U.S. Department of Transportation Publication No. FHWA NHI-06-089
 

Federal Highway Administration December 2006 

NHI Course No. 132012_______________________________ 

SOILS AND FOUNDATIONS 

Reference Manual – Volume II 

TTeessttiinngg

EExxppeerriieennccee

TThheeoorryy

National Highway Institute
 
NOTICE 

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

facts and the accuracy of the data presented herein. The contents do not necessarily 

reflect policy of the Department of Transportation. This report does not constitute a 

standard, specification, or regulation. The United States Government does not endorse 

products or manufacturers. Trade or manufacturer's names appear herein only because 

they are considered essential to the objective of this document. 
 

 

 

 

 

Technical Report Documentation Page 

1. Report No. 

FHWA-NHI–06-089 

2. Government Accession No. 3. Recipient’s Catalog No. 

4. Title and Subtitle 

SOILS AND FOUNDATIONS 

REFERENCE MANUAL – Volume II 

5. Report Date

 December 2006 

6. Performing Organization Code 

7. Author(s) 

Naresh C. Samtani*, PE, PhD and Edward A. Nowatzki*, PE, PhD 

8. Performing Organization Report No. 

9. Performing Organization Name and Address 

Ryan R. Berg and Associates, Inc. 

2190 Leyland Alcove, Woodbury, MN 55125 

* NCS GeoResources, LLC 

640 W Paseo Rio Grande, Tucson, AZ 85737 

10. Work Unit No. (TRAIS) 

11. Contract or Grant No. 

DTFH-61-02-T-63016 

12. Sponsoring Agency Name and Address 

National Highway Institute 

U.S. Department of Transportation 

Federal Highway Administration, Washington, D.C. 20590 

13. Type of Report and Period Covered 

14. Sponsoring Agency Code 

15. Supplementary Notes 

FHWA COTR – Larry Jones 

FHWA Technical Review – Jerry A. DiMaggio, PE; Silas Nichols, PE; Richard Cheney, PE; 

Benjamin Rivers, PE; Justin Henwood, PE. 

Contractor Technical Review – Ryan R. Berg, PE; Robert C. Bachus, PhD, PE; 

Barry R. Christopher, PhD, PE 

This manual is an update of the 3rd Edition prepared by Parsons Brinckerhoff Quade & Douglas, Inc, in 2000. 

Author: Richard Cheney, PE. The authors of the 1st and 2nd editions prepared by the FHWA in 1982 and 1993, 

respectively, were Richard Cheney, PE and Ronald Chassie, PE. 

16. Abstract 

The Reference Manual for Soils and Foundations course is intended for design and construction professionals involved 

with the selection, design and construction of geotechnical features for surface transportation facilities. The manual is 

geared towards practitioners who routinely deal with soils and foundations issues but who may have little theoretical 

background in soil mechanics or foundation engineering. The manual’s content follows a project-oriented approach 

where the geotechnical aspects of a project are traced from preparation of the boring request through design 

computation of settlement, allowable footing pressure, etc., to the construction of approach embankments and 

foundations. Appendix A includes an example bridge project where such an approach is demonstrated. 

Recommendations are presented on how to layout borings efficiently, how to minimize approach embankment 

settlement, how to design the most cost-effective pier and abutment foundations, and how to transmit design 

information properly through plans, specifications, and/or contact with the project engineer so that the project can be 

constructed efficiently. 

The objective of this manual is to present recommended methods for the safe, cost-effective design and construction of 

geotechnical features. Coordination between geotechnical specialists and project team members at all phases of a 

project is stressed. Readers are encouraged to develop an appreciation of geotechnical activities in all project phases 

that influence or are influenced by their work. 

17. Key Words 18. Distribution Statement 

Subsurface exploration, testing, slope stability, embankments, cut slopes, shallow 

foundations, driven piles, drilled shafts, earth retaining structures, construction. 

No restrictions. 

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price 

UNCLASSIFIED UNCLASSIFIED 594 

Form DOT F 1700.7(8-72) Reproduction of completed page authorized 
[THIS PAGE INTENTIONALLY BLANK] 
PREFACE 

This update to the Reference Manual for the Soils and Foundations course was developed to 

incorporate the guidance available from the FHWA in various recent manuals and Geotechnical 

Engineering Circulars (GECs). The update has evolved from its first two versions prepared by 

Richard Cheney and Ronald Chassie in 1982 and 1993, and the third version prepared by 

Richard Cheney in 2000. 

The updated edition of the FHWA Soils and Foundations manual contains an enormous amount 

of information ranging from methods for theoretically based analyses to “rules of thumb” 

solutions for a wide range of geotechnical and foundation design and construction issues. It is 

likely that this manual will be used nationwide for years to come by civil engineering 

generalists, geotechnical and foundation specialists, and others involved in transportation 

facilities. That being the case, the authors wish to caution against indiscriminate use of the 

manual’s guidance and recommendations. The manual should be considered to represent the 

minimum standard of practice. The user must realize that there is no possible way to cover all 

the intricate aspects of any given project. Even though the material presented is theoretically 

correct and represents the current state-of-the-practice, engineering judgment based on local 

conditions and knowledge must be applied. This is true of most engineering disciplines, but it is 

especially true in the area of soils and foundation engineering and construction. For example, 

the theoretical and empirical concepts in the manual relating to the analysis and design of deep 

foundations apply to piles installed in the glacial tills of the northeast as well as to drilled shafts 

installed in the cemented soils of the southwest. The most important thing in both applications is 

that the values for the parameters to be used in the analysis and design be selected by a 

geotechnical specialist who is intimately familiar with the type of soil in that region and 

intimately knowledgeable about the regional construction procedures that are required for the 

proper installation of such foundations in local soils. 

General conventions used in the manual 

This manual addresses topics ranging from fundamental concepts in soil mechanics to the 

practical design of various geotechnical features ranging from earthworks (e.g., slopes) to 

foundations (e.g., spread footings, driven piles, drilled shafts and earth retaining structures). In 

the literature each of these topics has developed its own identity in terms of the terminology and 

symbols. Since most of the information presented in this manual appears in other FHWA 

publications, textbooks and publications, the authors faced a dilemma on the regarding 

terminology and symbols as well as other issues. Following is a brief discussion on such issues. 

FHWA NHI-06-089 Preface 

Soils and Foundations – Volume II P - 1 December 2006 
 

• Pressure versus Stress 

The terms “pressure” and “stress” both have units of force per unit area (e.g., pounds per 

square foot). In soil mechanics “pressure” generally refers to an applied load distributed 

over an area or to the pressure due to the self-weight of the soil mass. “Stress,” on the other 

hand, generally refers to the condition induced at a point within the soil mass by the 

application of an external load or pressure. For example, “overburden pressure,” which is 

due to the self weight of the soil, induces “geostatic stresses” within the soil mass. Induced 

stresses cause strains which ultimately result in measurable deformations that may affect the 

behavior of the structural element that is applying the load or pressure. For example, in the 

case of a shallow foundation, depending upon the magnitude and direction of the applied 

loading and the geometry of the footing, the pressure distribution at the base of the footing 

can be uniform, linearly varying, or non-linearly varying. In order to avoid confusion, the 

terms “pressure” and “stress” will be used interchangeably in this manual. In cases where 

the distinction is important, clarification will be provided by use of the terms “applied” or 

“induced.” 

• Symbols 

Some symbols represent more than one geotechnical parameter. For example, the symbol Cc 

is commonly used to identify the coefficient of curvature of a grain size distribution curve as 

well as the compression index derived from consolidation test results. Alternative symbols 

may be chosen, but then there is a risk of confusion and possible mistakes. To avoid the 

potential for confusion or mistakes, the Table of Contents contains a list of symbols for each 

chapter. 

• Units 

English units are the primary units in this manual. SI units are included in parenthesis in the 

text, except for equations whose constants have values based on a specific set of units, 

English or SI. In a few cases, where measurements are conventionally reported in SI units 

(e.g., aperture sizes in rock mapping), only SI units are reported. English units are used in 

example problems. Except where the units are related to equipment sizes (e.g., drill rods), 

all unit conversions are “soft,” i.e., approximate. Thus, 10 ft is converted to 3 m rather than 

3.05 m. The soft conversion for length in feet is rounded to the nearest 0.5 m. Thus, 15 ft is 

converted to 4.5 m not 4.57 m. 

FHWA NHI-06-089 Preface 

Soils and Foundations – Volume II P - 2 December 2006 
 

•	 Theoretical Details 

Since the primary purpose of this manual is to provide a concise treatment of the 

fundamental concepts in soil mechanics and an introduction to the practical design of various 

geotechnical features related to highway construction, the details of the theory underlying 

the methods of analysis have been largely omitted in favor of discussions on the application 

of those theories to geotechnical problems. Some exceptions to this general approach were 

made. For example, the concepts of lateral earth pressure and bearing capacity rely too 

heavily on a basic understanding of the Mohr’s circle for stress for a detailed presentation of 

the Mohr’s circle theory to be omitted. However, so as not to encumber the text, the basic 

theory of the Mohr’s circle is presented in Appendix B for the reader’s convenience and as 

an aid for the deeper understanding of the concepts of earth pressure and bearing capacity. 

•	 Standard Penetration Test (SPT) N-values 

The SPT is described in Chapter 3 of this manual. The geotechnical engineering literature is 

replete with correlations based on SPT N-values. Many of the published correlations were 

developed based on SPT N-values obtained with cathead and drop hammer methods. The 

SPT N-values used in these correlations do not take in account the effect of equipment 

features that might influence the actual amount of energy imparted during the SPT. The 

cathead and drop hammer systems typically deliver energy at an estimated average 

efficiency of 60%. Today’s automatic hammers generally deliver energy at a significantly 

higher efficiency (up to 90%). When published correlations based on SPT N-values are 

presented in this manual, they are noted as N60-values and the measured SPT N-values 

should be corrected for energy before using the correlations. 

Some researchers developed correction factors for use with their SPT N-value correlations to 

address the effects of overburden pressure. When published correlations presented in this 

manual are based upon values corrected for overburden they are noted as N160. Guidelines 

are provided as to when the N60-values should be corrected for overburden. 

•	 Allowable Stress Design (ASD) and Load and Resistance Factor Design (LRFD) 

Methods 

The design methods to be used in the transportation industry are currently (2006) in a state of 

transition from ASD to LRFD. The FHWA recognizes this transition and has developed 

separate comprehensive training courses for this purpose. Regardless of whether the ASD or 

LRFD is used, it is important to realize that the fundamentals of soil mechanics, such as the 

FHWA NHI-06-089 Preface 

Soils and Foundations – Volume II P - 3 December 2006 
determination of the strength and deformation of geomaterials do not change. The only 

difference between the two methods is the way in which the uncertainties in loads and 

resistances are accounted for in design. Since this manual is geared towards the fundamental 

understanding of the behavior of soils and the design of foundations, ASD has been used 

because at this time most practitioners are familiar with that method of design. However, for 

those readers who are interested in the nuances of both design methods Appendix C provides 

a brief discussion on the background and application of the ASD and LRFD methods. 

FHWA NHI-06-089 Preface 

Soils and Foundations – Volume II P - 4 December 2006 
ACKNOWLEDGEMENTS 

The authors would like to acknowledge the following events and people that were instrumental 

in the development of this manual. 

•	 Permission by the FHWA to adapt the August 2000 version of the Soils and Foundations 

Workshop Manual. 

•	 Provision by the FHWA of the electronic files of the August 2000 manual as well as other 

FHWA publications. 

•	 The support of Ryan R. Berg of Ryan R. Berg and Associates, Inc. (RRBA) in facilitating the 

preparation of this manual and coordinating reviews with the key players. 

•	 The support provided by the staff of NCS Consultants, LLC, (NCS) - Wolfgang Fritz, Juan 

Lopez and Randy Post (listed in alphabetical order of last names). They prepared some 

graphics, some example problems, reviewed selected data for accuracy with respect to 

original sources of information, compiled the Table of Contents, performed library searches 

for reference materials, and checked internal consistency in the numbering of chapter 

headings, figures, equations and tables. 

•	 Discussions with Jim Scott (URS-Denver) on various topics and his willingness to share 

reference material are truly appreciated. Dov Leshchinsky of ADAMA Engineering 

provided copies of the ReSSA and FoSSA programs which were used to generate several 

figures in the manual as well as presentation slides associated with the course presentation. 

Robert Bachus of Geosyntec Consultants prepared Appendices D and E. Allen Marr of 

GeoComp Corporation provided photographs of some laboratory testing equipment. Pat 

Hannigan of GRL Engineers, Inc. reviewed the driven pile portion of Chapter 9. Shawn 

Steiner of ConeTec, Inc. and Salvatore Caronna of gINT Software prepared the Cone 

Penetration Test (CPT) and boring logs, respectively, shown in Chapter 3 and Appendix A. 

Robert (Bob) Meyers (NMDOT), Ted Buell (HDR-Tucson) and Randy Simpson (URSPhoenix) provided comments on some sections (particularly Section 8.9). 

•	 Finally, the technical reviews and recommendations provided by Jerry DiMaggio, Silas 

Nichols, Benjamin Rivers, Richard Cheney (retired) and Justin Henwood of the FHWA, 

Ryan Berg of RRBA, Robert Bachus of GeoSyntec Consultants, Jim Scott of URS, and 

Barry Christopher of Christopher Consultants, Inc., are gratefully acknowledged. 

FHWA NHI-06-089 Preface 

Soils and Foundations – Volume II P - 5 December 2006 
 

 

SPECIAL ACKNOWLEDGEMENTS 

A special acknowledgement is due of the efforts of Richard Cheney and Ronald Chassie for their 

work in the preparation of the previous versions of this manual. It is their work that made this 

course one of the most popular FHWA courses. Their work in developing this course over the 

past 25 years is acknowledged. 

With respect to this manual, the authors wish to especially acknowledge the in-depth review 

performed by Jerry DiMaggio and time he spent in direct discussions with the authors and other 

reviewers. Such discussions led to clarification of some existing guidance in other FHWA 

manuals as well as the introduction of new guidance in some chapters of this manual. 

FHWA NHI-06-089 Preface 

Soils and Foundations – Volume II P - 6 December 2006 
 

 

SI CONVERSION FACTORS 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You 

Know 

Multiply By To Find Symbol 

LENGTH 

mm 

m 

m 

Km 

millimeters 

meters 

meters 

kilometers 

0.039 

3.28 

1.09 

0.621 

inches 

feet 

yards 

miles 

in 

ft 

yd 

mi 

AREA 

mm2 

m2 

m2 

ha 

km2 

square millimeters 

square meters 

square meters 

hectares 

square kilometers 

0,0015 

10.758 

1.188 

2.47 

0.386 

square inches 

square feet 

square yards 

acres 

square miles 

in2 

ft2 

yd2 

ac 

mi2 

VOLUME 

ml 

l 

m3 

m3 

milliliters 

liters 

cubic meters 

cubic meters 

0.034 

0.264 

35.29 

1.295 

fluid ounces 

gallons 

cubic feet 

cubic yards 

fl oz 

gal 

ft3 

yd3 

MASS 

g 

kg 

Tones 

grams 

kilograms 

tonnes 

0.035 

2.205 

1.103 

ounces 

pounds 

US short tons 

oz 

lb 

tons 

TEMPERATURE 

oC Celsius 1.8oC + 32 Fahrenheit oF 

WEIGHT DENSITY 

kN/m3 kilonewtons / cubic 

meter 

6.36 Pound force / cubic foot pcf 

FORCE and PRESSURE or STRESS 

N 

kN 

kPa 

kPa 

newtons 

kilonewtons 

kilopascals 

kilopascals 

0.225 

225 

0.145 

20.88 

pound force 

pound force 

pound force / square inch 

pound force / square foot 

lbf 

lbf 

psi 

psf 

PERMEABILITY (VELOCITY) 

cm/sec centimeter/second 1.9685 feet/minute ft/min 
[THIS PAGE INTENTIONALLY BLANK]
 
SOILS AND FOUNDATIONS 

VOLUME II 

TABLE OF CONTENTS 

Page 

LIST OF FIGURES ............................................................................................................. vii 

LIST OF TABLES ................................................................................................................ xii 

LIST OF SYMBOLS ........................................................................................................... xiv 

8.0 SHALLOW FOUNDATIONS ................................................................................ 8-1 

8.01 Primary References ........................................................................................ 8-1 

8.1 GENERAL APPROACH TO FOUNDATION DESIGN ............................. 8-1 

 8.1.1 Foundation Alternatives and Cost Evaluation ................................... 8-2 

 8.1.2 Loads and Limit States for Foundation Design ................................. 8-3 

8.2 TYPES OF SHALLOW FOUNDATIONS ................................................... 8-4 

8.2.1 Isolated Spread Footings ................................................................... 8-4 

 8.2.2 Continuous or Strip Footings............................................................. 8-6 

 8.2.3 Spread Footings with Cantilevered Stemwalls .................................. 8-7 

8.2.4 Bridge Abutments .............................................................................. 8-7 

8.2.5 Retaining Structures........................................................................... 8-9 

8.2.6 Building Foundations......................................................................... 8-9 

8.2.7 Combined Footings ............................................................................ 8-9 

8.2.8 Mat Foundations .............................................................................. 8-11 

8.3 SPREAD FOOTING DESIGN CONCEPT AND PROCEDURE............... 8-12 

8.4 BEARING CAPACITY ............................................................................... 8-15 

8.4.1 Failure Mechanisms ......................................................................... 8-16 

8.4.1.1 General Shear ....................................................................... 8-16 

8.4.1.2 Local Shear .......................................................................... 8-18 

8.4.1.3 Punching Shear .................................................................... 8-18 

 8.4.2 Bearing Capacity Equation Formulation ......................................... 8-18 

 8.4.2.1 Comparative Effect of Various Terms in Bearing 

 Capacity Formulation .......................................................... 8-22 

 8.4.3 Bearing Capacity Correction Factors............................................... 8-23 

 8.4.3.1 Footing Shape (Eccentricity and Effective Dimensions)..... 8-24 

 8.4.3.2 Location of the Ground Water Table ................................... 8-27 

8.4.3.3 Embedment Depth ............................................................... 8-28 

8.4.3.4 Inclined Base........................................................................ 8-29 

8.4.3.5 Inclined Loading .................................................................. 8-29 

8.4.3.6 Sloping Ground Surface....................................................... 8-30 

8.4.3.7 Layered Soils ....................................................................... 8-30 

 8.4.4 Additional Considerations Regarding Bearing Capacity 

 Correction Factors............................................................................ 8-32 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II i December 2006 
 8.4.5 Local or Punching Shear.................................................................. 8-33 

 8.4.6 Bearing Capacity Factors of Safety ................................................. 8-35 

8.4.6.1 Overstress Allowances......................................................... 8-35 

 8.4.7 Practical Aspects of Bearing Capacity Formulations ...................... 8-36 

8.4.7.1 Bearing Capacity Computations .......................................... 8-36 

8.4.7.2 Failure Zones ....................................................................... 8-38 

8.4.8 Presumptive Bearing Capacities ...................................................... 8-40 

 8.4.8.1 Presumptive Bearing Capacity in Soil ................................. 8-40 

 8.4.8.2 Presumptive Bearing Capacity in Rock ............................... 8-40 

8.5 SETTLEMENT OF SPREAD FOOTINGS................................................. 8-44 

8.5.1 Immediate Settlement ...................................................................... 8-44 

 8.5.1.1 Schmertmann’s Modified Method for Calculation of 

 Immediate Settlements ......................................................... 8-45 

 8.5.1.2 Comments on Schmertmann’s Method................................ 8-47 

 8.5.1.3 Tabulation of Parameters in Schmertmann’s Method ......... 8-52 

 8.5.2 Obtaining Limiting Applied Stress for a Given Settlement............. 8-54 

8.5.3 Consolidation Settlement ................................................................. 8-54 

8.6 SPREAD FOOTINGS ON COMPACTED EMBANKMENT FILLS........ 8-55 

 8.6.1 Settlement of Footings on Structural Fills ....................................... 8-57 

8.7 FOOTINGS ON INTERMEDIATE GEOMATERIALS (IGMs) 

 AND ROCK ................................................................................................. 8-58 

8.8 ALLOWABLE BEARING CAPACITY CHARTS .................................... 8-60 

 8.8.1 Comments on the Allowable Bearing Capacity Charts ................... 8-62 

8.9 EFFECT OF DEFORMATIONS ON BRIDGE STRUCTURES................ 8-64 

 8.9.1 Criteria for Tolerable Movements of Bridges.................................. 8-68 

8.9.1.1 Vertical Movements............................................................. 8-68 

8.9.1.2 Horizontal Movements ........................................................ 8-69 

 8.9.2 Loads for Evaluation of Tolerable Movements Using 

 Construction Point Concept ............................................................. 8-70 

