MCE Maximum Considered Earthquake 

MCEER Multidisciplinary Center for Earthquake Engineering Research 

MCU Modular Concrete Units 

MD Maximum Displacement 

M-O Mononobe-Okabe 

MSE Mechanically Stabilized Earth 

NATM New Austrian Tunneling Method 

NCMA National Concrete Masonry Association 

NEHRP National Earthquake Hazards Reduction Program 

NMSZ New Madrid Seismic Zone 

PCC Portland Cement Concrete 

PGA Peak Ground Acceleration 

PGD Peak Ground Displacement 

PGV Peak Ground Velocity 

PTI Post Tensioning Institute 

PVC Polyvinyl Chloride 
xix

PWPP Profile Wall Plastic Pipe 

RC Relative Compaction 

RCBC Reinforced Concrete Box Culvert 

RCLS Reinforced Concrete Long Span 

RCP Reinforced Concrete Pipe 

RQD Rock Quality Designation 

SAS Structural Approach Slabs 

SG Strong Ground Shaking 

SIDD Standard Installation for Direct Design 

SL Slumping 

SPT Standard Penetration Test 

SRSS Square Root of the Sum of the Squares 

SRW Segmental Retaining Wall 

UCP Unreinforced Concrete Pipe 

UMP Unreinforced Masonry Pipe 

USGS United States Geological Survey 

SYMBOLS 

CHAPTER 2: WALLS AND RETAINING STRUCTURES 

αAE = Inclination of active failure surface. 

β = Wall batter; inclination of the back face of the retaining wall. 

β2 = Batter of the front face of the wall; inclinations of the front face of the retaining wall. 

γ = Unit weight. 

γ’ = Submerged unit weight. 

γD = Surcharge. 
xx

γt = Total unit weight of the backfill. 

∆ = Total horizontal component of movement. 

∆ρAE, ∆ρPE = Dynamic effects to be added or subtracted to the static values. 

δ = Wall/wallfill interface friction angle. 

δf = Interface friction angle between the base of the foundation and the soil. 

δw = Wall/soil interface friction angle. 

μ = Coefficient of friction between the reinforcement and the wallfill. 

ρAE = Angle of the sliding surface of the active portion of the bearing capacity failure. 

φ = Angle of friction. 

φb = Wall base/foundation soil interface friction angle. 

φf = Friction angle of the foundation soil. 

φw = Internal friction angle of the backfill. 

ψ = Wall batter. 

AD = Anchor force. 

AR = Anchor plate resistance. 

B = Width of the footing. 

b = Width of reinforcement. 

c = Cohesion of the foundation soil. 

D = Depth of embedment of the wall toe. 

d = Residual displacement; Horizontal distance. 

D/H = Embedment depth ratios. 

e = Eccentricity. 

f = Friction factor. 
xxi

F = Sum of the horizontal forces. 

Fγd = Depth factor for soil friction term. 

Fγi = Inclination factor for soil friction term. 

FA = Design force. 

Fa = Site coefficients. 

Fc

i

 = Connection capacities of reinforcement layers. 

Fdyn = Tension in the reinforcement at depth z; Dynamic tensile force. 

fN = Resisting force. 

Fqd = Depth factor for surcharge term. 

Fqi = Inclination factor for surcharge term. 

Fsta = Static tensile force. 

Fstatic = Static factor of safety. 

g = Acceleration due to gravity. 

h = Height of anchor plate. 

H = Height. 

⎯h = Vertical distance from the line of action of PAE to the toe of the wall footing. 

i = Backfill inclination. 

j = Facing unit. 

KA = Static lateral earth pressure coefficient. 

ke = Function of the horizontal and vertical seismic coefficients. 

kh = Coefficient of horizontal component of acceleration. 

kh

b = Coefficient of horizontal component of acceleration for yield due to seismic reduction of 

bearing capacity. 

kh

OT = Coefficient of horizontal component of acceleration at threshold of overturning. 
xxii

kh

s

 = Coefficient of horizontal component of acceleration at threshold for sliding. 

(kh)ANC = Critical acceleration for anchor failure. 

(kh)RT = Critical threshold acceleration for rotation about top of wall. 

ko = Peak ground acceleration coefficient accounting for local soil conditions. 

kv = Vertical acceleration component. 

L = Length of the wall used to compute N. 

Le = Length of the reinforcement beyond the failure zone defined by ρAE. 

Lw = Width of the wall facing. 

MD = Driving moment. 

MR = Resisting moment capacity. 

n = Shear transfer coefficient. 

N = Number of reinforcement layers; sum of the vertical forces transmitted to the soil. 

Nγ = Soil friction bearing capacity factor. 

NcE = Seismic bearing capacity factor. 

Nq = Surcharge bearing capacity factor. 

NqE = Seismic bearing capacity factor. 

NγE = Seismic bearing capacity factor. 

q = Overburden due to depth of the footing. 

PAE = Active lateral earth pressure. 

PAS = Driving force. 

plE = Seismic limit to the bearing pressure. 

PPE = Passive resistance from solid placed over the toe of the wall. 

R = Rotation mode; Bearing pressure from foundation soil. 
xxiii

rf = Magnification factor. 

Sdyn = Interface shear stress. 

Ss = Mapped short-period acceleration response parameter. 

Sv = Reinforcement spacing. 

T = Translation mode. 

V = Velocity. 

Vu = Shear strength of the interface between modular blocks. 

w = Vertical settlement. 

Ww = Weight of the retaining wall; Weight of the facing column. 

x = Width of contact along the base of the footing. (eq. 2-17). 

Xc = Horizontal distance from the centroid of the wall to the toe of the wall footing. 

Yc = Vertical distance from the centroid of the wall to the toe of the wall footing. 

Yc

i

 = Corresponding moment arms of Fc

i

. 

z = Depth to the ground water surface below the base of the footing. 

CHAPTER 3: SLOPES, EMBANKMENTS, AND ROCKFALLS 

A = Peak ground acceleration. 

AF = Aperture factor. 

amax = Peak ground acceleration. 

D = Displacement; deformation. 

h = Height of embankment. 

Ja = Joint alteration number. 

Jn = Joint set number. 

Jr = Joint roughness number. 
xxiv

Jv = Total number of joints per cubic meter. 

ka = Peak induced acceleration. 

kmax = Peak acceleration induced within a sliding mass. 

ky = Yield acceleration. 

(N1)60-CS = Clean sand blowcount. 

Neq = Number of cycles. 

Q = Rock quality. 

QRF = Seismic rock fall susceptibility index. 

Sr = Residual undrained shear strength in psf. 

T = Predominant period of the time history. 

To = Natural period. 

V = Velocity. 

Vmax = Low-strain maximum shear wave velocity. 

Vs = Strain-dependent shear wave velocity of the soil. 

CHAPTER 4: TUNNELS 

γ = Shear strain. 

smax γ = Maximum free-field shear strain. 

t γ = Total unit weight of geologic medium. 

∆ff = Free-field soil shear deformation over tunnel height. 

∆pE = Lateral earth pressure on tunnel wall. 

∆r = Racking distortion of the tunnel over tunnel height. 

ε = Axial strain. 

ε

ab = Maximum axial strain due to combined axial and bending deformations. 
xxv

σ = Compressive or tensile stress. 

σab = Maximum axial stress due to combined axial and bending deformations. 

σV = Vertical total stress. 

τ = Shear stress. 

νl = Poisson’s ratio of the liner. 

 νm = Poisson’s ratio of geologic medium. 

θ = Angle from horizontal of line from center to perimeter of tunnel in plane of tunnel cross 

section. 

φ = Angle of direction of seismic wave propagation in horizontal plane with respect to tunnel 

longitudinal axis. 

1/ρ = Curvature. 

A11 = Cross sectional area of lining (see eqs. 4-6 and 4-7). 

A12 = Area of unit length of lining (see eq. 4-29 and fig. 4-11). 

amax = Peak horizontal ground acceleration at ground surface. 

aP = Peak particle acceleration caused by P-waves. 

aR = Peak particle acceleration caused by R-waves. 

aS = Peak particle acceleration caused by S-waves. 

av = Peak vertical ground acceleration at ground surface. 

C = Compressibility ratio. 

Cm = Shear wave velocity of geologic medium. 

Cm

′ = Effective shear wave velocity of geologic medium. 

CP = Apparent propagation velocity of P-waves. 

CR = Propagation velocity of R-waves. 

CS = Apparent propagation velocity of S-waves. 
xxvi

CV = Seismic earth pressure coefficient. 

D = Diameter of tunnel. 

Di = Inside diameter of tunnel lining. 

Do = Outside diameter of tunnel lining (Do = D). 

E1 = Young’s modulus of tunnel lining. 

f = Maximum frictional force per unit length of tunnel. 

F = Flexibility ratio, circular tunnel. 

Fr = Flexibility ratio, rectangular tunnel. 

g = Acceleration of gravity. 

Gm = Shear modulus of geologic medium. 

Gm

′ = Effective shear modulus of geologic medium. 

H = Height of tunnel. 

h = Depth to center of tunnel. 

I11 = Moment of inertia of lining cross section (see eq. 4-7). 

I12 = Moment of inertia of unit length of lining (see eq. 4-17, eq. 4-29 and fig. 4-11). 

Ka = Longitudinal soil spring constant per unit length of tunnel. 

Kh = Transverse soil spring constant per unit length of tunnel. 

Ko = Coefficient of lateral earth pressure at rest. 

kh = Horizontal earthquake coefficient. 

L = Wavelength. 

M = Moment. 

P-wave = Compressional wave. 

Q = Tunnel axial force. 
xxvii

(Qmax)f = Maximum frictional force. 

R = Reduction factor. 

Rr = Tunnel racking coefficient. 

R-wave = Rayleigh wave. 

S = Tunnel racking stiffness. 

S-wave = Shear wave. 

t = Lining thickness. 

Τ = Τhrust force. 

TP,S,R = Period of seismic P-wave, S-wave and R-wave, respectively. 

V = Shear force. 

VP = Peak particle velocity caused by P-waves. 

VR = Peak particle velocity caused by R-waves. 

VS = Peak particle velocity caused by S-waves. 

w = Tunnel width. 

Y = Distance from the neutral axis of the cross section to the extreme fiber of the tunnel lining 

(see eqs. 4-1, 4-2 and 4-3). 

Z = Depth of soil above tunnel. 

APPENDIX A: CHARACTERISTICS OF SURFACE WAVES 

CR(T) = Site-specific dispersion curve. 
 
1

CHAPTER 1: INTRODUCTION 

The performance of highway bridges is often considered to be the main determinant in the seismic 

performance of a highway system. This is due, in large part, to the fact that there are often many 

more bridges in a region than other types of highway structures or components. Damage to bridges 

is typically more visible than that to these other types of structures. However, these other 

components and structures of the highway system may also be important in assuring satisfactory 

seismic performance of the system. 

For example, retaining walls or slopes in highway embankments or excavations provide ground 

stability at the edges of a highway corridor and protect adjacent property. Tunnels, although much 

less prevalent than bridges, may comprise important components of the transportation system 

since, in many cases, a tunnel may provide the only link between two sections of a highway 

system; i.e., there may be little or no redundancy in the highway or transit system corridor. 

Consequently, adequate seismic performance of tunnels may be critical. Culverts through or 

beneath highway embankments are depended on to control surface water flows, and a seismically 

induced failure could lead to flooding or erosion of a highway or the surrounding area. Finally, 

failure of a highway roadway due to seismically induced failure of an embankment or its 

foundation may prevent traffic flow until time-consuming repairs can be made. 

In 1983, the Federal Highway Administration (FHWA) published a landmark manual that 

provided recommendations for screening, evaluating, and retrofitting highway bridges subjected 

to earthquakes (FHWA, 1983). That manual was updated and reissued in 1995 (FHWA, 1995). 

Similar guidance, however, has never been developed for these other structures that comprise a 

typical highway system. 

The current edition expands the coverage of the previous publications and is published in two 

parts. Part 1 covers the screening, evaluation, and retrofitting of highway bridges. It extends the 

guidance provided in the earlier 1983 and 1995 FHWA manuals, based on recent experiences in 

California, Japan, and other countries, and the results of comprehensive research programs 

sponsored by the FHWA, the California Department of Transportation, and other agencies. Part 2 

covers these other important highway system structures, namely retaining structures, slopes, 

tunnels, culverts, and roadways. 

1.1. SCOPE 

This manual provides guidance on the seismic evaluation and retrofit design of retaining 

structures, slopes, tunnels, culverts, and roadways. This includes guidance on (a) screening for 

potential seismic vulnerabilities; (b) conducting a detailed evaluation; and (c) describing strategies 

for retrofit design. In addition, discussion is provided for classifying each structure by type, 

construction, or expected performance. This is needed since different types of a given structure 

(e.g., different types of retaining walls) may have different failure modes and will therefore require 
2

somewhat different approaches to seismic vulnerability screening, detailed evaluation, and 

retrofitting. 

1.1.1. SCREENING 

In general, prior to embarking on a detailed seismic evaluation of a highway system structure, an 

initial screening is carried out to determine whether there is a potential for reduced performance 

due to a complete or partial seismically induced failure of the structure. The screening 

methodologies recommended herein are intended to be easy to apply, yet somewhat conservative. 

If a structure passes the screening criteria, this indicates that there is a low risk of failure and more 

detailed evaluation or retrofitting is not likely required. If the structure doesn’t pass the initial 

screening step, the owning agency or its designated engineer must decide if a more detailed 

evaluation, and potential retrofitting, is warranted. 

There are a number of considerations that must be included regarding the decision to conduct 

detailed evaluations and, for those structures deemed vulnerable to seismic demands, retrofitting. 

Among these are the cost of further evaluation and retrofitting, and the importance of the structure. 

This is discussed further in section 1.2. 

1.1.2. DETAILED EVALUATION 

A detailed seismic evaluation is carried out to determine whether or not the structure may fail 

seismically and, if so, whether a seismic retrofit should be considered. If retrofit is required, these 

evaluations would continue as a part of retrofit design. Detailed evaluation procedures are 

presented for each structure type, focusing on the modes of failure most likely to pose the greatest 

risk. Emphasis, where possible, is on the presentation of step-by-step simplified evaluation 

procedures that are readily applied yet are reliable and generally accepted in practice. Reference is 

made to more detailed analytical approaches that should be considered either for more detailed 

confirmatory analysis or when simplified procedures are not available. 

1.1.3. RETROFIT DESIGN STRATEGIES 

Guidance is presented regarding alternative approaches and strategies that may be considered in 

the seismic strengthening of a structure that is determined to be seismically vulnerable from the 

screening or evaluation process. In some cases, contingency measures are described that may be 

considered where retrofit design may be judged to be impractical or economically unwarranted. 

The approaches and strategies presented herein are those that have been utilized in similar retrofit 

design situations. 
3

1.2. DESIGN EARTHQUAKES, GROUND MOTIONS, AND PERFORMANCE 

CRITERIA FOR SEISMIC SCREENING, EVALUATION, AND RETROFIT DESIGN 

In general, the design earthquakes and ground motions to be used in screening, evaluation, and 

retrofit design of highway structures covered herein are the same as those described in Part 1. 

Furthermore, as described in Part 1, a two-level evaluation and design approach may be considered 

and is encouraged to assure a higher level of performance for more frequently occurring ground 

motions. 

In evaluating the highway system structures described in this report, it is important to recognize 

that the failure or large deformations of some components may not necessarily comprise a life 

safety risk. For example, a retaining wall or a slope may translate up to or more than a meter, yet 

may not pose a life safety risk to users of the highway system. However, consideration must not be 

restricted to only the impact on the highway system from structure damage, but also to potential 

collateral damage and life safety for other structures that may be affected by the failure of the 

highway structure; e.g., a facility or structure located directly above or below a retaining wall or 

slope. 

Furthermore, decisions on whether to seismically retrofit a highway system structure may depend 

on its importance and criticality, and cost-benefit considerations. For example, a decision may be 

made to seismically retrofit a tunnel if it provides non-redundant access to an area and if the 

damage to the tunnel could disrupt post-earthquake traffic flow, even though such damage may not 

be life threatening. Considerations of facility importance, cost-effectiveness, or prioritization for 

retrofit are not explicitly considered herein, but their importance must be recognized in developing 

an overall evaluation and retrofitting program, and in making decisions for individual facilities. 

The primary goal of any seismic evaluation and retrofitting program should be to minimize the risk 

of unacceptable damage and the potential for loss of life; however, such decisions must be 

tempered by cost considerations and the performance of such structures in prior earthquakes. 

Transportation structures must be classified as to their importance with respect to traffic flow and 

the impacts on society due to damage or closure of the structure or associated highway. It is 

recommended that two classifications of importance be considered for the transportation structures 

addressed in this report: standard and essential (refer to Part 1, chapter 1). 

Decisions regarding the level of detailed evaluation and retrofitting of the highway structures 

covered in this report should include consideration of its importance and the cost of retrofitting. 

The owning agency may determine that earthquake damage is acceptable, if it can be easily 

repaired or functionality can be restored relatively quickly (e.g., gravel or asphalt can be quickly 

and temporarily applied to damaged roadways). Standard structures may not warrant retrofitting 

to provide the same level of performance as newly designed structures; however, life safety 

concerns should be addressed. Essential structures, however, may typically warrant significant 

investments in evaluation and retrofitting, in order to ensure both life safety and some level of 

post-earthquake functionality. This is a decision that the owning agency must make. 
4

1.3. REPORT OUTLINE 

This report addresses the seismic vulnerability evaluation and retrofitting of the major highway 

system structures other than bridges. Each chapter contains a section on classification, preliminary 

screening, detailed evaluation, and retrofitting. Chapter 2 covers retaining structures (other than 

those directly attached to a bridge), chapter 3 covers slopes and rock fall related to highway cuts 

and fills, chapter 4 addresses transportation tunnels, chapter 5 covers flexible and rigid culverts, 

and culvert joints, and chapter 6 addresses rigid and flexible roadways. 
5

CHAPTER 2: WALLS AND RETAINING STRUCTURES 

2.1. INTRODUCTION 

This chapter on walls and retaining structures describes procedures for classifying earth retaining 

structures that function as components of a highway system, screening them relative to their 

seismic vulnerability, and evaluating their performance during earthquake loading using 

simplified methods. It also describes retrofitting strategies and methods to repair or mitigate the 

effects of earthquake shaking. This chapter does not cover retaining structures that are an 

integral part of a bridge, i.e., abutments and wing walls. 

Consistent with the performance criteria described in Part 1, the seismic vulnerability of 

retaining structures is assessed with respect to life safety issues. Life safety issues include 

collapse of the retaining structure. The possibility of unacceptable damage to nearby essential 

structures may also give cause for assessing the level of service of the retaining structure. 

As demonstrated in the 1995 Kobe earthquake, the most common collapse mechanisms for 

retaining structures subjected to earthquake loading include excessive tilting leading to an 

overturning instability, or structural failure, cracking of concrete gravity or cantilever retaining 

walls (Koseki et al., 1996). This chapter describes a force based approach whereby factors of 

safety are evaluated relative to external stability, and internal stability is evaluated by comparing 

the applied loads to the structural resistance. The force based approach for evaluating external 

stability is employed as a tool to identify cases where excessive deformations leading to collapse 

are possible. In these cases, more detailed deformation analyses are recommended. 

Retaining walls may also slide outward as well as rotate due to seismic loads. The soil behind 

them slumps possibly causing secondary damage to structures they support, or protect, such as 

highway fills and buildings above or below the wall. If seismically induced deformation of 

retaining structures is excessive, nearby essential structures or facilities may suffer unacceptable 

loss of service including interruption of utilities, structural damage, or loss of access and regress. 

Therefore, for those cases where the serviceability of nearby essential facilities is deemed 

important, this chapter will also address level of service issues related to estimating and 

controlling seismically induced permanent deformations due to sliding, overturning and loss of 

bearing capacity. 

2.2. CLASSIFICATION OF WALL TYPES 

Salient details of the wall descriptions appropriate to screening and evaluation for seismic 

retrofit are presented herein. A complete description of retaining wall classifications and proper 

terminology are presented in Geotechnical Engineering Circular No. 2: Earth Retaining Systems

(Sabatini, 1997). 
6

In general, walls are classified as rigid gravity and semi-gravity walls, prefabricated modular 

gravity walls, anchored walls, mechanically stabilized earth walls, non-gravity cantilevered 

walls, and in-situ reinforced walls. 

2.2.1. RIGID GRAVITY AND SEMI-GRAVITY WALLS 

Retaining walls that rely on their mass to resist lateral earth pressures transferred from the 

backfill are referred to as gravity and semi-gravity walls. The walls are considered rigid and are 

usually not fully constrained against rotation or displacement at the base. It is generally assumed 

that deformations are sufficient to mobilize active conditions within the backfill and passive 

pressure at the toe if buried. 

2.2.1.1. Gravity Walls 

Gravity retaining walls may be mass concrete (figure 2-1), or masonry. Prior to 1960, these 

walls were the most popular construction practice. Mass concrete walls are generally 

proportioned such that a minimum amount of reinforcing steel is required. The mass of the wall 

limits tensile stress in the concrete. Minimum reinforcing steel may be required to control 

cracking due to the tendency for concrete to undergo volume changes from shrinkage and 

temperature variation. 

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Figure 2-1. Mass concrete gravity wall. 

2.2.1.2. Semi-Gravity Walls 

Semi-gravity walls including cast in-place concrete cantilever/counterfort retaining walls (figure 

 2-2) are similar to gravity-type walls, but are designed such that a portion of the backfill is used 

to contribute to stability. When the stability is evaluated, the wall and the backfill placed over 

the heel of the footing are considered to act as a unit. Less concrete is used to construct a 

cantilever wall than for a mass gravity wall. However, large flexural stresses are generated near 

the base of the wall stem, and heel of the footing. Therefore, these members require significant 

amounts of reinforcing steel. Counterforts may be added to buttress the wall stem to reduce the 

moments and reinforcing requirements. 
7

Gravity and semi-gravity retaining walls may be supported on shallow or deep foundations. In 

general, retaining walls supported by piles or drilled shafts are not vulnerable to collapse except 

from structural failure of pile-head connections, or liquefaction of the foundation soil. Therefore, 

the majority of the guidelines for evaluating these wall types is with respect to shallow 

foundations, i.e., spread footings. 

Counterforts

Figure 2-2. Inverted T-type cantilever wall. 

2.2.2. PREFABRICATED MODULAR GRAVITY WALLS 

Prefabricated modular gravity walls incorporate soil into the mass of the wall system as in crib walls 

or gabion walls (figure 2-3). These wall types also rely on mass for stability. Materials such as 

ballast or boulders are contained with cribbing or wrapped within a wire mesh. Cribbed or gabion 

units are connected to form a coherent mass to resist inertia forces, and applied lateral earth 

pressures. Internal stability must also be analyzed with respect to sliding, bulging between units, or 

the structural integrity of the cribbing. 

Stretcher

Headers

Face of Wall

Note: Cells to be

filled with soil

Figure 2-3. Crib wall. 
8

2.2.3. ANCHORED WALLS 

Anchored walls are constructed with vertical elements that are embedded into the soil with tiebacks to restrain the top. Facing elements are used to support retained soil. Vertical wall 

elements may consist of discrete vertical elements (e.g., piles, caissons, drilled shafts) spanned 

by structural facing (e.g., wood or reinforced concrete lagging, precast or cast into place concrete 

panels, wire or fiber reinforced concrete, or metal elements such as sheet piles). The discrete 

vertical elements typically extend deeper into the ground than the facing to provide vertical and 

lateral support. Alternatively, the vertical wall elements are continuous (e.g., sheet-piles) and, 

therefore, also form the structural facing. Tie-backs can be anchored to flat “deadmen” or 

battered piles; or grouted anchors may be used. A typical anchored wall is depicted in figure 2-4. 

The most common application of anchored walls is for waterfront structures, but they are also 

used sometimes in dry or drained conditions. Of particular interest are tied-back walls used to 

retain highway fills on sloping ground, or for approach embankments. The backfill used to 

construct tied-back walls in dry conditions is select and often densified. 

When used as waterfront structures, tied-back walls are usually constructed by driving sheetpiles and dredging to the desired depth. Often the dredged material is used as additional backfill. 

Thus, unlike tied-back walls constructed in dry soil, the soil at the toe and anchor of a waterfront 

tied-back wall necessary to provide passive resistance is often loose, fine grained, and below the 

water table. 

If Waterfront

Structure

H

D

Tie Rod

Anchor

Sheet Piles

Ah

Wale

Dredge line or natural soil

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Figure 2-4. Anchored wall. 
9

2.2.4. MECHANICALLY STABILIZED EARTH (MSE) WALLS 

MSE walls (i.e., reinforced soil, figure 2-5) incorporate some type of reinforcing element in the 

soil to help resist lateral earth pressures. The analysis of MSE walls, described in section 2.4.5, 

treats the reinforced fill, referred to as wall fill, as a gravity retaining wall that supports the 

unreinforced backfill placed behind it. The external stability analysis of an MSE wall is similar 

to that of any other gravity-type retaining wall. In addition, an analysis of the internal stability to 

evaluate structural integrity of the reinforcements must be performed. 

Reinforcements may be in the form of strips, sheets, bar mats, or grids. They may be made from 

metallic materials such as mild steel, galvanized steel, or aluminum. Nonmetallic reinforcements 

are generally polymeric materials consisting of polypropylene, polyethylene, or polyester 

polymers. Geotextiles and geogrids are popular types of polymeric reinforcement. 

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Finished Grade

Mechanically Stabilized

Earth Mass

Facing

Reinforcing Inclusions

Limits of Construction

Excavation

Original Ground

Surface

Retained

Backfill

Foundation Soil

Leveling Pad

Elias and Christopher, 1997 

Figure 2-5. Generic cross section of MSE structure. 

Depending on the level of strain required to mobilize the working stress levels in the 

reinforcement, reinforcements are extensible, or relatively inextensible. The deformation of 

relatively inextensible reinforcement at failure is much less than the deformability of the soil. 

Relatively inextensible reinforcement may not reach levels of strain required to develop active 

earth pressures for the entire height of the wall. For extensible reinforcement, the deformation at 

failure is comparable to, or even greater than, the deformation of the soil. Typically, metallic 

strip, or bar mat, type of reinforcement is relatively inextensible and geotextiles are extensible. 

Certain details of the screening and evaluation procedure described in sections 2.3.3 and 2.4.5 

are related to the type of wall facing incorporated into the MSE wall system. As described by 

Holtz et al. (1995), a variety of facings may be used with MSE walls including modular concrete 

units (MCU), wrap around facings, segmental concrete panels, full-height concrete panels, 

metallic facings, timber facings, or gabion facings. With the exception of MCUs, the wall facing 

is mainly for protection from erosion and exposure to the environment. MCUs are considered to 

have mass that contributes to the stability of the MSE wall system. 
10

2.2.5. OTHER WALL TYPES 

In addition to the retaining wall types described in the sections above, others are available, 

including non-gravity cantilever walls with an embedded toe such as sheet-pile walls, etc., soil 

nail walls, reticulated micropile walls, slurry walls, concrete diaphragm walls, and deep mixed 

soil walls. These walls are not considered to be a significant portion of the existing inventory, 

and are not discussed explicitly in the following sections. 

Due to their flexibility, analysis of the dynamic response of the backfill behind non-gravity 

cantilever retaining walls is complicated. Some information on design and analysis of soil nail 

walls is described by Byrne et al. (1996b). Reticulated micropile walls are described by Bruce 

and Juran (1997). 

Many retaining walls in the larger urban areas support soundwalls that range in height from 3.5 

to 5 meters. In some areas, such as the northeast U.S., designers consider a substantial lateral 

wind load, but in very seismically active areas, such as California, seismic load may control the 

design. For seismic evaluation of retaining walls that support soundwalls, the forces and 

moments transferred to the top of the retaining wall should be considered. These details are not 

included within the analyses and equations presented in this manual. 

2.3. SCREENING 

Screening of retaining walls is intended to identify those walls susceptible to damage in 

earthquakes, and therefore candidates for detailed evaluation. The procedure is conservative in 

the sense that some walls are included in the category for detailed evaluation that will eventually 

be assessed as not at high risk to seismic loading and no retrofit measures will be required. The 

screening procedure requires a minimum amount of information including location, site 

conditions, wall height, base width (if applicable), type of retaining wall, and proximity of 

essential facilities. This information can be obtained from existing records, soil and geologic 

maps, and should always entail a site visit. 

The screening guidelines presented in this section are for retaining walls in which neither the 

backfill nor foundation soils will undergo liquefaction. The user must screen the site for the 

liquefaction hazard as described in chapter 3, Part 1 of this manual. 

This section assumes that the user has estimated the anticipated peak ground acceleration (PGA) 

at the site of the retaining wall. The user is referred to chapter 2, Part 1 of this manual for 

guidance. Additional guidance on assessing seismic ground motions at retaining walls sites is 

contained in section 2.4.1.3 in this chapter. 

The user must also investigate the possibility of the retaining wall being engulfed in a global 

failure mechanism. This mode of failure is in the category of slope stability as described in 

chapter 3, Part 1 of this manual. 
11

2.3.1. GENERAL SCREENING CRITERIA 

The general screening criteria are described with respect to gravity and concrete cantilever 

retaining structures. Special considerations that must be taken into account relative to tied-back 

and MSE retaining walls are described in sections 2.3.2 and 2.3.3. 

Retaining structures are screened with respect to two sets of information described below. The 

first set (level 1) screens the retaining walls with respect to the potential for seismically induced 

problems related to life safety issues and possibly with respect to level of service. The second set 

(level 2) involves visual observation of the wall, condition assessment, and an evaluation of the 

level of safety of the wall with respect to static loading. Walls that are determined to not require 

seismic evaluation on the basis of a level 1 screening must still pass the scrutiny of a level 2 

screening before a final determination is made. Level 2 screening need not be applied to walls 

that are selected for detailed seismic evaluation based on the results of level I screening since a 

site visit is part of the detailed seismic evaluation. 

2.3.1.1. Level 1 

Relevant modes of failure as they relate to life safety issues are depicted in figure 2-6 (a) and (b). 

Modes of failure include: 

• Overturning of the retaining wall or excessive tilting due to loss of bearing capacity. 

• Structural failure of the wall. 

Level of service and excessive damage to nearby essential facilities is described in figure 2-6 (c). 

Overturning of retaining walls is a concern particularly for tall, slender retaining walls. 

Increments of seismically induced tilting, or rotation, of the wall accumulate during cycles of 

strong ground shaking. Long-period and long duration earthquakes are of particular concern due 

to potentially high ground velocity, or large number of cycles of strong ground shaking, 

respectively. Screening of the inventory should be performed to identify tall, slender walls and 

the corresponding seismic hazard. Wall slenderness ratios (height/base width, H/B) greater than 

2.0 and/or walls where the horizontal distance from the toe to the center of gravity is less than 

half the width of the base are a serious concern in areas where the seismic hazard at the site is a 

peak horizontal ground acceleration in excess of 0.3 g. Slenderness ratios less than two may be 

a problem for special circumstances, e.g., walls with a high backslope angle. 

Seismically induced structural failure of retaining walls is due to overstressing of structural 

components of the retaining wall system. Accelerations associated with earthquake ground 

motions, and present within the backfill, have a twofold effect on the lateral earth pressure 

applied to the backface of a retaining wall. The first is an increase in the lateral thrust, and the 

second is that the line of action of the lateral thrust is raised with respect to the base of the wall. 

For high levels of peak ground acceleration, this can lead to significant increases in bending 

moments within the wall stem, and at the toe and heel of the wall footing. Since for a properly 

designed reinforced concrete structure a load factor of 1.7 was typically applied to static earth 

loads (AASHTO, 1996; ACI, 1999), reinforced concrete retaining walls should not suffer a 
12

. .

..

.. . .

. .

.. .

. . . . .

. .

.

.

.

.

.

.

.

.

. . .

.

. .

.

. .

.

. . . . . . . . . .

.

.

.

.

.

.

.

. .

.

.

..

. . . . . . .

.

..

.

.

.

. .

. .. . .

..

.

.

Construction

Joint (Cracking)

a. Overturning Due to Excessive Tilting

b. Structural Failure on the Wall

c. Excessive Damage to Nearby Critical Facilities

Figure 2-6. Seismically induced distress of retaining walls. 

structural failure unless high levels of acceleration are considered or the wall has some form of 

structural deficiency. 

The structural failure shown in figure 2-6(b) is taken from the report prepared by Koseki et al. 

(1996), and the construction joint is with respect to a particular wall constructed in Japan. Many 

of the walls that suffered severe structural distress from the Kobe earthquake, as reported by 

Koseki et al. (1996), were over 60 years old, and unreinforced. Walls designed by today’s 

standards may not fail in this manner, but walls not properly designed or detailed are vulnerable 

to collapse and need to be evaluated.

Structural deficiencies include inadequate section, poor construction joints, and lack of 

reinforcement or internal support (buttresses, counterforts). Detailed seismic evaluation is 
13

recommended for sites with a seismic hazard associated with peak horizontal ground 

accelerations in excess of 0.3 g, or walls with structural deficiencies. 

Retaining walls founded on pile foundations (or drilled shafts) may also be vulnerable to 

structural failure at the pile-head connections. During a seismic event, pile loads will be 

redistributed and additional shear forces will be transferred to the pile foundation. Pile-head 

connections should be evaluated for the case of seismic loading applied to the retaining wall 

system. 

Seismically induced damage to nearby structures is due to loss of level of service from 

deformation of the wall backfill that may result from tilting or sliding of the retaining wall. The 

potential for damage depends on the proximity of nearby structures or facilities such as 

pavements, and especially railroad tracks. If structures and facilities on top of the backfill are 

located within the zone of failure behind the wall, as shown in figure 2-7, small deformations of 

the retaining wall may be significant. Structures located within 1.5 H of the wall backface may 

be vulnerable to wall displacement. 

1.5H

H

Failure

Plane Zone of

Failure

Retaining Wall

Backfill

34 AE

Structure

O

Figure 2-7. Structure loaded within zone of active failure wedge. 

Detailed evaluation of retaining walls should be considered whenever essential facilities are 

located within 1.5 times the height of the wall with respect to the backface, and seismic hazard at 

the site is associated with a horizontal component of peak ground acceleration in excess of 0.1 g. 

However, detailed evaluation is not necessary if all the following conditions are satisfied: 

• Retaining wall displacements of 75 mm can be tolerated. Seismic hazard at the site is 

associated with a horizontal component of peak ground acceleration less than 0.3 g. 

• Permanent surcharge loads are not applied within 0.5 H of the backface. 

• Backfill slope is less than 10°. 
14

• Loose, saturated soils are not present, i.e., saturated cohesionless soils with SPT-N values 

less than 10. 

2.3.1.2. Level 2 

Static safety factors should be checked as described in GEC No. 2: Earth Retaining Systems

(Sabatini, 1997). Soil parameters required for geotechnical engineering considerations may be 

available from original design calculations or estimated based on knowledge of existing site 

conditions. Static factors of safety for sliding and overturning should be at least 1.5 and 2.0, 

respectively. Appropriate factors of safety for bearing capacity and global stability vary 

depending on subsurface conditions, performance requirements and other conditions (AASHTO, 

2002; Vesic, 1973). Compared to the original construction, a change in the wall geometry or soil 

conditions due to distress and/or lack of appropriate maintenance may result in a safety factor 

different from that intended in the original design. Distress may include cracking and/or 

corrosion of the wall or footing, differential settlements or tilting of the wall, or flooding of the 

backfill or foundation material. Walls not meeting minimum requirements for static loading are 

certainly candidates for detailed seismic evaluation and should be screened accordingly. 

The level 2 screening requires a site visit whereby visual observations are employed to determine 

the current condition of existing retaining walls. Excessive tilting, or settlement of the wall, are 

important signs of distress originating in the foundation soil which should be documented. Signs 

of structural distress that must be documented include spalling concrete at the face of the wall 

and/or discoloration of the concrete due to corrosion of reinforcing steel; poor construction 

joints, and excessive cracking of concrete. Retaining walls that exhibit visible signs of excessive 

distress should be included in the category for detailed evaluation. 

2.3.1.3. Summary 

In general, for walls that meet the minimum requirements for static factor of safety, detailed 

evaluation is not required if the following conditions are met: 

• No visible signs of distress. 

• Backfill or foundation soils are not liquefiable. 

• Wall slenderness ratios (height/base width, H/B) are less than 2.0. 

• Surcharge loads are low and the backfill slope is not steep. 

• Essential facilities are not located in proximity to the wall. 

• Seismic hazard at the site is associated with a horizontal component of peak ground 

acceleration less than 0.3 g. 

A flowchart that summarizes application of the general screening guidelines, evaluation 

procedures and design of retrofit is presented in figure 2-8. 
15

Screening of

Retaining Walls

Level 1

External Stability Structural Integrity Nearby Critical Facility

Need

for

Detailed

Evaluation

Need

for

Detailed

Evaluation

Level 2

Condition Assessment

Stop

Special Ground

Motion Study

Collect Additional Information

for Detailed Evaluation

Evaluate Collapse

Force-Based Analysis

Structural Evaluation Evaluate External Stability

FS >

1.0

FS >

1.0 Stop

Simple Evaluation

of Deformation

Stop Danger

Design of Retrofit

Evaluate Critical Facilities

Detailed Deformation

Analysis

Tolerable

Deformation Stop

YES

NO

NO

YES

YES

NO

NO YES YES

NO

NO

YES

YES

YES

NO

Need

for

Special Ground

Motion

Study

Figure 2-8. Flowchart summarizing the general procedure for screening, evaluation and 

retrofit of retaining walls. 
16

2.3.2. ANCHORED WALLS 

When used as waterfront structures along rivers or for harbor facilities, anchored walls are at 

great risk due to the liquefaction hazard. The potential for liquefaction is aggravated by the use 

of dredged material for backfill as described in section 2.2.3. Many such walls have failed 

dramatically in earthquakes. Waterfront structures must be considered highly suspect and 

evaluated carefully for retrofit, or replacement, if even a moderate earthquake is anticipated. 

In their review of 110 tied-back, waterfront walls in Japan, Gazetas et al. (1990) indicate that, 

where liquefaction issues are not a concern, it is usually the anchor that is the weak component 

in current designs. The example presented in section 2.4.4 shows that tied-back walls designed 

with a static factor of safety of 2 could fail by anchor pullout, causing rotation around the bottom 

at a coefficient of horizontal acceleration applied within the backfill of approximately 0.2. Thus, 

tied-back walls not properly designed for seismic effects are at risk even in moderate 

earthquakes. 

A secondary screening procedure is described in section 2.4.4 for rapid evaluation of anchored 

walls with respect to pullout failure. More detailed evaluation is then performed for walls that 

are categorized as potentially vulnerable to this failure mechanism. 

2.3.3. MSE WALLS 

To date, no significant earthquake-induced damage to MSE walls have been reported in the 

literature. According to Tatsuoka et al. (1995) MSE walls performed very well in the 1995 Kobe 

earthquake; although at one location some permanent seismically induced displacement was 

observed. However, conventional gravity walls located in the vicinity of the referenced MSE 

wall suffered catastrophic damage. Kavazanjian et al. (1997) report that MSE walls also 

performed well in the 1989 Loma Prieta earthquake. 

For MSE walls, the main concern is the effect of earthquake-induced ground accelerations to 

increase lateral earth pressure and involve a larger volume of soil in the active failure region. 

The increased lateral earth pressures transfer a dynamic increment of tensile force to the 

reinforcement. The largest relative increases in reinforcement force occur in the uppermost 

layers in a reinforced soil wall (Bathurst and Cai, 1995). Also, the critical failure surface 

becomes flatter, affecting the pullout resistance that can be mobilized along the reinforcement. 

Most MSE walls that are found to be deficient from a seismic analysis do not have adequate 

reinforcement length near the top of the wall. Considering the pullout resistance, as described in 

section 2.4.5, the length of reinforcement required to resist earthquake-induced tensile forces is 

typically 10 percent greater than the length required for static loading conditions. 

In summary, for MSE walls, there is a need to assess the adequacy of reinforcement near the top 

of the wall, particularly for walls with facings that include modular concrete units, segmental 

concrete panels, or gabion facings. 
17

2.4. EVALUATION OF RETAINING WALLS 

2.4.1. INFORMATION REQUIRED FOR DETAILED EVALUATION 

Detailed seismic evaluation requires considerably more information about the retaining wall than 

that required for preliminary screening. Additional time and expense is required to collect asbuilt details of the wall and site features, and to obtain parameters for the backfill and foundation 

soils. 

It may be necessary to conduct a site investigation, and retrieve soil and/or rock samples for 

laboratory testing. It is also important for the user to document the condition of the retaining 

walls being evaluated. Man-made construction materials may have decayed or corroded over 

time, and the wall dimensions and/or material properties used in the initial design may no longer 

prevail. Nondestructive evaluation to assess the condition of the retaining wall and/or sampling 

and laboratory testing of materials may be required. 

2.4.1.1. Wall Details 

Necessary information includes the wall and foundation dimensions, the geometry of the backfill 

(i.e., slope of the backfill surface), drainage conditions, and depth of burial at the toe of the wall. 

Most of the necessary information, described in the subsections below, may be obtained from 

existing construction drawings. If construction drawings are not available, it will be necessary to 

collect information via a site visit. An invasive, or a nondestructive, evaluation will be necessary 

if portions of the wall are buried and inaccessible. 

The foundation type must be identified as deep or shallow. For a description of methods that may 

aid in identifying unknown foundation types and conditions, the user is referred to the work of 

Olsen (1996). For shallow foundations, the bearing grade, thickness, and width of the foundation 

must be determined. For deep foundations, the length of the foundation elements must be 

established, as well as their number, distribution, diameter, and reinforcement details; and pile 

cap, and pile to cap connection details. 

A typical backfill geometry considering construction of the retaining wall is shown in figure 2-9. 

It is likely that during construction of the wall, the contractor minimized placement of backfill to 

the extent allowed by the owner, or as constrained by site conditions. Often, during construction, 

in-situ soils are cut back at a steep angle. The use of heavy compaction equipment in close 

proximity to the wall backface is usually avoided such that backfill soils may not be very wellcompacted there. Considering these aspects of wall construction, it is quite possible that backfill 

and in-situ soils have distinct characteristics. During seismic loading, both are contributing to the 

response of the retaining wall system and their appropriate strength should be identified for use 

in the seismic evaluation. 

The geometry of the backfill should be assessed during the site investigation. It may possibly be 

defined by as-built drawings and pre-construction soil investigation. If not, the backfill should 

be probed with shallow borings or test pits to identify the extent of the backfill placed during 

construction. The number and depth of borings or test pits are a function of the wall and backfill 
18

geometry, and the depth and character of the backfill and underlying soils. For test borings, 

Standard Penetration Testing (ASTM D1586, 1984a) should be done at two ft intervals with 

continuous sampling. Soils retrieved with the split spoon sampler or from test pits should be 

visually identified at the site by a geotechnical engineer, soil scientist or geologist using the 

standard practice described in ASTM D2488 (1984b). If fine grained soils are encountered, 

“undisturbed” samples should be retrieved for testing as described in section 2.4.1.2. The data 

obtained from the test borings should be analyzed by a geotechnical engineer to identify the 

interface between backfill and in-situ soils, run appropriate laboratory tests if necessary, and 

assign appropriate properties to each for use in subsequent analyses. 

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+

+ +

+

+

+

+

+

+

+

Backfill with suitable

excavated material

Underdrain Filter

Existing Ground

Topsoil or Slope Protection

Subgrade of roadway or

finished ground surface

Highway Embankment Material

Select structure fill, compacted to

95% of std. proctor maximum density

Existing Ground

Figure 2-9. Backfill geometry considering construction of the retaining wall. 

2.4.1.1(a). Gravity Walls

Necessary wall parameters include the wall height, weight, batter, details of the foundation, and 

backfill drainage conditions. If the wall is vulnerable to tilting (overturning stability), 

dimensions of the wall must be known to compute the center of gravity for use in the procedure 

described in section 2.4.2.2(a). Dimensions of the retaining wall should be well established for a 

detailed analysis. Bowles (1977) provides guidance on the common proportions of gravity 

retaining walls in terms of the wall height as shown in figure 2-10. Dimensions shown in figure 

2-10 are used as a starting point for the design of retaining walls. They may be used as a rough 

guideline for estimating dimensions. The actual dimensions of constructed walls may deviate 

significantly from figure 2-10. 

It is very important for the analysis of overturning stability to identify the toe of the retaining 

wall. During the site investigation, the toe of the wall footing should be located by visual 

observation, if necessary, by excavating a shallow trench. Caution should be exercised when 
19

planning this investigation so as not to remove any toe support required for static stability of the 

wall. Alternatively, shallow probe holes can be advanced with augers to identify the location of 

the toe. 

Soil samples should be retrieved near the toe of the wall to identify near-surface foundation soils. 

If these soils are fine grained, and test results are not available, undisturbed samples of the 

foundation soil should be retrieved and tested as described in section 2.4.1.2. 

.3 m

min

min

20 mm

1 m

D .12

to

.17H

.12

to

.17H

H

.5 to .7 H

Toe

Heel

Stem

.3 m

min

min

20 mm

1 m H

.1 H

.1 H

.5 to .7H

D

a. Gravity Wall b. Cantilever Wall

Bowles, 1977 

Figure 2-10. Approximate dimensions for various components 

of a retaining wall. 

2.4.1.1(b). Concrete Cantilever Retaining Walls (Inverted T-Type)

The same information described in the section above is also required for concrete cantilever 

retaining walls. In addition, the length of the heel of the retaining wall should be established 

such that soil placed over the heel can be included in the analysis. Details of steel reinforcement 

used in concrete cantilever walls should also be determined. 

If available, construction documents should be utilized, but for older walls this information may 

not be available. The rough guidelines in figure 2-10 should only be used as a last resort, and 

used in preliminary calculations. If a more detailed evaluation for retrofit is undertaken, the wall 

dimensions should be explored as part of a site investigation. 
20

Many retaining wall footings are placed against undisturbed material where the footing concrete 

is placed without the use of forms. This most likely results in an overpour, i.e., a portion of the 

footing will be unreinforced. It may be possible to locate the edge of the footing with a probe or 

soundings as part of the site investigation, but the fact that the concrete may be unreinforced, and 

is likely cracked, needs to be recognized. If the toe and heel of the footing is exposed, the 

reinforcing steel may be located with a pacometer. Otherwise, if the edge of the footing appears 

to be cast directly against the foundation soil, a nominal distance of 0.3 meters should be 

discounted from the heel and toe of the footing to account for the possibility of an overpour. 

2.4.1.1(c). Tied-Back Walls

The user should identify the type of wall system according to the descriptions referenced in 

section 2.2.3. Dimensions and yield strengths of the structural elements comprising the wall 

system should be quantified. The depth of embedment of the vertical elements should also be 

known. 

Detailed knowledge of the tie-back system is particularly important to the seismic analysis of the 

retaining wall system. Knowledge of the type and length of the wall anchor and the anchor head 

assembly is required. If grouted anchors are employed, the length of the bonded and unbonded 

portions should be known as well as the level of prestress. In instances where corrosion, or loss 

of anchorage, is an issue, the user should make an assessment of the in-service state of the tieback. 

2.4.1.1(d). MSE Walls

The user should describe the type of wall system and facing units according to the descriptions 

given in section 2.2.4. Type, spacing and length of reinforcement should be determined. 

Dimensions of the wall facing units should also be established as well as details of the 

connection between the reinforcements and wall facing. 

2.4.1.2. Soil Properties 

Soil parameters should be obtained for the backfill and foundation soil from the results of a site 

investigation. The stratigraphy of the foundation soils should be identified as well as the type of 

soil used for backfill. Knowledge of soil unit weight, and shear strength parameters, including 

cohesion and angle of friction is needed. For the foundation soil, these values can often be 

inferred from the results of in-situ testing performed during the preconstruction site 

investigation. In the United States the Standard Penetration Test is the most popular in-situ test. 

More recent investigations may include results from cone penetration or pressure meter testing. 

In-situ test results may not be available for backfill if the site investigation was done prior to 

construction of the wall. Properties of backfill and in-situ soils may be investigated by sampling 

and performing appropriate laboratory tests. In lieu of this, a value of 34° is a conservative 

estimate of the internal angle of friction for a clean, well-graded, free-draining backfill. Fine 

grained soils are sheared under undrained conditions during seismic loading. Therefore, for fine 

grained soils, the undrained strength should be used in the evaluation. Appropriate laboratory 

strength tests should be performed on undisturbed samples retrieved from the site, or appropriate 
21

in-situ testing should be performed to determine the undrained strength. Alternatively, the 

method described by Ladd (1991) can be used to estimate the undrained strength during shear. 

Peak and residual strengths should be determined. Details of sampling, testing and proper 

evaluation of soil properties are described in Geotechnical Engineering Circular No. 5 (Sabatini, 

2002). 

Interface friction between the wall face and backfill is estimated based on data available in the 

literature (AASHTO, 2002). For concrete wall facings and free draining granular backfill, an 

interface friction coefficient between one-half and two thirds the value of the tangent of the 

internal friction angle of the backfill is often employed. The base friction angle at the interface 

between the wall foundation and the foundation soil is often higher than the interface wall 

friction angle. If concrete is placed directly against a cohesionless foundation soil, the interface 

friction angle may equal the internal angle of friction for the foundation soil. 

Current practice for cohesionless soils is to assume that the internal and interface friction angles 

are not rate dependent. Friction angles determined for static loading are used in the seismic 

evaluation procedure. The peak shear strength of the soil is used in the evaluation for seismic 

resistance and corresponding threshold accelerations. However, when a deformation analysis is 

performed, the residual strength of the soil should be considered if the soil has undergone large 

permanent deformation. 

The user should also establish the position of the groundwater table(s). The shear resistance of 

saturated cohesionless soils may degrade during seismic loading. If pore water pressures increase 

during cycles of shear loading, the effective stress and corresponding shear strength of the soil 

will decrease. Unless the retaining wall is a waterfront structure (quay wall), the backfill is 

generally free draining and not saturated. However, for waterfront structures and saturated 

foundation, soil degradation of shear strength during cyclic loading may be an important issue. 

Once the properties of the backfill and foundation soil have been evaluated, it is necessary to 

assess the liquefaction potential at the site of the retaining wall and assess the potential for 

degradation of shear strength due to cyclic loading of saturated cohesionless soils. 

The procedure referred to in chapter 3, Part 1 of this manual may be used to determine if a site is 

a candidate for detailed evaluation of liquefaction potential. Retaining walls located on sites 

susceptible to liquefaction will deform due to a severe loss of shear strength within the 

foundation soil. Procedures for estimating the degradation of shear strength of cohesionless soils 

as a function of peak ground acceleration are generalized in Edinger (1989). Also, Ebeling and 

Morrison (1992) describe a method for considering the degradation of shear strength for 

saturated cohesionless soils. 

The static undrained strength of cohesive soils should be reduced by 15 percent per 

recommendations of Makdisi and Seed (1979) to account for effects from cyclic loading. 

Retaining walls located on sites not susceptible to liquefaction may undergo seismically induced 

permanent deformation due to increased lateral thrust behind the retaining wall and from the 

inertia force acting on the wall itself. In what follows, procedures to evaluate seismic 

vulnerability from these effects are discussed for walls classified as gravity walls, concrete 

cantilever walls (inverted T-walls), tied-back walls, and mechanically stabilized earth walls. 
22

2.4.1.3. Ground Motions 

In general, it is acceptable to assume that free-field peak ground accelerations estimated for the 

site, as described in Part 1 of this manual, are uniformly applicable to the wall and retained soil. 

However, in some cases, local site soil response effects and/or two-dimensional response effects 

may be significant and not adequately captured by the site free-field peak ground acceleration. 

Examples of cases where local response effects may be more significant include: fills of 

substantial extent constructed behind the wall where the dynamic stiffness of the fill is 

significantly different from that of the underlying geologic materials for which free-field ground 

motions were estimated (for example, embankment fills constructed over bedrock); walls with 

high slopes behind the walls; and tall walls. Conducting a site-specific analysis to evaluate local 

response effects and accelerations to be used in retaining wall seismic evaluations is always an 

option to using free-field accelerations defined for the site. 

Various methods may be considered for assessing local response effects, including: simplified 

embankment or slope response analysis methods (refer to chapter 3); one-dimensional analysis 

of wall backfills above underlying materials to bedrock; and two-dimensional analysis of wallsoil foundation systems (for example, see Kavazanjian et al., 1997). A geotechnical earthquake 

engineering specialist should evaluate whether special analyses are needed and carry out such 

analyses. 

2.4.2. GRAVITY AND SEMI-GRAVITY WALLS 

Seismic evaluation of gravity walls must consider the dynamic increment of lateral earth 

pressure, the inertial response of the wall, and the effect of seismic loading on the shear strength 

of the foundation soils and backfill. Evaluation of forces are described in section 2.4.2.1, and 

their effect on external stability of gravity retaining walls are described in section 2.4.2.2. 

Section 2.4.2.3 considers the structural integrity of gravity retaining walls for seismic loading 

conditions. In section 2.4.2.4, a displacement-based analysis is described for evaluation of the 

potential for damage and loss of serviceability to essential facilities located in close proximity to 

the wall. 

Gravity and semi-gravity retaining walls founded on pile (or drilled shaft) foundations may be 

vulnerable to collapse if the piles are founded in liquefiable soils. The external stability of 

retaining walls founded on deep foundations within liquefied foundation soils can be evaluated 

using procedures described in Recommended LRFD Guidelines for the Seismic Design of 

Highway Bridges (ATC/MCEER, 2003). 

2.4.2.1. External Forces Acting on Gravity or Semi-Gravity Retaining Walls Considering 

Seismic Loading 

Figure 2-11 shows the forces acting on a gravity retaining wall during seismic loading. Forces 

acting on the wall are from inertial response, lateral earth pressure from the backfill (PAE), 

passive resistance from soil placed over the toe of the wall (PPE), and bearing pressure from the 

foundation soil (R). Lateral earth pressure includes the static component and the dynamic 
23

increment. It is also important to consider the inertial loading applied to the foundation soil, and 

its effect on bearing capacity. 

2

i

PAE

hA

k Wh w

(1-k )Ww w

w

PPE D

2

F

N R

f

v

Figure 2-11. Forces acting on coherent gravity structure. 

In general, these forces relate to the stability of the retaining wall with respect to sliding, 

overturning, and loss of bearing capacity. However, from the standpoint of the life safety 

performance criteria, mechanisms for collapse of gravity or semi-gravity retaining walls include 

overturning, loss of bearing capacity and/or structural failure of the wall. Unless an essential 

facility is located within close proximity to the retaining wall, the sliding mode of failure is not 

catastrophic and, in fact, is the preferred mode of wall movement. 

Methods to compute lateral earth pressures and seismic bearing capacity are described in the 

subsections below. Procedures to evaluate the seismic stability of gravity or semi-gravity 

retaining walls with respect to overturning and loss of bearing capacity, respectively, are 

described in section 2.4.2.2. 

2.4.2.1(a). Seismic Lateral Pressure (Thrust) on Walls

If the wall is allowed to deform enough to mobilize active earth pressure, lateral earth pressures 

that develop behind rigid retaining walls during earthquake loading may be evaluated using a 

rigid plastic model to describe soil behavior. This approach was followed by Okabe (1926), and 

Mononobe and Matsuo (1929), who performed a modified Coulomb analysis where the inertial 

load on the failed wedge was included in the analysis. The Mononobe-Okabe (M-O) equation for 

the active earth pressure coefficient for seismic loading may be expressed as: 
24

( )

( ) ( )( )

( )()

2

w

AE 2

2 w w w

w

w

cos - - K = 

sin + sin - -i

cos cos + + 1+ cos cos + + cos i -

φ θ β

⎡ θ ⎤ φ φ δ θ β βθ δ ⎢ ⎥ ⎢ δ βθ β ⎥ ⎣ ⎦

 (2-1) 

where: 

-1 h

v

k

 = tan 1- k

⎛ ⎞ θ ⎜ ⎟ ⎝ ⎠ (2-2) 

and: 

kh and kv are coefficients of horizontal and vertical accelerations, 

φw is the internal friction angle of the backfill, 

β is the wall batter, 

δw is the wall/soil interface friction angle, 

 i is the backfill inclination. 

The coefficient of horizontal acceleration applied to the backfill, kh, is taken as the peak ground 

acceleration divided by the acceleration due to gravity, Amax/g, unless: (1) Amax is greater than 

the threshold and (2) the threshold acceleration for sliding is less than the threshold accelerations 

for overturning or tilting from seismically induced loss of bearing capacity. If conditions (1) and 

(2) apply, kh is the threshold acceleration for sliding. kh

s

. 

The active thrust, PAE, maybe calculated as: 

( ) 2

AE v AE t

1

P H kK = 1-

2

γ (2-3) 

where: 

PAE is the active thrust and includes the static component plus the dynamic increment, 

γt is the total unit weight of the backfill, 

H is the wall height. 

It is important to note that this solution is limited in that: 

• A constant value for the angle of wall friction, δw, must be assumed. 

• There is no moment equilibrium equation so that the line of action of the thrust PAE is not 

involved. 

• Wall deformation must be sufficient to mobilize the active condition within the backfill. 

• Cohesion is not included in the analysis. 
25

• Irregular geometry of the backfill surface is not considered. 

• The effects of a submerged backfill are not included. 

• Equation (2-2) has no real solution of θ+ >i φ . Physically, this implies that an equilibrium 

condition will not exist. 

The orientation of the failure surface associated with equation 2-1 becomes flatter as the level of 

acceleration increases, and when θ + i = φ, the predicted failure surface is horizontal. In 

practice, cohesionless soil is unlikely to be present for a great distance behind a retaining wall 

and encompass the entire failure wedge under seismic conditions. In some cases, free draining 

cohesionless soil may only be placed in the static active wedge (i.e., at a 60 degree angle) with 

the remainder of the soil being cohesive embankment fill (c- φ soil) or even rock. In these 

instances, earthquake-induced active pressure should be determined using trial wedges as shown 

in figure 6-25 in Part 1 of this manual. 

In instances where the backfill includes fined grained soils such as clay, silty-clay, or clayey silt, 

and the shear strength includes a component from cohesion, graphical solutions such as the trial 

wedge method (see Part 1 of this manual; Bowles, 1977; ASCE, 1994) may be employed to 

compute the active lateral earth pressure. The trial wedge method for determination of lateral 

earth pressure may also incorporate irregular geometry of the backfill surface. In the trial wedge 

method (figure 6-25, Part 1), it is assumed that the failure surface for the active condition is 

planar. This assumption is consistent with that of Mononobe-Okabe. The retaining wall 

geometry is drawn to scale and various trial failure wedges are evaluated. Each trial failure 

wedge has a failure surface with its origin at the base of the retaining wall, but the inclination of 

the failure surface with respect to the horizontal is varied for each trial. Force polygons are 

constructed which include: 

• The weight of the trial wedge. 

• Inertial forces acting on the trial wedge due to vertical and horizontal components of ground 

acceleration. 

• Resultant of the normal force and frictional component of shear resistance along the 

assumed failure surface. 

• Resultant of the pore water pressure acting along the assumed failure surface. 

• Resultant of the cohesive component of shear resistance along the failure surface. 

• Resultant of the active thrust acting at the wall face. 

A number of trial wedges are evaluated from which the maximum active thrust and critical angle 

of the failure surface are determined. The backfill may be considered to consist of more than one 

material, however, only one wall interface friction angle and one backfill soil friction angle may 

be included in the analysis. For backfill with multiple soil layers, total lateral load should be 
26

calculated using an appropriate limiting equilibrium method of analysis as described by ASCE 

(1994). 

This report assumes that backfills are not submerged. For the case of backfills that are either not 

free draining, or are located along a waterfront, the effects of a submerged backfill on the 

computation of lateral earth pressure must be included in the analysis. The reader is referred to 

Ebeling and Morrison (1992) for guidance on including the effects of a submerged backfill on 

computation of lateral earth pressure. 

2.4.2.1(b). Passive Restraint

In many instances, the base of a retaining wall is embedded to some depth within the foundation 

soil. Effects of foundation embedment include the development of passive restraint against 

sliding, and a contribution to bearing capacity from the surcharge. 

Some deformation is required for the passive restraint to be fully mobilized. As deformations 

continue, passive restraint is mobilized, and seismic resistance is increased. When full passive 

restraint is mobilized, a steady state seismic resistance prevails at a given level of acceleration. 

For the passive seismic limit state: 

( ) 2

PE v PE t

1

P H kK = 1-

2

γ (2-4) 

where KPE is expressed as: 

( )

( ) ( )( )

( )()

2

w

PE 2

2 w w w

w

w

cos - +

K = 

sin + sin - + i

cos cos - + 1- cos cos - + cos i -

φ θ β

⎡ θ ⎤ φ φ δ θ β βθ δ ⎢ ⎥ ⎢ δ βθ β ⎥ ⎣ ⎦

 (2-5) 

The value of KPE computed with equation 2-5 increases significantly with increasing wall/soil 

friction angle, δw. The value of δw should be chosen carefully to avoid calculating an 

unconservatively high value of KPE.. Morrison and Ebeling (1995) show that eq. (2-5) is 

unconservative for problems involving low to moderate acceleration fields with interface friction 

greater than or equal to one-half the angle of internal friction. 

Equation 2-5 is plotted in figure 2-12, which portrays how the passive thrust decreases with an 

increase in level of acceleration. Therefore, at high acceleration levels ( kh > 0.4 g), the benefits 

of embedment at the toe of the retaining wall are diminished compared to that at low levels of 

acceleration. 
27

= 40

35

30

25

= 0

= 0

= 0

= 0

K

i

V o

o

o

o

o

o

o

4.5

4

3

2

1

0

0 0.1 0.2 0.3 0.4 0.5

k

KPE

h

 Davies et al., 1986 

Figure 2-12. Effect of horizontal and vertical seismic 

coefficients on active and passive pressure coefficients. 

2.4.2.1(c). Seismic Bearing Capacity

Richards et al. (1990), Richards and Shi (1991 and 1994) and Shi (1993) studied seismically 

induced reduction of bearing capacity. Seismic bearing capacity factors are developed 

considering shear tractions transferred to the soil surface as well as the effect of inertial loading 

on the soil in the failed region below the footing. For simplicity, a “Coulomb-type” of failure 

mechanism is considered within the foundation consisting of an active wedge directly beneath 

the retaining wall and a passive wedge that provides lateral restraint. 

For retaining walls, shear transfer between the footing and foundation soil is conveniently 

described by a shear transfer coefficient, n, where: 

F

n = 

N tan f

φ (2-6) 

and: 
28

F is the sum of the horizontal forces, 

N is the sum of the vertical forces transmitted to the soil, 

φf is friction angle of the foundation soil. 

The analytic solution gives a bearing capacity formula in terms of seismic bearing capacity 

factors NqE, NCE, and NγE, similar to its counterpart for the static case, as: 

lE cE qE E

1 ' p cN qN B N 2 = + +γ γ (2-7) 

where, 

q is the overburden due to depth of the footing, D, i.e., q= γD, 

c is the cohesion of the foundation soil, 

γ is the unit weight of the foundation soil, 

B’

 is equal to B-2e, where B is the width of the footing and e is eccentricity computed as 

described in section 2.4.2.2(b), 

 plE is the seismic limit to the bearing pressure. 

Figure 2-13 presents the ratio of seismic to static bearing capacity factors (NqE/Nqs, NcE/Ncs, 

NγE/Nγs). These ratios depend on the friction angle of the foundation soil, φf, seismic acceleration 

coefficient, kh, and shear transfer coefficient, n. The ratio for NcE/Ncs is presented in terms of the 

friction factor f = F/Nkh = ntan(φf)/kh, instead of n. Using the bearing capacity ratios presented in 

figure 2-13, and static bearing capacity factors for vertical, concentric loading with no depth 

correction from Vesic (1973), the seismic bearing capacity factors for use in equation 2-7 can be 

determined. 

Equation 2-7 does not include the effect of a submerged, or partially submerged, foundation on 

the computed bearing capacity. For fine-grained soils and relatively dense, well-graded, coarsegrained soils, equation 2-7 may be modified to incorporate the effect of a submerged foundation. 

Due to the low permeability of the soil, the pore water and soil skeleton are considered to move 

in unison during the ground motion. If the foundation soil is submerged above the base of the 

footing, use the effective stress to compute q in the second term of equation 2-7, and the 

submerged unit weight in the third term. If the foundation soil is submerged below the base of 

the footing, use an equivalent unit weight in the third term of equation 2-7 as γe = γ’(1- z/B) + 

γ(z/B), where γ’ is submerged unit weight, z is the depth to the groundwater surface below the 

base of the footing, and B is the width of the footing. If z is greater than or equal to B, then γe = γ.

For foundations with loose, saturated, coarse-grained soils, there is currently no reliable, 

simplified method for computing seismic bearing capacity. However, since these soils are likely 

to be susceptible to liquefaction, remediation will be considered as a result of the screening 

exercise described in section 2.3. 
29

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.00.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Phi = 30 degree Phi = 35 degree Phi = 40 degree

n = 0 n = 0 n = 0

n = 0.25 n = 0.25

n = 0.25

n = 0.5

n = 0.5

n = 0.5

n = 0.75

n = 0.75 n = 0.75

k

k

k

h

h

h

f = 0

o o o o = 10 20 30 40 1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.00.0 0.2 0.4 0.6 0.8 1.0

f = 1

= 10

20

30

40

o

o

o

o

0.0 0.2 0.4 0.6 0.8 1.0

f = 2

= 10

20

30

40

o

o

o

o

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

Phi = 40 degree

n = 0

n = 0.25

n = 0.5

n = 0.75

0.0 0.2 0.4 0.6 0.8 1.0

Phi = 35 degree

n = 0

n = 0.25

n = 0.5

n = 0.75

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.00.0 0.2 0.4 0.6 0.8 1.0

Phi = 30 degree

n = 0

n = 0.25

n = 0.5

n = 0.75

c. N /N

N /N

E

E

s

s

a. N /N

N /N

q

q

q

q

E

E

s

s

b. N /N

N /N

c

c

c

c

E

E

s

s

 Shi, 1993 

Figure 2-13. Ratio of seismic to static bearing capacity factors. 
30

2.4.2.2. External Stability of Gravity or Semi-Gravity Retaining Walls Considering 

Seismic Loading: Critical Acceleration kh for Loss of Equilibrium 

In this manual, the component of vertical acceleration, kv, is not included in the calculations for 

evaluating the external stability of retaining walls. Depending on the correlation with the 

horizontal component, vertical accelerations may have either a favorable or an unfavorable 

impact on the stability of the retaining wall system. However, considering the time history of 

acceleration associated with an earthquake, it is assumed that the net effect of including vertical 

accelerations in the analyses is not significant. As described in section 2.1, the goal of this 

retrofit manual is to evaluate vulnerability relative to collapse, or, in some cases, to loss of 

serviceability due to excessive deformations. For these criteria, the performance depends on the 

net effect of the time history, and not on a single pulse of acceleration. Therefore, it is considered 

reasonable to ignore the vertical component of acceleration in calculations for external stability. 

For the design of new structures, or facilities where yielding of the structure is not allowed, it 

may be appropriate to include kv in the calculations as described by Ebeling and Morrison 

(1992). 

2.4.2.2(a). Overturning Stability (Tilting) – Moment Equilibrium

The overturning stability of the retaining wall is evaluated by comparing moments tending to 

drive the system towards overturning to those tending to resist overturning. A factor of safety is 

defined as the ratio of the resisting to the driving moments. 

Evaluation of overturning stability needs to consider the line of action of the lateral earth 

pressure. The line of action is determined assuming the dynamic increment of lateral earth 

pressure acts at 0.6 H from the base of the wall stem and the static component acts at 0.33 H 

(Seed and Whitman, 1970). The static component of lateral earth pressure is the lateral earth 

pressure coefficient determined with kh and kv equal to zero. The dynamic increment may be 

determined by subtracting the static component from the total dynamic thrust. 

The factor of safety relative to overturning stability is computed as follows: 

Driving Moment: 

_

M k WY P cos( ) h P sin( )(D / 3)(sin ) D h c AE w PE w 2 2 = + δ+ β + δ−β β (2-8) 

Resisting Moment: 

M WX P sin( )(B h sin ) P cos( )D / 3 R c AE w PE w 2

−

= + δ +β − β + δ −β (2-9) 

where: 

MD is the driving moment, 

kh is the coefficient of the horizontal component of peak ground acceleration, 

Ww is the weight of the retaining wall, 

Yc is the vertical distance from the centroid of the wall to the toe of the wall footing, 
31

⎯h is the vertical distance from the line of action of PAE to the toe of the wall footing. 

Xc is the horizontal distance from the centroid of the wall to the toe of the wall footing, 

B is the width of the wall footing, 

D is the depth of embedment of the wall toe, 

β2 is the batter of the front face of the wall as shown in figure 2-11. 

If the threshold acceleration for sliding is less than the peak ground acceleration, then kh is 

limited to the sliding threshold, i.e., kh ≤ kh

slide. This applies to the wall inertia term as well as 

calculation of lateral earth pressure in terms of equations 2-2 (or the graphical procedure for 

lateral earth pressure) and 2-8, respectively. 

Safety Factor Against Overturning Instability: 

O.T. R

S

D

M F

M= (2-10) 

The wall is considered stable with respect to overturning if the computed factor of safety is equal 

to or greater than one. If this is the case, further analysis with respect to the overturning mode of 

failure is not required. For retaining walls founded on soils, bearing capacity failure, as described 

in section 2.4.2.2(b), will occur before the overturning mode of failure becomes critical. 

However, for retaining walls founded on rock, the overturning mode of failure may be relevant. 

If the computed safety factor is less than one, more detailed evaluation is required. Further 

evaluation addresses the seismic resistance, or threshold acceleration, and yielding of the wall 

system. Computation of threshold acceleration and seismically induced deformation of the 

retaining wall are discussed in the following paragraphs. 

Since earthquake loads are transient, rotation of the retaining wall will only occur when the 

ground acceleration exceeds some threshold value of acceleration, at which the safety factor is 

one. The threshold acceleration may be determined by iteration with different values of kh in 

equations 2-8 through 2-10. For the purpose of the iteration process, the user is reminded that the 

values of PAE and PPE depend on kh.

The wall rotates in increments each time the threshold acceleration is exceeded. Collapse due to 

overturning is caused by repeated pulses of ground acceleration in excess of the threshold. Due 

to rotation, the geometry of the wall system is affected. The wall center of gravity is moved 

closer to the point of rotation. Thus, as the wall rotates, the ability of the wall to sustain a 

resisting moment is diminished. This phenomenon is referred to as the P-∆ effect. As a simple 

check on stability, the threshold acceleration is compared to the anticipated peak ground 

acceleration at the site. If the peak ground acceleration exceeds the threshold acceleration by 

more than 0.25 g, the wall is not considered safe, and design of retrofit is required as described 

in section 2.5. Alternatively, in lieu of going directly to retrofit design, the wall deformation 

may be computed by integrating the equation of motion as described by Zeng and Steedman 

(2000). This requires selection of an appropriate earthquake record for the analysis. If the more 

detailed analysis confirms that deformation is excessive and may lead to collapse, design of 

seismic retrofit is recommended. 
32

For masonry walls, toppling of the wall face must also be considered as described in section 

2.4.5.1. 

2.4.2.2(b). Bearing Capacity Failure –Vertical Equilibrium

The stability of the retaining wall with respect to seismically induced reduction of bearing 

capacity is evaluated by comparing the vertical force resultant at the base of the retaining wall to 

the seismic bearing capacity of the foundation soils computed with equation 2-7. Equation 2-7 

requires that the eccentricity of the load with respect to the midpoint of the footing be computed 

as:

B M M R D e

2 N

− = − (2-11) 

A factor of safety relative to a bearing capacity failure is defined as the ratio of the seismic 

bearing capacity to the vertical force resultant. The factor of safety relative to seismically 

induced loss of bearing capacity is computed as follows: 

Vertical Force Resultant: 

N P sin( ) W P sin( ) = δ+ AE w w PE w 2 β + − δ−β (2-12) 

Resultant of Shear Traction Transferred to Foundation Soil: 

F P cos( ) k W P cos( ) N tan = δ+ AE w h w PE w 2 f β + − δ−β ≤ δ (2-13) 

where δf is the interface friction angle between the base of the foundation and the foundation 

soil. 