8.10 SPREAD FOOTING LOAD TESTS ........................................................... 8-72 

8.11 CONSTRUCTION INSPECTION .............................................................. 8-73 

8.11.1 Structural Fill Materials ................................................................... 8-73 

8.11.2 Monitoring ....................................................................................... 8-75 

9.0 DEEP FOUNDATIONS .......................................................................................... 9-1 

9.1 TYPES OF DEEP FOUNDATIONS AND PRIMARY REFERENCES...... 9-3 

 9.1.1 Selection of Driven Pile or Cast-in-Place (CIP) Pile Based on 

Subsurface Conditions ....................................................................... 9-5 

 9.1.2 Design and Construction Terminology .............................................. 9-5 

9.2 DRIVEN PILE DESIGN-CONSTRUCTION PROCESS............................. 9-7 

9.3 ALTERNATE DRIVEN PILE TYPE EVALUATION............................... 9-18 

 9.3.1 Cost Evaluation of Alternate Pile Types.......................................... 9-19 

9.4 COMPUTATION OF PILE CAPACITY.................................................... 9-20 

9.4.1 Factors of Safety .............................................................................. 9-23 

9.5 DESIGN OF SINGLE PILES...................................................................... 9-29 

 9.5.1 Ultimate Geotechnical Capacity of Single Piles in 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II ii December 2006 
 Cohesionless Soils ........................................................................... 9-29 

9.5.1.1 Nordlund Method................................................................. 9-29 

 9.5.2 Ultimate Geotechnical Capacity of Single Piles in Cohesive Soils . 9-47 

9.5.2.1 Total Stress – α-method....................................................... 9-47 

9.5.2.2 Effective Stress – β-method ................................................. 9-52 

 9.5.3 Ultimate Geotechnical Capacity of Single Piles in Layered Soils... 9-59 

 9.5.4 Plugging of Open Pile Sections ....................................................... 9-60 

 9.5.5 Time Effects on Pile Capacity ......................................................... 9-64 

9.5.5.1 Soil Setup ............................................................................. 9-64 

9.5.5.2 Relaxation ............................................................................ 9-65 

 9.5.6 Additional Design and Construction Considerations....................... 9-66 

 9.5.7 The DRIVEN Computer Program ................................................... 9-67 

 9.5.8 Ultimate Capacity of Piles on Rock and in Intermediate 

 Geomaterials (IGMs) ....................................................................... 9-75 

9.6 DESIGN OF PILE GROUPS....................................................................... 9-76 

 9.6.1 Axial Compression Capacity of Pile Groups ................................... 9-78 

9.6.1.1 Cohesionless Soils ............................................................... 9-78 

9.6.1.2 Cohesive Soils...................................................................... 9-79 

 9.6.1.3 Block Failure of Pile Groups ............................................... 9-81 

 9.6.2 Settlement of Pile Groups ................................................................ 9-82 

 9.6.2.1 Elastic Compression of Piles ............................................... 9-82 

 9.6.2.2 Settlement of Pile Groups in Cohesionless Soils ................. 9-83 

 9.6.2.3 Settlement of Pile Groups in Cohesive Soils ....................... 9-84 

9.7 DESIGN OF PILES FOR LATERAL LOAD ............................................. 9-84 

9.8 DOWNDRAG OR NEGATIVE SHAFT RESISTANCE ........................... 9-87 

9.9 CONSTRUCTION OF PILE FOUNDATIONS .......................................... 9-90 

 9.9.1 Selection of Design Safety Factor Based on Construction Control . 9-90 

9.9.2 Pile Driveability ............................................................................... 9-90 

9.9.2.1 Factors Affecting Drivability ............................................... 9-91 

 9.9.2.2 Driveability Versus Pile Type.............................................. 9-93 

 9.9.3 Pile Driving Equipment and Operation ........................................... 9-94 

 9.9.4 Dynamic Pile Driving Formulae ...................................................... 9-97 

 9.9.5 Dynamic Analysis of Pile Driving ................................................. 9-100 

9.9.6 Wave Equation Methodology ........................................................ 9-103 

 9.9.6.1 Input to Wave Equation Analysis ...................................... 9-105 

 9.9.6.2 Output Values from Wave Equation Analysis ................... 9-106 

 9.9.6.3 Pile Wave Equation Analysis Interpretation...................... 9-106 

9.9.7 Driving Stresses ............................................................................. 9-108 

 9.9.8 Guidelines for Assessing Pile Drivability...................................... 9-109 

 9.9.9 Pile Construction Monitoring Considerations ............................... 9-112 

9.9.10 Dynamic Pile Monitoring .............................................................. 9-114 

9.9.10.1 Applications ..................................................................... 9-115 

 9.9.10.2 Interpretation of Results and Correlation with Static 

 Pile Load Tests ................................................................ 9-117 

9.10 CAST-IN-PLACE (CIP) PILES ................................................................ 9-119 

9.11 DRILLED SHAFTS................................................................................... 9-123 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II iii December 2006
 9.11.1 Characteristics of Drilled Shafts .................................................... 9-124 

 9.11.2 Advantages of Drilled Shafts......................................................... 9-125 

 9.11.1.1 Special Considerations for Drilled Shafts ........................ 9-126 

 9.11.3 Subsurface Conditions and Their Effect on Drilled Shafts............ 9-126 

9.12 ESTIMATING AXIAL CAPACITY OF DRILLED SHAFTS................. 9-127 

 9.12.1 Side Resistance in Cohesive Soil................................................... 9-129 

 9.12.1.1 Mobilization of Side Resistance in Cohesive Soil ........... 9-130 

 9.12.2 Tip Resistance in Cohesive Soil .................................................... 9-131 

 9.12.2.1 Mobilization of Tip Resistance in Cohesive Soil............. 9-131 

 9.12.3 Side Resistance in Cohesionless Soil............................................. 9-132 

 9.12.3.1 Mobilization of Side Resistance in Cohesionless Soil ..... 9-133 

 9.12.4 Tip Resistance in Cohesionless Soil .............................................. 9-133 

 9.12.4.1 Mobilization of Tip Resistance in Cohesionless Soil....... 9-134 

 9.12.5 Determination of Axial Shaft Capacity in Layered Soils or Soils 

 with Varying Strength with Depth................................................. 9-136 

 9.12.6 Group Action, Group Settlement, Downdrag and Lateral Loads .. 9-136 

 9.12.7 Estimating Axial Capacity of Shafts in Rocks............................... 9-140 

9.12.7.1 Side Resistance in Rocks.................................................. 9-140 

9.12.7.2 Tip Resistance in Rocks ................................................... 9-141 

 9.12.8 Estimating Axial Capacity of Shafts in Intermediate 

 GeoMaterials (IGM’s) ................................................................... 9-142 

9.13 CONSTRUCTION METHODS FOR DRILLED SHAFTS...................... 9-142 

9.14 QUALITY ASSURANCE AND INTEGRITY TESTING OF 

 DRILLED SHAFTS................................................................................... 9-146 

 9.14.1 The Standard Crosshole Sonic Logging (CSL) Test ..................... 9-146 

 9.14.2 The Gamma Density Logging (GDL) Test .................................... 9-149 

 9.14.3 Selecting the Type of Integrity Test for Quality Assurance .......... 9-152 

9.15 STATIC LOAD TESTING FOR DEEP FOUNDATIONS....................... 9-153 

 9.15.1 Reasons for Load Testing .............................................................. 9-153 

 9.15.2 Advantages of Static Load Testing................................................ 9-153 

 9.15.3 When to Load Test ......................................................................... 9-154 

 9.15.4 Effective Use of Load Tests........................................................... 9-156 

9.15.4.1 Design Stage .................................................................... 9-156 

9.15.4.2 Construction Stage ........................................................... 9-156 

 9.15.5 Prerequisites for Load Testing....................................................... 9-157 

 9.15.6 Developing a Static Load Test Program ........................................ 9-158 

 9.15.7 Compression Load Tests................................................................ 9-158 

9.15.7.1 Compression Test Equipment .......................................... 9-160 

 9.15.7.2 Recommended Compression Test Loading Method ........ 9-165 

 9.15.7.3 Presentation and Interpretation of Compression 

 Test Results ...................................................................... 9-165 

 9.15.7.4 Plotting the Failure Criteria ............................................. 9-166 

 9.15.7.5 Determination of the Ultimate (Failure) Load ................. 9-167 

 9.15.7.6 Determination of the Allowable Geotechnical Load ....... 9-168 

9.15.7.7 Load Transfer Evaluations ............................................... 9-168 

 9.15.8 Other Compression Load Tests...................................................... 9-171 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II iv December 2006 
 9.15.8.1 The Osterberg Cell Method ............................................. 9-171 

9.15.8.2 Statnamic Test Method .................................................... 9-176 

 9.15.9 Limitations of Compression Load Tests ........................................ 9-179 

 9.15.10Axial Tension and Lateral Load Tests ........................................... 9-179 

10.0 EARTH RETAINING STRUCTURES .............................................................. 10-1 

10.01 Primary References ...................................................................................... 10-4 

10.1 CLASSIFICATION OF EARTH RETAINING STRUCTURES ............... 10-4 

 10.1.1 Classification by Load Support Mechanism.................................... 10-4 

 10.1.2 Classification by Construction Method ........................................... 10-6 

 10.1.3 Classification by System Rigidity.................................................... 10-7 

 10.1.4 Temporary and Permanent Wall Applications................................. 10-7 

10.1.5 Wall Selection Considerations ......................................................... 10-8 

10.2 LATERAL EARTH PRESSURES .............................................................. 10-8 

 10.2.1 At-Rest Lateral Earth Pressure ...................................................... 10-10 

 10.2.2 Active and Passive Lateral Earth Pressures................................... 10-12 

 10.2.3 Effect of Cohesion on Lateral Earth Pressures .............................. 10-16 

 10.2.4 Effect of Wall Friction and Wall Adhesion on Lateral 

 Earth Pressures............................................................................... 10-16 

 10.2.5 Theoretical Lateral Earth Pressures in Stratified Soils .................. 10-23 

 10.2.6 Semi Empirical Lateral Earth Pressure Diagrams ......................... 10-24 

 10.2.7 Lateral Earth Pressures in Cohesive Backfills............................... 10-24 

10.3 LATERAL PRESSURES DUE TO WATER............................................ 10-27 

10.4 LATERAL PRESSURE FROM SURCHARGE LOADS......................... 10-29 

10.4.1 General........................................................................................... 10-29 

10.4.2 Uniform Surcharge Loads .............................................................. 10-31 

 10.4.3 Point, Line, and Strip Loads .......................................................... 10-31 

10.5 WALL DESIGN ........................................................................................ 10-35 

 10.5.1 Steps 1, 2, and 3 – Established Project Requirements, 

 Subsurface Conditions, Design Parameters ................................... 10-36 

 10.5.2 Step 4 – Select Base Dimension Based on Wall Height ................ 10-37 

 10.5.3 Step 5 – Select Lateral Earth Pressure Distribution....................... 10-37 

 10.5.4 Step 6 – Evaluate Bearing Capacity .............................................. 10-41 

10.5.4.1 Shallow Foundations ........................................................ 10-41 

10.5.4.2 Deep Foundations ............................................................. 10-42 

 10.5.5 Step 7 – Evaluate Overturning and Sliding ................................... 10-43 

 10.5.6 Step 8 – Evaluate Global Stability................................................. 10-44 

 10.5.7 Step 9 – Evaluate Settlement and Tilt............................................ 10-45 

 10.5.8 Step 10 – Design Wall Drainage Systems ..................................... 10-45 

10.5.8.1 Subsurface Drainage......................................................... 10-46 

10.5.8.2 Drainage System Components ......................................... 10-48 

10.5.8.3 Surface Water Runoff....................................................... 10-50 

10.6 EXTERNAL STABILITY ANALYSIS OF A CIP CANTILEVER 

 WALL ........................................................................................................ 10-52 

10.7 CONSTRUCTION INSPECTION .............................................................10.56 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II v December 2006 
11.0 GEOTECHNICAL REPORTS ............................................................................ 11-1 

11.01 Primary References ...................................................................................... 11-1 

11.1 TYPES OF REPORTS................................................................................. 11-1 

 11.1.1 Geotechnical Investigation Reports ................................................. 11-2 

 11.1.2 Geotechnical Design Reports........................................................... 11-3 

 11.1.3 GeoEnvironmental Reports.............................................................. 11-6 

11.2 DATA PRESENTATION............................................................................ 11-7 

 11.2.1 Boring Logs ..................................................................................... 11-7 

 11.2.2 Boring Location Plans ..................................................................... 11-8 

 11.2.3 Subsurface Profiles .......................................................................... 11-9 

11.3 TYPICAL SPECIAL CONTRACT NOTES ............................................. 11-11 

11.4 SUBSURFACE INFORMATION MADE AVAILABLE TO BIDDERS 11-14 

11.5 LIMITATIONS (DISCLAIMERS) ........................................................... 11-15 

12.0 REFERENCES....................................................................................................... 12-1 

APPENDICES 

APPENDIX A: APPLE FREEWAY PROJECT 

APPENDIX B: MOHR’S CIRCLE AND ITS APPLICATIONS IN GEOTECHNICAL 

ENGINEERING 

APPENDIX C: LOAD AND RESISTANCE FACTOR DESIGN (LRFD) 

APPENDIX D: USE OF THE COMPUTER PROGRAM ReSSA 

APPENDIX E: USE OF THE COMPUTER PROGRAM FoSSA 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II vi December 2006 
LIST OF FIGURES 

Figure Caption Page 

8-1 Geometry of a typical shallow foundation (FHWA, 2002c; AASHTO, 2002) ... 8-5 

8-2 Isolated spread footing (FHWA, 2002c).............................................................. 8-5 

8-3 Continuous strip footing (FHWA, 2002c) ........................................................... 8-6 

8-4 Spread footing with cantilever stemwall at bridge abutment .............................. 8-8 

8-5 Abutment/wingwall footing, I-10, Arizona ......................................................... 8-8 

8-6 Footing for a semi-gravity cantilever retaining wall (FHWA, 2002c) ................ 8-9 

8-7 Combined footing (FHWA, 2002c) ................................................................... 8-10 

8-8 Spill-through abutment on combination strip footing (FHWA, 2002c) ............ 8-10 

8-9 Typical mat foundation (FHWA, 2002c) ........................................................... 8-11 

8-10 Shear failure versus settlement considerations in evaluation of allowable 

 bearing capacity ................................................................................................. 8-13 

8-11 Design process flow chart – bridge shallow foundation (modified after 

 FHWA, 2002c)................................................................................................... 8-14 

8-12 Bearing capacity failure of silo foundation (Tschebotarioff, 1951) .................. 8-15 

8-13 Boundaries of zone of plastic equilibrium after failure of soil beneath 

continuous footing (FHWA, 2002c) .................................................................. 8-16 

8-14 Modes of bearing capacity failure (after Vesic, 1975) (a) General shear 

(b) Local shear (c) Punching shear .................................................................... 8-17 

8-15 Bearing capacity factors versus friction angle ................................................... 8-20 

8-16 Notations for footings subjected to eccentric, inclined loads (after Kulhawy, 

1983) .................................................................................................................. 8-25 

8-17 Eccentrically loaded footing with (a) Linearly varying pressure distribution 

(structural design), (b) Equivalent uniform pressure distribution (sizing the 

footing)............................................................................................................... 8-26 

8-18 Modified bearing capacity factors for continuous footing on sloping ground, 

(after Meyerhof, 1957, from AASHTO 2004 with 2006 Interims) ................... 8-31 

8-19 Modes of failure of model footings in sand (after Vesic, 1975, AASHTO 

2004 with 2006 Interims)................................................................................... 8-33 

8-20 Approximate variation of depth (do) and lateral extent (f) of influence of 

footing as a function of internal friction angle of foundation soil ..................... 8-39 

8-21 (a) Simplified vertical strain influence factor distributions, (b) Explanation 

of pressure terms in equation for Izp (after Schmertmann, et al., 1978) ............ 8-46 

8-22 Example allowable bearing capacity chart ........................................................ 8-60 

8-23 Components of settlement and angular distortion in bridges (after 

Duncan and Tan, 1991)...................................................................................... 8-65 

9-1 Situations in which deep foundations may be needed 

(Vesic, 1977; FHWA, 2006a) .............................................................................. 9-2 

9-2 Deep foundations classification system (after FHWA, 2006a) ........................... 9-4 

9-3 Driven pile design and construction process (after FHWA, 2006a) .................... 9-8 

9-4 Typical load transfer profiles (FHWA, 2006a).................................................. 9-24 

9-5 Soil profile for factor of safety discussion (FHWA, 2006a).............................. 9-26 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II vii December 2006 
9-6 Nordlund’s general equation for ultimate pile capacity (after 

 Nordlund, 1979) ................................................................................................. 9-31

9-7 Relationship of δ/φ and pile soil displacement, V, for various types of piles 

(after Nordlund, 1963) ...................................................................................... 9-36 

9-8 Design curves for evaluating Kδ for piles when φ = 25°
 

(after Nordlund, 1963) ...................................................................................... 9-37 

9-9 Design curves for evaluating Kδ for piles when φ = 30°
 

(after Nordlund, 1963) ...................................................................................... 9-38 

9-10 Design curves for evaluating Kδ for piles when φ = 35°
 

(after Nordlund, 1963) ...................................................................................... 9-39 

9-11 Design curves for evaluating Kδ for piles when φ = 40°
 

(after Nordlund, 1963) ...................................................................................... 9-40 

9-12 Correction factor, CF for Kδ when δ ≠ φ (after Nordlund, 1963)....................... 9-41 

9-13 Chart for estimating αt coefficient and bearing capacity factor N′q 

 (FHWA, 2006a) ................................................................................................. 9-44

9-14 Relationship between maximum unit pile toe resistance and friction angle for 

cohesionless soils (after Meyerhof, 1976) ......................................................... 9-45 

9-15 Adhesion values for driven piles in mixed soil profiles, (a) Case 1: piles 

driven through overlying sands or sandy gravels, and (b) Case 2: piles driven 

through overlying weak clay (Tomlinson, 1980)............................................... 9-49 

9-16 Adhesion factors for driven piles in stiff clays without different overlying 

Strata (Case 3) (Tomlinson, 1980)..................................................................... 9-50 

9-17 Chart for estimating β coefficient as a function of soil type φ′
 

(after Fellenius, 1991)........................................................................................ 9-57 

9-18 Chart for estimating Nt coefficients as a function of soil type φ′ angle 

(after Fellenius, 1991)........................................................................................ 9-58 

9-19 Plugging of open end pipe piles (after Paikowsky and Whitmann, 1990) ........ 9-61 

9-20 Plugging of H-piles (FHWA, 2006a) ................................................................. 9-61 

9-21 DRIVEN project definition screen .................................................................... 9-69 

9-22 DRIVEN soil profile screen – cohesive soil...................................................... 9-69 

9-23 DRIVEN cohesive soil layer properties screen ................................................. 9-70 

9-24 DRIVEN soil profile screen – cohesionless soil................................................ 9-70 

9-25 DRIVEN cohesionless soil layer properties screen ........................................... 9-71 

9-26 DRIVEN soil profile screen – Pile type selection drop down menu and pile 

 detail screen ....................................................................................................... 9-71 

9-27 DRIVEN toolbar output and analysis options ................................................... 9-72 

9-28 DRIVEN output tabular screen.......................................................................... 9-73 

9-29 DRIVEN output graphical screen for end of driving......................................... 9-74 

9-30 DRIVEN output graphical screen for restrike ................................................... 9-74 

9-31 Stress zone from single pile and pile group (after Tomlinson, 1994)................ 9-77 

9-32 Overlap of stress zones for friction pile group (after Bowles, 1996) ................ 9-77 

9-33 Measured dissipation of excess pore water pressure in soil surrounding full 

scale pile groups (after O’Neill, 1983) .............................................................. 9-80 

9-34 Three dimensional pile group configuration (after Tomlinson, 1994) .............. 9-81 

9-35 Equivalent footing concept (after Duncan and Buchignani, 1976) ................... 9-85 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II viii December 2006 
9-36 Stress distribution below equivalent footing for pile group (FHWA, 2006a) ... 9-86 

9-37a Common downdrag situation due to fill weight (FHWA, 2006a) ..................... 9-88 

9-37b Common downdrag situation due to ground water lowering (FHWA, 2006a) . 9-88 

9-38 Typical components of a pile driving system .................................................... 9-95 

9-39 Typical components of a helmet ........................................................................ 9-96 

9-40 Hammer-pile-soil system ................................................................................. 9-100 

9-41 Typical Wave Equation models (FHWA, 2006a) ............................................ 9-104 

9-42 Summary of stroke, compressive stress, tensile stress, and driving capacity 

vs. blow count (blows/ft) for air-steam hammer.............................................. 9-107 

9-43 Graph of diesel hammer stroke versus blow count for a constant 

 pile capacity ..................................................................................................... 9-108 

9-44 Suggested trial hammer energy for Wave Equation analysis .......................... 9-109 

9-45 Pile and driving equipment data form.............................................................. 9-113 

9-46 Typical force and velocity traces generated during dynamic measurements .. 9-116 

9-47 Cast-in-Place (CIP) pile design and construction process (modified after 

 FHWA, 2006a)................................................................................................. 9-120 

9-48 Typical drilled shaft and terminology (after FHWA, 1999) ............................ 9-124 

9-49 Portions of drilled shafts not considered in computing ultimate side 

resistance (FHWA, 1999) ................................................................................ 9-129 

9-50 Load-transfer in side resistance versus settlement for drilled shafts in 

cohesive soils (FHWA, 1999).......................................................................... 9-130 

9-51 Load-transfer in tip resistance versus settlement for drilled shafts in 

cohesive soils (FHWA, 1999).......................................................................... 9-132 

9-52 Load-transfer in side resistance versus settlement for drilled shafts in 

cohesionless soils (FHWA, 1999) ................................................................... 9-134 

9-53 Load-transfer in tip resistance versus settlement for drilled shafts in 

cohesionless soils (FHWA, 1999) ................................................................... 9-136 

9-54 Steps in construction of drilled shafts by the dry method (a) drill, (b) clean, 

(c) position concrete cage, (d) place concrete ................................................. 9-143 

9-55 Steps in construction of drilled shafts by the wet method (a) start drilling 

and introduce slurry (bentonite or polymer) in the excavation PRIOR to the 

encountering the known piezometric level, (b) continue drilling with slurry 

in the excavation, (c) clean the excavation and slurry, (d) position 

reinforcement cage, and (e) place concrete by tremie ..................................... 9-144 

9-56 Steps in construction of drilled shafts by the casing method (a) start 

drilling and introduce casing in the excavation PRIOR to encountering 

the known piezometric level and/or caving soil, (b) advance the casing 

through the soils prone to caving, (c) clean the excavation, (d) position 

reinforcement cage, and (e) place concrete and remove the casing if it is 

temporary ......................................................................................................... 9-144 

9-57 Photographs of exhumed shafts (a) shaft where excavation was not 

adequately clean, (b) shaft where excavation was properly cleaned 

 (FHWA, 2002d) ............................................................................................... 9-145 

9-58 Schematic of CSL test (Samtani, et al., 2005)................................................. 9-147 

9-59 Single plot display format for the CSL data for shaft with five tubes 

 (Samtani, et al., 2005)...................................................................................... 9-148 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II ix December 2006 
9-60 Schematic of GDL Test (Samtani, et al., 2005)............................................... 9-150 

9-61 Single plot display format for the GDL data for shaft with four tubes 

 (Samtani, et al., 2005)...................................................................................... 9-151 

9-62 Basic mechanism of a compression pile load test............................................ 9-159 

9-63 Typical arrangement for applying load in an axial compressive test 

 (FHWA, 1992c) ............................................................................................... 9-161 

9-64 Load application and monitoring components (FHWA, 2006a) ..................... 9-162 

9-65 Load test movement monitoring components (FHWA, 2006a)....................... 9-163 

9-66 Typical compression load test arrangement with reaction piles 

 (FHWA, 2006a) ............................................................................................... 9-163 

9-67 Typical compression load test arrangement using a weighted platform 

 (FHWA, 2006a) ............................................................................................... 9-164 

9-68 Presentation of typical static pile load-movement results (a) Davisson’s 

method, (b) Double-tangent method ................................................................ 9-166 

9-69 Example of residual load effects on load transfer evaluation 

 (FHWA, 2006a) ............................................................................................... 9-170 

9-70 Sister bar vibrating wire gages for concrete embedment (FHWA, 2006a) ..... 9-170 

9-71 Are-weldable vibrating wire strain gage attached to H-pile (Note: 

protective channel cover shown on left) (FHWA, 2006a) ............................... 9-171 

9-72 Comparison of reaction mechanism between Osterberg Cell and Static test .. 9-172 

9-73 Some details of the O-cell test (after www.bridgebuildermagazine.com) ........... 9-173 

9-74 Photograph of an O-cell................................................................................... 9-173 

9-75 O-cell assembly attached to a reinforcing cage with other instrumentation.... 9-174 

9-76 Schematic of Statnamic test ............................................................................. 9-177 

9-77 Photograph of Statnamic test arrangement, showing masses being 

accelerated inside gravel-filled sheath ............................................................. 9-177 

10-1 Schematic of a retaining wall and common terminology .................................. 10-1 

10-2 Variety of retaining walls (after O’Rourke and Jones, 1990) ........................... 10-3 

10-3 Classification of earth retaining systems (after O’Rourke and Jones, 1990)..... 10-5 

10-4 Effect of wall movement on wall pressures (after Canadian Foundation 

Engineering Manual, 1992) ............................................................................... 10-9 

10-5 Coulomb coefficients Ka and Kp for sloping wall with wall friction and 

sloping cohesionless backfill (after NAVFAC, 1986b)................................... 10-13 

10-6 (a) Wall Pressures for a cohesionless soil, and (b) Wall pressures for soil 

with a cohesion intercept – with groundwater in both cases (after Padfield 

and Mair, 1984) ............................................................................................... 10-15 

10-7 Wall friction on soil wedges (after Padfield and Mair, 1984) ......................... 10-16 

10-8 Comparison of plane and log-spiral failure surfaces (a) Active case and (b) 

Passive case (after Sokolovski, 1954).............................................................. 10-20 

10-9 Passive coefficients for sloping wall with wall friction and horizontal 

backfill (Caquot and Kerisel, 1948, NAVFAC, 1986b) .................................. 10-21 

10-10 Passive coefficients for vertical wall with wall friction and sloping backfill 

(Caquot and Kerisel, 1948, NAVFAC, 1986b)................................................ 10-22 

10-11 Pressure distribution for stratified soils ........................................................... 10-23 

10-12 Computation of lateral pressures for static groundwater case ......................... 10-27 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II x December 2006 
10-13 (a) Retaining wall with uniform surcharge load and (b) Retaining wall with 

line loads (railway tracks) and point loads (catenary support structure)......... 10-30 

10-14 Lateral pressure due to surcharge loadings (after USS Steel, 1975) ............... 10-32 

10-15 Potential failure mechanisms for rigid gravity and semi-gravity walls ........... 10-35 

10-16 Typical dimensions (a) Cantilever wall, (b) Counterfort wall (Teng, 1962) ... 10-38 

10-17 Design criteria for cast-in-place (CIP) concrete retaining walls (after 

 NAVFAC, 1986b) ............................................................................................ 10-39 

10-18 CIP abutment with integral wingwalls............................................................. 10-40 

10-19 Typical movement of pile-supported cast-in-place (CIP) wall with soft 

foundation ........................................................................................................ 10-42 

10-20 Resistance against sliding from keyed foundation .......................................... 10-43 

10-21 Typical modes of global stability (after Bowles, 1996)................................... 10-44 

10-22 Potential sources of subsurface water.............................................................. 10-46 

10-23 Typical retaining wall drainage alternatives .................................................... 10-47 

10-24 Drains behind backfill in cantilever wall in a cut situation ............................. 10-48 

11-1 Example table of contents for a geotechnical investigation report .................... 11-4 

11-2 Example table of contents for a geotechnical design report .............................. 11-5 

11-3 Example boring location plan for retaining walls RW-11 and RW-12 

 retaining an on-ramp to a freeway ..................................................................... 11-9 

11-4 Subsurface profile along the baseline between retaining walls RW-11 and 

RW-12 shown in Figure 11-3 .......................................................................... 11-10 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II xi December 2006 
LIST OF TABLES 

No. Caption Page 

8-1 Estimation of friction angle of cohesionless soils from Standard Penetration 

Tests (after AASHTO, 2004 with 2006 Interims, FHWA, 2002c) .................... 8-19 

8-2 Bearing Capacity Factors (AASHTO, 2004 with 2006 Interims) ..................... 8-20 

8-3 Variation in bearing capacity with changes in physical properties or 

 dimensions ......................................................................................................... 8-23 

8-4 Shape correction factors (AASHTO, 2004 with 2006 Interims) ....................... 8-27 

8-5 Correction factor for location of ground water table 

(AASHTO 2004 with 2006 Interims) ................................................................ 8-27 

8-6 Depth correction factors (Hansen and Inan, 1970; AASHTO, 2004 with 2006 

Interims) ............................................................................................................. 8-28 

8-7 Inclined base correction factors (Hansen and Inan, 1970; AASHTO, 

2004 with 2006 Interims)................................................................................... 8-29 

8-8 Allowable bearing pressures for fresh rock of various types 

 (Goodman, 1989) ............................................................................................... 8-42 

8-9 Presumptive values of allowable bearing pressures for spread foundations 

on rock (modified after NAVFAC, 1986a, AASHTO 2004 with 2006 

 Interims) ............................................................................................................. 8-43 

8-10 Suggested values of allowable bearing capacity (Peck, et al., 1974) ................ 8-43 

8-11 Values of parameters used in settlement analysis by Schmertmann’s method.. 8-53 

8-12 Typical specification of compacted structural fill used by WSDOT (FHWA, 

2002c) ................................................................................................................ 8-57 

8-13 Shape and rigidity factors, Cd, for calculating settlements of points on 

loaded areas at the surface of a semi-infinite elastic half space (after 

Winterkorn and Fang, 1975) .............................................................................. 8-59 

8-14 Tolerable movement criteria for bridges 

(FHWA, 1985; AASHTO, 2002, 2004) ............................................................. 8-68 

8-15 Example of settlements evaluated at various critical construction points ......... 8-71 

8-16 Inspector responsibilities for construction of shallow foundations ................... 8-74 

9-1 Pile type selection based on subsurface and hydraulic conditions ...................... 9-6 

9-2 Typical piles and their range of loads and lengths............................................. 9-18 

9-3 Pile type selection pile shape effects ................................................................. 9-19 

9-4 Cost savings recommendations for pile foundations (FHWA, 2006a) .............. 9-21 

9-5 Recommended factor of safety based on construction control method ............. 9-25 

9-6a Design table for evaluating Kδ for piles when ω = 0° and V = 0.10 to 

1.00 ft3/ft (FHWA, 2006a) ................................................................................. 9-42 

9-6b Design table for evaluating Kδ for piles when ω = 0° and V = 1.0 to 

10.0 ft3

/ft (FHWA, 2006a) ................................................................................. 9-43 

9-7 Approximate range of β and Nt coefficients (Fellenius, 1991).......................... 9-53 

9-8 Soil setup factors (after FHWA, 1996) .............................................................. 9-65 

9-9 Responsibilities of design and construction engineers ...................................... 9-92 

9-10 Summary of example results from wave equation analysis ............................. 9-106 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II xii December 2006 
9-11 Maximum allowable stresses in pile for top driven piles 

(after AASHTO, 2002, FHWA, 2006a) ........................................................... 9-110 

9-12 Osterberg cells for drilled shafts ...................................................................... 9-174 

9-13 Osterberg cells for driven piles ........................................................................ 9-174 

10-1 Wall friction and adhesion for dissimilar materials (after NAVFAC, 1986b) 10-18 

10-2 Design steps for gravity and semi-gravity walls.............................................. 10-36 

10-3 Suggested gradation for backfill for cantilever semi-gravity and gravity 

 retaining walls .................................................................................................. 10-37 

10-4 Inspector responsibilities for a typical CIP gravity and semi-gravity wall 

project .............................................................................................................. 10-56 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II xiii December 2006 
LIST OF SYMBOLS 

Chapter 8 

A Angular distortion 

A' Effective footing area 

AASHTO American Association of State Highway and Transportation Officials 

ASD Allowable stress design 

B Width 

B'f Effective footing width 

bc, bγ, bq Base inclination correction factors 

Bf Footing width 

Bf* Modified footing width for bearing capacity analysis of footings on sands 

c Cohesion of soil 

c* Reduced effective cohesion for punching shear 

C1 Correction factor for embedment depth 

C2 Correction factor for time-dependent settlement increase 

Cc Compression indices 

Cd Shape and rigidity factors 

Cwγ, Cwq Groundwater correction factors 

Df Depth of embedment 

DI Maximum depth of strain influence 

DIP Depth to maximum strain influence factor 

DL Dead load 

do Depth of influence of footing 

DOSI Depth of Significant Influence 

dq Embedment depth correction factor 

Dr Relative density of sand 

Dw Depth of water table 

E Elastic modulus of soil 

eB Eccentricity in direction of footing width 

eL Eccentricity in direction of footing length 

Em Young’s modulus of rock mass 

eo Initial void ratio 

f Lateral extent of influence of footing 

FD Foundation design specialist 

FHWA Federal Highway Administration 

FS Factor of safety 

ft Foot 

GT Geotechnical specialist 

Hc Thickness of soil layer considered 

IGM Intermediate geomaterial 

Iz Strain influence factor 

IZB Strain influence factor at footing elevation 

IZP Maximum strain influence factor 

kPa Kilopascal 

L Length 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II xiv December 2006 
L'f	 Effective footing length 

Lf Footing length 

LL Live load 

LRFD Load resistance factor design 

MPa Megapascal 

MSE Mechanically stabilized earth 

n Number of soil layers 

N SPT blow count value 

N160	  SPT blow count corrected for depth and hammer efficiency 

Nc, Nq, Nγ	 Bearing capacity factors 

Ncq, Nγq Bearing capacity factors modified for sloping ground surface 

Ns	 Slope stability factor 

OCR Overconsolidation ratio 

P Applied footing load 

po	  Effective overburden pressure 

pop	 effective stress at depth of peak strain influence factor 

psf Pounds per square foot 

q Uniform surcharge pressure at the base of the footing 

qall Allowable bearing capacity 

qeq	 Equivalent uniform bearing pressure 

qmax	 Maximum bearing pressure under the footing 

qmin	 Minimum bearing pressure under the footing 

qult gross	 Gross ultimate bearing capacity 

qult net 	 Net ultimate bearing capacity 

qult	 Ultimate bearing capacity 

RQD Rock quality designation 

S Settlement 

S, 2S, 3S Settlement contours 

sc, sq, sγ	 Shape correction factors 

Si	  Settlement of i-th soil layer 

SL Distance between adjacent foundations (span length) 

SLS Serviceability limit state 

St Sensitivity of clay 

ST Structural specialist 

t time 

tsf Tons per square foot 

ULS Ultimate limit state 

X Modification factor for determination of elastic modulus 

zi	 

 Depth to soil layer i 

α	 Footing inclination from horizontal 

γ 	 Unit weight of soil 

γ'	 Effective unit weight of soil 

γa Unit weight of soil above the footing 

γb Submerged unit weight of soil 

δ Differential settlement 

δv	  Vertical settlement at surface 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II xv December 2006 
∆H Consolidation settlement 

∆Hi Settlement factor for soil layer i 

∆p Net load intensity at foundation depth 

ν Poisson’s ratio 

φ Angle of internal friction 

φ* Reduced effective soil friction angle for punching shear 

φ' Effective angle of internal friction 

Chapter 9 

A Cross-sectional area of the pile 

AASHTO American Association of State Highway and Transportation Officials 

Ap	  Cross-sectional area of an unplugged pile 

API American Petroleum Institute 

as	  Acceleration of the drilled corresponding to Fso 

As	  Shaft surface area 

ASD Allowable stress design 

Asi	 Pile interior surface area 

ASTM American Society for Testing and Materials 

At	  Pile toe area 

At	  Tip area of rock socket 

b Pile diameter or width 

B Width of the pile group 

BPF Blows per foot 

C Wave propagation velocity of pile material 

ca 	 Pile adhesion 

Cd	 

 Pile perimeter at depth d 

CF	  Correction factor for Kδ when δ ≠ φ

CIDH Cast-in-drilled hole 

CIP Cast-in-place 

COR Coefficient of restitution 

cps counts per second 

CPT Cone penetration test 

CSL Cross-hole sonic logging 

CSLT Cross-hole sonic logging tomography 

cu	 

 Average undrained shear strength 

cu1	 Weighted average of the undrained shear strength over the depth of pile 

embedment for the cohesive soils along the pile group perimeter 

cu2	 Average undrained shear strength of the cohesive soils at the base of the pile 

group to a depth of 2B below pile toe level 

D Pile embedment length 

d Center to center distance 

d Depth 

D Diameter of the shaft 

D Distance from ground surface to bottom of clay layer or pile toe 

DR	  Diameter of rock socket 

E Modulus of elasticity of pile material 

FHWA NHI-06-089 Table of Contents 

Soils and Foundations – Volume II xvi December 2006 
Ei	 

 Intact rock modulus 

Em	 Rock mass modulus 

En Driving energy 

EN Engineering News 

Er	 Manufacturer’s rated hammer energy 

f'c	 28-day compressive strength of concrete 

FHWA 	 Federal Highway Administration 

fpe 	 Pile prestress 

FS Factor of safety 

fs	 

 Unit shaft resistance 

fsi Interior unit shaft resistance 

fsi	 Ultimate unit load transfer in side resistance 

fso	  Exterior unit shaft resistance 

Fso	  Force measured by the load cell at the point at which the slope of the rebound 

curve is zero 

fso	 

 Ultimate unit shaft resistance 

fy	 Yield stress of steel 

g Acceleration of gravity 

GDL Gamma-gamma density logging 

H Distance of ram fall 

If	  Influence factor for group embedment 

IGM Intermediate geomaterial 

IR Impulse response 

k Constant which varies from 0.1 to 1 based on hammer type 

Ks	  Earth pressure coefficient 

Kδ	  Coefficient of lateral earth pressure at depth d 

L Effective length of the pile 

LR	  Length of rock socket 

LRFD Load and resistance factor design 

LVDT Linear variable displacement transducer 

M Mean 

n Number of piles in group 

N Number of layers used in the analysis 

N SPT blows per foot 

N′	 SPT value corrected for overburden pressure 

N′q Bearing capacity factor 

N' Average corrected SPT N160 value within depth B below pile toe 

N1	 Average corrected SPT N160 for each soil layer 

N1 Overburden corrected blowcount 

N160	 Overburden-normalized energy-corrected blowcount 

N60	 Energy-corrected SPT-N value adjusted to 60% efficiency 

Nb	 

 Number of hammer blows per 1 inch final penetration 

Nc	 Bearing capacity factor 

NCHRP National Cooperative of Highway Research Program 

NDT Non-destructive test 

NML Neutron moisture logging 

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Soils and Foundations – Volume II xvii December 2006 
Nt	 

 Toe bearing capacity coefficient 

P Safe pile load 

pa	 Atmospheric pressure (2.12ksf or 101kPa) 

pd Average effective overburden pressure at the midpoint of each soil layer 

pd Effective overburden pressure at the center of depth increment ∆d 

PDA Pile driving analyzer 

pf Design foundation pressure 

po Effective overburden pressure 

po	 

 Effective overburden stress at depth zi 

PSL Perimeter sonic logging 

pt Effective overburden pressure at the pile toe 

PVC Polyvinyl chloride 

Q Test load 

Qa	 Allowable geotechnical soil resistance 

Qa 	 Design load 

QA Quality assurance 

Qavg	 

 Average load in the pile 

Qh	 

 Applied Pile Head Load 

Qs	 

 Ultimate skin capacity 

Qsr	 Ultimate side resistance in rock 

qSR	 

 Unit skin resistance of rock 

Qt	 

 Ultimate tip (base or end) capacity 

qL	 Limiting unit toe resistance 

qt	 Unit toe resistance or unit end bearing 

Qtr	 Ultimate tip resistance in rock 

qtr	 Unit tip resistance of rock 

Qu	 

 Ultimate geotechnical pile capacity or ultimate axial load or ultimate pile 

capacity 

qu	 

 Uniaxial compressive strength of rock 

Qu Ultimate capacity of each individual pile in the pile group 

Qug	 Ultimate capacity of the pile group 

Qult	 Ultimate axial capacity 

R Total soil resistance against the pile 

R1, R2	 

 Deflection readings at measuring points 

RQD Rock quality designation 

Rs	 

 Total skin resistance 

Rs	 

 Ultimate shaft resistance 

Rs1, Rs2, Rs3	 Resistance in different soil layers 

Rt 	 Total toe resistance 

Rt 	 Ultimate toe resistance 

Rt (max) Maximum ultimate toe resistance 

Rt	 Estimated toe resistance 

Rt	 Pile toe resistance 

RT	 Total static resistance of the drilled shaft 

Ru Ultimate pile capacity 

Rult	 Delivered hammer energy for an assigned driving soil resistance 

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Soils and Foundations – Volume II xviii December 2006 
s Estimated total settlement 