The shear transfer coefficient, n, is computed with equations 2-6, 2-12, and 2-13. Using the shear 

transfer coefficient, and the friction angle of the foundation soil, φf, find the seismic bearing 

capacity factors NcE, NqE, and NγE as described in section 2.4.2.1(c). Compute the seismic 

bearing capacity, plE, using equation 2-7 and the safety factor against seismically induced 

bearing capacity failure as: 

B.C. lE

S

p B F

N

′ = (2-14) 

The wall is considered stable with respect to seismically induced loss of bearing capacity if the 

computed factor of safety for the peak acceleration is equal to or greater than one. If this is the 

case, further analysis with respect to the seismically induced loss of bearing capacity is not 

required. If the computed safety factor is less than one, further evaluation is required. Further 

evaluation is similar to that described in section 2.4.2.2(a). However, in this case, the procedure 

involves iteration of equations 2-11 through 2-14 to find the threshold acceleration relative to 

bearing capacity. As a simple check on stability, the threshold acceleration is compared to the 

anticipated peak ground acceleration that is representative of the earthquake hazard at the site. 
33

For the case of seismically induced loss of bearing capacity, if anticipated peak ground 

acceleration exceeds the threshold acceleration by more than 0.2 g, the wall is not considered 

safe, and design of retrofit is required as described in section 2.5. Alternatively, in lieu of going 

directly to retrofit design, the wall deformation may be computed by integrating the coupled 

equations of motion as described by Siddharthan et al. (1992). If the more detailed analysis 

confirms that deformations lead to collapse, design of seismic retrofit is recommended. 

2.4.2.3. Structural Integrity of Gravity or Semi-Gravity Retaining Walls Considering 

Seismic Loading 

For evaluating the structural integrity of retaining walls, the vertical component of acceleration, 

kv, should be included in the calculations. At an instant of time, vertical accelerations may have a 

negative impact on structural integrity. Structural failure of retaining wall components is 

considered to be instantaneous, and does not require the accumulation of deformation as does the 

consideration of external stability, where kv is not included in the calculations (see section 

2.4.2.2.) Estimation of kv for use in the analysis is described in Part 1 of this manual. 

The structural evaluation compares stresses, shear forces and bending moments computed at 

critical locations within the wall stem, and at the toe of the wall footing, to the ultimate capacity 

of the appropriate section. If the ultimate capacities are exceeded, design of seismic retrofit is 

required as described in section 2.5. Sections 2.4.2.3(a) and (b) describe salient features of the 

analysis for the wall stem and footing, respectively. It will be assumed that the gravity retaining 

wall is plain concrete. Application of the procedure for reinforced concrete sections is described 

in section 2.4.3. 

2.4.2.3(a). Analysis of Wall Stem

Analysis of the wall stem requires calculation of shear and bending moments at the critical cross 

section along the height of the stem. The critical cross section depends upon a combination of 

the magnitude of shear and bending moment, and the cross sectional area. For a uniform cross 

section, the critical section is at the base of the stem where the moment and shear force are 

maximum. For non-uniform cross section, several sections may need to be evaluated in order to 

locate the critical cross section. 

Computation of shear and bending moments need to consider the distribution of seismic lateral 

earth pressure along the wall stem. The distribution of lateral earth pressure is determined by 

assuming that the dynamic increment of lateral earth pressure acts at 0.6 H from the base of the 

wall stem and the static component acts at 0.33 H. This results in the pressure distribution shown 

in figure 2-14. Lateral earth pressure coefficients, including the dynamic increment, may be 

determined with equation 2-1. The static component of lateral earth pressure is the lateral earth 

pressure coefficient determined with kh and kv equal to zero. If graphical methods are used to 

determine active lateral earth pressure, compute the earth pressure coefficient using the thrust 

determined by the trial wedge method and equation 2-3. The seismically induced inertia force 

applied to the wall stem must also be included in the calculation of the maximum bending 

moment and shear force. 
34

H

H/3

P

K H 0.2 K H (K + 0.2 K ) H

0.8 K H 0.8 K H

mH

P

P = P + P

+

+ + +

+ A

A

A

A

dyn dyn

dyn

dyn

dyn dyn

AE

+ =

a. Static Component b. Dynamic Increment c. Dynamic (total)

Pressure Distribution

0.6H

Figure 2-14. Assumed distribution of dynamic earth pressure. 

Shear and normal stress at the cross section is computed considering the computed shear force, 

bending moment, the weight of the stem, and the vertical component of active earth pressure. 

Allowable stresses for tension, compression, and shear are determined according to ACI (2002). 

Load factors are taken as unity for seismic evaluation of existing retaining walls. 

2.4.2.3(b). Analysis of Footing 

The analysis of the structural integrity of the wall footing requires that the contact pressure at the 

base of the footing be determined. It will be assumed that the contact pressure at the base of the 

footing varies in a linear fashion, and may be computed with equations 2-15 through 2-17. 

The distribution of contact pressure depends on the eccentricity of the resultant of the applied 

force system. If e ≤ B/6, the variation of contact pressure follows the shape of a trapezoid with 

maximum contact pressure at the toe of the footing, and minimum contact pressure at the heel 

computed as: 

max

6e N q 1 B BL

⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠ (2-15) 

min

6e N q 1 B BL

⎛ ⎞ = − ⎜ ⎟ ⎝ ⎠
35

If e > B/6, there is not full contact at the base of the footing and the variation of contact pressure 

follows the shape of a triangle with the maximum contact pressure at the toe of the footing 

computed as: 

max

4N

q 3L(B 2e) = − (2-16) 

and, 

x 1.5(B 2e) = − (2-17) 

where: 

L is the length of the wall used to compute N, 

x is the width of contact along the base of the footing.

2.4.2.4. Loss of Service of Essential Facilities 

Essential facilities may include lifelines, important highways, bridge approach fills, or important 

structures. Seismically induced deformation of a nearby retaining wall may be responsible for 

loss of service to essential facilities. Allowable deformation of the wall depends on the 

deformation that the essential facility may tolerate, and the attenuation relationship for the wall 

displacement field. 

When the tolerable deformation is exceeded, there may be significant loss of service to the 

facility. Several factors are examined to establish the deformation that a facility may tolerate. 

These include type of access to the facility, utilities, and the capacity to resist differential 

settlement. Input is required from a number of disciplines including geotechnical, structural, and 

emergency management. The tolerable displacement for essential facilities is established on a 

case-by-case basis. Assessment of the tolerable loss of service to essential facilities is beyond 

the scope of this chapter. However, to complete the analysis, a determination of tolerable 

displacement should be made. 

The displacement field is attenuated with respect to distance, therefore distance between the 

facility and the retaining wall is an important parameter. For backfills with coarse grained soils, 

assume that (1) the horizontal displacement and the vertical settlement immediately behind the 

wall are equal, and (2) surface displacements are linearly attenuated within a distance of two 

times the height of the retaining wall (Clough and O’Rourke, 1990). 

This section presents information that may be used to evaluate the potential for the retaining 

structure to undergo permanent seismically induced deformation and to estimate the magnitude 

of deformations that may occur. The estimated deformation of the retaining wall is compared to 

the allowable deformation in order to decide if seismic retrofit is required. 
36

2.4.2.4(a). Secondary Screening Procedure for Assessing Vulnerability to Seismically Induced 

Permanent Deformation 

As discussed in section 2.4.2.2, the threshold coefficient of acceleration is the ground 

acceleration beyond which the wall will begin to slide or rotate. For gravity or semi-gravity 

retaining walls that fail in a sliding mode of failure, Richards and Elms (1979) describe a method 

for computing threshold acceleration. Figure 2-15 presents results obtained by Richards and 

Elms (1979) showing the relationship between threshold acceleration and static factor of safety 

for vertical retaining walls with level, cohesionless backfill. For the data presented in figure 2-

15, it is assumed that the backfill has an angle of friction, φ, equal to 35°, wall/backfill interface 

friction angle δ= φ /2, and wall base/foundation soil interface friction angle, φb, equal to 35°. 

Figure 2-15 is a useful tool for secondary screening of retaining walls that may fail in the sliding 

mode, and identifying those that are not susceptible to seismic damage. The screening method 

assumes that the wall will slide before it rotates. The possibility of seismically induced tilting or 

loss of bearing capacity should be checked, as described in sections 2.4.2.2(a) and (b), to verify 

that the procedure is appropriate. The following steps describe the screening method for gravity 

or semi-gravity retaining walls that fail in a sliding mode of failure. 

14

12

10

8

6

4

2

0

0.0 0.1 0.2 0.3 0.4 0.5 0.6

k h

s

Fstatic

=

= =

b = 35 = 2 o

kv i = 0

Richards and Elms, 1979 

Figure 2-15. Relationship between static factor of safety 

and threshold acceleration, s

h k , for sliding. 
37

Screening Method for Gravity or Semi-Gravity Retaining Walls that Fail in a Sliding Model 

1. Determine the static factor of safety with respect to a sliding failure of the retaining wall. 

2. Using the static factor of safety, and figure 2-15, obtain the threshold acceleration coefficient for 

sliding, kh

s

. 

3. Compare the threshold acceleration coefficient to the estimated peak ground acceleration 

coefficient at the site of the retaining wall. 

4. If the threshold acceleration coefficient is greater than the anticipated peak ground acceleration 

coefficient, the wall may be eliminated from the list of potential candidates for detailed 

evaluation (provided other applicable criteria are satisfied). 

If some permanent displacement of the retaining wall is acceptable, higher levels of ground 

acceleration may be tolerated without the need for detailed seismic evaluation and retrofit. Elms 

and Martin (1979) estimate that, for sliding walls in which kh

s

 is greater than the coefficient of 

peak ground acceleration (kh) divided by two, the seismically induced permanent translation will 

be less than 254(kh) (in millimeters) in most cases. This suggests that in areas where the peak 

ground acceleration coefficient is less than 0.3, detailed evaluation is not necessary for walls if: 

• They have a static factor of safety with respect to sliding greater than 2.0. 

• They will not fail by tilting or seismic loss of bearing capacity. 

• An outward displacement of 75 mm can be tolerated. 

If the secondary screening procedure indicates that detailed evaluation is required, the user must 

follow the procedure for evaluating deformations described in sections 2.4.2.4(b) and (c). The 

procedure involves the determination of the seismic resistance, or threshold acceleration, as 

described in section 2.4.2.4(b) followed by estimation of seismically induced deformation 

described in section 2.4.2.4(c). The procedure considers a variety of possible modes of failure 

including translation (T mode), rotation with respect to the base of the wall footing (RB mode) 

and mixed rotation/sliding (R/T mode). The “critical” threshold acceleration for evaluation of 

seismically induced deformation of the retaining wall is considered the lowest threshold 

acceleration determined for sliding (kh

s

), seismic reduction of bearing capacity (kh

b

), or 

overturning (kh

OT). Evaluation of the critical threshold acceleration provides an indication of the 

prevailing mode of failure. 

For masonry walls, internal stability must also be analyzed with respect to sliding or bulging 

between units. See section 2.4.5.2 for details. 

2.4.2.4(b). Determination of Threshold Acceleration

The evaluation of seismically induced deformation of gravity or semi-gravity retaining walls 

involves the determination of a threshold acceleration beyond which permanent deformation of 

the gravity or semi-gravity wall will occur. Three values need to be computed from equilibrium; 
38

kh

s

, kh

OT, and khb

. A thorough seismic analysis must investigate the possibility of both a sliding 

mode of failure as well as a bearing capacity failure introducing rotation. The possibility of 

overturning instability that involves rotation with respect to the toe of the wall footing is 

discussed in section 2.4.2.2(a). Since seismic bearing capacity factors are dependent on ground 

acceleration, determination of the threshold acceleration requires an iterative procedure. It is 

initially assumed that there is no cohesion, no depth of embedment, and kv = 0. These 

simplifying assumptions are not necessary for the procedure and can be included without much 

difficulty as described at the end of this section. The procedure for determination of threshold 

acceleration described below is based on the work of Richards et al. (1996) and Fishman and 

Richards (1997a, 1997b). 

Although the backfill is usually granular, if necessary, the foundation soil may be assumed to 

have some cohesive strength. There may also be some depth to the foundation. Either or both 

may be included by using figures 2-13 (a) and (b) for NqE ⁄ Nqs and NcE ⁄ Nqs, and equation 2-7 in 

steps 6 and 7 of the procedure for determination of threshold accelerations. 

The threshold acceleration is compared to the peak ground acceleration applied by the design 

earthquake to the wall system. If kh

s

, kh

b

, and kh

OT are greater than kh, the local, external stability 

of the wall is safe from the standpoint of seismic design, and further evaluation is not required if 

other applicable criteria are satisfied. If kh

s

, kh

b

, or kh

OT are less than kh, deformation analysis as 

described in section 2.4.2.4(c) must be performed. If the estimated seismically induced 

deformations are greater than the acceptable level of deformation, design of seismic retrofit is 

required as described in section 2.5. 

The possibility of a mixed mode failure is evaluated in step 9(b). In this case, the value of kh

s

 is 

less than the peak ground acceleration, and less than the threshold acceleration for bearing 

capacity, kh

b

. Because shear transfer is limited at the base of the wall, ground acceleration in 

excess of kh

s

 cannot be transferred to the retaining wall. Thus, during sliding deformation, the 

wall inertia force and lateral earth pressure from the backfill cannot exceed the peak values at 

which sliding is initiated. However, the inertial force within the foundation soil beneath the 

retaining wall, as described in section 2.4.2.1(c) will continue to increase in response to the 

ground motion. Threfore, the possibility for a loss of bearing capacity subsequent to sliding 

exists. The seismically induced loss of bearing capacity subsequent to a sliding failure mode is 

referred to as “mixed mode.” 

Passive Restraint: In many instances, the base of a retaining wall is embedded to some depth 

within the foundation soil. Effects of foundation embedment include the development of passive 

restraint against sliding, and a contribution to bearing capacity from the surcharge. Both of these 

effects may be incorporated into the analytic method described in this section. Passive resistance 

may prevent sliding from occurring, resulting in a more damaging failure mode (e.g., 

overturning). 
39

Procedure for Determination of Threshold Accelerations for Walls that May Fail by 

Sliding or Loss of Bearing Capacity 

1. Assume a trial value for kh and determine PAE as described in section 2.4.2.1(a). 

2. Compute the vertical force resultant, N, as: 

N = sin( + ) + P W AE w δw β (2-18) 

3. Compute the result of the shear traction to be transferred to the foundation soil as: 

F = PAE cos(δw +β)+khWw (2-19) 

4. Compute the shear transfer coefficient, n, using equation (2-6). 

5. Sliding will occur if F = N tanδf and therefore: 

Fs

slide Ntanδf = 

F (2-20) 

6. where δf is the interface friction angle between the abutment footing and the foundation soil. 

7. Given the friction angle of the foundation soil, φf, and the shear transfer co-efficient, n, from step 

4, find the seismic bearing capacity factors from figure 2-13. 

8. Compute the seismic bearing capacity plE using equation (2-7). 

9. Bearing capacity failure will occur when N = plE B′ and therefore: 

Fs

B.C. pAEB'

 = 

N (2-21) 

10. Iterate on kh to determine the threshold values given when F.S. =1. That is: 

a. If Fs

B.C. determined in step 8 is nearly equal to one, and FsSlide from step 5 is greater than 

one, stop the iteration procedure since the assumed value for kh is the threshold value for 

bearing capacity failure, kh

b

, which occurs first. 

b. If Fs

Slide determined in step 5 is nearly equal to one and FsB.C. is greater than one, stop the 

iteration procedure since the assumed value for kh is the threshold value for sliding failure, 

kh

s

. In this case, when sliding occurs first, there is still the potential for a bearing capacity 

failure at a higher acceleration introducing a mixed mode. To estimate kh

b

 > kh

s set, N and 

F at their constant values for sliding, compute NγE from equation (2-7) with plE = N/B′ and 

determine kh

b from figure 2-13. 

c. If neither of these conditions are met, select a higher trial value for kh and return to step 1. 
40

Some deformation is required for the passive restraint to be fully mobilized. Small lateral 

displacements may occur at sliding threshold accelerations that do not reflect the development of 

any passive restraint (Fishman and Richards, 1996). As deformations continue, passive restraint 

is mobilized, and seismic resistance is increased. When full passive restraint is mobilized, a 

steady-state seismic resistance prevails at a given level of acceleration. Furthermore, the 

surcharge above the base of the embedded foundation provides a significant increase in the 

seismic bearing capacity. 

To include passive restraint in the procedure for determination of threshold acceleration revise 

equations 2-18 and 2-20 as follows: 

N P sin( ) W P sin( ) = δ+ AE W W PE W 2 β + − δ−β (2-18 revised) 

f PE w 2

slide

N tan P cos( ) FS

F

δ+ δ −β = (2-20 revised) 

where β and β2 are the inclinations of the backface and front face of the retaining wall as shown 

in figure 2-11. 

 2.4.2.4(c). Estimation of Seismically Induced Deformation

The critical threshold acceleration for evaluation of seismically induced deformation of the 

retaining wall is considered the lowest threshold acceleration determined for sliding (kh

s

), 

seismic reduction of bearing capacity (kh

b

), or overturning (kh

OT). If the critical threshold 

acceleration is kh

s

, the wall will fail in a translation ( T) mode of failure. If kh

b

, or kh

OT are 

critical, the rotation with respect to the base (RB) mode needs to be investigated. If kh

s

 is critical, 

an RB mode of failure is also possible since seismic reduction of bearing capacity occurs during 

sliding as described in step 9(b) of the procedure for evaluation of critical threshold acceleration. 

For gravity or semi-gravity walls that fail in a T mode, a simple, semi-empirical, displacement 

based seismic analysis may be used. More computational effort is required to evaluate walls that 

fail in the RB or RB/T mixed modes. The RB and mixed modes will be discussed at the end of 

this section. For seismic evaluation of existing walls that that fail in a T mode, the following 

procedure, based on the work of Richards and Elms (1979), is described. 

It should be noted that equation 2-22 renders a conservative estimate of displacement. 

Alternatively, the relative displacement between the retaining wall and foundation soil may be 

determined by double integration of the difference between an appropriate acceleration time 

history for the site and corresponding wall acceleration. The corresponding wall acceleration 

considers the sliding threshold acceleration. Figure 2-16 demonstrates the increments of 

displacement accumulated by the sliding wall when the ground acceleration exceeds kh

s

. 
41

. .

. .

. .

. .

. .

. .

.

. .

. .

. .

. .

. .

. . . . .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. .

. . .

.

. .

. .

. .

. Absolute . velocity

Wall

relative

velocity

Relative displacement

Soil

acceleration

Wall

acceleration

a

a

a a

b ac d

b

b

b b

Vr o d

c c c c

d

d

d d

t t t t

x x .. . kh

o

Richards and Elms, 1979 

Figure 2-16. Incremental failure by base sliding. 

Procedure for Evaluating Walls with a Sliding Mode of Failure (T Mode) 

1. Determine the weight of the existing wall. 

2. Estimate the peak horizontal ground acceleration coefficient, kh, and peak horizontal velocity, V, 

considering the earthquake hazard at the site. The velocity V, corresponding to kh and distance 

from the source of the earthquake, may be estimated as described in chapter 4. 

3. Using the threshold acceleration, kh

s

, determined from section 2.4.2.4(b), estimate the residual 

displacement, d, as: 

⎛ ⎞ = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

4 2

h

s h h

V k d 0.087

k g k (2-22) 

where g is the acceleration due to gravity. When using equation 2-22, V and g must be in 

consistent units. 

4. Compare the displacement computed in step 3 with the displacement that may be tolerated. 
42

P = P S LE

AE

w

P

total

h

a

d

a

b

f

ba

d

f

f

AE

Ph

a

b

e

f

t

f

t t Footing

Soil

Soil

Footing

c

d

b c

a

d

e

f

e

d

b

a

c

Relative

velocity 0 0 x x

a

b

c

d

e

f

t

Settlement, w

.. .

Richards et al., 1993 

Figure 2-17. Incremental bearing capacity failure by Coulomb sliding wedge 

mechanism. 

The sliding block approach can be applied to the Coulomb Mechanism described in section 

2.4.2.1(c) to estimate movement of footings when the ground acceleration exceeds kh

b

(g) as 

shown in figure 2-17. This calculation assumes that the line of action of N crosses the wall 

footing within the middle third and therefore the wall will slide and settle whenever kh

b

 is 

exceeded. The total horizontal component of movement will be the same as that for sliding but 

computed using kh

b as the threshold acceleration as: 

4 2

h

b

h h

V k u 0.087

kg k

⎧ ⎫ ∆= = ⎨ ⎬ ⎩ ⎭

 (2-23) 

The vertical settlement will then be: 

w 2 tan = ∆ ρAE (2-24) 

where ρAE is the angle of the sliding surface of the active portion of the bearing capacity failure 

region given by, 

( )( ) ( ) ( )( ) ( ) ( ) ( )

( ) ( ) ( )

ww w w w w -1

AE w

w w

tan - - i tan - - i + cot - - 1+ tan + + cot - - - tan - - i

 = - + tan

1+ tan + + tan - - i + cot - -

⎡ ⎤ φφ φ φ φ θ θ θβ β θ θβ θ δ ⎢ ⎥ ρ φ θ ⎢ ⎥ δ β θ θ φθβ ⎡ ⎤ φ ⎢ ⎣ ⎦ ⎥ ⎣ ⎦

 (2-25) 
43

Equations 2-23 and 2-24 do not consider the RB or RB/T mixed modes of failure that may 

accompany the loss of bearing capacity. 

Deformation analyses that consider the RB or mixed RB/T modes of failure are not routine and 

require the use of specialized software involving numerical integration. A procedure that 

involves numerical integration of coupled equations of motion is described by Siddharthan et al. 

(1992). This procedure investigates the possibility of both sliding and rotation modes occurring 

simultaneously (RB or RB/T modes). Also, a procedure is described by Rafnsson and Prakash 

(1994) and Prakash et al. (1995a,1995b) for computing both sliding and rocking displacements 

of rigid retaining walls. For walls that may fail by overturning with respect to the toe (special 

case of RB mode) the user is also referred to the method described by Zeng and Steedman 

(2000). 

A simple method for assessing the potential for large displacements for walls that fail by tilting 

or seismic reduction of bearing capacity is described in section 2.4.2.2. If the simple approach 

indicates that the retaining wall is vulnerable to excessive deformation by tilting or rotation then 

either a more detailed analysis can be performed to confirm the result, or the design of seismic 

retrofit is recommended as described in section 2.5. 

2.4.3. CONCRETE CANTILEVER WALLS (INVERTED T WALLS) 

The analysis for seismic vulnerability of inverted T-shaped cantilever walls follows a similar 

procedure as that for gravity walls. External stability is evaluated as described in sections 2.4.2.2 

(a) and (b). Proximity of nearby structures and the potential for seismically induced deformation 

is investigated as described in section 2.4.2.4. However, in the case of a cantilever wall, soil 

placed over the heel of the footing is considered to contribute to the mass of the wall. 

Structural details of the wall stem and footing must also be considered similar to gravity walls as 

described in section 2.4.2.3. These elements are treated as cantilever sections, subjected to earth 

pressures from either the backfill or the soil bearing pressures. The wall stem is treated as a 

cantilever fixed at the top of the footing. The toe of the footing is treated as a cantilever fixed at 

the front face of the wall stem and acted on by the soil contact pressure. The heel of the footing 

is treated as a cantilever fixed at the back face of the wall stem loaded by its own weight, the 

contact soil pressure, the vertical component of active earth pressure (i.e., from friction between 

backfill placed over the heel and the backfill behind the heel), and that of the backfill placed on 

top of it. The vertical acceleration component may increase the vertical force applied to the heel. 

Due to the cantilever action of the wall elements, reinforced concrete is used to resist the flexural 

stresses. Ultimate strength design, as described in ACI (2002), is used to check the capacity of 

the sections. For earthquake loading, and seismic evaluation of existing retaining walls for 

retrofit, load factors and reduction factors are taken as unity. 
44

2.4.4. ANCHORED WALLS 

2.4.4.1. Secondary Screening Procedure for Anchored Walls 

Figure 2-18 shows an empirical chart, developed by Gazetas et al. (1990), useful for screening 

tied-back walls relative to the need for seismic evaluation and possible retrofit. In figure 2-18, 

anchored sheet-pile walls are screened into one of three distinct zones or categories. Past 

experience indicates that anchored bulkheads falling into Zone I suffered little or no earthquakeinduced damage, those within Zone II have suffered moderate degrees of damage, and those in 

Zone III have suffered severe, unacceptable, damage. The chart is based on the observed 

performance of waterfront structures. Before using the chart, the engineer must ensure that 

liquefaction failure of cohesionless soils in the backfill or foundation is unlikely. Application to 

bulkheads with backfill and foundation soils that are not submerged should be done with caution. 

For walls with dry backfill, use of figure 2-18 may be unconservative for high levels of peak 

ground acceleration, and very tall walls. 

.

. .

. .

.

.

.

.

.

. .

.

0

1

2

3

4

Degree of Damage

Zone I

Zone II

Zone III

2

1.5

1

0.5

0

-0.5

0 0.5 1

Embedment Participation Index (EPI)

Effective Anchor Index (EAI)

Gazetas et al., 1990 

Figure 2-18. Chart for seismic screening of anchored walls. 

To use figure 2-18, two indices for the retaining wall must be computed including the Effective 

Anchor Index (EAI) and the Embedment Participation Index (EPI). The EAI is described with 

the aid of figure 2-19 in terms of the horizontal distance, d, from the active failure surface to the 

tie-rod connecting point: 

EAI = d/H (2-26) 
45

H

d

AE

Effective “Point”

of Rotation

Active Failure Surface

L

f

D

Gazetas et al., 1990 

Figure 2-19. Definition of the effective anchor index: EAI =d/H. 

The active failure surface is assumed to originate at the effective “point” of rotation, defined at 

point f below the dredge line: 

' o

e f 0.5(1 k ) 0.02( 20 ) H D ≈ +− ⎡ ⎤ φ − ≤ ⎣ ⎦ (2-27) 

where, ke is a function of the horizontal and vertical seismic coefficients, ke = kh /(1-kv). Gazetas 

et al. (1990) recommend that kh be taken as two thirds of the peak horizontal ground acceleration 

coefficient. For cohesionless soils under the water table, ke is increased to ke’ = 1.5ke. Having 

established ke’, the angle αAE can be approximated as: 

o ' 1.75

AE e 45 135(k ) 2

φ α ≈ +− (2-28) 

αEA will become small as '

e k approaches tan φ . 

For uniform backfill and foundation, the EPI can be approximated as: 

PE 2

AE

K EPI r (1 r) K

≈ + (2-29) 

where, r = f/(f+H) and the ratio KPE/KAE can be determined with the aid of figure 2-20. 

Figure 2-18 can be used as a screening tool with the following procedure. 
46

Screening Method for Tied-Back Walls 

1. Determine the height, H, of the tied-back wall, the depth of embedment, D, and the location of the 

anchor block. 

2. Given the peak ground acceleration at the site, compute ke = kh /(1-kv) and increase by a factor of 

1.5 for cohesionless soils beneath the water table. 

3. Using equation 2-27, estimate the location of the effective point of rotation, f, and use equation 2-

28 to estimate the inclination of the active failure surface, αAE, behind the wall. 

4. Sketch the wall as shown in figure 2-19, find “d” based on “f” and αAE, and compute EAI as 

described by equation 2-26. 

5. Using figure 2-20, determine the ratio of KPE/KAE and compute EPI as described by equation 2-29. 

6. Using figure 2-18, and the values of EAI and EPI, determine if the wall is in Category I, II, or III. 

7. If the wall is in Category I, further evaluation is not required. If the wall is in Category II, further 

evaluation is required if movement or noticeable damage of the wall cannot be tolerated. If the 

wall is in Category III, detailed evaluation and retrofit of the wall is required. 

25

20

15

10

5

0

0 0.1 0.2 0.3

= 35

= 35

= 30

= 30

= - 15

= 0

= - 15

= 0

o

o

o

o

o

o

o

o

Seismic Coefficient, k

K

K

PE

AE

e

Gazetas et al., 1990 

Figure 2-20. Ratio of active and passive earth pressure coefficients 

as a decreasing function of ke.
47

2.4.4.2. Evaluation Procedure for Anchored Walls 

The analysis presented in this section is for backfill and foundation soils that are not submerged. 

 While waterfront anchored bulkheads may be the most common form of a anchored wall 

encountered, they are not often found retaining a highway structure. Many times anchored walls 

are used to support highway fills, where free water is not involved. See section 2.4.2.1 (a) for 

guidance on lateral earth pressure computations involving submerged soils. 

The vertical acceleration component, kv, is not included in the calculations for the reasons 

described in section 2.4.2.2. If the wall is located in proximity to an essential facility, and the 

wall is not allowed to yield, kv should be included in the calculations of lateral earth pressure. 

Figure 2-21 depicts the forces on a tied-back wall subjected to seismic loading. For a tied-back 

wall, seismic effects shown in figure 2-22 combine in various ways to reduce the static factor of 

safety to 1.0, and initiate deformation of the wall. Three effects are involved, and three 

fundamental modes of failure are possible as follows: 

1. Initially, prior to the accumulation of seismically induced deformation, the anchor makes the 

top part of the wall more rigid and the dynamic increment of lateral earth pressure may 

exceed that for the active state. This may cause excessive bending moments in the sheet 

piling, or possibly break the tie rod. However, reports of this mode of failure are infrequent 

in earthquake reconnaissance reports and the failure mode is not discussed further. 

2. The passive resistance at the toe of the wall decreases with increasing acceleration as 

described by figure 2-12. If the anchor does not fail, this may lead to rotation of the wall 

about the top as the base lurches outward. 

L

A

H

D

2/3D

AS

P

P

H /2

2/3 H

Static slip

surfaces

PS

A

A

A

H

h

h

P

P

AE

AS

PS

E

AS

A

A

A

PS

PE

Figure 2-21. Forces on an anchored wall. 
48

3. Finally, and perhaps most important, with increasing levels of ground acceleration, the active 

wedge behind the wall and passive wedge in front of the anchor grow in size by ∆ρAE and 

∆ρPE, respectively. At the point in which there is destructive interference between the active 

and passive wedges, as shown in figure 2-22, anchor resistance becomes compromised. 

Destructive interference plus the seismically induced increase in the tie rod force, ∆AE, can 

cause premature failure of the anchor and subsequent rotation with respect to the bottom of 

the wall. Thus, the anchor lurches outward at each excursion of acceleration above the 

threshold level, triggering outward movement of the top of the wall accompanied by tension 

cracks and settlement of the ground behind the anchor. 

The relationship between ground acceleration and ρAE and ρPE is described by equations 2-25 

and 2-30. For convenience, equation 2-25 is repeated here. 

( )( ) ( ) ( )( ) ( ) ( ) ( )

( ) ( ) ( )

ww w w w w -1

AE w

w w

tan - - i tan - - i + cot - - 1+ tan + + cot - - - tan - - i

 = - + tan

1+ tan + + tan - - i + cot - -

⎡ ⎤ φφ φ φ φ θ θ θβ β θ θβ θ δ ⎢ ⎥ ρ φ θ ⎢ ⎥ δ β θ θ φθβ ⎡ ⎤ φ ⎢ ⎣ ⎦ ⎥ ⎣ ⎦

 (2-25 repeated) 

( )( ) ( ) ( ) ( ) ( )( )

( )( ( ) ( )

ww w w w w -1

PE w

w w

tan - + i tan - + i + cot - + 1+ tan + + cot - + + tan - + i

 = - - + tan

1+ tan - + tan - + i + cot - +

⎡ ⎤ φφ φ φ φ θ θ θβ βθ θβ θ ⎤ ⎤ δ ⎢ ⎦ ⎦ ⎥ ρ φ θ ⎢ ⎥ β θ θ φθ β φ ⎤ δ ⎢ ⎦ ⎥ ⎣ ⎦

 

 (2-30) 

Dynamic

interference zone

Anchor

Failure surface - static

- dynamic

Static

Static

Dynamic

A

A

P PAE

PA

PP

P

H

PPE

k g

k g

h

v

E

A

Figure 2-22. Seismic effects on anchored walls. 
49

2.4.4.2(a). Passive Toe Failure - Rotation About the Top 

The stress resultants acting on the wall are shown in figure 2-21. In this figure, ∆PAE, and ∆PPE

are the dynamic effects to be added or subtracted to the static values and hence: 

∆PAE = PAE - PAS (2-31) 

∆ PPE = PPE - PPS (2-32) 

where PAE, PPE, can be determined as described in sections 2.4.2.1(a) and (b). Static values of 

lateral pressure may be obtained by using kh = kv= 0. For steel piles, the interface wall friction, 

δw = 0 is a reasonable value (Neelakantan et al., 1992). Assuming that the wall/soil interface 

friction angle, δw, is zero is conservative since active earth pressures are relatively higher, and 

passive earth pressures are relatively lower compare to values computed with δw ≠ 0. 

The dynamic increments of lateral earth pressure are assumed to act as shown in figure 2-21. 

From moments taken about the anchor point, the driving moment is: 

2 H MP HA P A D AS A h AE h 3 2

⎛ ⎞⎛⎞ = − +∆ − ⎜ ⎟⎜⎟ ⎝ ⎠⎝⎠ (2-33) 

and the resisting moment capacity is given by: 

( ) D MP PH A R PS PE A h 3

⎛ ⎞ = −∆ − − ⎜ ⎟ ⎝ ⎠ (2-34) 

Thus, the factor of safety against failure by rotation about the top is MR/MD, and the critical 

threshold acceleration, (kh)RT, can be calculated from the condition that FS = 1.0 when MD = MR. 

2.4.4.2(b). Anchor Failure - Rotation of Base

The anchor force is computed by summing the forces in the horizontal direction. Thus, the 

anchor force including static plus seismically induced internal forces is: 

( ) 1 2 2 A (H D K D K ) D AE PE 2 =γ + − (2-35) 

In the absence of destructive interference between the active and passive failure wedges in front 

of the anchor, the resistance that can be provided by an anchor plate is: 

( ) 1 2 A hK K R PE AE 2 =γ − (2-36) 
50

Thus, the factor of safety against anchor failure inducing rotation about the bottom of the wall is 

AR/AD, and the critical acceleration, (kh)ANC, is calculated from the condition that FS = 1.0 when 

AD = AR. 

For any given design, the destructive interference, further reducing the anchor resistance, can be 

evaluated from equations 2-25 and 2-30 which describe the active and passive slip surface angles 

for different acceleration levels. It is recommended that the possibility of interference be 

evaluated from a sketch of the wall system, drawn to scale, that includes the active and passive 

slip surfaces. 

Example 2-1 demonstrates the application of the procedure for seismic evaluation of anchored 

walls. Table 2-1 is a summary of results from example 2-1. 

Table 2-1. Results from application of seismic evaluation procedure for 

anchored walls (described in Example 2-1). 

Recommendation 

for Static Design 

D/H AD = AR

Static 

(kN/m) 

(kh)RT From 

Eq. 2-33 & 

2-34 

(kh)ANC From 

Eq. 2-35 & 

2-36 

AD = AR

Retrofit 

(kN/m) 

(1) (2) (3) (4) (5) (6) 

1 0.48 59 0.34 0.23 170 

2 0.35 48 0.15 0.07 87 

3 0.58 59 0.43 0.30 221 

2.4.5. MSE WALLS 

The seismic evaluation of MSE walls described in this chapter applies to walls less than 12 

meters high. Generally, seismic evaluation of MSE retaining walls involves consideration of 

both external and internal resistance to seismic loading. Potential modes of failure including 

sliding, bearing capacity, rupture failure, and pullout are depicted in figure 2-23. In addition, 

slope or general failure should be evaluated as described in chapter 3. 

In response to external loading, the reinforced wall fill is treated as a coherent mass (figure 2-

24). As such, the external stability analysis for MSE walls follows a procedure similar to that 

detailed for gravity retaining walls described in section 2.4.2. This includes consideration of 

sliding, overturning, bearing capacity and global failure modes. Loads on the reinforced wall fill 

include lateral earth pressure from the unreinforced backfill, inertial loading due to seismic 

excitation, and from any applied surcharge. 

The assumption that the reinforced wall fill behaves as a coherent mass presumes that it is 

internally stable. Internal stability requires that the reinforcement does not fail by rupture, 

pullout or at the connection to the wall face. An important issue is the location of the failure 

surface within the reinforced wall fill as it affects the length required to resist pullout, figure 2-

25. 
51

Example 2-1. Application of the Procedure for Seismic Evaluation 

of Anchored Walls 

A six meter high retaining wall with tie-backs connected one meter below ground level will be evaluated. 

The soil properties for design are φw = 35°, δw = 0, and unit weight of backfill and foundation soil, γ = 20 

kN/m3

. Seismic evaluations are performed with reference to three different static designs including 

recommendations of the BS Code of Practice (1951) and the Canadian Foundation Engineering Manual 

(1978), the U.S.S. Steel Sheet Piling Design Manual (1975), and The Naval Facilities Design Manual 

NAVFAC DM-7 (1982). The three recommendations for static design are described below: 

1. BS Code of Practice (1951) and the Canadian Foundation Engineering Manual (1978) 

recommend that a safety factor of 2.0 be applied to the coefficient of passive earth pressure. 

2. The U.S.S. Steel Sheet Piling Design Manual (1975) recommends that the theoretical limiting 

depth of embedment be obtained without incorporating any safety factor. This theoretical depth 

of embedment is increased by at least 20 percent to arrive at the design depth of embedment 

similar to AASHTO (2002). 

3. The Naval Facilities Design Manual NAVFAC DM-7 (1982) recommends that a safety factor of 

2.0 be applied to the coefficient of passive earth pressure. The theoretical depth of embedment 

computed with the safety factor is then increased by 20 percent to arrive at the design depth of 

embedment. 

The embedment depth ratios, D/H, and anchor forces, AD, computed for the static case using each of 

the recommendations is presented in columns (2) and (3) of table 2-1. The acceleration (kh)RT to initiate 

rotation about the anchor position is found by equations 2-33 and 2-34. The acceleration for anchor 

failure, (kh)ANC, is found by equations 2-35 and 2-36. The height of anchor plate, h, used in equation 2-

36 is that which satisfies the static design.

In all cases examined, the acceleration required for anchor failure, (kh)ANC, is less than that required for 

failure by rotation about the anchor position, (kh)RT. Consequently, the anchor will fail first which is 

consistent with observations described in section 2.3.2. For any of these static designs, the seismic 

efficiency of the system can be increased by increasing the anchor resistance, AR, described by 

equation 2-36. For example, for the given D/H ratios, the retrofit design of the anchor may be 

determined from equation 2-35 by putting kh = (kh)RT. The design anchor forces AD (retrofit) = AR (retrofit) 

thus obtained are presented in column six of table 2-1. These forces are much greater than those found 

by conventional static methods. Thus, for the same D/H ratio, we can enhance the seismic stability of 

an anchored retaining wall by retrofitting the anchor(s) to carry the balanced anchor forces. The retrofit 

anchors must be at a distance L, as shown in figure 2-21 but with P and AE P instead of PE P and AS

P , to avoid any destructive interferenc PS e at the retrofit design value of (kh)RT. 
52

(a) Base Sliding (b) Overturning (c) Bearing Capacity

(Excessive Settlement)

(d) Tensile Over-stress (e) Pullout (f) Internal Sliding

(g) Shear Failure

(Bulging)

(h) Connection Failure (i) Local Overturning

(Toppling)

Figure 2-23. Modes of failure for MSE walls. 

PAE

PA

b

W

f

H

L

0.6H

kh

w

Figure 2-24. Forces acting on MSE wall for external stability analysis. 
53

Reinforcement

Failure Surface

Le

AE

Figure 2-25. Assumed failure surface within the reinforced wall fill. 

The seismic internal stability analysis examines the increased reinforcement tension, an increase 

in the percent of total lateral force carried by reinforcement elements in the upper portions of the 

wall, and the required increased length of the reinforcement layers. 

Seismic lateral earth pressures are computed using equations 2-1, 2-2 and 2-3 from the 

Mononobe-Okabe analysis described in section 2.4.2.1(a). The peak friction angle is used to 

represent the shear strength of the soils. Included in the analysis are horizontal accelerations, the 

inclination of the back face, and the friction at the interface between the wall facing and 

reinforced fill (an estimate of δw=2/3φw can be used) and between reinforced fill and backfill (an 

estimate of δ=φ can be used). 

The maximum acceleration developed in the wall is estimated based on an empirical equation 

proposed by Segrestin and Bastick (1988). 

kh = (1.45- ko)ko ≥ ko (2-37) 

where: 

ko is the peak ground acceleration coefficient accounting for local soil conditions, 

kh is the maximum wall acceleration coefficient at the wall centroid. 
54

This equation is intended to consider the dynamic response of the wall. According to Segrestin 

and Bastick, low ground accelerations are significantly amplified within the wall. The maximum 

wall acceleration is applied to both the reinforced soil and the wall facing. However, the value of 

kh applied to the wall system, including the wall facing, reinforced soil, and retained soil should 

not exceed the threshold acceleration for sliding. For MSE walls, threshold accelerations for 

sliding, kh

s

, are generally less than 0.4g. 

Procedures that consider potential for collapse of the wall, and loss of serviceability of nearby 

structures, are described in sections 2.4.5.1 and 2.4.5.2, respectively. The procedures described 

herein are based on the equations described by Bathurst and Cai (1995). 

2.4.5.1. Evaluation Procedure for MSE Walls for Collapse 

Collapse of MSE walls from overturning or seismically induced reduction of bearing capacity, as 

described in sections 2.4.2.2(a) and (b), is not likely. Therefore, these modes of failure need not 

be investigated for detailed evaluation of the need for seismic retrofit. Potential modes of 

collapse include tension failure of the reinforcements, failure of connection of the reinforcement 

to the wall face, and possibly toppling of the wall facing. These modes of collapse are discussed 

in the following subsections. 

2.4.5.1(a). Tension in Reinforcements

The influence of seismic loading on the magnitude of tensile reinforcement loads can be 

explored by computing a magnification factor, rf, that is the ratio of dynamic tensile force Fdyn, to 

static tensile force Fsta, for a reinforcement layer at depth z below the wall crest. Results of this 

calculation for reinforcement layers at five different depths below the wall crest reported by 

Bathurst and Cai (1995) are presented in figure 2-26. The data illustrates that the largest relative 

increases in reinforcement force occur in the shallowest layers. 

In lieu of figure 2-26, reinforcement tension is computed, as shown in figure 2-27, using the 

contributory area approach and an assumed distribution of the Mononobe-Okabe lateral earth 

pressure similar to figure 2-14, such that the dynamic increment of lateral thrust acts at 0.6 H 

from the base and the static component acts at 0.33 H. The inertia force on the wall facing must 

also be considered in the analysis. Based on this approach, the equation for computing the 

tensions in the reinforcements considering earthquake loading is: 

w

dyn dyn A dyn h v

z L F 0.8 K cos( ) (K 0.6 K )cos( ) k HS H H

⎡ ⎤ = ∆ δ−ψ + − ∆ δ−ψ + γ ⎢ ⎥ ⎣ ⎦ (2-38) 

where: 

Fdyn is the tension in the reinforcement at depth z, 

∆Kdyn is KAE - KA, 

KA is the static lateral earth pressure coefficient, i.e., with kh = 0, 

δ is the wall/wall fill interface friction angle, 

ψ is the wall batter (-ψ =β, see figure 2-11), 
55

Lw is the width of the wall facing, 

γ is the unit weight of the wall fill, 

H is the height of the wall fill, 

Sv is the reinforcement spacing at depth z. 

If Fdyn is greater than the allowable tension in the reinforcement for seismic loading conditions, 

design of seismic retrofit is required as described in section 2.5. 

10

9

8

7

6

5

4

3

2

1

0

0.0 0.1 0.2 0.3 0.4 0.5 0.6

= 35

= 0

= 0.6

= 2 /3

= 0

= 0.1

k = -2k /3

k = 0

k = +2k /3

0.2

0.3

0.4

0.6

0.8

z/H

L /H

r

r

F

F

F

F

dyn

sta

=

w

v

v

v

h

h

Kh

o

o

o

o

Bathurst and Cai, 1995 

Figure 2-26. Influence of seismic coefficients, kh and kv, and normalized depth 

below crest of wall, z/H, on dynamic force amplification factor, rF. 

Seismic Design with Polymeric Reinforcement: The stress strain response of HDPE exhibits 

visco-elastic behavior and is load rate dependent. The tensile strength corresponding to dynamic 

loads with velocities in the range of seismic loading is greater than the allowable tensile strength 

for long-term gravity loads. The user should consult the manufacturer’s literature for information 

on the rate dependent tensile strength of polymeric reinforcement, or conduct tension tests using 

appropriate rates of loading. Currently, no test standard exists for evaluating the rate dependent 

tensile strength of polymeric reinforcement. 
56

.

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..

..

.....

..

.

H

z

L

S F

Dynamic Earth

Pressure Distribution

Reinforcement

Layer (typical)

w (K + 0.2 K ) Hcos( ) A dyn

dyn

dyn v

0.8 K Hcos( ) -

-

K W h w

Bathurst and Cai, 1995 

Figure 2-27. Tensile load in a reinforcement layer due to seismic lateral earth 

pressure and wall inertia. 

Considering the increased tensile strength, and the safety factor used for static design, it will 

often be found that the number of reinforcement layers required for seismic design does not 

exceed the number required for the long-term gravity loading. However, since the line of action 

of the dynamic increment of lateral earth pressure is higher than that for long-term gravity 

loading, the distribution used for the static design may not place enough reinforcement near the 

top of the wall (Bonaparte et al., 1986). 

2.4.5.1(b). Connection Details

The influence of increased dynamic forces on connection load is identical to the analysis 

described in section 2.4.5.1 (a) for reinforcement overstressing. As described by AASHTO 

(2002), the tension at the wall face is considered to be between 80 percent and 100 percent of the 

maximum tension computed in the reinforcement. Compared to static loading, a larger tension in 

the reinforcements is allowed since it is not necessary to apply a reduction factor for creep 

effects. The safety factor at the connection is evaluated as the ratio of the connection strength to 

the tension at the wall face. 

If stacked concrete block units are used as facia, the connection strength may be modeled with a 

Coulomb-type failure law with a maximum cut-off load. For seismic loading, the frictional 

component of the shear strength is reduced to 80 percent of the value used to compute the static 
57

shear strength (Elias and Christopher, 1997). Peak connection capacities may be sensitive to 

rates of loading, but further research is required to define this relationship.

If the safety factor at the connection is less than one, design of seismic retrofit is required as 

described in section 2.5. 

2.4.5.1(c). Seismic Analysis of Segmental Reinforced Walls and Toppling of the Wall Face 

Bathurst and Cai (1995) propose a method of seismic analysis applicable to segmental retaining 

walls (SRWs). Segmental retaining walls utilize stacked concrete block units as the facia system 

together with extensible sheets of polymeric materials (geosynthetics) that internally reinforce 

the retained soils and anchor the facia. Often the wall is battered 3° to 15° from the vertical into 

the retained soils. 

The proposed analysis is a pseudo-static analysis by which factors of safety are computed for 

various failure modes. Internal and external stability analyses must consider the same failure 

modes as for other types of MSE retaining walls. Modes of failure, unique to SRWs, that address 

issues of internal sliding and facing stability (figure 2-23) include: 

• Internal sliding along a layer of reinforcement whereby the potential failure surface 

daylights at the wall face after passing through the interface between the modular blocks. 

• Bulging of the modular blocks at the wall face. 

• Toppling of the wall face. 

For the purpose of evaluating the need for seismic retrofit due to collapse, in addition to the 

modes of failure discussed in sections 2.4.5.1 (a) and (b), only failure by toppling at the wall face 

needs to be considered. 

Toppling of the wall face: Resistance to overturning is due to the self weight of the column of 

stacked concrete blocks, and resistance due to the connection capacity of the reinforcement 

layers above the toe of the target facing unit, as shown in figure 2-28. The factor of safety with 

respect to toppling is calculated as: 

N

i i

R v cc

i 1

OT

w 2

A dyn h

M (1 k ) F Y

FS

1 zz 1 L K cos( ) (0.4 0.1 ) K cos( ) k Hz

6 H H 2H

+

± +

= ⎡ ⎤ δ−ψ + − ∆ δ−ψ + γ ⎢ ⎥ ⎣ ⎦

∑

 (2-39) 

where: 

MR is the resistance to overturning due to facing column self-weight above the toe of the 

target facing unit, 

N is the number of reinforcement layers, 
58

Fc

i

 is the connection capacities of reinforcement layers, 

Yc

i

 are the corresponding moment arms of Fc

i

. 

If the computed factor of safety with respect to toppling is less than one, seismic retrofit is 

required as described in section 2.5. 

A B

Horizontal component

of dynamic earth

pressure distribution

(See Figure 2-14)

z

H

Ww

z/2

o

xc -

k L z h w

m z

Fc

N

P cos( - ) AE

(z)

F

F

c

c

i+1

i+1

i+1

i+2

i+3

i+4

y

y

y

y

c

c

c

c

.

Bathurst and Cai, 1995 

Figure 2-28. Overturning moment at an interface within the wall facing of an SRW due to 

seismic lateral earth pressure and wall inertia. 

2.4.5.2. Proximity of Structures to MSE Walls 

Nearby essential facilities may be affected by deformations of MSE walls. The potential for 

these deformations may be evaluated using procedures similar to those for gravity or semigravity walls as described in section 2.4.2.4. Potential failure mechanisms that can lead to 

excessive deformation of MSE walls include external sliding failure, pullout failure of 

reinforcements; and, for SRWs, internal sliding instability, and bulging of the wall facing. 

Evaluations of these modes of failure, within the context of loss of serviceability of nearby 

structures, are described in sections 2.4.5.2(a) through 2.4.5.2(d), respectively. 
59

2.4.5.2(a). External Sliding Stability

MSE walls can be screened relative to the need for detailed evaluation of a sliding failure using 

the procedure described in section 2.4.2.4(a). The structure is viewed as a gravity retaining wall 

having the dimensions of the reinforced wall fill. Compared to conventional gravity retaining 

walls, the static factor of safety relative to a sliding mode of failure for MSE walls is relatively 

high. This is because the length of reinforcements for MSE walls is often governed by “pullout” 

requirements rather than sliding stability. For many MSE walls, the static factor of safety for 

external stability considering the sliding mode is 4 or higher. Figure 2-15 indicates that the 

threshold acceleration coefficient for this condition is greater than 0.3. 

If the screening procedure indicates that deformations are a potential problem, a more detailed 

evaluation is required. The deformation analysis considers a sliding mode of failure at the base 

of the reinforced wall fill. The method considers effects from horizontally applied acceleration, 

including increased lateral thrust applied by the unreinforced backfill, and an inertia force acting 

within the reinforced wall fill as shown in figure 2-24. 

The external sliding analysis is the same as that described in section 2.4.2.4. The analysis is 

performed for a coherent gravity structure having the dimensions of the reinforced wall fill as 

shown by figure 2-24. The procedure only considers a sliding mode of failure, therefore steps 

(6), (7) and (8) of the procedure described in section 2.4.2.4(b) are not necessary and iterations 

are performed until the threshold acceleration for sliding, kh

s

, is obtained. 

2.4.5.2(b). Pullout 

The effect of applied horizontal and vertical acceleration on the inclination of the potential 

failure surface within the reinforced soil, described by equation 2-25 is considered when 

computing the required anchorage length of the reinforcement. Pullout may lead to unacceptable 

deformation and damage to nearby essential facilities. 

The resistance to pullout from the portion of the reinforcement beyond the potential failure 

surface is computed as: 

TR = 2 Le μ γ z (1-kv) b (2-40) 

where Le is the length of the reinforcement beyond the failure zone defined by ρAE, b is the width 

of reinforcement, and μ is the coefficient of friction between the reinforcement and the wall fill. 

For sheet reinforcement, use b = 1 and TR as force per unit length. The value of μ should be 80 

percent of that determined from static load tests. Studies by Bathurst and Cai (1995) indicate that 

the required reinforcement anchorage for seismic loading is sensitive to the vertical component 

of acceleration, kv. The pullout resistance is compared to the reinforcement tension computed 

with equation 2-38. If the pullout resistance is less than the computed reinforcement tension, 

design of seismic retrofit as described in section 2.5 is required. 
60

2.4.5.2(c). Internal Sliding Stability (for SRWs and MCUs)

The analysis for internal sliding stability, figure 2-23, is similar to that for the external stability 

analysis described in section 2.4.5.2(a). The dimensions of the coherent gravity mass considered 

in the internal sliding stability analysis are described by the width of the reinforced wall fill and 

the height of the wall fill above the layer of reinforcement where the potential for sliding is being 

investigated. Contributions to sliding resistance are from the interlock shear strength between the 

modular blocks at the facing, and the interface shear resistance along the length of the 

reinforcement. The shear resistance between modular blocks may also be described with a 

Coulomb-type failure law. The shear strength between modular blocks is determined as 

described by NCMA Test Method SRWU-2 (NCMA, 1996). The shear resistance along the 

reinforcement is often less than for the shear resistance of a failure plane through soil. It is 

recommended that the user assess the shear strength of the reinforcement/soil interface by 

laboratory direct shear tests as described by ASTM D5321. 

Using the procedure described in section 2.4.2.4(b), equation 2-20 is modified to account for the 

shear resistance of the modular blocks at the wall face as: 

f u

slide

N tan V F.S.

F

δ + = (2-41) 

where 

Vu is the shear strength of the interface between modular blocks. 

The shear resistance at the wall facing is related to the above weight of the facing column, Ww. 

At large inclination angles, the magnitude of Ww may be less than the weights of the individual 

facing units above the interface elevation, due to the effect of the facing column units leaning 

into the reinforced soil mass. Studies conducted by Bathurst and Cai (1995) indicate the potential 

for interface shear failure under seismic loading increases with proximity of the shear interface 

to the crest of the wall. However, the effect of vertical acceleration on calculated dynamic 

factors of safety diminishes with height of interface. 

The procedure only considers a sliding mode of failure, therefore steps (6), (7) and (8) of the 

procedure described in section 2.4.2.4(b) are not necessary and iterations are performed until the 

threshold acceleration for sliding, kh

s

, is obtained. The procedure is applied to each 

reinforcement interface along the height of the wall. The minimum kh

s

 thus determined governs 

the analysis. If the minimum kh

s

 is greater than kh, this mode of failure is not a concern. If the 

minimum kh

s

 is less than kh, a deformation analysis as described in section 2.4.2.4(c) is 

performed. The deformations are compared to acceptable levels of deformation to determine if 

seismic retrofit is required. 

2.4.5.2(d). Bulging Shear Failure

Bulging is caused by a shear failure at the interface between modular blocks at the wall face. The 

wall facing is treated as a shear beam, as shown in figure 2-29, in which the integrated lateral 

earth pressure (similar to that shown in figure 2-24) must equal the sum of the forces in the 
61

reinforcement layers. The effect of wall inertia is included in the analysis. The total force carried 

by reinforcement layers located above the facing unit “j” is calculated as the area ABCD of the 

lateral earth pressure distribution, plus the facing column inertial force over the same height. The 

out-of-balance force to be carried through shear at the bottom of the facing unit “j” is simply the 

sum of the incremental column inertia force kh∆Ww

j

 plus the force due to CDEF in the figure. 

The locally maximum interface shear forces will occur at reinforcement elevations: 

v wv

dyn dyn A dyn h

z S L HS S [0.8 K cos( ) (K 0.6 K )cos( )( ) k ] H 4H H 2

γ = ∆ δ−ψ + − ∆ δ−ψ − + (2-42) 

where 

Sdyn is the interface shear stress at depth z. 

The interface shear strength is compared to the shear strength of the interface between modular 

blocks, Vu, at each level of reinforcement.If Sdyn is greater than Vu , design of seismic retrofit is 

required as described in section 2.5. 

A B

C

F

D

E

Horizontal component

of dynamic earth

pressure distribution

z

H

S

S

k W S

F

S = k W + AREA dyn

dyn

dyn

h

h

w

w

j

j

CDEF

i

i

i v

v

i

i +1

Bathurst and Cai, 1995 

Figure 2-29. Shear force at an interface within the wall facing of an SRW due to seismic 

lateral earth pressure and wall inertia. 
62

2.5. DESIGN OF SEISMIC RETROFIT FOR EARTH RETAINING STRUCTURES 

An understanding of the basic concepts presented in section 2.4 will allow the engineer to 

evaluate various options to strengthen walls and reduce their seismic vulnerability. In fact, 

results from the evaluation procedures described in section 2.4 suggest the appropriate 

retrofitting strategies, since not only is the threshold acceleration evaluated, but also the critical 

failure mode. 

In general, retrofitting can involve one or more of the following: 

• Tie-backs (with grouted, helical, or expanding anchors). 

• Increase in the footing width. 

• Reinforcing the concrete wall stems. 

• Added passive restraint by burying the toe. 

• Minipiles. 

• Soil reinforcement near the top. 

• Soil modification. 

This listing is in the approximate order of their general effectiveness. Tie-backs, for example, are 

useful in almost every situation for all types of walls, while soil modification by adding 

admixtures or grouting is more expensive and time consuming. 

Retrofit for liquefaction vulnerability is not discussed in this part of the manual. Where walls 

(particularly tied-back bulkheads used as waterfront structures) are susceptible to liquefaction, 

special remedial measures may be required as presented in chapter 11, Part 1 of this manual. 

2.5.1. GRAVITY AND SEMI-GRAVITY WALLS 

From the evaluation procedure described in section 2.4.2, the critical or threshold acceleration 

corresponding to each mode of failure is determined and an estimate made of the seismic 

deformation. The mode of deformation with the lowest threshold acceleration occurs first, 

although for severe earthquakes, mixed types of deformation may occur as less critical failure 

modes are initiated at higher acceleration levels. Figure 2-30 shows the three modes of failure 

and appropriate retrofitting measures for each. 

As can be seen, tie-backs are a universal retrofitting measure but they must be installed properly. 

They must be long enough to extend beyond the slip surface described by equation 2-25 with 

enough anchorage length to develop the design force, FA. The spacing and size of the tie-backs is 

computed such that FA will improve horizontal and moment equilibrium to counter PAE and khW 

to the point where the resulting increase in threshold acceleration eliminates or reduces the 

seismic displacement to an acceptable level. Equilibrium calculations using the concepts 
63

discussed in section 2.4.2 and 2.4.4 may be applied to establish the required value of FA and 

design of the deadman anchorage. Note that the inertia of the gravity wall must be included in 

the equilibrium equations, and shear resistance at the base of the wall may be included in the 

force moment equilibrium equations. Tie-backs have the added advantage of increasing the 

normal force on the slip surface so that not only are the seismic driving forces resisted, but the 

shear strength resisting slip is increased. 

If grouted anchors are employed, the user is referred to Sabatini et al. (1998) for details of the 

anchor design. The effect of the anchor load on the wall must also be addressed in the design. 

Effects on the wall from the anchor load include bearing stress, punching shear, bending moment 

and the associated shear stress. 

Increasing the footing width is also an excellent retrofitting strategy for walls where sliding, or 

rotation about the base, is the failure mode. Various ways of adding to the width are possible and 

only one of many viable designs is shown in figure 2-31(a). In this approach, heavy wire mesh is 

used for tensile reinforcement because of its relatively short development length, reducing the 

amount the original toe must be undercut. Care must be exercised when considering this option 

such that its implementation does not compromise the original design. 

Toe Burial

Minipiles

Tie-backs

Slip Surface PAE

k W

A

A

h

.

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. . . . . . . . . . . . . . . .. . . . . . .. . . . . . .. . . . . .

Soil Reinforcement

Slip Surface

Tie-backs

P

Footing Extension k W

Minipiles

h

AE

Slip Surface Toe Burial Tie-backs

k W PAE h

.

.. ...

.

.

..

.

..

.

..

.

..

.

..

.

.

..

.

..

.

.

..

.

..

.

.

..

.

..

.

.

..

.

..

.

.

..

.

..

.

.

..

.

..

.

..

.

..

.

..

.

..

.

.

..

.

.

.

.

a. Sliding b. Tilting

c. Global Stability

Figure 2-30. Retrofit strategies for gravity and semi-gravity walls. 
64

.. .

.

.. ..... .

.. .... .. .

...

.

. ..

.

..

..

.. .. ..

. .

.

.. .

.

...

.

... . . ..

.

.

.

.

.

.

.

...

.

Width Extension

Wire Mesh

Reinforcement ld

PPE

(small)

R N E E

SE

..

.

.

..

.

.

.

.

...

.

.

..

...

..

..

.

. ...

.

.

...

.. ... . .

.

....

. ..

.....

. .....

...

Extension “Key”

t/3

PPE

RE

NE

h

t

a. Width Extension b. Extension Plus Passive Key

Figure 2-31. Retrofitting by increasing the width of the base. 

The increased footing width has an effect on sliding resistance due to the increase in wall weight; 

overturning stability due to increased wall weight and distance between the toe and centroid of 

the wall; and seismic bearing capacity due to increase in footing width. The increase in threshold 

acceleration and corresponding reduction in seismically induced displacement can be evaluated 

as described in section 2.4.2. Also, the structural integrity of the footing must be evaluated, 

particularly with respect to the bending moments, which may be higher than those considered in 

the original design. 

Adding passive resistance at the toe by burial is a possible retrofitting strategy for walls where 

sliding is critical but is not nearly as effective in preventing tilting. The passive resistance can be 

computed directly from equations 2-4 and 2-5. The increase in seismic bearing capacity due to 

the surcharge loading is given by use of figure 2-13 and equation 2-7. 

Retrofit by adding width to the toe can be combined with added passive resistance by deepening 

the design of figure 2-31(a), as shown in figure 2-31(b). This, as in all retrofitting strategies, is 

constrained by the physical conditions of the site, access and material availability. There are 

added advantages to this design. First, the additional passive restraint at the face of the key is 

less likely to be disturbed. Secondly, it is possible to design its depth, h, such that the resultant 

force on the additional block of concrete acts below the upper third of the toe thickness, t. This 

will reduce the amount of steel reinforcement required. The structural integrity of the footing 

must also be checked and the effect of concentrated vertical load near the toe with respect to 

bending moment considered in the design. 
65

Minipiles, as shown in figure 2-30, are certainly a viable retrofitting approach, particularly to 

prevent tilting of concrete cantilever-type walls. More than one row of piles is desirable, but 

there may not be enough space at the toe of an existing footing to allow installation of two rows 

of piles. The retrofit design should include a check for overturning with respect to a pivot point 

at the pile-heads, and the pile-heads should be designed for moment transfer, i.e., they should be 

design as fixed head piles. Piles will increase the rigidity of the foundation near the front of the 

footing, so the design calculations should include analysis of the potential for differential 

settlement, but the use of short piles will minimize this effect. Also, if pressure grouted minipiles are used, there will be some improvement in the foundation soil beneath the footing. 

The foundation should be analyzed as a spread footing. The pile elements are intended to extend 

the apparent depth of the footing and provide a deeper-seated failure surface associated with the 

bearing capacity of the footing. The required pile lengths would be relatively short; less than 3 

m. 

The piles need to be designed to carry moment, lateral load and transfer the seismic increment of 

bearing pressure near the toe of the footing. They must be drilled deep enough at the toe to 

extend below the bearing capacity zone. They will also provide some added resistance to sliding 

through dowel action. To be most effective, the piles should be battered outward, but generally, 

there will not be enough clearance at the toe without extending the footing. Minipiles are 

relatively more expensive but, quick, simple and less disruptive than extending the footing. The 

reader is referred to Bruce and Juran (1997) for details on the design of minipiles. Similar to tiebacks or grouted anchors, the effect of load transfer on the structural integrity of the footing must 

be addressed in the design. 

The other retrofitting approaches of soil reinforcement and soil modification will generally be 

less effective and more costly than the four strategies already outlined. Thus, they will not be 

discussed further. Only in very special cases must the engineer turn to them where there is no 

room for extending, deepening, or burying the toe, tie-backs for some reason are not feasible, 

and minipiles cannot be used. 

Finally, it should be noted that except for minipiles, these retrofitting strategies are applicable to 

all types of gravity walls. The figures were drawn for a cantilever wall only for convenience. 

2.5.2. CONCRETE CANTILEVER WALLS - STRUCTURAL FAILURE OF THE WALL 

For all wall types, structural failure due to increased lateral earth pressures is possible in severe 

earthquakes with peak horizontal ground acceleration greater than 0.4 g. For design of structural 

retrofit, the dynamic increment of lateral earth pressure should be assumed to act at 0.6 H from 

the base of the wall. Thus, for example, in a cantilever wall, if the lateral thrust is doubled due to 

seismic forces, then the moment at the base of the stem will more than double. 

There are a number of methods for adding moment resistance to cantilever wall stems. Use of 

cover plates is a simple and viable option. Other options include adding buttress elements or tiebacks. The important thing is that the engineer recognizes this potential failure mode for severe 
66

earthquakes. Structural collapse, unlike the accumulation of increments of deformation due to 

periodic slip, can be catastrophic. 

2.5.3. ANCHORED WALLS 

The evaluation procedure described in section 2.4.4 dictates the appropriate retrofitting strategies 

for tied-back walls. As demonstrated by example 2-1, considering walls designed using current 

standards for static design, the failure mode in an earthquake would be by anchor failure and 

rotation about the bottom. For current static designs, rotation around the anchor is less likely 

since the corresponding threshold acceleration is relatively high. 

Thus, the best retrofitting approach is to increase the strength of the anchor and increase its 

embedment length to avoid destructive interference. Thus from figure 2-32, the retrofit anchor 

should be at: 

E AE PE l (H D)cot h cot = + ρ + ρ (2-43)

and designed to take a seismic anchor force given by equation 2-35. This will increase the 

threshold acceleration to above 0.35 g for tied-back walls with a D/H ratio greater than 0.5. Even 

for very severe earthquakes, walls retrofitted to threshold accelerations greater than 0.35 g will 

not move more than 0.1 meters, unless the anchor fails structurally. 

If instability at the toe of the wall is a problem, the retrofit strategy might include installing an 

additional row of tie-backs. 

l

E

Retrofit Anchor Dynamic

Interference Zone

Anchor

Failure Surface - static

- dynamic

Static

Static

Dynamic

H

h

k g

k g

h

v

E

E E

D

A

Figure 2-32. Seismic effects and retrofit for tied-back walls. 
67

2.5.4. MSE WALLS 

To date, mechanically stabilized earth walls, in all varieties and configurations, have an excellent 

history of performance in earthquakes. However, the evaluation procedure described in section 

2.4.5 will indicate that some, relatively taller, MSE walls in severe earthquake hazard zones may 

need careful evaluation for possible retrofitting. 

If reinforcements near the top of the wall are overstressed, it may be feasible to add additional 

reinforcements near the top of the wall. If access to the backfill is a problem, soil nails drilled 

through the existing wall face may be used. Added soil nails may be considered to carry only the 

dynamic increment in forces because the deformations required to transfer static loads to the 

nails will not necessarily occur. Bearing plates may be used to distribute the nail loads at the 

wall face. The user is referred to Byrne et al. (1996b) for details of soil nails. 

If the increase in lateral thrust and the potential for a sliding failure is a problem, the front of the 

wall may be buttressed, or the backfill may be modified to reduce the driving forces. 

Modification to retained soil may include ground modification such as grouting, partial 

replacement with lightweight fill, or decreasing the slope angle of the backfill surface. 

As discussed in section 2.4.5, the standard static design of MSE walls often leads to insufficient 

development length for the reinforcement in the upper part of the wall when considering seismic 

loading. Retrofit options include tying on to the existing reinforcements at the top of the wall to 

add development length. The splice should be designed to transfer a load equal to the ultimate 

tensile strength of the reinforcement. 

According to Bathurst and Cai (1995), designers of SRWs typically maximize the unreinforced 

height of wall at the crest while maintaining the required static factor of safety. This strategy 

results in unacceptably low margins of safety against toppling at the top of the structure under 

seismic loading conditions. Reinforcement layers with adequate connection capacity must be 

introduced close to the wall crest to minimize the potential for this failure mechanism. 

2.6. SCREENING, SEISMIC EVALUATION AND DESIGN OF SEISMIC RETROFIT 

FOR A RETAINING WALL 

The description and background information for the retaining wall described in this example 

problem was adapted from Example 3 presented in FHWA Geotechnical Engineering Circular 

No. 3, Design Guidance: Geotechnical Earthquake Engineering for Highways, Volume II - 

Design Examples (Kavazanjian et al., 1997). This example problem is presented for illustrative 

purposes only. The data does not apply to any particular location, but are used to illustrate an 

application of the equations and concepts described in this manual. 
68

EXAMPLE PROBLEM 2 - SCREENING, SEISMIC EVALUATION AND DESIGN OF SEISMIC 

RETROFIT FOR A RETAINING WALL 

An existing retaining wall is part of an underpass along a highway near Memphis, Tennessee. The wall 

varies in height from 0.5 m to 7 m along the underpass alignment. To complete the screening, evaluation 

and design of seismic retrofit for the wall, the following tasks need to be performed: 

• It has been decided to evaluate the wall for ground motions for the maximum considered earthquake 

(MCE) which has a seven percent probability of being exceeded in 75 years at this site. Refer to Part 

1 of this manual for a discussion of ground motions to be used for retrofit design. 

• Apply screening criteria and assess the need for seismic evaluation. 

• Check the design of the wall for static loading conditions. 

• Perform a seismic evaluation of the wall. 

• Design and seismic evaluation of retrofit strategy. 

Source Materials Required 

The source materials required to solve this problem include: 

• Seismic Retrofitting Manual for Highway Structures, Parts 1 and 2 (i.e., this manual). 

• Subsurface profile information. 

• As-built details of the retaining wall. 

• Standard Specifications for Highway Bridges (AASHTO, 2002). 

• USGS Probabilistic Earthquake Acceleration and Spectral Acceleration Maps for the United States 

(1996). 

• NEHRP Guidelines for the Seismic Rehabilitation of Buildings, FEMA 273 (BSSC, 1997). 

• Building Code Requirements for Structural Concrete (ACI 318-02) (see ACI, 1995a). 

• Recommendation for Prestressed Rock and Soil Anchors, PTI (1996). 

• FHWA Geotechnical Engineering Circular No. 3, Design Guidance: Geotechnical Earthquake 

Engineering for Highways (Kavazanjian et al., 1997). 

Geologic and Seismic Setting 

The site is situated in the gulf coastal plain section of the coastal plain physiographic province. The region 

is referred to as the Mississippi embayment. The topography of the area is characterized as gentle to 

steep, with occasional discontinuities created by the flat lying alluvial plains of the streams in the area. 

These topographic features have formed as a result of the glacial erosion of the uppermost tertiary and 

quaternary formations and by subsequent deposition of a thick covering of loess deposits during the late 

stages of the pleistocene glaciation. 

Approximately 915 to 1200 m of quaternary, tertiary, and cretaceous age sediments were deposited within 

the Mississippi embayment in the Memphis area. The surface and subsurface geologic units of this area 

consist predominantly of unconsolidated silt, sand, clay, gravel and lignite deposits. 
69

The retaining wall is located within the New Madrid Seismic Zone (NMSZ), the source of three major 

earthquakes and several thousand aftershocks between 1811 and 1814. The NMSZ strikes in the 

northeasterly direction, and extends about 175 km from near Memphis, Tennessee in the south to Cairo, 

Illinois in the north. 

Geotechnical Information 

The site is underlain by the Memphis sand formation, which consists mainly of coarse sand with lenses or 

beds of clay and silt at various horizons. 

Subsurface information at the site was obtained through a series of cone penetration tests (CPTs) and 

borings drilled using rotary wash borings with drilling mud to depths of 60 meters. Standard penetration 

tests (SPTs) were performed at intervals of 1.5 m in the borings. SPT split-spoon samples recovered from 

the borings were visually classified, and index property tests were performed on several samples. The 

normalized and standardized SPT N (blow count) distribution with depth is provided in the following 

subsections. 

Groundwater was not encountered in the test borings. Therefore, the potential for liquefaction is not a 

factor in the seismic vulnerability of the retaining wall. 

Wall Information 

The wall is described as a reinforced concrete cantilever wall. The figure below shows the geometry, 

dimensions, and structural details of the wall. 

0.7 m

No. 6 Bars @ 250 mm c-c

No. 6 Bars @ 300 mm c-c

No. 8 Bars @ 250 mm c-c

No. 6 Bars @ 400 mm c-c

76 mm clear

(typ)

7 m

No. 8 Bars @ 250 mm c-c

4 m

0.7 m

0.4 m

2 m

Standard Hook
70

Step 1: Evaluate Ground Motions at the Site 

• Site location: 35.15o latitude, 89.6o longitude. 

• Maximum considered earthquake has a seven percent probability of exceedance in 75 years. 

• Based on USGS (2002) - see website: http://eqhazmaps.usgs.gov. 

• PGA = 0.31g (this is the PGA in a bedrock outcrop at the site - need to consider site effects). 

• Therefore, according to the screening guide, detailed evaluation is required since the PGA > 0.3g. 
71

0

10

20

30

40

50

60

70

80

90

0 50 100 150 200 250

Initial Shear Modulus (Mpa)

Depth (m)

Step 2: Collect Information Needed for Seismic Evaluation 

1. Site conditions:

• Very deep soil deposit which consists mainly of coarse sand with 

lenses or beds of clay and silt at various horizons. 

• Based on CPT data, the variation of initial shear modulus up to a 

depth of 90 meters is shown in the figure. 

• From this figure, the average initial shear modulus is 175 MPa. 

• Unit weight is 18 KN/ m3

 and mass density is ρ = 1.83 Mg/m3. 

• Average shear wave velocity: 

3 2

s 3

G 175 x 10 KN/m V 309 m/ s

1.83 Mg/m == = ρ . 

• Based on FEMA 273 (1997), site class is Class D (stiff soil with 180 m/s < Vs < 365 m/s or with 15 < 

N ≤ 50 or 50 kPa ≤ Su < 95 kPa). 

• To determine kh for the seismic evaluation of the retaining wall, multiply the peak bedrock 

acceleration by the appropriate site coefficient: 

Fa = site coefficients, 

Ss = mapped short-period acceleration response parameter, 

Ss = 0.60 from USGS (1996) for 35.15o

 latitude and 89.6 longitude (see http://eqhazmaps.usgs.gov), 

Fa = 1.3 from FEMA 273 (1997), w/ Ss ≈ 1.0. 

• Therefore, kh = Fa x PGA = 1.3 x 0.31 ≈ 0.4. 
72

0

5

10

15

20

25

0 10 20 30 40 50

Normalized and Standardized SPT N Values

(Blows/300 mm)

Depth (m)

Design

2. Soil properties:

• Foundation soil 

See SPT data shown in the figure. 

Average N for top 10 m is 12. 

for N = 12: φ ≈ 32°; Dr ≈ 40 percent; and γ = 18 kN/m3

. 

Correlation between N and Φ for sands as described by 

Peck et al., 1974. 

• Wall backfill 

Φ= 35°, 

γ = 18 kN/m3

, 

δw – wall friction = 0° (conservative assumption), 

δb – friction at base = 30° (from AASHTO 5-5-2B). 
73

Step 3: Check Design of Wall for Static Loading Conditions 

 Weight of Wall Arm Moment w.r.t. Toe 

Stem 0.7 x 6.3 x 23.5 kN/m3

= 104 kN/m 

0.7/2 + 0.4 = .75 (m) 104 x .75 = 78 kN x m/m 

Footing 0.7 x 4 x 23.5 = 65.8 kN/m 4/2 = 2 (m) 65.8 x 2 = 132 kN x m/m 

Soil 6.3 x 2.9 x 18.1 

kN/m3

 = 331 kN/m 

2.9/2 + 1.1 = 2.6m 331 x 2.6 = 861 kN x m/m 

 501 kN/m 1071 kN x m/m 

0.7 m

7 m

0.7 m

B=4m

0. 4m

2 m

= 35

= 0

= 18.1 kN/m

= 32

o

o

o

f

3

Evaluate Limit State for Static Loading 

• 2

AS AS S

1 P KH

2 = γ . 

o 2 o

AS

35 K tan 45 0.271

2

⎛ ⎞ = −= ⎜ ⎟

⎝ ⎠

. 

H = 7m. 

• 2

AS

1 Therefore, P (0.271) (18.1) 7 120 kN/m 2 = = . 

W = 501 kN

N = 501 kN

P = 120 kN/m

fN

7/3 = 2.33 m

AS

1071/501 = 2.13 m
74

1. Check sliding resistance:

• For mass concrete on coarse sand, use f = tan 30° = 0.58 (see AASHTO table 5-5-2-B). 

• Fslide = Resisting Force

Driving Force . 

Resisting Force = fN = 0.58 (501 kN) = 291 kN. 

Driving Force = PAS = 120 kN. 

• slide

291 Therefore, F 2.4 1.5 120

= => OK. 

2. Check for overturning:

• MDriving = PAS (h) = 120 kN/m x 2.33m 280 kN x m/m = . 

• MResistance = W x = 501 kN x 2.13m = 1067 kN x m/m. 

• FOverturn = 

1067

280

 = 3.8 > 2.0 OK. 

3. Check eccentricity of result:

• Resistance Driving

v

B M M

e

2 F

− = − . 

Fv = W. 

B = 4m. 

• 4 1067 280 Therefore, e 0.429m 2 501

− =− = ; 

B 4 .67 e

6 6

== > ′ OK. 

4. Check bearing capacity:

• Generalized bearing capacity equations are from Meyerhoff (1953) with C = 0, and shape 

factors = 1. 

• For depth inclination factors, see Meyerhoff (1953) or ASCE (1994). 

• ult qi qd q i d

1 q F F ( D) N F F B N 2 γγ γ = γ+ γ ′ . 

Fqi = inclination factor for surcharge term; 

2

F 1 qi 90

⎛ ⎞ α = − ⎜ ⎟ ⎝ ⎠

1 120 tan 13.5

501

− ⎛ ⎞ α= = ° ⎜ ⎟ ⎝ ⎠ . 

• Therefore, 

2

qi

13.5 F 1 0.72

90

⎛ ⎞ =− = ⎜ ⎟ ⎝ ⎠ . 
75

Fqd = depth factor for surcharge term = p

D 1 0.1 K

B

+ ; 1 + 0.1 tan 32 2 45

2 4

⎛ ⎞ + ⎜ ⎟ ⎝ ⎠ = 1.09. 

2 γ= = = D surcharge 2 x 18.1 36.2 kN/m . 

D = 2 m. 

γ = 18.1kN/m3. 

Nq = surcharge bearing capacity factor for φ = 32o

; Nq = 23.18 (see AASHTO table 4-4-7-1A). 

Fγi

 = inclination factor for soil friction term. 

2 2

i

13.5 F 1 1 0.33

32 γ

⎛ ⎞ α ⎛ ⎞ =− =− = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ φ ⎝ ⎠ . 

Fγd = depth factor for soil friction term = Fqd = 1.09. 

B' = B - 2e = 4m - 2(0.429m) = 3.14m.

Nγ = soil friction bearing capacity factor for φ = 32°; Nγ = 30.22. (see AASHTO table 4-4-7-1A). 

• ult

1 Therefore, q (0.72)(1.09)(36.2) 23.18 (0.33)(1.09)(18.1)(3.14)(30.2) 2

= +

 659 309 968 =+= kN/m2

. 

N W 501kN/m 2 q 159 kN/m B B 3.14 m == = = ′ ′ . 

ult

Bearing

q 968 F 63

q 159

= = => OK. 

Compute Reinforcing Steel Requirements 

1. Find shear and bending moment at base of wall stem:

6.3 m

2.1 m

V

M

max

max

P = p(6.3)1/2 = 98 kN/m

P = K (6.3) = 0.271(18.1)(6.3) = 31 kN/m2

a
76

• M P h 98 (2.1) 206 kN x m/m max == = . 

• M 1.7 M 350 kN x m/m u max = = (from ACI 9-2-4). 

• s y

u sy '

c

0.59 A f

M Af d

f b

⎛ ⎞

=φ − ⎜ ⎟

⎝ ⎠

 (from ACI 10-2). 

Φ = 0.9 (from ACI 9.3), 

fy = 414 MN/m2

, '

c

f = 28 MN/m2, 

b = 1m, 

d = 0.7m - .076m - .0127 = 0.61 (from ACI 7-7-1). 

2. #8 bars at 250 mm c-c:

• 2 22

s

1000 mm/m A 510 mm /#8bar x 2040 mm /m .00204 m /m

250 mm/bar = == . 

• u

0.59 (.00204)(414) M 0.9 (.00204) 414 0.61 28(1)

⎛ ⎞ = − ⎜ ⎟ ⎝ ⎠

 = 0.45 MN/m 

 = > 450 kN x m/m 1.7 Mmax OK. 

• Steel ratio As .00204 0.0033

bd (1)(.61) ρ= = = . 

• min

y

200 200 .0033

f 60,000 ρ= = = OK (see ACI 10-5). 

•

'

c max

y y

f 600 0.85 0.0217

f 600 f

⎛ ⎞

ρ= β = ⎜ ⎟

+ ⎝ ⎠

 OK (see ACI 10-3-3). 

• Requirement for shrinkage and temperature: 

set ρ = .0018 OK (see ACI 2-12). 

3. Horizontal steel:

• #6 bars @ 250 mm c-c each face. 

• 2 22

s

1000 A 2 faces x 284 mm /# 6bar x 2272 mm /m .002272 mm /m

250 = == . 

• For walls, ρmin = .0025 (see ACI 14-3-3, based on gross area of concrete). 

• min

.002272 .0032

0.7 x 1m ρ = => ρ OK. 
77

Check Shear Capacity 

• V 1.7 98 kN/m 167 kN/m u = = ( ) . 

• ( ) '

c c φ =φ v 0.17 f bd (see ACI 11-3). 

• = 0.85 (see ACI 9-3-2-3). 

• φ c v = 0.85 (.17) 28 0.7(1) = 0.535 MN/m 535 kN/m = . 

• c φv 1.7V > OK. 

Heel Design 

• q = q1 + q2 - q3. 

• ( ) 3 2 q H t 18.1 kN/m x (7m 0.7m) 114.0 kN/m 1 =γ − = − = (from soil above the heel). 

• 3 2 q x t 23.5 kN/m x 0.7m 16.45 kN/m 2 c =γ = = (from mass of concrete slab). 

1. Determine bearing pressures at heel and toe of wall foundation:

• toe heel

W 6e q 1 B B

⎛ ⎞ = ± ⎜ ⎟ ⎝ ⎠

( ) 2

toe

501 kN 6 0.429m

1 205.8 kN/m q 4m 4m

⎛ ⎞

=± = = ⎜ ⎟

⎝ ⎠

. 

2 = = 44.7 kN/m qheel . 

e = 0.429 m, 

B = 4m, 

W = 59 kN. 

• 22 2

3

2.9m q 44.7 kN/m 40.275 kN/(m x m) x 103.09 kN/m 2

=+ = . 

• ( ) 22 2 V q x 2.9 m 114.0 kN/m 16.45 kN/m 103.09 kN/m x 2.9 m == + −

= 79.3 kN/m . 

• ( )

2

2 22 2 2.9m M 114.0 kN/m 16.45 kN/m 44.7 kN/m x 40.275 kN/m x m

2

=+− − . 

• x 

3 2.9m

6 =−= 360.6 kN x m/m 163.7 kN x m/m 196.9 kN x m/m . 

• V 1.7V 1.7 79.3 kN/m 134.81 kN/m u == = ( ) . 

• M 1.7M 1.7 196.9 kN x m/m 335 kN/m u == = ( ) . 
78

2. Check for shear:

• ' V 0.17 f bd c c = 2 = 0.17 28 MN/m x 1m x 0.7m 0.629 MN/m = . 

• Assume: b = 1 m; d = 0.7 m. 

• V 0.85 x 629 kN/m 535 kN/m 135 c φ = => . 

• Therefore, section is adequate. 

3. Check flexural reinforcement:

• No. 8 bars at 250 mm c-c. 

• 2 A .00204 m /m s = . 

• .025 0.7m .076m 0.61m

2

α= − − = . 

• s y

u sy '

c

0.59 A f

M A f d x 450 kN/m 335

f b

⎛ ⎞

=φ = > ⎜ ⎟

⎝ ⎠

OK. 

• .0033 ρ = (satisfies ACI 10-5, 10-3-3 and 7-12). 

Toe Design 

• q = -q2 + q3. 

• q2 = γc t = 23.5 kN/m3

 x (0.7 m) = 16.45 kN/m2 (from mass of concrete slab). 

• q3 = soil reaction = 205.8 kN/m2

 - 40.275 2 2 0.4m kN/m x m x 197.7 kN/m

2 = . 

• V = q x 0.4m = ( ) 2 2 − + 16.45 kN/m 197.7 kN/m 0.4m = 72.518 kN/m. 

• Vu = 1.7 ( ) 72.518 kN/m = 123.3 kN/m. 

• ( )

2

2 2 0.4m M 16.45 kN/m 205.8 kN/m 40.275

2

=− + − kN/m2

 x m 

3 (0.4m) 14.72

6 = kN x m/m. 

• Mu = 1.7 (14.72 kN x m/m) = 25.0 kN/ x m/m. 

• Shear is less than that for heel, therefore section is adequate. 

• Moment is less than that for heel, therefore ρ = ρmin. 

• Use #8 bars spaced at 250 mm c-c.
79

Step 4: Summary of Static Design Check 

1. External stability requirements:

• Fslide = 2.4 > 1.5 OK. 

• Foverturn = 3.8 > 2.0 OK. 

• e = 0.429m < B/6 OK. 

• Fbearing = 6 > 3 OK. 

2. Stem:

• Mmax = 206 kN x m/m Vmax = 98 kN/m 

• Mu = 450 kN x m/m φVc = 535 kN/m 

• Mu > 1.7 Mmax OK φVc > 1.7 Vmax OK

3. Heel:

• Mmax = 197 kN x m/m Vmax = 79.3 kN/m 

• Mu = 450 kN x m/m φVc = 535 kN/m 

• Mu > 1.7 Mmax OK φVc > 1.7 Vmax OK

4. Toe:

• Mmax = 14.7 kN x m/m Vmax = 72.5 kN/m 

• Mu = 450 kN x m/m φVc = 535 kN/m 

• Mu > 1.7 Mmax OK φVc > 1.7 Vmax OK

5. Conclusion:

Static design meets existing standards. Since the peak ground motion with a three percent chance of 

being exceeded in 75 years at this site is greater than 0.3 g, perform a seismic evaluation and 

determine the need for seismic retrofit. 
80

Step 5: Seismic Evaluation of Wall 

1. Sliding threshold:

• Try = s

n k 0.34 (with passive restraint). 

• K 35 , 0, i k 0 0.516 @ k 0.34 AE v h ( ) φ= ° δ= β= = = = = (see eq. 2-1). 

• KPE = 2.97 (see eqs. 2-1 and 2-5). 

• Solve for Equil. ΣF = 0. 

• ΣF = 1/2 KAE γH2

 - 1/2 KPE γD2 + Wkh - Wf = 0. 

• Therefore, ΣF = 1

2 (0.516)(18.1) 72

 - 1

2 (2.97) 18.1 (2)2

 + 501 (0.34) - 501 (0.58) = 229 - 108 

+ 170 - 291 = 0. 

• slide

h k 0.34g = OK. 

2. Check sliding threshold with no passive restraint:

• Try s

h k 0.22 = . 

• KAE = 0.41. 

• ΣF = 1

2 (0.41) (18.1) 72

 + 501 (.22) - 501 (0.58) = 182 + 110 - 291 ≈ 0. 

• slide

h k 0.22g = without passive resistance OK. 

3. Check overturn - rotation mode:

• Try OT

h k 0.35 = . 

• h = H/3 for rotation w.r.t. toe. 

• KAE = 0.53. 

• KPE = 3.0. 

• ΣM = 0 = 1

2

 KAE γH2 H

3

 + Wkh Y - 1

2

 KPE γD2 D

3

 - W X (see eqs. 2-8, 2-9, 2-10). 

•

6.3 .7 6.3 104 0.7 65.8 331 0.7

2 22 Y

501

⎛ ⎞ ⎛⎞ ⎛ ⎞ ++ + + ⎜ ⎟ ⎜⎟ ⎜ ⎟ ⎝ ⎠ ⎝⎠ ⎝ ⎠ = = 3.39. 
81

• Therefore, ΣM = 1

2 (0.53) (18.1) 

3 7

3 + 501 (0.35) (3.39) - 1

2 (3.0) 18.1 

3 (2)

3 - 501 (2.14) = 

548.4 + 594.4 - 72.4 - 1072.14 = -1.74 ≈ 0. 

• Therefore, OT

h k 0.35 ≈ . 

4. Compute bearing capacity threshold:

• Assume tilt

h k 0.2g = . 

• KAE = 0.396. 

• ∆K = KAE - KAS = 0.396 - 0.271 = 0.125. 

• KPE = 3.29. 

4(a). Compute shear stress transferred to base of foundation:

• F = 1

2

 KAE γ H2

 + Wkh - 1

2

 KPE γ D2

= 

1

2 (.396) 18.1 (7)2

 + 501 (0.2) - 1

2 (3.29) (18.1) (2)2

 = 175.6 + 100.2 - 119.46 = 156.71. 

•

( )

F 156.71 n 0.501

Nf 501 tan 32° == = (see eq. 2-6). 

• qE

qS

N

0.43

N = (see figure 2-13). 

• Therefore, NqE = 23.18 x 0.43 = 9.97; NqS = 23.18. 

• E

S

N

0.21

N

γ

γ

= (see figure 2-13). 

• Therefore, NγE = 30.2 x 0.21 = 6.35; NγS = 30.2. 

4(b). Compute eccentricity:

• Find h assuming PAS acts at H/3 and Pdyn acts at 0.6H. 

•

( ) ( ) AS

AE

H 7

K K 0.6 H 0.271 .125 .6 7

3 3 h

K .396

⎛ ⎞ + ∆ + ⎜ ⎟ ⎝ ⎠ = = = 2.923. 
82

• ( )( )() ( ) 2 2

o AE h

1 1 M K H h k Wy .396 18.1 7 2.92 2 2 = γ+ = + 0.2 (501) 3.39 

 = 513.3 + 339.7 = 853.0. 

• 2 2

R PE

1 D1 2 M K D Wx (3.29) (18.1) 2 2 32 3

⎛ ⎞ = γ += + ⎜ ⎟ ⎝ ⎠ 501 (2.14) = 79.40 

 + 1071 = 1150.4 (see eq. 2-11). 

• B 4 1150.4 853 ( ) M M R o e 2 0.59 1.41

2 N 2 501

− ⎛ ⎞ − = − = − =− = ⎜ ⎟ ⎝ ⎠ . 

• B′ = B - 2e = 4 - 2 (1.41) = 1.19m. 

• qult = γDNqE + 1⁄2γB’NγE = 18.1(2)9.97 + 1⁄2(18.1)1.19(6.35) = 360.9 + 68.39 = 429.3 kN/m2

. 

• q = 

N

B′

 = 

501 2 421 429 kN/m

1.19 = ≈ . 

• Therefore, tilt

h k 0.2. =

Summary of Threshold Accelerations 

Sliding slide

h k 0.34 

Overturning rotate

h k 0.35 

Bearing Capacity tilt

h k 0.2 

Therefore, tilt rotate slide

hh h kk k < <

• tilt

h k 0.2 = is the critical threshold acceleration. This is considered marginally acceptable since 

tilt

h k + 0.25 = 0.45 ≈ kh (see section 2.4.2.2 (b)). 
83

Evaluate Structural Integrity 

• Check moment at base of stem using A = 0.4g. 

• KAE = 0.581 KPE = 2.82. 

• ∆K = KAE - KAS = 0.581 - 0.271 = 0.31. 

• Find h1 assuming PAS acts at H / 3 and P 1 dyn acts at 0.6H1. 

• H1 = height of stem = 7m - 0.7m = 6.3. 

• AS 1 1 ( ) ( )

AE

K H / 3 K 0.6 H 0.271 6.3 / 3 0.31 (0.6) 6.3 h

K 0.581

+∆ + = = = 3.0 m. 

D1 = 2m - 0.7 = 1.3m. 

KHWsoil = 0.4 ⋅ 18.1 kN/m3

 x 

2.9m x 6.3m = 132 kN/m. 

Arm = 6.3 m/2 – 3.15 m. 

• PAE = 

1

2 γ 2 H K 1 AE = 

1

2 (18.1) (6.3)2

 (0.581) = 209 kN/m. 

• Wstem = γc (d)(H1) = 23.5 x 0.7 x 6.3 = 104 kN/m. 

• PPE = 

1

2 γ 2 D K 1 PE = 

1

2 (18.1) (1.3)2

 (2.8) = 43 kN/m. 

• Mmax = Wstem x kh

6.3

2

⎛ ⎞ ⎜ ⎟ ⎝ ⎠ + PAE (3.0) - PPE (.43) + Wsoil x Kh x 

6.3

2

⎛ ⎞ ⎜ ⎟ ⎝ ⎠ = 1155. 

• Mu = φ AS fy

S y

'

c

0.59 A f

d

f (b)

⎛ ⎞ ⎜ ⎟ −

⎝ ⎠

. 

• Use a load factor of 1.0 for collapse prevention objective. Therefore, check Mmax ≤ Mu. 

φ = 1.0 for earthquake loading and collapse prevention objective, 

fy = 414 MN/m2

, '

c

f = 28 MN/m2, 

d = 0.7m - .076 - .013 = 0.611 m, 

k Wh stem

(H1)/2

PPE

1/3D1

MMax

h W stem 1

V

k Wh soil

PAE
84

b = 1 m, 

AS = 20.4 cm2

/m - .00206 m2/m. 

• Mu = (1.0) (.00206) (414) ( )

( )

.59 .00206 414

.611

28 1m

⎛ ⎞ ⎜ ⎟ −

⎝ ⎠

= 0.853 (.588) = 0.501 MN x m/m = 500 

kN – m/m. 

• Mmax > Mu Not Good. 

1. Structural integrity of heel:

• Use eccentricity and bearing pressure at the bearing capacity threshold acceleration, tilt

h k . 

• q = q1 + q2 - q3. 

• q1 = 114.0 kN/m2 (from soil above heel). 

• q2 = γc x t = 23.5 kN/m3 x 0.7m = 16.45 kN/m2 (from mass of concrete slab). 

• q1 + q2 = 130.45 kN/m2. 

• Determine bearing pressures at heel and toe of wall foundation. 

• toe

heel

q = 

W 6e 1

B B

⎛ ⎞ ± ⎜ ⎟ ⎝ ⎠ . 

e = 1.4, 

B = 4 m, 

W = 501 kN, 

6e = 8.4. 

• 6e > B, therefore, use eq. 2-16. 

• max

4N

q 3L(B 2e) = − . 

N = 501 kN, 

L = 1 m, 

B = 4 m, 

e = 1.4 m. 

4(501 KN) 2 557 k

3(1m)(4m 2(1.4m)) = = N/m − (at toe). 

• x 1.5 (B 2e) 1.5 (4m 2 (1.4m)) 1.8m = −= − = (from toe towards heel; see eq. 2-17). 
85

Distribution under heel is then: 

557 2

2 1 309.4 kN k x

1.8m m xm

N/m = . 

Pressure at edge of heel is then: 

309.4 2 2 kN/m x m x 0.7m 216.6 k = N/m . 

Shear due to bearing pressure at heel is then: 

2 0.7m 216.6 k x 75.8 k

2

N/m N/m = . 

• 2 V 130.45 k x 2.9m 75.8 k 302.5 k = −= N/m N/m N/m. 

• ( )2

2 2.9m 0.7m M 130.45 k x 75.8 k x 530.9 k

2 3 = −= N/m N/m Nx m/m . 

Check for Shear 

• c

2 V 0.17 28 M x 1m x 0.7m = N/m = 0.629 MN/m = 629 kN/m > 302.5 kN/m. 

• Therefore, the section is OK for shear. 

Check Flexural Reinforcement 

• AS = 0.00206 m2. 

• d = 0.7m – 0.076 – 0.013m = 0.611m. 

• S y

u Sy '

c

0.59 A f

M Af d

f b

⎛ ⎞ = − ⎜ ⎟

⎝ ⎠

 = 0.00206m2 x 414 MN/m2

2 2

2

0.59(0.00206m ) x 414 MN/m 0.611m

28 MN/m x 1m

⎛ ⎞ ⎜ ⎟ −

⎝ ⎠

= 505.7 kN x m/m < M = 530.9 kN x m/m. 

• Therefore, the steel is not adequate. 

2. Structural integrity of toe:

• q = -q2 + q3. 

• q2 = γc x t = 23.5 kN/m2 (0.7m) = 16.45 kN/m2. 

0.4 m 0.7 m

0.7 m

4 m
86

• Soil bearing reaction: qmax = 557 kN/m2

qmin = 557 kN/m2

 - 0.4m x 216.6 kN/m2m = 470.4 kN/m2. 

• q = -16.45 kN/m2 + 470.4 kN/m2 + 216.6 kN/m2m x 

X

2 . 

• V = 453.91 kN/m2 x +216.6 kN/m2m x 

2 x

2 (x = 0.4 m) 

= 181.56 kN/m + 17.33 kN/m = 198.9 kN/m. 

•

2 2

2 x x2 2 M 453.91 k x 216.6 kN/m m x x X

2 23

= + N/m

=+ = 36.3 kN x m/m 4.62 kN x m /m 40.92 kN x m/m . 

The shear resistance from the concrete section is the same as for the heel: 

• 629 kN/m > 199 kN/m. 

• Therefore, the section is adequate. 

The moment resistance from the toe is the same as for the heel (same steel): 

• 505.7 kN x m/m > 40.9 kN x m/m. 

Therefore, the steel is adequate. 
87

Step 6: Summary of Seismic Evaluation 

1. Using kh = 0.4, all computed safety factors for external stability are less than one. Therefore, the wall 

will yield during the MCE. 

2. The critical threshold acceleration is 0.2 g and the associated mode of failure is loss of bearing 

capacity and tilting of the wall. Large rotation (tilting) of the wall may result from the MCE, but the wall 

is not likely to collapse from overturning. 

3. The moment capacity of the wall stem and heel is not adequate to resist the loads from the MCE. 

Therefore, seismic retrofit is required. The retrofit strategy needs to address the structural integrity of the 

wall stem and heel. 
88

Step 7: Design Seismic Evaluation of Retrofit Strategy 

Two retrofit strategies are: 

• Increase moment resistance of stem and/or heel; or, 

• Decrease moment in stem and/or heel. 

It will be difficult to increase the moment resistance at the heel of the wall, since it is buried and access is 

difficult. Decreasing the maximum moment in the stem and heel is a more readily obtainable objective. 

Placing a tie-back through the wall stem will serve to reduce moments in both the stem and heel. 

The following calculations describe design of the tie-back retrofit strategy. The MCE is considered with a 

corresponding peak ground acceleration at the site of 0.4 g. First, the tie rod force required for equilibrium 

is computed and then external stability checks (including sliding and bearing capacity) are pursued. 

Moments in the wall stem and heel are checked and, finally, design calculations in support of anchor 

system details are presented. Anchor system details include the anchor spacing, required total length of 

the anchor, the length of the bonded zone of the anchor, and transfer of the anchor loads to the wall face. 
89

1. Add tie-back – will reduce moment in stem and heel of wall: 

1.25 m

15o

 

5.75 m

y

PPE D/3

0 S

(1) B/2 - e N

x

0.4 m

W

h

PAE

F tie

E.Q. cos 15o

k Wh

F tie

E.Q. o sin 15

Note: Use e computed for static loading. Consider E.Q. Ftie to balance overturning moment from dynamic increment. 

• Sum moments about pt. 0 and solve for Ftie. 

• Sum forces in the horizontal direction and solve for F. 

• Check to see if F ≈ N tan δ: 

W = 501 kN, 

N = W = 501 kN, 

⎯x = 2.13m, 

⎯y = 3.39m, 

B 4 e 0.429 1.57m

2 2 −= − = , 

kh = 0.4g, 

KAE = 0.581, 

∆K = 0.31, 

KAS = 0.271, 

KPE = 2.82. 

• h = 

7

AS

AE

H 7

K K(0.6) H 0.271 .31 x (0.6)

3 3 3.33m

K 0.581

⎛ ⎞ + ∆ ⎜ ⎟ + ⎝ ⎠ = = . 
90

2. Sum moments w.r.t. 0 and solve for 

E.Q. Ftie :

Force Arm Moment 

1. E.Q. F cos 15 tie ° 5.75m + E.Q. F (5.75)(.966) tie

2. W = 501 kN/m ⎯x = 2.13 m + 1067 kN – m/m 

3. PPE = 

1

2 γD2

 KPE = 102 kN/m D

3

 = 

2

3 (2) = 1.33 m + 136 kN x m/m 

4. PAE = 

1

2 γ H2

 KAE = 258 kN/m h = 3.33 m - 859 kN x m/m 

5. khW = 0.4 (501) = 200 kN/m ⎯y = 3.39 m - 679 kN x m/m 

6. N = 501 kN/m B

2

 - e = 1.57 m - 787 kN x m/m 

7. E.Q. F sin 15 tie ° 0.4m + E.Q. F (.4)(.26) tie

• ΣMo = 0 = 5.66 E.Q. F - 1122. tie

• Therefore, E.Q. F = tie

1122

5.66

 = 198 kN/m. 

• Solve for F. 

• ΣFH = 0 = -PAE - kh W + PPE + S + E.Q. Ftie cos 15°. 

• Therefore, F = -191 + 258 + 200 - 102 = 165 kN/m. 

• Check Fmax = N(f) = 501 x 0.58 = 291 kN/m. 

• F max > F is OK. 

3. Check bearing capacity with 

E.Q. Ftie :

• kh = 0.4. 

• F = 165 kN/m. 

• e = 0.429m. 

• B' = 4-2(.429) = 3.14m. 

• N = 501 kN + 195 sin 15o

 = 551 kN. 

• Therefore, n = F 165 0.479

N tan 551 tan 32 = = φ . 
91

• qe

qs

N

0.33

N = ; Nqe = 23.18 x 0.33 = 7.65. 

• E

S

N

0.15

N

γ

γ

= ; NγE = 30.22 x 0.15 = 4.53. 

• qult = γD NqE + 

1

2 (γ) B' NγE = 18.1 (2) 7.65 + 12 (18.1) (3.14) 4.53 = 405 MN/m2

. 

• N 551 q 175 B' 3.14 == = kN/m2 . 

• Therefore, B.C.

S

405 F 2.3

175 = = . 

4. Check moment in wall stem with 

E.Q. Ftie :

cos 15° 

198 cos 15° = 191 kN. 

W = kh γc tstem + AE

stem

P

H

 + kh γsoil Lheel 

 = 0.4 (23.5) 0.7 + 209

6.3 + 0.4 (18.1) 2.9 = 61 kN/m2

. 

• Mmin = -248 kN x m/m places back row of reinforcing steel in tension. 

• Mu = 500 kN x m/m. 

6.3 m

1.25 m

M

V

F

kN/m2 W

o

o

tie

E.Q.

1.25 m 1.88 m

-76.25 kN/m 114 kN/m

-47 kN x m/m

59.5 kN - m/m

KN - m/m

-194 kN/m

-248

-+ -+

Shear Diagram Moment Diagram

3.17 m
92

• Mu > 248 OK. 

• Mmax = 65 kN/m (65 kN/m is placing tension on outside face of wall). 

• On outside face, #6 bars are spaced 300 mm c-c. 

• Cross sectional area of #6 bar = 284 mm2

. 

• AS = 284 

2 mm

300mm

 = 0.9466 mm2

/mm = .00095 m2/m. 

• Mu = φ AS fy

S y

'

c

0.59 A f

d

f (b)

⎛ ⎞ ⎜ ⎟ −

⎝ ⎠

 d = .7 - .076 - .0095 = 0.623 m 

= 1.0 (.00095) (414) .59 (.00095) 414 0.611

28 (1m)

⎛ ⎞ ⎜ ⎟ −

⎝ ⎠

 = 0.393 (0.603) 

= 0.237 MN x m/m = 237 kN x m/m. 

• Mu > 65 kN/m OK. 

5. Check Vmax (at 2 = 1.25 m):

Vmax = E.Q. Ftie cos 15o

 - 1.25 (60) = 191 - 75 = 116 

kN/m. 

' V 0.17 f bd 0.17 28 (1)(.7) c c = = = 629 kN/m. 

 Vc > Vmax OK. 

6. Check structural integrity of heel after retrofit:

• q = q1 + q2 - q3. 

• q1 = 114.0 kN/m2

 (from soil above heel). 

• q2 = γc x t = 23.5 kN/m3

 x 0.7 m = 16.45 kN/m2 (from mass of concrete slab). 

• q1 + q2 = 130.45 kN/m2

. 

• Determine bearing pressures at heel and toe of wall foundation. 

• v toe

heel

F 6e q 1 B B

⎛ ⎞ = ± ⎜ ⎟ ⎝ ⎠

551 kN 6 (0.429m) 1

4m 4m

⎛ ⎞ = ± ⎜ ⎟ ⎝ ⎠ = 225.46 kN/m (at toe), 49.1 kN/m (at heel). 

e = 0.429 m, 

B = 4 m, 

W = 501 kN, 

1.25 m

F cos15

V

M

60 kN/m2

tie

max

o
93

Fv = W + eq

tie F sin 15° = 551 kN, 

6e = 2.574 m. 

• 6e < B (equation 2-15) OK. 

• Pressure distribution will then be as follows: 

0.4 m 0.7 m 2.9 m

49.1 kN/m

225.5 kN/m

• This pressure distribution is practically the same as in the static case. Therefore, the steel in the heel 

and toe will be adequate for the retrofitted dynamic loading case. 

• Geometry of grouted anchor. 1.25 m

15

L = 8.2 m free

Lbond

AE = 40o

o

φ = 35°, 

kh = 0.4, 

KAE = 0.581, 

ρAE = 40°, 

i = β = kv = δ = 0. 

• Find Lbond and required anchor size. 

• Space anchors at 5m c-c. 

• Fanchor = 195 kN/m x 5m = 975 kN. 

• According to PTI (1995) guidelines, fall = 0.6 Fu. (AASHTO, 2002, Section 7, Division 1A, increases 

by 1.5 for earthquake loading). 

• Therefore, Fu = 

975 1083 kN

0.6 x 1.5 = . 
94

• Use Dywidag grade 160 36mm diameter prestressing steel bars, Fu = 1125 kN. 

• Find anchor

b

d w

F L = π τ . 

d = diameter of the drill hole - use 100 mm, 

τw = working bond stress along the interface between soil and grout. 

• PTI (1996): for pressure grouted anchor in medium coarse sand - medium density average ultimate 

soil/grout bond stress is ≈ 0.66 Mpa. 

• Use a factor of safety = 2.0 (for proof testing). 

• τw = 

0.66

2 = 0.33 Mpa. 

• b

975 kN x 1000 L 9.4m

(100mm) .33MPa = = π . 

• Ltotal = Lfree + Lb = 8.2 + 9.4 = 17.6m. 

7. Check wall structural integrity (in long dimension):

1 2

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

- -

-

-

-

- -

-

- -

-

-

-

-

- -

-

- -

2.5 m

2.5 m 2.5 m 5.0 m

0.20 m Strip

W

975 kN 975 kN

Assumed

Failure

Plane

0.7 m

bo

• Assume the line load, w, acts uniformly across this strip of the wall 

kN kN 975 975 w 195 k

2.5m 5.0m 2.5m

N/m + = = + + . 

• Maximum shear will occur at tie locations. 

• V = 195 kN/m x 2.5m = 488 kN. 

•

2

max

2.5 m M 195 kN x 609

2 = = kN x m. 
95

8. Check one-way shear:

• '

c c v 0.17 f = x b x d (see ACI 11-3). 

'

c

f = 28 MN/m2, 

b = 2.5 m, 

d = 0.7 m. 

• Therefore c v 0.17 28 = (2.5)(.7) = 1.57 MN = 1570 kN > 488 kN OK. 

9. Check two-way shear:

• '

c co v 0.34 f b d = (see ACI 11-37).

• Plate dimensions are 130 mm x 240 mm x 45 mm. 

• bo = (.13m + 0.7m) 2 + (.24 + .7m) 2 = 3.54 m (see ACI 11-12-13). 

• d = 0.7m. 

• vc = 0.34 28 3.54 x .7 = 4.46 MN = 4460 kN > 975 kN. 

10. Check bearing stress on plate:

• Plate hole ≈ 38 mm diameter. 

• Aplate = .13m x .24m - π

2 (.038)

4

 = .03m2

 = .85 '

c f A1 (2) = .85 (28 MPa) .03 m2

 (2) = 1.428 MN > 

0.975 MN (see ACI 10-17, Design Bearing Strength). 

11. Compute moment capacity of 2.5m strip of wall:

• S y

u Sy '

c

0.59A f

M Af d

f b

⎛ ⎞ = − ⎜ ⎟

⎝ ⎠

. 

• #6 bars @ 250mm; area of #6 = 284 mm2

. 

• 2 22

S

2500mm A 284 mm x 2840mm .00284m

250mm = == . 

• fy = 414 MN/m2

; b = 2.5m. 

• '

c

f 28 = MN/m2, d = 0.7m - .076m - .025 = 0.6m. 

• u

0.59(.00284) 414 M .00284 (414) .6 28(2.5)

⎡ ⎤ = − ⎢ ⎥ ⎣ ⎦

 = 0.693 MN x m = 693 kN x m > 609 kN/m OK. 
 
97

CHAPTER 3: SLOPES, EMBANKMENTS, AND ROCKFALLS 

3.1. INTRODUCTION 

Earthquake-induced landslides and instability of slopes and embankments have caused extensive 

damage to highway systems in past earthquakes. This damage has resulted in deaths and 

significant monetary losses. Earthquake-induced landslides can block or undermine roads, 

impact and bury vehicles, and seriously inhibit post-earthquake relief efforts. For example, the 

January 17, 1994 Northridge, California earthquake triggered more than 11,000 landslides (Harp 

and Jibson, 1995), many of which affected the local highway systems. Rockfalls inundated 

roadways and landslides, slumps, and blockslides cut off access to many mountain areas for 

several days following the earthquake. 

This section describes procedures for classifying, screening, and evaluating the performance of 

embankments and slopes that support or are adjacent to highway structures during earthquake 

loading (figure 3-1). It also describes retrofitting strategies and methods to repair or mitigate the 

effects of earthquake shaking. 

The effects of earthquakes on highway systems include the following phenomena: 

• Liquefaction and lateral spreading of subgrade soils beneath a natural slope or a highway 

embankment that may lead to slope failure. 

• Permanent deformations of man-made embankments/natural slopes supporting or adjacent to 

highway structures that may lead to cracking or failure of roadway pavements. 

• Reactivation of old, existing landslides due to earthquake shaking. 

• Earthquake-induced rockfalls on nearby slopes that may block or disrupt roadway traffic. 

3.2. CLASSIFICATION 

For the purposes of screening and evaluating the potential for hazards to highway structures from 

seismically induced slope instability, landslides, and rockfalls, it is useful to classify and 

characterize these features based on observed performance and experience during past 

earthquakes. Keefer (1984) and Keefer and Wilson (1989) have examined earthquake-induced 

landsliding and slope failures from more than 40 case histories and classified them into 14 types 

on the basis of topography, material type, and velocity of movement. They further subdivided 

these landslide types into three categories, as shown in table 3-1. 
98

Figure 3-1. Flowchart for screening, evaluating, and retrofitting embankments 

and slopes adjacent to highway structures. 
99

Table 3-1. Characteristics of earthquake-induced landslides. 

Type of Movement Internal 

Disruption1

Water 

Content2

Velocity3

 Depth4

Category I

(failure mechanism) 

Falls, disrupted slides, and avalanches: highly to very highly 

disrupted internally, fast-moving, generally shallow, dislodged 

from steep slopes 

Rock Falls 

(bounding, rolling, free falling) 

High or very 

high 

D-W Extremely rapid Shallow 

Rock Slides 

(translational sliding on basal shear 

surface) 

High D-W Rapid to extremely 

rapid 

Shallow 

Rock Avalanche 

(complex, involving sliding and/or flow as 

stream of rock fragments) 

Very high D-W Extremely rapid Deep 

Soil Falls 

(bouncing, rolling, free falling) 

High D-W Extremely rapid Shallow 

Soil Slides 

(translational sliding on basal shear 

surface or zone of weakened, sensitive 

clay) 

High D-W Moderate to rapid Shallow 

Soil Avalanches 

(translational sliding; subsidiary flow) 

Very high D-W Very rapid to 

extremely rapid 

Shallow 

Category II

(failure mechanism) 

Slumps, block slides, and slow earth flows: relatively coherent 

slides, slower moving than Category I landslides, generally 

deep-seated, dislodged from moderate to steep slopes 

Rock slumps 

(sliding on basal shear surface: 

component of headward rotation) 

Slight to 

moderate 

M-W Slow to rapid Deep 

Rock Block Slides 

(translational sliding on basal shear 

surface) 

Slight to 

moderate 

M-W Slow to rapid Deep 

Soil Slumps 

(sliding on basal shear surface; 

component of headward rotation) 

Slight or 

moderate 

D-W Slow to rapid Deep 

Soil Block Slides 

(translational sliding on basal shear 

surface) 

Slight or 

moderate 

D-W Slow to very rapid Deep 

Slow Earth Flows 

(translational sliding on basal shear 

surface; minor internal flow) 

Slight W-VW Very slow to 

moderate with 

very rapid surges 

Variable 

(Continued) 
100

Table 3-1. Characteristics of earthquake-induced landslides (continued). 

Type of Movement Internal 

Disruption1

Water 

Content2

Velocity3 Depth4

Category III 

(failure mechanism)

Lateral spread and flows: landslides involving significant 

component of fluid flow, fast-moving, dislodged from gentle to 

moderately steep slopes 

Soil Lateral Spreads 

(translational on basal zone of liquefied 

gravel, sand, silt, or weakened sensitive 

clay) 

Generally 

moderate 

occasionally 

slight or high 

W Very rapid Variable 

Rapid Soil Flows 

(flow) 

Very high D-W Very rapid to 

extremely rapid 

Shallow 

Subaqueous Landslide 

(translational on basal zone of liquefied 

gravel, sand, silt, or weakened, sensitive, 

clay) 

Generally high 

or very high; 

occasionally 

moderate 

W-VW Rapid to extremely 

rapid 

Shallow 

Notes: 

1. Internal Disruption: Slight, landslide consisting of one or a few coherent blocks; moderate, landslide consisting of 

several coherent blocks; high, landslide consisting of numerous small blocks and individual soil grains and rock 

fragments; very high, landslide almost completely disaggregate into individual soil grains or small rock fragments. 

2. Water Content: D=Dry, no visible moisture; M=moist, some water but no free water and may behave as a plastic 

solid but not a liquid; W=wet, contains enough water to act in part as a liquid, has water flowing from it, or supports 

significant bodies of standing water; VW=very wet, contains enough water to flow as a liquid under low gradients 

(terms from Varnes, 1978). 

3. Velocity: Extremely slow, less than 0.6 m/yr; very slow, between 0.6 and 1.5 m/yr; slow, between 1.5 m/yr and 

1.5 m/mo; moderate, between 1.5 m/mo and 1.5 m/d; rapid, between 1.5 m/d and 0.4 m/min; very rapid, between 

0.3 m/min and 3 m/s; extremely rapid, more than 3 m/s (terms from Varnes, 1978). 

4. Depth: Shallow, generally less than 3 m; deep, generally more than 3 m. 

after Keefer, 1984, and Keefer and Wilson, 1989 

Category I Landslides include rock and soil falls, toppling failures, slides, and avalanches and 

are generally the most widespread. These are characterized by highly disrupted masses and 

generally shallow failure surfaces and are fast moving and dislodged from steep slopes. 

Rockfalls and rock slides (figure 3-2) are either boulders or disrupted masses of rock that 

descend down the slope by bounding, rolling, or free fall. Rock properties associated with these 

failures are: strength of cementation, degree of weathering, and fracture spacing. An example of 

rockfalls along the Pacific Coast Highway, California, caused by the 1973 Point Mugu 

earthquake is shown in figure 3-3. Rock avalanches are associated with features such as: 

closely spaced fractures, moderate or intense weathering, planes of weakness, weak cementation, 

and evidence of previous failures. Rock falls are the most abundant landslides and the third 

leading cause of landslide-related deaths in historical earthquakes. 
101

Hansen and Franks, 1991

Figure 3-2. Rock fall mechanism and resulting hazard. 

 Wilson and Keefer, 1985 

Figure 3-3. Rock falls along the Pacific Coast highway caused by 

the 1973 Point Mugu earthquake. 
102

Toppling failures occur when the center of gravity of a rock mass extends beyond its base and 

causes it to topple over (figure 3-4). Toppling most commonly occurs in columnar rock masses 

in which the fractures dip steeply into the face of the slope. Columnar basalts and rocks with 

well-developed bedding or foliation planes are typically susceptible to this mode of failure. 

Flexural toppling in hard rock slopes 

with well developed steeply dipping 

discontinuities.

Block-flexure toppling characterized 

by pseudo-continuous flexure of long 

columns by accumulated motions 

along numerous cross joints.

 Hoek and Bray, 1981 

Figure 3-4. Examples of toppling failures. 

Soil slides and soil avalanches are highly disrupted masses that occur in silty or sandy natural 

soils and poorly compacted fills of low plasticity, or in lightly cemented, weathered, and highly 

fractured soft rock on generally steep slopes. Examples of this type of landslide are shown in 

figure 3-5. Hundreds of similar landslides in loose silty and sandy soils were triggered by the 

1971 San Fernando earthquake.

Category II Landslides include rock and soil slumps, block slides, and slow earth flows. These 

are coherent sliding masses that move on bounding basal shear surfaces (figure 3-6). They are 

slow moving and located on generally deep-seated failure surfaces, occurring mainly on 

relatively steep slopes. An example of a large block slide in Anchorage, Alaska that occurred 

during the 1964 earthquake is shown in figure 3-7. 

Soil block slides consist of one or a few coherent blocks that slide in a translational manner, 

exhibiting little or no rotation. Most have grabens at their heads and pressure ridges at their toes. 

Similar landslides, in somewhat different geologic environments, have been triggered by several 

southern California earthquakes, including the 1940 Imperial Valley, the 1952 Kern County, the 

1966 Parkfield, and the 1971 San Fernando. 

Rock slumps and rock slides (see figure 3-8) are most often associated with weakly cemented 

sedimentary rocks or involve indurated rocks that are intensely weathered, closely fractured, 

weak, and interbedded with soft material. Many move on a weak bedding plane. 
103

Wilson and Keefer, 1985; photograph taken from Harp et al., 1981 

Figure 3-5. Aerial view of coalescing disrupted soil slides caused by the 

1976 Guatemala earthquake. Slides stripped away vegetation and sheets of 

sandy residual soil, generally less than 0.6 m thick, exposing white pumice 

bedrock. Slopes in the foreground are approximately 30 m high. 

Hansen and Franks, 1991 

Figure 3-6. Examples of landslides with discrete basal shear surfaces. 
104

Wilson and Keefer, 1985; courtesy of the U.S. Army 

Figure 3-7. Aerial view of the Native Hospital slide, a large soil block 

slide in Anchorage, Alaska, caused by the 1964 earthquake. 

Firm Bedded Rock

Soft Erodible Rock

Source Area

Main Track

Depositional 

Area

Hansen and Franks, 1991 Hansen and Franks, 1991 

Figure 3-8. Rock slump failure 

mechanism. 

 Figure 3-9. Soil slump failure mechanism. 
105

Soil slumps, soil block slides, and slow soil flows (figure 3-9) are deep-seated rotational failures 

that occur in natural deposits in alluvial or coastal flood plains. They occur along locally steep 

free faces such as stream and canal banks. They also occur in gentle to moderately steep 

hillslopes with shallow or perched water tables. 

The most common material involved in earthquake-induced soil slumps is man-made fill (Keefer 

and Wilson, 1989). Most fills that fail are loose and poorly compacted or are placed on soft 

foundations such as river channel or marsh deposits. The density and quality of compaction and 

the foundation conditions are probably more important than the composition of the fill in 

determining its susceptibility to failure. 

Category III Landslides include soil lateral spreads (figure 3-10) and rapid soil flows. These 

landslides include a significant component of fluid flow, are fast moving, and usually occur on 

gentle to moderately steep slopes. They are typically initiated as a result of soil liquefaction 

caused by earthquake-induced buildup of pore pressure in saturated cohesionless deposits, loss 

of strength in sensitive clays, and poorly constructed man-made fills. These types of failures are 

addressed in detail in Part 1 of this manual. 

Firm Clay

Soft Clay with 

Water-Bearing Silt Bedrock and Sand Layers

Hansen and Franks, 1991 

Figure 3-10. Lateral spread failure mechanism. 

According to the results of the study by Wilson and Keefer (1985), materials that are most 

susceptible to earthquake-induced landslides and the predominant types of landslides in each 

material are as follows: 

• Weakly cemented, weathered, or intensely fractured rocks: these are susceptible to rockfalls, 

slides, avalanches, slumps, and block slides. 

• More indurated rocks where predominant discontinuities dip out of slopes: these materials 

are susceptible to rockfalls and slides, block slides, avalanches, and possibly slumps. 

• Loose unsaturated sands: these are susceptible to disrupted soil slides and soil avalanches. 

• Loose, partly to completely saturated sand, silt, or loess: these are susceptible to soil slumps, 

block slides, lateral spreads, subaqueous landslides, and rapid soil flows. 

• Saturated soils containing sand and gravel layers alternating with sensitive clay: these are 

susceptible to disrupted soil slides, soil avalanches, and rapid soil flows. 
106

• Granular soils that are slightly cemented or contain a clay binder: these are susceptible to 

soil falls. 

• Uncompacted or poorly compacted man-made fills containing little or no clay: these are 

susceptible to soil slumps, block slides, lateral spreads, and rapid soil flows. 

3.3. SCREENING PROCEDURES 

The potential for landsliding or downslope movement in slopes and embankments is dependent 

on slope geometry (i.e., slope height and steepness); subsurface soil, rock, and groundwater 

conditions; past embankment or slope performance; and level and duration of earthquake ground 

shaking. The procedures for screening involve reviewing geologic and topographic maps, 

reviewing available data on the subsurface conditions, and performing a reconnaissance of the 

site and adjacent areas. A review of available aerial photographs is desirable. In some areas, 

governmental agencies have prepared slope stability maps showing existing landslides and/or 

areas of relative slope instability; these should be reviewed if available. If appropriate, 

geologists and engineers in government agencies knowledgeable in the performance of natural 

slopes in the area should be contacted. 

The following general guidelines may be used as screens to delineate highway segments 

susceptible to seismically induced ground instability. More detailed guidance for delineating 

areas susceptible to slope instability is given in the Transportation Research Board (TRB) 

Special Report 247, Landslides Investigation and Mitigation, edited by Turner and Schuster 

(1996). 

3.3.1. PRELIMINARY SCREENING PROCEDURES 

It can be assumed that a significant hazard due to earthquake-induced landsliding does not exist 

at a particular site if all of the following criteria are satisfied: 

• The site is not located on, above, or below a slope that displays cracking or other signs of 

actual or incipient slope movement. There is not an obvious hazard to the site from falling 

rocks or shallow soil flows on slopes located above the site. 

• The site is not located within a preexisting active or ancient landslide, and there are no 

landslides on slopes of similar geometry and geology in the site vicinity. 

• The site is not located on or adjacent to a slope with geometric, geologic, and groundwater 

conditions known to be susceptible to landslides. This criterion should be evaluated based 

on both local experience and worldwide observations of conditions known to be especially 

susceptible to earthquake-induced landslides. Based on a United States Geological Survey 

(USGS) review of case histories of earthquake-induced landslides in the Los Angeles region, 

Wilson and Keefer (1985) compiled a profile of the general types of geologic environments 

and characteristics most likely to produce landslides during future earthquakes. These 
107

characteristics are shown in table 3-2 and may generally be applied to other regions with 

similar seismic and geologic environments. 

• The site is not located in a zone that has been mapped as having a moderate or high landslide 

potential (seismic or static). This criterion utilizes regional maps of observed or postulated 

landslides that are triggered under static and/or seismic conditions. Seismic slope stability 

maps based on stability analyses and past seismic performance are available for several areas 

of the country including: San Francisco Bay Area, California (Wieczorek et al., 1985 and 

Manson et al., 1990); Los Angeles area, California (Jibson and others, 1998; Harp and 

Jibson, 1995; and Wilson and Keefer, 1985); urban corridor of Utah (Keaton et al., 1987a 

and Keaton et al., 1987b); and others. Currently, the California Geological Survey (formerly 

the California Division of Mines and Geology) is developing seismic slope stability maps 

that can be accessed by computer on the Internet at www.consrv.ca.gov. Other static and 

seismic landslide hazard maps may also be used for screening purposes. 

• The site is not located on embankments constructed of poorly compacted soils that exhibit 

signs of settlement and cracking, or on embankments underlain by poor foundation soils. 

• The site is not located on potentially liquefiable soils or sensitive clays that could lose 

significant strength during earthquake shaking. 

• The site does not show surface manifestations of the presence of subsurface water (springs 

and seeps), or potential pathways or sources of concentrated water infiltration on or upslope 

of the site. 

• Judgments from experts familiar with local conditions conclude that an earthquake-induced 

landsliding hazard is unlikely to exist at the site. 

If preliminary screening procedures listed above indicate a potential for landsliding or slope 

instability at a particular site, then, depending on the importance of the slope and the 

consequences of failure, an evaluation of its seismic stability should be performed using 

procedures that are described in section 3.4. 

3.3.2. SUPPLEMENTAL SCREENING CRITERIA FOR ROCKFALLS 

In addition to the screening criteria provided above, alternate procedures may be used to screen 

sites for susceptibility to rockfalls. Harp and Noble (1993) developed a rock classification 

system to evaluate the susceptibility of rockfalls to seismic loading. They modified an 

engineering classification originally used in tunnel design, known as the rock mass quality 

designation (Q), for use in rating the susceptibility of rock slopes to seismically induced failure. 

Based on analysis of Q-value and rockfall concentrations during the 1980 earthquake sequence 

near Mammoth Lakes, California, they defined a “well-constrained” upperbound relationship 

that shows that the number of rockfalls for a site decreases rapidly with increasing Q. Using a 

probability density function, they modeled the decay of number of rockfalls per site versus Q. 
108

Table 3-2. Geologic environments likely to produce earthquake-induced landslides 

 in the Los Angeles region. 

Landslide 

Type 

Type of 

Material 

Minimum 

Slope 

Inclination in 

Degrees 

Remarks 

Rock Falls 

Rocks weakly cemented, intensely 

fractured, or weathered; contain 

conspicuous planes of weakness 

dipping out of slope or contain 

boulders in a weak matrix. 

40 

Particularly common near ridge 

crests and on spurs, ledges, 

artificially cut slopes, and slopes 

undercut by active erosion. 

Rock Slides (See description above). 35 

Occasionally reactivate 

preexisting rock slide deposits. 

Particularly common in hillside 

flutes and channels, on artificially 

cut slopes, and on slopes 

undercut by active erosion. 

Rock 

Avalanches 

Rocks intensely fractured and 

exhibiting one of the following 

properties: significant weathering, 

planes of weakness dipping out of 

slope, weak cementation, or evidence 

of previous landsliding. 

25 

Restricted to slopes of >150 m 

relief that are undercut by active 

erosion. 

Rock Slumps 

Intensely fractured rocks, preexisting 

rock slump deposits, shale, and other 

rocks containing layers of weakly 

cemented or intensely weathered 

material. 

15 

Rock Block 

Slides 

Rocks having conspicuous bedding 

planes or similar planes of weakness 

dipping out of slopes. 

15 

Soil Falls Granular soils that are slightly 

cemented or contain clay binder. 40 

Particularly common on stream 

banks, terrace faces, coastal 

bluffs, and artificially cut slopes. 

Disrupted Soil 

Slides Loose, unsaturated sands. 15 

Soil 

Avalanches (See description above). 25 

Occasionally reactivate 

preexisting soil avalanche 

deposits. 

Soil Slumps 

Loose, partly to completely saturated 

sand or silt; uncompacted or poorly 

compacted man-made fill composed of 

sand, silt, or clay; preexisting soil 

slump deposits. 

10 

Particular common embankments 

built on soft, saturated foundation 

materials, in hillside cut-and-fill 

areas, and on river and coastal 

flood plains. 

 (Continued)
109

Table 3-2. Geologic environments likely to produce earthquake-induced landslides 

 in the Los Angeles region (continued). 

Landslide 

Type 

Type of 

Material 

Minimum 

Slope 

Inclination 

in Degrees 

Remarks 

Soil Block 

Slides 

Loose, partly or completely saturated 

sand or silt; uncompacted or slightly 

compacted man-made fill composed of 

sand or silt; bluffs containing horizontal 

or subhorizontal layers of loose, 

saturated sand or silt. 

5 

Particularly common in areas of 

preexisting landslides along river 

and coastal flood plains, and on 

embankments built on soft, 

saturated foundation materials. 

Slow Earth 

Flows 

Stiff, partly or completely saturated 

clay and preexisting earth-flow 

deposits. 

10 

Soil Lateral 

Spreads 

Loose, partly or completely saturated 

silt or sand; uncompacted or slightly 

compacted man-made fill composed of 

sand. 

0.3 

Particularly common on river and 

coastal flood plains, embankments 

built on soft, saturated foundation 

materials, delta margins, sand 

dunes, sand spits, alluvial fans, 

lakeshores, and beaches. 

Rapid Soil 

Flows 

Saturated, uncompacted or slightly 

compacted man-made fill composed of 

sand or sandy silt (including hydraulicfill earth dams and tailings dams); 

loose, saturated granular soils. 

2.3 

Subaqueous 

Landslides Loose, saturated granular soils. 0.5 Particularly common on delta margins. 

Notes:

Soil lateral spreads can generally occur on gently sloping ground underlain by liquefied soil. They require 

earthquake inertia forces to induce liquefaction and temporary instability that result in successive down 

slope movement during earthquake shaking. Rapid soil flows and flow slides, on the other hand, generally 

occur in liquefied materials located on steeper slopes or in dams and embankments. Flow movements 

occur when the gravitational forces acting on a ground slope exceed the strength of the liquefied material 

within the slope. 

Wilson and Keefer, 1985

They developed a seismic rockfall susceptibility index, QRF, that is calculated with the following 

equation: 

v r RF

n a

115 3.3J J 1 Q J J AF

⎡ ⎤ − ⎡ ⎤⎡ ⎤ = ⎢ ⎥⎢ ⎥⎢ ⎥ ⎣ ⎦⎣ ⎦⎣ ⎦ (3-1) 
110

where: 

QRF is the seismic rockfall susceptibility index, 

Jv is the total number of joints per cubic meter, 

Jn is the joint set number, 

Jr is the joint roughness number, 

Ja is the joint alteration number, and 

AF is the aperture factor. 

For site-specific screening of rockfall susceptibility using the rockfall susceptibility index, the 

parameters listed above should be estimated based on field observations by a geologist 

knowledgeable in rock mechanics. Values for the parameters Jn, Jr, Ja, and AF should be chosen 

from tables 3-3 through 3-5 based on observed field conditions. The total number of joints per 

cubic meter, Jv, is measured in the field by adding the number of joints for each joint set. If each 

of the three orthogonal directions is exposed, Jv is the sum of the joints per meter in each 

direction. According to Harp and Noble (1993), the aperture factor, which quantifies the 

openness of rock fractures, is the most significant indicator of earthquake-induced rockfall 

susceptibility. While this characteristic is not particularly significant for static stability, 

earthquake vibratory loadings induce relative movement between rock fragments that lead to 

rocks breaking loose and falling. 

Using the model and empirical data from the Mammoth Lakes earthquake sequence, they 

established four categories of rockfall susceptibility based on percentages of observed rockfalls 

within areas of different ranges of QRF. The categories are as follows: 

Category A: QRF < 1.41 highly susceptible. 

Category B: = 1.41 - 2.83 susceptible. 

Category C: = 2.83 - 3.87 moderately stable. 

Category D: > 3.87 mostly stable. 

Generally, rockfall susceptibility can be screened out for sites classified as Category C and D. 

However, the above relationship was established for magnitude 6.0 earthquakes, which had peak 

ground accelerations (in the zone of strong shaking) of about 0.3 g to 0.5 g, and did not account 

for the effects of the distance from the seismic source on rockfall concentrations. For other 

earthquakes, however, distance from the seismic source and earthquake magnitude would affect 

the concentration of rockfalls and have to be accounted for in the analysis. These categories are 

used only in a preliminary screening analysis. Since measurement and assessment of factors 

required to calculate QRF values can be done rapidly, many sites can be evaluated quickly. QRF

values are then used in a preliminary analysis to decide whether a site located near or below rock 

slopes is unsafe, needs further study, or is relatively safe from seismically induced rockfall 

hazards. 

In addition to the rockfall susceptibility index, the rockfall hazard rating system developed by 

the Federal Highway Administration (Pierson and Van Vickle, 1993) may be used for rockfall 

screening. This system was designed to help highway agencies prioritize their rockfall hazard 

mitigation projects based on factors such as slope and highway geometry, risk to motorists, 

geologic conditions, past occurrence of rockfalls, and effectiveness of present rockfall mitigation 

measures. Sites with potential rockfall hazards are prioritized based on a point system. Local 
111

Table 3-3. Description and ratings for the parameters RQD, Jn and Jr. 

Rock Quality, Q = (RQD/Jn) x (Jr/Ja) x (Jw/SRF) 

1. Rock Quality Designation (RQD)1

A. Very Poor ....................................................... 0-25 

B. Poor................................................................ 25-50 

C. Fair ................................................................. 50-75 

D. Good............................................................... 75-90 

E. Excellent......................................................... 90-100 

2. Joint Set Number............................................ (Jn) 

A. Massive, no or few ........................................ 0.5-1.0 

B. One joint set ................................................... 2 

C. One joint set plus random .............................. 3 

D. Two joint sets ................................................. 4 

E. Two joint sets plus random ............................ 6 

F. Three joint sets............................................... 9 

G. Three joint sets plus random.......................... 12 

H. Four or more joint sets, random, 

 heavily jointed, “sugar cube,” etc. .................. 15 

I. Crushed rock, earthlike .................................. 20 

3. Joint Roughness Number............................... (Jr) 

(a) Rock wall contact and 

(b) Rock wall contact before 10cm shear 

A. Discontinuous joints ....................................... 4 

B. Rough or irregular, undulating........................ 3 

C. Smooth, undulating ........................................ 2 

D. Slickensided, undulating ................................ 1.5 

E. Rough or irregular, planar .............................. 1.5 

F. Smooth, planar............................................... 1.0 

G. Slickensided, planar....................................... 0.5 

 (c) No rock wall contact when sheared 

H. Zone containing clay minerals thick 

 enough to prevent rock wall contact ............. 1.0 (nominal) 

I. Sandy, gravelly or crushed zone thick 

enough to prevent rock wall contact .............. 1.0 (nominal)

Notes: 

(i) Where RQD is reported or 

measured as ≤ 10 (including 0) 

a nominal value of 10 is used to 

evaluate Q in equation 1. 

(ii) RQD intervals of 5, i.e., 100, 95, 

90, etc. are sufficiently accurate. 

Note: 

(i) For intersections (3.0 x Jn). 

Notes: 

(i) Add 1.0 if the mean spacing of 

the relevant joint set is greater 

than 3 m. 

(ii) Jr = 0.5 can be used for planar 

slickensided joints having 

lineations, provided the 

lineations are favorably 

orientated. 

Note: 

1

RQD is a core recovery ratio in which the lengths of all sound rock core pieces greater than 4 inches 

are summed and divided by the length of the core run.

Barton et al., 1974
112

Table 3-4. Description and ratings for the parameter Ja. 

1. Joint Alteration Number (Ja) Φr (approx.) 

(a) Rock wall contact 

A. Tightly healed, hard, non-softening, 

 impermeable filling, i.e., quartz or 

 epidote .......................................................... 0.75 (-) 

B. Unaltered joint walls, surface only................ 1.0 (25°-35°) 

C. Slightly altered joint walls, non- 

 softening mineral coatings, sandy 

 particles, clay-free disintegrated rock........... 2.0 (25°-30°) 

D. Silty- or sandy-clay coatings, small 

 clay fraction (non-softening) ........................ 3.0 (20°-25°) 

E. Softening or low-friction clay mineral 

 coatings, i.e., kaolinite, mica. Also 

 chlorite, talc, gypsum and graphite, 

 etc., and small quantities of swelling 

 clays. (Discontinuous coatings, 1-2 mm 

 or less in thickness) ..................................... 4.0 (8°-16°) 

Note: 

(i) Values of (Φr) are intended as 

an approximate guide to the 

mineralogical properties of the 

alteration products if present.

Barton et al., 1974

Table 3-5. Description and ratings for AF. 

1. Aperture AF 

A. All joints tight...................................................1.0 

B. Most joints tight, a few open as much 

 as 2 cm ...........................................................2.5 

C. Most joints tight, a few loose, open 

 as much as 5 cm.............................................5.0 

D. Significantly (20 percent) open, as 

 much as 10 cm................................................ 7.5 

E. Greatly (60 percent) open, as much as 

 20 cm ..............................................................10.0 

F. Gaping open, many joints open > 20 cm........15.0 

Notes: 

(i) If perched or loose rocks are 

common, increase by one. 

(ii) If pervasive joints dip out of slope, 

increase by one. 

Harp and Noble, 1993; modified from Barton et al., 1974
113

seismicity and its effects on the occurrence and magnitude of rockfalls were not considered in 

this system. Nevertheless, the rockfall hazard rating system may be a useful tool for preliminary 

screening of rockfall hazards. 

3.3.3. SUPPLEMENTAL CRITERIA FOR CATEGORY III LIQUEFACTION-INDUCED 

LANDSLIDES 

Category III Landslides are primarily caused by soil liquefaction (or loss of strength in sensitive 

clays) induced by earthquake shaking. Section 3.2, Part 1 of this manual contains screening 

criteria for liquefiable sediments and procedures to evaluate potential for lateral spread and rapid 

soil flows. 

3.4. EVALUATION PROCEDURES 

When a potential for landsliding or slope instability is identified during the preliminary 

screening stage, detailed engineering analyses will be required to evaluate the potential for 

failure, instability, or downslope movement during a postulated seismic event. In situations 

where the hazard is judged to be so obvious and severe, the user can proceed directly from 

screening to retrofit design (eliminating further hazard evaluation, except as needed to design the 

retrofit). 

3.4.1. EVALUATION OF CATEGORY I LANDSLIDES 

Well-accepted evaluation procedures for Category I Landslides are not available. If the 

screening phase indicates a potential for Category I Landslides, additional site-specific seismic 

stability analyses should be conducted and engineering judgment exercised by individuals with 

expertise in rock mechanics and rock slope stability. 

3.4.2. EVALUATION OF CATEGORY II LANDSLIDES 

If the screening phase indicates a potential for Category II Landslides, slope stability analyses 

should be performed to evaluate the specific hazard. The general method for evaluating seismic 

stability of slopes and embankments involves both the pseudo-static and deformation analysis 

procedures. The evaluation is performed in the following sequence: 

Step 1: Perform a pseudo-static slope stability analysis. If the resulting factor of safety is 

greater than 1.0, no further evaluation or retrofit are necessary. If the factor of safety 

is less than 1, indicating potential deformations, continue to step 2, or step 2 may be 

bypassed and retrofitting may conservatively be recommended at this point. 

Step 2: Perform a deformation analysis. If the predicted deformations are acceptable, no 

further evaluation or retrofit is required. If the predicted deformations are 

unacceptable, retrofitting strategies should be considered. 
114

3.4.2.1. Pseudo-Static Slope Stability Analysis Procedure 

Pseudo-static slope stability analyses conservatively evaluate the potential for occurrence of a 

slope failure due to earthquake loading. If the results of the pseudo-static analysis indicate a 

factor of safety less than 1, then the potential for slope movement exists and a deformation 

analysis may be appropriate to quantify the down slope displacements. 

3.4.2.1(a). Necessary Data for Analysis

Prior to performing engineering analyses to assess landslide potential, the data gathered in the 

screening stage should be supplemented if necessary. More detailed geologic reconnaissance 

and mapping may be needed. If preexisting landslides were identified at the site in the screening 

stage, subsurface investigations may be required to assess the slide geometry. Available 

geotechnical data should be reviewed to assess the engineering properties of the subsurface 

materials in the slope(s). If sufficient data are lacking, field and laboratory testing may be 

required. For slopes located in stiff, nonsensitive clays, dry sands, and dense saturated sands that 

do not liquefy or lose their strength during earthquake shaking, the stability of the slopes can be 

evaluated using pseudo-static analysis and/or deformation analysis procedures. Slopes on 

potentially liquefiable soil and sensitive clays can be evaluated using procedures described in 

Part 1 of this manual. 

Several methods are available for determining the appropriate soil strength parameters to be used 

in pseudo-static and deformation analyses. In-situ and laboratory test methods should be used 

that measure strengths applicable to short-term loading and, in the case of soils below the water 

table, undrained conditions. In-situ strength parameters are commonly estimated from 

unconfined compression, unconsolidated undrained triaxial and consolidated undrained triaxial 

tests on “undisturbed” samples. Duncan et al. (1990) developed a procedure for evaluating 

undrained strength under conditions of rapid drawdown, which are similar to conditions during 

earthquake loading. This procedure incorporates the effects of anisotropic consolidation on the 

undrained strength, thus avoiding problems associated with estimating pore pressures induced by 

earthquake shaking. The U.S. Army Corps of Engineers (1970) recommends using a composite 

shear strength envelop that is constrained by the drained strength envelop at low confining 

pressures, and the undrained strength envelop at higher confining pressures. This approach 

provides a conservative strength interpretation compared to Duncan’s (1990) method. 

Some engineering methodologies recommend increasing the undrained static shear strength of 

soils to account for the transient nature of seismic loading. However, soil strength does not 

always increase during earthquake shaking. When subjected to long durations of strong shaking, 

some soils decrease in strength due to the effects of pore water pressure buildup. Therefore, 

unless a reduction can be justified, static undrained strength should be used in pseudo-static 

analyses. Makdisi and Seed (1978) recommended that the static undrained strength of soft to 

medium stiff clays be reduced by 20 percent to account for strength loss during strong 

earthquake shaking. 

Residual undrained shear strengths should be used to represent liquefiable sediments. A residual 

strength condition exists after large strains have occurred and additional shearing will not further 

decrease the strength or volume of the soil. Seed and Harder (1990) developed a correlation for 
115

residual strength with equivalent clean sand SPT blowcounts , (N1)60-CS (figure 3-11). The lower 

bound of the correlation shown in figure 3-11 is thought to be a conservative estimate of residual 

strength. A curve passing through the lower third of the range shown in figure 3-11 is 

considered a reasonable estimate to use in stability analyses. This lower-third residual strength is 

estimated based on the average corrected standard penetration blow counts for a particular 

stratum. 

0 8 4 12 16 20 24

1200

2000

1600

800

400

0

.

.

Earthquake-induced liquefaction and sliding case histories where

SPT data and residual strength parameters have been measured.

Earthquake-induced liquefation and sliding case histories where

SPT data and residual strength parameters have been estimated.

Construction-induced liquefaction and sliding case histories.

Lower San Fernando Dam

Residual Undrained Shear Stength, S (psf) r

Equivalent Clean Sand SPT Blowcount, (N ) 1 60-cs

Seed and Harder, 1990

Figure 3-11. Relationship between corrected “clean sand” blowcount (N1) 60-cs

and underdrained residual strength (Sr) from case studies. 

3.4.2.1(b). Analysis Procedure

In pseudo-static slope stability analyses, inertial forces generated by the earthquake are 

represented by an equivalent static horizontal force (seismic coefficient) acting on the potential 

sliding mass. In this analysis, the seismic coefficient should generally be equal to the peak 

ground acceleration in the vicinity of the slope. 