S Pile penetration per blow 

SD Standard deviation 

SE Sonic echo 

sf Settlement at failure 

SPT Standard penetration test 

SRD Soil resistance to driving 

sui Undrained shear strength in a layer ∆zi 

sut Undrained shear strength of the soil at the tip of the shaft 

su Undrained shear strength 

TL Temperature logging 

TTI Texas Transportation Institute 

uk Hydrostatic pore water pressure 

US Ultra-seismic 

us Excess pore water pressure 

V Computed velocity 

V Volume per foot for pile segment 

VC Theoretical compression wave velocity in concrete 

VR Velocity reductions 

W Weight of pile 

W Weight of ram 

W Weight of shaft 

WEA Wave equation analysis 

wp Weight of the plug 

Ws Total weight of the drilled shaft 

WSDOT Washington State Department of Transportation 

z Depth of the penetration 

Z Length of the pile group 

z Depth to the center of the ith

i layer 

αi Adhesion factor in a layer ∆zi 

αt Dimensionless factor dependent on pile depth-width relationship 

δ Interface friction angle between pile and soil 

ηg Pile group efficiency 

Ψ Ratio of undrained shear strength of soil to effective overburden pressure 

∆ Elastic deformation 

∆d Length if pile segment 

∆L Elastic shortening of the pile 

∆L Length of pile between two measured points under no load condition 

∆z Thickness if layer i 

α Adhesion factor 

αE Reduction factor to account for jointing in rock 

β Bjerrum-Burland beta coefficient 

φ' Effective soil friction angle 

φ Soil friction angle 

γ' i Effective unit weight of the ith layer 

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Soils and Foundations – Volume II xix December 2006 
σa AASHTO allowable working stress 

ω Angle of pile taper measured from the vertical 

Chapter 10 

AASHTO American Association of State Highway and Transportation Officials 

ASTM American Society for Testing and Materials 

B Base width 

c' Effective cohesion 

ca adhesion between concrete and soil 

CIP Cast-in-place 

cw Wall adhesion 

e Eccentricity 

ERS Earth retaining structures 

FHWA Federal Highway Administration 

FSbc Factor of safety against bearing capacity failure 

FSs Factor of safety against sliding 

H Height of retaining wall 

hw Distance from ground surface to water table 

K Ratio of horizontal to vertical stress 

Ka Coefficient of active earth pressure 

Kac Coefficient of active earth pressure adjusted for wall adhesion 

Ko Coefficient of lateral earth pressure “at rest” 

Kp Coefficient of passive earth pressure 

Kpc Coefficient of passive earth pressure adjusted for wall adhesion 

m Coefficient to relate wall height to distance of load from retaining wall 

n Coefficient to relate wall height to depth from ground surface 

MSE Mechanically stabilized earth 

OCR Over consolidation ratio 

p0 Vertical pressure at a given depth 

pa ' Active effective pressure 

ph Lateral earth pressure at a given depth 

pp' Passive effective pressure 

q, qs Vertical surcharge load 

Q1, Q2,Qp Surcharge loads 

qeq Equivalent uniform bearing pressure 

qmax Maximum bearing pressure 

qmin Minimum bearing pressure 

SOE Support of excavation 

u Pore water pressure 

W Weight at base of wall 

Y Horizontal deformation of retaining wall 

z Depth from surface 

zw Depth from water table 

β Angle of slope 

θ Slope of wall backface 

Ω Dimensionless coefficient 

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Soils and Foundations – Volume II xx December 2006 
 

 

 

 

 

 

 

∆ph Increase in lateral earth pressure due to vertical surcharge 

δ Wall friction 

δb friction angle between soil and base 

γ' Effective soil unit weight 

γ Soil unit weight 

γsat Saturated soil unit weight 

γw Unit weight of water 

φ Angle of internal friction of soil 

φ' Effective (drained) friction angle 

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Soils and Foundations – Volume II xxi December 2006 
[THIS PAGE INTENTIONALLY BLANK] 
CHAPTER 8.0 

SHALLOW FOUNDATIONS 

Foundation design is required for all structures to ensure that the loads imposed on the 

underlying soil will not cause shear failures or damaging settlements. The two major types 

of foundations used for transportation structures can be categorized as “shallow” and “deep” 

foundations. This chapter first discusses the general approach to foundation design including 

consideration of alternative foundations to select the most cost-effective foundation. 

Following the general discussion, the chapter then concentrates on the topic of shallow 

foundations. 

8.01 Primary References: 

The two primary references for shallow foundations are: 

FHWA (2002c). Geotechnical Engineering Circular 6 (GEC 6), Shallow Foundations. 

Report No. FHWA-SA-02-054, Author: Kimmerling, R. E., Federal Highway 

Administration, U.S. Department of Transportation. 

AASHTO (2004 with 2006 Interims). AASHTO LRFD Bridge Design Specifications, 3rd 

Edition, American Association of State Highway and Transportation Officials, Washington, 

D.C. 

8.1 GENERAL APPROACH TO FOUNDATION DESIGN 

The duty of the foundation design specialist is to establish the most economical design that 

safely conforms to prescribed structural criteria and properly accounts for the intended 

function of the structure. Essential to the foundation engineer’s study is a rational method of 

design, whereby various foundation types are systematically evaluated and the optimum 

alternative selected. The following foundation design approach is recommended: 

1. Determine the direction, type and magnitude of foundation loads to be supported, 

tolerable deformations and special constraints such as: 

a. Underclearance requirements that limit allowable total settlement. 

b. Structure type and span length that limits allowable deformations 

and angular distortions. 

c. Time constraints on construction. 

d. Extreme event loading and construction load requirements. 

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Soils and Foundations – Volume II 8 - 1 December 2006 
 In general, a discussion with the structural engineer about a preliminary design will 

provide this information and an indication of the flexibility of the constraints. 

2. Evaluate the subsurface investigation and laboratory testing data with regard to 

reliability and completeness. The design method chosen should be commensurate 

with the quality and quantity of available geotechnical data, i.e., don't use stateof-the-art computerized analyses if you have not performed a comprehensive 

subsurface investigation to obtain reliable values of the required input 

parameters. 

3. Consider alternate foundation types where applicable as discussed below. 

8.1.1 Foundation Alternatives and Cost Evaluation 

As noted earlier, the two major alternate foundation types are the “shallow” and “deep” 

foundations. Shallow foundations are discussed in this chapter. Deep foundation 

alternatives including piles and drilled shafts are discussed in the next chapter. Proprietary 

foundation systems should not be excluded as they may be the most economical alternative 

in a given set of conditions. Cost analyses of all feasible alternatives may lead to the 

elimination of some foundations that were otherwise qualified under the engineering study. 

Other factors that must be considered in the final foundation selection are the availability of 

materials and equipment, the qualifications and experience of local contractors and 

construction companies, as well as environmental limitations/considerations on construction 

access or activities. 

Whether it is for shallow or deep foundations, it is recommended that foundation support cost 

be defined as the total cost of the foundation system divided by the load the foundation 

supports in tons. Thus, the cost of the foundation system should be expressed in terms of 

dollars per ton load that will be supported. For an equitable comparison, the total 

foundation cost should include all costs associated with a given foundation system including 

the need for excavation or retention systems, environmental restrictions on construction 

activities, e.g., vibrations, noise, disposal of contaminated excavated spoils, pile caps and cap 

size, etc. For major projects, if the estimated costs of alternative foundation systems during 

the design stage are within 15 percent of each other, then alternate foundation designs should 

be considered for inclusion in contract documents. If alternate designs are included in the 

contract documents, both designs should be adequately detailed. For example, if two pile 

foundation alternatives are detailed, the bid quantity pile lengths should reflect the estimated 

pile lengths for each alternative. Otherwise, material costs and not the installed foundation 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 2 December 2006 
cost will likely determine the low bid. Use of alternate foundation designs will generally 

provide the most cost effective foundation system. 

A conventional design alternate should generally be included with a proprietary design 

alternate in the final project documents to stimulate competition and to anticipate value 

engineered proposals from contractors. 

8.1.2 Loads and Limit States for Foundation Design 

Foundations should be proportioned to withstand all anticipated loads safely including the 

permanent loads of the structure and transient loads. Most design codes specify the types of 

loads and load combinations to be considered in foundation design, e.g., AASHTO (2002). 

These load combinations can be used to identify the “limit” states for the foundation types 

being considered. A limit state is reached when the structure no longer fulfills its 

performance requirements. There are several types of limit states that are related to 

maximum load-carrying capacity, serviceability, extreme event and fatigue. Two of the more 

common limit states are as follows: 

•	 An ultimate limit state (ULS) corresponds to the maximum load-carrying capacity 

of the foundation. This limit state may be reached through either structural or 

geotechnical failure. An ultimate limit state corresponds to collapse. The ultimate 

state is also called the strength limit state and includes the following failure modes 

for shallow foundations: 

o	 bearing capacity of soil exceeded, 

o	 excessive loss of contact, i.e., eccentricity, 

o	 sliding at the base of footing, 

o	 loss of overall stability, i.e.,, global stability, 

o	 structural capacity exceeded. 

•	 A serviceability limit state (SLS) corresponds to loss of serviceability, and occurs 

before collapse. A serviceability limit state involves unacceptable deformations or 

undesirable damage levels. A serviceability limit state may be reached through the 

following mechanisms: 

o	 Excessive differential or total foundation settlements, 

o	 Excessive lateral displacements, or 

o	 Structural deterioration of the foundation. 

 

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Soils and Foundations – Volume II 8 - 3 December 2006 
 The serviceability limit state for transportation structures is based upon economy and 

the quality of ride. The cost of limiting foundation movements should be compared 

to the cost of designing the superstructure so that it can tolerate larger movements, or 

of correcting the consequences of movements through maintenance, to determine 

minimum life cycle cost. More stringent criteria may be established by the owner. 

All relevant limit states must be considered in foundation design to ensure an adequate 

degree of safety and serviceability. Therefore, all foundation design is geared towards 

addressing the ULS and the SLS. In this manual, the allowable stress design (ASD) 

approach is used. Further discussion on ASD and other design methods such as the Load and 

Resistance Factor Design (LRFD) can be found in Appendix C. 

8.2 TYPES OF SHALLOW FOUNDATIONS 

The geometry of a typical shallow foundation is shown in Figure 8-1. Shallow foundations 

are those wherein the depth, Df, of the foundation is small compared to the cross-sectional 

size (width, Bf, or length, Lf). This is in contradistinction to deep foundations, such as driven 

piles and drilled shafts, whose depth of embedment is considerably larger than the crosssection dimension (diameter). The exact definition of shallow or deep foundations is less 

important than an understanding of the theoretical assumptions behind the various design 

procedures for each type. Stated another way, it is important to recognize the theoretical 

limitations of a design procedure that may vary as a function of depth, such as a bearing 

capacity equation. Common types of shallow foundations are shown in Figures 8-2 through 

8-9. 

8.2.1 Isolated Spread Footings 

Footings with Lf/Bf ratio less than 10 are considered to be isolated footings. Isolated spread 

footings (Figure 8-2) are designed to distribute the concentrated loads delivered by a single 

column to prevent shear failure of the soil beneath the footing. The size of the footing is a 

function of the loads distributed by the supported column and the strength and 

compressibility characteristics of the bearing materials beneath the footing. For bridge 

columns, isolated spread footings are typically greater than 10 ft by 10 ft (3 m by 3 m). 

These dimensions increase when eccentric loads are applied to the footing. Structural design 

of the isolated footing includes consideration for moment resistance at the face of the column 

in the short direction of the footing, as well as shear and punching around the column. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 4 December 2006 
Lf 

Df 

Bf 

Figure 8-1. Geometry of a typical shallow foundation (FHWA, 2002c, AASHTO 2002). 

Figure 8-2. Isolated spread footing (FHWA, 2002c). 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 5 December 2006 
8.2.2 Continuous or Strip Footings 

The most commonly used type of foundation for buildings is the continuous strip footing 

(Figure 8-3). For computation purposes, footings with an Lf/Bf ratio ≥ 10 are considered to 

be continuous or strip footings. Strip footings typically support a single row of columns or a 

bearing wall to reduce the pressure on the bearing materials. Strip footings may tie columns 

together in one direction. Sizing and structural design considerations are similar to those for 

isolated spread footings with the exception that plane strain conditions are assumed to exist 

in the direction parallel to the long axis of the footing. This assumption affects the depth of 

significant influence (DOSI), i.e., the depth to which applied stresses are significantly felt in 

the soil. For example, in contrast with isolated footing where the DOSI is between 2 to 4 

times the footing width, the DOSI in the case of the strip footings will always be at least 4 

times the width of the footing as discussed in Section 2.4.1 of Chapter 2. The structural 

design of strip footings is generally governed by beam shear and bending moments. 

Figure 8-3. Continuous strip footing (FHWA, 2002c). 

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Soils and Foundations – Volume II 8 - 6 December 2006 
8.2.3 Spread Footings with Cantilevered Stemwalls 

An earth retaining system consisting of a spread footing supporting a cantilevered retaining 

wall is frequently used to resist lateral loads applied by a backfill and other external loads 

that may be acting on top of the backfill (refer to Figures 8-4 and 8-5). The system must 

offer resistance to both vertical and horizontal loads as well as to overturning moments. The 

spread footing is designed to resist overturning moments and vertical eccentric loads caused 

by the lateral earth pressures and the horizontal components of the externally applied loads 

acting on the cantilever stemwall. The wall itself is designed as a simple cantilevered 

structure to resist the lateral earth pressures imposed by the backfill and other external loads 

that may be applied on top of the backfill. 

8.2.4 Bridge Abutments 

Bridge abutments are required to perform numerous functions, including the following: 

•	 Retain the earthen backfill behind the abutment. 

•	 Support the superstructure and distribute the loads to the bearing materials below the 

spread footing, assuming that a spread footing is the foundation system chosen for the 

abutment. 

•	 Provide a transition from the approach embankment to the bridge deck. 

•	 Depending on the structure type, accommodate shrinkage and temperature 

movements within the superstructure. 

Spread footings with cantilevered stemwalls are well suited to perform these multiple 

functions. The general arrangement of a bridge abutment with a spread footing and a 

cantilevered stemwall is shown in Figures 8-4 and 8-5. In the case of weak soils at shallow 

depths, deep foundations, such as drilled shafts or driven piles, are often used to support the 

abutment. There are several other abutment types such as those that use mechanically 

stabilized earth (MSE) walls with spread foundations on top or with deep foundation 

penetrating through the MSE walls. Several different types of bridge abutments are shown in 

Figure 7-2 in Chapter 7. 

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Soils and Foundations – Volume II 8 - 7 December 2006 
Figure 8-4. Spread footing with cantilever stemwall at bridge abutment. 

Figure 8-5. Abutment/wingwall footing, I-10, Arizona. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 8 December 2006 
8.2.5 Retaining Structures 

The foundations for semi-gravity concrete cantilever retaining walls (inverted “T” walls) are 

essentially shallow spread footings. The wall derives its ability to resist loads from a 

combination of the dead weight of the backfill on the heel of the wall footing and the 

structural cantilever of the stem (Figure 8-6). 

Figure 8-6. Footing for a semi-gravity cantilever retaining wall (FHWA, 2002c). 

8.2.6 Building Foundations 

When a building stemwall is buried, partially buried or acts as a basement wall, the stemwall 

resists the lateral earth pressures of the backfill. Unlike bridge abutments where the bridge 

structure is usually free to move horizontally on the abutment or the semi-gravity cantilever 

wall, the tops or the ends of the stemwalls in buildings are frequently restrained by other 

structural members such as beams, floors, transverse interior walls, etc. These structural 

members provide lateral restraint that affects the magnitude of the design lateral earth 

pressures 

8.2.7 Combined Footings 

Combined footings are similar to isolated spread footings except that they support two or 

more columns and are rectangular or trapezoidal in shape (Figure 8-7). They are used 

primarily when the column spacing is non-uniform (Bowles, 1996) or when isolated spread 

footings become so closely spaced that a combination footing is simpler to form and 

construct. In the case of bridge abutments, an example of a combined footing is the so-called 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 9 December 2006 
“spill-through” type abutment (Figure 8-8). This configuration was used during some of the 

initial construction of the Interstate Highway System on new alignments where spread 

footings could be founded on competent native soils. Spill-through abutments are also used 

at stream crossings to make sure that foundations are below the scour depth of the stream. 

Figure 8-7. Combined footing (FHWA, 2002c). 

2 

1 

Original Ground 

Abutment Fill 

Toe of Side Slope 

Toe of End Slope 

Figure 8-8. Spill-through abutment on combination strip footing (FHWA, 2002c). 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 10 December 2006 
Due to the frame action that develops with combined footings, they can be used to resist 

large overturning or rotational moments in the longitudinal direction of the column row. 

There are a number of approaches for designing and constructing combined footings. The 

choice depends on the available space, load distribution among the columns supported by the 

footing, variations of soil properties supporting the footing, and economics. 

8.2.8 Mat Foundations 

A mat foundation consists of a single heavily reinforced concrete slab that underlies the 

entire structure or a major portion of the structure. Mat foundations are often economical 

when spread footings would cover more than about 50 percent of the plan area of the 

structure’s footprint (Peck, et al., 1974). A mat foundation (Figure 8-9) typically supports a 

number of columns and/or walls in either direction or a uniformly distributed load such as 

that imposed by a storage tank. The principal advantage of a mat foundation is its ability to 

bridge over local soft spots, and to reduce differential movement. 

Structures founded on relatively weak soils may be supported economically on mat 

foundations. Column and wall loads are transferred to the foundation soils through the mat 

foundation. Mat foundations distribute the loads over a large area, thus reducing the 

intensity of contact pressures. Mat foundations are designed with sufficient reinforcement 

and thickness to be rigid enough to distribute column and wall loads uniformly. Although 

differential settlements may be minimized by the use of mat foundations, greater uniform 

settlements may occur because the zone of influence of the applied stress may extend to 

considerable depth due to the larger dimensions of the mat. Often a mat also serves as the 

base floor level of building structures. 

REINFORCED CONCRETE MAT 

Figure 8-9. Typical mat foundation (FHWA, 2002c). 

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Soils and Foundations – Volume II 8 - 11 December 2006 
Mat foundations have limited applicability for bridge support, except where large bridge 

piers, such as bascules or other movable bridge supports, bear at relatively shallow depth 

without deep foundation support. This type of application may arguably be a deep 

foundation, but the design of such a pier may include consideration of the base of the bascule 

pier as a mat. Discussion of mat foundation design is included in FHWA (2002c). 

A more common application of mat foundations for transportation structures includes lightly 

loaded rest area or maintenance facilities such as small masonry block structures, sand 

storage bins or sheds, or box culverts constructed as a continuous structure. 

8.3 SPREAD FOOTING DESIGN CONCEPT AND PROCEDURE 

The geotechnical design of a spread footing is a two-part process. First the allowable soil 

bearing capacity must be established to ensure stability of the foundation and determine if the 

proposed structural loads can be supported on a reasonably sized foundation. Second, the 

amount of settlement due to the actual structural loads must be predicted and the time of 

occurrence estimated. Experience has shown that settlement is usually the controlling factor 

in the decision to use a spread footing. This is not surprising since structural considerations 

usually limit tolerable settlements to values that can be achieved only on competent soils not 

prone to a bearing capacity failure. Thus, the allowable bearing capacity of a spread 

footing is defined as the lesser of: 

•	 The applied stress that results in a shear failure divided by a suitable factor of safety (FS); 

this is a criterion based on an ultimate limit state (ULS) as discussed previously. 

or 

•	 The applied stress that results in a specified amount of settlement; this is a criterion based 

on a serviceability limit state (SLS) as discussed previously. 