Recommendations for selecting an appropriate pseudo-static seismic coefficient were provided 

by Seed (1979) and Hynes and Franklin (1984). Both approaches were developed for 

embankment dams and were based on a level of acceptable deformation that would not 

compromise the integrity of the embankment. Using a limit of about 1 m (3.3 feet) as a criterion 
116

for acceptable performance, Seed (1979) recommended using seismic coefficients of 0.1 and 

0.15 (together with a factor of safety of 1.15) for earthquakes of magnitude 6.5 and 8.25, 

respectively. This recommendation was made for embankments composed of materials that do 

not lose more than 15 percent of their strength due to earthquake shaking and that are subjected 

to peak crest accelerations of less than 0.75 g. 

Hynes and Franklin (1984) suggested using a pseudo-static seismic coefficient of one-half the 

peak acceleration at bedrock underlying the embankment. This recommendation was also based 

on limiting the permanent deformations to 1 m (3.3 feet), after accounting for amplification 

effects at the crest of the embankment. It is clear that the level of acceptable or tolerable 

deformations governs the selection of a seismic coefficient for use in pseudo-static stability 

analyses. While deformations of 1 m (3.3 feet) may be acceptable for evaluating the performance 

of earth and rockfill dams and embankments, structures or pavements supported on 

embankments or on natural or man-made slopes may not tolerate such levels of permanent 

deformations. Accordingly, the results of earthquake-induced deformations published by 

Makdisi and Seed (1978) were used to estimate values of the seismic coefficient (used together 

with a factor of safety of one) for various assumed levels of permanent displacements. Using the 

ratio of ky/kmax (where ky is the seismic coefficient resulting in a factor of safety of one, and kmax

is the peak acceleration induced within a potential sliding mass), and the upper-bound 

deformations estimated by Makdisi and Seed (1978), values of the seismic coefficient were 

estimated and found to be a function of the specified permanent deformation and earthquake 

magnitude. For permanent deformations that usually are tolerated by structures (on the order of 

2.5 to 5 cm (one to two inches)), the corresponding seismic coefficient is about 70 to 80 percent 

of the peak acceleration. 

It is therefore recommended that, at the preliminary evaluation phase, a seismic coefficient equal 

to the peak acceleration induced within the potential sliding mass be conservatively used in the 

stability analysis. Using this approach, a computed factor of safety greater than one will ensure 

that estimated earthquake-induced slope deformations are limited to acceptable levels. 

The peak or maximum acceleration, kmax, induced within a potential sliding mass (average of the 

peak accelerations over the mass) must be estimated. Often this value is assumed equal to the 

free-field ground surface acceleration, amax. This neglects possible amplification of accelerations 

on a slope due to topographic effects, but also neglects decreases in acceleration due to reduction 

of ground motion with depth and spatial averaging over the sliding mass. A specific evaluation 

of kmax considering amplifying and reducing effects can always be made using dynamic response 

analysis or simplified methods. Simplified procedures for estimating the response of 

embankment dams were developed by Makdisi and Seed (1978, 1979). Their procedure 

provided estimates of the maximum crest acceleration and a distribution of the maximum 

average acceleration, kmax, with depth of sliding surface within the embankment. Ashford and 

Sitar (1994) performed two-dimensional dynamic response analyses of steep, weakly cemented 

sand slopes, using a generalized hyper-element method (Deng, 1991). The results of their 

analyses showed that the peak acceleration computed at the crest of the slope is amplified 

relative to the free-field ground motions beyond the crest of the slope. The amplification due to 

topographic effects was dependent on the slope geometry and the frequency content of the input 

motion. For the sites they analyzed, the computed peak accelerations at the crest of the slope 
117

were, on average, about 50 percent higher than those estimated in the free-field beyond the crest 

of the slope. They also analyzed steep slopes comprised of soils or weathered rock overlying 

hard rock formations, and found that amplification of accelerations at the ground surface 

(beyond the crest of the slopes) due to site response effects were much greater than those due to 

topographic effects. Thus, Ashford and Sitar (1994) recommended an approach that incorporates 

site amplification effects by performing one-dimensional site response, and then accounting for 

topographic effects at the crest of the slope by increasing the peak value of the free-field 

response by 50 percent. The results of the two-dimensional response analyses showed that the 

estimated amplification using the Makdisi and Seed Simplified (one-dimensional) procedure for 

embankments is much higher than that computed for the steep slopes. Ashford and Sitar (1994) 

also developed curves of normalized kmax/amax values for various depths of the sliding mass 

(similar to those of Makdisi and Seed, 1978). Their curves are of the same general shape, but 

cover a broader range than the profiles developed by Makdisi and Seed (1978). Their kmax/amax

relationship varied with the frequency content of the input motion and the slope angle. The 

steepest slopes provided the upper bound of the variation kmax/amax with depth. 

The approach to estimating the peak acceleration within a potential sliding mass is as follows: 

(a) For small slopes having generally uniform subsurface conditions, the free-field peak ground 

acceleration can be used as an average pseudo-static seismic coefficient. (b) For steep slopes of 

weathered rock or soil overlying hard rock formations, the approach of Ashford and Sitar (1994) 

could be used. (c) For sites with complex geometries and material properties, or for essential or 

critical facilities and structures, a site-specific two-dimensional dynamic response analysis is 

recommended to estimate kmax. The induced acceleration is estimated in the transverse “down 

slope” direction of the embankment or slope. For embankment slopes, in addition to the 

simplified procedure of Makdisi and Seed (described above), an amplification curve developed 

by Harder (1991) based on recorded motions during several earthquakes (on the crests of 

embankment dams) can also be used in estimating kmax. 

The factor of safety for a given seismic coefficient can be estimated using limit equilibrium slope 

stability methods. Methods of slope stability analyses for soil slopes are described in detail by 

Duncan (1996) in the Transportation Research Board, Special Publication 247, Landslide 

Investigation and Mitigation. Several computer programs capable of performing pseudo-static 

slope stability analyses are available commercially such as UTEXAS3 (Wright, 1991), 

SLOPE/W (GEO-SLOPE International Ltd., 1998), PCSTABLE (Siegel, 1975), or XSTABL 

(Sharma, 1997). Use of such computational aids is recommended considering the number of 

iterations required to locate the critical failure surface. 

A computed factor of safety greater than one indicates that the slope is stable and further 

evaluations are not required. A computed factor of safety of less than one does not imply failure 

but indicates that the slope will yield and deformations can be expected. In this case, an estimate 

of the expected slope deformations should be made using the procedures described in section 

3.4.2.2. 

3.4.2.1(c). Special Considerations for Rock Slopes

The static and seismic stability of rock slopes is often primarily dependent on the orientation and 

characteristics of the rock bedding, jointing, and fractures rather than on the properties of the 
118

intact rock. Characterization of the engineering properties of the rock mass may require detailed 

engineering geologic field assessments and laboratory testing. Norrish and Wyllie (1996) 

present methods for static analyses of rock slopes including kinematic analyses to account for 

adverse bedding, joints and potential wedge failure. The methods for seismic analysis are not as 

well developed, but generally consist of applying the pseudo-static seismic coefficient to the 

rock mass model. Norrish and Wyllie (1996) should be consulted for a description of models 

and methods of rock slope stability analysis. Figure 3-12 illustrates an analysis model for a 

simple case. 

Norrish and Wyllie, 1996 

Figure 3-12. Horizontal and vertical seismic coefficients for pseudostatic analysis of rock slopes. 

Due to the variety of failure mechanisms of rock slopes, this document does not review the 

analytical methods used to analyze the stability of rock slopes. Analytical methods for rock 

slope stability under seismic loading are presented in Norrish and Wyllie (1996). 

3.4.2.2. Deformation Analysis Procedures 

Simplified procedures for estimating deformations of slopes during earthquake shaking are based 

on the concept of yield acceleration originally proposed by Newmark (1965). Newmark's 

method has been modified and augmented by several investigators (Goodman and Seed, 1966; 

Ambraseys, 1973; Sarma, 1975; Franklin and Chang, 1977; Makdisi and Seed, 1978; HynesGriffin and Franklin, 1984; Wilson and Keefer, 1985; Lin and Whitman, 1986, Ambraseys and 

Menu, 1988; and Yegian et al., 1991). The procedure assumes that movement occurs on a well 

defined slip surface and that the material behaves elastically at acceleration levels below the 

yield acceleration but develops perfectly plastic behavior above yield. The procedure involves 

the following steps: 
119

Step 1: Determine the yield acceleration, ky, using limit equilibrium pseudo-static slope 

stability methods as described in the preceding section. The yield acceleration 

corresponds to the seismic coefficient that would result in a factor of safety of one. 

Step 2: Determine the peak horizontal acceleration experienced by the potential sliding mass, 

kmax, as described in the preceding section. 

Step 3: Calculate the ratio of ky to kmax and estimate the potential deformation using one or 

more of several methods discussed below. 

Deformation analysis procedures contained herein can lead to inaccurate results for brittle rocks 

and soils, which are characterized by a substantial reduction in strength upon yielding. Using 

deformation analysis procedures that assume perfectly plastic behavior above yield with 

strengths equal to the yield strength will underestimate deformations in these materials. Brittle 

soils include weakly cemented sands common in the western U.S. and loess deposits common in 

the midwestern U.S. Procedures for the evaluation of brittle soils can be found in Ashford and 

Sitar, 1994, and Sitar and Clough, 1983. 

3.4.2.2(a). Yield Acceleration, ky

A yield acceleration, ky, i.e., the acceleration at which a potential sliding surface would develop 

a factor of safety of unity, is determined using limit equilibrium pseudo-static slope stability 

methods as described above. Values of the yield acceleration are dependent primarily on the 

slope geometry, the undrained shear strength of the slope material, and the location of the 

potential sliding surface. 

3.4.2.2(b). Peak Acceleration Induced Within the Sliding Mass, kmax

Guidance for estimating peak or maximum acceleration, kmax, induced within a potential sliding 

mass (average of the peak accelerations over the mass) is provided in section 3.4.2.1(b). 

3.4.2.2(c). Estimating Deformation, D 

Several methods for estimating deformation using the Newmark method have been developed. 

Each of these is based on the following methodology. For a specified potential sliding mass, the 

induced acceleration, kmax, is compared with the yield acceleration, ky. When the induced 

acceleration exceeds the yield acceleration, downslope movements will occur along the direction 

of the assumed failure plane. The movement will stop when the induced acceleration drops 

below the yield acceleration and when the induced velocity drops to zero. The magnitude of the 

potential displacements can be calculated by the simple double-integration procedure of an 

accelerogram as illustrated in figure 3-13 (note that ky is shown in the figure to vary with the 

level of acceleration, however, unless the material suffers rapid loss of strength during shaking, 

ky is generally assumed to be constant). 

The most commonly used simplified method for estimating deformation was developed by 

Makdisi and Seed (1978) for estimating displacements in embankments. Charts relating the 

displacements as a function of the ratio of the yield acceleration to the maximum induced 

acceleration (ky/kmax) are shown in figures 3-14 and 3-15. The displacements shown in figures 
120

3-14 and 3-15 are normalized with respect to the amplitude of the peak induced acceleration, 

kmax (expressed as a decimal fraction of gravity), the acceleration of gravity, and the predominant 

natural period of the soil embankment or slope, To. The procedure was developed based on To

values ranging from 0.5 seconds to 1.5 seconds. To can be estimated for embankments with the 

following equation: 

o

s

h T 2.6

V = (3-2) 

where: 

h = height of embankment 

Vs = strain-dependent shear wave velocity of the soil 

Makdisi and Seed (1979) developed a simplified procedure to estimate strain compatible To for 

embankment slopes. Strain compatible shear wave velocities in soils decrease with increasing 

levels of ground shaking. In the absence of a dynamic response analysis, recommended values of 

strain compatible shear wave velocities are as follows: for ground shaking on the order of about 

0.1 g, the value of Vs can be assumed equal to 0.8 Vmax (where Vmax is the low-strain maximum 

shear wave velocity); for strong ground shaking levels of the order of 0.7 g, the value of Vs can 

be assumed equal to 0.45 Vmax. For small slopes of uniform stiff soil, the predominant period of 

the earthquake acceleration time history can be used in the analysis. The predominant period of 

an earthquake acceleration time history is a function of earthquake magnitude, source to site 

distance, and site conditions. Relationships for estimating the frequency content (natural period) 

of ground motions were developed by Rathje et al. (1998). Typical values of these periods range 

between 0.4 and 0.7 seconds. 

Goodman and Seed, 1966 

Figure 3-13. Integration of acceleration time history to determine 

velocities and displacements. 
121

The displacement relationships shown in figures 3-14 and 3-15 are presented for a range of 

earthquake magnitudes. The earthquake magnitude can be selected based on either the mean 

magnitude (de-aggregated) from seismic hazard analyses, or the maximum credible earthquake 

magnitude obtained from deterministic estimates (see Part I). 

The Newmark sliding block analysis concept was also employed by Franklin and Chang (1977), 

who computed permanent displacements based on a large number of recorded acceleration timehistories from previous earthquakes and a number of synthetic records. Their results are shown 

in figure 3-16 in terms of upper bound envelope curves for standardized maximum 

displacements versus the ratio of the yield acceleration to the maximum earthquake acceleration. 

The time-histories used by Franklin and Chang (1977) all were scaled to a peak ground 

acceleration of 0.5g and peak ground velocity of 0.76 m/s (30 inches per second). The 

displacement, D (in inches), for particular values of peak ground acceleration, A, and velocity, 

V, may be obtained by multiplying the standardized maximum displacement by the quantity 

V2

/1800A, where V is in units of inches per second and A is a decimal fraction of gravity 

(V2

/0.01285A; where V is in m/s; and D is in meters). 

Yegian et al. (1991) performed similar analyses using 86 ground motion records. Their 

computed normalized displacements are shown in figure 3-17. The computed displacements 

were normalized with respect to the peak induced acceleration, ka, the number of equivalent 

cycles, Neq, and the square of the predominant period of the time history, T. U/K g T -seconds max 0

10

1

0.1

0.01

0.001

0.0001

0 0.2 0.4 0.6 0.8 1.0

M~8 1/4

M~7 1/2

M~6 1/2

K /Ky max

Makdisi and Seed, 1978 Makdisi and Seed, 1978 

Figure 3-14. Variations of normalized 

permanent displacement with yield 

acceleration – summary of all data. 

 Figure 3-15. Variations of average 

normalized displacement with yield 

acceleration. 
122

Franklin and Chang, 1977 

Figure 3-16. Upper bound envelope curves of permanent displacements for all 

natural and synthetic records analyzed 

The number of equivalent cycles is a function of earthquake magnitude and can be estimated as 

follows (Seed and Idriss, 1982). 

Earthquake Magnitude Number of Significant Cycles, Neq

5.25 2-3 

6 5 

6.75 10 

7.5 15 

8.5 26 
123

K / K y a

10

1

10-1

10-2

10-3

10-4 

10-5

0.0 0.2 0.4 0.6 0.8 1.0

Developed Function

K = K a max

Normalized Permanent Deformation D / K N T r a eq 2

Yegian et al., 1991 

Figure 3-17. Variation of normalized permanent deformation with yield acceleration. 

A simple comparison of the methods described above was made using a postulated magnitude 

7.5 earthquake with kmax equal to 0.5 g and 0.7 g, and a yield acceleration, ky of 0.3 is presented 

in table 3-6. The Franklin and Chang (1977) method, whose curves represent an upper bound 

relationship, produced the largest deformations for both values of kmax. The Makdisi and Seed 

(1978) and Yegian et al. (1991) methods provided similar deformations for both acceleration 

levels. Generally, these deformation analysis methods provided similar results. Further 

illustration of these deformation analysis methods are provided in Example Problem 3.2 (see 

section 3.6). 

In addition to the simplified procedures described above, screening and evaluation procedures 

were developed by a committee (organized through the ASCE, Los Angeles Section) to 

implement guidelines of the Division of Mines and Geology (DMG) Special Publication 117- 

Guidelines for Analyzing and Mitigating Landslide Hazard in California (Blake et al., 2002). 

The document provides guidelines on field and laboratory procedures, preliminary screening 

procedures, and simplified analyses procedures for evaluating slope stability and earthquakeinduced deformations. 

For slopes with complex geometries and material properties (that could not be approximated by 

simplified analysis procedures as described above), and for slopes and embankments supporting 

essential structures, detailed dynamic analyses and Newmark-type deformation analyses are 

required. These analyses include the use of equivalent linear (strain-dependant) finite element 

procedures such as the program QUAD4M (Hudson et al., 1994). This widely used dynamic 

analysis program provides estimates of earthquake-induced stresses and accelerations within the 
124

Table 3-6. Comparison of deformation analysis methods. 

Deformation (cm) 

Method Case 1: 

kmax=0.5g 

Case 2: 

kmax = 0.7g 

Assumptions 

Makdisi & Seed 

(1978) 3 14 To = 0.36 sec (Seed et al., 1968) 

Yegian et al. (1991) 3.5 13 To = 0.36 sec (Seed et al., 1968) 

Franklin & Chang 

(1977) 

5 (rock) 

7 (soil) 

19 (rock) 

43 (soil) 

Velocities estimated using Sadigh and Egan (1998) 

Kmax =0.5 g: v= 50 cm/s (rock); 60 cm/s (soil) 

Kmax =0.7g: v= 60 cm/s (rock); 90 cm/s (soil) 

entire embankment or slope. The analysis also provides time histories of the average induced 

seismic coefficient for specified potential sliding masses within the slope. The time histories are 

compared with the yield acceleration for the corresponding sliding mass and are doubleintegrated to estimate the earthquake-induced permanent deformations. 

Two-dimensional nonlinear finite element and finite difference programs also have recently been 

used to estimate the dynamic response, liquefaction potential, and permanent deformations of 

slopes and embankments. The program FLAC (Itasca, 1998), is a finite difference (large strain) 

computer program that can model nonlinear, coupled effective stress behavior during seismic 

loading. Such rigorous numerical modeling procedures, however, require considerable 

experience and judgment to properly calibrate model parameters; and their results are usually 

compared with commonly used (empirically based) simplified analyses. 

3.4.3. EVALUATION OF CATEGORY III LANDSLIDES 

Category III Landslides include soil lateral spreads and rapid soil flows. Procedures to evaluate 

these conditions are included in Part 1 of this manual.

3.5. RETROFITTING PROCEDURES 

Detailed procedures for stabilizing soil and rock slopes are presented in the Transportation 

Research Board Special Report 247, Landslides Investigation and Mitigation (Turner and 

Schuster, 1996, editors). Both Category I and II landslides include rock and soil stability issues. 

Retrofit procedures for landslides are best categorized by whether the slope needing stabilization 

is composed of rock or soil. Procedures for stabilizing rock slopes are presented by Wyllie and 

Norrish (1996) and Branwer (1994); stabilization procedures for soil slopes are presented by 

Holtz and Schuster (1996). 
125

3.5.1. ROCK SLOPES 

Methods of stabilization of rock slopes are described in detail by Wyllie and Norrish (1996) and 

Branwer (1994). Wyllie and Norrish (1996) describe three categories for stabilization and 

protection of rock slopes: (1) reinforcement; (2) rock removal; and (3) protection. Retrofitting 

measures in these three categories are listed in figure 3-18. Selecting the appropriate 

stabilization system is dependent on several issues that are usually site-specific. These issues 

include service life, importance of highway structure, environmental concerns, construction time, 

economics and others. 

Rock Cut 

Stabilization and

Protection

Stabilization

Measures

Reinforcement

Protection

Measures

Rock Removal

• Rock Bolting

• Dowels

• Tied-Back Walls

• Shotcrete

• Buttresses

• Drainage

• Shot-in-place 

 buttress

• Resloping

• Trimming

• Scaling

• Ditches

• Mesh 

• Catch Fences

• Warning Fences

• Rock Sheds

• Tunnels

Wyllie and Norrish, 1996 

Figure 3-18. Categories of rock slope stabilization 

measures. 

1. Rock Reinforcement

A number of techniques are used for rock slope reinforcement. These techniques are shown 

schematically in figure 3-19. A feature common to 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. 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. With this approach, multiple rock columns are bolted together in order 

to move the center of gravity of the combined rock mass to within its base. 

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 reduced shrinkage. The strength of 

the rock often governs the strength of the anchor. Approximate values of allowable bond 

stress between grout and various rock types are listed in table 3-7. These approximate ranges 

can be used to estimate anchor strengths in the absence of laboratory or field test data. 
126

1

2

3

4 5

6

ψ opt ψ

ψp

t

1 Reinforced concrete dowel to prevent loosening of 

slab at crest

2 Tensioned rock anchors to secure sliding failure 

along crest

3 Tieback wall to prevent sliding on fault zone

4 Shotcrete to prevent raveling of zone of fractured rock

5 Drain hole to reduce water pressure within slope

6 Concrete buttress to support rock above cavity

Wyllie and Norrish, 1996

Figure 3-19. Rock slope reinforcement methods. 

Table 3-7. Allowable bond stresses in cement-grout anchors. 

Rock Strength and 

Type 

Allowable Bond Stress 

(MPa) 

Compressive Strength Range 

(MPa) 

Strong 1.05 – 1.40 >100 

Medium 0.7 - 1.05 Approx. 50-100 

Weak 0.35 - 0.7 Approx. 20-50 

Granite, basalt 0.55 - 1.0 

Dolomitic limestone 0.45 - 0.7 

Soft limestone 0.35 - 0.5 

Slates, strong shales 0.3 - 0.45 

Weak shales 0.05 - 0.3 

Sandstone 0.3 - 0.6 

Concrete 0.45 - 0.90 

Wyllie, 1991 

2. Rock Removal

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 3-20. 
127

1

2

3

4

5

1 Resloping of unstable weathered material in upper part of slope

2 Removal of rock overhang by trim blasting

3 Removal of trees with roots growing in cracks

4 Hand scaling of loose blocks in shattered rock

5 Clean ditch

Wyllie and Norrish, 1996

Figure 3-20. Rock-removal methods for slope 

stabilization. 

3. Protective Measures Against Rockfalls

Another effective method of protection against the hazards of rockfalls is to let the falls 

occur and control the distance and direction of travel. 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 barrier, which either 

stop the rockfall over some distance or deflect it away from the facility being protected. 

Richie (1963) developed charts for estimating the required width and depth of rock catch 

ditches in relation to the height and face angle of the nearby slope (figure 3-21). Most catch 

ditches require a barrier between the ditch and the highway to stop falling or shattered rocks 

from reaching the roadway. Loose granular material may also be used in the ditch to absorb 

energy from falling rocks. 

A variety of barriers can be constructed to either enhance the performance of excavated 

ditches or form catchment zones at the toes of slopes. The required type of barrier and its 

dimensions depend on the energy of the falling blocks, the slope dimensions, and the 

availability of construction materials. 

Details of various types of barriers are provided by Wyllie and Norrish (1996). Examples of 

these barriers include gabions and concrete blocks, and geofabric-reinforced soil barriers. 

Flexible rock catch fences and attenuators also are commonly used and include woven wirerope nets, flex-post rockfall fences, and draped wire mesh. Figure 3-22 details the main 

components of a rockfall retaining net system used by the California Department of 

Transportation (Smith and Duffy, 1990). 
128

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 pavement or 

railway rather than to withstand a direct impact (figure 3-23, McCauley et al., 1985). 

Design of such structures must also be based on the energy required to redirect the falling 

rocks and boulders. The California Department of Transportation (Caltrans) report on 

rockfall mitigation (McCauley et al., 1985) evaluated various mitigation techniques that can 

be used. The Caltrans report also provides a summary of the mitigation methods used by 14 

selected states that responded to their survey. The results of the survey are summarized in 

figure 3-24. From this survey, mesh fences, catch ditches, rock bolts and dowels, controlled 

blasting, and flattening and scaling slopes were the most widely applied rock slope 

mitigation methods. 

Richie, 1963

Figure 3-21. General design criteria for shaped ditches. 
129

1 psi = 6.9 kPa

1 ft = 0.305 m

Wire Rope

Anchor

5/8” Wire Rope Min.

with Braking Element

W 8x48 Steel Post

Nonshrink Concrete &

Sand Grout Compressive

Strength of 3,500 psi min. Wire Rope

Protector Friction Brake

Wire Rope Net

Drill Hole

4” O

Chain Link Mesh

Concrete Strength

of 3,500 psi min.

10’- 0”

2 1⁄2”max.

3’- 0” min.

3” max.

30”

12’- 0” ( 6”) _

+

10’- o”

Smith and Duffy, 1990 

Figure 3-22. Side view of rock fall restraint net system with fully embedded posts and 

anchor support. 

 McCauley et al., 1985 

Figure 3-23. Example of rock shed. 
130

States AK AZ CO HI ID MT NV NH NM OR UT VT WA WY

F X XXX X X latten Slope

S XXX XXXX X cale or Trim

Skewed, Multiple Angle

Slopes X

SX X lope Designed to Geology

C X XX X XX X ontrolled Blasting

S X ub-Surface Drainage

R X X XX X X X X ockbolt or Dowels

S X XX XX hotcrete or Gunnite

A X XXX XX nchored Wire Mesh

C X able Lashing

RX X etaining Wall

SX X lope at Max. Steepness

H XX ighway Relocation

B XX X XX ench

S XX X tandard Guard Rail

M XX etal Barrier

P XXX X X CC Jersey Barrier

G X XX abion

Earth Berm X

Intercepting Slope Ditch X

S X X X XX X XX X X haped Ditch at Grade

"Telephone Pole" Retainer X

D X XXX X X XX X raped Wire Mesh

Aggregate in Ditch Line X

M X etal Bin Wall

W X XX X X XX X ire Mesh Fence

Note: 

 Chart prepared from the responses sent to Caltrans from other states, other methods may also be used 

by listed states. Combinations of mitigation measures are also used. 

McCauley et al., 1985 

Figure 3-24. Rock slope mitigation methods used by selected states. 
131

3.5.2. SOIL SLOPES 

Approaches to the design of remedial measures for landslides, potential slope failures, and 

design of stable slopes can be categorized as follows (Holtz and Schuster, 1996): 

• Avoid the problem and relocate the facility to a stable site. 

• Reduce the driving forces that tend to cause movement and sliding. 

• Increase the forces resisting movement. 

A summary of these three approaches is given in table 3-8. 

• Avoidance of Problem

Geologic and geotechnical reconnaissance studies should reveal adverse conditions affecting 

stability of slopes, such as poor surface drainage, seepage on existing natural slopes, hillside 

creep, existing landslides, and soft foundations. Facilities could be relocated to avoid these 

potential problem areas, particularly existing landslides. If relocation or realignment of a 

proposed facility is not practical, partial or complete removal of the unstable material could 

be considered. If relocation and/or removal of unstable material is too costly, an alternative 

design is to span the unstable area with a bridge supported on piles or drilled shafts founded 

well below the unstable material and capable of withstanding lateral loads from it. 

• 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. 

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. 

Proper surface drainage should be implemented to prevent water from flowing across the 

face of the slope and from seeping into the slope. Diversion ditches and interceptor drains 

are used when large volumes of runoff are anticipated. Methods to control subsurface water 

are discussed in “Increase in Resisting Forces,” below. 

Finally, lightweight backfill materials have been used in embankment construction to reduce 

driving forces tending to cause instability. 
132

Table 3-8. Summary of approaches to potential stability problems. 

Category Procedure Best Application Limitations Remarks 

Avoid problem Relocate 

facility 

As an alternative 

anywhere 

Has none if studied 

during planning phase; 

has large cost if location 

is selected and design 

is complete; also has 

large cost if 

reconstruction is 

required 

Detailed studies of proposed 

relocation should ensure 

improved conditions 

Completely or 

partially 

remove 

unstable 

materials 

Where small 

volumes of 

excavation are 

involved and where 

poor soils are 

encountered at 

shallow depths 

May be costly to control 

excavation; may not be 

best alternative for large 

landslides; may not be 

feasible because of 

right-of-way 

requirements 

Analytical studies must be 

performed; depth of 

excavation must be 

sufficient to ensure firm 

support 

 Install bridge 

At sidehill locations 

with shallow soil 

movements 

May be costly and not 

provide adequate 

support capacity for 

lateral forces to restrain 

landslide mass 

Analysis must be performed 

for anticipated loading as 

well as structural capability 

Reduce driving 

forces 

Change line or 

grade 

During preliminary 

design phase of 

project 

Will affect sections of 

roadway adjacent to 

landslide area 

-- 

 Drain surface 

In any design 

scheme; must also 

be part of any 

remedial design 

Will only correct surface 

infiltration or seepage 

due to surface 

infiltration 

Slope vegetation should be 

considered in all cases 

Drain 

subsurface 

On any slope 

where lowering of 

groundwater table 

will increase slope 

stability 

Cannot be used 

effectively where slide 

mass is impervious 

Stability analysis should 

include consideration of 

seepage forces 

 Reduce weight At any existing or 

potential slide 

Requires lightweight 

materials that may be 

costly or unavailable; 

excavation waste may 

create problems; 

requires right-of-way 

Stability analysis must be 

performed to ensure proper 

placement of lightweight 

materials 

Increase 

resisting 

forces; 

Apply external 

force 

Use buttress 

and counterweight fills; toe 

berms 

At an existing landslide; in 

combination with 

other methods 

May not be effective on 

deep-seated landslides; 

must be founded on a 

firm foundation; requires 

right-of-way 

Consider reinforced steep 

slopes for limited right-ofway 

(Continued) 
133

Table 3-8. Summary of approaches to potential stability problems (continued). 

Category Procedure Best Application Limitations Remarks 

Increase 

resisting 

forces; 

Apply external 

force 

(continued) 

Use structural 

systems 

To prevent 

movement before 

excavation; where 

right-of-way is 

limited 

Will not stand large 

deformations; must 

penetrate well below 

sliding surface 

Stability and soil-structure 

analyses are required 

 Install anchors Where right-of-way 

is limited 

Requires ability of 

foundation soils to resist 

shear forces by anchor 

tension 

Study must be made of insitu soil shear strength; 

economics of method 

depends on anchor capacity, 

depth, and frequency 

Increase 

internal 

strength 

Drain 

subsurface 

At any landslide 

where water table 

is above shear 

surface 

Requires experienced 

personnel to install and 

ensure effective 

operation 

-- 

Use reinforced 

backfill 

On embankments 

and steep fill 

slopes; land-slide 

reconstruction 

Requires long-term 

durability of 

reinforcement 

Must consider stresses 

imposed on reinforcement 

during construction 

Install in-situ 

reinforcement 

As temporary 

structures in stiff 

soils 

Requires long-term 

durability of nails, 

anchors, and micropiles 

Design methods not well 

established; requires 

thorough soils investigation 

and properties testing 

Use 

biotechnical 

stabilization 

On soil slopes of 

modest heights 

Climate; may require 

irrigation in dry seasons; 

longevity of selected 

plants 

Design is by trial and error 

plus local experience 

Treat 

chemically 

Where sliding 

surface is well 

defined and soil 

reacts positively to 

treatment 

May be reversible; longterm effectiveness has 

not been evaluated; 

environmental stability 

unknown 

Laboratory study of soilchemical treatment must 

precede field installations; 

must consider environmental effects 

Use electroosmosis 

To relieve excess 

pore pressure and 

increase shear 

strength at a 

desirable 

construction rate 

Requires constant direct 

current power supply 

and maintenance 

Used when nothing else 

works; emergency 

stabilization of landslides 

 Treat thermally 

To reduce 

sensitivity of clay 

soils to action of 

water 

Requires expensive and 

carefully designed 

system to artificially dry 

or freeze subsoils 

Methods are experimental 

and costly 

Holtz and Schuster, 1996; modified from Gedney and Weber, 1978 
134

• 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 buttress is 

shown in figure 3-25. Notice in this figure that a toe drain was installed to further facilitate 

drainage. 

In situations where buttress fills are not feasible because of geometry, cost, or space 

limitations, conventional retaining structures, piles, and reinforced earth slopes and walls 

may be used as an alternative. These methods are summarized in figure 3-26. The methods 

are divided into two groups, depending on whether they provide external or internal support. 

Examples of both systems are shown in figure 3-27. 

Techniques that are used to increase the internal strength of potentially unstable soil include: 

subsurface drainage, soil reinforcing systems, vegetative and biotechnical stabilization, and 

other less common methods such as chemical, electrical (electro-osmosis), and thermal 

stabilization. Details of these procedures are presented by Holtz and Schuster (1996). 

Colluvium

Highly Weathered 

 Zone

 Shale with occasional 

interbedded layers of 

siltstone, sandstone, and limestone

Drain

Gedney and Weber, 1978 

Figure 3-25. Rock buttress used to increase forces resisting slope failure. 
135

Externally Stabilized

Systems

Internally Stabilized

Systems

In-Situ Walls

• timber

• precast concrete

• sheet piles

• soldier piles

• cast in-situ

 - slurry walls

 - secant pile

 - tangent pile

• bored-in-place

 (piles not 

 contiguous)

• soil cement

Gravity Walls

• masonry

• concrete

• cantilever

• counterfort

• gabion

• crib

• bin

• cellular

 cofferdam

Reinforced Soil

• metallic, 

 polymeric and 

 organic reinforcing 

 strips and grids

• anchored earth

In-Situ

Reinforcement

• soil nailing

• reticulated

 micro piles

• soil doweling

Braced

• cross-lot

• rakers

Tied-Back

• augured

• belled

• pressure-

 injected

HYBRID SYSTEMS — SPECIAL MATERIALS

• tailed gabions

• tailed masonry

• polymer-impregnated soil

• low density fills

 - low-density concrete

 - expanded polystyrene

Holtz and Schuster, 1996; modified from O’Rourke and Jones, 1990 

Figure 3-26. Classification scheme for earth retention systems. 

Holtz and Schuster, 1996; modified from O’Rourke and Jones, 1990 

Figure 3-27. Examples of externally and internally stabilized earth retention systems. 
136

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 3-28. 

Geosynthetic products such as geotextiles and geocomposites have been used for 

drainage and slope stabilization in several of the situations described above. Geotextiles 

have often been used as replacements of graded granular filters. Geocomposites have 

been installed in areas where access is difficult, behind retaining structures, and in other 

places where interception of seepage is desired. 

Other less common methods of improving drainage and controlling groundwater include: 

electro-osmosis, vacuum dewatering, siphon drains, and blasting of rock slopes. 

Toe

Drain

Horizontal

Gravity

Drains

Seal Surface Fractures

Vertical Gravity Drains

Pumped Wells

Upslope 

Drainage Ditches

Limestone Bedrock

Gedney and Weber, 1978 

Figure 3-28. Types of vertical and horizontal drains used to lower the 

groundwater in natural slopes. 

3.6. EXAMPLE PROBLEMS 

The following are three example cases that illustrate the screening and evaluation procedures 

described earlier in this chapter. Additional case examples may be found in Geotechnical 

Engineering Circular #3, Design Guidance: Geotechnical Earthquake Engineering for 

Highways, Volume II – Design Examples (Kavazanjian et al., 1997). 
137

EXAMPLE PROBLEM 3.1 – ROCKFALL HAZARD SCREENING, EVALUATION, AND 

RETROFIT 

This example presents the steps involved in screening and evaluating a site for potential earthquakeinduced rockfalls. The example problem is illustrated in accompanying sketches. 

a. Review of Available Information 

(1) Site conditions. A highway is located at the base of an approximately 15.2 m (50 ft) high slope 

cut into rock. The edge of the pavement and usable shoulder is 4.6 m (15 ft) back from the toe 

of the slope. The ratio of the slope width to the slope height is approximately 0.75:1 (H:V). 

Inspection of the face of the cut-slope indicates that the slope is stable. The natural slope 

surface located above the crest of the cut-slope is covered with rock rubble of varying sizes. 

The highway pavement is founded on competent rock. 

(2) Site history and seismic setting. Minor rockfalls have been known to periodically occur along 

this section of highway under static conditions. This site has been shaken in the past by several 

small earthquakes. Rockfalls have occurred following each of these events. Local seismicity 

indicates that the site is located in an area capable of experiencing moderate to large 

earthquakes (magnitude 6.5). Seismic landslide hazard maps have not been developed for this 

area. 

b. Earthquake-Induced Landslide Screening 

(1) To conclude that a landsliding hazard does not exist, each of the landslide screening criteria 

presented in section 3.3.1 must be satisfied. The site is not located in an area designated to 

have a high susceptibility to earthquake-induced landslides based on available maps. A field 

visit to the site identified rock rubble above the crest of the cut-slope that may indicate 

susceptibility to rockfalls. Review of historic site information indicates that rockfalls have been a 

problem in the past. The occurrence of rockfalls during past earthquakes and under static 

conditions indicate future susceptibility to earthquake-induced rockfalls. Thus, criterion “a” is not 

satisfied, indicating that further evaluation is required. 

c. Evaluation Procedures 

 Because rockfall shave occurred during historical seismic events, a clear hazard requiring remediation 

is indicated. Therefore, further hazard evaluations were not needed, and studies were made to identify 

an appropriate remediation method. 

1 ft = 0.305 m
138

d. Hazard Mitigation 

Given the site conditions, 

two retrofit approaches 

were considered (see 

sketch): (1) prevent 

rockfalls from reaching 

the highway by 

constructing a catchment 

ditch and (2) eliminate the 

hazard by rock removal. 

(1) Catchment ditch. 

The Richie (1963) 

method for 

estimating 

catchment ditch 

dimensions was used for this site (figure 3-22). For a slope height of 15.2 m (50 ft) and an 

inclination of 0.75 horizontal to 1 vertical, the Richie (1963) chart indicates that a ditch would 

need to be 4.6 m (15 ft) wide and 1.2 m (4 ft) deep to control the travel of falling rocks. This 

chart also indicates that given the slope geometry, a barrier fence between the ditch and the 

highway would not be necessary. Based on the chart, we chose to deepen the ditch to 1.2 m (4 

ft) below the highway surface. Fortunately, this section of highway was already constructed with 

a 4.6 m (15 ft) wide unused shoulder. Had less shoulder width been available, then the 

catchment ditch dimensions would have to be modified or an alternate remediation method 

considered. 

(2) Rock removal. Figure 3-22 illustrates an alternate rockfall mitigation approach in which the 

loose rock rubble located above the cut-slope is removed. Physical removal of the rubble is a 

very effective remediation approach because it essentially eliminates the hazard. However, this 

approach may be very expensive if the quantity of loose rock is large, access to the slope is 

difficult, or the site conditions are hazardous. 

1 ft = 0.305 m

4
139

EXAMPLE PROBLEM 3.2 – LANDSLIDE HAZARD SCREENING AND EVALUATION 

This example presents the steps involved in screening and evaluating a site for potential earthquakeinduced landsliding hazards. The example problem is illustrated in the accompanying sketch. 

a. Review of Available Information

(1) Soil conditions. A highway 

pavement is located 6.1 m (20 

ft) back from the crest of a12 m 

(40 ft) high slope (see sketch). 

The inclination of the slope is 

approximately 1.5:1 (H:V). Soil 

conditions at the site consist of 

clay with a uniform undrained 

shear strength (cohesion) of 

approximately 55.2 kPa 

(1150 psf) and a unit weight of 

18.0 kN/m3

 (115 pcf). Bedrock 

is located approximately 18m 

(60 ft) below the highway 

surface, and groundwater is not present at the site. 

(2) Historic earthquake effects and postulated earthquake parameters. This site has been shaken 

by several moderate earthquakes. However, no known historic information indicates that 

earthquake-induced landsliding occurred. Inspection of the site shows that the slope is stable 

under static conditions. Seismic landslide hazard maps have not been developed for this area. 

Site-specific analyses determined the MCE to have a moment magnitude of approximately 6.5 to 

produce a peak horizontal acceleration at the site of 0.40 g. The predominant period of the 

induced acceleration time history, To, was estimated to be 0.3 seconds. 

b. Earthquake-Induced Landslide Screening 

(1) To conclude that a landsliding hazard does not exist, each of the landslide screening criteria 

presented in section 3.3.1 must be satisfied. The stability of the slope during past earthquakes 

and present site conditions indicate no significant susceptibility to landsliding. The site is not 

located in an area designated to have a high susceptibility to earthquake-induced landsliding 

based on available maps. A field visit to the site identified several cracks at the crest of the 

slope that may indicate actual slope movement. Thus, criterion “a” is not satisfied, indicating 

further evaluation is required. 

c. Evaluation Procedures 

The general method for evaluating the seismic stability of slopes involves both pseudo-static and 

deformation analysis procedures, as illustrated below. 

(1) Pseudo-static slope stability analysis 

Pseudo-static slope stability analyses conservatively evaluate the potential for slope failure due 

to earthquake loading. If the results of the pseudo-static analysis indicate potential deformation 

of the slope (factor of safety < 1), a deformation analysis is performed to estimate the 

displacement. A static limit-equilibrium slope stability analysis performed for the site (not shown 

here, but following standard practice) determined that the critical failure surface would intersect 

the highway pavement (see sketch). This failure surface was then used for the pseudo-static 

slope stability analysis. The seismic coefficient was assumed to be equal to the peak horizontal 

γ

Clay

γ = 115 pcf

c = 1150 psf

(18 kN/m )

(55.2 kPa)

1 ft = 0.305 m

3
140

acceleration of 0.40 g. The results of the pseudo-static analysis indicate a marginal 

susceptibility to earthquake-induced landsliding with a factor of safety of 0.92. A deformation 

analysis was then performed to estimate the displacement. 

(2) Deformation analysis 

The deformation analysis procedure is based on Newmark’s (1965) concept of yield 

acceleration. For a specified potential sliding mass, the acceleration induced by the earthquake 

is compared with the yield acceleration. When the induced acceleration exceeds the yield 

acceleration, downslope movements will occur along the direction of the assumed failure plane. 

The movement will stop after the induced acceleration drops below the yield acceleration. 

a. Yield acceleration, ky. The yield acceleration is the acceleration at which the potential 

sliding surface would develop a factor of safety of unity. For this site, ky was determined to 

be 0.30 g by iteratively adjusting the seismic coefficient in the pseudo-static analysis until 

the factor of safety reached a value of unity. 

b. Peak or maximum acceleration, kmax. This parameter represents the peak or maximum 

acceleration induced within the sliding mass. kmax was assumed to be equal to the peak 

horizontal acceleration of 0.40 g. 

c. Acceleration ratio. The acceleration ratio is calculated by dividing the yield acceleration, ky, 

by the maximum acceleration, kmax. For this example, the acceleration ratio is equal to 

0.75. 

d. Deformation. Several simplified methods based on the concept of yield acceleration 

originally proposed by Newmark (1965) are utilized to estimate deformation (see table 

below). 

1. Makdisi and Seed (1978). The Makdisi and Seed (1978) method normalizes 

displacement by kmax, To, and gravity (figure 3.15). Based on the ratio of ky to kmax of 

0.75 and a moment magnitude of 6.5, the normalized displacement is equal to 

approximately 0.003 seconds (note that the units of seconds will be replaced by inches 

when the normalizing values are factored out). An estimated deformation of 0.4 cm 

(0.14 inches) was calculated by multiplying the normalized displacement by the values 

of kmax, To, and gravity. 

2. Franklin and Chang (1977). The range of the Franklin and Chang (1977) simplified 

method has a lower bound of 2.5 cm (one inch) of deformation (figure 3.16). The 

critical acceleration ratio of 0.75 is outside this range. However, judging from the trend 

of the curves, a deformation of less than 2.5 cm (one inch) can be assessed. 
141

3. Yegian et al. (1991). The Yegian et al. (1991) simplified method for estimating 

permanent deformation normalizes displacement by kmax, 2 To , number of cycles, and 

gravity (figure 3-17). A magnitude 6.5 earthquake contains approximately eight cycles 

(from Seed and Idriss, 1982). Based on the ratio of ky to kmax of 0.75, the normalized 

permanent deformation was estimated to be 0.001. An estimated deformation of 0.3 

cm (0.1 inch) was determined by multiplying the normalized displacement value of 

0.001 by the values of kmax, 2 To , number of cycles, and gravity. 

Method Estimated Deformation in cm (inches) 

Makdisi and Seed (1978) 0.35 (0.14) 

Franklin and Chang (1977) < 2.5 (< 1) 

Yegian et al. (1991) < 0.25 (0.1) 

d. Hazard Mitigation 

The amount of acceptable deformation is dependent on the tolerance of the pavement and acceptable 

damage. For this example problem, each deformation analysis method predicted less than 2.5 cm 

(one inch) of displacement. This magnitude of displacement was determined to be acceptable. Thus, 

stabilization methods were not needed at this site. 
142

EXAMPLE PROBLEM 3.3 – LANDSLIDE HAZARD SCREENING, EVALUATION, AND 

RETROFIT OF EMBANKMENTS 

This example presents the steps 

involved in screening, evaluating, 

and retrofitting a site for potential 

earthquake-induced landsliding 

hazards. The example problem 

is illustrated in accompanying 

sketches. 

a. Review of Available 

Information

(1) Soil conditions. A 6.1 m 

(20 foot) high highway 

embankment is 

constructed of poorly 

compacted fill material (see sketch). The inclination of the embankment slope is approximately 

1.5:1 (H:V). The native foundation materials are dense and stable. Groundwater is not present 

at the site. The embankment does show some signs of settlement and cracking. 

(2) Historic earthquake effects and earthquake parameters. Since the highway was constructed, 

this site has not been shaken by any moderate to large earthquakes. Inspection of the site 

shows that the slope is stable under static conditions. Site-specific analyses determined the 

MCE to have a moment magnitude of approximately 7.5 and a peak horizontal acceleration of 

0.50 g. The predominant period of the induced acceleration time history, To, was estimated to 

be 0.3 seconds. 

b. Earthquake-Induced Landslide Screening 

(1) To conclude that a landsliding hazard does not exist, each of the landslide screening criteria 

presented in section 3.3.1 must be satisfied. Because this is a man-made embankment, general 

screening criterion “e” is particularly applicable. The settlement and cracking observed in the 

embankment indicate that the embankment is constructed of poorly compacted fill or is underlain 

by poor foundation materials. Thus, criterion “e” is not satisfied, indicating that further evaluation 

is required.

c. Evaluation Procedures 

The general method for evaluating the seismic stability of slopes involves both pseudo-static and 

deformation analysis procedures, as illustrated below. 

(1) Pseudo-static slope stability analysis 

Pseudo-static slope stability analyses conservatively evaluate the potential for slope failure due 

to earthquake loading. If the results of the pseudo-static analysis indicate a factor of safety < 1, 

a deformation analysis is performed to estimate the displacement. A static limit-equilibrium 

slope stability analysis performed for the site determined that the critical failure surface would 

intersect the highway pavement (see sketch). This failure surface was then used for the 

pseudo-static slope stability analysis. The seismic coefficient was assumed to be equal to the 

peak horizontal acceleration of 0.50 g. The results of the pseudo-static analysis indicate a 

(22 kN/m )

(9.6 kPa)

(19 kN/m )

(7.7 kPa)

(21.2 kN/m )

(38 kPa)

3

3

3

1 ft = 0.305 m
143 

significant susceptibility to earthquake-induced landsliding with a factor of safety of 0.58. A 

deformation analysis was then performed to estimate the displacement. 

(2) Deformation analysis 

The deformation analysis procedure is based on Newmark’s (1965) concept of yield 

acceleration. For a specified potential sliding mass, the acceleration induced by the earthquake 

is compared with the yield acceleration. When the induced acceleration exceeds the yield 

acceleration, downslope movements will occur along the direction of the assumed failure plane. 

The movement will stop after the induced acceleration drops below the yield acceleration. 

(a) Yield acceleration, ky. The yield acceleration is the acceleration at which the potential sliding 

surface would develop a factor of safety of unity. For this site, ky was determined to be 0.12 g 

by iteratively adjusting the seismic coefficient in the pseudo-static analysis until the factor of 

safety reached a value of unity. 

(b) Peak or maximum acceleration, kmax. This parameter represents the peak or maximum 

acceleration induced within the sliding mass. kmax was assumed to be equal to the peak 

horizontal acceleration of 0.50 g. 

(c) Acceleration ratio. The acceleration ratio is calculated by dividing the yield acceleration, ky, 

by the maximum acceleration, kmax. For this example, the acceleration ratio is equal to 0.24. 

(d) Deformation. Several simplified methods based on the concept of yield acceleration 

originally proposed by Newmark (1965) are utilized to estimate deformation (see table 

below). 

1. Makdisi and Seed (1978). The Makdisi and Seed (1978) method normalizes 

displacement by kmax, To, and gravity (figure 3-15). Based on the ratio of ky to kmax of 

0.24 and a moment magnitude of 7.5, the normalized displacement is equal to 

approximately 0.21 seconds (note that the units of seconds will be replaced by 

inches when the normalizing values are factored out). An estimated deformation of 

31 cm (12 inches) was calculated by multiplying the normalized displacement by the 

values of kmax, To, and gravity. 

2. Franklin and Chang (1977). The range of the Franklin and Chang (1977) simplified 

method provides upper bound estimates of permanent ground deformation (figure 

3-16). For the critical acceleration ratio of 0.24 and using the curve based on all 

natural earthquake records, an estimated upper bound deformation of 81 cm (32 in) 

was calculated. 
144 

3. Yegian et al. (1991). The Yegian et al. (1991) simplified method for estimating 

permanent deformation normalizes displacement by kmax, 2 To , number of cycles, and 

gravity (figure 3-17). A magnitude 7.5 earthquake contains approximately fifteen 

cycles (from Seed and Idriss, 1982). Based on the ratio of ky to kmax of 0.24, the 

normalized permanent deformation was estimated to be 0.04. An estimated 

deformation of 26.5 cm (10 in) was determined by multiplying the normalized 

displacement value of 0.04 by the values of kmax, 2 To , number of cycles, and gravity. 

Method Estimated Deformation in cm (inches) 

Makdisi and Seed (1978) 30 (12) 

Franklin and Chang (1977) 80 (32) 

Yegian et al. (1991) 35 (10) 

d. Hazard Mitigation 

The amount of acceptable deformation is dependent on the tolerance of the pavement and acceptable 

damage. For this example problem, the deformation analysis methods predicted deformations 

between 26.5 and 81 cm (10 and 32 in). This magnitude of displacement was determined to be 

unacceptable. Thus, retrofitting was necessary at this site. 

Several retrofitting approaches were considered. Based on availability of materials, economics, and 

other factors, the construction of a rock buttress appeared to be the most feasible. Pseudo-static 

slope stability analyses of the embankment as described above were repeated with rock buttresses of 

varying dimensions. The rock buttress served to increase the resisting forces along the slide plane 

and to force the critical failure surface to exit the embankment above the top of the rock buttress (see 

sketch). By forcing the critical failure surface to exit above the rock buttress, the mass of sliding 

material decreases substantially, resulting in reduced permanent ground deformation. The final 

dimensions of the rock buttress were 3 m (10 ft) in height and 2.4 m (8 ft) wide at the top with a 2:1 

(H:V) slope of the outer surface. For the improved embankment, the estimated earthquake-induced 

displacement is less than 8 cm (3 in). 

(18.9 kN/m ) 3

1 ft = 0.305 m
145

CHAPTER 4: TUNNELS 

4.1. INTRODUCTION 

This chapter describes procedures for the seismic screening and evaluation of tunnels and 

discusses strategies for seismic retrofit design of tunnels. In general, tunnels have performed 

well during earthquakes in comparison to the performance of aboveground structures. This can 

be attributed to the fact that a fully embedded tunnel tends to move with the ground and, in 

general, does not experience the strong inertial response of aboveground structures. The fact that 

the amplitude of seismic ground motion tends to reduce with depth below the ground surface 

also reduces tunnel damage. 

Nevertheless, moderate to major damage has been experienced by many tunnels during 

earthquakes, as summarized by Dowding and Rozen (1978), Owen and Scholl (1981), Sharma 

and Judd (1991), and Power et al. (1998), among others. The greatest incidence of severe 

damage has been associated with large ground displacements due to ground failure, i.e., fault 

rupture through a tunnel, landsliding (especially at tunnel portals), and soil liquefaction. Ground 

shaking in the absence of ground failure has produced a lower incidence and degree of damage 

in general, but has resulted in moderate to major damage to many tunnels. Near-surface 

rectangular cut-and-cover tunnels in soil have been especially vulnerable to transient seismic 

lateral ground displacements, which tend to cause racking of a tunnel over its height and 

increased lateral pressures on the tunnel walls. 

Some tunnels constitute a non-redundant transportation corridor that may be essential in the 

post-earthquake environment, e.g., highway and transit tunnels. Application of the guidelines 

for screening, detailed evaluation, and, where necessary, retrofit design of tunnels presented in 

this chapter can aid in identifying and mitigating life safety hazards in ordinary tunnels or loss of 

functionality in an essential or critical tunnel. 

4.2. TUNNEL CLASSIFICATION 

Tunnels can be grouped into three broad categories: (1) bored tunnels; (2) cut-and-cover tunnels; 

and (3) submerged tubes. These categories of tunnels exhibit distinctly different design features 

and construction methods. 

4.2.1. BORED TUNNELS 

Bored (or mined) tunnels are constructed by excavating the opening and constructing the support 

system below ground. These tunnels may be constructed in a variety of geologic environments 

ranging from hard rock to soft soils. Construction procedures involve the use of tunneling 

machines, drilling and blasting, and other techniques. The initial, primary, or temporary 
146

lining/support system is usually constructed as the tunnel is excavated. The cross sectional 

shape of the tunnel is usually circular or semi-circular (e.g., horseshoe-shaped; straight-sided 

with semicircular dome). The New Austrian Tunneling Method (NATM) (Rabcewicz, 1964) of 

tunnel construction utilizes construction and initial support methods that limit the amount of 

ground deformation and dilation and enhance the ability of the ground to arch and support itself 

by forming a ground arch reinforced with structural elements. Based upon convergenceconfinement theory (AFTES, 1978), the NATM has been successfully used in many ground 

conditions. In weak or fractured rock, it essentially consists of installing supports in a timely 

manner before (presupport) or soon after excavation, such as the installation of rock dowels and 

shotcrete support immediately following a short (2 to 4 feet) advance of the excavation face. 

4.2.1.1. Bored Tunnels in Soft Ground 

Soft ground tunnels are constructed by either two-pass or one-pass lining methods. In the twopass method, the initial support system may consist of steel ribs and lagging, liner plate, or 

precast segmented lining. The final support system consists of a cast-in-place concrete liner. In 

the one-pass system, the liners are typically bolted and gasketed, precast segmented liners. 

4.2.1.2. Bored Tunnels in Rock 

Tunnels in rock have methods of support that vary from none (in massive hard rock) to a 

temporary rib and lagging liner followed by a cast-in-place concrete final liner. Rock dowels or 

rock bolts are often installed as the excavation progresses to aid in allowing the rock to support 

itself and to stabilize loose blocks of rock in the vicinity of the opening. 

4.2.2. CUT-AND-COVER TUNNELS 

Cut-and-cover tunnels are constructed by excavating the opening from the ground surface, 

constructing the tunnel structure within the excavated opening, and backfilling above the top of 

the structure, as well as adjacent to the sides of the structure if it has not been constructed 

immediately against the excavation face. This method of construction is often used for relatively 

shallow tunnels (< 50 feet). The tunnel structure is typically rectangular in shape and of cast-inplace reinforced concrete construction. 

4.2.3. SUBMERGED TUBES 

Submerged tubes are constructed of prefabricated steel or concrete sections placed in shallowly 

excavated trenches on river and sea bottoms. These segments are floated into position and then 

sunk and connected. The trench is then backfilled and the tube covered. To overcome 

buoyancy, submerged tubes typically have enlarged cross sections for increased mass. Tube 

cross sections may be circular or rectangular (figure 4-1). 
147

Ballast Ballast

Multi-Lane

Concrete Box

Steel Shell

Typical 2-Lane

Double Steel Shell

Double Steel Shell

Fort McHenry

Tunnel, Baltimore

Steel Shell

Single Steel Shell

Steel shell

Typical 2-Lane

Concrete Box

Gursoy, 1985 

Figure 4-1. Cross sections of submerged tubes. 

4.3. SCREENING GUIDELINES 

4.3.1. OBJECTIVE OF SCREENING STAGE 

The objective of the screening stage is to identify tunnels that have a substantial risk of poor 

performance during the design earthquake(s). The potential outcomes of the screening process 

are: (1) the tunnel is expected to meet the performance objective during the design earthquake(s) 

(see chapter 1), and no further evaluations of the tunnel are required; (2) the tunnel may not meet 

the performance objective, and further evaluations are needed to assess performance; and (3) the 

tunnel clearly does not meet the performance objectives, and retrofit measures are required. For 

tunnels identified through the screening process as falling into categories (2) or (3), the decision 

as to whether to conduct further evaluations and retrofit design, and the priority for such actions, 

depends on the importance of the tunnel as established by the responsible agency (see chapter 1). 
148

4.3.2. FACTORS INFLUENCING TUNNEL SEISMIC PERFORMANCE 

Various factors may influence tunnel seismic performance. These factors are described briefly 

below. Guidelines for considering these factors in screening-level evaluations are presented in 

section 4.3.3. 

4.3.2.1. Seismic Hazard 

Components of seismic hazard that may influence tunnel performance include: 

• Intensity of Ground Shaking. The potential effects of vibratory ground shaking range from 

minor cracking of a concrete liner to collapse of the liner (if present) and major caving of 

geologic materials into the tunnel. For purposes of evaluating tunnel performance, the 

intensity of ground shaking is typically quantified by peak ground acceleration (PGA), peak 

ground velocity (PGV), peak ground displacement (PGD), and strong motion duration. For 

screening-level evaluations, PGA at the ground surface is usually used as an index of the 

shaking intensity, since acceleration is the parameter usually recorded and most readily 

estimated. For more detailed evaluations, ground motions at the depth of the tunnel and 

frequency content (response spectra) may also be estimated. In addition, for tunnels located 

close to active faults (within approximately 15 km), the unique characteristics of near-fault 

ground motion may become important, especially the possible presence of strong long-period 

pulses of ground motion that can lead to high ground acceleration, velocity, and 

displacement that may be especially damaging. 

• Fault Rupture. If an active fault crosses the tunnel alignment, there is a hazard of direct, 

shearing displacement though the tunnel in the event of a moderate to large magnitude 

earthquake. Such displacements may range from a few inches to greater than ten feet and, in 

many cases, may be concentrated in a narrow zone along the fault. Fault rupture can and has 

had very damaging effects on tunnels. A related hazard is tectonic uplift and subsidence, if 

such movements cause enough differential deformation of the tunnel to be damaging. 

• Landsliding. Landsliding through a tunnel, whether statically or seismically induced, can 

result in large, concentrated shearing displacements and either full or partial collapse of 

tunnel cross sections. Landslide potential is greatest when a preexisting landslide mass 

intersects the tunnel. A statically stable landslide mass may be activated by earthquake 

shaking. The hazard of landsliding is usually greatest in shallower parts of a tunnel 

alignment and at tunnel portals. 

• Soil Liquefaction. For tunnels located in soils below the groundwater table, there could be a 

potential for liquefaction if loose to medium-dense cohesionless soils (sands, silts, gravels) 

are adjacent to the tunnel. Potential effects of liquefaction of soils adjacent to a tunnel 

include: (a) increased lateral pressures on the lining or walls of the tunnel, which could lead 

to failure of the lining or walls depending on their design; (b) flotation or sinking of a tunnel 

embedded in liquefied soil, depending on the relative weight of the tunnel and the soils 

replaced by the tunnel; and (c) lateral displacements of a tunnel if there is a free face toward 

which liquefied soil can move and/or if the tunnel is constructed below sloping ground. 
149

4.3.2.2. Geologic Conditions 

Potentially hazardous geologic conditions include fault rupture or tectonic uplift and subsidence, 

landslides, and liquefiable soils as discussed above. In addition, other unfavorable geologic 

conditions could lead to unsatisfactory seismic tunnel performance unless recognized and 

adequately accounted for in the tunnel design and construction. Unfavorable geologic conditions 

include: soft soils; rocks with weak planes intersecting a tunnel, such as shear zones or well 

developed weak bedding planes and well developed joint sets that are open or filled with 

weathered and decomposed rock; failures encountered during tunnel construction that may have 

further weakened the geologic formations adjacent to a tunnel (e.g., cave-ins or running ground 

leaving incompletely filled voids or loosened rock behind a lining; squeezing ground with 

relatively low static factor of safety against lining collapse); and adjacent geologic units having 

major contrast in stiffness that can lead to stress concentrations or differential displacement. 

4.3.2.3. Tunnel Design, Construction, and Condition 

Elements of tunnel design, construction, and condition that may influence tunnel seismic 

behavior include: (1) whether seismic loadings and behavior were explicitly considered in tunnel 

design; (2) the nature of the tunnel lining and support system (e.g., type of lining, degree of 

contact between lining/support systems and geologic material, use of rock bolts and dowels); (3) 

junctions of tunnels with other structures; (4) history of static tunnel performance in terms of 

failures and cracking or distortion of lining/support system; and (5) current condition of 

lining/support system, such as degree of cracking of concrete and deterioration of concrete or 

steel materials over time. 

In evaluating an existing tunnel in the screening stage or in a more detailed evaluation, or in 

designing retrofit measures, it is important to obtain as complete information as possible on the 

tunnel design, construction, and condition and the geologic conditions along the tunnel 

alignment. To obtain this information, the design and evaluation team should review the design 

drawings and design studies, as-built drawings, construction records as contained in the 

construction engineer daily reports and any special reports, maintenance and inspection records, 

and geologic and geotechnical reports and maps. Special inspections and investigations may be 

needed to adequately depict the existing conditions and determine reasons for any distress to the 

tunnel. 

4.3.3. SCREENING GUIDELINES 

4.3.3.1. Screening Guidelines Applicable to All Types of Tunnels 

There are certain conditions that would clearly indicate a potentially significant seismic risk to a 

bored tunnel, cut-and-cover tunnel, or submerged tube and thus require more detailed 

evaluations. These conditions include: 

• An active fault intersecting the tunnel. 

• A landslide intersecting the tunnel, whether or not the landslide is active. 
150

• Liquefiable soils adjacent to the tunnel. 

• History of static distress to the tunnel (e.g., local collapses, large deformations, cracking or 

spalling of the liner due to earth movements), unless retrofit measures were taken to stabilize 

the tunnel. 

4.3.3.2. Additional Screening Guidelines for Bored Tunnels 

If the above conditions do not exist, then the risk to a bored tunnel is a function of the tunnel 

design and construction, the characteristics of the geologic media, and the level of ground 

shaking. In this section, additional screening guidelines are presented considering these factors 

and empirical observations of tunnel performance during earthquakes. 

Figure 4-2 presents a summary of empirical observations of the effects of seismic ground 

shaking on the performance of bored tunnels. The figure is from the study by Power et al. 

(1998), which updates earlier presentations of tunnel performance data by Dowding and Rozen 

(1978), Owen and Scholl (1981), and Sharma and Judd (1991). The data are for damage due 

only to shaking. Damage that was definitely or probably attributed to fault rupture, landsliding, 

and liquefaction is not included. The data are for bored tunnels only; data for cut-and-cover 

tunnels and submerged tubes are not included in figure 4-2. 

Figure 4-2. Summary of empirical observations of seismic ground shaking 

induced damage to bored tunnels. 
151

Figure 4-2 incorporates observations for 192 tunnels from ten moderate to large magnitude 

earthquakes (moment magnitude MW 6.6 to 8.4) in California, Japan, and Alaska. Note that many 

of the points in the figure represent multiple observations (i.e., the same damage state, lining 

types, and estimated acceleration for different tunnels). Ninety-four of the observations are from 

the moment magnitude MW 6.9 1995 Kobe, Japan, earthquake. This earthquake produced by far 

the most observations for moderate to high levels of shaking (estimated peak ground 

accelerations [PGAs] at ground surface above the tunnels in the range of about 0.4 g to 0.6 g for 

the Kobe data). Peak ground accelerations in figure 4-2 are estimated for actual or hypothetical 

outcropping rock conditions at ground surface above the tunnel. Other observations are from 

moderate to large (MW 6.7 to 8.4) earthquakes in California and Japan. The complete database is 

presented in Power et al. (1998). Figure 4-2 shows the level of damage induced in tunnels with 

different types of linings subjected to the indicated levels of ground shaking. Damage was 

categorized into four states: none for no observable damage; slight for minor cracking and 

spalling; moderate for major cracking and spalling, falling of pieces of lining and rocks; and 

heavy for major cave-ins, blockage, and collapse. The figure indicates the following trends: 

• For PGAs equal to or less than 0.2 g, ground shaking caused very little damage in tunnels. 

• For PGAs in the range of about 0.2 g to 0.5 g, there are some instances of damage ranging 

from slight to heavy. Note that the three instances of heavy damage are all from the 1923 

Kanto, Japan, earthquake. For the 1923 Kanto earthquake observations with PGA equal to 

0.25 g shown on figure 4-2, the investigations for this tunnel indicated the damage may have 

been due to landsliding. For the other two Kanto earthquake observations, collapses 

occurred in the shallow portions of the tunnels. 

• For PGAs exceeding about 0.5 g, there are a number of instances of slight to moderate 

damage (and one instance of heavy damage noted above for the Kanto earthquake). 

• Tunnels with stronger linings appear to have performed better, especially those tunnels with 

reinforced concrete and/or steel linings. 

The trends in figure 4-2 can be used as one guide in assessing the need for further evaluations of 

the effects of ground shaking on bored tunnels. 

Guidelines for assessing the need for further evaluations of bored tunnels for the failure mode of 

ground shaking induced damage are presented in table 4-1. The following are examples of poor 

and good lining/support systems for use with table 4-1. 

Poor lining/support system: 

• Timber or unreinforced masonry lining. 

• Unreinforced concrete in soil or very poor rock. 
152

Table 4-1. Assessment of need for seismic evaluations of bored tunnels as related to 

tunnel lining/support system, geologic conditions, and level of ground shaking. 

Geologic Conditions 

Lining/Support System 

Soil or Extremely 

Poor Rock 

Sheared and 

Jointed Rock 

Sound Rock 

Unlined A B C 

Poor lining/support system A B C 

Good lining/support system C C D 

A Evaluation desirable for any ground shaking level. 

B Evaluation desirable for moderate shaking levels, PGA > 0.2 g. 

C Evaluation desirable for high ground shaking levels PGA > 0.5 g. 

D No evaluation needed for any ground shaking level.

• Lining/support system in poor condition (e.g., deteriorated or otherwise weak concrete; 

moderately to severely cracked concrete; moderately to severely corroded metal 

linings/support systems). 

• Linings in poor contact with geologic materials (frequent voids between lining and geologic 

materials). 

Good lining/support system: 

• Linings specifically designed for seismic loading consistent with the seismic environment of 

the tunnel, geologic conditions, and good seismic design practice. 

• Reinforced concrete or steel liners in good contact with geologic materials. 

• Unreinforced concrete liners in good contact with fair to good rock; rock dowels or rock 

bolts providing arch support. 

Consistent with the criteria in section 1.2 of this manual, the guidelines in table 4-1 are for a 

performance objective of life safety and collapse prevention for non-critical tunnels during an 

upper-level rare earthquake. More conservative guidelines may be appropriate for critical or 

essential tunnels that have functionality performance objectives. 

Table 4-1 does not explicitly cover tunnel connections with other structures. If a connection has 

been well designed to transmit forces or to accommodate displacements, it may be screened on 

the basis of the third line in table 4-1. However, if the strength or displacement capacity of a 

connection is questionable, the connection should be screened on the basis of the second line in 

the table. 
153

4.3.3.3. Additional Screening Guidelines for Cut-and-Cover Tunnels 

The seismic performance of shallow cut-and-cover box-like tunnels has been relatively poor in 

comparison to the performance of bored tunnels. This was especially evident during the 1995 

Kobe, Japan, earthquake (O’Rourke and Shiba, 1997; Power et al., 1998). The relatively poor 

performance of cut-and-cover tunnels may reflect: (1) relatively softer near-surface geologic 

materials surrounding these types of structures as compared to the harder materials that often 

surround bored tunnels at greater depths; (2) higher levels of acceleration at and near the ground 

surface than at depth (due to tendencies for vibratory ground motions to reduce with depth below 

the ground surface); and (3) vulnerability of these box-like structures to seismically induced 

racking deformations of the box cross section (figure 4-3d), unless specifically designed for 

these forces. Cut-and-cover tunnels in soil (the more common geologic condition for these types 

of tunnels) tend to be more vulnerable than those excavated into rock because of the larger soil 

shear deformations causing the tunnel racking. Tunnels in soft soil may be especially 

vulnerable. The most important determinant in assessing whether more detailed seismic 

evaluations of cut-and-cover tunnels are required is whether the original design considered 

loadings and deformations consistent with the seismic environment and geologic conditions, and 

especially, whether racking behavior was taken into account in the seismic analysis, design, and 

detailing of the structure. 

4.3.3.4. Additional Screening Guidelines for Submerged Tubes 

Submerged tubes are particularly susceptible to permanent ground movements during seismic 

shaking. Tubes are typically located at shallow depths and in soft or loose soils. Liquefaction of 

loose cohesionless soils may cause settlement, uplift (flotation), or lateral spreading. 

Earthquake shaking may also cause permanent displacement of soft clay soils on sloping ground. 

Joints connecting tube segments must accommodate the relative displacement of adjacent 

segments while maintaining a watertight seal. Generally, submerged tubes can be screened out 

from more detailed evaluations if the original design appropriately considered and analyzed the 

potential for ground failure modes and if joints have been carefully designed to achieve water 

tightness. 

4.4. EVALUATION PROCEDURES 

Described in this section are procedures for the detailed evaluation of tunnels for seismic 

loading. Procedures for evaluating tunnels for vibratory ground shaking are presented in section 

4.4.1. Procedures for the evaluation of tunnels for the hazards of fault rupture displacement, 

landsliding, and liquefaction are presented in sections 4.4.2 and 4.4.3. 

4.4.1. EVALUATION FOR GROUND SHAKING 

4.4.1.1. General 

When a tunnel is subjected to seismic waves, two principal types of deformation occur. The first 

type consists of deformations occurring along the longitudinal axis of the tunnel, which include 
154

both axial and curvature deformations. The second is deformations perpendicular to the tunnel 

longitudinal axis in the plane of the tunnel cross section. Figure 4-3 shows these principal types 

of deformation. 

Axial and curvature deformations are induced by components of seismic waves that propagate 

along the tunnel longitudinal axis (Newmark, 1967; Keusel, 1969; Yeh, 1974; St. John and 

Zahrah, 1987). Axial deformations are generated by the components of seismic waves that 

produce particle motions parallel to the longitudinal axis of the tunnel and cause alternating 

compression and tension (figure 4-3a). Components of seismic waves producing particle 

motions in directions perpendicular to the longitudinal axis cause curvature (figure 4-3b). 

Seismic waves propagating perpendicular to the tunnel longitudinal axis in the plane of the 

tunnel cross section distort the cross sectional shape of the structure, resulting in “ovaling” 

deformations of a circular (or semicircular) tunnel cross section (figure 4-3c) and “racking” 

deformations of a rectangular cross section (figure 4-3d). 

Wang, 1993; Owen and Scholl, 1981 

Figure 4-3. Tunnel response to seismic waves. 
155

Both axial and curvature deformations along the tunnel longitudinal axis and ovaling and racking 

deformations of the tunnel cross section can produce significant damage to tunnels. Gross 

instabilities of the tunnel, involving shaking-induced caving of geologic materials into the 

tunnel, would generally be associated with inertial forces acting in the plane of the tunnel cross 

section. Therefore, assessment of the potential for inertial force-induced caving into tunnels is 

addressed as part of the evaluation procedures for tunnel cross sectional deformation. 

The procedures described in subsequent sections provide methods for evaluating shakinginduced strains and stresses in a tunnel. They must be combined with the preexisting static 

strains and stresses in assessing the effects of earthquake shaking on tunnel performance. The 

assessment of static loads is described in tunnel design manuals and other publications, e.g., U.S. 

Army Corps of Engineers (1997). The strains and stresses induced in a tunnel must be assessed 

relative to the adopted performance criterion or criteria. For a life safety/collapse prevention 

performance criterion during an upper-level or “maximum” earthquake, strains beyond the 

elastic range may be acceptable; their effects should be evaluated by structural engineers who are 

knowledgeable in inelastic structural behavior. 

4.4.1.2. Broad Guidelines for Analyses for Ground Shaking

This section provides broad guidelines for the application and relative importance of different 

types of analyses for ground shaking. These are grouped below into (1) analyses for axial and 

curvature deformations along the tunnel longitudinal axis, and (2) analyses of tunnel cross 

sectional response. Then in sections 4.4.1.3 and 4.4.1.4, the analysis methods and their 

applications are described in detail. 

• Evaluation of axial and curvature deformations along tunnel longitudinal axis (section 4.4.1.3 

below). 

- Simplified Analyses (section 4.4.1.3(a)). Free-field analyses described in section 

4.4.1.3(a) below should be conducted. An important component of the evaluation is a 

seismological assessment of the type of seismic wave field (body S-waves or surface Rwaves) that could be present and govern tunnel response. Generally, S-waves would not 

result in excessive strains and stresses in a tunnel, but R-waves in basin environments 

could be more damaging if associated with strong ground motions. 

Although simplified soil-tunnel interaction formulations are also presented in section 

4.4.1.3(a), these are generally not recommended to be applied because reductions in 

response due to interaction may not be justified because of uncertainties associated with 

simplified interaction formulations as well as ground motion phenomena neglected in 

simplified approaches (i.e., ground motion incoherence described in section 4.4.1.3). 

- Numerical Analyses (section 4.4.1.3(b)). More sophisticated numerical analysis 

methods should be considered if simplified approaches are inconclusive. These 

approaches should especially be considered for situations where a tunnel abuts structures 

of significantly different response characteristics such as a portal structure, ventilation 

structure, or transit station. 
156

• Evaluation of deformations of tunnel cross section (section 4.4.1.4 below). 

- Simplified Analyses (section 4.4.1.4(a)). Except for critical junctions of a tunnel to 

other structures, the deformations of a tunnel cross section are likely to be a more 

important mode of response than axial and curvature deformations along the longitudinal 

axis. Generally, simplified analyses methods described in section 4.4.1.4(a) below 

should be sufficient to check stability of cross sections against local failure of the lining 

in weak soil or rock zones or to analyze for the response modes of ovaling or racking of 

the tunnel cross section. For shallow rectangular cut-and-cover tunnels, seismic earth 

pressure analyses should also be conducted. However, simplified earth pressure 

analyses involve more uncertainty than simplified racking analyses. 

- Numerical Analyses (section 4.4.1.4(b)). Numerical analysis methods should be 

considered in cases where simplified analysis methods are less applicable, more 

uncertain, or inconclusive, such as earth pressures against rectangular structures, or 

where case history data indicate relatively higher seismic vulnerability for the type of 

tunnel, such as rectangular cut-and-cover tunnels. 

4.4.1.3. Evaluation of Axial and Curvature Deformations along the Longitudinal Tunnel 

Axis 

Two levels of analytical approaches are described below: simplified or closed-form solutions, 

and numerical analysis methods. Figure 4-4 summarizes methods for analyzing axial and 

curvature deformations. 

It should be noted that simplified approaches typically incorporate the assumption that the 

seismic wave field along a tunnel is that of plane waves in which the waves have the same 

amplitudes at different locations along the tunnel and differ only in their arrival time. Numerical 

analysis methods may incorporate the same assumptions. However, if local soil conditions would 

lead to differential soil amplification along a tunnel, these effects would typically be 

incorporated in numerical analyses. 

Wave-scattering and complex three-dimensional wave propagation, which can lead to 

differences in wave amplitudes along a tunnel, have been neglected in practice. These 

differences, termed ground motion incoherence (refer, for example, to Abrahamson et al., 1987; 

Abrahamson, 1993) would tend to increase strains and stresses in the longitudinal direction. For 

example, figure 4-5, from Abrahamson (1993), illustrates that at shorter separation distances, 

strains associated with incoherence may equal or exceed those due to plane wave propagation 

(termed wave passage in figure 4-5). However, the effects of incoherence on tunnel response has 

not yet been systematically studied. Therefore, until guidance on the effects of incoherence is 

developed, the results of simplified analyses based on plane wave assumptions should be 

interpreted conservatively. The effects of incoherence and variable geology on tunnel response 

can be modeled using numerical analyses if warranted. 
157

Simplified /

Closed-form

Solutions

Numerical

Analysis

Free-Field

Effects of 

Soil-tunnel

Interaction

Axial and

Curvature

Deformations

Figure 4-4. Approaches for analyzing a tunnel for longitudinal axial and 

curvature deformations. 

4.4.1.3(a). Simplified Analyses/Closed-Form Solutions

In many cases, tunnels can be considered flexible in response to axial and curvature 

deformations. In these cases, strains and stresses are estimated using free-field solutions, 

assuming that the tunnel conforms to the imposed deformations from the surrounding geologic 

media. Soil-tunnel interaction may reduce response relative to free-field solutions. Simplified 

analyses for soil-structure interaction are addressed in the section following the presentation of 

the free-field solutions below. 

Free-field Solutions: Table 4-2 summarizes the axial and shear strains and bending curvature 

generated by seismic waves propagating at an angle φ in the horizontal plane with respect to the 

longitudinal axis of a tunnel (figure 4-6). Equations are given in table 4-2 for strains due to 

compressional (P) and shear (S) body waves and Rayleigh (R) surface waves, and each strain 

reaches its maximum value at a different φ angle, as shown in the table. Axial strains rather 

than shear strains are typically of primary significance in tunnel design and performance. In the 

absence of significant surface waves, S-waves typically cause the largest strains and are the 

governing wave type. Strains induced by P-waves generally do not govern. Under certain 

circumstances, R-waves may result in the highest strains and should be considered in design. 

Figure 4-7 illustrates axial force, shear forces, and moments induced in a tunnel by components 

of seismic waves propagating in the direction of the tunnel longitudinal axis. 
158

Abrahamson, 1993 

Figure 4-5. Example of maximum relative displacements associated with 

seismic wave propagation. The effects of wave passage and incoherency 

are shown separately and combined. The dashed lines correspond to 

constant strains of 10-3 and 10-4. 

P-waves

S-waves

R-waves

x

y

z

Figure 4-6. Seismic waves causing longitudinal axial and bending strains. 
159

Table 4-2. Strains and curvature induced by seismic wave propagating along a tunnel. 

Wave Type Axial Strain Shear Strain Curvature 

P 2

P

V

cos

C

ε = φ P

P

V sin cos

C γ = φ φ P 2

2

P

1 a sin cos

C = φ φ

ρ

P-wave 

P max

P

V for 0

C

ε = φ = ° P max

P

V for 45

2C γ = φ= ° P

2 max P

1 a 0.385 for 35.27

C = φ = °

ρ

S

S

V sin cos

C

ε = φ φ S 2

S

V

cos

C γ = φ S 3

2

S

1 a

cos

C = φ

ρ

S-wave 

S max

S

V for 45

2C

ε = φ= ° S max

S

V for 0

C γ = φ = ° S

2 max S

1 a for 0

C = φ = °

ρ

R 2

R

V

cos

C

ε = φ R

R

V sin cos

C γ = φ φ R 2

2

R

1 a sin cos

C = φ φ

ρ

Compressional 

Component 

R max

R

V for 0

C

ε = φ= ° R max

R

V for 45

2C γ = φ = ° R

2 max R

1 a 0.385 for 35.27

C = φ = °

ρ

R

R

V

cos

2C γ = φ R 2

2

R

1 a

cos

C = φ

ρ

R-wave 

Shear 

Component 

R max

R

V for 0

C γ = φ = ° R

2 max R

1 a for 0

C = φ = °

ρ

where: 

 VP = soil particle velocity caused by P-waves 

aP = soil particle acceleration caused by P-waves 

CP = apparent propagation velocity of P-waves 

VS = soil particle velocity caused by S-waves 

aS = soil particle acceleration caused by S-waves 

CS = apparent propagation velocity of S-waves 

VR = soil particle velocity caused by R-waves 

aR = soil particle acceleration caused by R-waves 

CR = propagation velocity of R-waves 

1/ρ = curvature

St. John and Zahrah, 1987; and Yeh, 1974 
160

Figure 4-7. Induced forces and moments caused by seismic waves propagating along 

the longitudinal tunnel axis. 

Strains and stresses due to combined axial and curvature deformations can be obtained by 

treating the tunnel as an elastic beam. Using beam theory, the maximum axial strain, ε ab, is 

given by combining the axial strains generated by longitudinal deformations and curvature 

deformations in a horizontal plane: 

ab 2 2 P P

2

P P

V a cos Y sin cos

C C

⎡ ⎤

ε = ⎢ ⎥ φ + φ φ

⎣ ⎦

 for P-waves (4-1) 

ab 3 S S

2

S S

V a sin cos Y cos

C C

⎡ ⎤

ε = ⎢ ⎥ φ φ + φ

⎣ ⎦

 for S-waves (4-2) 

ab 2 2 R R

2

R R

V a cos Y sin cos

C C

⎡ ⎤

ε = ⎢ ⎥ φ + φ φ

⎣ ⎦

 for R-waves (4-3) 

Within the elastic range, the axial stress due to combined axial and curvature deformations is: 

ab ab σ= ε El for P-, S-, and R-waves (4-4) 
161

where: 

Y is the distance from the neutral axis of the cross section to the extreme fiber of the 

tunnel lining, 

E1 is the Young’s modulus of tunnel lining, 

aP is the peak particle acceleration associated with P-wave, 

aS is the peak particle acceleration associated with S-wave, 

aR is the peak particle acceleration associated with R-wave, 

VP is the peak particle velocity associated with P-wave, 

CP is the apparent velocity of P-wave propagation, 

VS is the peak particle velocity associated with S-wave, 

CS is the apparent velocity of S-wave propagation, 

VR is the peak particle velocity associated with R-wave, and 

CR is the velocity of R-wave propagation. 

The magnitude of axial strain due to curvature deformation is typically small compared to that 

due to axial deformation. As the radius of the tunnel increases, the contribution to axial strain 

from curvature deformation increases. The angle of wave propagation, φ, that maximizes the 

combined axial strain depends on the wave characteristics and the geometry of the tunnel, and 

can be derived by trial and error. If the curvature contribution to axial (longitudinal) strain is 

insignificant, then the values of φ that maximize axial strains are given in table 4-2. If the 

curvature contribution to axial strain is found to be significant, then it is suggested that the two 

terms in equations 4-1, 4-2, and 4-3 be combined as the square root of the sum of the squares 

(SRSS), because peak particle velocity and acceleration will not necessarily be in phase. 

In equations (4-1) and (4-2), the P- and S-wave velocities, CP and CS, represent apparent 

horizontal wave propagation velocities at the elevation of the tunnel. Generally, these apparent 

velocities correspond to seismic wave propagation through the deeper rocks rather than to the 

velocities of the shallower soils and rocks in which the tunnel may be located. Based on 

analyses of data from ground motion spatial arrays (O’Rourke et al., 1982; Chang et al., 1986; 

Abrahamson, 1985, 1992, 1995), the apparent velocity of S-waves in the direction of horizontal 

wave propagation varies from about 2 to 4 km/sec. A velocity of 2 km/sec is recommended 

unless larger values can be justified for the specific seismic environment of the tunnel. Apparent 

P-wave velocities in the direction of wave propagation generally range from about 4 to 8 km/sec. 

P-wave propagation seldom governs induced strains and stresses in tunnels because the 

associated peak particle accelerations and velocities are usually much smaller than those 

associated with S-waves. 

When tunnels are present in deep deposits of soil sediments, it is possible that the induced strains 

and stresses will be governed by surface (Rayleigh) waves. Factors which tend to increase the 

importance of R-waves relative to S-waves are: (1) R-wave propagation velocities tend to be 

smaller than S-wave apparent propagation velocities (note that since R-waves propagate 

horizontally through the shallower geologic media, their wave propagation velocities as 

measured in spatial arrays are “actual” rather than “apparent” velocities); and (2) maximum axial 

strain (neglecting contributions from curvature) is equal to VR/CR for R-waves and VS/2CS from 

S-waves (table 4-2). Factors which tend to reduce the importance of R-waves relative to Swaves are: (1) the peak particle velocity in a time history is usually associated with S-waves 
162

(velocity, VS) rather than R-waves (VR), especially in the near-source region, which is more 

likely to have potentially damaging strong ground motions; and (2) R-wave amplitudes may 

decrease faster with depth than S-wave amplitudes, thus reducing the importance of R-waves for 

deep tunnels. 

A seismologic assessment is required to determine whether a tunnel is in a geologic and seismic 

environment in which surface waves should be considered and to estimate VR and CR for strain 

calculations. In general, surface waves should be considered if the tunnel is located in a 

sedimentary basin. Examples of sedimentary basins in the United States in which prominent 

surface waves have been observed include the Los Angeles basin, San Fernando Valley, San 

Bernardino Valley, and Santa Clara Valley, California. These basins are characterized by soil 

sediments at least several hundreds of feet deep and valley widths of several kilometers to tens of 

kilometers. Further discussions of surface waves including current knowledge regarding VR and 

CR are presented in Appendix A. It is noted that with the current state-of-knowledge, selection 

of parameters for analysis of tunnel longitudinal response due to surface waves involves greater 

uncertainty than parameter selection for body waves. 

Peak particle velocities and accelerations used in the formulations in table 4-2 and equations (4-

1) through (4-3) (VP and aP for P-waves, VS and aS for S-waves, and VR and aR for R-waves) 

represent the velocities and accelerations at the elevation of the tunnel. Because ground motions 

generally decrease with depth below the ground surface, these parameters generally have lower 

values than estimated for ground surface motions (e.g., Chang et al., 1986). The ratios of ground 

motion values at tunnel depths to those at the ground surface may be taken as the ratios 

summarized in table 4-3 unless lower values are justified based on site-specific assessments. 

Ground motion attenuation relationships for estimating ground surface motions that are 

applicable to the tectonic environment and geologic conditions at the tunnel location should be 

used to estimate ground surface motions. The ratios summarized in table 4-3 can then be applied 

to obtain ground motions at the tunnel depth. For tunnels in rock, ground surface motions should 

be estimated at a hypothetical rock outcrop using rock attenuation relationships and the ratios in 

table 4-3 applied to the rock outcrop motions. 

Table 4-3. Ratios of ground motion at tunnel depth to motion 

at ground surface. 

Tunnel Depth (m) Ratio of Ground Motion at Tunnel Depth to 

Motion at Ground Surface 

< 6 1.0 

6 to 15 0.9 

15 to 30 0.8 

> 30 0.7 

A number of attenuation relationships are available for estimating peak ground surface 

accelerations, but few attenuation relationships are available for estimating peak ground surface 

velocities. The ratios of peak ground velocity (km/sec) to peak ground acceleration (g) for soil 

and rock summarized in table 4-4 may be used to estimate peak ground velocities in the absence 
163

of site-specific assessments. The relationships in table 4-4 are for use with peak ground 

acceleration attenuation relationships for shallow crustal earthquakes in the western United 

States. These types of earthquakes are the primary sources of seismic hazard in most parts of the 

western United States. For subduction zone earthquakes, such as those that occur along coastal 

regions of Washington, Oregon, northwest California and Alaska, and for earthquakes in the 

central and eastern United States, ground motion prediction relationships developed for those 

regions should be used. 

Due to the vertical component of a Rayleigh (R) wave, axial strain due to curvature in the 

vertical plane is equal to (see table 4-2): 

ab 2 R

2

R

a Y cos

C

ε = φ for R-waves (4-5) 

which is out of phase with the axial strains due to the horizontal component of an R-wave given 

in equation 4-3. 

Example calculations of axial strains and stresses in a tunnel using free-field solutions are 

provided in examples 4-1 and 4-2 for shear (S) waves and Rayleigh (R) waves, respectively. 

Table 4-4. Ratios of peak ground velocity to peak ground acceleration 

in rock and soil. 

Ratio of Peak Ground Velocity (cm/sec) to Peak 

Ground Acceleration (g) 

Source-to-Site Distance (km) 

Moment 

Magnitude, MW

0 - 20 20 – 50 50 - 100 

Rock* 

6.5 

7.5 

8.5 

67 

97 

120 

80 

110 

130 

90 

124 

145 

Stiff Soil* 

6.5 

7.5 

8.5 

92 

130 

150 

98 

135 

155 

104 

140 

161 

Soft Soil* 

6.5 

7.5 

8.5 

138 

195 

225 

147 

203 

233 

156 

210 

242 

* In this table, the sediment types represent the following low-strain shear wave 

velocity (Cm) ranges: rock ≥ 750 m/sec; stiff soil 200 m/sec – 750 m/sec; and soft 

soil < 200 m/sec. The relationship between peak ground velocity and peak ground 

acceleration in soft soils is poorly constrained. 

adapted from Sadigh and Egan, 1998 
164

Effects of Soil-Tunnel Interaction: The effects of soil-tunnel interaction on reducing axial 

strain ( ε ), shear strain ( γ ), and curvature (1/ρ) in a tunnel can be estimated using reduction 

factors given by St. John and Zahrah (1987) using beam-on-elastic-foundation theory. The freefield values of ε , γ , and (1/ρ) given in table 4-2 may be multiplied by the following reduction 

factors, R, to account for soil-tunnel interaction: 

For axial strain, R = 

l l1 2 2

a

1

E A 2 1 ( ) cos K L

π

+ φ

 (4-6) 

For shear strain and curvature in a horizontal plane, 

R = 4

l l1 4

h

1

E I 2 1 cos

K L

⎛ ⎞ π

+ ⎜ ⎟ φ ⎝ ⎠

 (4-7) 

where: 

E is the Young’s modulus of tunnel lining, l

A is the cross sectional area of the lining, l1

K is the transverse soil spring constant per unit length of tunnel, h

K is the longitudinal soil spring constant per unit length of tunnel, a

L is the wavelength of the P-, S-, or R-wave, and 

l1 I is the moment of inertia of the lining cross section. 

 (e.g., for circular liners: ( ) 4 4

o i

l1

D D

I

64

π − = ) 

St. John and Zahrah (1987) indicate that the transverse and longitudinal soil spring constants for 

use in equations 4-6 and 4-7 are the same and equal to: 

m m

a h

m

16 G (1 v ) H K K

(3 4 v ) L

π − = = − (4-8) 

where: 

H is the height of tunnel (diameter, D, for circular tunnels), 

Gm is the shear modulus of the medium, 

vm is the Poisson’s ratio for the medium, 

Do is the outside diameter of tunnel lining (Do = D), and 

Di is the inside diameter of tunnel lining. 

For shear or bending in a vertical plane, the spring constant KV is used in the preceding 

equations, and tunnel height, H, is replaced by width, w. If the geologic medium is of 

approximately equal stiffness all around the tunnel, KV can be taken equal to Kh (equation 4-8). 

If the soil medium above the tunnel is much softer than the geologic medium beneath it, such as 

for a near-surface cut-and-cover tunnel or a tube, then: 
165

m

V

m

2 G w K

(1 ) L

π = − ν

 (4-9) 

The wavelength, L , of P-waves, S-waves, and R-waves is related to the apparent velocity of Pwave and S-wave propagation, CP and CS; the velocity of R-wave propagation, CR; and the wave 

period, TP,S,R, for the respective waves, by: 

L = (CP, CS or CR) TP,S,R (4-10) 

For purposes of using this expression, TP,S,R can be assumed equal to the period at which the 

maximum displacement occurs. Typically, displacements occur at relatively long periods, and a 

value of TP,S,R equal to 2 seconds may be assumed unless L is evaluated from a site-specific 

study. 

Shear modulus, Gm, is related to shear wave velocity, Cm, of the geologic medium adjacent to the 

tunnel by the equation: 

t 2 G C m m g

γ = (4-11) 

where: 

t γ is the total unit weight of the geologic medium, 

g is the acceleration of gravity. 

For calculation of soil-structure interaction effects, it is recommended that “effective” values of 

Gm and Cm be used. Use of the effective values accounts in an approximate way for nonlinear 

soil behavior, i.e., the decrease of soil shear modulus with increasing level of ground shaking 

and soil shear strain. The effective values are denoted Gm

′ and Cm′ . For rock, the ratio of 

C /C m m

′ , where Cm is the low-strain or maximum shear wave velocity, can be assumed equal to 

1.0. For soil, in the absence of a site-specific study, C /C m m

′ can be assumed equal to 0.45 for a 

peak ground acceleration (PGA) at the ground surface of 0.7 g and equal to 0.8 for a PGA of 0.1 

g. Values of C /C m m

′ may be interpolated for other accelerations. 

The axial force in the lining is limited by the maximum frictional forces that can be developed 

between the lining and the surrounding soils. The maximum frictional force, (Qmax)f, can be 

estimated to be equal to the frictional force per unit length times one-quarter of the wavelength 

(Sakurai and Takahashi, 1969): 

max f

fL (Q ) 4 = (4-12) 

where: 

f is the maximum frictional force per unit length of the tunnel. 

Examples 4-1 and 4-2 illustrate the calculation of the soil-structure interaction effect. 
166

In section 4.4.1.3, it was suggested that the results of simplified analyses of axial and curvature 

deformations be interpreted conservatively, because the effects of ground motion incoherence 

might add significantly to the response, yet guidance for a systematic evaluation of incoherence 

effects has not yet been developed. There is also uncertainty regarding soil-structure interaction 

effects calculated using simplified procedures; for example, different approaches for the 

evaluation of soil spring constants have been proposed (e.g., St. John and Zahrah (1987); Owen 

and Scholl (1981); Public Works Research Institute (1976); SFBART (1960)). Therefore, in 

applying simplified procedures, it is recommended that the effect of soil-structure interaction in 

reducing axial and curvature deformations be neglected, except for limiting the maximum 

frictional force using equation 4-12. However, if equations 4-6 and 4-7 should be applied, it is 

recommended that the reduction factor, R, be limited to a minimum value equal to 0.7. 

Junctions: At a junction of a tunnel to a stiffer structure, such as a ventilation structure or a 

transit station, strains will tend to be larger than along the running tunnel. Assuming the 

structure is a rigid boundary, the axial strain can be approximated as twice the strain calculated 

using the formulations presented in the preceding paragraphs. 

4.4.1.3(b). Numerical Analysis

Generally, the inertia of a tunnel is small compared to that of the surrounding soil mass. 

Therefore, it is possible to conduct the analysis of axial and curvature deformations as a quasistatic analysis in which displacement time histories are applied to soil springs connected to a 

model of the tunnel. Computer codes available for this type of numerical model include ADINA 

(1996), ABAQUS (Hibbitt, Karlsson & Soreson, Inc., 1998), and SADSAP (Wilson, 1998). 

4.4.1.4. Evaluation of Deformations of Tunnel Cross Section 

Similar to approaches for the analysis of axial and curvature deformations, both 

simplified/closed-form solutions and numerical analysis methods may be used for the analysis of 

the tunnel cross section. Figure 4-8 summarizes the analytical methods, which are described 

below. 

4.4.1.4(a). Simplified Analyses/Closed-Form Solutions

Analysis of Bored Tunnels 

Pseudo-static Stability Analysis: A check should be made of the ability of the tunnel support 

system (lining and/or rock bolts or dowels) to resist inertia forces applied to the roof of the 

tunnel. The inertia forces can be approximated as a pseudo-static force equal to the estimated 

peak vertical ground acceleration (expressed as a decimal fraction of g) at the tunnel level times 

the static loads used for the roof design. The vertical peak ground acceleration may be assumed 

equal to the horizontal peak ground acceleration estimated as described in section 4.4.1.3(a). 

This may be somewhat conservative because vertical peak ground accelerations tend to be 

smaller than horizontal peak ground accelerations. However, for close distances to earthquake 

sources, ratios of vertical to horizontal peak ground accelerations tend to exceed the commonly 

used two-thirds ratios (e.g., Silva, 1997). 
167

Simplified /

Closed-form

Solutions

Numerical

Analysis

Circular

(Bored)

Tunnel

Rectangular

Cut-andCover

Tunnel

Finite

Element/

Finite

Difference

Model

Discrete

Element

Model

Stability

Analysis

Ovaling

Analysis

Racking

Analysis

Earth

Pressure

Analysis

Ovaling/

Racking

Deformations

of Tunnel

Cross Section

Figure 4-8. Approaches for seismic analysis of tunnel cross section. 

A pseudo-static analysis is inherently conservative because the seismic inertia forces act in a 

destabilizing direction only for short instances of time. Nevertheless, the analysis is useful in 

indicating a potential stability problem. 

If a weak zone, such as a zone of soft, sheared rock, exists adjacent to a tunnel, or a zone of 

relatively weak bedding or joint planes dips toward the tunnel, a pseudo-static analysis can also 

be made of the potential for caving of the weak mass into the tunnel. The analysis is illustrated 

schematically in figure 4-9. 

Analysis of Ovaling of Circular Tunnels: The cross section of a tunnel should be analyzed for 

the ovaling deformations imposed by the geologic media assuming vertically propagating shear 

waves (figure 4-3c). Simplified analyses using static solutions generally may be used. Dynamic 

amplification effects on the response of the cross section can generally be neglected because 

these effects typically do not increase lining stresses by more than 5 percent to 15 percent 

(SFBART, 1960; Chen et al., 1979; Owen and Scholl, 1981). In general, if the predominant 

wavelength of the vertically propagating shear waves is greater than eight times the tunnel 

height, dynamic amplification effects will be insignificant (Merritt et al., 1985). 
168

W

KhW

KvW

Figure 4-9. Pseudo-static stability analysis for weak zone adjacent to tunnel. 

For purposes of assessing whether there is a potential for significant dynamic amplification, the 

predominate wavelength of the vertically propagating shear wave can be estimated as the 

product of the predominant period of acceleration ground shaking times the effective or straindependent shear wave velocity, ′ Cm , of the medium in which the tunnel is located. The 

predominant period of acceleration ground shaking is typically about 0.3 second for stiff soils 

and rocks and longer than 0.3 second for soft soils. A period of 0.3 second can be assumed in 

the absence of a site-specific study. The effective or strain-dependent shear wave velocity is 

discussed in section 4.4.1.3(a) following equation 4-11. 

If the predominant wavelength calculated using these guidelines is less than eight times the 

tunnel height, a dynamic amplification of 15 percent above the forces and moments obtained 

from the static solutions presented below may be assumed. Alternatively, either the predominant 

wavelength may be estimated from a one-dimensional site response analysis discussed later in 

this section, or a dynamic time history soil-structure interaction analysis may be conducted to 

determine tunnel response, as discussed in section 4.4.1.4(b). 

The closed-form elastic static solutions of Wang (1993) and Penzien and Wu (1998) may be used 

to estimate the dynamic (pseudo-static) thrust force (T ), shear force ( V ), and moment (M) in 

the tunnel lining (figures 4-10 and 4-11). These solutions account for the interaction of the 

tunnel lining with the surrounding soil or rock. Wang (1993) adapted earlier solutions for 

external loading on a tunnel by Peck et al. (1972) (based on previous work by Burns and 

Richard, 1964; and Hoeg, 1968) to the seismic loading case for the condition of full slip (zero 

tangential shear stress) between tunnel and geologic medium. Similarly, he adapted the solution 

of Schwartz and Einstein (1980) (based on Hoeg’s work) for the no-slip condition (continuity of 

displacements at tunnel and geologic medium interface). Penzien and Wu (1998) independently 

developed solutions for full-slip and no-slip conditions. 
169

Figure 4-10. Forces and moments in tunnel lining due to ovaling. 

T

t

V M

 Il2 = bt3

 bl = 1 unit

 Al2 = bt

b

12

Figure 4-11. Area and moment of inertia for ovaling 

analysis of circular tunnel. 

The solutions of Wang (1993) and Penzien and Wu (1998) for full slip are the same and can be 

expressed as follows: 

Thrust force, T( ) G DK sin 2 m smax θ = ′ γ θ (4-13) 
170

Shear force, V( ) 2G DK cos 2 m smax θ = ′ γ θ (4-14) 

Moment, 2

m smax

1 M( ) G D K sin 2 2

θ = ′ γ θ (4-15) 

where: m

m

1 v K

F 2.5 3v

− = + −

 (4-16) 

F, termed the flexibility ratio, is the ratio of the shear stiffness of the geologic medium to that of 

the tunnel liner: 

2 3

m l

l l2

G (1 v )D F

24E I

′ − = (4-17) 

where: 

θ is the angle relative to horizontal axis through center of tunnel (figure 4-10), 

D is the diameter of the tunnel, 

smax γ is the free-field shear strain at tunnel elevation induced by earthquake ground 

shaking, 

Gm

′ is the effective shear modulus of the geologic medium (refer to text following 

equation 4-11 for evaluation of Gm

′ ), 

E1 is the Young’s modulus of the liner, 

νm is the Poisson’s ratio of geologic medium, 

νl is the Poisson’s ratio of the liner, and 

l2 I is the moment of inertia of the lining cross section per unit length of tunnel (fig. 4-

11). 

The formulations of Penzien and Wu (1998) for the no-slip condition are the following: 

Thrust force, T( ) 2G DK sin 2 m smax θ = ′ ′γ θ (4-18) 

Shear force, V( ) 2G DK cos 2 m smax θ = ′ ′γ θ (4-19) 

Moment, 2

m smax

1 M( ) G D K sin 2 2

θ = ′ ′γ θ (4-20) 

where: 

m

m

1 v K

F 3 4v

− ′ = + −

 (4-21 ) 

Note that equations 4-13 through 4-16 and 4-18 through 4-21 have been rearranged from the 

equations originally presented by Penzien and Wu (1998). 
171

The formulation of Wang (1993) for thrust for the no-slip condition can be expressed as: 

m 2 smax

1 T( ) G (1 a ) sin 2 2

θ + ′ γ θ (4-22) 

Following the same approach used by Wang (1993), the formulation for moment for the no-slip 

condition is derived as: 

2

m 2 3 smax

1 M( ) G D (1 a 2a ) sin 2 8

θ= − − ′ γ θ (4-23) 

where: 

( )( ) ( )2

m m0

1 a F 1-2v 1 C C 1 2v 2 / a

2

⎧ ⎫ ⎨ ⎬ −− − + ⎩ ⎭ 2 = (4-24) 

3 m m0 ( ) ( ) 1 a F C 1 2 1 C 1 2 2 /a

2

⎧ ⎫ = −ν + − −ν − ⎨ ⎬ ⎡ ⎤ ⎣ ⎦ ⎩ ⎭ (4-25) 

( )( ) 2

o m m mm m

5 a F 3 2 1 2 C C 8 6 6 8v

2

⎡ ⎤ = −ν + −ν + −ν +ν + − ⎡ ⎤ ⎣ ⎦ ⎢ ⎥ ⎣ ⎦ (4-26) 

Flexibility ratio, F, is given by equation 4-17. Compressibility ratio, C, is : 

( )

( )

2

m l

l m

G1 D

C

Et1 2

′ − ν = − ν

 (4-27) 

where: 

t is the lining thickness (figure 4-11). 

The earthquake loading for the calculation of ovaling is represented by the maximum free-field 

shear strain, smax γ , over the height of the tunnel produced by vertically propagating shear waves. 

The maximum free-field shear strain preferably should be estimated using numerical methods 

such as a one-dimensional site response analysis (e.g., SHAKE [Schnabel et al., 1972; Idriss and 

Sun, 1992]). For deep tunnels, smax γ can be approximated as: 

S

smax

m

V

C γ = ′ (4-28) 

where: 

VS is the peak particle velocity in the geologic medium at the tunnel depth. 

Cm

′ is the effective shear wave velocity of the geologic medium at the tunnel depth. 

These parameters can be estimated as discussed in the paragraphs following equations 4-4 and 

4-11. 
172

The maximum thrust force and bending moment both occur at angles of 45 degrees from the 

horizontal diametric axis of the tunnel (figure 4-10). 

The maximum compressive and tensile stresses in the cross section induced by the earthquake 

can be obtained by combining the stresses from the thrust force and bending moment: 

( ) ( )

l2 l2

T M (t / 2)

A I

θ θ

σ= ± (4-29) 

where: 

t, A12, and I12 are, respectively, the thickness, area, and moment of inertia of the lining 

cross section (figure 4-11). 

In general, the equations for a full-slip condition lead to higher moments than the equations for a 

no-slip condition. Higher thrust forces are generally obtained for a no-slip condition, and thrust 

forces predicted by the Wang (1993) formulation are generally much higher than those predicted 

by the Penzien and Wu (1998) formulation, especially for stiffer geologic media. The reasons for 

the difference in the thrust force from the two formulations for the no-slip condition are not 

understood at present. 

In application, it is recommended that the maximum stress from equation 4-29 be obtained using 

the full-slip or no-slip formulation that leads to the highest stress (equations 4-13 and 4-15 for a 

full-slip condition; equations 4-18 and 4-20 or equations 4-22 and 4-23 for a no-slip condition). 

Example 4-3 illustrates the calculation of dynamic (pseudo-static) stresses in a circular tunnel 

due to ovaling. Example 4-5 illustrates the calculation of the combined static and dynamic 

(pseudo-static) stresses in circular tunnels for two different types of tunnel linings and for soft 

and stiff geologic media. Penzien and Wu (1998) present an example showing how the critical 

tension stress in a concrete lining increases and then decreases with increasing lining thickness 

due to soil-lining interaction. 

It should be noted that the equations in this section were derived assuming the structure behaves 

elastically. When inelastic deformations are predicted to occur in the lining, nonlinear inelastic 

analyses should be performed when necessary to ensure that the lining will have adequate 

ductility. 

Analysis of Rectangular Tunnels 

Similar to the analysis of circular tunnels for ovaling, rectangular tunnel sections should be 

analyzed for the imposed racking deformations assuming vertically propagating shear waves. In 

addition, the walls and roof of the tunnel should be analyzed for dynamic earth pressures. 

Racking Deformation Analysis: Wang (1993) developed a simplified procedure incorporating 

soil-structure interaction for the analysis of racking of rectangular tunnels (figure 4-3d). The 

procedure was developed based on a series of dynamic finite element analyses of a number of 

cases with varying soil and structural dynamic properties and structure geometries. The cases 

analyzed covered the following conditions: 
173

• The ratio of the depth to the center of the structure, h, to the structure height, H, ranged from 

1.1 to 2.0 (figure 4-12). 

• Average shear modulus of the soils surrounding the structure ranged from 11,000 to 

72,000 kPa (230 to 1500 ksf), with corresponding shear wave velocities of 75 to 200 m/sec 

(250 to 650 ft/sec). 

• The vertical distance between the bottom of the structure and the top of underlying stiff 

soils/rock was equal to or greater than the height of the structure. 

• Rigid body rotation was excluded. 

• Five types of one-barrel and two-barrel rectangular structures were investigated. Structure 

widths, w, ranged from 4.6 to 27.5 m (15 to 90 feet), and structure heights, H, ranged from 

4.6 to 8 m (15 to 26 feet). 

• Two artificial earthquake ground motion time histories, representing western and 

northeastern U.S. earthquakes, were used. 

Figure 4-12. Definition of terms for Wang (1993) procedure for analysis of 

racking of a rectangular tunnel. 
174

The following procedure is followed to assess the structure response and behavior: 

Step 1: Estimate the free-field effective soil shear deformation, ∆ff , over the height of the 

structure, H, due to vertically propagating shear waves (figure 4-12). 

The free-field shear deformation, ∆ff , should be estimated using site response analyses 

(e.g.,computer code SHAKE [Schnabel et al., 1972; Idriss and Sun, 1992]). Due to the influence 

of seismic waves reflecting from the ground surface, shear strain is more reliably estimated for 

shallow tunnels using site response analyses than using simplified formulations (equation 4-28). 

Step 2: Determine the relative flexibility of the soil and the structure. 

A flexibility ratio, Fr, is defined as the ratio of the free-field effective soil shear stiffness to that 

of the structure, and is given by: 

m

r

G w F = 

S H

′ (4-30) 

where: 

S is the racking stiffness, i.e., the force required to cause a unit racking deflection of 

the structure, 

w is the width of the structure, 

H is the height of the structure, and 

Gm

′ is the shear modulus of the medium. 

These terms are defined in figure 4-12. 

Step 3: Estimate the racking distortion of the structure. 

From a series of dynamic finite element analyses, Wang (1993) presented results showing the 

relationship between the structure racking and the flexibility ratio. The racking coefficient, Rr, is 

the ratio of the racking distortion of the structure embedded in the soil, ∆r , to that of the freefield soils, ∆ff , over the height of the structure: 

r

r

ff

R ∆ = ∆ (4-31) 

The values of Rr vs. Fr obtained from the dynamic finite element analyses are shown in figures 

4-13(a) and 4-13(b). Also shown in these figures are curves from closed-form static solutions 

for circular tunnels. 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 and previously reported by Wang (1993) and Penzien (2000), the 

curves from the closed-form 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 tunnel as a function of the flexibility ratio defined by equation 4-30. The analytical 

expressions for the curves in figure 4-13 are the following: 
175

For full slip: ( ) m r

r

r m

41 F

R

F 2.5 3

− ν = + −ν

 (4-32) 

For no slip: ( ) m r

r

r m

41 F

R

F 34

− ν

+−ν = (4-33) 

Several observations can be made from figure 4-13. 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 soil (exactly equal to that of the soil for the no slip 

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 ( ) m 4 1− ν , which is the case 

of an unlined cavity. R 41 r m = −ν ( ) also describes the racking ratio of an unlined circular cavity 

(Penzien and Wu, 1998). 

Step 4: Perform structural analysis to determine forces, moments, and detailing 

 requirements. 

Two pseudo-static lateral force models are recommended by Wang (1993) (figure 4-14). The 

lateral forces should be applied to produce a racking deformation on the structure equal to the 

calculated value. If the displacements are large enough to cause inelastic deformation of the 

structure, inelastic pushover analyses (ATC, 1995) should be performed to assess structural 

behavior. The more critical responses from the two force models should be used for design. 

Under the loading from the maximum design earthquake, inelastic deformation in the structure 

may be allowed depending on the performance criteria and provided that overall stability of the 

tunnel is maintained. Detailing of the structural members and joints should provide for adequate 

internal strength, ductility, and energy absorption capability. 

Wang (1993) conducted parametric analyses to identify the influences of relative stiffness, 

structure geometry, ground motion characteristics, embedment depth, and foundation stiffness on 

the racking coefficient, Rr. Results of these analyses indicate that the relative stiffness between 

the rectangular structure and the surrounding medium has the most significant influence on Rr. 

The effects of structure geometry and ground motion characteristics were negligible. Additional 

analyses were performed to determine the influence of embedment depth. In these analyses, 

depths of embedment ranged from 0 to 40 feet for a structure with a height of 15 feet. The 

results indicate that the calculated racking coefficient is relatively independent of embedment 

depth when h/H > 1.5 (figure 4-12). Penzien (2000) further observed that as h/H reduces below 

1.5, the racking coefficient decreases rather slowly, and the reduction is only about 20 percent 

for a reduction of h/H from 1.5 to 0.5. 
176

modified from Wang, 1993 

Figure 4-13. Racking coefficients for rectangular tunnels. 

Example 4.4 illustrates the calculation of racking of a rectangular tunnel. 

Earth Pressure Analysis: For a tunnel that is stiff relative to the surrounding soil (i.e., flexibility 

ration, Fr ≤ 1.0, equation 4-30), the walls of the structure should be further checked for their 

capacity to withstand dynamic earth pressures. Dynamic lateral earth pressures acting on the 

walls are the increment of inertia-induced earth pressures that are added to or subtracted from the 

static lateral earth pressures (see figure 4-15). They tend to increase earth pressures on one side 

of a structure while simultaneously reducing earth pressures on the opposite side. A check 

should be made that the tunnel racking induced by the dynamic pressures does not unreasonably 

exceed the shear deformations of the surrounding ground. 
177

Wang, 1993 

Figure 4-14. Simplified frame analysis models for analysis of racking 

of a rectangular tunnel. 

 
178

z

H

ps = Static, at rest lateral earth pressure

∆pe = Seismic increment of lateral earth pressure

pS

∆pE

Figure 4-15. Lateral earth pressures acting on the walls of a 

cut-and-cover rectangular tunnel. 

The dynamic lateral earth pressure on a tunnel wall, E ∆p , may be estimated by the following 

equation for shallowly embedded tunnels where the ratio of the depth of soil above the tunnel, Z, 

to the height of the tunnel wall, H, is less than 0.5: 

∆ = p Ck H Z E Vh t γ ( ) + (4-34) 

where: 

CV is the seismic earth pressure coefficient, 

kh is the horizontal earthquake coefficient, 

t γ is the total unit weight of soils, 

H is the height of the wall, and 

Z is the depth of soil above the tunnel. 

As shown in figure 4-15, E ∆p is assumed to act on the wall as a uniform pressure. This 

formulation is based on the dynamic lateral earth pressure procedures developed by Seed and 

Whitman (1970) and Wood (1973) as summarized in Power et al. (1998). The seismic earth 

pressure coefficient, CV, may be assumed equal to 0.4 and 1.0 for tunnels founded on soil and 
179

rock, respectively. kh should be taken, perhaps somewhat conservatively, as the horizontal 

ground surface acceleration expressed as a decimal fraction of gravity. 

Considerable uncertainty exists regarding the magnitude of these pressures, especially for a fully 

embedded structure such as a tunnel. Numerical analyses should be considered for estimating 

dynamic lateral earth pressures, especially for depths of embedment to the top of the tunnel 

exceeding approximately one-half the tunnel height (i.e., Z / H 0.5 > ). A state-of-the-art review 

of dynamic earth pressures is presented by Whitman (1991). 

Vertical seismic forces may be exerted on the roof of a cut-and-cover tunnel due to vertical 

accelerations in the soil backfill mass above the tunnel. The seismic forces in a backfill over a 

shallow tunnel can be obtained by multiplying the estimated vertical peak ground acceleration 

times the backfill mass. 

Having estimated the seismic (and static) earth pressures, structural analysis is carried out to 

check the capacity of the walls and roof to resist these pressures. The static (gravity) and inertial 

forces in the roof and the inertial forces in the walls should be added to the earth pressures in 

determining the total static plus seismic loads. 

4.4.1.4(b). Numerical Analysis

Two-dimensional finite element and finite difference models may be used to analyze the cross 

section of a tunnel. Equivalent linear methods may be used to approximate nonlinear behavior 

of soils. Computer codes for linear or equivalent linear dynamic time history analysis include 

FLUSH (Lysmer et al., 1975), SASSI (Lysmer et al., 1991), and QUAD4-M (Hudson et al., 

1994). The computer program FLAC (Itasca, 1998; Wang and Makdisi, 1999) can incorporate 

nonlinear behavior in soil materials through the incorporation of nonlinear (or bilinear) 

constitutive models. 

In cases where movement along weak planes in the geologic media (shear zones, bedding planes, 

joints) may potentially cause local stress concentrations and failures in a tunnel, dynamic time 

history analyses using discrete element models may be considered. In these models, the 

soil/rock mass is modeled as an assemblage of discrete blocks. The blocks may be modeled as 

either rigid or deformable materials, each behaving according to a prescribed stress-strain 

relationship. The relative movements of the blocks along weak planes are modeled using forcedisplacement relationships in both normal and shear directions. Figure 4-16 illustrates an 

example of a discrete element model, where joints and bedding planes are included for analyses. 

UDEC (Itasca, 1992) and DDA (Shi, 1989) are two computer codes that can be used for this type 

of numerical analysis. 

Because of the complexity of the tunnel-soil interaction problem, consideration should be given 

to using numerical analysis methods. Use of these methods is especially desirable for analysis of 

the cross sections of cut-and-cover box tunnels in soil because of the relative seismic 

vulnerability of these structures (as compared to bored tunnels) based on earthquake 

observations. 
180

Akky et al.,1994 1

Figure 4-16. Discrete element model of tunnel. 

4.4.2. EVALUATION FOR FAULT RUPTURE 

4.4.2.1. General 

Assessing the behavior of a tunnel that may be subject to the direct shear displacements along a 

fault includes, first, characterizing the free-field fault displacement (i.e., displacements in the 

absence of the tunnel) where the fault zone crosses the tunnel and, second, evaluating the effects 

of the characterized displacements on the tunnel. 

In general, if moderate to large fault displacements occur in narrow zones in relatively hard 

geologic media, the tunnel may experience severe local damage that can be reduced only by 

special design to accommodate the displacements or must be anticipated in contingency repair 

plans. Design and contingency measures are discussed in section 4.5.2. Severe local damage to 

linings or walls of tunnels could generally be expected for fault movements on the order of a few 

inches or more occurring on discrete planes in rock. On the other hand, if displacements are 

small and/or are distributed over a wide zone, it is possible that only minor or moderate damage 

to tunnels may occur, especially if the tunnel is ductile or articulated. The effect of cracking or 

joint separation on the water tightness and potential for flooding of a tunnel should be carefully 

evaluated. 

One factor that affects the behavior of a tunnel in a fault rupture zone is the direction of slip 

relative to the tunnel axis. For steel linings susceptible to buckling, relative slip that would place 

a tunnel in compression tends to be more damaging than slip that would elongate the tunnel. The 

development of cracks or gaps in a lining due to either elongation or compression may result in 

unacceptable water inflow. 
181

4.4.2.2. Assessing the Amount of Fault Displacement 

Assessing the amount and distribution of fault displacement is an activity requiring the effort of 

geologists who are knowledgeable of the character of displacements in fault rupture zones. 

Empirically based relationships, such as those developed by Wells and Coppersmith (1994), can 

be utilized to estimate the amount of fault displacement as a function of earthquake magnitude 

and type of faulting. Figure 4-17 is an example of such a relationship, which shows that the 

amount of displacement is strongly dependent on earthquake magnitude and can reach maximum 

values of several feet or even tens of feet for large-magnitude earthquakes. 

4.4.2.3. Analyzing Tunnels for Fault Displacement 

When subjected to fault differential displacements, a buried structure with shear and bending 

stiffness tends to resist the deformed configuration of the fault offset, which induces axial and 

shear forces and bending moments in the structure. The axial deformation is resisted by the 

frictional forces that develop at the soil-tunnel interface in the axial direction, while shear and 

curvature deformations are caused by the soil resistance normal to the tunnel lining or walls. 

Wells and Coppersmith, 1994 

Figure 4-17. Relationship between maximum surface fault displacement (MD) and 

earthquake moment magnitude, Mw, for strike-slip faulting. 
182

In general, analytical procedures for evaluating tunnels subjected to fault displacements follow 

those used for buried pipelines. Three analytical methods have been utilized in the evaluation 

and design of linear buried structures (ASCE Committee on Gas and Liquid Fuel Lifelines, 

1984). They are: 

• Newmark-Hall procedure. 

• Kennedy et al. procedure. 

• Finite element approach. 

The Newmark-Hall (1975) and Kennedy et al. (1977) approaches were originally developed for 

analyzing buried pipelines subjected to discrete fault displacements. Both approaches assume 

that the structural axial deformation is restrained by the soil-structure frictional forces. In the 

Newmark-Hall method, it is assumed that the structure “breaks free” from the surrounding soils 

by climbing out of a shallow trench and remains straight between two anchored points. In the 

Kennedy et al. approach, the buried structure is modeled like a cable; induced curvatures and 

resulting bending stresses are calculated ignoring the bending stiffness of the structure. 

The Newmark-Hall method is generally not applicable to tunnels because the size of the tunnel 

and depth of burial would generally preclude the possibility of the tunnel climbing out of the 

ground and straightening itself out. The Kennedy et al. method may be used, although the 

bending stiffness is not negligible for many tunnels. This method would generally overestimate 

the bending curvature by neglecting the bending stiffness. The finite element method is 

preferred because it can incorporate the most realistic models of the tunnel and surrounding 

geologic media. The tunnel is modeled using finite elements, which may incorporate nonlinear 

behavior (figure 4-18). Transverse and axial springs connected to the tunnel model soil normal 

pressures on the tunnel lining or walls and axial frictional resistance (figure 4-19); these springs 

may also incorporate nonlinear behavior if applicable (figure 4-20). Many finite element codes 

may be considered for analyzing the response of tunnels to fault displacement. A few of these 

are ADINA (1996), ABAQUS (Hibbitt, Karlsson and Sorensen, 1998), PIPLIN (Structural 

Software Development Co., 1981), ANSR-III (Oughourlian and Powell, 1982), and STARDYNE 

(Research Engineers, 1995). 

4.4.3. EVALUATION FOR LANDSLIDING OR LIQUEFACTION 

If liquefiable soil deposits or unstable soil masses susceptible to landsliding are identified along 

the tunnel alignment, then more detailed evaluations may be required to assess whether 

liquefaction or landsliding would be expected to occur during the design earthquake and to 

assess impacts on the tunnel. 
183

ASCE Committee on Gas and Liquid Fuel Lifelines, 1984 

Figure 4-18. Analytical model of tunnel structure at fault crossing. 
184

ASCE Committee on Gas and Liquid Fuel Lifelines, 1984 

Figure 4-19. Schematic illustration of soil-structure model of tunnel at fault 

crossing. 
185

ASCE Committee on Gas and Liquid Fuel Lifelines, 1984 

Figure 4-20. Analytical model of soil restraint for tunnel at fault crossing. 
186

If slope movements due to landsliding or lateral spreading movements due to liquefaction 

intersect a tunnel, the potential effects of these movements on the tunnel are similar to those of 

fault displacement. As is the case for fault displacements, tunnels generally would not be able to 

resist landsliding or lateral spreading concentrated displacements larger than a few inches 

without experiencing locally severe damage. 

If liquefaction were predicted to occur adjacent to a tunnel lining or wall, a potential 

consequence could be yielding of the lining or wall due to the increased lateral earth pressure in 

the liquefied zone. The pressure exerted by a liquefied soil may be as large as the total 

overburden pressure. The potential for liquefaction to cause uplift of a tunnel embedded in 

liquefied soil, or for the tunnel to settle into the soil, should also be checked. 

4.5. RETROFIT STRATEGIES 

Retrofit strategies are discussed in the following subsections for the potential failure modes of 

ground shaking-induced failure, fault displacement-induced failure, and landsliding- and 

liquefaction-induced failure. 

4.5.1. GROUND SHAKING-INDUCED FAILURE 

4.5.1.1. Bored Tunnels 

4.5.1.1(a). Tunnels in Rock

Tunnels in rock have levels of support that range from a temporary rib and lagging liner with a 

cast-in-place concrete final liner, to rock bolts and rock dowels, to little or no support. To 

enhance seismic, as well as static, performance of tunnels in rock, retrofit methods should be 

used that limit the amount of deformation and enhance the ability of the ground to support itself 

by forming a ground arch reinforced with structural elements (Bischoff and Smart, 1976; Lang 

1962, 1972, 1981). Weak zones or rock wedges should be supported by rock bolts, stronger 

liners, or other methods to prevent them from shaking loose and producing additional loads on 

and possibly collapsing a liner during seismic loading (figure 4-21). For tunnels in weak rock, it 

may be desirable to install a continuous or patterned system of rock bolts and dowels and 

shotcrete support (figure 4-22). Chemical grouting may be considered in areas of highly jointed 

or fractured rock. 

In rock tunnels for railroads, the tunnels are often enlarged to carry higher-profile and highercapacity cargo cars (see for example Millar et al., 1991). Typically, the crown of the tunnel is 

mined, and new more “flexible” support consisting of rock bolts and shotcrete is installed. Older 

railroad tunnels are often supported with large timbers, which have rotted away or burned (from 

engine smoke). The timbers are removed and the tunnel enlarged and provided with larger 

clearances by replacing the timbers with rock bolts and shotcrete. Rehabilitation methods 

similar to those used for enlarging railroad tunnels may also be applied to seismic retrofitting of 

highway tunnels. 
187

Figure 4-21. Rock bolt stabilization 

of rock wedge. 

Figure 4-22. Rock bolt reinforcement in 

soft or fractured rock. 

It is critical that a tunnel lining be in good contact with the geologic media (whether rock or 

soil). The quality and completeness of contact grouting between the liner and the geologic 

media may be investigated by taking core samples as well as by geophysical techniques 

(e.g., ground penetrating radar or impact echo techniques). Contact grouting should be 

employed if significant voids are present behind a liner. Various materials may be used for 

contact grouting, including conventional grout, cellular or foam concrete, and polyurethane or 

other chemical grouts. Examples of application of contact grouting are described by Grimm and 

Parish (1985), Russel (1987, 1993), Navin and Hutchinson (1992), and Grodner et al. (1998). 

An example of the combined application of rock bolts, shotcrete, and contact grouting to 

rehabilitate a tunnel is the FHWA/National Park Service Ft. Baker-Ft. Barry tunnel originally 

constructed in 1918 (California Builders and Exchange, 1994). 

If tunnel linings are locally weak due to cracked, deteriorated, or otherwise low-strength 

concrete or masonry, spot repairs may be employed by removing and replacing weak zones with 

shotcrete or alternative materials such as resin-impregnated fabric or polymeric membranes. Use 

of such materials when a limited area needs structural rehabilitation is discussed by Abramson 

and Boscardin (1999) and Russell (1999). Weak zones of existing liners may be removed by 

conventional methods such as jack-hammering or techniques such as hydro-demolition 

(e.g., Soast, 1989). After the concrete or masonry is removed, additional reinforcement may be 

added and a new shotcrete or concrete liner placed. 

Extensively deteriorated, cracked, or otherwise weak concrete or masonry liners may require 

either the demolition and replacement of the liner or the strengthening of the liner by 

constructing an inner liner or installing stiffeners and arch beams (Madden, 1999). Typically, 

strains in tunnel liners in rock will be small, and reinforcing steel in concrete liners may not be 

required. Nevertheless, the use of reinforcing steel is desirable to provide a more ductile and 

stronger material if strong seismic shaking is anticipated. 
188

4.5.1.1(b). Tunnels in Soil/Soft Ground

As indicated in section 4.2.1.1, circular tunnels in soil are typically constructed using a two-pass 

or one-pass lining system. In the two-pass system, the primary, initial, or temporary support 

typically consists of steel ribs and lagging, liner plate, or precast concrete segmented lining. The 

final support consists of a cast-in-place liner. While many concrete tunnel liners do not require 

reinforcing, based on calculations for static-plus-seismic loading, it is desirable to provide 

reinforcing if strong seismic shaking could occur. During strong shaking, reinforcing provides a 

lattice to hold cracked concrete together without major spalling or collapse. 

Single-pass liners are typically bolted and gasketed steel plate or precast concrete segmented 

liners. The segments are typically staggered along the length of the tunnel so the segments’ 

radial or longitudinal joints are not continuous, forming "T" joints as shown in figure 4-23. 

Segments forming a continuous radial joint have the disadvantage that all the gaskets meet at 

four corners, increasing the potential for groundwater leakage. Staggering the segments is 

beneficial from a seismic point of view because it provides better interlocking among adjacent 

segments. Bolting together the segments of the liner is desirable for seismic design to provide 

continuity of the lining and reduce the potential for local lining failure. At the same time, the 

steel bolts provide a ductile fastening material. The Japan Tunneling Association indicated that 

there were no reports of damage to segmented-lining tunnels from the Kobe earthquake 

(Fukuchi, 1995). 

Unbolted segmented liners are frequently used. Advantages and disadvantages of various joint 

shapes are discussed by McCusker (1989) and Iftimie (1994). The potential seismic advantage 

of unbolted radial joints is that the moments induced by racking behavior can be further reduced, 

since little or no moment is transmitted across the joint. On the other hand, such joints are 

locations of shear weakness and are more susceptible to local failure during racking distortion. 

A variation of an unbolted radial joint is the use of a guide rod centered on the radial joint 

surface (AFTES, 1999). The guide rod is made of hard plastic and does not provide for any 

clamping force or moment or tension connection. It does allow rotation and provides a 

mechanical shear connector. Clough (1981) observed that the ability of unbolted liners to 

withstand earthquake loading requires research. 

Special connectors across circumferential joints in tunnel liners in soft soil may sometimes be 

desirable to accommodate large axial strains and curvatures. If such connectors are installed, it 

is important that they not become weak points where local transverse shear deformation might 

occur. Examples of joint details are shown in figures 4-24 and 4-25. The "seismic isolation 

washer" shown in figure 4-24 is a highly compressible element that was proposed for the TransTokyo Bay highway tunnel. The detail in figure 4-25, which was proposed for the Osaka South 

Port Tunnel, incorporates a rubber gasket to resist the compressive force, a cable to resist tensile 

force, and an omega-shaped rubber gasket for secondary water tightness. The effect of joints on 

potential for water inflow and design measures to achieve the required water tightness should 

always be evaluated. 
189

City of San Diego, CA/Parsons Engineering Science, 1995 

Figure 4-23. Precast concrete segmental liner. 

Other joint designs which accommodate larger movements may incorporate practices employed 

on other projects, not originally intended for seismic shaking. Circumferential joints, for 

example, may be reinforced with continuous longitudinal bolts through the segments as was used 

for the West Akli tunnel in Seattle for an ancient landslide crossing (Madden et al., 1994) and 

the South Bay Ocean Outfall in San Diego for active fault crossings (Kaneshiro et al., 1996a, 

1996b) (the design for the latter project is discussed in section 4.5.2 and illustrated in figure 4-

35). 
190

modified from Ono et al., 1992 

Figure 4-24. Example of flexible circumferential joint detail in tunnel lining with seismic 

isolation washer. 

Kiyomiya, 1995 

Figure 4-25. Example of a flexible circumferential joint detail in tunnel lining. 
191

Many retrofit strategies for soil tunnels may be similar to those for rock tunnels and include the 

following: 

• Spot repairs over a limited area by removing weak concrete and installing shotcrete, 

concrete, or alternative materials. Tunnels with steel liner plates may be strengthened in 

corroded or otherwise vulnerable areas with welded steel plates. 

• Contact grouting. 

• Ground improvement by chemical or compaction grouting. 

• Demolishing an existing liner and constructing a new liner with temporary ground support 

provided and/or liner replacement performed in short segments using sequential excavation 

methods. 

• Constructing an inner liner of reinforced concrete or a steel pipe with concrete in the annulus 

between the pipe and the existing liner. 

• Increasing deformation capacity of a liner by construction of special joints, such as the 

“seismic isolation washer” (figure 4-24) and joint details described in sections 4.5.1.3 and 

4.5.1.4. 

• Strengthening or increasing ductility of joints of segmented liners by local concrete removal 

and installation of steel connectors. 

Water inflow may limit retrofit choices for some tunnels in soil. 

4.5.1.2. Cut-and-Cover Tunnels 

The key to the retrofit of reinforced concrete, box-type cut-and-cover tunnels is to capture the 

main modes of behavior in the analysis of the tunnel cross section, including uncertainty in the 

induced stresses due to uncertainties in soil properties and uncertainties in response of the 

tunnel-soil system. Modes of behavior that must be adequately quantified include racking 

(figure 4-3d) and bulging of sidewalls and roof due to static-plus-seismic earth pressures. As 

pointed out by Owen and Scholl (1981), the seismically induced racking behavior of box-type 

cut-and-cover tunnels results in tension being induced on the inside faces of the corners of the 

box, whereas earth pressures result in tension at the inside middle part of the walls and roof. To 

design for the racking behavior, they recommended that longitudinal reinforcing steel in the 

walls be extended into the adjacent slabs and hooked at the far face, as illustrated in figure 4-26. 

Not shown in figure 4-26 is the transverse confinement reinforcing which is important for ductile 

behavior. 

4.5.1.3. Submerged Tubes 

Submerged tubes present several seismic retrofit challenges. Liquefaction-induced flotation is a 

potential concern when tubes are placed on and backfilled with loose sandy soil. Settlements 

could occur due to liquefaction and consolidation of sandy soils below a tunnel. Lateral 
192

Extend Rebar

to Far Face 

and Hook

Standard

Lap

Owen and Scholl, 1981 

Figure 4-26. Corner reinforcing details for seismic design of box-type tunnel. 

movement of a tunnel on gently sloping ground is a potential concern due to earthquake-induced 

lateral spreading in either liquefied soils or soft clays. 

The seismic vulnerability evaluation and retrofit design of the Posey and Webster Street tubes by 

Caltrans is summarized in the following paragraphs as an illustration of vulnerabilities and 

retrofit strategies for this type of tunnel (Caltrans/Parsons Brinckerhoff, 1998; Anderson, 1998; 

Schmidt and Hashash, 1998; Hashash et al., 1998; Boulanger et al., 1998; Schmidt and Hashash, 

1999). These tube-type vehicular tunnels pass beneath the Oakland estuary between the 

communities of Oakland and Alameda, California. During the 1989 Loma Prieta earthquake, 

accelerations at the tunnel locations were low enough that the tunnels did not experience 

significant structural damage. However, the earthquake caused some leaking at the connections 

between the tube segments, which was thought to have been caused by some liquefaction of the 

soil adjacent to the tubes (Yashinsky, 1998). Also, backfill soils over the tubes at the Alameda 

portals liquefied during the earthquake. Backfill around the tubes consists of sand for the 

Webster Street tube and a mixture of soft clay and sand for the Posey tube. For both these 

tunnels, seismic vulnerability studies conducted by Caltrans concluded that backfill around the 

tubes would likely liquefy and cause flotation of the tubes during potential earthquakes that 

could be larger and much closer to the sites than the Loma Prieta earthquake. In addition, 

dynamic analysis of the tunnels indicated that continuous joints connecting the approximately 
193

200 foot-long tube segments (made continuous during the original construction by connecting 

the reinforcing bars of adjacent tube sections) would experience large tensile and shear forces 

that could result in uncontrolled cracking of the tubes, leakage of water, and possible flooding. 

The analysis also indicated that large compressive forces would be transmitted at the continuous 

connections of the tubes to the portal buildings at the tube ends, causing damage to the buildings 

and the tubes. 

Retrofit design measures adopted by Caltrans for these tunnels included: (1) ground 

improvement to prevent flotation of the tubes; (2) cutting loose the joints and redesigning them 

so they would not transmit tensile forces while maintaining compression and shear capacity; and 

(3) providing gaps at the tube-portal-building joints to minimize the transmittal of interaction 

forces between the tubes and the buildings. 

The concept adopted to prevent tube flotation was to construct isolation walls using ground 

improvement methods adjacent to the tubes that would prevent liquefied soils outside the walls 

from moving beneath the tubes. This concept is not intended to prevent liquefaction of soils 

beneath the tube; rather it is intended to prevent flotation by interrupting the flotation 

mechanism. The ground improvement methods adopted to create the isolation walls consist of 

three rows of stone columns constructed in the backfill sands of the Webster Street tube and a 

continuous jet grout column wall constructed in the mixed clay and sand backfill of the Posey 

tube. Typical cross sections illustrating the isolation wall designs are shown in figures 4-27 

and 4-28. A typical detail of the as-built, redesigned joint between Posey tube segments is 

shown in figure 4-29. 

4.5.1.4. Junctions and Transitions 

Special detailing may need to be considered at the junction of a tunnel to a relatively stiffer 

structure such as a ventilation structure or a transit station, because relatively large seismically 

induced strains and forces may be generated at such junctions (see section 4.4.1.3(a)). This 

situation, for example, was found for the tubes connecting to portal buildings described in 

section 4.5.1.3. Special joints may need to be provided to allow movement between the tunnel 

and the adjoining structure and therefore reduce forces at these junctions. Figure 4-30 illustrates 

a seismic joint designed to allow three-dimensional movement at the junction of the transbay 

tube and a ventilation structure of the San Francisco Bay Area Rapid Transit (BART) (Douglas 

and Warshaw, 1971; Bickel and Tanner, 1982); sixty of these joints were provided around the 

perimeter of the transbay tube. 

Stresses also tend to be concentrated at locations along a tunnel where there is an abrupt change 

in stiffness of the geologic media, such as where a tunnel passes from rock to soil. Again, 

stresses and strains can be reduced by providing flexible joints at such transitions. The North 

Point tunnel in the San Francisco Wastewater System, for example, passes through an abrupt 

soil-rock interface (Owen and Scholl, 1981). For this interface, a special seismic joint was 

designed to accommodate 0.3 m of lateral displacement over a length of 15 m. A 2.5 cm 

thickness of crushable foam in the joint allowed the pipe to conform to the predicted 

displacements (figure 4-31). Another approach to design at an abrupt soil-rock transition is 

overexcavation of the rock and backfilling with soil to create a more gradual transition. 
194

Symm About

Tube

Approximate OG

Stone Column Gravel

Drainage Blanket

Slope Varies Existing Tube

Backfill

Pretube

Construction

Soil

Stone Columns, Typ

Tube

Tube

CL

CL

CL

Caltrans/Parsons Brinckerhoff, 1998 

Figure 4-27. Typical stone column placement around Webster tube. 

Approximate OG

Natural Soil

Tube

Jet Grout

Column Wall

Extend 2.4 m (8’) Below Original

Excavated Trench Bottom

1.2 m (4’-0”)Dia.

Min.

Existing

Tube Backfill

Varies

Natural Soil

1. 5 (5’) Sand +

- Stiff Clay

Col.

Typ

Tube

and WA Line

CL

CL

CL

1.5 m (5’-0”)

13.7 m (45’-0”)

11.3 m (37’-0”)

.......... . .

.

. . .

...... . .

.... . ...

. . ....... . .

.

.... . .

..

........ . ........ . ........ . ...... . ...... . .

..

...... . .

..... . ...........

6 m

(19’-9”)

Caltrans/Parsons Brinckerhoff, 1998 

Figure 4-28. Typical jet grout column around Posey tube. 
195

Caltrans/Parsons Brinckerhoff, 1998 

T. Jackson, personal communication, 2003 

Figure 4-29. Redesigned joint preventing tension and allowing compression and shear forces 

between segments of Posey tube. 

. 
196

COLLAR

BOOT

GASKETS

ASSEMBLY

WIRE ROPE

BOOT

FIXED RING

GASKETS

WIRE ROPE

 ASSEMBLY

TEFLON

BRACKET

SOCKET

Exterior

Face of 

Tube

Inside Face of Tube

Vertical

Sliding Face

Lubrication

 Tube

Bearing

Plate

Horiz.

Sliding

Face

Exterior Face of

 Tube

Bearing Plate

Faced with Teflon

Inside Face of Tube

Douglass and Warshaw, 1971; Bickel and Tanner, 1982 

Figure 4-30. Seismic joint for transbay tube. 

4.5.2. FAULT DISPLACEMENT-INDUCED FAILURE 

Retrofit strategies for portions of tunnels crossing active faults and potentially subject to fault 

displacement depend on the magnitude of the displacement and the width of the zone over which 

the displacement is distributed, as well as the geologic conditions. 

If large displacements are concentrated in a narrow zone, a retrofit strategy is to enlarge the 

tunnel across and beyond the displacement zone. This has been discussed or suggested in a 

number of publications, including Rosenbluth (1977), Owen and Scholl (1981), Brown et al. 

(1981), Desai et al. (1989), Rowe (1992), and Abramson and Crawley (1995), and has been 

implemented in rapid transit tunnels including San Francisco’s BART and Los Angeles’ Metro 

tunnels. 
197

2.75 m (9’- 0”)

Approved Neoprene Ring

(tightly fitted continuously

around tunnel lining) Crushable Styrofoam

(glued all around)

Tunnel Lining

.6 m (2’ - 0”) Collar

25 mm (1”)

25 mm (1”)

76 mm (3”)

25 mm (1”) Clearance

1.22 m (4’ - 0”) 13 #8 Hoops as Shown

#6 @ 0.23 m (8”)

Approved Sealant

(all around)

1

1

.3 m (1’- 0”) .3 m (1’- 0”) .3 m (1’- 0”)

NOTE: 1 in. = 25.4 mm; 1 ft = 0.3048 m.

Owen and Scholl, 1981 

Figure 4-31. Seismic joint for North Point tunnel. 
198

The concept of an enlarged tunnel to accommodate fault displacement is illustrated in figure 4-

32. The tunnel is made wide enough that the fault displacement will not close the tunnel and 

traffic can be resumed after repairs are made. Repairs include removal of lining and rock debris 

in the damaged tunnel sections, restoration of lining continuity, and repair of the pavement 

section in a highway tunnel, or realignment of the rails in a transit tunnel. The length of tunnel 

over which enlargement is made is a function of both the amount of fault displacement and the 

permissible curvature of the roadway or trackway. An S-shaped roadway or trackway is 

required after the earthquake in the enlarged tunnel region. The longer the enlarged tunnel, the 

smaller the post-earthquake curvature. The design of the enlarged Los Angeles Metro tunnel 

across the Hollywood fault zone is illustrated in figure 4-33. As shown in the cross section in 

the figure, the design allows for fault movement upward and to the left. After fault movement, 

the track in the enlarged tunnel, resting on ballast rock, would be realigned and ballast rock 

placed at the new line and grade after repair. 

Figure 4-32. Enlarged tunnel at fault crossing, plan view, strike-slip faulting. 
199

LA County MTA/Parsons Brinckerhoff, 1994 

Figure 4-33. Design of LA Metro tunnel across Hollywood fault zone. 
200

An enlarged tunnel may also surround an inner tunnel that is backfilled with frangible 

backpacking such as cellular concrete (figure 4-34). Cellular concrete is readily available at low 

cost and has a history of use in underground projects (Huff, 1971). It can be made with varying 

amounts of void space and may be engineered to have unit weights as low as 2.4 to 3.9 kN/m3

. It 

also has a relatively low yield strength to minimize lateral loads on the tunnel liner, but has 

adequate strength to resist normal soil pressures and other seismic loads such as minor ground 

shock and soil “loosening” load or other vertical loads above the excavation. It is highly 

compressible at strains of 60 percent or even more. It also has stable long-term properties with 

respect to hardening, chemical resistance, and creep behavior. 

If fault movements are small and/or distributed over a relatively wide zone, it is possible that a 

tunnel may be designed to accommodate the fault displacement by providing articulation of the 

tunnel liner using ductile joints. The effect is to allow the tunnel to distort into an S-shape 

through the fault zone without rupture and with repairable damage. The closer the joint spacing, 

the better the performance of the liner. This approach may not be feasible for fault 

displacements exceeding a few inches. 

Figure 4-34. Enlarged tunnel section with final liner and frangible 

backpacking to accommodate fault displacement. 

Design of a lining to accommodate fault displacement becomes more feasible in soft soils where 

the tunnel lining can more effectively redistribute the displacements. The requirements for 

tunnel water-tightness must be evaluated when considering the use of joints. 

An example of a segmented lining designed to accommodate small fault displacements is that of 

the South Bay Ocean Outfall shown in figure 4-35 (Kaneshiro et al., 1996a, 1996b). Largediameter longitudinal bolts extending through the precast concrete segments provide a certain 

amount of ductility for longitudinal extension and articulation in the fault zone. Figure 4-36 

illustrates a different approach to joints in segmented tunnels to withstand small fault 

movements. The joint design and neoprene seals permit extensional, compressional, and 

rotational movements while maintaining water-tightness. 
201

Kaneshiro et al., 1996 

Figure 4-35. Segment reinforcing and circumferential joint detail, precast concrete segmental 

liner used in Rose Canyon fault zone for South Bay Tunnel Ocean Outfall Project, San Diego. 
202

Precast Pipe

76 mm (3”)

76 mm (3”)

76 mm (3”) 76 mm (3”) 76 mm (3”)

Neoprene Compression

Seal on Spigot End

Outside Face

Neoprene

Compression

Seal on Bell

End

Plastic Liner

Where Indicated

Gasket Seal on

Spigot End

(See Detail A)

Pipe Wall

Thickness

25 mm (1”)

102 mm (4”)

127 mm (5”)

13 mm (1/2”) 13 mm (1/2”) 13 mm (1/2”)

DETAIL A

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Desai et al., 1989 

Figure 4-36. Flexible joint proposed for segmented tunnel lining in fault zone. 

An example of a joint designed to accommodate small fault displacements in a cast-in-place 

reinforced concrete tunnel lining is shown in figure 4-37. Compressive and tensile movement of 

the joint occurs in the fiberboard joint filler and through placing the No. 7 reinforcing bars in a 

pre-molded sleeve and bond breaker. The joints were placed on 10 foot centers (3 m) over a 

distance of about 56 m (185 feet) to resist a total displacement of approximately 300 mm (12 

inches) in any direction. 