Both of the above considerations are a function of the least lateral dimension of the footing, 

typically called the footing width and designated as Bf as shown in Figure 8-1. The effect of 

footing width on allowable bearing capacity and settlement is shown conceptually in Figure 

8-10. The allowable bearing capacity of a footing is usually controlled by shear-failure 

considerations for narrow footing widths as shown in Zone A in Figure 8-10. As the footing 

width increases, the allowable bearing capacity is limited by the settlement potential of the 

soils supporting the footing within the DOSI which is a function of the footing width as 

discussed in Section 2.4 of Chapter 2. Stated another way, as the footing width increases, the 

stress increase “felt” by the soil may decrease but the effect of the applied stress will extend 

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Soils and Foundations – Volume II 8 - 12 December 2006 
 

Allowable bearing capacity line based on 

ultimate limit state consideration (i.e., no 

consideration of settlement), qall = qult/FS

Allowable Bearing Capacity, ksf (kPa)

Contours of allowable 

bearing capacity for a 

given settlement 

3S 

2S 

S 

ZONE B 

Settlement Controls 

ZONE A 

Shear Controls Settlement 

values 

Effective Footing Width, ft (m) 

Figure 8-10. Shear failure versus settlement considerations in evaluation of allowable 

bearing capacity. 

more deeply below the footing base. Therefore, settlements may increase depending on the 

type of soils within the DOSI. This is schematically shown in Zone B in Figure 8-10. 

The concept of decreasing allowable bearing capacity with increasing footing width for the 

settlement controlled cases is an important concept to understand. In such cases, the 

allowable bearing capacity is the value of the applied stress at the footing base that will result 

in a given settlement. Since the DOSI increases with increasing footing width, the only way 

to limit the settlements to a certain desired value is by reducing the applied stress. The more 

stringent the settlement criterion the less the stress that can be applied to the footing which in 

turn means that the allowable bearing capacity is correspondingly less. This is conceptually 

illustrated in Figure 8-10 wherein it is shown that decreasing the settlement, i.e., going from 

3S to 2S to S decreases the allowable bearing capacity at a given footing width. An example 

of the use of the chart is presented in Section 8.8. 

The design process flow chart for a bridge supported on spread footings is shown in Figure 

8-11. In the flow chart, the foundation design specialist is a person with the skills necessary 

to address both geotechnical and structural design. Section 8.4 discusses the bearing 

capacity aspects while Section 8.5 discusses the settlement aspects of shallow foundation 

design. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 13 December 2006 
 

 

 

 

 

 

 

 

 

 

1. Develop preliminary layout of a 

bridge (ST) 

2. Review existing geologic and 

subsurface data (GT) 

3. Field reconnaissance (GT) 

4. Determine depth of footing for 

scour and frost protection 

(Hydraulic, GT) 

6. Subsurface exploration and 

laboratory testing (GT) 

7. Calculate allowable bearing 

capacity based on shear and 

settlement considerations (GT/FD) 

9. Check overall (global) stability 

by using service (unfactored) loads 

(GT/FD) 

11. Check stability of footing for 

overturning and sliding (ST/FD) 

5. Determine loads applied to the 

footing (ST) 

10. Size the footing by using service 

(unfactored) loads (ST/FD) 

12. Complete structural design of 

the footing by using factored loads 

(ST) 

8. Calculate sliding and passive soil 

resistance (GT/FD) 

ST – Structural Specialist 

FD – Foundation Design Specialist 

GT – Geotechnical Specialist 

Figure 8-11. Design process flow chart – bridge shallow foundation (modified after 

FHWA, 2002c). 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 14 December 2006 
8.4 BEARING CAPACITY 

This section discusses bearing capacity theory and its application toward computing 

allowable bearing capacities for shallow foundations. 

A foundation failure will occur when the footing penetrates excessively into the ground or 

experiences excessive rotation (Figure 8-12). Either of these excessive deformations may 

occur when, 

(a) the shear strength of the soil is exceeded, and/or 

(b) large uneven settlement and associated rotations occur. 

The failure mode that occurs when the shear strength is exceeded is known as a bearing 

capacity failure or, more accurately, an ultimate bearing capacity failure. Often, large 

settlements may occur prior to an ultimate bearing capacity failure and such settlements may 

impair the serviceability of the structure, i.e., the ultimate limit state (ULS) has not been 

exceeded, but the serviceability limit state (SLS) has. In this case, to control the settlements 

within tolerable limits, the footprint and/or depth of the structure below the ground may be 

dimensioned such that the imposed bearing pressure is well below the ultimate bearing 

capacity. 

Figure 8-12. Bearing capacity failure of silo foundation (Tschebotarioff, 1951). 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 15 December 2006 
8.4.1 Failure Mechanisms 

The type of bearing capacity failure is a function of several factors such as the type of the 

soil, the density (or consistency) of the soil, shape of the loaded surface, etc. This section 

discusses three failure mechanisms. 

8.4.1.1 General Shear 

When a footing is loaded to the ultimate bearing capacity, a condition of plastic flow 

develops in the foundation soils. As shown in Figure 8-13, a triangular wedge beneath the 

footing, designated as Zone I, remains in an elastic state and moves down into the soil with 

the footing. Although only a single failure surface (CD) is shown in Zone II, radial shear 

develops throughout Zone II such that radial lines of failure extending from the Zone I 

boundary (CB) change length based on a logarithmic spiral until they reach Zone III. 

Although only a single failure surface (DE) is shown in Zone III, a passive state of stress 

develops throughout Zone III at an angle of 45o

 – (φ′/2) from the horizontal. This 

configuration of the ultimate bearing capacity failure, with a well-defined failure zone 

extending to the surface and with bulging of the soil occurring on both sides of the footing, is 

called a “general shear” type of failure. General shear-type failures (Figure 8-14a) are 

believed to be the prevailing mode of failure for soils that are relatively incompressible and 

reasonably strong. 

Q 

II 

I III 

D C 

A B E

L = ∞ q 

ψ

Figure 8-13. Boundaries of zone of plastic equilibrium after failure of soil beneath 

continuous footing (FHWA, 2002c). 

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Soils and Foundations – Volume II 8 - 16 December 2006 
LOAD 

(a) GENERAL SHEAR 

LOAD 

(b) LOCAL SHEAR 

LOAD 

SETTLEMENT SETTLEMENT SETTLEMENT 

(c) PUNCHING SHEAR 

TEST AT 

GREATER 

DEPTH 

SURFACE TEST 

Figure 8-14. Modes of bearing capacity failure (after Vesic, 1975) (a) General shear (b) 

Local shear (c) Punching shear 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 17 December 2006 
 

8.4.1.2 Local Shear 

Local shear failure is characterized by a failure surface that is similar to that of a general 

shear failure but that does not extend to the ground surface. In the case of a local shear 

failure the failure zone ends somewhere in the soil below the footing (Figure 8-14b). Local 

shear failure is accompanied by vertical compression of soil below the footing and visible 

bulging of soil adjacent to the footing, but not by sudden rotation or tilting of the footing. 

Local shear failure is a transitional condition between general and punching shear failure. 

Local shear failures may occur in soils that are relatively loose compared to soils susceptible 

to general shear failure. 

8.4.1.3 Punching Shear 

Punching shear failure is characterized by vertical shear around the perimeter of the footing 

and is accompanied by a vertical movement of the footing and compression of the soil 

immediately below the footing. The soil outside the loaded area is not affected significantly 

(Figure 8-14c). The ground surface adjacent to the footing moves downward instead of 

bulging as in general and local shear failure. Punching shear failure generally occurs in loose 

or compressible soils, in weak soils under slow (drained) loading, and in dense sands for 

deep footings subjected to high loads. 

Note that from a perspective of bridge foundation design, soils so obviously weak as to 

experience local or punching shear failure modes should be avoided for supporting shallow 

foundations. Additional guidance on dealing with soils that fall in the intermediate or local 

shear range of behavior is provided in Section 8.4.5. 

8.4.2 Bearing Capacity Equation Formulation 

In essence, the bearing capacity failure mechanism is similar to the embankment slope failure 

mechanism discussed in Chapter 6. In the case of footings, the ultimate bearing capacity is 

equivalent to the stress applied to the soil by the footing that causes shear failure to occur in 

the soil below the footing base. For a concentrically loaded rigid strip footing with a rough 

base on a level homogeneous foundation material without the presence of water, the gross 

ultimate bearing capacity, qult, is expressed as follows (after Terzaghi, 1943): 

qult = c (N c )+ q (Nq ) + 0.5 (γ)(Bf )(Nγ ) 8-1

 “Cohesion” term “Surcharge” term Foundation soil “Weight” term 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 18 December 2006 
where: c = cohesion of the soil (ksf) (kPa) 

q = total surcharge at the base of the footing = qappl + γa Df (ksf) (kPa) 

 qappl = applied surcharge (ksf)(kPa) 

 γa = unit weight of the overburden material above the base of the 

footing causing the surcharge pressure (kcf) (kN/m3) 

Df = depth of embedment (ft) (m) (Figure 8-1) 

γ = unit weight of the soil under the footing (kcf) (kN/m3

) 

Bf = footing width, i.e., least lateral dimension of the footing (ft) (m) (Figure 8-1) 

Nq = bearing capacity factor for the “surcharge” term (dimensionless) 

φ

2

Nc = bearing capacity factor for the “cohesion” term (dimensionless) 

= e π tan φ tan2 (45° + ) 8-2 

= (N q -1) cotφ for φ > 0 ° 8-3

 = 2 + π = 5.14 for φ = 0 ° 8-4 

Nγ = bearing capacity factor for the “weight” term (dimensionless) 

 = 2 (Nq + 1) tan( φ ) 8-5 

Many researchers proposed different expressions for the bearing capacity factors, Nc, Nq, and 

Nγ. The expressions presented above are those used by AASHTO (2004 with 2006 Interims). 

These expressions are a function of the friction angle, φ. Table 8-1 can be used to estimate 

friction angle, φ, from corrected SPT N-value, N160, for cohesionless soils. Otherwise, the 

friction angle can be measured directly by laboratory tests or in situ testing. The values of 

Nc, Nq, and Nγ as computed for various friction angles by Equations 8-3/8-4, 8-2, and 8-5, 

respectively are included in Table 8-1 and in Figure 8-15. Computation of ultimate bearing 

capacity is illustrated in Example 8-1. 

Table 8-1 

Estimation of friction angle of cohesionless soils from Standard Penetration Tests 

(after AASHTO, 2004 with 2006 Interims; FHWA, 2002c) 

Description Very Loose Loose Medium Dense Very Dense 

Corrected SPT N160 0 4 10 30 50 

Approximate φ, degrees* 25 – 30 27 – 32 30 – 35 35 – 40 38 – 43 

Approximate moist unit 

weight, (γ) pcf* 70 – 100 90 – 115 110 – 130 120 – 140 130 – 150 

* Use larger values for granular material with 5% or less fine sand and silt. 

Note: Correlations may be unreliable in gravelly soils due to sampling difficulties with splitspoon sampler as discussed in Chapter 3. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 19 December 2006 
Bearing Capacity Factors

100 

10 

1 

Nq 

Nc 

Nγ

0 5 10 15 20 25 30 35 40 45 

Friction Angle, degrees 

Figure 8-15. Bearing capacity factors versus friction angle. 

Table 8-2 

Bearing Capacity Factors (AASHTO, 2004 with 2006 Interims) 

φ Nc N

q

 Nγ φ Nc N

q

 Nγ 

0 5.14 1.0 0.0 23 18.1 8.7 8.2 

1 5.4 1.1 0.1 24 19.3 9.6 9.4 

2 5.6 1.2 0.2 25 20.7 10.7 10.9 

3 5.9 1.3 0.2 26 22.3 11.9 12.5 

4 6.2 1.4 0.3 27 23.9 13.2 14.5 

5 6.5 1.6 0.5 28 25.8 14.7 16.7 

6 6.8 1.7 0.6 29 27.9 16.4 19.3 

7 7.2 1.9 0.7 30 30.1 18.4 22.4 

8 7.5 2.1 0.9 31 32.7 20.6 26.0 

9 7.9 2.3 1.0 32 35.5 23.2 30.2 

10 8.4 2.5 1.2 33 38.6 26.1 35.2 

11 8.8 2.7 1.4 34 42.2 29.4 41.1 

12 9.3 3.0 1.7 35 46.1 33.3 48.0 

13 9.8 3.3 2.0 36 50.6 37.8 56.3 

14 10.4 3.6 2.3 37 55.6 42.9 66.2 

15 11.0 3.9 2.7 38 61.4 48.9 78.0 

16 11.6 4.3 3.1 39 67.9 56.0 92.3 

17 12.3 4.8 3.5 40 75.3 64.2 109.4 

18 13.1 5.3 4.1 41 83.9 73.9 130.2 

19 13.9 5.8 4.7 42 93.7 85.4 155.6 

20 14.8 6.4 5.4 43 105.1 99.0 186.5 

21 15.8 7.1 6.2 44 118.4 115.3 224.6 

22 16.9 7.8 7.1 45 133.9 134.9 271.8 

1000 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 20 December 2006 
Example 8-1: Determine the ultimate bearing capacity for a rigid strip footing with a rough 

base having the dimensions shown in the sketch below. Assume that the 

footing is concentrically loaded and that the total unit weight below the base 

of the footing is equal to the total unit weight above the base of the footing, 

i.e., in terms of the symbols used previously, γ = γa. First assume that the 

ground water table is well below the base of the footing and therefore it has 

no effect on the bearing capacity. Then, assume that the groundwater table is 

at the base of the footing and recompute the ultimate bearing capacity. 

. 

Bf = 6 ft 

Df = 5 ft 

γ=125 pcf 

γa = 125 pcf φ = 20°

c = 500 psf 

Solution: 

Assume a general shear condition and enter Table 8-2 for φ= 20° and read the bearing 

capacity factors as follows: 

Nc = 14.8, Nq = 6.4, Nγ = 5.4. These values can also be read from Figure 8-15. 

qult= c (Nc ) + γa (Df ) (Nq ) + 0.5 (γ)(Bf )(N γ ) 

qult = (500 psf)(14.8) + (125 pcf) (5 ft) (6.4) + 0.5(125 pcf) (6 ft)(5.4) 

= 7,400 psf + 4,000 psf + 2,025 psf 

qult = 13,425 psf 

Effect of water: If the ground water table is at the base of the footing, i.e., a depth of 5 ft 

from the ground surface, then effective unit weight should be used in the “weight” term as 

follows: 

qult = (500 psf)(14.8) + (125 pcf) (5 ft) (6.4) + 0.5(125 pcf - 62.4 pcf) (6 ft)(5.4) 

= 7,400 psf + 4,000 psf + 1,014 psf 

qult = 12,414 psf 

Sections 8.4.2.1 and 8.4.3.2 further discuss the effect of water on ultimate bearing capacity. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 21 December 2006 
8.4.2.1 Comparative Effect of Various Terms in Bearing Capacity Formulation 

In Equation 8-1, the first term is called the “cohesion” term, the second term is called the 

“surcharge” term since it represents the loads above the base of the footing, and the third 

term is called the “weight” term since it represents the weight of the foundation soil in the 

failure zone below the base of the footing. Consider now the effect that each of these terms 

has on the computed value of the ultimate bearing capacity (qult). 

•	 Purely cohesive soils, φ = 0 (corresponds to undrained loading): In this case, the 

last term is zero (Nγ = 0 for φ = 0) and the first term in Equation 8-1 is a constant. 

Therefore the ultimate bearing capacity is a function of only the cohesion as it 

appears in the cohesion term in Equation 8-1 and the depth of embedment of the 

footing as it appears in the surcharge term in Equation 8-1. For this case, the footing 

width has no influence on the ultimate bearing capacity. 

•	 Purely frictional or cohesionless soils, c =0 and φ > 0: In this case, there will be 

large changes in ultimate bearing capacity when properties and/or dimensions are 

changed. The embedment effect is particularly important. Removal of the soil over 

an embedded footing, either by excavation or scour, can substantially reduce its 

ultimate bearing capacity and result in a lower factor of safety than required by the 

design. Removal of the soil over an embedded footing can also cause greater 

settlement than initially estimated. Similarly, a rise in the ground water level to the 

ground surface will reduce the effective unit weight of the soil by making the soil 

buoyant, thus reducing the surcharge and unit weight terms by essentially one-half. 

Table 8-3 shows how bearing capacity can vary with changes in physical properties or 

dimensions. Notice that for a given value of cohesion, the effect of the variables on the 

bearing capacity in cohesive soils is minimal. Only the embedment depth has an effect on 

bearing capacity in cohesive soils. Also note that a rise in the ground water table does not 

influence cohesion. Interparticle bonding remains virtually unchanged unless the clay is 

reworked or the clay contains minerals that react with free water, e.g., expansive minerals. 

Table 8-3 also shows that for a given value of internal friction angle, the effect on 

cohesionless soils is significant when dimensions are changed and/or a rise in the water table 

takes place. The embedment effect is particularly important. Removal of soil from over an 

embedded footing, either by excavation or scour, can substantially reduce the ultimate 

bearing capacity and possibly cause catastrophic shear failure. Rehabilitation or repair of an 

existing spread footing often requires excavation of the soil above the footing. If the effect 

of this removal on bearing capacity is not considered, the footing may move downward 

resulting in structural distress. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 22 December 2006 
Table 8-3 

Variation in bearing capacity with changes in physical properties or dimensions 

Properties and Dimensions 

γ = γa = effective unit weight 

γ′ = effective unit weight; Df = embedment depth 

Bf = footing width (assume continuous footing) 

Cohesive Soil Cohesionless Soil 

φ = 0 

c = 1,000 psf 

qult (psf) 

φ = 30o 

c = 0 

qult (psf) 

A. Initial situation: γ = 120 pcf, Df = 0', Bf = 5' 

deep water table 

5,140 6,720 

B. Effect of embedment: γ = 120 pcf,, Df = 5', 

Bf = 5', deep water table 

5,740 17,760 

C. Effect of width: γ = 120 pcf, Df = 0', Bf = 10' 

deep water table 

5,140 13,440 

D. Effect of water table at surface: γ′ = 57.6 

 pcf, Df = 0', Bf = 5' 

5,140 3,226 

8.4.3 Bearing Capacity Correction Factors 

A number of factors that were not included in the derivations discussed earlier influence the 

ultimate bearing capacity of shallow foundations. Note that Equation 8-1 assumes a rigid 

strip footing with a rough base, loaded through its centroid, that is bearing on a level surface 

of homogeneous soil. Various correction factors have been proposed by numerous 

investigators to account for footing shape adjusted for eccentricity, location of the ground 

water table, embedment depth, sloping ground surface, an inclined base, the mode of shear, 

local or punching shear, and inclined loading. The general philosophy of correcting the 

theoretical ultimate bearing capacity equation involves multiplying each of the three terms in 

the bearing capacity equation by empirical factors to account for the particular effect. Each 

correction factor includes a subscript denoting the term to which the factor should be applied: 

“c” for the cohesion term, “q” for the surcharge term, and “γ” for the weight term. Each of 

these factors and suggestions for their application are discussed separately below. In most 

cases these factors may be used in combination. 

The general form of the ultimate bearing capacity equation, including correction terms, is: 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 23 December 2006 

qult = cNcsc bc + qNqCwqsq bq dq + 0.5γ Bf N γCwγs γbγ 8-6 
where: sc, sγ and sq are shape correction factors 

bc, bγ and bq are base inclination correction factors 

Cwγ and Cwq are groundwater correction factors 

dq is an embedment depth correction factor to account for the shearing resistance 

along the failure surface passing through cohesionless material above the bearing 

elevation. Recall that the embedment is modeled as a surcharge pressure applied 

at the bearing elevation. To be theoretically correct, the “q” in the surcharge term 

consists of two components, one the embedment depth surcharge to which the 

correction factor applies, the other an applied surcharge such as the traffic 

surcharge to which the correction factor, by definition, does not apply. Therefore, 

theoretically the “q” in the surcharge term should be replaced with (qa + γDf dq) 

where qa is defined as an applied surcharge for cases where applied surcharge is 

considered in the analysis; 

Nc, Nq and Nγ are bearing capacity factors that are a function of the friction angle 

of the soil. Nc, Nq and Nγ can be obtained from Table 8-2 or Figure 8-15 or they 

can be computed by Equation 8-3/8-4, 8-2 and 8-5, respectively. As discussed in 

Section 8.4.3.6, Nc and Nγ are replaced with Ncq and Nγq for the case of sloping 

ground or when the footing is located near a slope. In these cases the Nq term is 

omitted. 

The following sections provide guidance on the use of the bearing capacity correction 

factors, and whether or not certain factors should be used in combination. 

8.4.3.1 Footing Shape (Eccentricity and Effective Dimensions) 

The following two issues are related to footing shape: 

•	 Distinguishing a strip footing from a rectangular footing. The general bearing 

capacity equation is applicable to strip footings, i.e., footings with Lf/Bf ≥ 10. 