An alternative to retrofitting a tunnel to withstand faulting displacements is to instead make 

contingency plans to facilitate repair as rapidly as possible after the earthquake. Modifications 

to portal structures may be made to facilitate safe ingress and emergency repair. Temporary 

supports and other materials essential to the rapid repair of the tunnel may be stockpiled, and 

tunneling and other specialty contractors may be put under contract in advance of the earthquake 

event. 
203

“B” Line

“A” Line

19 mm (3/4”) Bituminous

Fiber Board

(Pre-molded)

Pre-molded Sleeve

(Styrofoam or Equiv.)

#4 (TYP)

PVC Waterstop

(U-formed)

Fill with Sealant

(Mastic)

Bond Breaker

Styrofoam Filler

25 mm (1”) Dia. x 19 mm (3/4”)

#7 (TYP)

254 mm (10”) TYP 254 mm (10”) LAP

254 mm (10”)

#4 x 457 mm

(1’-6”)Long

@300 mm (12”)

O. C. TYP

Frame, 1995 

Figure 4-37. Flexible joint detail for Coyote Dam outlet tunnel. 

4.5.3. LANDSLIDING- AND LIQUEFACTION-INDUCED FAILURE 

If landsliding- or liquefaction-induced lateral spreading movements through a tunnel are a 

significant hazard, the hazard may be mitigated by stabilizing the landslide or stabilizing the 

ground to prevent liquefaction and/or resulting lateral spreading movements. It is doubtful that a 

tunnel can be designed to resist or accommodate the movements associated with these 

phenomena unless the hazard is localized and the amount of rock or soil involved in the 

phenomena is small. Other hazard mitigation approaches are rerouting the tunnel to avoid the 

hazard or making contingency plans. 

If the predicted effects of liquefaction are to cause local buildup of pore water pressure adjacent 

to the walls of a tunnel, an alternative retrofit measure is to strengthen the walls to resist the 

increased lateral earth pressures. 

Seismic (as well as static) landsliding has historically been a cause of failure at tunnel portals. 

The most effective mitigation is generally to stabilize the unstable earth mass. Portal structures 

also represent locations of change in geometry and stiffness and therefore are locations for 

concentrated forces at the connection of the tunnel and the portal. Either the connection must be 

strong enough to resist the large forces that may develop, or a joint must be designed to allow 

relative movement and reduce the forces. 

4.6. EXAMPLES OF TUNNEL SCREENING, EVALUATION, AND RETROFIT 

STRATEGIES 

Examples 4-1 through 4-4 illustrate details of analytical methodologies for seismic evaluation of 

tunnels. Example 4-5 provides a hypothetical example of the overall process of seismic 

screening, seismic evaluation, and development of seismic retrofit strategies.
204

EXAMPLE PROBLEM 4.1 – AXIAL AND CURVATURE DEFORMATION ALONG THE 

TUNNEL LONGITUDINAL AXIS DUE TO S-WAVES 

1. Earthquake parameters: 

Earthquake moment magnitude, Mw = 7.5 

Earthquake source-to-site distance = 10 km 

Peak ground acceleration at ground surface above the tunnel, amax = 0.5 g 

2. Tunnel parameters: 

Reinforced concrete circular tunnel: 

D = 6 m 

t = 0.3 m 

El = 24.8 x 106 kPa 

Il1 = 25.4 m4 

Al1 = 5.65 m2 

Depth = 100 m 

3. Soil parameters: 

γt = 19.0 kN/m3 

Cm

' = 800 m/s 

vm = 0.3 

f = 6,000 kN/m 

Assume that the shaking at the tunnel elevation is dominated by shear (S) body waves (i.e., for purposes 

of this example, an assessment has been made that significant surface waves are unlikely to occur at the 

tunnel during the design earthquake). 

a. Determine the seismic ground shaking parameters at the tunnel depth: 

aS = 0.7 amax = 0.7(0.5 g) = 0.35 g (Table 4-3) 

VS = (97 cm/s g) (0.35 g) = 34 cm/s = 0.34 m/s (Table 4-4) 

Cs = 2 km/s and Ts = 2 seconds (default values) 

L = CS ⋅ TS = 2000 m/s (2 s) = 4000 m (Eq. 4-10) 

b. Determine the axial strain and stress from combined longitudinal and curvature deformations, 

assuming negligible soil-tunnel interaction: 

⎡ ⎤

ε = ⎢ ⎥ φ φ + φ

⎣ ⎦

ab 3 S S

2

S S

V a sin cos Y cos

C C for S-waves (Eq. 4-2) 

⎡ ⎤ ε = ° °+ ° ⎢ ⎥ ⎣ ⎦

ab 3

2

0.34 0.35(9.81) sin45 cos45 3 cos 45

2000 2000
205

− ε= + = ab 7 0.000085 9.1(10 ) 0.000085

σ= ⋅ = ab 6 0.000085(24.8 10 kPa) 2100kPa (Eq. 4-4) 

c. Evaluate the effect of soil-tunnel interaction: 

γ ′ ′ = = t 2 6 G C 1.24(10 ) kPa m m g

 (Eq. 4-11) 

π − ′ = = −

m m

a h

m

16 G (1 v ) D K K

(3 4v ) L (Eq. 4-8) 

π − == = −

6

a h

16 1.24(10 )(1 0.3) 6 K K 36,300 kPa (3 4(0.3)) 4000

−

⎧ ⎫ ⎪ ⎪ ⎛ ⎞ π

= + ⎨ ⎬φ ⎜ ⎟ ⎪ ⎪ ⎝ ⎠ ⎩ ⎭

1 2

l l1 2

a

E A 2 R 1 cos

K L (Eq. 4-6) 

−

⎧ ⎫ ⎪ ⎪ ⎛ ⎞ π = + °= ⎨ ⎬ ⎜ ⎟ ⎪ ⎪ ⎝ ⎠ ⎩ ⎭

1 2 6 24.8(10 )5.65 2 2 R 1 cos 45 0.99

36300 4000

Based on the above calculation, the effects of soil-tunnel interaction will not significantly reduce the 

longitudinal strains or stresses in the tunnel lining. 

d. Check the axial force, Q, against the maximum force that can be developed by friction of the soil 

against the tunnel lining: 

=σ ⋅ = ⋅ = ab Q A 2100 5.65 11,900 kN l1

max f == = fL (6000)(4000) (Q ) 6,000,000 kN 4 4 (Eq. 4-12) 

Q (Q ) ; < max f thus, the axial force is not limited by frictional capacity. 
206

EXAMPLE PROBLEM 4.2 - AXIAL AND CURVATURE DEFORMATION ALONG THE 

TUNNEL LONGITUDINAL AXIS DUE TO R-WAVES

1. Earthquake parameters: 

Earthquake moment magnitude, Mw = 7.5 

Earthquake source-to-site distance = 20 km 

2. Tunnel parameters: 

Reinforced concrete circular tunnel

D = 6 m 

t = 0.3 m 

El

 = 24.8 x 106 kPa 

Il1 = 25.4 m4 

Al1 = 5.65 m2 

Depth to top of tunnel, Z = 15 m 

3. Soil parameters: 

γt = 17.0 kN/m3 

Cm

' = 250 m/s 

vm = 0.45 

f = 1500 kN/m 

Assume that the shaking at the tunnel elevation is dominated by Rayleigh (R) surface waves (i.e., for 

purposes of this example, an assessment has been made that significant surface waves producing the 

strong ground velocities and displacements are likely to occur at the tunnel during the design 

earthquake). 

a. Determine the seismic ground shaking parameters at the tunnel depth. From a site-specific 

assessment, it was determined that: 

aR = 0.20 g 

VR = 30 cm/s = 0.30 m/s 

CR = 500 m/s and TR = 2 seconds 

L = CR ⋅ TR = 500 m/s (2 s) = 1000 m (Eq. 4-10) 

b. Determine the axial strain and stress from combined longitudinal and curvature deformations in the 

horizontal plane, assuming negligible soil-tunnel interaction: 

⎡ ⎤

ε = ⎢ ⎥ φ + φ φ

⎣ ⎦

ab 2 2 R R

2

R R

V a cos Y sin cos 

C C for R-waves (Eq. 4-3) 

⎡ ⎤ ε = °+ ° ° ⎢ ⎥ ⎣ ⎦

ab 2 2

2

0.30 0.20(9.81) cos 0 3 sin0 cos 0

500 500

ε= += ab 0.0006 0 0.0006 

σ = ε= ab ab E1 14,880 kPa (Eq. 4-4) 
207

c. Determine the axial strain and stress from curvature deformations in the vertical plane, assuming 

negligible soil-tunnel interaction: 

ε= φ − ab 2 R

2

R

a Y cos for R waves

C (Eq. 4-5) 

( ) ε = °= ab 2

2

0.20 9.81

3 cos 0 0.00002

500

(Negligible compared to axial strain determined in (b) above.) 

d. Evaluate the effect of soil-tunnel interaction: 

γ ′ ′ = = t 2 G C 108,000 kPa m m g

 (Eq. 4-11) 

π − ′ = = −

m m

a h

m

16 G (1 v ) D K K

(3 4v ) L (Eq. 4-8) 

π − == = − a h16 (108000)(1 0.45) 6 K K 15,000 kPa (3 4(0.45)) 1000

−

⎧ ⎫ ⎪ ⎪ ⎛ ⎞ π

= + ⎨ ⎬φ ⎜ ⎟ ⎪ ⎪ ⎝ ⎠ ⎩ ⎭

1 2

l l1 2

a

E A 2 R 1 cos

K L (Eq. 4-6) 

( ) −

⎧ ⎫ ⎪ ⎪ ⎛ ⎞ π = + °= ⎨ ⎬ ⎜ ⎟ ⎪ ⎪ ⎝ ⎠ ⎩ ⎭

1 6 2

2 24.8(10 ) 5.65 2 R 1 cos 0 0.730

15,000 1000 (Eq. 4-6) 

σ=ε = ab ab E R 10,900 kPa l

e. Check the axial force, Q, against the maximum force that can be developed by friction of the soil 

against the tunnel lining: 

=σ ⋅ = = ab Q A 10,900 (5.65) 61,600 kN l1

max f == = fL (1500)(1000) (Q ) 375,000 kN 4 4 (Eq. 4-12) 

Q (Q ) ; < max f thus, the axial force is not limited by frictional capacity. 
208

EXAMPLE PROBLEM 4.3 - OVALING DEFORMATION OF A CIRCULAR TUNNEL 

1. Earthquake parameters: 

Earthquake moment magnitude, Mw = 7.5 

Earthquake source-to-site distance = 10 km 

Peak ground acceleration at ground surface above the tunnel, amax = 0.5 g 

2. Tunnel parameters: 

Reinforced concrete circular tunnel

D = 6 m 

t = 0.3 m 

El

 = 24.8 x 106 kPa 

Il2 = 0.0023 m4

/m 

Al2 = 0.3 m2

/m 

vl

 = 0.2 

Depth to top of tunnel, Z = 15 m 

3. Soil parameters: 

γt = 19.0 kN/m3

Cm

' = 250 m/s 

vm = 0.3 

a. Determine the seismic ground shaking parameters at the tunnel depth: 

aS = 0.85 amax = 0.85(0.5 g) = 0.425 g (Table 4-3) 

VS = (130 cm/s g) (0.425 g) = 55 cm/s = 0.55 m/s (Table 4-4) 

γ== = ′

s

smax

m

V 0.55 0.0022

C 250 (Eq. 4-28) 

b. Determine the normal stress in the liner assuming full slippage condition: 

γ ′ ′ = = t 2 G C 121,000 kPa m m g

 (Eq. 4-11) 

′ − =

2 3

m l

l l2

G (1 v )D F

24E I (Eq. 4-17) 

− = =

2 3

6

121000 (1 (0.2) ) 6 F 18.3

24(24.8(10) )0.0023

− − = == + − +−

m

m

1 v 1 0.3 K 0.0351

F 2.5 3v 18.3 2.5 3(.3) (Eq. 4-16) 
209

θ = ′ γ θ T( ) G DK sin2 m smax (Eq. 4-13) 

T(45 ) (121000)6(0.0351)(0.0022)sin2(45 ) 56.1 kN/m ° = °=

θ = ′ γ θ 2

m smax

1 M( ) G D K sin2 2 (Eq. 4-15) 

° = °= ⋅ 1 2 M(45 ) (121000)6 (0.0351)(0.0022) sin2(45 ) 168 kN m/m 2

σ= ± = ± =

l2 l2

T M(t / 2) 56.1 168(0.3 / 2) 11,100 kPa A I 0.3 0.0023 (Eq. 4-29) 

c. Determine the normal stress in the liner assuming no slippage condition using Penzien and Wu 

(1998): 

− − ′ === + − +−

m

m

1 v 1 0.3 K 0.0348

F 3 4v 18.3 3 4(.3) (Eq. 4-21) 

θ = ′ ′γ θ T( ) 2G DK sin2 m smax (Eq. 4-18) 

T(45 ) 2 (121000)6(0.0348)(0.0022)sin2(45 ) 111 kN/m ° = °=

θ = ′ ′γ θ 2

m smax

1 M( ) G D K sin2 2 (Eq. 4-20) 

° = °= ⋅ 1 2 M(45 ) (121000)6 (0.0348)(0.0022)sin2(45 ) 166 kN m/m 2

σ= ± = ± =

l2 l2

T M(t / 2) 111 166(0.3 / 2) 11,200 kPa A I 0.3 0.0023 (Eq. 4-29) 

d. Determine the normal stress in the liner assuming no slippage condition using Wang (1993): 

( )

( )

′ − ν − == = − ν −

2 2 m 1

6

1 m

G1 D 121000(1 0.2 )6 C 0.234

Et 1 2 24.8(10 )0.3(1 2(0.3)) (Eq. 4-27) 

( )( ) ⎡ ⎤ = − + − + − + +− ⎡ ⎤ ⎣ ⎦ ⎢ ⎥ ⎣ ⎦

2

o m m mm m

5 a F 3 2v 1 2v C C 8v 6v 6 8v

2 (Eq. 4-26) 

( )( ) ⎡ ⎤ = − + − + − + +− ⎡ ⎤ ⎣ ⎦ ⎢ ⎥ ⎣ ⎦

2

o

5 a 18.3 3 2(0.3) 1 2(0.3) 0.234 0.234 8(0.3) 6(0.3) 6 8(0.3) 2

a 49.5 o =
210

( )( ) ( ) ⎧ ⎫ = − −− − + ⎨ ⎬ ⎡ ⎤ ⎣ ⎦ ⎩ ⎭

2

2 m mo

1 a F 1 2v 1 C C 1 2v 2 /a

2 (Eq. 4-24) 

( )( ) ( )( ) ⎧ ⎫ = − −− −+ = ⎨ ⎬ ⎡ ⎤ ⎣ ⎦ ⎩ ⎭

2

2

1 a 18.3 1 2(0.3) 1 0.234 0.234 1 2(0.3) 2 / 49.5 0.152 2

( ) ( ) ⎧ ⎫ = − + − − ν− ⎨ ⎬ ⎡ ⎤ ⎣ ⎦ ⎩ ⎭ 3 m mo

1 a F C 1 2v 1 C 1 2 2 / a

2 (Eq. 4-25) 

( ) ( ) ⎧ ⎫ = − +− − − = ⎨ ⎬ ⎡ ⎤ ⎣ ⎦ ⎩ ⎭ 3

1 a 18.3 0.234 1 2(0.3) 1 (0.234) 1 2(0.3) 2 / 49.5 0.362 2

θ= + ′ γ θ m 2 smax

1 T( ) G D(1 a ) sin2 2 (Eq. 4-22) 

° = + °= 1 T(45 ) 121000(6)(1 0.152)0.0022sin2(45 ) 920 kN/m 2

θ= − − ′ γ θ 2

m 2 3 smax

1 M( ) G D (1 a 2a ) sin2 8 (Eq. 4-23) 

°= − − °= ⋅ 1 2 M(45 ) 121000(6) (1 0.152 2(0.362))0.0022sin2(45 ) 149 kN m/m 8

σ= ± = ± =

l2 l2

T M(t / 2) 920 149(0.3 / 2) 12,800 kPa A I 0.3 0.0023 (Eq. 4-29) 

e. Conclusion: 

It is recommended that the maximum stress be obtained using the formulation that produces the highest 

stress. Of the three methods for estimating stress in the liner due to cross sectional deformation, the 

Wang (1993) no slippage condition formulations estimate the highest normal stress (12,800 kPa) in the 

liner. 
211

EXAMPLE PROBLEM 4.4 - RACKING DEFORMATION OF A RECTANGULAR TUNNEL 

1. Earthquake parameters: 

Earthquake moment magnitude, Mw = 7.5 

Earthquake source-to-site distance = 10 km 

Peak horizontal ground acceleration at ground surface above the tunnel, amax = 0.5 g 

Peak vertical ground acceleration at ground surface above the tunnel, av, = 0.4 g 

2. Tunnel parameters: 

Width, w = 18 m 

Height, H = 6 m 

Depth to top of tunnel, Z = 5 m 

Tunnel founded on soil 

3. Soil parameters: 

γt = 17.0 kN/m3 

Cm

' = 80 m/s 

vm = 0.4 

Racking Deformation Analysis

a. Determine the free-field soil shear deformation, ∆ff:

γs max = 0.0056 (estimated using site response analyses) 

∆ = γ ff smaxH

∆= = ff (0.0056)(6) 0.034 m

b. Determine the flexibility ratio, Fr: 

γ ′ ′ = = t 2 G C 11,000 kPa m m g

 (Eq. 4-11) 

′ = m

r

G w F

SH (Eq. 4-30) 

Through structural analysis, the force required to cause a unit racking deflection (1 m) for a unit length 

(1 m) of the cross section, S, was determined to be 150,000 kPa. Note that for the flexibility ratio, Fr, to 

be dimensionless, the units of S must be in force per area. 

r = = 11000(18) F 0.22

150000(6)

For Fr = 0.22 and Vm = 0.4, the full slip relationship produces a racking coefficient, Rr, of 0.34 and the noslip relationship produces a Rr = 0.32 (figure 4-13b). The greater racking coefficient produced by the fullslip relationship is used to determine the racking deformation of the tunnel. 
212

c. Determine the racking deformation of the structure, ∆r: 

∆= ∆ r r ff R (Eq. 4-31) 

∆= = r 0.34(0.034) 0.012 m

d. Determine the stresses in the structure by performing a structural analysis with an applied racking 

deformation of 0.012 m as shown in figure 4-14. Both the point load and triangularly distributed load 

pseudo-lateral force models should be applied to identify the maximum forces in each location of the 

liner. 
213

EXAMPLE PROBLEM 4.5 - SEISMIC SCREENING EVALUATION AND RETROFIT 

STRATEGIES FOR A HYPOTHETICAL TUNNEL 

Description of Tunnel 

A bored transit tunnel 18 feet (5.49 m) in diameter passes through bedrock and into a soil-filled 

sedimentary basin. The depth to the top of the tunnel in both rock and soil is 15 m. The bedrock is 

moderately jointed and locally intensely sheared. The soil at the tunnel grade is a medium stiff clay. The 

groundwater table is 3 m below the ground surface. The tunnel in rock has a 0.3 m-thick unreinforced 

concrete liner that is moderately cracked locally. The tunnel in soil has a steel segmented liner having 

the cross section shown in the figure below (after Penzien and Wu, 1998). Assessment of the concrete 

lining by inspection, coring, and geophysical sounding indicates that the concrete has moderate strength 

but has frequent voids behind the lining. The segmented lining appears to be undamaged and is 

constructed immediately against the excavation face. 

Seismic Environment 

An active earthquake fault capable of generating a moment magnitude MW 7.5 earthquake is located a 

closest distance of 2 km from the tunnel at the basin edge. Based on current national seismic ground 

motion maps, the level of ground shaking for seismic evaluation and retrofit design (if required) is a peak 

acceleration of 0.50 g at the ground surface at the basin edge. This acceleration is judged to be 

applicable to soil or rock. 

CG

30” (762 mm)

y=4.958”

7” (178 mm)

(125.9 mm)

_

(15.9 mm) 5”

8

1 (36.5 mm) 7”

16 1 (36.5 mm) 7”16

Ci

C = 52.1 mm 0

ci

c 0

Penzien and Wu, 1998 

Screening

Based on the screening guidelines in section 4.3.3 and table 4-1, the level of ground shaking, soil and 

geologic conditions, and the condition of the liner, the tunnel cannot be screened out as seismically 

adequate for ground shaking. The tunnel is not known to be intersected by an active fault, a landslide, or 

liquefiable soils (section 4.3.3.1). Therefore, further seismic evaluation is required only for ground 

shaking. 
214

Evaluation and Retrofit 

1. Concrete liner parameters: 

D = 5.49 m 

Al2 = 0.3 m2

/m 

Il2 = 2.25 x 10-3 m4

/m 

′

c

f = 20.7 x 103 kPa 

t = 0.3 m 

El

 = 22 x 106 kPa 

vl

 = 0.2 

co = ci

 = 0.15 m (distance to outer and inner fiber of lining from center of gravity of lining) 

Z = 15 m 

Hw = 12 m (distance to groundwater table above tunnel) 

2. Steel liner parameters: 

D = 5.49 m

Al2 = 0.0314 m2/m 

Il2 = 9.63 x 10-5 m4

/m 

fy = 249 x 103

 kPa 

El

 = 20.4 x 1010 N/m2 

vl = 0.3 

co = 0.0521 m (figure 4-38) 

ci

 = 0.1259 m (figure 4-38) 

Z = 15 m 

Hw = 12 m (distance to groundwater table above tunnel) 

3. Soil parameters: 

γt = 17.0 kN/m3 

′ Cm = 80 m/s 

′ Gm = 1.109 x 107

 N/m2 (eq. 4-11) 

′ Em = 32.1 x 106

 N/m2 [= 2(1 + vm) ′ Gm ] 

vm = 0.45 

Ko = 0.5 (coefficient of static lateral earth pressure at rest) 

γs-max = 0.007 

4. Rock parameters: 

γt = 19.65 kN/m3 

′ Cm = 800 m/s 

′ Gm = 12.8 x 108

 N/m2

′ Em = 33.3 x 108

 N/m2 [= 2 (1+ vm) ′ Gm ] 

vm = 0.3 

Ko = 0.3 (coefficient of static lateral earth pressure at rest) 

γs-max = 0.0005 

Note: The elastic properties of the soil and rock under static and dynamic conditions have been assumed 

to be equal. It was judged that the softening of the soil and rock resulting from construction of the tunnel 

would be similar to the softening that would occur during earthquake shaking. 
215

Axial and Curvature Deformations Along the Tunnel Longitudinal Axis (section 4.4.1.3) 

Concrete tunnel in rock, response due to S-waves:

Peak ground acceleration, as, peak ground velocity Vs, and apparent wave propagation velocity, Cs at 

tunnel level: 

as = 0.85 (0.50 g) = 0.425 g (Table 4-3) 

Vs = 0.425 g (97 cm/s) = 41 cm/s (Table 4-4) 

Cs = 2 km/s (default value) 

Axial strain and stress induced by axial component of S-wave: 

ε = φ φ s

s

V sin cos

C (Eq. 4-2)

ε= ° ° = 0.41 m/ s sin45 cos45 0.0001

2000 m/ s

σ= ⋅ = ⋅ 6 3 0.0001 (22 10 ) kPa 2.2 10 kPa

Axial strain and stress due to bending induced by transverse component of S-wave: 

ε = φ s 3

2

s

a Y cos

C

− ε= °= ×

2

3 6

2

(0.425g)(9.81m/ s ) (2.745m) cos 45 1.01 10 (2000m/ s) (Eq. 4-2)

(Note: Negligible for φ = 45° which maximizes strain due to axial component of S-wave.) 

− σ= ε= ⋅ ⋅ = 6 6 E (22 10 )(1.01 10 ) 22kPa l (negligible) 

Steel tunnel in soil, response due to S-waves:

as, Vs, and Cs at tunnel level:

as = 0.85 (0.50 g) = 0.425 g (Table 4-3)

Vs = 0.425 g (195 cm/s) = 83 cm/s (Table 4-4)

Cs = 2 km/s (default value for S-waves) 

Axial strain and stress due to axial component of S-wave: 

ε = φ φ s

s

V sin cos

C (Eq. 4-2)
216

ε= ° ° = 0.83m/ s sin45 cos45 0.00021

2000m/ s

σ= ⋅ = ⋅ 7 3 0.00021(20.4 10 ) 42.8 10 kPa

Axial strain and stress due to bending induced by transverse component of S-wave: negligible, as above 

for rock.

Steel tunnel in soil, response due to R-waves:

From a site-specific seismological assessment, it was determined that significant R-waves would be 

generated farther into the basin. From this assessment, it was determined that: 

VR = 30 cm/s 

CR = 0.5 km/s 

Axial strain and stress due to axial component of R-wave: 

ε = φ R 2

R

V

cos

C (Eq. 4-3) 

ε= ° = 0.30 m/ s 2 cos 0 0.0006

500 m/ s

σ= ⋅ = ⋅ 7 3 0.0006(20.4 10 ) 122 10 kPa

Axial strain and stress due to bending induced by the vertical component of R-wave: The vertical R-wave 

component is out of phase with the horizontal component and produces negligible axial strain compared 

to the horizontal component (see eq. 4-5). 

Discussion of Axial and Curvature Response Along the Tunnel Longitudinal Axis:

In this example, the calculated axial stresses are much less than the concrete compressive strength and 

steel yield strength but are approximately equal to the tensile strength of concrete taken as 0.1 ′

c

f . Soilstructure interaction (eq. 4-6), neglected in the calculations, would further reduce tunnel response in soil, 

but ground motion incoherence could increase response (section 4.4.1.3). Strains in the vicinity of the 

soil-rock contact could be increased by the geologic discontinuity. If increased by a factor of two, as 

discussed in section 4.4.1.3(a), stresses in the concrete liner would still be well below compressive 

strength while being about twice the tensile strength. The effects of the formation of circumferential 

tension cracks in the concrete liner in the vicinity of the soil-rock contact require structural evaluation. 

Seismic Retrofit:

The analysis of tunnel longitudinal response (longitudinal axial strains) indicates that axial stresses are 

well below the compressive strength of the concrete lining or the yield strength of the steel lining. Axial 

stresses may substantially exceed concrete tensile strength in the vicinity of the soil-rock contact. A 

structural evaluation is required to assess effects of tensile cracking. If retrofit is judged to be needed in 

the local region of the soil-rock contact, an appropriate retrofit measure would consist of removal of the 

unreinforced concrete lining and placement of a reinforced concrete lining. An alternative, if space 

permits, would be installation of an inner steel liner with grout in the annulus between steel and existing 

concrete. 
217

In areas where voids were found behind the concrete lining during inspection, grouting is desirable to 

assure continuous contact between the lining and the soil and rock. Areas where the lining was found to 

be moderately cracked during inspection could be considered for additional retrofit. If the cracking were 

indicative of locally excessive pressures against the lining due to geologically weak zones (e.g., a zone of 

highly sheared rock), strengthening of the liner by removal and replacement of sections of the liner with a 

reinforced concrete liner or placement of an interior steel liner could be considered. 

STEEL TUNNEL IN SOIL: OVALING DEFORMATION OF TUNNEL CROSS SECTION 

(SECTION 4.4.1.4) 

Analyses of stresses in the steel tunnel in soil are conducted in this section using two formulations. The 

conditions of full-slip and no-slip at the soil-tunnel interface are considered in both formulations. First, the 

formulation of Schwartz and Einstein (1980) is used for the calculation of static stresses; these static 

stresses are combined with the dynamic stresses computed using the method of Wang (1993). Second, 

the formulation of Penzien and Wu (1998) is used to calculate static and dynamic stresses. 

The intermediate calculations in these examples contain more significant figures than what is typically 

used in hand calculations. This was done to minimize the transmission of errors from the intermediate 

steps to the solutions. Calculations were conducted in the program Mathcad (Mathsoft, 1998). 

Equations for static stresses using the formulations of Schwartz and Einstein (1980) and Penzien and Wu 

(1998) can be found in the respective publications. Reference numbers for these equations are followed 

by †

" " or 

††

" " and do not appear in this manual. Equations for dynamic stresses are presented in this 

manual. 

The sign convention used for static and dynamic forces and moments is shown on figures 4-10 and 4-11. 

Compressive stresses are taken to be positive. The sign convention used for the calculation of static 

forces and moments by the formulation of Penzien and Wu (1998) has been changed to be consistent 

with figures 4-10 and 4-11. Thrusts and moments vary with position in the tunnel liner (i.e., vary with 

angle θ). The definition of θ is shown on figure 4-10. 

Steel Tunnel in Soil - Static Stresses in Soil at Tunnel Mid-depth:

Vertical total stress 

σ= + γ= + ⋅ = 3

v t

D 5.49 (Z ) (15 )(17 10 ) 301 kPa 2 2

Pore water stress 

= + γ= + ⋅ = 3

w w

D 5.49 u (H ) (12 )(9.81 10 ) 144 kPa 2 2

Vertical effective stress 

σ =σ = = - - v v ' u 301 144 157 kPa

Steel tunnel in Soil - Static Moment, Thrust, and Stress by Method of Schwartz and Einstein (1980) for 

the Condition of No-Slip between the Tunnel and the Soil:

-

− ⋅ − = = − ⋅

2 6 2

m l

2 11 2

l l2 m

E' r(1 v ) (32.1 10 )(2.745)(1 0.3 ) C*

E A (1 v ) (2.04 10 )(0.0314)(1 0.45 ) = 0.015696 (Eq. A-3 †

) 
218

-

- -

- -

⋅ = = ⋅ ⋅

3 2 6 32

m l

2 11 5 2

l l2 m

E' r (1 v ) (32.1 10 )(2.745 )(1 0.3 ) F*

EI (1 v ) (2.04 10 )(9.63 10 )(1 0.45 ) = 38.56438 (Eq. A-6 †

) 

− = ++ −

* m

0

m

C * F * (1 v ) a

C * F * C * F * (1 v ) (Eq. A-36 †

) 

 − − = =⋅ ++ −

3 (0.015696)(38.56438)(1 0.45) 8.555 10

(0.015696) (38.56438) (0.015696)(38.56438)(1 0.45)

+ −+ β =

++ −

m m

m

(6 F*)C * (1 v ) 2F * v

3F * 3C * 3C * F * (1 v ) (Eq. A-41b †

) 

 + −+ = = ++ −

(6 38.56438)(0.015696)(1 0.45) 2(38.56438)(0.45) 0.30147

3(38.56438) 3(0.015696) 3(0.015696)(38.56438)(1 0.45)

− = − + − β− β −

* m

2

mm m

C * (1 v ) b

2[C * (1 v ) 4v 6 3 C * (1 v )] (Eq. A-41c †

) 

− = −+ − − −(0.015696)(1 0.45)

2[(0.015696)(1 0.45) 4(0.45) 6(0.30147) 3(0.30147)(0.015696)(1 0.45)]

= − * b 0.541 2

= β= − =− * * a b ( 0.540)(0.30147) 0.163 (Eq. A-41d 2 2

†

) 

Static thrust: 

σ = + − +− + θ v * *

s 00 0 2

r ' T [(1 K )(1 a ) (1 K )(1 2a )cos(2 )] 2 (Eq. A-48a †

) 

− = + − ⋅ +− +− θ 3

s

(2.745m)(157kPa) T [(1 0.5)(1 8.556 10 ) (1 0.5)(1 2( 0.163))cos(2 )] 2 

=+ θ 320 72.6cos(2 )kN

m

Add component of thrust due to hydrostatic water pressure: 

T ur (144kPa)(2.745m) 395 h == = kN

m

= + + θ= + θ s T (320 395) 72.6cos(2 ) 715 72.6cos(2 )kN

m

Maximum and minimum static thrusts: 

max(T ) 788 s = kN

m

min(T ) 643 s = kN

m
219

Static moments: 

- - σ = +θ

2

v * *

s 0 22

r ' M (1 K )(1 2a 2b )cos(2 ) 4 (Eq. A-48b †

) 

= − −− +− θ

2

s

(2.745 )(157kPa) M (1 0.5)(1 2( 0.163) 2( 0.540))cos(2 ) 4

= θ M 36.3cos2 s

Maximum and minimum static moments: 

= ⋅ s max(M ) 36.3kN m

m

= − ⋅ s min(M ) 36.3kN m

m

Combine stresses from static thrust and moment. 

Stress at outer fiber of liner: 

0 45 90 135 180 225 270 315 360

600

700

800

Static Thrust

Angle (Theta - deg)

Force (kN/m)

0 45 90 135 180 225 270 315 360

50

0

50

Static Moment

Angle (Theta - deg)

Moment (kN-m/m)
220

σ = - s s0

so

l2 l2

T Mc

A I

Stress at inner fiber of liner: 

σ= + s si

si

l2 l2

T Mc

A I

Maximum and minimum combined stresses: 

-

σ= ⋅

σ= ⋅

σ= ⋅

σ= ⋅

4

so

3

so

4

si

4

si

max( ) 4.00 10 kPa

min( ) 5.55 10 kPa

max( ) 7.23 10 kPa

min( ) 2.67 10 kPa

Steel Tunnel in Soil - Dynamic Moment, Thrust, and Stresses by Method of Wang (1993) for the 

Condition of No-Slip between the Tunnel and the Soil:

γ ⋅ = = =⋅

2 3 2

t m 7

m 2

C' (17 10 )(80 ) G' 1.109 10 N

g (9.81) m (Eq. 4-11) 

-

− ⋅ - == = ⋅ ⋅

2 3 7 23

m l

11 5

l l2

G' (1 v )D (1.109 10 )(1 0.3 )(5.49 ) F 3.54323

24EI 24(2.04 10 )(9.63 10 ) (Eq. 4-17) 

-

-

− ⋅ == = − ⋅

2 7 2

m l

11

l m

G' (1 v )D (1.109 10 )(1 0.3 )(5.49) C 0.08653

E t(1 2v ) (2.04 10 )(0.0314)(1 2(0.45)) (Eq. 4-27) 

= − +− + − + +− 2

0 m m mm m

5 a F[(3 2v ) (1 2v )C] C( 8v 6v ) 6 8v 2 (Eq. 4-26) 

= − +− + − +

+− =

2

0

5 a 3.54323[(3 2(0.45)) (1 2(0.45))(0.08653)] (0.08653)( 8(0.45) 6(0.45 )) 2

6 8(0.45) 9.881

⎡ ⎤ = − −− − + ⎢ ⎥ ⎣ ⎦

2

2m m

0

1 1 a [F(1 2v )(1 C)] C(1 2v ) 2 2 a (Eq. 4-24) 

⎡ ⎤ = − − − −+ ⎢ ⎥ ⎣ ⎦

2

2

1 1 a [(3.54323)(1 2(0.45))(1 (0.08653))] (0.08653)(1 2(0.45)) 2 2 (9.881)

 = 0.235

⎡ ⎤ = − +− − − ⎢ ⎥ ⎣ ⎦ 3m m

0

1 1 a F[C(1 2v ) 1] C(1 2v ) 2 2 a (Eq. 4-25) 
221

⎡ ⎤ = − +− − − = ⎢ ⎥ ⎣ ⎦ 3

1 1 a (3.54323)[(0.08653)(1 2(0.45)) 1] (0.08653)(1 2(0.45)) 2 0.159 2 (9.881)

Dynamic thrust: 

= + γ θ d m 2 smax

1 T G' D(1 a ) sin(2 ) 2 (Eq. 4-22) 

 = ⋅ + θ= θ 1(1.109 10 )(5.49)(1 0.235)(0.007)sin(2 ) 263sin(2 ) 7 kN

2 m

Maximum and minimum dynamic thrusts: 

max(T ) 263 d = kN

m

min(T ) 263 d = − kN

m

Dynamic moment: 

= −− γ θ 2

d m 2 3 smax

1 M G' D (1 a 2a ) sin(2 ) 8 (Eq. 4-23) 

= ⋅ −− θ 7 2

d

1 M (1.109 10 )(5.49 )(1 (0.235) 2(0.159))(0.007)sin(2 ) 8

= θ ⋅ d M 131sin(2 )kN m

m

Maximum and minimum dynamic moments: 

= ⋅ d max(M ) 131kN m

m

= − ⋅ d min(M ) 131kN m

m

0 45 90 135 180 225 270 315 360

400

200

0

200

400 Dynamic Thrust

Angle (Theta - deg)

Force (kN/m)
222

Combine stresses from dynamic thrust and moment. 

Dynamic stress at outer fiber of liner: 

σ = - d d0

do

l2 l2

T Mc

A I

Dynamic stress at inner fiber of liner: 

σ= + d di

di

l2 l2

T Mc

A I

Maximum and minimum combined dynamic stresses: 

-

-

σ= ⋅

σ= ⋅

σ= ⋅

σ= ⋅

4

do

4

do

5

di

5

di

max( ) 6.240 10 kPa

min( ) 6.240 10 kPa

max( ) 1.794 10 kPa

min( ) 1.794 10 kPa

Steel Tunnel in Soil - Combined Static and Dynamic Stresses by Method of Schwartz and Einstein (1980)

and Wang (1993) for the Condition of No-Slip Between the Tunnel and the Soil:

Stress at outer fiber of liner: 

σ =σ +σ 0 so do

Stress at inner fiber of liner: 

σ =σ +σ i si di

Maximum and minimum combined stresses: 

0 45 90 135 180 225 270 315 360

200

100

0

100

200 Dynamic Moment

Angle (Theta - deg)

Moment (kN-m/m)
223

-

-

σ= ⋅

σ= ⋅

σ= ⋅

σ= ⋅

4

o

4

o

5

i

5

i

max( ) 8.75 10 kPa

min( ) 4.19 10 kPa

max( ) 2.09 10 kPa

min( ) 1.63 10 kPa

Maximum tensile and compressive stresses occur on the inside face of the liner. The maximum tensile 

and compressive stresses are 64 and 84 percent, respectively, of the yield stress. 

Steel Tunnel in Soil - Static Moment, Thrust, and Stresses by Method of Schwartz and Einstein (1980) for 

the Condition of Full-Slip between the Tunnel and the Soil:

′ − ⋅ − = = −⋅ −

2 6 2

* m l

2 11 2

l l2 m

E r(1 v ) (32.1 10 )(2.745)(1 0.3 ) C

E A (1 v ) (2.04 10 )(0.0314)(1 0.45 ) = 0.015696 (Eq. A-3 †

) 

−

′ − ⋅ − = = − ⋅ ⋅−

3 2 63 2

* m l

2 11 5 2

l l2 m

E r (1 v ) (32.1 10 )(2.745 )(1 0.3 ) F

EI (1 v ) (2.04 10 )(9.63 10 )(1 0.45 ) = 38.56438 (Eq. A-6 †

) 

− = ++ −

* m

0

m

C * F * (1 v ) a

C * F * C * F * (1 v ) (Eq. A-32a †

) 

 − − = =⋅ ++ −

3 (0.015696)(38.56438)(1 0.45) 8.555 10

(0.015696) (38.56438) (0.015696)(38.56438)(1 0.45)

+ −ν + − == = −ν + − ν − + −

* m

2

m m

(6 F*)(1 ) (6 38.56438)(1 0.45) a 0.436

2F * (1 ) 6(5 6 ) 2(38.56438)(1 0.45) 6(5 6(0.45)) (Eq. A-32b †

) 

0 45 90 135 180 225 270 315 360

4 .105

2 .105

0

2 .105

4 .105

Stress on Outside Face

Stress on Inside Face

Combined Static and Dynamic Stresses

Angle (Theta - deg)

Stress (kPa)
224

Static thrust: 

- -- σ′ =+ + θ v * *

s 00 0 2

r T [(1 K )(1 a ) (1 K )(1 2a )cos(2 )] 2 (Eq. A-47a †

) 

− = + − ⋅ +− − θ 3

s

(2.745m)(157kPa) T [(1 0.5)(1 8.556 10 ) (1 0.5)(1 2(0.436))cos(2 )] 2 

=+ θ 320 13.7cos(2 )kN

m

Add component of thrust due to hydrostatic water pressure: 

T ur (144kPa)(2.745m) 395 h == = kN

m

= + + θ= + θ s T (320 395) 13.7cos(2 ) 715 13.7cos(2 )kN

m

Maximum and minimum static thrusts: 

max(T ) 729 s = kN

m

min (T ) 701 s = kN

m

Static moment: 

σ′ = −− θ

2

v

s 02

r M (1 K )(1 2a )cos(2 ) 2 (Eq. A-47b †

) 

= −− θ

2

s

(2.745 )(157kPa) M (1 0.5)(1 2(0.436))cos(2 ) 2

= θ ⋅ s M 37.8 cos2 kN m

m

0 45 90 135 180 225 270 315 360

700

720

740

Static Thrust

Angle (Theta - deg)

Force (kN/m)
225

Maximum and minimum static moments: 

= ⋅ s max(M ) 37.8kN m

m

- = ⋅ s min(M ) 37.8kN m

m

Combine stresses from static thrust and moment. 

Stress at outer fiber of liner: 

σ= − s s0

so

l2 l2

T Mc

A I

Stress at inner fiber of liner: 

σ= + s si

si

l2 l2

T Mc

A I

Maximum and minimum combined stresses: 

-

σ= ⋅

σ= ⋅

σ= ⋅

σ= ⋅

4

so

3

so

4

si

4

si

max( ) 4.28 10 kPa

min( ) 2.74 10 kPa

max( ) 7.27 10 kPa

min( ) 2.71 10 kPa

Steel Tunnel in Soil - Dynamic Moment, Thrust, and Stresses by Method of Wang (1993) for the 

Condition of Full-Slip between the Tunnel and Soil:

γ ⋅ ′ = = =⋅

2 3 2

t m 7 2

m

C' (17 10 )(80 ) G 1.109 10 N/m

g (9.81) (Eq. 4-11) 

−

′ − ⋅ − == = ⋅ ⋅

2 3 7 23

m l

11 5

l l2

G (1 v )D (1.109 10 )(1 0.3 )(5.49 ) F 3.54323

24EI 24(2.04 10 )(9.63 10 ) (Eq. 4-17) 

0 45 90 135 180 225 270 315 360

50

0

50

Static Moment

Angle (Theta - deg)

Moment (kN-m/m)
226

− ν − == = + −ν + −

m

m

1 1 0.45 K 0.11719

F 2.5 3 3.54323 2.5 3(0.45) (Eq. 4-16) 

Dynamic thrust: 

= ′ γ θ T G DK sin(2 ) d m smax (Eq. 4-13) 

= ⋅ θ= θ (1.109 10 )(5.49)(0.11719)(0.007)sin(2 ) 49.9sin(2 ) 7 kN

m

Maximum and minimum dynamic thrusts: 

max(T ) 49.9 d = kN

m

= - d min(T ) 49.9kN

m

Dynamic moments: 

= ′ γ θ 2

d m smax

1 M G D K sin(2 ) 2 (Eq. 4-15) 

=⋅ θ 7 2

d

1 M (1.109 10 )(5.49 )(0.11719)(0.007)sin(2 ) 2

= θ ⋅ d M 137sin(2 )kN m

m

Maximum and minimum dynamic moments: 

= ⋅ d max(M ) 137kN m

m

- = ⋅ d min(M ) 137kN m

m

0 45 90 135 180 225 270 315 360

50

0

50 Dynamic Thrust

Angle (Theta - deg)

Force (kN/m)
227

Combine stresses from dynamic thrust and moment. 

Dynamic stress at outer fiber of liner: 

σ= − d d0

do

l2 l2

T Mc

A I

Dynamic stress at inner fiber of liner: 

σ= + d di

di

l2 l2

T Mc

A I

Maximum and minimum combined dynamic stresses: 

σ= ⋅

σ =− ⋅

σ= ⋅

σ =− ⋅

4

do

4

do

5

di

5

di

max( ) 7.26 10 kPa

min( ) 7.26 10 kPa

max( ) 1.80 10 kPa

min( ) 1.80 10 kPa

Steel Tunnel in Soil – Combined Static and Dynamic Stresses by Method of Schwartz and Einstein 

(1980) and Wang (1993) for the Condition of Full-Slip between the Tunnel and Soil:

Stress at outer fiber of liner: 

σ =σ +σ 0 so do

Stress at inner fiber of liner: 

σ =σ +σ i si di

Maximum and minimum combined stresses: 

0 45 90 135 180 225 270 315 360

200

0

200 Dynamic Moment

Angle (Theta - deg)

Moment (kN-m/m)
228

σ= ⋅

σ =− ⋅

σ= ⋅

σ =− ⋅

4

o

4

o

5

i

5

i

max( ) 9.81 10 kPa

min( ) 5.25 10 kPa

max( ) 2.10 10 kPa

min( ) 1.64 10 kPa

Maximum tensile and compressive stresses are very similar to those previously presented for the no-slip 

case. 

Steel Tunnel in Soil - Static Moment, Thrust, and Stresses by Method of Penzien and Wu (1998) for the 

Condition of No-Slip between the Tunnel and Soil:

+ ν ⋅ +

α= = =

−ν ⋅ −

10

l l2 m

d 2 62

m l

E A (1 ) (20.4 10 )(0.0314)(1 0.45) 115.835

E' r (1 ) (32.1 10 )(2.745)(1 0.3 ) (Eq. 47††) 

σ + +ν −ν α ′ ⋅ ++ ∆= + =

+α +α ⋅ +

2 2 3

v o m ld

dl 6

m d l l2 d

r(1 K )(1 ) 2ur (1 ) (157 10 )(2.745)(1 0.5)(1 0.45)

E' (1 ) EA (1 ) 32.1 10 (1 115.835)

 - ⋅ - + =⋅

⋅ +

3 22

4

10

2(144 10 )(2.745 )(1 0.3 )(115.835) 5.57 10 m

(20.4 10 )(0.0314)(1 115.835) (Eq. 49††) 

-

- -

∆ ⋅ ⋅ = = =⋅ ν

10 4

l l2 dl 5

d 2 2

l

E A (20.4 10 )(0.0314)(5.57 10 ) P 7.142 10 N/m

2r (1 ) 2(2.745)(1 0.3 ) (Eq. 58††) 

+ν − ν ⋅ ⋅+

α= =

−ν ⋅

10 -5

l l2 m m

s 3 2 3 62

m l

6EI (1 )(3 4 ) 6(20.4 10 )(9.63 10 )(1 0.45)(3 - 4(0.45))

r E' (1 ) (2.745 )(32.1 10 )(1- 0.3 )

 = 0.339 (Eq. 51††) 

0 45 90 135 180 225 270 315 360

4 .105

2 .105

0

2 .

105

4 .

105

Stress on Outside Face

Stress on Inside Face

Combined Static and Dynamic Stresses

Angle (Theta - deg)

Stress (kPa)
229

σ +ν ν ′ - - ⋅ + - - ∆= =

+α ⋅ +

3

vo m m

sl 6

m s

r(1 K )(1 )(3 4 ) (157 10 )(2.745)(1 0.5)(1 0.45)(3 4(0.45))

E' (1 ) 32.1 10 (1 0.339) 

 − = ⋅ 3 8.271 10 m (Eq. 50††) 

- -

- -

∆ ⋅⋅ ⋅ = θ= θ

ν

10 5 3

l l2 sl

s 32 3 2

l

3EI 3(20.4 10 )(9.63 10 )(8.271 10 ) P cos2 cos2

r (1 ) (2.745 )(1 0.3 ) 

 =⋅ θ 4 2.731 10 cos2 N m (Eq. 59††) 

Static thrust: 

= + = ⋅ θ+ ⋅ 4 5

s sd T P P 2.731 10 cos2 7.142 10 N

m

Maximum and minimum static thrusts: 

=

=

s

s

max(T ) 741kN

m

min(T ) 686kN

m

Static moment: 

- -

- -

∆ ⋅⋅ ⋅ = θ= θ

ν

10 5 3

l l2 sl

s 22 2 2

l

3EI 3(20.4 10 )(9.63 10 )(8.271 10 ) M cos2 cos2

2r (1 ) 2(2.745 )(1 0.3 ) 

 = ⋅ θ⋅ 4 3.748 10 cos2 N m/m (Eq. 59††) 

Maximum and minimum static moment: 

= ⋅

= − ⋅

s

s

max(M ) 37.4kN m

m

max(M ) 37.4kN m

m

0 45 90 135 180 225 270 315 360

600

700

800

Static Thrust

Angle (Theta - deg)

Force (kN/m)
230

Combine stresses from static thrust and moment. 

Stress at outer fiber: 

σ= − s so

so

l2 l2

T Mc

A I

Stress at inner fiber: 

σ= + s si

si

l2 l2

T Mc

A I

Maximum and minimum combined stresses: 

σ= ⋅

σ= ⋅

σ= ⋅

σ =− ⋅

4

so

4

so

4

si

4

si

max( ) 4.215 10 kPa

min( ) 3.336 10 kPa

max( ) 7.261 10 kPa

min( ) 2.713 10 kPa

Steel Tunnel in Soil – Dynamic Moment, Thrust, and Stresses by Method of Penzien and Wu (1998) for 

the Condition of No-Slip between the Tunnel and Soil:

γ ⋅ ′ ′ = = =⋅

3

t 2 2 72

m m

17 10 G C 80 1.109 10 N/m

g 9.81 (Eq. 4-11) 

−

′ − ν ⋅ − == = ⋅ ⋅

2 3 7 23

m l

10 5

l l2

G (1 )D 1.109 10 (1 0.3 )(5.49 ) F 3.54323

24EI 24(20.4 10 )(9.63 10 ) (Eq. 4-17) 

- -

- -

ν ′ == = +ν +

m

m

1 1 0.45 K 0.11595

F 3 4 3.54323 3 4(0.45) (Eq. 4-21) 

0 45 90 135 180 225 270 315 360

50

0

50

Static moment

Angle (Theta - deg)

Moment (kN-m/m)
231

Dynamic thrust: 

- = ′γ θ= ⋅ θ 7 T 2G' DK sin2 2(1.109 10 )(5.49)(0.11595)(0.007)sin2 d m s max 

 =⋅ θ 4 9.887 10 sin2 N/m (Eq.4-18) 

Maximum and minimum dynamic thrusts: 

=

= −

d

d

max(T ) 98.88kN

m

min(T ) 98.88kN

m

Dynamic moment: 

- = ′ ′γ θ= ⋅ θ 2 72

d m s max

1 1 M G D K sin2 (1.109 10 )(5.49 )(0.11595)(0.007)sin2 2 2 

 = ⋅ θ⋅ 5 1.356 10 sin2 N m/m (Eq. 4-20) 

Maximum and minimum dynamic moments: 

= ⋅

= − ⋅

d

d

max(M ) 136kN m

m

max(M ) 136kN m

m

0 45 90 135 180 225 270 315 360

100

0

100 Dynamic Thrust

Angle (Theta - deg)

Force (kN/m)
232

Combine stresses from dynamic thrust and moment. 

Dynamic stress at outer fiber of liner: 

σ= − d do

do

l2 l2

T Mc

A I

Dynamic stress at inner fiber of liner: 

σ= + s si

di

l2 l2

T Mc

A I

Maximum and minimum dynamic stresses: 

σ= ⋅

σ =− ⋅

σ= ⋅

σ =− ⋅

4

do

4

do

5

di

5

di

max( ) 7.02 10 kPa

min( ) 7.02 10 kPa

max( ) 1.80 10 kPa

min( ) 1.80 10 kPa

Steel Tunnel in Soil – Combined Static and Dynamic Stresses by Method of Penzien and Wu (1998) for 

the condition of No-Slip between the Tunnel and Soil

Stress at outer fiber: 

σ =σ +σ o so do

Stress at inner fiber 

σ =σ +σ i si di

0 45 90 135 180 225 270 315 360

200

0

200 Dynamic Moment

Angle (Theta - deg)

Moment (kN-m/m)
233

Maximum and minimum combined stresses 

σ= ⋅

σ =− ⋅

σ= ⋅

σ =− ⋅

4

o

4

o

5

i

5

i

max( ) 9.564 10 kPa

min( ) 5.016 10 kPa

max( ) 2.101 10 kPa

min( ) 1.646 10 kPa

Maximum tensile and compressive stresses are very similar to those previously presented for the 

methods of Schwartz and Einstein (1980), and Wang (1993) for no-slip and full-slip cases. 

Steel Tunnel in Soil - Static Moment, Thrust, and Stresses by Method of Penzien and Wu (1998) for the 

Condition of Full-Slip between the Tunnel and Soil:

+ ν ⋅ +

α= = =

−ν ⋅ −

10

l l2 m

d 26 2

m l

E A (1 ) (20.4 10 )(0.0314)(1 0.45) 115.835

E' r(1 ) (32.1 10 )(2.745)(1 0.3 ) (Eq. 47††) 

σ + +ν −ν α ′ ⋅ ++ ∆= + =

+α +α ⋅ +

2 2 3

v o m ld

dl 6

m d l l2 d

r(1 K )(1 ) 2ur (1 ) (157 10 )(2.745)(1 0.5)(1 0.45)

E' (1 ) EA (1 ) 32.1 10 (1 115.835) 

 - ⋅ - + =⋅

⋅ +

3 22

4

10

2(144 10 )(2.745 )(1 0.3 )(115.835) 5.57 10 m

(20.4 10 )(0.0314)(1 115.835) (Eq. 49††) 

-

- -

∆ ⋅ ⋅ = = =⋅ ν

10 4

l l2 dl 5

d 2 2

l

E A (20.4 10 )(0.0314)(5.57 10 ) P 7.142 10 N/m

2r(1 ) 2(2.745)(1 0.3 ) (Eq. 58††) 

0 45 90 135 180 225 270 315 360

4 .105

2 .105

0

2 .

105

4 .

105

Stress on Outside Face

Stress on Inside Face

Combined Static and Dynamic Stresses

Angle (Theta - deg)

Stress (kPa)
234

- -

-

+ν − ν ⋅ ⋅+

α= =

−ν ⋅

10 5

l l2 m m

s 3' 2 3 6 2

m 1

3EI (1 )(5 6 ) 3(20.4 10 )(9.63 10 )(1 0.45)(5 6(0.45))

r E (1 ) (2.745 )(32.1 10 )(1 0.3 )

= 0.325 (Eq. 51††) 

σ +ν ν ′ - - ∆ =

+ α

v om m

sl

m s

r(1 K )(1 )(3 4 )

E' (1 )

 

 - - − ⋅ + = =⋅ ⋅ +

3

3

6

(157 10 )(2.745)(1 0.5)(1 0.45)(3 4(0.45)) 8.814 10 m

32.1 10 (1 0.325) (Eq. 50††) 

- -

- -

∆ ⋅⋅ ⋅ = θ= θ

ν

10 5 3

l l2 sl

s 32 3 3

l

3EI 3(20.4 10 )(9.63 10 )(8.814 10 ) P cos2 cos2

2r (1 ) 2(2.745 )(1 0.3 ) 

 =⋅ θ 4 1.380 10 cos2 N m (Eq. 59††) 

Static thrust: 

= + = ⋅ θ+ ⋅ 4 5

s sd T P P 1.380 10 cos2 7.142 10 N

m

Maximum and minimum static thrusts: 

=

=

s

s

max(T ) 728kN

m

min(T ) 700kN

m

Static moment: 

- -

- -

∆ ⋅⋅ ⋅ = θ= θ

ν

11 5 3

l l2 sl

s 22 2 2

l

3EI 3(2.04 10 )(9.63 10 )(8.814 10 ) M cos2 cos2

2R (1 ) 2(2.745 )(1 0.3 ) 

 = ⋅ θ⋅ 4 3.788 10 cos2 N m/m (Eq. 59††) 

0 45 90 135 180 225 270 315 360

600

700

800

Static Thrust

Angle (Theta - deg)

Force (kN/m)
235

Maximum and minimum static moment: 

= ⋅

= − ⋅

s

s

max(M ) 37.8kN m

m

max(M ) 37.8kN m

m

Combine stresses from static thrusts and moment. 

Stress at outer fiber: 

σ= − s so

so

l2 l2

T Mc

A I

Stress at inner fiber: 

σ= + s si

si

l2 l2

T Mc

A I

Maximum and minimum combined stresses: 

σ= ⋅

σ= ⋅

σ= ⋅

σ =− ⋅

4

so

4

so

4

si

4

si

max( ) 4.280 10 kPa

min( ) 2.690 10 kPa

max( ) 7.271 10 kPa

min( ) 2.722 10 kPa

Steel Tunnel in Soil – Dynamic Moment, Thrust, and Stresses by Method of Penzien and Wu (1998) for 

the Condition of Full-Slip between Tunnel and Soil:

γ ⋅ ′ ′ = = =⋅

3

t 2 2 72

m m

17 10 G C 80 1.109 10 N/m

g 9.81 (Eq. 4-11) 

−

′ − ν ⋅ − == = ⋅ ⋅

2 3 7 23

m l

10 5

l l2

G (1 )D 1.109 10 (1 0.3 )(5.49 ) F 3.54323

24EI 24(20.4 10 )(9.63 10 ) (Eq. 4-17) 

0 45 90 135 180 225 270 315 360

50

0

50

Static moment

Angle (Theta - deg)

Moment (kN-m/m)
236

- -

- -

ν == = +ν +

m

m

1 1 0.45 K 0.11719

F 2.5 3 3.54323 2.5 3(0.45) (Eq. 4-16) 

Dynamic thrust: 

- = ′ γ θ= ⋅ θ 7 T G DK sin2 (1.109 10 )(5.49)(0.11719)(0.007)sin2 d m s max 

 =⋅ θ 4 4.997 10 sin2 N/m (Eq. 4-13) 

Maximum and minimum dynamic thrusts: 

=

= −

d

d

max(T ) 49.9kN

m

min(T ) 49.9kN

m

Dynamic moment: 

- = ′ 2 72 γ θ= ⋅ θ d m s max

1 1 M G D K sin2 (1.109 10 )(5.49 )(0.11719)(0.007)sin2 2 2 

 = ⋅ θ⋅ 1.372 10 sin2 N m/m 5 (Eq. 4-15) 

Maximum and minimum dynamic moments: 

= ⋅

= − ⋅

d

d

max(M ) 137.2kN m

m

max(M ) 137.2kN m

m

0 45 90 135 180 225 270 315 360

50

0

50 Dynamic Thrust

Angle (Theta - deg)

Force (kN/m)
237

Dynamic stress at outer fiber of liner: 

σ= − d do

do

l2 l2

T Mc

A I

Dynamic stress at inner fiber of liner: 

σ= + d di

di

l2 l2

T Mc

A I

Maximum and minimum dynamic stresses: 

σ= ⋅

σ =− ⋅

σ= ⋅

σ =− ⋅

4

do

4

do

5

di

5

di

max( ) 7.261 10 kPa

min( ) 7.261 10 kPa

max( ) 1.806 10 kPa

min( ) 1.806 10 kPa

Steel Tunnel in Soil – Combined Static and Dynamic Stresses by Method of Penzien and Wu (1998) for 

the Condition of Full-Slip between the Tunnel and Soil:

Stress at outer fiber: 

σ =σ +σ o so do

Stress at inner fiber 

σ =σ +σ i si di

Maximum and minimum combined stresses 

σ= ⋅

σ =− ⋅

σ= ⋅

σ =− ⋅

4

o

4

o

5

i

5

i

max( ) 9.80 10 kPa

min( ) 5.25 10 kPa

max( ) 2.10 10 kPa

min( ) 1.64 10 kPa

0 45 90 135 180 225 270 315 360

200

0

200 Dynamic Moment

Angle (Theta - deg)

Moment (kN-m/m)
238

Steel Tunnel in Soil - Summary of Thrusts and Moments: 

 NO SLIP FULL SLIP 

 SE/W** PW SE/W** PW 

Thrust Maximum 788 741 729 728 

(kN/m) Minimum 643 686 701 700 

Maximum 36. 3 37.4 37.8 37.8 

STATIC 

Moment 

(kN·m/m) Minimum -36.3 -37.4 -37.8 -37.8 

Thrust Maximum 263 98.8 49.9 49.9 

(kN/m) Minimum -263 98.8 -49.9 -49.9 

Maximum 131 137 136 137 

DYNAMIC 

Moment 

(kN·m/m) Minimum -131 -137 -136 -137 

0 45 90 135 180 225 270 315 360

4 .105

2 .105

0

2 .

105

4 .

105

Stress on Outside Face

Stress on Inside Face

Combined Static and Dynamic Stresses

Angle (Theta - deg)

Stress (kPa)
239

Steel Tunnel in Soil - Summary of Stresses*: 

 NO SLIP FULL SLIP 

 SE/W** PW SE/W** PW 

Inside Maximum 72.3 72.6 72.7 72.7 

Face Minimum -26.7 -27.1 -27.1 -27.2 

Maximum 40.0 42.1 42.8 42.8 

STATIC 

(MPa) 

Outside 

Face Minimum 5.55 33.3 2.74 26.9 

Inside Maximum 179 180 180 180 

Face Minimum -179 -180 -180 -180 

Maximum 62.4 70.2 72.6 72.6 

DYNAMIC 

(MPa) 

Outside 

Face Minimum -62.4 -70.2 72.6 72.6 

Inside Maximum 209 210 210 210 

Face Minimum -163 -164 -164 -164 

Maximum 87.5 95.6 98.1 98.0 

COMBINED 

(MPa) 

Outside 

Face Minimum -42.1 -50.1 -52.5 -52.5 

* Positive stresses are compressive, negative stresses are tensile. 

** Schwartz and Einstein (1980) was used for static, Wang (1993) was used for dynamic. 

Discussion of Ovaling Deformation of Steel Tunnel in Soil: 

Similar combined static and dynamic stresses were computed for the formulations of Schwartz and 

Einstein (1980), and Wang (1993), for static and dynamic stresses, respectively, and Penzien and Wu 

(1998) for static and dynamic stresses. Maximum tensile and compressive stresses were found to occur 

on the inside fiber (i.e., the inner edge of the flange) of the steel liner. Maximum tensile and compressive 

stresses are about 64 percent and 84 percent, respectively, of the yield stress. A need for retrofit is not 

indicated by the analysis. 

Concrete Tunnel in Rock - Ovaling Deformation of Tunnel Cross Section 

An ovaling analysis similar to that described in the preceding sections for the steel tunnel in soil was 

carried out for a concrete tunnel in rock. The results are summarized below. 
240

Concrete Tunnel in Rock - Summary of Thrusts and Moments: 

 NO SLIP FULL SLIP 

 SE/W** PW SE/W** PW 

Thrust Maximum 679 377 576 376 

(kN/m) Minimum 472 373 574 374 

Maximum 2.47 2.79 2.80 2.80 

STATIC 

Moment 

(kN·m/m) Minimum -2.47 -2.79 -2.80 -2.80 

Thrust Maximum 1447 28.4 14.2 14.2 

(kN/m) Minimum -1447 -28.4 -14.2 -14.2 

Maximum 34.5 39.0 39.0 39.0 

DYNAMIC 

Moment 

(kN·m/m) Minimum -34.5 -39.0 -39.0 -39.0 

Concrete Tunnel in Rock - Summary of Stresses*: 

 NO SLIP FULL SLIP 

 SE/W** PW SE/W** PW 

Inside Maximum 2.42 1.44 2.10 1.43 

Face Minimum 1.40 1.05 -1.72 1.06 

Maximum 2.09 1.43 2.10 1.44 

STATIC 

(MPa) 

Outside 

Face Minimum 1.73 1.07 1.73 1.06 

Inside Maximum 7.12 2.69 2.65 2.65 

Face Minimum -7.12 -2.69 -2.65 -2.65 

Maximum 2.52 2.50 2.55 2.55 

DYNAMIC 

(MPa) 

Outside 

Face Minimum -2.52 -2.50 -2.55 -2.55 

Inside Maximum 9.06 3.95 4.57 3.91 

Face Minimum -5.22 -1.45 -0.742 -1.40 

Maximum 4.44 3.76 4.48 3.81 

COMBINED 

(MPa) 

Outside 

Face Minimum 0.61 -1.26 -0.646 -1.31 

* Positive stresses are compressive, negative stresses are tensile. 

** Schwartz and Einstein (1980) was used for static, Wang (1993) was used for dynamic. 
241

Discussion of Ovaling Deformation of Concrete Tunnel in Rock: 

As with the steel tunnel liner in soil, the maximum combined static and dynamic stresses occur on the 

inside face of the concrete liner. The magnitude of the tensile and compressive stresses varies 

considerably with the assumption of full-slip or no-slip using the formulations of Schwartz and Einstein 

(1980), and Wang (1993). The formulation of Penzien and Wu (1998) gave similar stresses for both fullslip and no-slip, and in both cases, peak stresses were lower than the strength of the liner. Maximum 

tensile and compressive stresses computed using the formulation of Penzien and Wu (1998) were about 

70 and 19 percent of the liner strength, respectively. The formulation of Schwartz and Einstein (1980) and 

Wang (1993) gave peak stresses lower than the strength of the liner for the full-slip case: Peak tensile 

and compressive stresses were approximately 36 and 22 percent, respectively, of the liner strength. The 

no-slip formulation of Schwartz and Einstein (1980) and Wang (1993) gave much higher stresses than 

the other formulations, mainly due to higher computed dynamic thrusts. For this formulation, peak tensile 

and compressive stresses were about 250 and 44 percent, respectively, of the liner strength. Considering 

that some slip is likely to occur, it is judged that the ovaling deformations will not be large enough to 

cause collapse or significant spalling of the concrete tunnel in rock. 

Concrete Tunnel in Soil - Ovaling Deformation of Tunnel Cross Section 

An additional case of an unreinforced concrete tunnel in soil was considered to obtain the stresses for a 

concrete liner in relatively soft soil. The concrete tunnel and soil properties are the same as those 

described at the beginning of Example 4.5. The static and dynamic thrusts, moments, and stresses are 

summarized below: 

Concrete Tunnel in Soil - Summary of Thrusts and Moments: 

 NO SLIP FULL SLIP 

 SE/W* PW SE/W* PW 

Thrust Maximum 797 762 740 738 

(kN/m) Minimum 634 665 691 689 

Maximum 64.4 66.2 67.4 67.4 

STATIC 

Moment 

(kN·m/m) Minimum -64.4 -66.2 -67.4 -67.4 

Thrust Maximum 295 174 89.0 89.0 

(kN/m) Minimum -295 -174 -89.0 -89.0 

Maximum 233 239 244 244 

DYNAMIC 

Moment 

(kN·m/m) Minimum -233 -239 -244 -244 
242

Concrete Tunnel in Soil - Summary of Stresses*: 

 NO SLIP FULL SLIP 

 SE/W** PW SE/W** PW 

Inside Maximum 6.95 6.95 6.96 6.96 

Face Minimum -2.18 -2.19 -2.19 -2.20 

Maximum 6.41 6.63 6.80 6.79 

STATIC 

(Mpa) 

Outside 

Face Minimum -1.63 -1.87 -2.03 -2.03 

Inside Maximum 16.5 16.5 16.5 16.5 

Face Minimum -16.5 -16.5 -16.5 -16.5 

Maximum 14.5 15.4 16.0 16.0 

DYNAMIC 

(Mpa) 

Outside 

Face Minimum -14.5 -15.4 -16.0 -16.0 

Inside Maximum 19.5 19.5 19.6 19.5 

Face Minimum -14.7 -14.8 -14.8 -14.8 

Maximum 17.5 18.3 18.9 18.9 

COMBINED 

(Mpa) 

Outside 

Face Minimum -12.7 -13.6 -14.2 -14.2 

* Positive stresses are compressive, negative stresses are tensile. 

** Schwartz and Einstein (1980) was used for static, Wang (1993) was used for dynamic.

Discussion of Ovaling Deformation of Concrete Tunnel in Soil: 

As with the steel tunnel in soil and the concrete tunnel in rock, the maximum stresses for the concrete 

tunnel in soil occur on the inside face of the liner. Similar to the preceding analyses, stresses in the 

unreinforced concrete tunnel were calculated using the formulations of Schwartz and Einstein (1980) and 

Wang (1993), and Penzien and Wu (1998) for full-slip and no-slip. Similar stresses were obtained for all 

cases. Maximum compressive stresses were about 95 percent of the compressive strength of the tunnel. 

Tensile stresses were about seven times the tensile strength of the concrete liner. Because the tensile 

strength of the unreinforced concrete liner is exceeded, the analysis assumption of elastic behavior is not 

satisfied. However, the results indicate the need for retrofit of the unreinforced concrete tunnel in soil. 

Retrofit schemes to be considered include demolition of the existing liner and construction of a reinforced 

concrete or steel liner with temporary support provided during construction, and constructing an inner 

liner consisting of a steel pipe with concrete filling the annulus between the pipe and the existing liner. 
243

CHAPTER 5: CULVERTS 

5.1. INTRODUCTION 

Culverts are very common in the nation's transportation corridors. So far, their performance 

record during major earthquakes has been very positive, on the average, especially when 

compared to reported damage of other highway components, such as bridges. The primary 

reason is believed to be the ground level position that culverts occupy in the seismic force field. 

This position reduces and, in some cases, may eliminate the consideration of dynamic inertial 

forces, the major seismic design criterion for aboveground structures. However, seismic activity 

also produces transient ground motion and may produce permanent ground deformations, both of 

which can affect culvert performance under some circumstances. 

In addition, culverts exist in a wide variety of sizes, shapes, and types. Therefore, another reason 

why culvert failures do not widely occur may be that most culverts have small diameters that 

may be only marginally affected by earthquakes. Large span culverts that would be expected to 

experience greater seismic vulnerability are relatively sparse, partly because the demand for their 

capacity is not as common and because they are are relatively new and highly distributed among 

infrastructure systems. Hence, they do not have the same exposure risk from seismic activity as 

smaller diameter culverts. 

The risk of catastrophic consequences due to the collapse or failure of a culvert generally can be 

related to both the size and type of culvert. Generally, small diameter culverts do not sustain 

major damage during an earthquake unless the entire highway system, of which they are a part, 

also suffers the same level of damage. However, when medium to large size culverts are 

damaged to the point where they become partially or totally incapacitated and can no longer 

handle their design hydraulic capacity, impoundment of the inflow and eventual overtopping of 

the highway surface can result. For the hydraulic flows normally associated with medium to 

large size culverts, overtopping of the highway can lead to loss of the pavement, scour of the 

embankment and silt contamination of the downstream ecology. Secondary damage to the road 

surface can be life threatening due to the resulting hazard faced by the traveling public. 

While many factors in addition to the size of the culvert can contribute to its failure during a 

seismic event, reported case histories seem to indicate that the type of culvert also may be a 

factor under some circumstances. Permanent ground failure cases, particularly those related to 

liquefaction, can cause distortion or loss of soil envelope support. Flexible culverts (defined 

below under the culvert classification section) may distort or collapse due to the loss of support 

provided by the surrounding soil envelope. This, in turn, can lead to embankment loss and 

damage to the road surface, thus threatening lives. 

One of the goals of this chapter is to increase understanding of the factors that affect culvert 

performance during seismic events. This will be pursued through a combination of theoretical 

considerations and documented case histories. Other goals include the delineation of a 

systematic approach for screening culverts to determine the susceptibility of seismically induced 
244

damage and evaluating the need and extent for employing retrofit measures. Finally, a number 

of useful retrofit strategies to fortify culverts against this damage are reviewed. 

Large culverts over 6 m in span are becoming more commonplace every year. They are 

employed not only as hydraulic structures but also as grade separation structures. Damage or 

collapse of a large box culvert has similar consequences to the failure of a bridge. Yet, current 

AASHTO specifications do not require consideration of seismic design criteria for any type of 

buried structure, except as follows: 

Seismic effects for box culverts and buried structures need not be considered, except where they 

cross active faults (AASHTO, 2002). AASHTO does not provide guidance on how to design 

culverts when buried structures cross active faults. 

In addition, a systems approach to the development of culvert retrofit strategies is encouraged. 

Rather than considering culverts as discrete components in a facilities inventory, their role as 

links in a much bigger chain is important. Seismic retrofit strategies for culverts should be based 

on the levels of service and priorities of the particular transportation corridor of which they are a 

part. General considerations affecting the level of evaluation and the need for retrofitting 

culverts and other elements of the highway system are covered in chapter 1 of this report. 

Culverts, like other transportation facilities, require the input of multiple engineering disciplines 

in the design process. In addition to structural and geotechnical aspects, successful culvert 

performance requires application of the principles of hydraulics, hydrology, economics, roadway 

geometric design, as well as traffic capacity and safety considerations. A discussion of the entire 

process for culvert design is beyond the scope of this chapter. 

Many highway culverts utilize end appurtenances of some kind to channel hydraulic flows into 

and out of the culvert without causing erosion. Special end sections are available for small 

diameter culverts and typically require no additional design consideration. However, as the size 

of the culvert increases, these end appurtenances often become endwalls and wingwalls, which 

are essentially types of retaining walls. The seismic vulnerability and retrofit of retaining walls 

are addressed in chapter 2 of this report. 

5.2. CLASSIFICATION OF CULVERTS AND BACKGROUND INFORMATION

Culverts comprise a diverse group of products with large variations in the availability of material 

properties, geometric wall sections, sizes and shapes. For instance, diameters as small as 

300 mm and spans 15 m and larger are used in highway applications. They can be composed of 

concrete, steel, aluminum, plastic, and combinations of these. 

For the purposes of compiling and maintaining a national bridge inventory, the Federal Highway 

Administration (FHWA) differentiates culverts from bridges by the width of the span parallel to 

the roadway. Structures having less than a 6 m span are classified as culverts. However, this 

distinction is arbitrary from both a functional and a design viewpoint. The American 

Association of State Highway and Transportation Officials (AASHTO, 2002) publish design 

specifications for culverts that apply over a continuous range of sizes that extend well beyond the 
245

FHWA limit. General information on culverts can also be found in Highway Drainage 

Guidelines (AASHTO, 1999; FHWA, 2001) and in The Culvert Inspection, Material Selection 

and Rehabilitation Guideline, Volume 14 (AASHTO, 1999). 

In this chapter, highway culverts are defined as structures of any size that are fully surrounded 

and supported by a highway embankment or an earth fill at or near existing grade level. They 

may be factory-made in modular components, field constructed, or a combination. They may be 

based on standard designs covering a range of performance criteria or may be custom designed 

for a specific application. Their end purpose may be either to convey runoff or traffic (vehicular, 

pedestrian or wildlife) across a highway corridor. Ballinger and Drake (1995) compiled a list of 

manufactured culvert types, along with the range of sizes typically available in each type. These 

are illustrated in figures 5-1 and 5-2. 

Occasionally, culvert-like materials or assemblies are used for underground tunnels that extend 

significantly below the surface of the ground and underwater tubes that extend to great lengths 

beyond the crossing of highway corridors at or near grade level. These structures require 

additional and specialized design considerations that are beyond the scope of this chapter. 

Tunnels and underwater tubes are discussed in chapter 4. 

Structurally, culverts are complex. They perform as elements in a composite system consisting 

of the culvert itself and the soil continuum. The soil acts as both a load and resistance element in 

the composite. When a stable soil mass is properly compacted around the culvert, the loadcarrying capacity of the culvert-soil system exceeds the capacity of the culvert alone. The 

integrity of both elements in the composite is critical to its performance, not only under the 

action of static loads, but under dynamic excitation of earthquakes. Therefore, any consideration 

of the capacity of culverts must include recognition of the role played by the soil envelope. 

Culverts generally are divided into two major classes: flexible and rigid. Flexible culverts 

respond to loads differently than rigid culverts. Because their ring stiffness is small relative to 

the adjacent soil, flexible culverts depend upon a large strain capacity and the interaction with 

the surrounding soil to hold their shape while supporting the external pressures imposed upon 

them. On the other hand, the strain capacity of rigid culverts 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. More specific aspects of 

both flexible and rigid culverts relative to their seismic resistance are discussed in the following 

sections. 

5.2.1. FLEXIBLE CULVERTS - BACKGROUND AND DESIGN PHILOSOPHIES 

Flexible culverts typically are composed of either metal or thermoplastic materials. Highly 

efficient wall sections have evolved that maximize their section properties while conserving 

material. Corrugated metal pipe (CMP), originally composed of iron, was the first type of 

flexible culvert to be developed in the early part of this century. Modern CMP culverts are 

available in both steel and aluminum. A family of corrugated profiles having wall sections that 

are composed of a series of arcs and tangents are illustrated in figure 5-3. These sections have 

been shown to be stable structurally but may suffer in hydraulic performance compared to other 
246

Shapes Range of Sizes Common Uses 

Round Diameter 

0.15 m to 7.9 m 

Culverts, subdrains, sewers, 

service tunnels (all materials in 

smaller diameters, structural 

plate in larger diameters). 

Vertical 

Ellipse 

(5% 

Common) 

Diameter 

1.2 m to 6.4 m 

nominal; 

before elongating 

Culverts, sewers, service 

tunnels, recovery tunnels (CMP 

and structural plate). 

Pipe Arch 

Span x Rise 

1.42 m x 0.33 m 

to 

6.27 m x 4.01 m 

Where headroom is limited. 

Has hydraulic advantages at low 

flows (CMP and structural 

plate). 

Underpass 

Span x Rise 

1.73 m x 1.75 m 

to 

6.20 m x 5.41 m 

For pedestrians, livestock or 

vehicles (structural plate). 

Arch 

Span x Rise 

1.83 m x 0.55 m 

to 

7.62 m x 3.81 m 

For low clearance large 

waterway opening, and 

aesthetics (structural plate). 

Horizontal 

Ellipse 

Span 

2.1 m to 12.2 m 

Culverts, grade separations, 

storm sewers, tunnels (CMP 

and structural plate). 

Pear Span 

7.6 m to 9.1 m 

Grade separations, culverts, 

storm sewers, tunnels (structural 

plate). 

High Profile 

Arch 

Span 

6.1 m to 13.7 m 

Grade separations, culverts, 

storm sewers, tunnels, ammo 

ammunition magazines, earth 

covered storage (structural 

plate). 

Low Profile 

Arch 

Span 

6.1 m to 15.2 m 

Low, wide waterway enclosures, 

culverts storm sewers (structural 

plate). 

Box Culvert Span 

3.0 m to 7.9 m 

Low, wide waterway enclosures, 

culverts, storm sewers 

(structural plate). 

Specials Various 

For lining old structures or other 

special purposes. Special 

fabrication. 

adapted from Ballinger and Drake, 1995 

Figure 5-1. Available types and sizes of flexible culverts. 
247

Shapes Range of Sizes Common Uses 

Round 

Diameter 

0.3 m to 4.6 m 

(reinforced); 

0.1 m to 0.9 m 

(non-reinforced)

Culverts, storm drains, sewers. 

Pipe Arch 

Span x Rise 

0.4 m to 3.4 m 

equivalent 

diameter 

Culverts, storm drains, sewers. Used 

where head room is limited. 

Horizontal 

Ellipse 

Span x Rise 

0.5 m to 3.7 m 

equivalent 

diameter 

Culverts, storm drains, sewers. Used 

where head room is limited. 

Vertical 

Ellipse 

Span x Rise 

0.9 m to 3.7 m 

equivalent 

diameter 

Culverts, storm drains, sewers. Used 

where lateral clearance is limited. 

Rectangular 

Box Culvert 

Span 

0.9 m to 3.7 m 

Culverts, storm drains, sewers. For 

wide openings with limited head room. 

Arch Span 

7.3 m to 12.5 m

Culverts and storm drains. For low, 

wide waterway enclosures. 

Flat Top 

3-Sided 

Span 

4.3 m to 10.7 m

Culverts and storm drains. For low, 

wide waterway enclosures. 

Arch Top 

3-Sided 

Span 

4.9 m to 11.0 m

Culverts and storm drains. For low, 

wide waterway enclosures. 

adapted from Ballinger and Drake, 1995 

Figure 5-2. Available types and sizes of rigid culverts. 

culvert products. They are available in a variety of factory-made and field-assembled shapes 

ranging in size from 300 mm in diameter to 15 m in span and larger. In smaller diameters, they 

may be fabricated with either annular or helical corrugations. In larger sizes and special shapes, 

they are only available in field-erected modular plates having annular corrugations. 

Spiral rib is a more recent corrugation innovation. Also available in both steel and aluminum, its 

wall section consists of alternating lengths of smooth wall and box corrugations as illustrated in 
248

figure 5-4. They are known to be less structurally robust as the arc and tangent corrugation, but 

are more efficient from both material and hydraulic viewpoints. 

Culverts manufactured from thermoplastic materials employ one of two types: high-density 

polyethylene (HDPE) or polyvinyl chloride (PVC). Many formulations are available in each 

type. Also, a broad range of manufacturing processes for thermoplastic culverts facilitates 

maximization of both their structural and hydraulic efficiencies. As a result, many varieties of 

cross sections have evolved, some of which are illustrated in figure 5-5. Since their engineering 

properties are a function of both the formulation of the material and the wall section profile, 

significant variability exists from one product to the next. In addition, strength and modulus 

parameters of thermoplastic materials are temperature, time and stress history dependant, thus 

further complicating their design. 

Current AASHTO specifications deal with the complications inherent in thermoplastic culverts 

through simplistic lower bound assumptions, which are thought to be generally conservative. 

However, some issues remain to be addressed. These include local buckling control of thinwalled sections, recognition of the reduced load transfer that occurs from the soil envelope to the 

culvert wall compared to traditional high modulus (metal and concrete) culverts, and material 

formulations that assure long-term ductility and oxidation resistance. Research investigations on 

these topics are expected to result in future additional refinements to the material and design 

specifications of thermoplastic culverts. 

38 mm

51 mm

68 mm

75 mm

125 mm

150 mm

6.5 mm

13 mm

13 mm

25 mm

25 mm

50 mm

380 mm

140 mm

Note:

Dimensions are for steel.

Aluminum similar but not

available in all sizes.

190 mm

19 mm

19 mm

19 mm

292 mm

25 mm

Note:

Available in both steel

and aluminum.

AISI, 1993 AISI, 1993 

Figure 5-3. Corrugated metal culvert wall 

profiles. 

Figure 5-4. Spiral rib metal culvert wall 

profiles. 
249

Smooth Wall

Open Profile

Honeycomb Closed Profile

Rectangular Closed Profile

Open Profile Smooth Lined T-Rib Reinforced Open Profile

Figure 5-5. Selected examples of thermoplastic culvert wall profiles. 

The primary design considerations for small diameter flexible culverts are ring compression and 

resistance to general buckling (cross sectional collapse). For larger sizes and shapes other than 

circular, the flexural strength required by nonsymmetrical and concentrated live loads, including 

seismic loads, must be considered. To accomplish this, some applications may require the use of 

computerized numerical methods (Katona et al., 1976, 1979, 1981; Duncan, 1979; Leonards et 

al., 1981; Musser, 1989a). Secondary design considerations include resistance to local buckling 

of thin-wall sections and fatigue of pavement sections over installations having shallow covers in 

combination with heavy live loads. 

Implicit in the design assumptions for flexible culverts is the existence of adequate soil support. 

This is achieved by employing stable backfill materials surrounding the circumference of the 

culvert. Both the size of the envelope of stable material, and its placement method and quality, 

are factors that affect the successful performance of flexible culverts. 

From a seismic performance perspective, flexible culverts are attractive because they are very 

ductile. Five percent strain or higher is available in the basic material properties of steel, 

aluminum and thermoplastics. And, even higher equivalent strain capabilities are available in 

the longitudinal direction of corrugated sections due to accordion action. Statically safe flexible 

culverts generally have sufficient ductility to withstand seismic forces without permanent 

deformation or collapse. The weakness of flexible culverts is their dependence upon soil 

support, which can be reduced or lost during liquefaction of other permanent ground failure 

mechanisms associated with seismic events. Distortion or collapse of the culvert cross section is 
250

likely if soil support is reduced or lost. Thus, for seismic consideration, distortion or collapse of 

flexible culverts is generally associated with liquefaction, slope instability or faulting, all which 

are geotechnical or geologic issues rather than structural issues. 

5.2.2. RIGID CULVERTS – BACKGROUND AND DESIGN PHILOSOPHIES 

Modern rigid highway culverts consist primarily of reinforced concreted shapes that are either 

precast or cast-in-place. In the past, some unreinforced culverts were placed either as precast or 

cast-in-place pipe. The use of unreinforced concrete culverts is now limited for highway 

applications and they are not recognized in current AASHTO specifications (AASHTO, 2002). 

Because of their brittleness, unreinforced concrete culverts are not recommended for use in 

seismic regions. Reinforced concrete pipe (RCP) is almost always furnished precast in diameters 

ranging from 300 mm to 3,600 mm. Above this range of sizes, RCP is precast on the site or 

constructed cast-in-place. Rectangular four-sided box culverts can be furnished precast in spans 

ranging from 900 mm to 3,600 mm. Larger spans and multiple cell four-sided box culverts 

typically are constructed cast-in-place. Three-sided precast box culverts are a relatively recent 

innovation and can be furnished in spans up to 15 m. 

Whether precast or cast-in-place, the concrete cross sections are relatively smooth on both the 

inside and outside. Material efficiency is achieved by optimizing the wall thickness, the strength 

of the concrete and in the case of reinforced concrete, the placement and quantity of the steel 

reinforcement. In the case of precast circular cross sections, elliptically shaped reinforcement or 

specially placed reinforcing mats are sometimes employed to increase efficiency. 

The rupture strain of typical concrete under uniaxial compression is between 0.1 and 0.25 

percent, but can vary over a greater range, depending upon the quantity and characteristics of the 

aggregate and upon the water/cement ratio of the paste (Hobbs, 1983). Under uniaxial tension, 

the rupture strain capacity is an order of magnitude less, ranging between 0.005 and 0.01 percent. 

On the other hand, modern reinforcing steel can develop rupture tensile strains between seven 

and nine percent. However, the strain capacity of rebar at yield is approximately 0.2 percent. 

It is the approximate compatibility of the definable limit state strains between concrete rupture in 

compression and steel yield in tension that is used in the design of the reinforced concrete 

composite. The unused strain capacity of the steel beyond yield may further contribute to the 

inelastic ductility of the composite, provided adequate consideration is given to concrete 

confinement and to limiting concrete compressive and shear strains. But, since the concrete 

tension strain capacity is so low, some cracks in the tension surface of reinforced concrete 

bending members are nearly always anticipated, even at service loads. Exceptions to this are 

pretensioned and post-tensioned members. 

The width of tension surface cracks typically is regulated through both design criteria and quality 

assurance practices during manufacture and construction. In the case of highway applications, 

AASHTO specifications currently limit the width of surface cracks in reinforced concrete 

culverts to about 0.3 mm (AASHTO, 2002). 

The primary design method used for precast concrete pipe, either reinforced or unreinforced, is 

known as the Indirect Design Method. This means simply that their design is based on a 
251

laboratory test, known as the three-edge bearing test. The testing protocol calls for concentrated 

vertical loads applied at the crown and invert of a pipe specimen. The test results include the 

load at which the specimen either ruptures (in the case of unreinforced pipe) or exceeds 

allowable crack width requirements (in the case of reinforced pipe). Empirical bedding factors 

are used to translate three-edge bearing laboratory test values into actual field support conditions 

at the haunch and invert. The end result is that adequate soil envelope support from these 

regions of the pipe circumference are assumed in the design. However, this is much less than 

requiring that the total periphery of the soil envelope support the wall section, which is the case 

with flexible pipe. 

The Indirect Design Method was developed by Marston during the first quarter of this century 

(Marston et al., 1917; Marston, 1930). Since that time, a number of refinements have been made 

that provide a more direct design procedure that accounts for moments, shears, and thrusts 

around the periphery of the culvert wall (Paris, 1921; Olander, 1950). The latest methods 

employ computerized numerical models that evaluate the contribution provided by soil-structure 

interaction (Hegar, 1982). These have evolved into what is termed the Direct Design Method. 

Also, new installation types, known as SIDD (Standard Installations for Direct Design), have 

been developed to replace the empirical bedding factors developed by Marston. These 

installation types better represent the soil support conditions typically obtained using modern 

construction practices (ASCE, 1993). 

While the designs resulting from these refinements can be more efficient, their assumptions may 

be less tolerant to loss of backfill support, such as seismically induced ground instability, than 

earlier, less efficient designs. Currently, AASHTO jurisdictions are mixed on their adoption of 

direct versus indirect methodologies for design of RCP culverts. This is also the case with 

adoption of the new SIDD factors versus continuing to use the older Marston bedding factors. 

More work is required to quantify the difference in seismic retrofit requirements for RCP 

designed under the older versus the newer methodologies. 

Four-sided and three-sided box culverts, whether precast or cast-in-place, are designed using the 

same criteria as other reinforced concrete beams and columns. Rectangular shapes are analyzed 

assuming an indeterminate elastic frame and active or neutral soil pressures against the side, but 

do not account for soil-structure interaction. Most computer software currently available to the 

typical engineer can perform the structural analysis required for design. In addition, specialty 

software has been developed for this purpose (McGrath et al., 1988). 

On the other hand, arched-top three-sided box culverts account for soil-structure interaction by 

depending upon the passive soil restraint at the side to support the arching action of the top. 

Therefore, their design and analysis requires the use of computerized numerical models that can 

account for this interactive support (Katona et al., 1976, 1981; Beach, 1988; Musser, 1989a; 

McGrath et al., 1996). 

The advantage that rigid culverts have over flexible ones during earthquakes is their ability to 

provide a greater degree of brute strength during the loss of soil envelope support that might 

occur as a result of permanent ground deformations. A disadvantage is their brittle nature 

(ultimate strain capacity less than 0.1 percent). When the brute strength limit is reached, rigid 

culverts cannot shift overloads to the soil envelope through passive restraint without causing 
252

permanent damage to the structural shell. Also, they do not respond as well to transient ground 

motions where ductility is important. However, even if irreparable damage results, cases of 

catastrophic collapse of RCP during seismic events have not been documented in the literature. 

5.2.3. CULVERT JOINTS 

The primary objective of the seismic design of culvert joints is to maintain joint closure during 

ground shaking and after the occurrence of permanent ground deformation. Open joints can lead 

to soil fines migration, which over time can lead to loss of the backfill envelope and the collapse 

of the culvert and road surface. However, this action takes considerable time to develop and is 

not classed as an immediate threat to life safety or serviceability of the roadway. A secondary 

objective of the joint design is to relieve longitudinal stress built up in the continuous part of the 

culvert wall, provided that the primary objective of joint tightness is not compromised. 

During ground shaking, the optimum joint would provide longitudinal ductility in both tension 

and compression without reaching the end of its design travel length and without the loss of joint 

tightness. Joints that are assembled tightly in compression but are relatively free to move in 

tension are subject to joint hammering during the high frequency longitudinal oscillations 

typically associated with seismic ground shaking. This hammering can result in damage to the 

joint and a loss of joint tightness. In addition, joints that open as soon as they are extended in 

tension may allow infiltration of soil fines. This action may prevent them from fully closing 

during subsequent cycles of shaking, thus leading to further loss of soil tightness. 

During permanent ground deformation, the optimum joint would be capable of developing the 

full strength capacity of the culvert wall section in tension, compression, and shear while still 

remaining ductile. This is because the deformation demand at ground failure sites can become so 

great that typical joint designs utilizing the push-on type of assembly cannot accommodate such 

large seismically induced deformations without coming apart. The best design to withstand 

permanent ground deformations would be jointless culverts that could also maintain longitudinal 

ductility and cross sectional strength, even after losing the support of the confining soil envelope. 

No real culvert systems available today can provide all of these characteristics. However, some 

types approach this optimum performance more closely than others. 

As will be seen in the case histories that follow, culvert joints can be the weak link in the chain of 

total culvert performance during earthquakes. Hence, adequate joint design to resist the action of 

earthquakes is perhaps as strategic to overall culvert performance as the design of the wall 

section. Therefore, to increase understanding regarding this aspect of culvert performance, 

several types of commonly available joints are reviewed in the following subsections. 

5.2.3.1. Bell and Spigot Joints 

Bell and spigot joints are available for a number of thermoplastic and precast reinforced concrete 

pipe products, as shown in figure 5-6. They are generally furnished with rubber gaskets. 

Thermoplastic pipe joints typically allow 25-50 mm of longitudinal joint translation as well as 

1-3 degrees of joint rotation. Normal RCP bell and spigot designs do not allow for much 

longitudinal translation or rotation while still maintaining a sealed joint. An RCP joint 
253

Smooth Wall Thermoplastic Rectangular Closed Profile Thermoplastic

T-Rib Open Profile Thermoplastic Reinforced Concrete

Figure 5-6. Selected examples of bell and spigot culvert joints. 

configuration allowing 50-100 mm of joint translation is available by special order in some 

markets. 

While most thermoplastic and RCP bell and spigot designs develop some level of transverse 

shear strength at the joint, the full shear capacity of the culvert wall generally cannot be 

developed. This is due to a number of factors. Some RCP designs do not carry the full quantity 

of shell reinforcement into the joint. Even when the full wall sectional capacity is carried into 

the joint, the bell portion is acting at a slightly larger diameter, which is accompanied by a 

proportionate decrease in strength. This is true for both RCP and thermoplastic materials. Also, 

transverse forces tend to develop stress concentrations at one point around the joint 

circumference. Deformation mechanics suggests that flexible materials will distribute these 

stress concentrations more uniformly than rigid materials, hence developing a higher percentage 

of wall strength at the joint. 

The typical installation practice for bell and spigot joints is to push the pipe home, or in other 

words, to assemble the joint with the spigot end fully inserted into the bell. While this provides 

the greatest pull-out (tension) ductility available from a given design, it leaves no ductility in 

compression. Ideal installation practice for seismic performance would be 50 percent insertion. 

However, for most commercially available culvert products, the resulting travel length available 

in each direction (tension and compression) would be of little use during a seismically induced 

ground failure event. 

5.2.3.2. Tongue and Groove, Keyed and Butt Joints 

Tongue and groove, keyed and butt joints are used in many precast concrete culverts and in the 

expansion joints of nearly all cast-in-place concrete designs. Examples of these joints are shown 
254

in figure 5-7. The tongue and groove and keyed joints are similar because they both provide 

some level of restraint and strength to resist transverse forces. However, like bell and spigot 

RCP joints, they provide very little longitudinal or rotational ductility without separating. The 

spaces between both the tongue and groove and keyed joints typically are filled with cement 

grout but also may be fitted with an elastomeric pad or other sealant. In either case, the joint can 

be subjected to longitudinal hammering during dynamic shaking that can lead to cracking and 

spalling. This damage can result in loss of soil tightness. Also, as the joint opens or is damaged, 

backfill soil can infiltrate and prevent it from fully closing during subsequent cycles of shaking. 

The butt joint is used in some precast reinforced concrete designs. It is not usually grouted 

closed during construction but is assembled as close as possible. It is often wrapped with a 

geotextile or waterproofing membrane. However, the effectiveness of these wraps in 

maintaining joint closure during dynamic shaking is not known. Also, butt joints obviously 

provide no transverse strength and can be subject to damage from longitudinal hammering. 

Tongue and Groove

Keyed

Butt

Figure 5-7. Tongue and groove, keyed and butt 

joints in reinforced concrete culverts. 
255

5.2.3.3. Closure Bands and Couplings 

Closure bands are used primarily with corrugated and spiral rib metal pipes. They are 

manufactured in a wide variety of configurations. Examples of closure bands are illustrated in 

figure 5-8. Designs for culverts with annular corrugations utilize sections of matching 

corrugated pipe wall that are joined by angle iron flanges welded to the ends of the sections at 

two or three points around the circumference, thus forming a complete band. The band is 

tightened by cinching the flanges together with bolts located external to the pipe. The width of 

the band typically engages two or three annular corrugations on each culvert end that it joins. 

Closure Band Sleeve Gasket

Closure Band O-Ring Gasket

Sleeve Gasket

for Helical

O-Ring Gasket

for Annular

Closure

Band

Corrugated Metal

Semi-corrugated Metal

Flat Metal

Figure 5-8. Selected types of closure bands for corrugated 

metal culverts. 
256

This design provides both ductility and strength in all three degrees of freedom, as well as good 

closure against soil migration. However, pull-apart tests reveal that this type of closure band 

falls short of developing the full culvert wall strength. The bolted connections at the flanges are 

the weak link. An elastomeric gasket is sometimes inserted between the band and the pipe wall 

to improve water tightness but may also decrease the pull-apart strength of the connection. 

Another type of closure band employs flat steel sheet fabricated with edge corrugations (semicorrugated). Its typical use is to join spirally corrugated culverts having ends that are reformed 

into annular corrugations. It engages the reformed end in only one of its corrugations. Hence, 

while it is more efficient in materials, it lacks the same pullout capacity of the fully corrugated 

band that engages at least two corrugations on each end. Otherwise, the semi-corrugated design 

shares most of the other characteristics of the fully corrugated band. 

Flat or dimpled closure bands are provided for culverts with plain end spiral corrugations or 

spiral ribs. They provide some level of transverse strength but almost no longitudinal or 

rotational restraint. Since the band does not fit snugly into spirally corrugated culvert walls, the 

surrounding backfill envelope can be lost when spirally corrugated culverts without reformed 

ends are employed under some hydraulic conditions and when fine-grained soils are present. 

Most profile wall thermoplastic culverts employ shaped couplings to join plain end sections. 

These couplings are designed to fit the specific profile configuration of the culvert wall. They 

typically include a shaped rubber gasket to provide tightness against both moisture and soils 

migration. An example of such a coupling is shown in figure 5-9. Other designs employ a type 

of closure band. Molded plastic sheets with edges that match the exterior of the profile wall fit 

around the pipe ends and snap shut. Thermoplastic couplings perform similarly to thermoplastic 

bell and spigot joints in terms of their longitudinal and rotational ductility. They also provide 

some transverse strength. 

Shaped Coupling Shaped Gasket

Figure 5-9. Typical coupling for plain end thermoplastic culverts. 

5.2.3.4. Continuous Joints 

Three types of continuous joints are available for certain applications. Cast-in-place reinforced 

concrete often utilizes construction joints that are formed similar to tongue and groove or keyed 

joints, but carry dowels of reinforcing steel across the joints. A second type is corrugated metal 

structural plates that are field assembled with bolted connections. A third type is thermoplastic 

pipe with ends that are fused together, either by heat or solvent. The first two are used for 

relatively large culvert applications. 
257

The third type is used as a liner of relatively small diameter culverts, the outer shell of which 

consists of one of the other culvert types described herein. 

All three types of continuous joints share common characteristics relative to seismic 

performance. The most important aspect is that they develop a large portion of their wallsectional strength and ductility in all three degrees of freedom. 

5.3. SCREENING FOR POTENTIAL SEISMIC DAMAGE 

The objective of the screening process is to identify a subset of culvert sites that may require 

further evaluation at a more detailed level while dismissing sites that would not be expected to 

suffer significant damage and remain functional after an earthquake. Techniques for performing 

detailed evaluations of culverts are provided in section 5.4. 

Screening of culvert sites to determine the potential for earthquake-induced damage requires an 

understanding of the interrelationship between many complex factors, such as the following: 

• Magnitude of the earthquake. 

• Probable location of its origin. 

• Intensity of ground shaking expected to occur at the culvert site. 

• Likelihood that the fault displacement might rupture the ground surface or induce other 

ground failure mechanisms in the vicinity of the culvert. 

• Response of the culvert system to any of the factors listed above. 

Only the last item is dealt with exclusively in this chapter. The remaining factors are discussed 

briefly below. However, since they can influence the behavior of other highway system 

components as well, more detailed descriptions have been provided elsewhere in this manual. 

This section presents both the theoretical concepts related to seismically induced culvert damage 

as well as case histories that document the nature and extent of actual damage. These 

discussions provide important background that will be needed to support implementation of the 

decision-tree screening model given at the end of this section. 

5.3.1. THEORETICAL CONCEPTS RELATED TO SEISMICALLY INDUCED CULVERT 

DAMAGE 

Similar to other structures, seismic events can damage culverts through two primary causative 

mechanisms, permanent ground failure and transient ground shaking, the latter of which may 

also induce significant inertial forces. Permanent ground failures generally cause the largest 

deformations and greatest damage to culverts. Transient ground shaking can also damage 

culverts, but typically to a much more limited extent. Seismically induced inertial forces, which 
258

are the primary cause of damage to aboveground structures, seem to have little effect on culverts 

except for large diameter pipes and non-circular shapes, including box culverts, under heavy 

loads. 

The first step in screening culverts to determine the need for retrofit measures is to assess the 

potential that the causative mechanisms described above will occur at any given site. Theoretical 

concepts related to the occurrence and manifestation of these causative factors will be reviewed 

briefly in the following subsections. In addition, the likely responses to these causative factors 

will be discussed. 

5.3.1.1. Permanent Ground Failure 

Permanent ground failure can result from either of two major causes, fault rupture or ground 

deformation due to ground shaking. Fault rupture by itself can induce ground surface 

deformations in the vicinity of the rupture zone. The extent of this zone is typically limited to a 

distance of a few hundred meters from the principal trace of surface fault rupture. The resulting 

ground surface deformations can range from very slight to severe. 

Mild tectonic deformations may appear as undulations, bulges or depressions that extend over 

large areas but may produce only small differential effects local to a given culvert. Hence, they 

generally have little effect on culvert performance. On the other hand, severe tectonic 

deformations can produce compression zones, tension zones, ground surface offsets, either 

horizontal, vertical, or both, or the possible formation of chasms or ridges. The most severe of 

these manifestations would be impossible to protect against and, certainly, would impair the 

performance of culvert structures that happened to exist in their path. 

Nonetheless, where the existence of these challenges have been identified, other utilities, such as 

pressure water or gas pipelines, have devised engineered solutions that have successfully dealt 

with at least moderate tectonic deformations. These solutions typically have used one of two 

types of constructions. The first employs continuous ductile pipelines having full strength (often 

welded) joints. The second utilizes multiple sections of short pipes connected by flexible joints 

capable of developing significant tension, compression and lateral ductility without suffering 

pull-apart, damage or other loss of functionality. Similar technologies as these are also available 

for culverts. 

Ground shaking alone can also cause permanent ground failure. Liquefaction, collapse or sliding 

of unstable soil masses are the causative factors in these cases. Permanent ground failure that 

impacts culvert performance is often accompanied by the following site manifestations: 

• Embankment penetration. 

• Lateral and embankment spreading. 

• Slumping of fill and landslides. 

Identification of potential sites that might experience permanent ground failure requires 

significant expertise as well as the availability of site-specific geotechnical and seismological 

characteristics. Once estimates of ground deformations are provided for the design earthquake, 
259

they can be used to devise retrofit strategies. Or, they may lead to a decision favoring some 

means of ground remediation or stabilization to prevent ground failure, in which case culvert 

retrofit may not be necessary. Both ground failure prediction and ground remediation methods 

are discussed in Part 1 of this manual. 

5.3.1.2. Transient Ground Motion 

Transient ground motion may not result in permanent ground failure but still may induce strains 

and stresses in culverts that can lead to structural damage. The extent of this damage depends 

upon the level of shaking as well as the design and condition of the culvert. 

Transient ground motion produces both axial and transverse culvert strains or deformations. 

Components of seismic waves that propagate along the longitudinal axis of a culvert can produce 

joint hammering, joint pull-apart or transverse cracking. Components of seismic waves that 

propagate transversely to the longitudinal axis can produce ovaling, racking and other distortions 

of the culvert cross section. Transverse waves, whether vertical or horizontal, can also affect 

longitudinal culvert alignment. 

These manifestations of culvert distress caused by transient ground motion generally are not 

catastrophic except for the possible collapse of flexible types of culverts due to loss of soil 

support. Most culverts are believed to be too short in length and small in cross section to suffer 

major damage or immediate collapse as a direct result of such distress. However, joint 

separations and other induced damage can produce catastrophic collapse over time if there is 

erosion of soil into the culvert leading to loss of soil envelope support. In areas that suffer heavy 

shaking, post-seismic inspection and repair may be necessary in order to assure the long-term 

survivability of the culvert system. 

Transient ground shaking can also mobilize inertial forces induced in the backfill materials 

around and over the top of culverts. These inertial forces produce both horizontal and vertical 

overpressures that can increase the stress in the culvert cross section. Such transient stress risers 

do not typically lead to collapse, although they may induce local buckling or cracking of the 

wall. But, since all culverts depend to some degree upon the surrounding soil for their strength, 

these stress risers, when acting in conjunction with liquefaction or other causes of ground 

instability, can exacerbate the effect of the inertial forces due to reduction or elimination of 

support provided by the soil envelope. The extent of resulting damage depends upon the severity 

of this combination of effects but can produce distortion or collapse of the culvert cross section. 

Seismic ground accelerations are typically three-dimensional and are not necessarily in phase 

orthogonally. Hence, buried structures can experience tilting, racking, shear and unbalanced 

pressure increases, both horizontally and vertically. The longitudinal and transverse components 

of buried structure deformation and the types of seismic waves that can produce them are more 

fully discussed and illustrated in chapter 4. 

5.3.2. EMPIRICAL OBSERVATIONS OF SEISMICALLY INDUCED CULVERT DAMAGE 

In reviewing the following empirical data on seismically induced culvert damage, it is useful to 

differentiate between the causative mechanisms of damage and their manifestations. For 
260

instance, permanent ground failure caused by liquefaction can manifest itself in many forms of 

damage including misalignment, separation of joints, uneven settlement and even collapse of the 

culvert cross section. However, the likely causative factor, (i.e., liquefaction, collapse, slumping, 

fault rupture, etc.) can be readily ascertained by other site characteristics, such as the presence of 

unconsolidated sands or clays, the depth of the water table, the slope of the ground surface, 

observed tectonic ground deformations in the vicinity, etc. On the other hand, transitory 

longitudinal ground shaking, with or without inertial effects, can manifest itself in joint 

hammering, cross sectional deformation, cracking, etc. 

Of course, empirical observations will produce a mix of causative factors acting together. The 

challenge is to deduce the mechanisms that produce the most significant effects in any given 

observation. Accurate identification of the causes will result in selection of more appropriate 

evaluation techniques and retrofit strategies. 

Perhaps the most complete survey to date of culvert performance during seismic events was 

performed by Youd and Beckman (1996). Through a combination of personal observations and 

published reports, they documented culvert performance during six North American earthquakes. 

They identified not only effects but also probable causes of the damage. Table 5-1 categorizes 

their findings by culvert type and extent of damage. 

Another significant study by Davis and Bardet (1998) reported on the performance of 61 CMP 

and structural plate culverts that were shaken by the 1994 Northridge earthquake. Included in 

this study were 29 culverts that were 1 m or smaller in diameter and 32 that ranged from 1.07 m 

to 4.78 m in diameter or span. All 61 culverts were in the vicinity of the Van Norman Water 

Treatment Complex in the northern San Fernando Valley. Peak ground accelerations in this 

vicinity ranged from 0.48 g to 1.08 g horizontal and from 0.32 g to 0.85 g vertical. 

With the exception of one culvert that was damaged due to a severely corroded invert, none of 

the culverts 1 m and smaller in diameter suffered damage during this event. Of these smaller 

diameter culverts, two were in areas that may have suffered some degree of permanent ground 

deformations. The nature, causative factors or extent of deformations at these sites were not 

reported. 

The performance of the larger culverts ranged from no damage to complete collapse. While all 

of these larger culverts appeared to sustain some deformations, four seemed to be influenced by 

permanent ground deformations to some degree. Four others seemed to be influenced by 

preexisting conditions such as poor backfill and severe corrosion of the invert. No surface 

faulting occurred at this site. 

The following paragraphs describe in more detail specific observations of culvert damage and 

the causative mechanisms that produced them. Contributions from both Youd and Beckman 

(1996) and Davis and Bardet (1998) are included. 
261

Table 5-1. Summary of highway culvert performance. 

Permanent Ground Deformation 

Transient 

Ground 

Deformation 

Site Manifestation of 

Seismic Event 

EP LS SL LQ LA FR SG GS LO 

Totals

CMP Pipe 

Replace 4 1 1 1 7 

Repair 1 1 2 

No Repair 1 24 25 

Thermoplastic Pipe 

Replace 0 

Repair 0 

No Repair 1 1 

Reinforced Concrete Pipe 

Replace 1 1 

Repair 1 1 1 3 

No Repair 0 

Unreinforced Concrete Pipe 

Replace 1 1 

Repair 0 

No Repair 0 

Reinforced Concrete Box 

Replace 1 1 2 

Repair 2 4 3 9 

No Repair 1 4 14 1 20 

Notes: 

EP = Embankment Penetration 

LS = Lateral Spread 

SL = Slumping 

LQ = Liquefaction 

LA = Landslide 

FR = Fault Rupture 

SG = Strong Ground Shaking 

GS = Ground Shaking 

LO = Lateral Overpressures 

compiled from Youd and Beckman, 1996 
262

5.3.2.1. Embankment Penetration 

Strong ground shaking occurring during moderate to high magnitude seismic events can trigger 

the collapse of liquefiable or sensitive foundation soil layers below highway embankments. The 

resulting subsidence of these layers causes penetration of embankments into the unstable stratas 

and can damage highway culverts located in the vicinity of these stratas. This can lead to 

longitudinal and transverse bending of the culvert barrel sections, separation, misalignment and 

fracturing of the culvert joints and raising of the culvert ends above the flow line. A typical 

failure diagram is shown in figure 5-10. 

a. Before Earthquake

b. After Earthquake

Fill

Culvert

Culvert

Ground

Displacements

Saturated

Liquefiable

Soil

Youd and Beckman, 1996 

Figure 5-10. Penetration of embankment and culvert into liquefied foundation strata. 

While any culvert type would be subject to damage from embankment penetration into unstable 

foundation soils, Youd and Beckman (1996) reported that it was the most common cause of 

CMP culvert failure in the six earthquakes that they investigated. These events experienced 

magnitudes ranging from 6.4 to 9.2. The cause of damage at five CMP culvert sites and two 

cast-in-place reinforced concrete box culvert sites was attributed to embankment penetration. 

Four of the five CMP sites required major repair or replacement of the culvert. In two of the 

CMP cases, the road was rendered impassible by embankment penetration. At only one of the 

five sites, the battery of culverts maintained limited hydraulic functionality after the earthquake. 

Only minor repair was required at the two box culvert sites. 

Damage to the CMP culverts included vertical misalignment of the flow line, buckling or 

bending of the pipe underneath the fill, possibly at the joints, and raising of the culvert ends. 

Documented culvert sizes ranged from 760 to 1,070 mm in diameter. The embankments 

subsided as much as 0.9 m and spread laterally as much as 6 m. The resulting subsidence in the 
263

center of the embankment raised the culvert ends as much as 1.8 m. At most of the above 

described sites, the embankments and the surface pavements also suffered major damage. 

Damage to the two cast-in-place reinforced concrete box culverts were less severe than those 

described above. Longitudinal bending of the culverts opened transverse cracks, which were in 

the weak direction of reinforcement. The widths of the cracks ranged from as much as 13 mm in 

the floors of the boxes to hairline cracks in the top slabs. The box configurations included a 

triple-celled 2.6 m wide by 1.8 m high as well as a single-celled 2.4 m high by 2.4 m wide cross 

sectional configuration. In both of these cases, embankment penetration was slight. Surface 

damage included cracks in the pavement at the edge of the culverts and at other locations in the 

liquefied zone not over the culverts. In one case, blocks of asphalt road surface and concrete 

gutter were buckled and pulled apart. Total vertical misalignments of 6 to 10 mm were reported. 

It should be noted that a similar reinforced concrete box culvert as well as four CMP culverts 

were identified in the vicinity of the damaged box culverts described above. Upon inspection, 

they were found to have suffered no damage, even in the presence of 0.5 g accelerations. 

Obviously, ground instability was not a factor at these additional sites. 

Davis and Bardet (1998) inspected two CMP culverts that suffered beam-type bending during the 

Northridge earthquake. Both measured 1.52 m in diameter and were encased in concrete. Both 

performed well during the earthquake. Although the joints slightly separated due to foundation 

and embankment deformations, the concrete surrounding these culverts remained intact. 

Liquefaction was observed in the area. However, the magnitude of permanent ground 

deformation experienced at the culvert site was not reported. Concrete encasement appears to be 

a promising retrofit measure to prevent CMP joint pull-apart under embankment penetration. 

5.3.2.2. Lateral and Embankment Spreading 

Like embankment penetration, lateral spreading of ground surfaces and embankments are also 

caused by unstable foundation soils that either liquefy or collapse during strong ground shaking. 

Significant lateral spreading can occur, even over very gently sloping ground. Culvert damage 

usually associated with lateral spreading includes vertical and horizontal misalignment, pullapart of the joints and separation of the culverts from end appurtenances such as headwalls, 

wingwalls and flared end sections. Also, unbalanced horizontal and vertical pressures can 

overload culvert walls, causing ovaling, racking and overstress. 

Youd and Beckman (1996) documented culvert damage due to lateral spreading that extended as 

much as 1.8 m horizontally and 1.4 m vertically. Two CMP and two RCP culverts suffered 

major damage, although no road closures occurred. One of the CMP culvert sites was part of a 

dam. In addition to these four, one reinforced concrete box culvert suffered only minor damage. 

For most CMP, the major damage was observed to be joint and end appurtenance separation. 

However, in the case of a liquefaction zone experiencing ground accelerations exceeding 1.0g, a 

2,400 mm diameter CMP culvert collapsed. The cause of the collapse was attributed to 

excessive unbalanced lateral pressure. The height of cover over the failed section varied from 

4.2 to 12 m. The portion of the culvert having less than 3.7 m of cover did not appear to be 
264

damaged. The CMP was an extension of an older RCP of the same diameter. The connection 

was made at the deepest point. No damage was noted in the adjacent section of RCP. 

Considering these facts, another likely contributing factor to this failure was the loss of the soil 

envelope support due to the reduction of shear strength in the liquefied soil. Flexible culverts, 

such as CMP and plastic, depend almost entirely upon the shear capacity in soil support to 

maintain their shape under load. 

However, reporting on this same collapse, Davis and Bardet (1998) noted that only a portion of 

the culvert segments were in the liquefied zone. The remaining segments were in nonliquefiable bedrock and alluvium. Hence, they contend that strong ground shaking alone 

triggered the collapse along at least a portion of the culvert’s length. 

Damage in RCP culverts due to lateral spreading generally occurred at the joints. In addition, 

some RCP culverts suffered joint hammer, or opening and closing of the joints, during ground 

oscillations. This could have occurred with impact, intensifying the damage. Spalled concrete 

surfaces at joints and exposed rebar were noted during the inspections. 

Several cases of lateral spreading were also noted at sites having multiple barrels of cast-in-place 

reinforced concrete box culverts. Even where the construction joints in these structures were 

designed for strength transfer from one section to another, tension rupture of the rebar, spalling 

of the concrete and separation of the construction joints were observed. This may be indicative 

of a design deficiency that inadequately represents the strength capacity required for the joint to 

withstand a seismic event. 

Not withstanding this type of misalignment and joint damage, the barrels between the joints of 

CMP, precast reinforced concrete and cast-in-place reinforced concrete culverts all generally 

performed well under lateral spread. 

5.3.2.3. Slumping of Fill and Landslides 

This type of ground failure occurs at steep slopes composed of materials that becomes unstable 

during strong ground shaking. Slumping of fill or landslides can damage highway culverts 

installed at these locations. Damage could include longitudinal and transverse bending of culvert 

barrel sections or separation, misalignment and fracturing of the culvert joints. A typical failure 

diagram is illustrated in figure 5-11. 

Youd and Beckman (1996) reported only one instance of this type of culvert failure. The slump 

rotated and slid downward about 0.9 m. The 900 mm diameter CMP did not crush or tear, but 

rather rotated and stretched at the joints. The joints were pulled apart as much as 150 mm. 

Angular rotations about the joints were as much as 5 degrees. However, this particular culvert 

was over-wrapped with a 0.3 m to 0.6 m length of curved corrugated metal sheet at each joint. 

Hence, even though joint separation occurred, the culvert continued to function after the 

earthquake without being blocked by slumping soil. However, the road was impassible as a 

result of the slump. Apparently, the original design of the culvert assumed the potential 

occurrence of slope instability, since over-wrapping has not been a standard installation practice. 
265

Pavement

Joints

Culvert

Youd and Beckman, 1996 

Figure 5-11. Embankment slump (similar effect on culverts as landslide). 

5.3.2.4. Surface Faulting 

Surface faulting occurs when a fault rupture extends to the ground surface. Tectonic 

deformation zones can include vertical and lateral surface fractures, compression buckling, and 

crustal uplift or subsidence. Also, strong ground shaking generally accompanies surface 

faulting. Culvert failures associated with surface faulting include longitudinal and transverse 

bending of the culvert barrel sections, separation, misalignment and fracturing of the culvert 

joints and separation, fracture and collapse of culvert end sections. 

In an area where surface faulting, diffuse tectonic deformations and strong ground shaking of 

0.4 g occurred, Youd and Beckman (1996) inspected approximately 20 CMP and one plastic 

culvert. They found virtually no damage to the culverts or to the associated road pavements that 

could be attributable to the seismic event. However, none of these culvert alignments intersected 

surface fractures, even though many fractures occurred in the vicinity. Also, the ground 

upheaval due to faulting did not render the road impassible at the culvert sites. Nonetheless, the 

culverts had been subjected to strong ground shaking and mild tectonic deformations. 

Reinforced concrete pipe was also documented to do well in surface faulting zones experiencing 

mild tectonic deformations and where no surface fractures intersected the culvert alignment. 

However, they did find examples of RCP in areas where ground upheaval, fractures and 

significant offsets had occurred. Here moderate-to-severe damage of the RCP joints were noted. 

This included joint separations, misalignment, shear failure, spalling and exposure of the 

reinforcing steel. It was considered likely that some of the joint damage was attributable not 

only to surface faulting but to ground oscillations produced by longitudinal compression waves 

that resulted in joint hammering. However, no barrel fractures or spalling beyond the joints were 

noted. The road was passable after the earthquake. However, two RCP culverts required major 

repair or replacement of some sections as a result of the faulting. 
266

Reinforced concrete box culverts were also studied in areas of surface faulting. Where diffuse 

tectonic deformation occurred, cracks developed in the tension zones of wall cross sections. In 

many cases, these cracks were repairable. However, in areas of severe tectonic deformations and 

ground fracture, major shear and moment failures in the walls, inverts and roofs were 

experienced. Characteristically, the walls were deflected inward as much as 0.3 m at mid-height. 

Again, the road was passable but major repairs and replacement of portions of the culvert were 

required. 

5.3.2.5. Ground Shaking 

All of the above empirical observations involved permanent ground failure in one form or 

another. Ground shaking is transitory and, of course, occurs integrally with and is a part of the 

other responses detailed above. However, when it is not accompanied by some type of 

permanent ground failure mechanism, experience has shown that even strong ground shaking 

does not appear to cause catastrophic damage to smaller diameter highway culverts (1 m or less), 

whether flexible or rigid. Nevertheless, there are some circumstances under which ground 

shaking, acting alone or in combination with inertial effects, can impact culvert performance. 

These include culvert joints with little or no ductility in either tension or compression, large span 

culverts, culverts under high cover, culverts with non-circular cross sections and unreinforced 

concrete or masonry culverts. 

Youd and Beckman (1996) reported instances where RCP culverts experienced damage in the 

presence of ground shaking. However, none rendered the roads impassable. The evidence 

suggested that permanent ground failure mechanisms, such as liquefaction, were absent at these 

sites. In one case, a 2,210 mm diameter by 63.4 m length of RCP culvert under about 8 m of fill 

was damaged during the 1971 San Fernando earthquake. Distress was concentrated at the joints 

and included spalling with exposed rebars that were twisted and/or sheared. Cracks varied from 

5 to 10 mm in width. Also, displacements of 38 to 51 mm were noticeable at the joints. The 

culvert was later repaired using a protective steel liner plate. 

Youd and Beckman (1996) also inspected a number of reinforced concrete box culverts in areas 

that experienced 0.5 g to 1.0 g under 3 m or less of cover. Again, evidence of ground failure 

mechanisms was absent. No visible damage was detected in any of those inspected. However, a 

box culvert under 7.6 m of cover and another one under 20 m of cover suffered significant 

damage, which included lateral wracking and cracks in the walls and ceiling. Transient ground 

deformation likely contributed to the damage under these heavy covers. This damage was 

repaired after the earthquake. 

A 2,100 mm diameter unreinforced concrete pipe was also reported to have sustained damage in 

the presence of 0.5 g ground shaking, but without the presence of other ground failure 

mechanisms. Longitudinal cracks were practically continuous, mainly between the 8 and 11 

o'clock and 2 and 4 o'clock positions. Cracks up to one inch wide with lateral offsets up to one 

inch were noted. Also, peripheral cracks at joints were observed. A 183 m length was badly 

damaged and appeared no longer serviceable. The investigators suggested that unreinforced 

concrete may be too weak and brittle to provide satisfactory culvert performance in earthquake 

prone areas. 
267

Davis and Bardet (1998) suggested that either transverse or longitudinal ground shaking, or both, 

triggered axial and/or lateral deformation, wall buckling and bolt shear of one structural plate 

and portions of two CMP culverts during the Northridge earthquake. The structural plate was 

3.81 m in diameter. The CMP culverts, although at different locations, were both 2.44 m in 

diameter. As noted earlier, peak ground accelerations exceeding 1.0 g were experienced in the 

vicinity of these culverts. 

5.3.3. SUMMARY OF CULVERT SCREENING CRITERIA 

The above described theoretical and empirical observations of culvert performance under various 

modes of seismic response do not provide a statistically meaningful basis for analysis of all the 

factors involved in the resistance of culverts to seismic damage. However, they do provide a 

basis for a number of general and qualitative conclusions, which are summarized in the 

paragraphs that follow. 

First, zones of permanent ground failure were observed to produce the largest deformations and 

the greatest damage to culverts. Also, no culvert types, shapes or sizes were found to be immune 

to damage by this cause. However, the empirical observations reviewed above reveal that, under 

cases of moderate to severe liquefaction, thin-walled flexible culverts were found to be more 

susceptible to buckling or collapse of the cross section than rigid culverts. On the other hand, in 

areas exposed to slumping of fills, landslides or fault ruptures, joints that fail to provide 

continuity and ductility were found to exhibit the greatest liability. Furthermore, the 

deformations that could develop in zones of permanent ground failure may be so great that the 

capacity of normally available culvert systems of any type may not have the capacity to 

accommodate them without special design. 

Second, strong ground shaking, when not accompanied by ground failure, generally has not 

appeared to cause significant damage to small culverts one meter or less in diameter, regardless 

of type. However, the empirical evidence has shown that the damaging effect of ground shaking 

on culverts increases with size and length. This effect also varies with culvert shape and type. 

Circular cross sections are more resistant than noncircular. Ductile materials, such as metal, 

plastic or reinforced concrete perform better than unreinforced or brittle materials. Moreover, in 

the presence of strong ground shaking, longitudinal joint ductility in both tension and 

compression was observed to be important. Numerous cases of damage from joint hammering 

were noted, primarily in the rigid joint designs. 

These limited empirical observations as well as the theoretical considerations given above 

provide a basis for screening culverts relative to their need for further evaluation and, possibly, 

retrofit. The suggested logic for doing so is illustrated in figure 5-12. 

Only culvert systems commonly employed in highway applications are included. Still, the 

potential range of shapes, sizes, types, ground conditions and seismic effects make all but the 

most generalized treatment a daunting task. Undoubtedly, more detailed screening criteria could 

be developed and might be justified under some circumstances. 
268

Start

10

Design Retrofit

to Reduce

Culvert Deform

and/or

Increase Buckling

Capacity

14

Design Retrofit

to Reduce and/or

Resist Permanent

Ground Strain

13

Demand

>

Capacity

12

Evaluate

Culvert System

Strain Capacity

11

Evaluate

Permanent

Ground Strain

Demand

9

Deform.

and/or

Buckling

Exceeds

Allow.

8

Evaluate

Culvert X-Section

Deformation

and Bucking

Capacity

7

Residual

< 0.80

Static

6

Evaluate

Liquefied

Soil Shear

Capacity

5

CMP

CMBC

CMLS

PWPP

3

Invert

Within or

< Max. of

(0.5 D or 0.5 m)

Above

Liq. layer

4

Embank.

Height

> Min. of 1 m

Above

Invert

1

Liquefaction

Zone

2

Slump,

Landslide

or Fault Rupture

Zone

1 No No

No

No

No

No

No

No

Yes Yes

Yes

Yes

Yes

Yes

Yes

Yes

Match

Figure 5-12b

LEGEND:

D = diameter of span

g = gravitational acceleration

CMP = corrugated metal pipe

CMBC = corrugated metal box culvert

CMLS = corrugated metal long span

PWPP = profile wall plastic pipe

RCBC = reinforced concrete box culvert

RCLS = reinforced concrete long span

RCP = reinforced concrete pipe

UCP = unreinforced concrete pipe

UMP = unreinforced masonry pipe

.

Figure 5-12. Flowchart of screening procedure for culverts under (a) permanent ground 

deformation and (b) transient ground deformation. 
269

Design Retrofit

to Increase

Strength and/or

Deformation Capacity

of Culvert System

1

27

15

D <=1 m

or

g <= 0.2

16

1 m <

D

<= 2 m

17

CMP

PWPP

RCP

18

CMLS

RCLS

or

D > 5 m

21

Cover

<= 3 m

19

0.2 <

g

<= 0.5

22

CMBC

RCBC

20

UCP

UMP

23

Cover

<= 1 m

Detailed

Capacity/Demand

Strength & Deform.

Eval. due to Trans.

Ground Motion

Simplified

Capacity/Demand

Strength & Deform.

Eval. due to Trans.

Ground Motion

26

Demand

>

Capacity

End

24 25

Match

Figure 5-12a No

No No

No

No No

No

No

No

No

Yes

Yes Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Figure 5-12. Flowchart of screening procedure for culverts under (a) permanent ground 

deformation and (b) transient ground deformation. 
270

Figure 5-12(a) proposes logic for screening culverts under the action of permanent ground 

deformation. In order to make a retrofit decision, both the ground strain demand and the culvert 

system strain capacity must be evaluated in all three principal axes. Cases in which the 

liquefaction zone or its overburden would experience only minor strains are neglected, or 

screened-out. However, when flexible culverts exist in major liquefaction zones, an extra step is 

required. If a significant reduction in shear strength is predicted due to liquefaction, still another 

evaluation is then required to assess the magnitude of culvert deformations and the potential for 

buckling of the culvert cross section that could occur as a result of the loss of side support. 

Once a retrofit decision is made regarding permanent ground deformations and/or buckling of 

flexible culverts due to liquefaction, strong ground shaking alone must be considered. Figure 5-

12(b) proposes logic for screening culverts under the action of transient ground motion. Here the 

retrofit decision is based on the strength and deformation capacity of the culvert system 

compared to the demand generated by ground shaking. This requires a fundamentally different 

evaluation process than for permanent ground deformations, hence the development of two 

separate decision matrices. Again, the effects of transient ground motion must be evaluated in 

all three principal axes. 

Because case histories and theoretical considerations suggest that the influence of ground 

shaking is graduated over some scale, the decision matrix shown in figure 5-12(b) is also 

graduated. Smaller culverts and low level seismic events are screened out immediately. 

Culverts of intermediate size that are subjected to moderate loads and midlevel seismic events 

undergo a simplified evaluation process. Large, non-circularly shaped and unreinforced culverts 

subjected to mid and high level seismic events undergo a detailed evaluation process. It is 

anticipated that 95 percent (or higher) of highway culverts will be screened out by this decision 

matrix, not requiring retrofit. This is in agreement with both current perception of culvert 

performance during earthquakes as well as the limited case histories of ground shaking alone. 

Based on these flowcharts, two shortcuts can be observed for sites not susceptible to permanent 

ground displacements. First, retrofitting is not recommended for any culverts less than 1 m in 

diameter or with a design acceleration less than 0.2 g. Secondly, for CMP, plastic pipe, and rigid 

culverts with diameter less than 2 m, no retrofitting is recommended. 

The limits shown for the various branches of the decision matrices of figure 5-12(a) and (b) are 

thought to be somewhat conservative. However, it should be emphasized that no statistical basis 

for these limits can be reasonably derived from the small sample of case histories of culvert 

performance during earthquakes that has been documented to date. 

5.3.4. COMMENTARY ON SCREENING PROCEDURE 

The purpose of the screening procedure shown in figure 5-12(a) and (b) is to provide a rapid, 

low-cost approach to identify culverts with significant probability of collapsing or sustaining 

unacceptable damage during future earthquakes. Because culverts are generally resistant to 

seismic forces and because highway damage due to culvert damage or collapse can usually be 

repaired rapidly, highway agencies generally have not been concerned about the seismic hazards 

associated with culverts. However, to assure post-earthquake operability of critical highway 
271

segments, culverts must remain functional. Critical highways include those where closure, even 

for a short period of time, could immediately and adversely effect national defense, public safety, 

or emergency response, or where culvert blockage could lead to unacceptable environmental 

damage. Screening provides a logical first step for assessment of culvert performance. Although 

the screening procedure presented here is specifically for critical highway segments, the 

procedure may be applied to any highway system. 

The first step in the screening procedure (see figure 5-12(a)) is to determine whether the culvert 

lies in a liquefaction, slump, landslide or fault rupture hazard zone (Elements 1 and 2). If the 

culvert is not in one of these zones, then damage due to permanent ground deformation is 

unlikely, and the screening proceeds to an evaluation of effects of transient ground motions 

(figure 5-12(b)). If the culvert lies in one of these hazard zones, then culvert stability and 

permanent ground strain potential need to be evaluated. If the site is nonliquefiable, but within a 

slump, landslide or fault hazard zone (Element 2), the screening proceeds directly to an 

evaluation of permanent ground strain potential (Element 11). Procedures for estimating 

permanent ground strains are provided in chapters 3 and 4 of this manual. 

If the culvert lies in a liquefaction hazard zone, then damage is possible due to loss of side 

support (Element 3) or penetration of the highway embankment into the liquefied soil (Element 

4). To assure that loss of side support will not occur, the culvert should not lie within or 

immediately above the liquefiable layer. Based on past performance and conservative 

engineering judgment, significant loss of side support does not occur when the liquefiable layer 

lies more than twice the culvert diameter or a minimum of 0.5 m beneath the culvert invert 

(Element 3). 

Embankment penetration does not occur unless the embankment has sufficient weight to cause 

compression or shear failure within the liquefied foundation soil. Based on past performance, 

embankment heights greater than 1.0 m are required for significant penetration to occur. Thus, if 

the embankment height is less than 1.0 m (Element 3), penetration is not a significant hazard and 

the screening procedure proceeds to an evaluation of ground strain potential (Element 11). 

Procedures for estimating ground strain at liquefaction sites are provided in Part 1 of this manual. 

If the ground surrounding or overlying a culvert is susceptible to loss of sidewall support or 

embankment penetration, the screening continues to Element 5, culvert types. If the culvert is a 

rigid type, such as reinforced concrete (RCP) or unreinforced concrete (UCP) or masonry (UMP) 

pipe, the culvert is not vulnerable to loss of sidewall support or collapse due to embankment 

penetration and the screening proceeds directly to an evaluation of ground strain potential 

(Element 11). 

If the culvert is a flexible type of culvert, corrugated metal pipe (CMP), corrugated metal box 

culverts (CMBC), corrugated metal long span (CMLS) culverts or profile wall plastic pipe 

(PWPP), the screening proceeds to Element 6, evaluation of the shear strength of the liquefied 

soil. If the estimated residual strength of the liquefied soil is greater than 0.8 times the static 

shear strength, damaging loss of sidewall support is not likely and again the screening proceeds 

to Element 11, evaluation of permanent ground strain potential. If the soil is susceptible to large 

strength loss (greater than 20 percent), an evaluation of the deformation and buckling and 

capacity of the culvert is required (Element 8). If excess deformation or buckling is possible 
272

(Element 9), retrofit is needed to increase the buckling capacity to assure post-earthquake 

highway operability. Even after retrofit to prevent buckling, the culvert may still be vulnerable 

to failure due to excess ground strain. Thus, the screening proceeds to Element 11, an evaluation 

of permanent ground strain potential. 

If the calculated ground strains (Element 11) are less than the calculated strain capacity of the 

culvert (Elements 12 and 13), the culvert is not vulnerable to damage due to permanent ground 

displacement and the screening proceeds to an evaluation of the effects of transient ground 

motions (see figure 5-12(b), Element 15). If the calculated ground strains are greater than the 

capacity of the culvert can withstand, then retrofit is required to improve seismic culvert 

performance (Element 14). Such retrofit could include ground improvement to decrease ground 

strain potential or structural modification to improve culvert strain capacity. Procedures for 

these improvements are discussed in Part 1, and chapters 3 and 4 in this manual. 

The flowchart in figure 5-12(b) carries the screening process through an evaluation of culvert 

performance due to excitation by transient ground motions. If the culvert diameter is less than 

1.0 m or the anticipated peak acceleration, amax, is less than 0.2 g (Element 15), the culvert is too 

small or the motions too weak for damage to occur. The inherent strength of small-diameter 

culverts makes them very resistant to damage due to transient ground motions, and ground 

strains generated by motions with amax less than 0.2 g are too weak to damage even the most 

vulnerable culvert types. Thus, if the answer to the question in Element 15 is yes, the screening 

is complete and seismic damage is highly unlikely. 

If the diameter of the culvert is between 1.0 m and 2.0 m (Element 16) and the culvert is 

constructed from CMP, PWPP, or RCP (Element 17), the culvert is also immune to seismically 

generated damage and the analysis is complete. These types of culverts have proven to be 

resistant to transient seismic forces during past earthquakes. 

If the culvert diameter is greater than 5.0 m or the type is CMLS or RCLS, detailed strain 

capacity and demand analyses are required to assure that the culvert can withstand strains likely 

to be generated by the transient ground motions (Element 24). Few of these types of culverts 

have been shaken by large transient ground motions during past earthquakes to test their 

performance, so specialized analyses are required to assure their safety. If one of these long span 

culverts should collapse, the damage to the highway could present a safety hazard and be very 

disruptive to highway operations. 

If the culvert is less than 5.0 m diameter, the estimated amax is greater than 0.5 g (Element 19), 

and the culvert is unreinforced masonry (UMP) or concrete (UCP) pipe (Element 20), the 

structure is vulnerable to collapse and detailed seismic capacity/demand analyses are required to 

assure culvert safety (Element 24). 

If amax is greater than 0.5 g, the culvert type is other than UCP or UMP, and the cover is less than 

3.0 m thick (Elements 20 and 21), the culvert is immune to earthquake damage and the screening 

is complete. If the cover is greater than 3.0 m, inertial forces applied to the culvert through the 

cover material may be sufficient to overstress it and detailed capacity/demand analyses are 

required. Similarly, if the culvert is a box structure (CMBC or a RCBC) and the cover is less 

than 1.0 m, it is immune to seismically induced damage and the screening is complete. If the 
273

cover over a box structure is greater than 1.0 m thick, however, inertial forces may damage the 

culvert (Element 23) and analyses are required to assure safety. In this instance, simplified 

capacity/demand analyses may be applied to evaluate culvert performance (Element 25). These 

criteria are based on observed culvert performance and conservative engineering judgment. 

If the capacity/demand analyses (Elements 24 and 25) indicate that expected transient ground 

strains will not overstress the culvert, it is classified as safe and the screening and analysis is 

complete. If unacceptable damage is likely, then retrofit is required to strengthen the culvert. 

5.4. EVALUATION TECHNIQUES 

The flowcharts shown in figure 5-12(a) and (b) call for evaluations to be performed if certain 

criteria are met. In the case of permanent ground failure, the primary evaluation step requires 

estimation of the ground strains that are likely to be produced in directions that are both parallel 

and perpendicular to the axes of the culvert. These strain demands are compared with the 

capacity of the culvert system to either accommodate or resist them, which provides the basis for 

a retrofit decision. 

In liquefaction zones, an additional evaluation step is required for flexible culverts. The residual 

soil shear capacity must be determined. If it is found to be significantly less than the static 

capacity, the ability of the culvert cross section to resist buckling and large deformations must 

then be evaluated. 

In the case of transient ground motions, both the inertial force fields and transient ground strains 

that are likely to develop during the earthquake must be estimated for both the longitudinal and 

transverse axes of the culvert. These demands are then compared with the strength and 

deformation capacities of the culvert system to determine if seismic retrofit is needed. 

The following paragraphs describe some of the evaluation methods available to determine the 

effects of both permanent ground failure and transient ground motion on culverts. Since some of 

these methods apply to other highway components as well as to culverts, they may be treated 

elsewhere in this report, and references to other chapters are cited where appropriate. 

5.4.1. PERMANENT GROUND FAILURE 

To evaluate permanent ground failure, the basic assumption employed is that culverts will move 

coincidentally with the ground as seismically generated ground failure occurs. This assumption 

is conservative in that it neglects any deformation of the ground around the culvert and slippage 

between the culvert and the backfill. Most culvert types are not sufficiently strong to resist the 

forces imposed by ground failure; hence ignoring deformation and slippage is reasonable. 

During ground failure, culverts may be forced to undergo deformations that could be much larger 

than they are typically designed to accommodate, which can lead to damage. 

If the predicted ground displacements and strains are greater than the culvert can withstand 

without rupture, retrofit measures may be considered. Such displacements, however, would 
274

likely disrupt the roadway surface and joint separation of an underlying culvert may be of 

secondary importance. As noted in chapter 6, highway agencies in general prefer to rely on postearthquake repair of roadway damage as a mitigation strategy, rather than pre-earthquake retrofit 

measures. This preference also applies to culverts because culvert damage rarely leads to 

immediate catastrophic roadway damage. Thus, as part of any post-earthquake roadway repair, 

damaged culverts may also be repaired or replaced. Because active strategies are not being 

proposed or applied by highway agencies, no procedures or example calculations are given here 

for retrofit of culvert structures. 

Once permanent ground strain demands are estimated in both the longitudinal and transverse 

directions of the culvert axes, they must be compared to the strain capacity of the culvert system. 

If the demand exceeds the capacity, a retrofit decision must then be made. To avoid damage, 

retrofit strategies must be developed and deployed that will allow the culvert to accommodate the 

required deformations or remediate the ground and, thus, eliminate the cause of the potential 

ground failure. In some cases, a combination of both retrofit strategies may be the most cost 

effective solution. 

In order to design a culvert retrofit measure for potential ground failure, the first step is to 

estimate the strains that would likely be associated with this failure. Part 1 of this manual 

describes the analysis for liquefaction and its resulting ground strains. Analyses procedures for 

liquefaction induced ground failures are described in chapter 4. In this report, chapter 3 describes 

methods for estimated slope stability and associated ground movements, and chapter 4 describes 

methods for estimating fault displacements and assessing their effects on tunnels. However, since 

these methods were not developed and verified specifically for culverts, they may or may not be 

directly applicable to all the varieties and specific design aspects of culverts. Hence, their 

applicability must be assessed for the specific case under consideration. 

In addition, a number of other investigators have applied various theoretical and empirical 

evaluation methods to the prediction of the seismic performance of buried pipelines under the 

action of permanent ground failure. These include O’Rourke, T., et al. (1985, 1986), Wang et al. 

(1991), Yeh and Wang (1991), Miyajima and Kitaura (1991a, 1991b), Lopez and Berrones 

(1994), Honegger (1994), Liu and O’Rourke, M. (1997), and Trifunac and Todorovska (1997). 

However, these methods were developed primarily for pressure pipelines that extend over 

significant lengths. They have not been directly applied to culvert installations. While it is 

expected that many of these methodologies may be successfully adapted to culverts, much more 

theoretical development and experimental verification is needed to confirm the validity of such 

adaptation. 

Even though very little experience has been developed regarding the prediction of culvert 

performance during seismically induced permanent ground failure, it is expected that 

consideration of this aspect of performance will be required for important highway facilities that 

include medium to large culverts. A brief discussion of each major permanent ground failure 

mechanism and the recommended factors to be considered during evaluation are given below. 
275

5.4.1.1. Embankment Penetration 

Analytical or empirical procedures for predicting embankment penetration have not been 

developed for application in engineering practice. The following paragraphs provide guidance 

on factors controlling penetration and general procedures that could be applied to predict 

penetration and associated ground deformation. Embankment penetration is the vertical 

settlement of an embankment cross section caused by a classic shear failure of the underlying 

strata. Either single or double shear planes could develop. Some outward and upward motion of 

material within the failure envelope is likely to occur at the toe of the embankment slope. 

The first step in preventing damage to culverts due to embankment penetration is identification 

of locations where ground instability is likely to occur in the foundation soil below an 

embankment. The second step requires predicting the magnitude of the deformation. The 

following factors are known to be important in predicting the occurrence and magnitude of 

embankment penetration: 

• Presence of liquefiable or sensitive soil layers below embankments. 

• Presence of a water table. 

• Thickness of unstable strata. 

• Magnitude of ground shaking. 

• Height and geometry of embankment. 

5.4.1.2. Lateral and Embankment Spreading 

Guidance for the prediction of liquefaction and lateral spread displacement are covered in Part 1, 

chapter 4. These procedures can be applied to predict the occurrence of liquefaction and amount 

of possible lateral spread displacement at culvert sites. Liquefaction and lateral spread can occur 

with or without the presence of an embankment. Conservative estimates of the amount of 

extension of a culvert due to lateral spread can be made using the procedures in Part 1, chapter 4 

5.4.1.3. Slumping of Fills and Landslides 

Slumping of fills during ground shaking is a classical slope stability problem with a dynamic 

component. The slope deformation analysis methods described in chapter 3 can be used to 

predict both the occurrence of a slope failure due to earthquakes as well as the approximate 

travel length of the failure wedge. However, predicting the relative movements of a road surface 

or culvert within the sliding mass may be problematic except for small movements and simple 

geometric layouts. The following factors are known to be important in predicting the occurrence 

of slope failure during earthquakes: 

• Magnitude of ground shaking. 

• Slope of ground surface. 
276

• Geometry of critical failure surface. 

• Presence and depth of groundwater. 

• Geometry of the roadway cross section within the failure surface. 

• Frictional and cohesive strength of the in-situ materials. 

5.4.1.4. Surface Faulting 

If the surface trace of an active fault crosses a culvert alignment, geotechnical studies are 

required to assess the potential displacements that may occur in the event of an earthquake on the 

fault. Earthquake magnitude is an important factor in determining the amount of displacement, 

and correlations of fault displacement with magnitude have been developed as described in 

chapter 4. The determination of the possible distribution of displacements within the defined 

active fault zone (whether concentrated in a very narrow zone or distributed over a broad zone) 

requires geological assessments. 

5.4.2. TRANSIENT GROUND MOTION 

To evaluate the transient ground motion effects on culverts, the basic assumption employed for 

permanent ground failure regarding coincidental movement still applies to culvert deformations. 

However, transient ground deformations are typically much smaller than those experienced 

during permanent ground failures. Hence, they are not as likely to lead to culvert failures or to 

immediate collapse. Nevertheless, as documented previously, joint hammer and pull-apart due 

to transient ground motion can lead to the migration of fine soil particles, thus to the 

development of sink holes and, ultimately, to the collapse of road surfaces, which can be both 

expensive to repair and deadly to the unsuspecting motorist. 

On the other hand, the assumption of coincidental movement does not strictly apply to the 

component of transient ground motion responsible for inertia. This is because the intensity of 

inertial forces during a dynamic event is related to differences in mass rather than strain. Since 

culverts represent low mass inclusions, consisting mostly of air, that are surrounded by a high 

mass (soil) media, the potential for the development of inertial forces exists. Inertial effects can 

produce both racking and overpressure forces in the transverse axis of the culvert and frictional 

forces in the longitudinal axis. 

However, experience has shown that both transient ground strain and inertial forces are 

negligible for small culverts. Acting in all three principal axes, these effects become more 

dominant as earthquake intensities, culvert sizes and cover heights increase and with shapes that 

deviate from a circular cross section. Hence, the screening flowchart in figure 5-12(b) suggests a 

graduated consideration of culvert size, height of cover, and shape for transient ground motion. 