Therefore, footing shape factors should be included in the equation for the ultimate 

bearing capacity for rectangular footings with Lf/Bf ratios less than 10. 

•	 Use of the effective dimensions of footings subjected to eccentric loads. Eccentric 

loading occurs when a footing is subjected to eccentric vertical loads, a combination 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 24 December 2006 
of vertical loads and moments, or moments induced by shear loads transferred to the 

footing. Abutments and retaining wall footings are examples of footings subjected to 

this type of loading condition. Moments can also be applied to interior column 

footings due to skewed superstructures, impact loads from vessels or ice, seismic 

loads, or loading in any sort of continuous frame. Eccentricity is accounted for by 

distributing the non-uniform pressure distribution due to the eccentric load as an 

equivalent uniform pressure over an “effective area” that is smaller than the actual 

area of the original footing such that the point of application of the eccentric load 

passes through the centroid of the “effective area.” The eccentricity correction is 

usually applied by reducing the width (Bf) and length (Lf) such that: 

B′

f

 = Bf – 2eB 8-7 

L′

f

 = Lf – 2eL 8-8 

where, as shown in Figure 8-16, eB and eL are the eccentricities in the Bf

 and Lf 

directions, respectively. These eccentricities are computed by dividing the applied 

moment in each direction by the applied vertical load. It is important to maintain 

consistent sign conventions and coordinate directions when this conversion is done. 

The reduced footing dimensions B′f and L′f are termed the effective footing 

dimensions. When eccentric load occurs in both directions, the equivalent uniform 

bearing pressure is assumed to act over an effective fictitious area, A', where 

(AASHTO, 2004 with 2006 Interims): 

A′= B′

f

 L′

f 8-9 

Figure 8-16. Notations for footings subjected to eccentric, inclined loads 

(after Kulhawy, 1983). 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 25 December 2006 
The concept of an effective area loaded by an equivalent uniform pressure is an 

approximation made to account for eccentric loading and was first proposed by Meyerhof 

(1953). Therefore, the equivalent uniform pressure is often referred to as the “Meyerhof 

pressure.” The concept of equivalent footing and Meyerhof pressure is used for 

geotechnical analysis during sizing of the footing, i.e., bearing capacity and settlement 

analyses. However, the structural design of a footing should be performed using the actual 

trapezoidal or triangular pressure distributions that model the pressure distribution under an 

eccentrically loaded footing more conservatively. A comparison of the two loading 

distributions is shown in Figure 8-17. 

(a) (b) 

Figure 8-17. Eccentrically loaded footing with (a) Linearly varying pressure 

distribution (structural design), (b) Equivalent uniform pressure distribution (sizing 

the footing). 

Limiting eccentricities are defined to ensure that zero contact pressure does not occur at any 

point beneath the footing. These limiting eccentricities vary for soil and rock. Footings 

founded on soil should be designed such that the eccentricity in any direction (eB or eL) is 

less than one-sixth (1/6) of the actual footing dimension in the same direction. For footings 

founded on rock, the eccentricity should be less than one-fourth (1/4) of the actual footing 

dimension. If the eccentricity does not exceed these limits, a separate calculation for stability 

with respect to overturning need not be performed. If eccentricity does exceed these limits, 

the footing should be resized. 

The shape correction factors are summarized in Table 8-4. For eccentrically loaded footings, 

AASHTO (2004 with 2006 Interims) recommends use of the effective footing dimensions, 

B′f and L′f, to compute the shape correction factors. However, in routine foundation design, 

use of the effective footing dimensions is not practical since the effective dimensions will 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 26 December 2006 
change for various load cases. Besides, the difference in the computed shape correction 

factors for actual and effective footing dimensions will generally be small. Therefore the 

geotechnical engineer should make reasonable assumptions about the footing shape and 

dimensions and compute the correction factors by using the equations in Table 8-4. 

Table 8-4 

Shape correction factors (AASHTO, 2004 with 2006 Interims) 

Factor 

Friction 

Angle Cohesion Term (sc) Unit Weight Term (sγ) Surcharge Term (sq) 

Shape 

Factors, 

sc, sγ, sq 

φ = 0 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

f 

f 

5L 

B 1 1.0 1.0 

φ > 0 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

c 

q 

f 

f 

N 

N 

L 

B 1 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ −

f 

f 

L 

B 0.41 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

tan φ+ L 

B 1 

f 

f 

Note: Shape factors, s, should not be applied simultaneously with inclined loading factors, i. 

See Section 8.4.3.5. 

8.4.3.2 Location of the Ground Water Table 

If the ground water table is located within the potential failure zone above or below the base 

of a footing, buoyant (effective) unit weight should be used to compute the overburden 

pressure. A simplified method for accounting for the reduction in shearing resistance is to 

apply factors to the two terms in the bearing capacity equation that include a unit weight 

term. Recall that the cohesion term is neither a function of soil unit weight nor effective 

stress. The ground water factors may be computed by interpolating values between those 

provided in Table 8-5 (DW = depth to water from ground surface). 

Table 8-5 

Correction factor for location of ground water table 

(AASHTO, 2004 with 2006 Interims) 

DW CWγ CWq 

0 0.5 0.5 

Df 0.5 1.0 

> 1.5Bf + Df 1.0 1.0 

Note: For intermediate positions of the ground water table, interpolate 

between the values shown above. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 27 December 2006 
8.4.3.3 Embedment Depth 

Because the effect on bearing capacity of the depth of embedment was accounted for by 

considering it as an equivalent surcharge applied at the footing bearing elevation, the effect 

of the shearing resistance due to the failure surface actually passing through the footing 

embedment cover was neglected in the theory. If the backfill or cover over the footing is 

known to be a high-quality, compacted granular material that can be assumed to remain in 

place over the life of the footing, additional shearing resistance due to the backfill can be 

accounted for by including in the surcharge term the embedment depth correction factor, dq, 

shown in Table 8-6. Otherwise, the depth correction factor can be conservatively omitted. 

Table 8-6 

Depth correction factors 

(Hansen and Inan, 1970; AASHTO, 2004 with 2006 Interims) 

Friction Angle, φ (degrees) Df/Bf dq 

32 

1 

2 

4 

8 

1.20 

1.30 

1.35 

1.40 

37 

1 

2 

4 

8 

1.20 

1.25 

1.30 

1.35 

42 

1 

2 

4 

8 

1.15 

1.20 

1.25 

1.30 

Note: The depth correction factor should be used only when the soils above 

the footing bearing elevation are as competent as the soils beneath the 

footing level; otherwise, the depth correction factor should be taken as 1.0. 

Spread footings should be located below the depth of frost potential due to possible frost 

heave considerations discussed in Section 5.7.3. Figure 5-29 may be used for preliminary 

guidance on depth of frost penetration. Similarly, footings should be located below the depth 

of scour to prevent undermining of the footing. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 28 December 2006 
8.4.3.4 Inclined Base 

In general, inclined footings for bridges should be avoided or limited to inclination angles, α, 

less than about 8 to 10 degrees from the horizontal. Steeper inclinations may require keys, 

dowels or anchors to provide sufficient resistance to sliding. For footings inclined to the 

horizontal, Table 8-7 provides equations for the correction factors to be used in Equation 8-6. 

Table 8-7 

Inclined base correction factors (Hansen and Inan, 1970; AASHTO, 2004 with 2006 

Interims) 

Factor Friction 

Angle 

Cohesion Term (c) Unit Weight Term (γ) Surcharge Term (q) 

bc bγ bq 

Base 

Inclination 

Factors, 

bc, bγ, bq 

φ = 0 ⎟

⎠

⎞ ⎜

⎝

⎛ α − 147.3 

1 1.0 1.0 

φ > 0 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

φ

− − tanN b1 

b 

c 

q 

q (1-0.017α tanφ)

2

 (1-0.017α tanφ)

2 

φ = friction angle, degrees; α = footing inclination from horizontal, upward +, degrees 

8.4.3.5 Inclined Loading 

A convenient way to account for the effects of an inclined load applied to the footing by the 

column or wall stem is to consider the effects of the axial and shear components of the 

inclined load individually. If the vertical component is checked against the available bearing 

capacity and the shear component is checked against the available sliding resistance, the 

inclusion of load inclination factors in the bearing capacity equation can generally be 

omitted. The bearing capacity should, however, be evaluated by using effective footing 

dimensions, as discussed in Section 8.4.3.1 and in the footnote to Table 8-4, since large 

moments can frequently be transmitted to bridge foundations by the columns or pier walls. 

The simultaneous application of shape and load inclination factors can result in an 

overly conservative design. 

Unusual column geometry or loading configurations should be evaluated on a case-by-case 

basis relative to the foregoing recommendation before the load inclination factors are 

omitted. An example might be a column that is not aligned normal to the footing bearing 

surface. In this case, an inclined footing may be considered to offset the effects of the 

inclined load by providing improved bearing efficiency (see Section 8.4.3.4). Keep in mind 

that bearing surfaces that are not level may be difficult to construct and inspect. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 29 December 2006 
8.4.3.6 Sloping Ground Surface 

Placement of footings on or adjacent to slopes requires that the designer perform calculations 

to ensure that both the bearing capacity and the overall slope stability are acceptable. The 

bearing capacity equation should include corrections recommended by AASHTO as adapted 

from NAVFAC (1986b) to design the footings. Calculation of overall (global) stability is 

discussed in Chapter 6. 

For sloping ground surface, Equation 8-6 is modified to include terms Ncq and Nγq that 

replace the Nc and Nγ terms. The modified version is given by Equation 8-10. There is no 

surcharge term in Equation 8-10 because the surcharge effect on the slope side of the footing 

is ignored. 

q ult = c(Ncq ) sc bc + 0.5γ Bf (N γq ) Cwγ s γ bγ 8-10 

Charts are provided in Figure 8-18 to determine Ncq and Nγq for footings on (Figure 8-18a) 

or close to (Figure 8-18d) slopes for cohesive (φ = 0o

) and cohesionless (c = 0) soils. As 

indicated in Figure 8-18d, the bearing capacity is independent of the slope angle if the 

footing is located beyond a distance, ‘b,’ of two to six times the foundation width, i.e., the 

situation is identical to the case of horizontal ground surface. 

Other forms of Equation 8-10 are available for cohesive soils (φ = 0o

). However, because 

footings located on or near slopes consisting of cohesive soils, they are likely to have design 

limitations due to either settlement or slope stability, or both, the presentation of these 

equations is omitted here. The reader is referred to NAVFAC (1986a, 1986b) for discussions 

of these equations and their applications and limitations. 

Equation 8-10, which includes the width term for cohesionless soils, is useful in designing 

footings constructed within bridge approach fills. In this case, obtain Nγq from Figure 8­

18(c) or 8-18(f) and then compute the ultimate bearing capacity by using Equation 8-10. 

8.4.3.7 Layered Soils 

For layered soils, the reader is referred to the guidance provided in AASHTO (2004 with 

2006 Interims). 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 30 December 2006 
Figure 8-18. Modified bearing capacity factors for continuous footing on sloping ground 

(after Meyerhof, 1957, from AASHTO, 2004 with 2006 Interims) 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 31 December 2006 
8.4.4 Additional Considerations Regarding Bearing Capacity Correction Factors 

The inherent or implied factor of safety of a settlement-limited allowable bearing capacity 

relative to the computed ultimate bearing capacity is usually large enough to render the 

magnitude of the application of the individual correction factors small. Some comments in 

this regards are as follows: 

•	 AASHTO (2002) guidelines recommend calculating the shape factors, s, by using the 

effective footing dimensions, B′f and L′f. However, the original references (e.g., 

Vesic, 1975) do not specifically recommend using the effective dimensions to 

calculate the shape factors. Since the geotechnical engineer typically does not have 

knowledge of the loads causing eccentricity, it is recommended that the full footing 

dimensions be used to calculate the shape factors according to the equations given in 

Table 8-4 for use in computation of ultimate bearing capacity. 

•	 Bowles (1996) also recommends that the shape and load inclination factors (s and i) 

should not be combined. 

•	 In certain loading configurations, the designer should be careful in using inclination 

factors together with shape factors that have been adjusted for eccentricity (Perloff 

and Baron, 1976). The effect of the inclined loads may already be reflected in the 

computation of the eccentricity. Thus an overly conservative design may result. 

Further, the bearing capacity correction factors were developed with the assumption that the 

correction for each of the terms involving Nc, Nγ and Nq can be found independently. The 

bearing capacity theory is an idealization of the response of a foundation that attempts to 

account for the soil properties and boundary conditions. Bearing capacity analysis of 

foundations is frequently limited by the geotechnical engineer’s ability to determine material 

properties accurately as opposed to inadequacies in the theory used to develop the bearing 

capacity equations. Consider Table 8-2 and note that a one degree change in friction angle 

can result in a 10 to 15 percent change in the factors Nc, Nγ and Nq. Determination of the in 

situ friction angle to an accuracy of 1o is virtually impossible. Also note that the value of Nγ

more than doubles when the friction angle increases from 35o to 40o. Clearly, the 

uncertainties in the material properties will control the uncertainty of a bearing capacity 

computation to a large extent. The importance of the application of the correction factors 

is therefore secondary to adequate assessment of the inherent strength characteristics 

of the foundation soil through correctly performed field investigations and laboratory 

testing. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 32 December 2006 
Unfortunately, very few spread footings of the size used for bridge support have been loadtested to failure. Therefore, the evaluation of ultimate bearing capacity is based primarily on 

theory and laboratory testing of small-scale footings, with modification of the theoretical 

equations based on observation. 

8.4.5 Local or Punching Shear 

Several references, including AASHTO (2004 with 2006 Interims), recommend reducing the 

soil strength parameters if local or punching shear failure modes can develop. Figure 8-19 

shows conditions when these modes can develop for granular soils. The recommended 

reductions are shown in Equations 8-11 and 8-12. 

c* = 0.67c 8-11 

φ* = tan (0.67tan φ) 8-12 −1 

where: c* = reduced effective stress soil cohesion for punching shear (tsf (MPa)) 

φ* = reduced effective stress soil friction angle for punching shear (degrees) 

Figure 8-19. Modes of failure of model footings in sand (after Vesic, 1975; AASHTO, 

2004 with 2006 Interims) 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 33 December 2006 
Soil types that can develop local or punching shear failure modes include loose sands, quick 

clays (i.e., clays with sensitivity, St > 8; see Table 3-12 in Chapter 3), collapsible sands and 

silts, and brittle clays (OCR > 4 to 8). As indicated in Section 3.12, sensitivity of clay is 

defined as the ratio of the peak undrained shearing strength to the remolded undrained 

shearing strength. These soils present potential “problem” conditions that should be 

identified through a comprehensive geotechnical investigation. In general, these problem 

soils will have other characteristics that make them unsuitable for the support of shallow 

foundations for bridges, including large settlement potential for loose sands, sensitive clays 

and collapsible soils. Brittle clays exhibit relatively high strength at small strains, but they 

generally undergo significant reduction in strength at larger strains (strain-softening). This 

behavior should be identified and quantified through the field and laboratory testing program 

and compared to the anticipated stress changes resulting from the shallow foundation and 

ground slope configuration under consideration. 

Although local or punching shear failure modes can develop in loose sands or when very 

narrow footings are used, this local condition seldom applies to bridge foundations because 

spread footings are not used on obviously weak soils. In general, relatively large footing 

sizes are needed for structural stability of bridge foundations. 

The geotechnical engineer may encounter the following two situations where the application 

of the one-third reduction according to Equation 8-12 can result in an unnecessarily overconservative design. 

•	 The first is when a footing bears on a cohesionless soil that falls in the local shear 

portion of Figure 8-19. Note that a one-third reduction in the tangent of a friction 

angle of 38 degrees, a common value for good-quality, compacted, granular fill, 

results in a 73 percent reduction in the bearing capacity factor Nq, and an 81 percent 

reduction in Nγ. Also note that Figure 8-19 does not consider the effect of large 

footing widths, such as those used for the support of bridges. Therefore, provided 

that settlement potential is checked independently and found to be acceptable, 

spread footings on normally consolidated cohesionless soils falling within the 

local shear portion of Figure 8-19 should not be designed by using the one-third 

reduction according to Equation 8-12. 

•	 The second situation is when a spread footing bears on a compacted structural fill. 

The relative density of compacted structural fills as compared to compactive effort, 

i.e., percent relative compaction, indicates that for fills compacted to a minimum of 

95 percent of maximum dry density as determined by AASHTO T 180, the relative 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 34 December 2006 
density should be at or above 75 percent (see Figure 5-33 in Chapter 5). This 

relationship is consistent with the excellent performance history of spread footings in 

compacted structural fills (FHWA, 1982). Therefore, the one-third reduction should 

not be used in the design of footings on compacted structural fills constructed with 

good quality, granular material. 

8.4.6 Bearing Capacity Factors of Safety 

The minimum factor of safety applied to the calculated ultimate bearing capacity will be a 

function of: 

• The confidence in the design soil strength parameters c and φ, 

• The importance of the structure, and 

• The consequence of failure. 

Typical minimum factors of safety for shallow foundations are in the range of 2.5 to 3.5. A 

minimum factor of safety against bearing capacity failure of 3.0 is recommended for most 

bridge foundations. This recommended factor of safety was selected through a combination 

of applied theory and experience. Uncertainty in the magnitudes of the loads and the 

available soil bearing strength are combined into this single factor of safety. The 

general equation to compute the allowable bearing capacity as a function of safety factor is: 

 

where: qall = allowable bearing capacity (ksf) (kPa) 

qult = ultimate bearing capacity (ksf) (kPa) 

FS = the applied factor of safety 

8.4.6.1 Overstress Allowances 

Allowable Strength Design (ASD) criteria permit the allowable bearing capacity to be 

exceeded for certain load groups (e.g., seismic) by a specified percentage that ranges from 25 

to 50 percent (AASHTO, 2002). These overstress allowances are permitted for shortduration, infrequently occurring loads and may also be applied to calculated allowable 

bearing capacities. Construction loading is often a short-duration loading and may be 

considered for overstress allowances. Overstress allowances should not be permitted for 

cases where soft soils are encountered within the depth of significant influence (DOSI) 

or durations are such that temporary loads may cause unacceptable settlements. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 35 December 2006 

q 

q = ult 

all 8-13

FS 
8.4.7 Practical Aspects of Bearing Capacity Formulations 

This section presents some useful practical aspects of bearing capacity formulations. Several 

interesting observations are made here that provide practical guidance in terms of 

implementation and interpretation of the bearing capacity formulation and computed results. 

8.4.7.1 Bearing Capacity Computations 

The procedure to be used to compute bearing capacity is as follows: 

1.	 Review the structural plans to determine the proposed footing widths. In the absence 

of data assume a pier footing width equal to 1/3 the pier column height and an 

abutment footing width equal to 1/2 the abutment height. 

2.	 Review the soil profile to determine the position of the groundwater table and the 

interfaces between soil layer(s) that exist within the appropriate depth below the 

proposed footing level. 

3.	 Review soil test data to determine the unit weight, friction angle and cohesion of all 

of the impacted soils. In the absence of test data, estimate these values for coarsegrained granular soils from SPT N-values (refer to Table 8-3). NOTE SPT N-values 

in cohesive soils should not be used to determine shear strengths for final design 

since the reliability of SPT N-values in such soils is poor. 

4.	 Use Equation 8-6 with appropriate correction factors to compute the ultimate bearing 

capacity. The general case (continuous footing) may be used when the footing length 

is 10 or more times the footing width. Also the bearing capacity factor Nγ will 

usually be determined for a rough base condition since most footings are poured 

concrete. However the smoothness of the contact material must be considered for 

temporary footings such as wood grillages (rough), or steel supports (smooth) or 

plastic sheets (smooth). The safety factor for the bearing capacity of a spread footing 

is selected both to limit the amount of soil strain and to account for variations in soil 

properties at footing locations. 

5.	 The mechanism of the general bearing capacity failure is similar to the embankment 

slope failure mechanism. However, the footing analysis is a 3-dimensional analysis 

as opposed to the 2-dimensional slope stability analysis. The bearing capacity factors 

Nc, Nq and Nγ relate to the actual volume of soil involved in the failure zones. A 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 36 December 2006 
cursory study of the failure cross sections in Figure 8-13, discloses that the depth and 

lateral extent of the failure zones and the values of Nc, Nq and Nγ are determined by 

the dimensions of the wedge-shaped zone directly below the footing. As the friction 

angle increases, the depth and width of the failure zones increase, i.e., more soil is 

impacted and more shear resistance is mobilized, thereby increasing the bearing 

capacity. 