Due to their small numbers compared to other culvert types, little is known regarding the seismic 

performance of the largest and most noncircular culvert sizes and shapes. These include all large 

(long) spans of either concrete or metal as well as other types with diameters or spans greater 

than 5 m. For these types of culverts, detailed evaluations are recommended for moderate-to-
277

intense seismic events. The primary detailed evaluation method available for this culvert class 

consists of dynamic numerical modeling that assumes, as a minimum, linear elasticity. If 

permanent ground failure is also anticipated, large deflection theory and nonlinear material 

relationships should be included in the numerical analysis, the results of which should also be 

compared with empirical methods and case histories. 

On the other hand, seismic case histories are more available for culverts with intermediate sizes 

and shapes. Therefore, generally they can be safely evaluated for transient ground motion using 

simplified techniques. These simplified methodologies typically are closed-formed, equivalent 

static relationships that assume linear elasticity. Also, they are generally limited to circular or 

rectangular shapes. The results may be more conservative than would be obtained from the 

detailed methods described above. However, depending upon the size and length of the facility, 

the difference in the retrofit demand predicted by a detailed versus a simplified analysis may be 

overshadowed by the cost differential for performing these two types of evaluations. 

There is a large database of seismic performance histories for small diameter culverts. 

Generally, this history justifies neglecting the effects of transient ground motion for these 

facilities. Possible exceptions include unreinforced concrete and unreinforced masonry culverts 

subjected to intense ground shaking. 

In order to design a culvert retrofit measure that can accommodate transient ground motion, the 

first step is to estimate both the ground strains and the inertial forces associated with the seismic 

event being considered. The following subsections suggest methodologies that can be employed 

to evaluate these effects on culverts. 

5.4.2.1. Longitudinal Response of Culverts Due to Transient Ground Motion 

The following factors are known to be important in estimating the level of axial strain in a 

culvert associated with seismic waves propagating along the culvert longitudinal axis: 

• Types of seismic waves dominating the ground motion in the vicinity of the culvert. 

• Magnitude of acceleration and velocity components of these waves. 

• Frictional and cohesive strength of the site materials. 

• Height of cover. 

• Soil profile at the site. 

• Culvert wall materials and geometry. 

• Joint ductility. 

The analytical procedures described in chapter 4 for tunnels may be adequate for estimating the 

axial strains and stresses in a culvert wall due to seismic waves propagating along the culvert 

longitudinal axis. The modes of deformation are described in chapter 4 and illustrated in figure 

4-3(a) and (b). 
278

Under the action of transient ground motion, rigid culvert types are stiffer longitudinally than the 

surrounding soil. Also, they are stronger in this direction than the frictional forces that typically 

develop in an earthquake. Hence, any damage due to this response tends to concentrate at the 

joints. This damage typically consists of joint hammer and/or pull-apart (Youd and Beckman, 

1996). 

On the other hand, flexible culvert types typically have corrugated walls of one form or another, 

which results in a lower stiffness longitudinally than the surrounding soil (Takada et al., 1991). 

Hence, most of the longitudinal energy of transient ground motion is absorbed by flexible 

culverts without damage to either the culvert wall or to the joints. 

5.4.2.2. Transverse Response of Culvert Due to Transient Ground Motion 

Transient ground motions in the transverse direction of the culvert axis tend to produce racking 

or ovaling of the cross section. These deformation modes are illustrated in figure 4-3(c) and (d) 

in chapter 4 for circular and rectangular cross sections. In addition, transient ground motions can 

develop both horizontal and vertical inertial forces that can further exacerbate the distress in the 

cross section of the culvert. The horizontal component of these inertial forces can produce 

horizontal shear forces acting on the culvert roof as well as additional lateral earth pressures 

acting on the sides of the culvert. The vertical component can increase the vertical loads 

transmitted to the culvert roof from the overlying fill. At the same time, it can further add to the 

lateral earth pressures as well as produce frictional forces acting vertically on the sides of the 

culvert. 

Arching of the overlying fill generally is assumed to reduce the vertical static load pressures on 

culverts by some factor that depends upon both the culvert type and the backfill material. While 

arching action would be expected to persist under light to moderate ground shaking, it is not 

known whether it could continue to be maintained during heavy ground shaking. In the absence 

of experimental verification, it is safer to assume that arching action could not continue to be 

counted upon aboveground shaking that exceeded 0.5 g for non-liquefiable foundation materials. 

In chapter 4, closed form solutions and simplified procedures are presented for analyzing the 

cross sectional response of tunnels subjected to strong ground shaking. The solutions may be 

used for some culverts subject to the conditions of applicability described in chapter 4. For 

culverts that are assessed to be relatively seismically vulnerable (e.g., unreinforced concrete 

culverts, or culverts having marginal stability under static loads) and having an unacceptable 

consequence of failure, dynamic analyses using two-dimensional finite element or finite 

difference computer codes may be considered. Computer codes that could be considered for this 

purpose include FLUSH (Lysmer et al., 1975); SASSI (Lysmer et al., 1991), and FLAC (Itasca, 

1995). The program FLAC has the advantage over the linear or equivalent linear programs, such 

as FLUSH and SASSI, of incorporating nonlinear soil constitutive relationships that are able to 

model soil yielding under higher excitation levels. 

5.4.2.3. Examples of Culvert Evaluation Under Transient Ground Motion 

A number of investigators have applied various theoretical and empirical evaluation methods to 

the prediction of the seismic performance of buried pipelines under transient ground motion. 
279

These include O’Rourke, M. et al. (1978, 1980, 1981, 1984, 1988, 1990), Shah and Chu (1974), 

O’Rourke, T. et al. (1985), Yun and Kyriakides (1988), Miyajima and Kitaura (1991a and 

1991b), and Trifunac and Todorovska (1997). However, like those described above for 

permanent ground failures, these methods were developed primarily for pressure pipelines that 

extend over significant lengths. They have not been directly applied to culvert installations. 

Only a few examples of evaluation methods for transient ground motions applied to culverts or 

to culvert-like structures were available from published and unpublished sources. Some of these 

have been summarized below. 

Byrne et al. (1996a) investigated a three-hinged semi-circular reinforced concrete arch having a 

10.5 m span and a 5.2 m rise under 15 m of cover. They considered a seismic event having a 

peak horizontal ground acceleration of 0.2 g and a peak vertical ground acceleration of 0.13 g. 

Using full dynamic methods, they found seismically induced bending moments in the wall as 

high as 140 percent greater than static while wall compression forces were only 8 percent greater 

than static. These differences were based on the maximum for separate horizontal and vertical 

components. These investigators also employed equivalent static methods, which produced even 

greater differences between static and dynamic effects. 

Fenves (1989) and Musser (1989b) analyzed the seismic performance of a 13.0 m span by 5.3 m 

rise multi-radius corrugated steel earth covered (aboveground) arch used for military munitions 

storage. For ground accelerations that were about 25 percent greater than used by Byrne et al., 

and employing full dynamic methods, they found that seismically induced bending moments in 

the wall were as high as 200 percent greater than static while wall compression forces were about 

19 percent greater. Possessing much less soil confinement than a typical highway culvert, this 

example could provide insight into the upper limit of seismic responses that buried highway 

structures would be expected to undergo. 

Chen and Krauthammer (1987) performed an interesting dynamic parametric analysis of a 4 m 

square reinforced concrete box culvert under three configurations: on the surface, partially 

buried, and fully buried. They found that under the same dynamic regime, the accelerations it 

experienced were reduced by 25 to 30 percent when buried to its mid-height, compared to what it 

experienced sitting on the ground surface and subjected to the inertial effects of its own weight. 

When buried to a depth equal to its height, accelerations were reduced by 53 to 59 percent of 

what they were at the surface. Clearly, burial reduces inertial effects as well as adding to 

confinement and stiffness, which is why culverts perform better during earthquakes than 

aboveground structures. 

Davis and Bardet (1998) investigated a 2.4 m diameter corrugated metal culvert, part of which 

collapsed during the 1994 Northridge earthquake. They developed a pseudo-static buckling 

analysis method that was able to account for the failure. They also performed a limited 

parametric evaluation of the soil profiles along the culvert alignment, some of which did not 

collapse, and found that the peak ground acceleration and the reduction in stiffness of the 

embedding soil due to pore pressure buildup were the primary causative factors. They concluded 

that liquefaction was a contributing but not a necessary factor for failure. Indeed, while 

complete liquefaction would have most definitely led to collapse, partial liquefaction or other 

causes of reduction in the stiffness of the backfill envelope or the buckling capacity of the culvert 

cross section also could have led to collapse. 
280

5.5. RETROFITTING STRATEGIES 

The decisions surrounding seismic retrofit of culverts should be based on an optimization of 

structural, hydraulic, geotechnical and economic considerations. Many choices are available to 

achieve the same end. The timing of the culvert retrofit may be coordinated with normal repair 

or replacement cycles of other highway components, such as pavements. Linking culvert retrofit 

with other repair or replacement programs may influence the retrofit strategies selected. 

The design of the culvert retrofit strategy to resist either permanent ground failure or transient 

ground motion is based on an assessment of the seismic demand compared to the existing 

capacity of the culvert. Any shortfalls in capacity must be supplied by the retrofit feature or 

measure. The evaluation section of this chapter suggests methodologies for assessing seismic 

demand and dynamic capacity. Many culvert guides and design specifications, including those 

by AASHTO (1999) propose methodologies for assessing static culvert capacity. Some general 

guidelines are given below. 

5.5.1. GROUND REMEDIATION 

As noted earlier, most of the culvert damage associated with an earthquake occurs in conjunction 

with ground instability. Therefore, a primary culvert retrofit measure consists of identifying and 

remediating unstable ground that may exist along the culvert alignment. Identifying unstable 

ground and remediation planning measures are dealt with in chapters 3 and 4 as well as in Part 1 

of this manual. Therefore, they will not be treated in detail here. Some measures found to be 

effective in remediating seismically induced ground instability include: 

• Dynamic compaction. 

• Vibro-compaction. 

• Stone columns. 

• Slope stabilization. 

• Soil reinforcement. 

• Overexcavation/replacement. 

• Grouting. 

Dynamic compaction or vibro-compaction would induce stresses in a culvert due to both the 

overpressures and the settlement that occurs. These methods would generally not be applicable 

unless the culvert was removed while the ground was being stabilized. The removal option is 

discussed in more detail below. 

Some of the techniques listed above may be more effective for remediation of one type of ground 

instability than another. Also, a combination of these techniques may result in the most cost 
281

effective alternative. The primary design strategy involves estimating the reduction of both 

vertical or horizontal ground deformations that are to be achieved by remediation. 

5.5.2. REMOVE AND REPLACE 

Seismic retrofit of a transportation corridor requiring significant ground remediation may also 

require removal and replacement of the culverts along the corridor during construction of the 

remediation measure. In these cases, a secondary consideration includes the economic choice of 

replacing the existing culvert with a new one or salvaging and reinstalling the existing one. 

Obviously, only certain circumstances would justify salvaging and reinstalling an existing 

culvert. Some cases where this could be cost effective include relatively new culverts under 

shallow cover that are made of precast or pre-manufactured sections. Also, large, high value 

culvert installations that can be easily disassembled and reassembled in the field may fall into 

this category. 

If a salvaging option is selected, care must be exercised during removal of culverts in order to 

avoid mechanical damage that could be inflicted by earthmoving equipment. Another 

consideration is the necessity of preventing unbalanced earth or equipment loading that could 

rupture or collapse the culvert pipe during removal. Some types and sizes of flexible culverts 

may not be cost effective to salvage during removal, due to the careful excavation that would be 

required to avoid damage. 

In addition to the case of ground remediation, removal and replacement of a culvert makes sense 

if the cost of retrofitting the culvert exceeds the cost of replacing it with a more seismically 

resistant design. Still another case is if the culvert to be retrofitted is near the end of its useful 

life or is undersized. On the other hand, removal and replacement generally is not a practical 

option for deeply buried or cast-in-place culverts. 

5.5.3. CULVERT LINERS 

Many liners are available for the repair of culvert and pipeline interiors. This includes some of 

the new cured-in-place thermosetting plastic liner systems that are formed in-situ to fit snugly 

against the culvert wall interior. Most liners have been developed to inhibit corrosion and/or 

infiltration or exfiltration. An excellent review of these repair methodologies is given by 

Ballinger and Drake (1995) and will not be repeated here. These liners may be applicable to the 

seismic retrofit of culverts where improved joint ductility or the prevention of fines migration at 

damaged joints is needed. However, many liners are not specifically designed to improve the 

ductility or structural capacity of the culvert cross section, which limits their applicability to 

seismic retrofit. 

Liners that provide any significant structural improvement to the cross section may also reduce 

the hydraulic capacity of the culvert, simply because they reduce the existing cross section. The 

impact of whether this is important depends upon whether the culvert is designed to function at 

capacity and whether it operates under inlet or outlet control during the design hydrologic event. 

It is currently common practice by highway agencies to install small diameter culverts that are 

oversized from a hydraulic consideration in order to avoid future maintenance costs. In these 
282

cases, reducing the existing hydraulic capacity of the retrofitted culvert by installing a liner may 

not be an issue. 

Many embankment cross culverts operate under inlet control at their design discharge. That is, 

the culvert inlet acts as an orifice that controls the discharge of the culvert. In this case, the 

culvert barrel could be lined along most of its length without suffering any hydraulic 

consequences. The transition at the inlet end could then be reconstructed to a larger cross section 

in order to make up the capacity lost due to the wall thickness of the liner material. Typically, 

the inlet occurs at the toe of the embankment slope where cover height is minimal, further 

facilitating this retrofit approach. However, the inlet slope protection would also have to be 

modified or reconstructed in order to accommodate the larger opening. 

Culvert hydraulic capacity should be checked using the procedures in the Model Drainage 

Manual (AASHTO, 1999; FHWA, 2001). Culverts that operate under outlet control are affected 

by both the diameter and the frictional characteristics of the entire barrel length. In these cases, 

smooth-walled liners may be able to provide the hydraulic capacity lost due to their thickness, if 

they are used to line existing culverts that are internally corrugated. However, when this is not 

the case and a reduction in hydraulic capacity cannot be tolerated, another option is to install a 

parallel culvert. This additional culvert could be installed by jacking, augering, micro-tunneling, 

tunneling, or cut and cover methods. It could either augment or replace the existing one. 

As can be seen, many factors are involved and many options are available when using liners as a 

retrofit alternative. Therefore, the decision to line existing culverts and with what materials, or 

to add parallel culverts, should be based on an analysis of all the structural, hydraulic and 

economic risks associated with the requirements of the retrofit design scenario. 

Once a decision has been made to use a culvert retrofit strategy based on liners, a number of 

design and installation issues must also be addressed. For instance, it is important to clean the 

inside of the existing culvert thoroughly and to remove all deleterious material prior to 

installation. Except for cast-in-place liners, it is also important to fill the annular space between 

the liner wall and the existing culvert wall with grout. This is because liner design generally 

assumes full support around the periphery of the liner conduit. Often, culverts are subjected to 

hydrostatic pressure from groundwater, which without the support of the grout fill, could 

damage, severely deform or collapse the liner, if left unsupported. In addition to providing 

circumferential support, the grout fill prevents soil fines from migrating into the annular space 

between the liner and the host culvert through damaged or leaking joints, which can lead to the 

formation of sink holes and pavement settlement. However, successful grouting is generally 

limited to liners large enough in diameter to allow safe personnel access. 

During installation, grouting itself can cause damage to culvert liners if not properly controlled. 

It is important to use low-volume, bottom feed systems that are pressure controlled. Also, 

sufficient numbers of grout nipples must be provided, both in the cross sectional and longitudinal 

direction, to assure equal distribution of the grout as well to provide for air relief. Procedures for 

grouting lined culverts are treated in greater detail by Ballinger and Drake (1995). 

In summary, liners can improve the performance of joints and/or they can improve the 

performance of the barrel. To design the liner for joint performance, longitudinal ductility is the 
283

critical criterion. In the case of barrel performance, cross sectional strength and ductility are the 

critical criteria. 

In general, liners are perhaps the most versatile as well as the most cost effective retrofit 

materials currently available for improving the seismic performance of many existing culverts. 

Therefore, a more detailed discussion of specific liner types is given below. 

5.5.3.1. Cast-in-Place Liners 

Cast-in-place liners have been used extensively for repair of culverts damaged due to seismic 

activity, deterioration or other causes. To be effective as a seismic retrofit, the liner must be 

designed as a structural element with adequate reinforcement to develop both ductility and 

strength. An advantage of cast-in-place liners is that they can be custom fit to each application. 

An example of a circular cast-in-place liner is illustrated in figure 5-13. 

Existing Culvert

Reinforcing

Cage

Cast-in-Place

Liner

Figure 5-13. Cast-in-place culvert liner. 

Shotcrete is the material typically employed for cast-in-place liners. This material can include 

either wet or dry mortars, or concrete, that is pneumatically projected at high velocity onto the 

surface to be lined. For tunnel and overhead applications, the dry variety is most commonly 

employed. Shotcrete can be formulated to have both structural and durable qualities. Its 

manufacture and application can be strictly specified (ACI, 1995b). In addition, shotcrete can be 

applied in a thickness that would embed reinforcement and thus, be consistent with the strength 

and ductility objectives of the seismic retrofit objective. However, the application of shotcrete in 

these thicknesses requires personnel access to the facility. Therefore, a minimum culvert 

diameter of about 1,500 mm is required before this method is applicable. Also, strict adherence 

to specifications and the employment of experienced personnel are the key to a quality 

installation. 

Thorough cleaning and surface preparation are important in order to assure long-term adhesion 

of the liner to the substrate. Wire mesh or deformed rebar should be attached securely to the 

existing culvert barrel in order to maintain its position during placement. The design criteria of 
284

the reinforcement should be to maintain tension ductility as well as to enhance concrete 

confinement during the seismic event. 

Generally, the liner would be made continuous over the entire length of the culvert. If control 

joints are required, they should be carefully detailed so as to not defeat the purpose of the seismic 

retrofit. This generally means that they should be staggered to be opposite the joints of the host 

culvert. 

This may seem to contradict normal good construction practices that would position control 

joints where shrinkage cracks are most likely to develop, i.e., at the existing joints of the host 

culvert. However, depending upon the seismic design scenario, the greatest retrofit 

reinforcement may be required at the joints of the host culvert. Since control joints must have a 

reduced structural capacity to work properly, they should be placed where they are least needed 

for structural capacity. This generally means that they should be staggered opposite the joints of 

the host culvert. Undoubtedly, shrinkage and temperature cracks will still develop in the liner at 

the locations of host culvert joints. However, their structural consequence in a seismic event is 

insignificant compared to the goal of the retrofit strategy to increase the ductility of the host 

culvert joint. 

5.5.3.2. Field Erected Metallic Liners 

Like cast-in-place liners, field erected metallic liners also have been used extensively for repair 

of culverts damaged due to a number of causes. The most commonly available metallic liners 

are fabricated from steel sheets or plates into elements of a circular cross section that can be field 

bolted together from the inside. Two types are available, two-flange and four-flange as shown in 

figure 5-14. These lining systems are available in specific wall thicknesses and diameter 

increments ranging from about 1,500 mm to 7,500 mm. They can be fitted with grout nipples 

during fabrication to facilitate grouting the annular space between the liner and the existing 

culvert wall. They can be furnished galvanized to prolong their life in corrosive environments. 

The advantages of these liners are that they provide ductility and strength. The strength capacity 

exceeds that of the liner material itself because the liner provides confinement of the grout fill. 

This increases the shear capacity of the composite section. A disadvantage is that the hydraulic 

roughness of the finished interior surface is high. 

5.5.3.3. Sliplining 

Sliplining is the process of pushing or pulling sections of culvert pipe inside of an existing 

culvert and grouting the annular space between the old and new cross sections. Many types of 

materials as well as a wide range of sizes and shapes are available for this purpose including: 

• Corrugated metal. 

• Spiral rib metal. 

• Profile wall thermoplastic. 
285

Bolts are Staggered to Provide More Strength

Longitudinal Lap Joint

B

C C

B Plan

1257 mm

400 pi or

Elevation

942 mm

300 pi

Neutral Axis

500 mm

Section B-B

Section C-C

984, 492 or 246 mm

28.6 mm

406.5 mm

203.25

A R mm

O

Grout Hole if Required

NA 50 mm NA

X

406.5 mm

Section A-A

AISI, 1993 

Figure 5-14. Two-flange steel culvert liner plate (top) and four-flange steel culvert 

liner plate (bottom). 
286

• Smooth wall thermoplastic. 

• Fiber reinforced plastic (FRP). 

• Precast concrete. 

The design of the slipliner material depends upon the retrofit strategy employed. For slipliners 

that are intended to prevent joint separation and soil fines migration, the primary design criterion 

is longitudinal ductility. In this case, smooth wall thermoplastics may be the optimum choice. 

For slipliners that must help resist cross sectional deformation and buckling, a stiffer wall profile 

may be more desirable. Slipliners that act as combined structural elements with an existing 

culvert wall and with the grouted annular space between them can develop significantly 

increased structural capacity compared to the original culvert wall acting alone. If sufficient 

roughness can be shown to exist at the interfaces of the inner and outer components of this 

composite, then at least a portion of full composite action can be developed that will dramatically 

increase the structural capacity of the total section. 

Most potential slipliner materials must be adapted from standard precast or prefabricated 

products. Their primary application may have been as standalone culvert materials. Hence their 

joints, clearance dimensions, adaptability to the addition of grout nipples, and their ability to be 

pushed or pulled into place may not be compatible with the demands of the seismic retrofit 

objectives. Because the concept of seismically retrofitting culverts is so new, both the designer 

and the manufacturer may have to exercise significant ingenuity in order to develop systems that 

are both economically viable and structurally adequate for the intended installation techniques. 

Typical slipliner installation setups for both the push and pull cases are illustrated in figure 5-15. 

Phillips Driscopipe, 1995 

Figure 5-15. Push and pull techniques for installing HDPE sliplining. 
287

5.5.4. JOINT RETROFIT 

As stated earlier, one of the primary objectives of a culvert seismic retrofit is to maintain joint 

closure during ground shaking and after the occurrence of permanent ground deformation. 

Seismic retrofit schemes for culvert joints should evaluate both the longitudinal and rotational 

strain demand that are likely to be imposed on the joints by the design earthquake as well as the 

capacity of the existing joints to accommodate these strains without damage or separation. 

Details of joint performance can be obtained from manufacturer's literature (ACPA, 1992; AISI, 

1993; Uni-Bell, 1991). 

As with other structural components, when the strain demand of joints exceeds their capacity, a 

retrofit is recommended. Many of the lining systems described above are effective for 

retrofitting culvert joints. They do this by making the joints continuous. 

In larger culvert sizes that afford personnel access, another method of retrofitting joints employs 

specially fabricated internal metal sleeves with angle brackets and bolts. These can be designed 

to maintain joint closure even if the original culvert joints undergo damage or pull apart. These 

can be adapted to almost any pipe type or joint configuration. An example of this type of sleeve 

is illustrated in figure 5-16 for a corrugated metal pipe. 

Corrugated Internal

Coupling with Bolted

Angle Flanges

Corrugated Metal Pipe

(Internal View)

Detail of

Bolted Flanges

AISI, 1993 

Figure 5-16. Internal corrugated sleeve for joining CMP. 
 
289

CHAPTER 6: ROADWAYS 

6.1. INTRODUCTION 

Pavement damage has occurred during most large earthquakes. Permanent ground deformation 

or ground failure, however, has generally been the direct cause of damage. In a few instances, 

pavement disruption has occurred due to very intense ground motions that locally uplifted or 

flung pavement sections. These instances, however, have been relatively rare. Consequently, 

the great majority of pavement damage has been restricted to roadways underlain by poorly 

compacted embankment materials or foundation materials that are susceptible to seismically 

induced ground displacement. Common causes of foundation displacement include liquefaction 

of loose saturated granular layers, slope instability, and surface fault rupture. Hazard evaluation 

and retrofit procedures for these sources of damage are discussed in the following subsections. 

Although retrofit or other mitigative procedures are available to reduce or eliminate most 

pavement damage, these procedures generally are too expensive to be economically viable for all 

but the most critical pavement structures. Consequently, most highway agencies have elected to 

use a passive strategy of rapid repair of pavement damage after an earthquake, rather than an 

active strategy of retrofitting to prevent damage. Rapid repair is an acceptable mitigative strategy 

in that pavement damage can usually be repaired rather quickly compared to other types of 

damage, such as bridge and tunnel damage, and the potential for loss of life or personal injury is 

small. Thus, pavement damage generally classifies as an acceptable risk and little retrofit 

activity is occurring among highway agencies. There may be critical highway segments, 

however, that must be usable immediately after an earthquake where retrofit measures are 

warranted. The following subsections provide guidance for hazard identification, analysis, and 

implementation of retrofit measures for those critical highway segments. 

6.2. CLASSIFICATION 

Pavements are classified into two principal types: flexible pavements constructed of asphaltic 

concrete (ACP), and rigid pavements constructed of portland cement concrete (PCCP). Each 

pavement type is supported by a structural section consisting of a base course, embankment 

where needed, and foundation soil. 

For earthquake hazard consideration, further classification is based on potential for permanent 

deformation of the structural section. In nearly all instances of past earthquake-induced 

pavement damage, the damage was caused by permanent deformation of the supporting 

embankment or foundation rather than by failure solely within the paved surface. Many 

pavements are supported by embankments or foundations that are not susceptible to earthquakeinduced permanent deformation. Pavements on such stable substructures are practically immune 

to earthquake damage. Where foundations or embankments are likely to deform, damage to 

pavements and disruptions to traffic operations are likely to occur. At particularly vulnerable 

localities, pavement damage may be so severe that roadways are obstructed and repairs required 
290

before traffic operations can resume. Permanent deformation of embankments and foundations 

have adversely affected both flexible and rigid pavements. Causes of permanent deformation 

include: 

• Differential settlement due to seismic compaction of embankment or foundation materials. 

• Penetration, settlement, flow or spreading of highway embankments due to liquefaction or 

other weakening of embankment or foundation soils. 

• Vertical displacement of pavement sections due to embankment of slope instability. 

• Differential displacement due to fault rupture. 

6.3. SCREENING AND EVALUATION GUIDELINES 

6.3.1. STABLE EMBANKMENTS AND FOUNDATION 

6.3.1.1. Hazard 

In the absence of deformation or displacement of the foundation or embankment materials, even 

the most intense seismic shaking has not caused significant damage to flexible or rigid 

pavements. For example, numerous stable interstate, primary arterial, and secondary roadways 

were strongly shaken during the 1971 San Fernando, 1989 Loma Prieta, and 1994 Northridge 

earthquakes without damage to flexible or rigid pavements. Pavement damage occurred only at 

localities susceptible to some form of permanent embankment or foundation deformation or 

displacement. 

6.3.1.2. Screen 

Based on past performance, pavements supported by embankments and foundations not 

susceptible to ground deformation or failure have performed well. Special analysis or retrofit 

measures are not required for these pavements. Embankment and foundation failure modes that 

have caused damage to highway pavements are described in the following sections. 

Pavement sections can be considered safe against earthquake damage unless possible deleterious 

foundation or embankment deformation is indicated by one of the following assessments. 

6.3.2. COMPACTION OF EMBANKMENT AND FOUNDATION MATERIALS 

6.3.2.1. Hazard 

Settlements induced by seismic compaction of embankment and/or foundation soils may be 

disruptive to both flexible and rigid pavements. The breadth of the zone across that differential 

settlement occurs is generally as important to pavement damage as the amount of settlement. 

Where settlements are small, uniform, or distributed across wide zones, little damage occurs to 

either rigid or flexible pavements. Rigid pavements are generally able to bridge areas of small 
291

differential settlement and flexible pavements are usually sufficiently ductile to absorb small 

differential movements without 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 settlements. The stronger and longer the earthquake shaking, the thicker 

the fill, and the poorer the state of compaction, the greater the amount differential settlement and 

pavement damage. The photograph reproduced in figure 6-1 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 (M6.6). That bridge was part of a connector 

from northbound I-5 to eastbound I-210 in Sylmar, California. The highway was still under 

construction at the time of the 1971 San Fernando earthquake. This settlement was caused by 

seismic compaction and perhaps some spreading of the approach embankment. 

 Caltrans, reproduced from Prysoc and Egan, 1981 

Figure 6-1. 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. 

Backfills placed against bridge abutments have been particularly vulnerable to seismic 

compaction. Difficulties 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. For example, figure 6-2 shows pavement disruption due to 100 mm 
292

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 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. 

Caltrans, reproduced from Prysoc and Egan, 1981 

Figure 6-2. 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. 

6.3.2.2. Screen 

The primary criteria for identifying pavement sections susceptible to seismic compaction is to 

identify areas underlain by thick, poorly compacted embankments or loose foundation soils. 

Localities where these conditions typically occur include older roadways placed on 

embankments greater than a meter or two thick, newer roadways on fills greater than a few 

meters thick, or on foundation soils composed of loose natural materials such as collapsible soils 

or late Holocene deposits of sand, silts, or gravels. Areas most susceptible to differential 

settlement include bridge abutment-fill contacts and cut-fill contacts. 

6.3.2.3. Evaluation 

The first step in evaluating potential for settlement is to identify zones where poorly compacted 

materials could be incorporated into or lie beneath highway embankments. For screening 

purposes, this evaluation begins with an inventory of embankment thicknesses, ages of 
293

construction, and the compaction criteria applied during construction. The criteria listed in table 

6-1 may then be applied with this information to develop rough but generally conservative or 

high estimates of possible pavement settlement. This procedure is valid for settlements due to 

seismic compaction of dry to moist embankment fills. Settlement due to seismic compaction of 

foundation soils can also be estimated by extrapolation from this table. For this extrapolation, the 

criteria listed in table 6-1 are applied to granular foundation materials, including silts, sands and 

gravels. The thickness and compaction state of the foundation materials may be estimated from 

foundation reports, geologic information, etc. Table 6-2 provides criteria for estimating the 

density state of sands from standard penetration test (SPT) and cone penetration test (CPT) data, 

where such data is given in foundation reports. These criteria were developed for clean sands, 

but may be extrapolated to gravely and silty sands for screening purposes. As noted above, the 

most susceptible foundation materials to seismic compaction are granular sediments deposited 

during late to early Holocene age. Late Holocene sediments would likely be characterized by 

relative compactions less than 90 percent; early Holocene to late Pleistocene sediments would 

likely be characterized by relative compactions between 90 and 95 percent; and middle 

Pleistocene and older granular sediments would likely be characterized by relative compactions 

greater than 95 percent. Clay-rich sediments are generally immune to seismic compaction. 

Rough, but generally conservative estimates of embankment settlement can be calculated by 

multiplying the thickness of the embankment and susceptible foundation materials by 

appropriate volumetric strain values from table 6-1 and then summing the calculated settlements 

for the fill and foundation. This calculation assumes one-dimensional strain in the vertical 

direction. Where embankment spreading can occur, the actual vertical displacements may be 

greater than those predicted. Greater settlements than those estimated from table 6-1 may also 

occur where foundation soils or embankments are saturated and where increased pore water 

pressures or liquefaction may lead to enhanced settlement and other deleterious effects. 

Liquefaction is discussed in a later section. 

Table 6-1. Expected maximum volumetric strains in dry to moist soils due to seismic shaking. 

Earthquake Soil Condition - Relative Compaction (RC) 

Magnitude 

Mw

Acceleration 

Coefficient 

A 

Loose 

RC # 90% 

Moderately 

Dense 

90% < RC < 95% 

Dense 

RC $ 95% 

M ≥ 7 A ≥ 0.4 10% 5% 1% 

M ≥7 0.2 < A < 0.4 5% 2% 0.5% 

M ≥ 7 A ≤ 0.2 2% 0.5% 0.1% 

5 < M < 7 A ≥ 0.4 6% 3% 0.5 % 

5 < M < 7 0.2 < A < 0.4 2% 1% 0.2% 

5 < M < 7 A ≤ 0.2 1% 0.2% 0.05% 

M ≤ 5 A ≥ 0.4 3% 1% 0.2% 

M ≤ 5 0.2 < A < 0.4 1% 0.2% 0.05% 

M ≤ 5 A ≤ 0.2 0.5% 0.1% 0.01% 
294

Table 6-2. Relative density of sands estimated from standard (SPT) 

and cone (CPT) penetration test data. 

SPT N-value Normalized CPT tip 

resistance (qc/Pa) 

Relative Density Approximate Relative 

Compaction (RC) 

0-4 < 20 Very Loose RC < 90% 

4-10 20-40 Loose RC < 90% 

10-30 40-120 Medium 90 % < RC < 95 % 

30-50 120-200 Dense RC > 95 % 

Over 50 > 200 Very Dense RC > 95 % 

modified from Terzaghi et al., 1996; Kulhaway and Mayne, 1990

If settlements estimated using the criteria in table 6-1 are small (less than 50 mm), pavement 

damage from fill and ground settlement is unlikely. For most flexible or rigid pavements, 

settlements of a few tens of millimeters can be accommodated without obstructing traffic flow. 

Larger settlements (up to 0.5 m) will likely fracture the pavement and cause uneven surfaces that 

will greatly slow traffic flow, but without complete obstruction. If such settlements occur at 

bridge abutments without structural approach slabs or at other discontinuities in foundation, 

however, the roadway will likely be impassible until emergency repairs are made. 

Where subsurface conditions are uniform, settlements are likely to be rather even and nondamaging. Differential settlements are generally caused by local variations or discontinuities in 

subsurface soil conditions. The width of the zone of differential settlement generally decreases 

with the sharpness of the discontinuity. Pavement disruption is as much a function of the 

concentration or width of the zone of differential settlement as the total settlement. Thus, 

settlements near a bridge abutment or cut-fill contacts are generally more disruptive than similar 

settlements at localities without sharp lateral discontinuities in foundation materials. 

Where preliminary estimates indicate unacceptably large settlements, additional analyses of 

strain potential and settlement should be conducted. For example, settlement analyses using the 

Tokimatsu and Seed (1987) procedure might be applied. If the analyses continue to indicate 

larger than acceptable settlements, mitigation should be considered. Mitigative measures are 

described in a later section of this chapter. 

Table 6-1 was developed for this retrofit manual by evaluating and generalizing past 

observations of embankment settlement. For example, Prysoc and Egan (1981) documented 

roadway damage and differential settlements following the 1971 San Fernando earthquake. 

These investigators reported several instances of 50 mm to 100 mm (2 to 4 in) of differential 

settlement at bridge abutments in the heavily shaken Sylmar and San Fernando areas. Assuming 

an average embankment height of 4 m, the average vertical strains at these sites were between 1 

percent and 3 percent. That earthquake had a magnitude of 6.5 and peak accelerations in the 

heavily shaken area exceeded 0.4 g. Assuming that the fills were moderately dense (relative 

compaction between 90 percent and 95 percent), a conservative value of 3 percent was listed in 

table 6-1 for these seismic and fill conditions. 
295

Settlements as great as 600 mm (2 ft) were reported by Prysoc and Egan for a few bridge 

approach fills (figure 6-1). These larger settlements were confined to fills greater than 5 m thick 

and zones within 3 m of an abutment wall. The total vertical strains at these localities were 

between 5 percent and 10 percent, indicating that the effected embankments were looser (relative 

compaction less than 90 percent) than those where smaller strains developed. A vertical strain of 

6 percent is listed in the table for these soil conditions. 

Little settlement was observed at the fill-abutment contacts for several bridges on the Golden 

State Freeway (I-5) south of the separation of I-405. These bridges were in the heavily shaken 

area but pavements were unaffected. Vertical strains in these fills were 1 percent or less. 

Assuming those fills were well-compacted (relative compaction greater than 95 percent), a 

conservative strain of 1 percent is listed in the table. 

Strain values for other earthquake magnitudes and peak accelerations were extrapolated from the 

reported San Fernando settlements and verified using the procedure of Tokimatsu and Seed 

(1987) for calculating vertical strain. 

6.3.3. LIQUEFIABLE OR SOFT EMBANKMENT AND FOUNDATION MATERIALS 

6.3.3.1. Hazard 

Liquefaction of soils has been a major cause of embankment and foundation deformation as well 

as pavement damage. Both flexible and rigid pavements have been adversely affected. 

Liquefaction may lead to any of the types of ground deformation or ground failure listed below, 

depending on geometric and soil conditions at the site. Types and amounts of displacement 

depends on several factors including height and steepness of embankments, ground slope, and 

the depth, thicknesses and continuity of liquefiable layers. Similarly, very soft foundation soils 

under embankments have compressed or sheared during earthquake shaking, causing 

embankment deformation and pavement damage. 

Enhanced Ground Settlement—As noted in the previous section, earthquake shaking is an 

effective compactor of granular or cohesionless soils, dry, moist or saturated. Where loose soils 

are saturated and drainage is impeded, excess pore pressures develop during strong ground 

shaking. Soft saturated cohesive soils may also develop increased pore water pressures in zones 

of high cyclic stresses. Such pressures lead to progressive softening, greater cyclic shear 

deformations within the soil, and compaction or shear deformation. As pore pressures reach a 

certain critical level, effective stresses approach zero and the soil behaves as a liquid rather than 

a solid. At that point, liquefaction has occurred, which greatly enhances soil deformation and 

ground settlement, particularly beneath heavy embankments. 

Where highways are underlain by low embankments and flat terrain, ground settlement 

commonly mimics the thickness of underlying liquefiable layers in the foundation soils. Figure 

6-3 shows a section of Highway 5 south of Oshamanbe, Japan that settled differentially during 

the 1993 Hokkaido-Nansei-Oki earthquake (M7.8). 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 0.6 m between crests and troughs of the 

induced waves (Youd et al., 1995). 
296

Kiso-Jiban Consultants Co., Inc., Tokyo, reproduced from Youd et al., 1995 

Figure 6-3. Wavy pavement due to differential settlement enhanced by 

liquefaction during the 1993 Hokkaido-Nansei-Oki, Japan earthquake. 

The site is on Highway 5 south of Oshamanbe. 

Penetration and Spreading of Embankment Structures—Liquefaction or increased pore 

water pressures in soft soils beneath embankments usually leads to penetration of the 

embankment into the weakened soil, forming a bearing capacity type of failure as illustrated in 

figure 6-4. 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 6-5 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 (M7.5). 

The longitudinal fissure is indicative of embankment penetration and spreading. Greater 

penetration and disruption is illustrated in figure 6-6 that shows the Highway 36 approach to the 

Rio Estrella Bridge, also in eastern Costa Rica. This approach fill subsided about 2 m and spread 

laterally due to a combination of soil compaction, embankment penetration and embankment 

spreading. These actions severely disrupted the embankment and paved surface. In total, about 

30 percent of all highway pavements in the lowlands of eastern Costa Rica were disrupted by the 

effects of liquefaction, primarily embankment penetration and spreading, during the 1991 

earthquake (Cole et al., 1991). 
297

modified from Youd et. al, 1995 

Figure 6-4. Failure mechanism beneath embankments that split, settle, and 

spread due to liquefaction of foundation soils. 

University of Costa Rica 

Figure 6-5. Segment of Highway 36 near 

Caribbean coast in Costa Rica that split 

longitudinally, settled and spread laterally 

during 1991 earthquake by mechanism 

illustrated in figure 6-4. 

University of Costa Rica 

Figure 6-6. Disrupted fill and pavement at 

approach to collapsed Highway 36 bridge 

over Rio Estrella, Costa Rica. The disruption 

was due to liquefaction of foundation soils 

during 1991 earthquake. 
298

Lateral Spread—Lateral spread is a form of ground failure characterized by lateral 

displacement of surface soil layers over an underlying liquefied layer. The surface of the 

mobilized ground is commonly disturbed by open fissures, differential settlements, scarps, lateral 

shear zones, pressure ridges, etc. Structures built over or within lateral spreads, including 

highways, are commonly disrupted and displaced along with the underlying ground. Lateral 

spreads generally move down gentle slopes (usually less than 6 percent) or toward a free face, 

such as an incised river channel. Horizontal displacements typically range up to a few meters, 

but where shaking is particularly intense or of long duration and ground conditions are extremely 

vulnerable, larger displacements have occurred. Figure 6-7 shows a section of the Golden State 

Freeway (I-5) that was translated laterally by as much as 2 m from a large lateral spread (called 

the Juvenile Hall spread) during the 1971 San Fernando earthquake. Sheared and buckled 

pavement marked the lateral shear zones at either margin of the failure zone. Between these 

margins, the lateral spread and highway shifted as much as 2 m westward, causing minor 

curvature of the roadway. 

Where a highway is aligned parallel to the direction of movement, lateral spreads usually induce 

extensional features, such as open fissures and pulled apart pavement slabs at the head, and 

compressional features, such as pressure ridges and buckled pavement, at the toe. Figure 6-8 

shows a section of Highway 36 in Costa Rica that crossed the head of a lateral spread that 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 by compression at the toe, that was beneath the Rio Viscaya bridge. 

The displacement beneath the bridge sheared bearings and connections, causing the 

superstructure to collapse into the river (Priestly et al., 1991). 

R.F. Scott, reproduced from Scott, 1971 

Figure 6-7. 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 2 m of lateral spread displacement. 
299

M.J.N. Priestly, reproduced from Priestly et al., 1991 

Figure 6-8. Extensional fissures in flexible pavement caused by lateral 

spread of floodplain deposits toward Rio Viscaya during the 1991 

Costa Rica earthquake. 

Ground Oscillation—Ground oscillation generally occurs on nearly level ground underlain by a 

liquefied layer. In this instance, the liquefied layer decouples the surface layers from underlying 

nonliquefied ground. The decoupling allows large transient ground movements or waves to 

develop that may alternatively pull apart surficial soil layers and overlying structures, creating 

open fissures and fractures, and then jam the separated ground and structural elements back 

together, creating compressional shear and buckling. Permanent ground displacements at 

oscillation sites are generally small and chaotic, both in magnitude and in direction. Figure 6-9 

shows asphaltic concrete pavement on Highway 229 near the northern edge of the Assabu River 

valley that was fractured and overlapped due to ground oscillation during the 1993 HokkaidoNansei-Oki, Japan earthquake. The photo shows separated curb blocks, indicative of ground 

extension, near overlapped pavement structures, indicative of compression, at the same locality. 

Such juxtapositions of compressional and extensional features are common by-products of 

ground oscillation. Oscillation also typically occurs during the lateral spreading process, with 

mobilized soil blocks oscillating back and forth as they migrate horizontally down slope or 

toward a free face.

Flow Failure—Flow failure is the most catastrophic form of ground dislocation associated with 

liquefaction. Flow failures occur on relatively steep (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 and massive ground 

displacements. Substantial internal deformation usually occurs within the mobilized soil mass 

and overlying structures. Pavements on such failures are nearly always displaced and destroyed. 
300

T.L. Youd, reproduced from Youd et al., 1995 

Figure 6-9. Fractured and overlapped flexible pavement on 

Highway 229 near northern edge of Assabu River valley. The disruption 

was due to liquefaction and ground oscillation during 1993 HokkaidoNansei-Oki, Japan earthquake; note extensional separation between curb 

blocks at same locality. 

Figure 6-10 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 (M5.2). This failure 

dislodged a section of highway embankment that flowed into the lake, severing the roadway and 

blocking traffic. 

6.3.3.2. Screens for Liquefaction Hazard 

Detailed procedures for evaluating liquefaction hazard are given in Part 1 of this manual. These 

procedures should be used in detailed site investigations for implementation of retrofit measures. 

In addition, Youd (1998) prepared a screening guide for rapid assessment of liquefaction hazard 

at highway bridge sites. This guide is also generally valid for assessing liquefaction hazard to 

pavement structures as well, and may be used for initial hazard assessment. The screening guide 

presents a systematic application of standard criteria for assessing liquefaction and ground 

displacement potential. The general principle of screening, and the approach provided by Youd 
301

M.G. Bonilla, reproduced from Youd and Hoose, 1978 

Figure 6-10. Liquefaction-induced flow failure of roadway 

embankment into Lake Merced during 1957 Daly City, 

California earthquake. 

(1998), begins with re-evaluation of available analyses of liquefaction hazard at a site or in the 

area surrounding a site. The procedure continues with the application of geologic, seismic, 

hydrologic, and geotechnical criteria. The assessment progresses from the least complex, least 

time-consuming, and least data intensive to the more complex, time-consuming, and rigorous 

site-specific analyses. By this procedure, many sites may be evaluated and classified as low 

hazard with very little time and effort. Only sites with significant hazard need to be evaluated 

with the more sophisticated and time-consuming procedures. 

At each step, a conservative assessment of hazard is made. If there is clear evidence that 

liquefaction or damaging ground displacements are unlikely, the site is classified as low 

liquefaction hazard and low priority for further investigation, and the evaluation is complete for 

that site. If the available information indicates a higher hazard rating, or if the data is inadequate, 

incomplete or unclear, the site is classified as having a possible liquefaction hazard, and the 

analysis proceeds to the next step. If the available site information is insufficient to complete a 

liquefaction hazard analysis, then simplified seismic, geologic, and hydrologic criteria are used 

to prioritize the site for further investigation. 

6.3.3.3. Evaluation 

Procedures for evaluating the liquefaction hazard to highway grades and pavements, as well as 

other works, proceed in two steps: first, liquefaction susceptibility is evaluated using the 

procedures noted above and in Part 1. Second, potential for ground deformation and 

displacement is evaluated using procedures outlined in Part 1, chapter 4, and in the screening 

guide prepared by Youd (1998). 
302

6.3.4. POTENTIALLY UNSTABLE EMBANKMENTS, FOUNDATIONS OR SLOPES 

6.3.4.1. Hazard 

Slumps, block glides, rock and soil falls, and other types of landslides caused by unstable 

embankments, foundations or slopes have disrupted or impacted highway pavements during past 

earthquakes. The following incidents illustrate pavement damage caused by slope instability. 

Shallow Slump—Shallow slump of highway embankments located on steep slopes or weak 

foundations has been a major cause of disruption to highway grades and pavements during past 

earthquakes. Figure 6-11 shows a section of slumped embankment on Highway 5 between 

Oshamanbe and Yakumo, Japan (Harp and Youd, 1995). The slump occurred during the 1993 

Hokkaido-Nansei-Oki earthquake. In this instance, a major highway embankment slipped down 

a steep slope, destroying the highway and blocking the roadway to traffic for several weeks until 

repairs were made. The cause of failure was weakening of marshy foundation soils over where 

the embankment had been constructed. Liquefaction of sand layers within the marshy deposits 

also may have occurred. 

Oshamanbe Fire Department, reproduced from Harp and Youd, 1995 

Figure 6-11. Slump failure in Highway 5 embankment north of Oshamanbe, 

Japan during the 1993 Hokkaido-Nansei-Oki earthquake. Failure was 

due to weakening of soft foundation soils. 

Slumps with small displacements commonly fracture and offset pavement structures, but usually 

do not require embankment reconstruction, making repairs much easier to implement. Figure 

6-12 shows a highway section with both flexible and rigid highway pavement that was fractured 

and displaced a few hundred millimeters by slump movement during the 1971 San Fernando 

earthquake. This locality was on Blucher Avenue immediately east of the lower Van Norman 

reservoir. In this instance, repairs to the flexible pavement were more easily constructed, both 

temporarily and permanently, than to the rigid pavement. In general, flexible pavements are more 

easily repaired than rigid pavements. 
303

Shallow slumps, such as those described above, could have been prevented by ground 

modification to strengthen foundation soils prior to embankment construction. Remedial 

measures can also be applied after construction has been completed, but the cost is generally 

prohibitive except for the most critical structures. Hence, retrofit by strengthening of slopes to 

prevent pavement damage is rarely applied. 

Shoulders of causeways or embankments occasionally slide or slump due to steepness of the 

slope and poor compaction materials near the embankment face. Figure 6-13 shows a shoulder of 

a secondary roadway (California State Highway S22) that slid about 0.5 m down a steep 

embankment during the 1968 Borrego Mountain, California earthquake (M6.4). In this instance, 

the edge of the steep fill had been poorly compacted, allowing the shoulder to slip. The slumping 

produced a fissure and scarp between the unstable material in the shoulder and the wellcompacted fill beneath the interior of the roadway. 

Caltrans, reproduced from Prysoc and Egan, 1981 

Figure 6-12. Rigid and flexible pavements disrupted by slump failure of 

Blucher Avenue near Lower Van Norman reservoir during 

1971 San Fernando earthquake. 

Deep-Seated Landslides—Deep-seated slumps and block guides involve movement of large 

masses of soil or rock over failure surfaces that plunge tens of meters into underlying strata. 

These types of landslides typically generate surface displacement across narrow zones or a series 

of discrete rupture zones separated by blocks of intact ground. Figure 6-14 shows a single fissure 

and scarp across Summit Road in the Santa Cruz Mountains induced by movement of a deepseated slide that slipped a few hundred millimeters during the 1989 Loma Prieta earthquake 

(M7.1). That displacement separated and vertically offset the flexible roadway pavement. 
304

U.S. Geological Survey, reproduced from 

Castle and Youd, 1972 

Figure 6-13. Slump of Highway S22 fill east of Salton Sea during the 1968 

Borrego Mountain, California earthquake. 

Some of the more dramatic damage to urban streets and other structures as a consequence of 

deep-seated slumps and block glides occurred in Anchorage during the 1964 Alaska earthquake 

(M9.2). Figure 6-15 shows the massive disruption to 4th Street caused by the 4th Street 

landslide. The roadway was vertically offset by as much as 2.8 m across the headscarp and 

broken up within a graben area that formed below the headscarp. Away from the headscarp and 

graben areas, pavement damage was less severe, consisting of a few fissures within the interior 

of the slide and several pressure ridges at the margins and near the toe. Some ground dislocation 

and pavement damage also occurred at distances as far as 130 m inland from the headscarp, a 

consequence of a few tenths of a meter of sympathetic ground movement toward the landslide 

(Hansen, 1966). 

While shallow slumps may be prevented through ground remediation, deep-seated landslides, 

such as those shown in figures 6-14 and 6-15, are practically untreatable. These slides cut deeply 

into the underlying terrain with shear zones that are difficult to detect and strengthen, making 

remediation a formidable and generally prohibitively expensive task. 
305

E.W. Hart, reproduced from Hart et al., 1990 

Figure 6-14. Sinuous scarp in Summit Road caused by apparent movement of a 

deep-seated landslide during the 1989 Loma Prieta, California earthquake. 

U.S. Geological Survey 

Figure 6-15. Disruption to 4th Street, Anchorage, Alaska, caused by deep slump 

during 1964 Alaska earthquake; headscarp is about 2.8 m high. 
306

Debris Slides—Debris shaken loose from cut slopes and steep hillsides commonly accumulate 

on roadway surfaces. This debris may impede or block traffic and may damage the highway 

pavement. Rock fall debris has been particularly destructive to asphaltic concrete pavements. 

Figure 6-16 shows a steep rock slope from where rock fragments, some several meters in 

diameter, fell or bounced onto the highway pavement, temporarily blocking the roadway and 

pitting the surface where impacts occurred. The resulting divots were as much as 0.5 m deep. 

This damage occurred to a roadway around the perimeter of Okashiri Island during the 1993 

Hokkaido-Nansei-Oki, Japan earthquake. 

T.L. Youd 

Figure 6-16. Steep slopes along western shore of Okashiri Island from which 

numerous rock falls descended onto roadway pavement during 1993 Hokkaido-NanseiOki, Japan earthquake. The debris pitted pavement and blocked the highway. 

6.3.4.2. Preliminary Screening and Detailed Evaluation of Slope Instability 

Procedures for preliminary screening of slope instability hazard and for detailed analysis of 

stability for implementation of retrofit measures are presented in chapter 2, and are not repeated 

here. 

6.3.5. ACTIVE FAULTS 

Surface fault ruptures have disrupted highway pavements during several past earthquakes. For 

example, pavements were fractured and buckled at several localities due to a combination of 

thrust and strike-slip faulting during the 1971 San Fernando earthquake. Figure 6-17 shows 

buckled and overlapped rigid and flexible pavement structures on Highway I-5 immediately 

north of the junction with I-405. The pavement disruption was caused by thrust faulting near the 

Lower Van Norman reservoir during the 1971 San Fernando earthquake. The pavement damage 

was caused by approximately 0.3 m horizontal compression, 0.2 m left-lateral strike-slip, and 

0.3 m differential uplift across the fault rupture zone (Yerkes, 1992; Yerkes et al., 1974). 
307

Although both rigid and flexible pavements buckled and fractured, the flexible pavement was 

more easily repaired, both temporarily and permanently. Flexible pavements on many city streets 

were disturbed by fault rupture during the 1971 earthquake, but with only minor disruption to 

traffic operations. Rupture of rigid pavements generally created greater traffic obstructions and 

repair difficulties. 

Caltrans, reproduced from Prysoc and Egan, 1981 

Figure 6-17. Rigid and flexible pavements buckled and overlapped by thrust 

faulting on I-405 south of separation from I-5 during 

1971 San Fernando earthquake. 

Strike-slip faulting without a major dip-slip component is typically less disruptive to highway 

pavements than thrust or normal faulting. For example, during the 1979 Imperial Valley 

earthquake (M6.5), the rigid pavement of Interstate Highway 8 east of the Meloland overcrossing 

was offset about 0.6 m right laterally across two fault strands about 150 m apart. The faulting 

caused minor rotation and offset of rigid pavement slabs and curvature of the roadway, but no 

pavement buckling and little disruption to traffic. Similar magnitudes of right lateral 

displacement caused little damage to flexible pavements on county routes, such as McCabe and 

Heber Roads. At a few other roadway crossings, such as at Ralph Road, right-lateral 

displacement was accompanied by normal faulting with displacements as great as 0.4 m across 

narrow fault zones. This vertical faulting fractured and offset flexible pavements, but natural 

ramping up the scarps allowed traffic to cross the faulted section with only minor hindrance to 

the free flow of traffic on this country road (Sharp et al., 1982). 
308

6.3.5.1. Screens for Fault Rupture Hazard 

The following procedures for evaluation of fault rupture hazard are summarized from California 

Division of Mines and Geology Special Publication 42 (Hart, 1988) and from NEHRP 

Recommended Provisions for Seismic Regulations for New Buildings,Part 2 - Commentary

(BSSC, 1994). The evaluation of fault rupture hazard is based extensively on recency of slip 

along existing faults. The magnitude, sense, and frequency of surface fault rupture varies for 

different faults and in many instances along the same fault. Even so, past occurrences of faulting 

have generally mimicked previous faulting episodes, both in location, magnitude, and sense of 

displacement. 

The following three steps, in order of implementation, are commonly used for rapid screening of 

fault rupture hazard. Where the first step indicates negligible fault rupture hazard, the second and 

third steps may be abbreviated or eliminated. 

1. Active faults should be identified and delineated from review and analysis of published and 

unpublished geologic reports applicable to the region in question. Identification studies 

incorporate evaluation of regional fault patterns as well as local fault features along the 

highway alignment. From these studies, regional and local fault traces, groundwater barriers, 

and other fault features are delineated on topographic maps. The character of past faulting 

episodes should be noted, including widths of rupture zones, amounts and senses of 

displacements, dates of past activity, etc., as a basis for estimating future faulting hazard. 

2. A stereoscopic study of aerial photographs and other remotely sensed images incorporating 

the highway alignment may provide additional information on the locality and character of a 

potential fault rupture hazard. Data to be collected from a stereoscopic study include 

delineation of fault-related topography, vegetation and soil contrasts, and other lineaments of 

fault origin. Predevelopment air photos are essential to the detection of fault features. 

3. A field reconnaissance may be needed to further develop and define fault-related 

information, such as geologic and soil units, geomorphic features, springs, and deformation 

of man-made structures, etc. The field study should be detailed near the highway alignment 

(within a few hundred meters) and much less detailed beyond that proximity. 

6.3.5.2. Evaluation Procedures 

Evaluation of surface fault rupture hazard to engineered construction includes the following 

primary considerations: how large and what type of displacement is likely to occur and what is 

the probability of occurrence. Standardized procedures have not been developed for these 

calculations; engineering geologists and seismologists, however, routinely make estimates of 

total fault displacement using empirical criteria. These estimates require specialized procedures 

that are beyond the scope of this manual. Reviews of existing criteria and procedures, their 

application, and background information are given by Wells and Coppersmith (1994) and Reiter 

(1990). The reader is referred to these texts for methodologies for estimating fault rupture 

displacement and probability of occurrence. Further discussion of fault displacement, as it 

relates to retrofit of tunnels, is given in section 4.4.2. 
309

6.4. RETROFIT STRATEGIES 

Only a few retrofit measures have been applied to prevent earthquake-induced pavement 

damage. These measures are termed “active” strategies. The policy of nearly all highway 

departments is not to apply active retrofit measures, except for the construction of structural 

approach slabs, but to repair pavement damage as rapidly as possible following an earthquake. 

The wait and repair approach is termed a “passive” strategy. Because no active strategies are 

proposed or being applied by highway agencies, other than structural approach slabs which are 

discussed in Part 1, section 6.3.1.1, no guidance and example calculations are given here for the 

retrofit of pavement structures. 

6.4.1. PASSIVE STRATEGIES 

The general procedure or policy of most highway departments is to repair pavement damage as 

quickly as possible after an earthquake, rather than to take active measures to retrofit or mitigate 

pavement damage prior to the event. Most highway agencies are experienced and prepared to 

respond to emergencies requiring pavement repair. A few pavement engineers contacted during 

preparation of this manual felt that timely and efficient pavement repairs could be made 

following an earthquake without specific advanced preparation or stockpiling of materials. These 

engineers further indicated that repair of pavement damage will likely be a rather minor concern 

compared to other emergency needs, such as repair of bridge damage. Because of these more 

important seismic issues, little action or concern is being given to prevention or specific rapid 

repair strategies. 

6.4.2. ACTIVE STRATEGIES 

Active strategies may be necessary at critical sites where pavement damage cannot be tolerated. 

For example, post-earthquake operability of highways critical to national defense or emergency 

response may be sufficiently important that retrofit measures are warranted to prevent pavement 

damage. In addition, some particularly vulnerable localities may require retrofit measures for 

safety. For example, wire netting is routinely applied on steep rock slopes adjacent to major 

highways to restrain rockfall debris from entering traffic lanes. This safety procedure is 

justifiable for both static and earthquake conditions. Foundation strengthening or construction of 

structural slabs are viable measures at sites where embankment or foundation settlement or 

deformations are likely to occur across narrow zones that can be defined prior to an earthquake. 

Retrofit measures might include strengthening the foundation, construction of structural slabs to 

bridge narrow susceptible zones, or replacement of rigid pavements with flexible pavement for 

ease of repair. 

6.4.2.1. Structural Approach Slabs (SAS) 

Because approach fills to bridge abutments are likely to undergo compaction and settlement 

during seismic shaking, structural approach slabs (SAS) are a viable retrofit measure to reduce 

the likelihood of pavement damage and traffic obstruction at these localities. Design of 

settlement slabs is considered in Part 1, section 6.3.1.1 and is not considered further here. 

However, maintenance of structural approach slabs is an important issue to seismic performance. 
310

One major maintenance problem has been washing of materials from beneath slabs by storm 

water, creating voids beneath the SAS. If these voids become too large, they could lead to 

fracture of the slab. Such fracture could be triggered by seismic shaking. As a maintenance 

measure, the fill supporting SAS should be checked for voids during routine bridge inspections. 

If voids are detected, the voids should be filled with grout as a retrofit measure and slab drainage 

improved to prevent recurrence of these deleterious features. 

6.4.2.2. Use of Easily Repairable Pavement Sections 

At localities of persistent or expected ground movement, such as active landslides, creeping or 

active faults, etc., easily repaired pavements may be utilized to expedite repairs as pavement 

deformation and damage occurs. Such localities might include areas susceptible to seismic 

compaction, liquefaction, slope instability, and fault rupture. A plausible retrofit measure is 

replacement of rigid pavement with flexible pavement to provide more ductility to absorb 

deformation and to facilitate post-earthquake pavement repairs. Other retrofit measures might 

include reduced joint spacing to increase flexibility of rigid pavements in critical areas. 

6.4.2.3. Replacement of Inferior Pavement Structures 

Pavements supported by poorly compacted embankments or soft foundations are more 

susceptible to settlement and embankment deformation than pavements on well-compacted fill. 

Also, embankments with narrow shoulders and steep side slopes are more susceptible to damage 

than wider, more stable embankments. Thus, an important retrofit measure is to replace older, 

poor-quality embankments with higher-quality well-compacted materials. Such replacement 

should be scheduled during regular highway maintenance and improvement projects. 

6.4.2.4. Strengthen Foundations Beneath Roadway Grades 

Much of the pavement damage during past earthquakes has been due to foundation deformation 

and instability. Thus, a major retrofit measure is to strengthen potentially unstable foundation 

soils. Such strengthening might include any or all of the following procedures: 

• Compact soft or loose soils to reduce settlement and ground deformation potential. 

• Improve foundation drainage to lower water tables and increase foundation strength and 

liquefaction resistance. 

• Add berms or struts to embankments to improve slope stability. 

6.4.2.5. Clear and Strengthen Side or Cut Slopes 

Pavement damage as well as roadway obstruction has occurred from sliding, toppling, or falling 

of rock and soil debris from cut or side slopes. Possible retrofit measures include: 

• Clearance of loose debris from slopes to prevent slippage or falling onto paved surfaces. 

• Placement of wire netting to restrain debris. 

• Flattening of grades, rock-bolting, or otherwise strengthening slopes to improve stability and 

prevent slippage or falling of landslide debris. 
311

APPENDIX A: CHARACTERISTICS OF SURFACE WAVES 

A.1. INTRODUCTION 

A seismic surface wave is generated by the constructive interference of multiply reflected body 

waves trapped in a waveguide. Important shallow crustal waveguides include layered 

sedimentary deposits and sedimentary basins (nonplanar structures). These two types of 

waveguide typically exhibit a significant velocity contrast between them and the underlying 

geologic materials. 

A surface wave is transmitted along the free surface of the earth (i.e., it propagates horizontally) 

and its vibration is restricted to near the free surface. Because of their slower velocity, surface 

waves arrive after the main S-waves. There are two types of surface waves, Love waves and 

Rayleigh waves. The latter is of main interest for tunnels because of their capacity to induce 

large axial strain under certain conditions. The particle motion of a Rayleigh wave is elliptical 

and could be either retrograde or prograde (Mooney and Bolt, 1966). Another unique feature of 

a surface wave is the velocity dispersion; i.e., its propagation velocity is a function of the wave 

period. The material properties and the geometry of a waveguide determine the style of particle 

motion, amplitude (varying with depth), and velocity dispersion of a surface wave. In a multilayer medium, the surface wave velocity lies between that of the top layer and that of the bottom 

layer, with long-period surface waves having velocities approaching the latter. This property is 

useful when making a quick assessment of surface wave velocity in a layered medium. A more 

complete description and theoretical treatment of surface waves can be found in textbooks such 

as Bullen and Bolt (1985) and Aki and Richards (1980). 

A.2. EXAMPLES OF PROMINENT RAYLEIGH WAVES DURING EARTHQUAKES 

Rayleigh waves normally are considered a less important element of the recorded strong ground 

motions than S-waves because they generally produce weaker shaking than S-waves. However, 

when a surface wave is adequately excited or amplified, its particle velocity or displacement may 

be comparable to or even larger than the S-wave amplitude. The following summarizes several 

situations in which Rayleigh waves have been considered to be a significant element in recorded 

long-period motions. 

Example 1. 1995 Kobe earthquake 

Late-arriving, long-duration waves (two- to five-second period) were identified as Rayleigh 

waves at the soil sites of Takami (in Osaka City, about 40 km from the epicenter) and Osaka 

Meteorological Observatory (Yokoyama, 1996). The peak ground displacement at the site 

Takami is carried by the late arriving surface wave. Surface waves were insignificant or not 

found at the nearby rock sites of Kobe Meteorological Observatory and Chihaya. The velocity at 

which Rayleigh waves traveled across the Osaka plain was estimated to be 0.6 km/sec. The 

identified Rayleigh waves produced the peak horizontal displacement at Takami. 
312

Example 2. April 25, 1989 (Ms6.9) Guerrero earthquake – A case of incident surface waves 

being amplified by a sedimentary basin 

A broadband wave packet (1.0- to 12.5-second period) recorded at TACY (in the hill zone of 

Mexico City, about 300 km from the epicenter of the 1989 Guerrero earthquake) was identified 

as Rayleigh waves. Rayleigh waves were amplified by the soft soils of Mexico City as they 

entered the basin and contributed to the lengthening in ground shaking at recording stations D56 

and NZ31 inside the lake-bed zone (Gomez-Bernal and Saragoni, 1996). This observation is in 

line with the hypothesis that the large and long-duration shaking in the lake-bed zone of Mexico 

City during the M 8.0 1985 Michoacan Earthquake resulted from the interaction of deeply 

guided surface waves with local one-dimensional resonance (Chavez-Garcia et al., 1995). 

Chavez-Garcia et al. (1996) reported a Rayleigh wave velocity greater than 2.5 km/sec for two of 

the Rayleigh wave packets and a low velocity of 0.1 km/sec for the third packet that appeared 

only locally. 

Example 3. 1971 San Fernando earthquake 

Development of Rayleigh waves and their subsequent dispersion were observed along recording 

stations that lie on similar source-to-site azimuths (Hanks, 1975). Results of the two-dimensional 

simulation of the Los Angeles basin and San Fernando Valley (Vidale and Helmberger, 1988) 

suggest that both basins convert direct shear waves into surface waves. O’Rourke et al. (1984) 

analyzed eight pairs of nearby displacement records and suggested that the maximum observed 

horizontal strains can be modeled by the propagation of Rayleigh waves. 

Example 4. Loma Prieta earthquake and its aftershocks – A case of valley-induced surface 

waves 

The late-arriving ground motion (about three-second period) in the Colton Avenue record (at a 

distance of 29 km to the fault rupture) of the 1989 Loma Prieta mainshock earthquake was 

interpreted by Frankel et al. (1991) as caused by surface waves. The identified surface waves 

caused the peak ground velocity (37 and 36 cm/sec) and peak ground displacement (19 and 

17 cm) on both horizontal components of the record. Rayleigh waves were also identified on the 

array recordings of several Loma Prieta aftershocks inside the Santa Clara Valley (Frankel et al., 

1991). The interpretation of these Rayleigh waves as valley-induced waves is supported by a 

three-dimensional basin response simulation (Frankel and Vidale, 1992). The estimated Raleigh 

wave propagation velocity ranges from 1.0 km/sec to 2.0 km/sec. 

Pei and Papageorgiou (1996) interpreted the complex waveforms following the S-wave arrival 

on the mainshock recordings of the Gilroy array, which is also inside the Santa Clara Valley, as 

valley-induced surface waves. The fundamental mode and the first two higher modes of Rayleigh 

waves were interpreted: the phase velocity was estimated to be 0.4 km/sec for the fundamental 

mode and 1.2 km/sec for the first higher mode. The peak ground velocity of the Gilroy array 

records is carried by the direct S-wave; the particle velocity of the interpreted surface wave is 

less than 20 cm/sec and less than half of the peak ground velocity. 
313

Example 5. 1992 Landers-Big Bear aftershocks 

Analysis of records from a dense array inside the San Bernardino Valley indicated the existence 

of one- to three- second period surface waves at deep soil sites (Frankel, 1994). A threedimensional finite difference simulation of the San Bernardino Valley’s response to incident Swaves (Frankel, 1994) supported the interpretation that these observed ground motions were 

caused by basin-induced surface waves. The Rayleigh wave velocity was estimated to be 

approximately 1.0 km/sec. 

Example 6. Observations from the Los Angeles basin 

Joyner (2000) used the distance dependence of the time of maximum amplitude to distinguish 

surface waves and body waves. He studied the pseudovelocity response spectra of strong motion 

records from the Los Angeles basin and showed that late arriving surface waves with group 

velocity of about 1km/sec dominate the ground motion for periods of three seconds and longer. 

He explained the observed surface waves as basin-induced surface waves generated by 

conversion by body waves at the boundary of the Los Angeles basin. Joyner also speculated that 

between periods of 0.75 and three seconds, the maximum amplitude is carried by the body waves 

on some records and by the surface waves on others. 

Example 7. Observations from the 1999 Mw7.6 Chi-Chi Taiwan earthquake 

Preliminary examination of the strong motion data provided by the Central Weather Bureau in 

Taiwan indicates numerous cases of possible surface waves dominating the recorded motions in 

sedimentary basins and alluvial plains. Surface-wave-like phases in several recordings in Ilan, 

which is about 80 km northeast of the fault rupture, carry the peak ground velocity (in the range 

of 25 cm/sec to 30 cm/sec). Other likely examples of dominating surface waves are in the 

alluvial plain west of the fault rupture at a distance range of 30 to 80 km and with peak ground 

velocities of 20 cm/sec to 30 cm/sec. The period of the surface-wave-like arrival is five seconds 

and longer. There is one observation with a particle velocity of 50 cm/sec at a distance of 20 km 

(station CHY104) from the fault. It should be noted that these observations are preliminary and 

further studies are needed to verify the wave type and to estimate the propagation velocity. 

A.3. SUMMARY 

In summary, the above seven examples indicate that surface waves can be an important element 

of ground motions in sedimentary deposits at periods of about one second and longer. These 

surface waves are explained as due to either soil amplification of surface waves incident from the 

epicentral region or the conversion of incident S-waves into surface waves inside a sedimentary 

basin (basin-induced surface waves). The majority of these examples occurred at a distance of 

20 km or more from the earthquake source. In some records, the observed peak ground velocity 

is carried by the identified surface wave, while in others the particle velocity associated with the 

identified surface wave is only a fraction of the peak velocity. The two largest peak particle 

velocities of the identified surface wave described in the above examples are 30 cm/sec (Colton 

Ave. recording of the Loma Prieta earthquake) and 50 cm/sec (CHY104 station of the Chi-Chi 

earthquake). However, further work is needed to confirm the wave type of the latter. Most of 

the observed surface wave velocities, CR, are in a range of approximately 0.5 to 2.5 km/sec. This 
314

large variation reflects the diversity of the subsurface conditions and the surface wave period in 

each observation. It should be noted that when the subsurface velocity structure is known, 

numerical methods could also be used to determine the site-specific dispersion curve CR(T). The 

dispersion curve for a multiple-layer medium is relatively simple to calculate (Haskell, 1953; 

Mooney and Bolt, 1966). However, the calculation of surface wave velocity inside a 

sedimentary basin usually requires a complicated numerical method (for examples, Lysmer and 

Drake, 1972; Drake, 1972; Bard and Bouchon, 1980; Papageorgiou and Kim, 1993). 
315

ACKNOWLEDGMENT 

The following people contributed to Part 2 of this manual (in alphabetical order): 

Ian Buckle, University of Nevada, Reno; formerly Multidisciplinary Center for 

Earthquake Engineering Research, University at Buffalo 

Brian S.J. Chiou, California Department of Transportation; formerly Geomatrix 

Consultants, Inc. 

Kenneth Fishman, McMahon & Mann Consulting Engineers, P.C.; formerly University at 

Buffalo 

Ian Friedland, FHWA, formerly Applied Technology Council and Multidisciplinary 

Center for Earthquake Engineering Research, University at Buffalo 

Jon Kaneshiro, Parsons Engineering Science; formerly Geomatrix Consultants, Inc. 

Faiz Makdisi, Geomatrix Consultants, Inc. 

Geoffrey Martin, University of Southern California 

Samuel Musser, Utah Department of Transportation 

Karthik Narayanan, formerly Geomatrix Consultants, Inc. 

Maurice Power, Volume coordinator, Geomatrix Consultants, Inc. 

Rowland Richards, University at Buffalo 

Dario Rosidi, URS Corporation; formerly Geomatrix Consultants, Inc. 

Zhi-Liang Wang, Geomatrix Consultants, Inc. 

T. Leslie Youd, Brigham Young University 

The first draft of this document was reviewed by members of the Highway Seismic Research 

Council for FHWA contract DTFH61-92-C-00106. The second draft was reviewed by the 

FHWA Office of Infrastructure Research and Development, Turner-Fairbanks Highway 

Research Center. 

The FHWA COTR for this project was Mr. John O’Fallon, assisted by Dr. Phillip Yen. 

Editorial assistance was provided by Jane Stoyle and Hector Velasco, Multidisciplinary Center 

for Earthquake Engineering Research, University at Buffalo. 
 
317

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