6.	 Substantial downward movement of the footing is required to mobilize the shearing 

resistance within the entire failure zone completely. Besides providing a margin of 

safety on shear strength properties, the relatively large safety factor of 3 commonly 

used in the design of footings controls the amount of strain necessary to mobilize the 

allowable bearing capacity fully. Settlement analysis (Section 8.5) is recommended 

to compute the allowable bearing capacity corresponding to a specified limiting 

settlement. That allowable bearing capacity may result in a factor of safety with 

respect to ultimate bearing capacity much larger than 3. 

7.	 In reporting the results of bearing capacity analyses, the footing width that was used 

to compute the bearing capacity should always be included. Most often the 

geotechnical engineer must assume a footing width since bearing capacity analyses 

are completed before structural design begins. It is recommended that bearing 

capacity be computed for a range of possible footing widths and those values be 

included in the foundation report with a note stating that if other footing widths are 

used, the geotechnical engineer should be contacted. The state of the practice today 

is for the geotechnical engineer to develop location-specific bearing capacity charts 

on which allowable bearing capacity is plotted versus footing width for a family of 

curves representing specific values of settlement. Refer to Figure 8-10 for a 

schematic example of such a chart. 

8.	 The net ultimate bearing pressure is the difference between the gross ultimate bearing 

pressure and the pressure that existed due to the ground surcharge at the bearing 

depth before the footing was constructed, q (= γaDf

). The net ultimate bearing 

pressure can thus be computed by subtracting the ground surcharge (q) from Equation 

8-6: 

 

qult net = qult – q 8-14 

qult net = cN csc bc + q (Nq − 1) Cwqsq bq dq + 0.5γ Bf N γCwγ s γ bγ 8-15 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 37 December 2006 
The structural designer will typically include the self-weight of the concrete footing 

and the backfill over the footing (approximately equal to γaDf) in the loads that 

contribute to the applied bearing stress. Therefore, if the geotechnical engineer 

computes and reports a net ultimate bearing pressure, the effect of the surcharge 

directly over the footing area is counted twice. Reporting an allowable bearing 

capacity computed from a net ultimate bearing pressure is conservative and generally 

not recommended provided that a suitable factor of safety is maintained against 

bearing capacity failure. If the geotechnical engineer chooses to report an allowable 

bearing capacity computed from a net ultimate bearing pressure, this fact should be 

clearly stated in the foundation report. 

8.4.7.2 Failure Zones 

Certain practical information based on the geometry of the failure zone is as follows: 

1.	 The bearing capacity of a footing is dependent on the strength of the soil within a 

depth of approximately 1.5 times footing width below the base of the footing unless 

much weaker soils exist just below this level, in which case a potential for punching 

shear failure may exist. Continuous soil samples and SPT N-values should be 

routinely specified within this depth. If the borings for a structure are done long 

before design, a good practice is to obtain continuous split spoon samples for the top 

15 ft (4.5 m) of each boring where footings may be placed on natural soil. The cost 

of this sampling is minimal but the knowledge gained is great. At a minimum, 

continuous sampling to a depth of 15 ft (4.5 m) will generally provide the following 

information: 

a. thickness of existing topsoil. 

b. location of any thin zones of unsuitable material. 

c. accurate determination of depth of existing fill. 

d. improved ground water determination in the critical zone. 

e. representative samples in this critical zone to permit reliable determination of 

strength parameters in the laboratory and confident assessment of bearing 

capacity. 

2. Often questions arise during excavation near existing footings as to the effect of soil 

removal adjacent to the footing on the bearing capacity of that footing. In general, 

for weaker soils the zone of lateral influence extends outside the footing edge less 

than twice the footing width. Reductions in bearing capacity can be estimated by 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 38 December 2006 
considering the effects of surcharge removal within these zones. The theoretical 

lateral extent of this zone is shown in Figure 8-20. This figure is also useful in 

determining the effects of ground irregularities on bearing capacity or the effects of 

footing loads on adjacent facilities. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

d o /B, f/B 

do/B 

f/B 

do 

B/2 f 

I 

II 

III 

B/2 

0 5 10 15 20 25 30 35 40 45 

Angle of Internal Friction, φ, degrees 

Figure 8-20. Approximate variation of depth (do) and lateral extent (f) of influence 

of footing as a function of internal friction angle of foundation soil. 

As noted earlier, the general mechanism by which soils resist a footing load is similar to the 

foundation of an embankment resists shear failure. The load to cause failure must exceed the 

available soil strength within the failure zone. When failure occurs the footing plunges into 

the ground and causes an uplift of the soil adjacent to the sides of the footing. The resistance 

to failure is based on the soil strength and the amount of soil above the footing. Therefore, 

the bearing capacity of a footing can be increased by: 

1.	 replacing or densifying the soil below the footing prior to construction. 

2.	 increasing the embedment of the footing below ground, provided no weak soils 

exist within 1.5 times the footing width. 

Common examples of improving bearing capacity are the support of temporary footings on 

pads of gravel or the embedment of mudsills a few feet below ground to support falsework. 

The design of these support systems is primarily done by bearing capacity analysis in which 

the results of subsurface explorations and testing are used. Structural engineers who review 

falsework designs should carefully check the soil bearing capacity at foundation locations. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 39 December 2006 
8.4.8 Presumptive Bearing Capacities 

Many building codes include provisions that arbitrarily limit the amount of loading that may 

be applied on various classes of soils by structures subject to code regulations. These 

limiting loads are generally based on bearing pressures that have been observed to result in 

acceptable settlements. The implication is that on the basis of experience alone it may be 

presumed that each designated class of soil will safely support the loads indicated without the 

structure undergoing excessive settlements. Such values listed in codes or in the technical 

literature are termed presumptive bearing capacities. 

8.4.8.1 Presumptive Bearing Capacity in Soil 

The use of presumptive bearing capacities for shallow foundations bearing in soils is 

not recommended for final design of shallow foundations for transportation structures, 

especially bridges. Guesses about the geology and nature of a site and the application of a 

presumptive value from generalizations in codes or in the technical literature are not a 

substitute for an adequate site-specific subsurface investigation and laboratory testing 

program. As an exception, presumptive bearing values are sometimes used for the 

preliminary evaluation of shallow foundation feasibility and estimation of footing 

dimensions for preliminary constructability or cost evaluations. 

8.4.8.2 Presumptive Bearing Capacity in Rock 

Footings on intact sound rock that is stronger and less compressible than concrete are 

generally stable and do not require extensive study of the strength and compressibility 

characteristics of the rock. However, site investigations are still required to confirm the 

consistency and extent of rock formations beneath a shallow foundation. 

Allowable bearing capacities for footings on relatively uniform and sound rock surfaces are 

documented in applicable building codes and engineering manuals. Many different 

definitions for sound rock are available. In simple terms, however, “sound rock” can 

generally be defined as a rock mass that does not disintegrate after exposure to air or 

water and whose discontinuities are unweathered, closed or tight, i.e., less than about 

1/8 in (3 mm) wide and spaced no closer than 3 ft (1 m) apart. Table 8-8 presents 

allowable bearing pressures for intact rock recommended in selected local building codes 

(Goodman, 1989). These values were developed based on experience in sound rock 

formations, with the intention of satisfying both bearing capacity and settlement criteria in 

order to provide a satisfactory factor of safety. However, the use of presumptive values may 

lead to overly conservative and costly foundations. In such cases, most codes allow for a 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 40 December 2006 
variance if the request is supported by an engineering report. Site-specific investigation and 

analysis is strongly encouraged. 

In areas where building codes are not available or applicable, other recommended 

presumptive bearing values, such as those listed in Table 8-9, may be used to determine the 

allowable bearing pressure for sound rock. For footings designed by using these published 

values, the elastic settlements are generally less than 0.5 in (13 mm). Where the rock is 

reasonably sound, but fractured, the presumptive values listed in Tables 8-8 and 8-9 should 

be reduced by limiting the bearing pressures to tolerable settlements based on settlement 

analyses. Most building codes also provide reduced recommended bearing pressures to 

account for the degree of fracturing. 

Peck, et al. (1974) presented an empirical correlation of presumptive allowable bearing 

pressure with Rock Quality Designation (RQD), as shown in Table 8-10. If the 

recommended value of allowable bearing pressure exceeds the unconfined compressive 

strength of the rock or allowable stress of concrete, the allowable bearing pressure should be 

taken as the lower of the two values. Although the suggested bearing values of Peck, et al. 

(1974) are substantially greater than most of the other published values and ignore the effects 

of rock type and conditions of discontinuities, they provide a useful guide for an upperbound estimation as well as an empirical relationship between allowable bearing values and 

the intensity of fracturing and jointing (Table 8-10). Note that with a slight increase of the 

degree of fracturing of the rock mass, for example when the RQD value drops from 100 

percent to 90 percent, the recommended bearing capacity value is reduced drastically from 

600 ksf (29 MPa) to 400 ksf (19 MPa). 

In no instance should the allowable bearing capacity exceed the allowable stress of the 

concrete used in the structural foundation. Furthermore, Peck, et al. (1974) also suggest that 

the average RQD for the bearing rock within a depth of the footing width (Bf) below the base 

of the footing should be used if the RQD values within the depth are relatively uniform. If 

rock within a depth of 0.5Bf is of poorer quality, the RQD of the poorer quality rock should 

be used to determine the allowable bearing capacity. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 41 December 2006 
Table 8-8 

Allowable bearing pressures for fresh rock of various types (Goodman, 1989) 

Rock Type Age Location Allowable Bearing 

Pressure tsf (MPa) 

Massively bedded limestone5 U.K.6 80 (3.8) 

Dolomite L. Paleoz. Chicago 100 (4.8) 

Dolomite L. Paleoz. Detroit 20-200 (1.0 – 9.6) 

Limestone U. Paleoz. Kansas City 20-120 (0.5 – 5.8) 

Limestone U. Paleoz. St. Louis 50-100 (2.4 – 4.8) 

Mica schist Pre-Camb. Washington 20-40 (0.5 – 1.9) 

Mica schist Pre-Camb. Philadelphia 60-80 (2.9 – 3.8) 

Manhattan schist Pre-Camb. New York 120 (5.8) 

Fordham gneiss Pre-Camb. New York 120 (5.8) 

Schist and slate - U.K.6 10-25 (0.5 – 1.2) 

Argillite Pre-Camb. Cambridge, MA 10-25 (0.5 – 1.2) 

Newark shale Triassic Philadelphia 10-25 (0.5 – 1.2) 

Hard, cemented shale - U.K.6

 40 (1.9) 

Eagleford shale Cretaceous Dallas 13-40 (0.6 – 1.9) 

Clay shale - U.K.6

 20 (1.0) 

Pierre shale Cretaceous Denver 20-60 (1.0 – 2.9) 

Fox Hills sandstone Tertiary Denver 20-60 (1.0 – 2.9) 

Solid chalk Cretaceous U.K.6

 13 (0.6) 

Austin chalk Cretaceous Dallas 30-100 (1.4 – 4.8) 

Friable sandstone and 

claystone 

Tertiary Oakland 8-20 (0.4 – 1.0) 

Friable sandstone 

(Pico formation) 

Quaternary Los Angeles 10-20 (0.5 – 1.0) 

Notes: 

1 According to typical building codes; reduce values accordingly to account for weathering or 

unrepresentative fracturing 

2

 Values from Thorburn (1966) and Woodward, Gardner and Greer (1972). 

3 When a range is given, it relates to usual range in rock conditions. 

4 Sound rock that rings when struck and does not disintegrate. Cracks are unweathered and 

open less than 10 mm. 

5 Thickness of beds greater than 3 ft (1 m), joint spacing greater than 2 mm; unconfined 

compressive strength greater than 160 tsf (7.7 MPa) (for a 4 in (100 mm) cube). 

6 Institution of Civil Engineers Code of Practice 4. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 42 December 2006 
 

 

 

Table 8-9 

Presumptive values of allowable bearing pressures for spread foundations on rock 

(modified after NAVFAC, 1986a, AASHTO 2004 with 2006 Interims) 

Type of Bearing Material Consistency In 

Place 

Allowable Bearing Pressure 

tsf (MPa) 

Range Recommended 

Value for Use 

Massive crystalline igneous and metamorphic rock: 

granite, diorite, basalt, gneiss, thoroughly cemented 

conglomerate (sound condition allows minor 

cracks) 

Hard, sound 

rock 

120-200 

(5.8 - 9.6) 

160 

(7.7) 

Foliated metamorphic rock: Slate, schist (sound 

condition allows minor cracks) 

Medium-hard, 

sound rock 

60-80 

(2.9-3.8) 

70 

(3.4) 

Sedimentary rock; hard cemented shales, siltstone, 

sandstone, limestone without cavities 

Medium-hard, 

sound rock 

30-50 

(1.4-2.4) 

40 

(1.9) 

Weathered or broken bedrock of any kind except 

highly argillaceous rock (shale). RQD less than 25 Soft rock 16-24 (0.8-1.2) 

20 

(1) 

Compacted shale or other highly argillaceous rock 

in sound condition Soft rock 16-24 (0.8-1.2) 

20 

(1) 

Notes: 

1. For preliminary analysis or in the absence of strength tests, design and proportion shallow foundations to 

distribute their loads by using presumptive values of allowable bearing pressure given in this table. Modify the 

nominal value of allowable bearing pressure for special conditions described in notes 2 through 8. 

2. The maximum bearing pressure beneath the footing produced by eccentric loads that include dead plus normal 

live load plus permanent lateral loads shall not exceed the above nominal bearing pressure. 

3. Bearing pressures up to one-third in excess of the nominal bearing values are permitted for transient live load 

from wind or earthquake. If overload from wind or earthquake exceeds one-third of nominal bearing pressures, 

increase allowable bearing pressures by one-third of nominal value. 

4. Extend footings on soft rock to a minimum depth of 1.5 in (40 mm) below adjacent ground surface or surface of 

adjacent floor, whichever elevation is the lowest. 

5. For footings on soft rock, increase allowable bearing pressures by 5 percent of the nominal values for each 1 ft 

(300 mm) of depth below the minimum depth specified in Note 4. 

6. Apply the nominal bearing pressures of the three categories of hard or medium hard rock shown above where 

the base of the foundation lies on rock surface. Where the foundation extends below the rock surface, increase 

the allowable bearing pressure by 10 percent of the nominal values for each additional 1ft (300 mm) of depth 

extending below the surface. 

7. For footings smaller than 3 ft (1 m) in the least lateral dimension, the allowable bearing pressure shall be the 

nominal bearing pressure multiplied by the least lateral dimension. 

8. If the above-recommended nominal bearing pressure exceeds the unconfined compressive strength of intact 

specimen, the allowable pressure equals the unconfined compressive strength. 

Table 8-10 

Suggested values of allowable bearing capacity (Peck, et al., 1974) 

RQD (%) Rock Mass Quality Allowable Pressure 

ksf (MPa) 

100 Excellent 600 (29) 

90 Good 400 (19) 

75 Fair 240 (12) 

50 Poor 130 (6) 

25 Very Poor 60 (3) 

0 Soil-like 20 (1) 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 43 December 2006 
8.5 SETTLEMENT OF SPREAD FOOTINGS 

The controlling factor in the design of a spread footing is usually tolerable settlement. 

Estimation of settlement may be routinely accomplished with adequate geotechnical data and 

knowledge of the structural loads. The accuracy of the estimation is only as good as the 

quality of the geotechnical data and the estimation of the actual loads. Settlements of spread 

footings are frequently overestimated by engineers for the following reasons: 

1. The structural load causing the settlement is overestimated. In the absence of actual 

structural loads, geotechnical engineers conservatively assume that the footing pressure 

equals the maximum allowable soil bearing pressure. 

2. Settlement occurring during construction is not subtracted from total predicted amounts 

(See discussion in Section 8.9 for more details). 

3. Preconsolidation of the subsoil is not accounted for in the analysis. Preconsolidation 

may be due to a geologic load applied in past time or to removal of significant amounts 

of soil in construction prior to placement of the foundation. This error can cause a 

grossly overestimated settlement. 

As explained in Chapter 7, there are two primary types of settlement, immediate (short-term) 

and consolidation (long-term). The procedures for computing these settlements under spread 

footings are similar to those under embankments as discussed in Chapter 7. The following 

sections illustrate the computation of immediate and consolidation settlements. 

8.5.1 Immediate Settlement 

As noted in Chapter 7, there are several methods available to evaluate immediate settlements. 

Modified Hough’s method was introduced in Chapter 7 and was illustrated by an example. 

Modified Hough’s method can also be applied to shallow foundations by using the same 

approach demonstrated in Chapter 7. Studies conducted by FHWA (1987) indicate that 

Modified Hough’s procedure is conservative and over-predicts settlement by a factor of 2 or 

more. Such conservatism may be acceptable for the evaluation of the settlement of 

embankments due to reasons discussed in Chapter 7. However, in the case of shallow 

foundations such conservatism may lead to unnecessary use of costlier deep foundations in 

cases where shallow foundations may be viable. Therefore, use of a more rigorous procedure 

such Schmertmann’s modified method (1978) is recommended for shallow foundations, and 

is presented here. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 44 December 2006 
 

 

 

8.5.1.1 Schmertmann’s Modified Method for Calculation of Immediate Settlements 

An estimate of the immediate settlement, Si, of spread footings can be made by using 

Equation 8-16 as proposed by Schmertmann, et al. (1978). 

8-16 

n ⎛ Iz ⎞ Si = C1C2 ∆p ∑∆Hi where ∆Hi = Hc ⎜ ⎟ ⎝ XE ⎠ i=1 

where: Iz = strain influence factor from Figure 8-21a. The dimension Bf 

represents the least lateral dimension of the footing after correction for 

eccentricities, i.e. use least lateral effective footing dimension. The 

strain influence factor is a function of depth and is obtained from the 

strain influence diagram. The strain influence diagram is easily 

constructed for the axisymmetric case (Lf/Bf = 1) and the plane strain 

case (Lf/Bf ≥ 10) as shown in Figure 8-21a. The strain influence 

diagram for intermediate conditions can be determined by simple 

linear interpolation. 

n = number of soil layers within the zone of strain influence (strain 

influence diagram).

 ∆p = net uniform applied stress (load intensity) at the foundation depth (see 

Figure 8-21b). 

E = elastic modulus of layer i based on guidance provided in Table 5-16 in 

Chapter 5. 

X = a factor used to determine the value of elastic modulus. If the value of 

elastic modulus is based on correlations with N160-values or qc from 

Table 5-16 in Chapter 5, then use X as follows. 

X = 1.25 for axisymmetric case (Lf/Bf = 1) 

X = 1.75 for plane strain case (Lf/Bf ≥ 10) 

Use interpolation for footings with 1 < Lf/Bf ≤ 10 

If the value of elastic modulus is estimated based on the range of 

elastic moduli in Table 5-16 or other sources use X = 1.0. 

FHWA NHI-06-089 8 – Shallow Foundations 

Soils and Foundations – Volume II 8 - 45 December 2006 
o −=∆ ppp

p

(a) 

5.0

op 

zp 

p 

p 1.05.0I ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ∆

+=

below)b(see 

Plane Strain Lf/Bf ≥ 10 

Axisymmetric 

Lf/Bf =1 

Lf = Length of footing 

Bf = least width of footing 

Bf/2 

Bf 

2Bf 

3Bf 

4Bf 

Bf
 

(width of footing)
 

∆p = p − po
 

po 

Bf /2 (for axisymmetric case) pop 

Bf (for plane strain case) 

(b) 

Depth to Peak Strain 

Influence Factor, Izp 

Figure 8-21. (a) Simplified vertical strain influence factor distributions, (b) Explanation 

of pressure terms in equation for Izp (after Schmertmann, et al., 1978). 

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 C1 = a correction factor to incorporate the effect of strain relief due to 

embedment where: 

⎛ p ⎞ o C1 =1−0.5 ⎟

⎟ ⎜⎜ ≥ 0.5	 8-17 ⎝ ∆p ⎠

where po is effective in-situ overburden stress at the foundation depth 

and ∆p is the net foundation pressure as shown in Figure 8-21b 

C2 = a correction factor to incorporate time-dependent (creep) increase in 

settlement for t (years) after construction where: 

⎛ t(years)⎞ C2 =1+ 0.2 log10 ⎜ ⎟ 8-18 ⎝ 0.1 ⎠

8.5.1.2 Comments on Schmertmann’s Method 

•	 Effect of lateral strain: Schmertmann and his co-workers based their method on the 

results of displacement measurements within sand masses loaded by model footings, as 

well as finite element analyses of deformations of materials with nonlinear stress-strain 

behavior that expressly incorporated Poisson’s ratio. Therefore, the effect of the lateral 

strain on the vertical strain is included in the strain influence factor diagrams. 

•	 Effect of preloading: The equations used in Schmertmann’s method are applicable to 

normally loaded sands. If the sand was pre-strained by previous loading, then the actual 

settlements will be overpredicted. Schmertmann, et al. (1978) recommend a reduction in 

settlement after preloading or other means of compaction of half the predicted settlement. 

Alternatively, in case of preloaded soil deposits, the settlement can be computed by using 

the method proposed by D’Appolonia (1968, 1970), which includes explicit 

consideration of preloading. 

•	 C2 correction factor: The time duration, t, in Equation 8-18 is set to 0.1 years to 

evaluate the settlement immediately after construction, i.e., C2 = 1. If long-term creep 

deformation of the soil is suspected then an appropriate time duration, t, can be used in 

the computation of C2. As explained in Sections 5.4.1 and 7.6, creep deformation is 

not the same as consolidation settlement. This factor can have an important influence 

on the reported settlement since it is included in Equation 8-16 as a multiplier. For 

example, the C2 factor for time durations of 0.1 yrs, 1 yr, 10 yrs and 50 yrs are 1.0, 1.2, 

1.4 and 1.54, respectively. In cohesionless soils and unsaturated fine-grained cohesive 

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soils with low plasticity, time durations of 0.1 yr and 1 yr, respectively, are generally 

appropriate and sufficient for cases of static loads. Where consolidation settlement is 

estimated in addition to immediate settlement, C2 = 1 should be used. 

The use of Schmertmann’s modified method to calculate immediate settlement is illustrated 

numerically in Example 8-2. 

Example 8-2: A 6 ft x 24 ft footing is founded at a depth of 3 ft below ground elevation with 

the soil profile and average N160 values shown. Determine the settlement in 

inches (a) at the end of construction and (b) 1 year after construction. There is 

no groundwater. The footing is subjected to an applied stress of 2,000 psf. 

Ground Surface 

Clayey Silt 3 ft γt = 115 pcf; N160 = 8 

Sandy Silt B = 6 ft 3 ft γt = 125 pcf; N160 = 25 

f

Coarse Sand 5 ft γt = 120 pcf; N160 = 30 

Sandy Gravel 25 ft γt = 128 pcf; N160 = 68 

Solution: 

Step 1: Begin by drawing the strain influence diagram. The Lf/Bf ratio for the footing is 

24′/6′ = 4. From Figure 8-21(a), determine the value of the strain influence factor at the base 

of the footing, IZB, as follows: 

IZB = 0.1 for axisymmetric case (Lf/Bf = 1) 

IZB = 0.2 for plane strain case (Lf/Bf ≥ 10) 

Difference between axisymmetric Lf/Bf and plane strain Lf/Bf = 9 

Difference between axisymmetric IZB and plane strain IZB = 0.1 

Use linear interpolation for Lf/Bf = 4: 

∆(Lf/Bf) with respect to axisymmetric Lf/Bf = 4-1 = 3. Therefore 

(0.2 − 0.1 ) 0.1 IZB = 0.1+ ( ) 3 = 0.1+ = 0.133

9 3 

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Step 2: Determine the maximum depth of influence, DI, as follows: 

DI = 2Bf for Lf/Bf = 1 

DI = 4Bf for Lf/Bf >10 

By using linear interpolation Lf/Bf = 4 as before: 

∆ (Lf/Bf) with respect to axisymmetric Lf/Bf = 4-1 = 3. Therefore 

(4B f − 2B f )( ) 2B 6B + 2B D f 8Bf

I f = 2B + 3 = 2B f + f = f = 9 3 3 3 

8 D = ( I 6ft )=16ft 

3 

Step 3: Determine the depth to the peak strain influence factor, DIP, as follows: 

From Figure 8-21(a) DIP = Bf/2 for Lf/Bf = 1 

DIP = Bf for Lf/Bf > 10 

Use linear interpolation for Lf/Bf = 4: 

∆( Lf/Bf) with respect to axisymmetric Lf/Bf = 4-1 = 3. Therefore 

⎛ Bf ⎞ ⎜Bf − ⎟ Bf ⎝ 2 ⎠ B D = + ( ) 3 = f B B

+ f 3 f + Bf 4B = f

IP = 2 9 2 6 6 6 

4 DIP = (6 ft )= 4 ft

6 

Step 4: Determine the value of the maximum strain influence factor, IZP, as follows: 

0.5 ⎛ ⎞ ⎜ ∆p ⎟ I ZP = 0.5 + 0.1⎜ ⎟ ⎜ p ⎟ ⎝ op ⎠

∆p = 2,000 psf − 3ft (115pcf )=1,655psf 

pop = 3ft (115 pcf )+ 3ft (125pcf )+1ft (120 pcf )

pop = 345 psf + 375psf +120 psf =840 psf 

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1,655psf IZP = 0.5 + 0.1 = 0.64 

840psf 

Step 5: Draw the IZ vs. depth diagram as follows and divide it into convenient layers by 

using the following guidelines: 

•	 The depth of the peak value of the strain influence is fixed. To aid in the 

computation, develop the layering such that one of the layer boundaries occurs at 

this depth even though it requires that an actual soil layer be sub-divided. 

•	 Limit the top layer as well as the layer immediately below the peak value of 

influence factor, Izp, to 2/3Bf or less to adequately represent the variation of the 

influence factor within DIP. 

•	 Limit maximum layer thickness to 10 ft (3 m) or less. 

•	 Match the layer boundary with the subsurface profile layering. 

In accordance with the above guidelines, the influence depth of 16 ft is divided into 4 layers 

as shown below. Since the strain influence diagram starts at the base of the footing, the 

thickness of Layer 1 corresponds to the thickness of the sandy silt layer shown in the soil 

profile. Likewise, Layer 4 corresponds to the thickness of the sandy gravel layer that has 

been impacted by the strain influence diagram. The sum of the thicknesses of Layers 2 and 3 

correspond to the thickness of the coarse sand layer shown in the soil profile. The subdivision is made to account for the strain influence diagram going though its peak value 

within the coarse sand layer. The minimum and maximum layer thicknesses are 1 ft (Layer 

2) and 8 ft (Layer 4), respectively. The layer boundaries are shown by solid lines while the 

layer centers are shown by dashed lines. 

Step 6: Determine value of elastic modulus Es from Table 5-16 from Chapter 5. 

Layer 1: Sandy Silt: E = 4N160 tsf 

Layer 2: Coarse Sand: E = 10N160 tsf 

Layer 3: Coarse Sand: E = 10N160 tsf 

Layer 4: Sandy Gravel: E = 12N160 tsf 

Since the elastic modulus Es is based on correlations with N160-values obtained from Table 

5-16, calculate the X multiplication factor as follows: 

X = 1.25 for Lf/Bf = 1 

X = 1.75 for Lf/Bf ≥ 10 

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Influence Factor (Iz) 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 

0 0 

Layer 1 

Layer 2 

Layer 3 

Layer 4 

Iz 

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 

Influence Factor (Iz) 

4
 4

Depth below footing (ft)

8 8 

12
 12
 

16 16 

20 20 

Use linear interpolation for Lf/Bf = 4 

∆ (Lf/Bf) with respect to axisymmetric Lf/Bf = 4-1 = 3 

(1.75 − 1.25) X =1.25+ ( ) 3 =1.42 

9 

Step 7: Using the thickness of each layer, Hc, and the relevant values for that particular layer, 

determine the settlement by setting up a table as follows: 

Layer Hc

 (inches) 

N160 E 

(tsf) 

XE 

(tsf) 

Z1

(ft) 

IZ at Zi c 

Z 

i H 

XE 

I

H =∆

(in/tsf) 

1 36 25 100 142 1.5 0.323 0.0819 

2 12 30 300 426 3.5 0.577 0.0163 

3 48 30 300 426 6 0.533 0.0601 

4 96 68 816 1,159 12 0.213 0.0177 

Σ Hi= 0.1760 

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⎛ p ⎞

o ⎛ 3ft ×115 pcf ⎞ C ⎜ ⎟ 1 =1− 0.5 =1 − 0.5 ⎜ ⎟ = ⎜ ⎜ 0.896

∆p ⎟ ⎟ ⎝ 1655 psf ⎝ ⎠ ⎠

Step 8: Determine embedment factor (C1) and creep factor (C2) as follows: 

a) Embedment factor 

b) Creep Factor 

⎛ t(years)⎞ C2 =1+ 0.2 log10⎜ ⎟ ⎝ 0.1 ⎠
 

•	 For end of construction t(yrs) = 0.1 yr (1.2 months) 

⎛ 0.1⎞ C2 =1+ 0.2 log10 ⎜	 ⎟ =1.0 ⎝ 0.1⎠

• For end of 1 year: 

⎛ 1 ⎞ C2 =1+ 0.2 log10 ⎜ ⎟ =1.2 ⎝ 0.1⎠

Step 9: Determine the settlement at end of construction as follows: 

Si =C1C2∆p∑ Hi 

⎛ ⎞

( )( )⎜ 1,655psf ⎟⎛ in ⎞ Si = 0.896 1.0 ⎜ ⎟⎜0.1760 ⎟ ⎜ psf tsf 2,000 ⎟⎝ ⎠ ⎝ tsf ⎠
 

S i = 0.130inches

Step 10: Determine the settlement after 1 year as follows: 

⎛1.2 ⎞ Si = 0.130 inches⎜	 ⎟ = 0.156inches ⎝1.0 ⎠

8.5.1.3 Tabulation of Parameters in Schmertmann’s Method 

To facilitate computations, Table 8-11 presents a tabulation of the various parameters 

involved in computation of settlement by Schmertmann’s method. This table was generated 

by using the linear interpolation scheme demonstrated in Example 8-2. Linear interpolation 

may be used for Lf/Bf values between those presented in Table 8-11. 

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Table 8-11 

Values of parameters used in settlement analysis by Schmertmann’s method 

Lf/Bf 

Iz at 

footing 

base, 

IZB 

Depth 

to Izp, 

DIP 

Depth of 

IZ 

diagram, 

DI 

X 

factor Lf/Bf 

Iz at 

footing 

base, 

IZB 

Depth 

to Izp, 

DIP 

Depth of 

IZ 

diagram, 

DI 

X 

factor 

Note 1 Note 1 Note 2 Note 1 Note 1 Note 2 

1.00 0.100 0.500 2.000 1.250 6.00 0.156 0.778 3.111 1.528 

1.25 0.103 0.514 2.056 1.264 6.25 0.158 0.792 3.167 1.542 

1.50 0.106 0.528 2.111 1.278 6.50 0.161 0.806 3.222 1.556 

1.75 0.108 0.542 2.167 1.292 6.75 0.164 0.819 3.278 1.569 

2.00 0.111 0.556 2.222 1.306 7.00 0.167 0.833 3.333 1.583 

2.25 0.114 0.569 2.278 1.319 7.25 0.169 0.847 3.389 1.597 

2.50 0.117 0.583 2.333 1.333 7.50 0.172 0.861 3.444 1.611 

2.75 0.119 0.597 2.389 1.347 7.75 0.175 0.875 3.500 1.625 

3.00 0.122 0.611 2.444 1.361 8.00 0.178 0.889 3.556 1.639 

3.25 0.125 0.625 2.500 1.375 8.25 0.181 0.903 3.611 1.653 

3.50 0.128 0.639 2.556 1.389 8.50 0.183 0.917 3.667 1.667 

3.75 0.131 0.653 2.611 1.403 8.75 0.186 0.931 3.722 1.681 

4.00 0.133 0.667 2.667 1.417 9.00 0.189 0.944 3.778 1.694 

4.25 0.136 0.681 2.722 1.431 9.25 0.192 0.958 3.833 1.708 

4.50 0.139 0.694 2.778 1.444 9.50 0.194 0.972 3.889 1.722 

4.75 0.142 0.708 2.833 1.458 9.75 0.197 0.986 3.944 1.736 

5.00 0.144 0.722 2.889 1.472 10.00 0.200 1.000 4.000 1.750 

5.25 0.147 0.736 2.944 1.486 > 10 0.200 1.000 4.000 1.750 

5.50 0.150 0.750 3.000 1.500 

5.75 0.153 0.764 3.056 1.514 

Notes: 

1. The depths are obtained by multiplying 

the value in this column by the footing 

width, Bf. 

2. If elastic modulus is not based on SPT 

or CPT, then X=1.0. See Section 8.5.1.1 

for a discussion on values of X factor. 

Legend IZB 

DI 

DIP 

IZ 

Depth below footing 

Strain 

Influence, 

Diagram 

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8.5.2 Obtaining Limiting Applied Stress for a Given Settlement 

As indicated in Section 8.3, the allowable bearing capacity based on settlement 

considerations is defined as “the applied stress that results in a specified amount of 

settlement.” Thus, the quantity of interest is often the limiting applied stress for a specified 

amount of settlement. In this case, Equation 8-16 can be inverted and solved to obtain the 

limiting applied stress, ∆p, for a given settlement, Si. By repeating the computation for a 

range of settlement values, the curves shown in Zone B of Figure 8-10 can be generated. It is 

important to realize that the applied stress computed by the inverted form of Equation 8-16 is 

a uniform stress. Consequently, that value of stress should be compared to the Meyerhof 

equivalent uniform pressure (qeq) acting on an effective footing width as shown in Figure 8­

17b and not the maximum stress (qmax) of the trapezoidal pressure distribution on the total 

footing width as shown in Figure 8-17a. It is for this reason that the X-axis of an allowable 

bearing capacity chart refers to an effective footing width and not total footing width. 

8.5.3 Consolidation Settlement 

The procedures to compute consolidation settlements discussed in Chapter 7 can be applied 

to spread footings also. The following example illustrates the method for determining 

consolidation settlement due to a load applied to a spread footing. 

Example 8-3:	 Determine the settlement of the 10 ft × 10 ft square footing due to a 130 

kip axial load. Assume the gravel layer is incompressible. 

130 kips 

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Rock 

10′

4′

10′

Gravel 

γt = 130 pcf 

Normally consolidated clay 

γ′ = 65 pcf, eo = 0.75, Cc = 0.4 
Solution: 

Find overburden pressure, po, at center of clay layer 

po = (14 ft × 130 pcf) + (5 ft × 65 pcf) = 2,145 psf 

Find change in pressure ()p) at center of clay layer due to applied load. Use the approximate 

2:1 stress distribution method discussed in Section 2.5 of Chapter 2. 

130 kips 130 kips ∆p = = = 0.208 ksf = 208psf

(10ft + 15 2 ft) 625ft 

Use Equation 7-2 to calculate the magnitude of consolidation settlement. 

In reality, the magnitude of the total settlement of the foundation would be the sum of the 

consolidation settlement of the clay and the immediate settlement of the gravel. The gravel 

was assumed to be incompressible in this example. However, in practice, the component of 

the total settlement due to the immediate settlement of the gravel would be determined by 

using Schmertmann’s method with only that portion of the strain influence diagram in the 

gravel being considered. 

8.6 SPREAD FOOTINGS ON COMPACTED EMBANKMENT FILLS 

Geotechnical engineers have long recognized the desirability of placing footings on 

engineered fills. In general, the load imposed by the weight of the fill is many times that of 

the imposed footing load. If adequate time is allowed for the foundation soils to settle under 

the fill load, subsequent application of a smaller structural load will result in negligible 

settlement of the structure. In bridge construction, common practice is to build the approach 

embankment excluding the area to be occupied by the abutment and allow settlement to 

occur prior to abutment construction. Details of the settlement of approach embankment fills 

are presented in Chapter 7. 

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C ∆H = H c ⎛ p log ⎜ o + ∆p ⎞

⎟ 10 ⎜ ⎟ 1 + e o ⎝ po ⎠

⎛ 0.4 ⎞ ⎛ 2,145psf + 208psf ⎞ ∆H =10 ft ⎜ ⎟log ⎜ ⎟ 10 = ⎜ =⎟ 0.09 ft 1.1in ⎝1 + 0.75 ⎠ ⎝ 2,145psf ⎠
Field evaluation of spread footings placed in or on engineered fills constructed of select 

granular material, show that spread footings provide satisfactory performance, i.e., minimal 

vertical and lateral displacements, if all relevant factors are considered in the design of the 

embankment and the footing. A performance evaluation of spread footings on compacted 

embankment fills was conducted through a joint study between FHWA and the Washington 

State Department of Transportation (FHWA, 1982). A visual inspection was made of the 

structural condition of 148 highway bridges supported by spread footings on engineered fills 

throughout the State of Washington. The approach pavements and other bridge 

appurtenances were also inspected for damage or distress that could be attributed to the use 

of spread footings on engineered fill. This review, in conjunction with detailed survey 

investigations of the foundation movement of 28 selected bridges, was used to evaluate the 

performance of spread footings on engineered fills. None of the bridges investigated 

displayed any safety problems or serious functional distress. The study concluded that 

spread footings can provide a satisfactory alternative to deep foundations, especially when 

high embankments of good quality borrow materials are constructed over satisfactory 

foundation soils. Further studies were made to substantiate the feasibility of using spread 

footings in lieu of more expensive deep foundation systems. Cost analyses showed that 

spread footings were 50 to 65 percent less expensive than the alternate choice of deep 

foundations. Studies of foundation movement showed that bridges easily tolerated 

differential settlements of 1 to 3 inches (25 to 75 mm) without serious distress. 

In addition to the FHWA (1982) study which was limited to the bridges in the State of 

Washington, a nationwide study of 314 bridges was conducted (FHWA, 1985). The 

nationwide study arrived at similar conclusions. Unfortunately many agencies continue to 

disregard spread footings as alternative foundations for highway structures. Yet another 

study (NCHRP, 1983), states the following: 

"In summary, it is very clear that the tolerable settlement criteria currently 

used by most transportation agencies are extremely conservative and are 

needlessly restricting the use of spread footings for bridge foundations on 

many soils. Angular distortions of 1/250 of the span length and differential 

vertical movements of 2 to 4 inches (50 to 100 mm), depending on span 

length, appear to be acceptable, assuming that approach slabs or other 

provisions are made to minimize the effects of any differential movements 

between abutments and approach embankments. Finally, horizontal 

movements in excess of 2 inches (50 mm) appear likely to cause structural 

distress. The potential for horizontal movements of abutments and piers 

should be considered more carefully than is done in current practice." 

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It is recommended that compacted structural fills used for supporting spread footings 

should be a select and specified material that includes sand- and gravel-sized particles. 

Furthermore, the fill should be compacted to a minimum relative compaction of 95% 

based on Modified Proctor compaction energy. This structural fill should extend for 

the entire embankment below the footing. FHWA (2002c) notes that the Washington 

Department of Transportation (WSDOT) successfully used the gradation listed in Table 8-12 

to design spread footings for the I-5 Kalama Interchange. WSDOT limited the maximum 

bearing pressures to 3 tsf (290 kPa) and the measured settlements were found to be less than 

1.5 in (40 mm) within the fill. In addition to WSDOT, the Nevada Department of 

Transportation (NDOT) commonly uses spread foundations founded within compacted 

structural embankment fills. 

Direct shear testing of materials such as those described in Table 8-12 is not practical on a 

project-by-project basis since such materials require large specialized test equipment. 

Therefore the design of spread footings on compacted sand and gravel is based on a 

combination of experience and the results of infrequent large-scale laboratory testing on 

specified gradations of select fill materials. Materials specifications are then developed 

based on the specified gradations to ensure good quality control during construction. This 

procedure helps ensure that the conclusions from the laboratory tests are valid for the 

construction practices used to place the fills. 

Table 8-12 

Typical specification of compacted structural fill used by WSDOT (FHWA, 2002c) 

Sieve Size Percent Passing 

4” (100 mm) 100 

2” (50 mm) 75 – 100 

No. 4 (4.75 mm) 50 – 80 

No. 40 (0.425 mm) 30 max 

No. 200 (0.075 mm) 7 max 

Sand Equivalent (See Note 1) 42 min 

Notes: 

1. See Section 5.3.4.1 in Chapter 5 for a discussion of sand equivalent test. 

8.6.1 Settlement of Footings on Structural Fills 

Calculation of the settlement of a spread footing supported in or on an engineered fill 

requires an assumption about the compressibility of the fill material. Because structural fills 

should be constructed of good-quality granular materials and by following good construction 

techniques, the estimation of settlement lends itself to the application of the methods 

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discussed in this Chapter. To estimate settlements of footings in structural fills by 

Schmertmann’s method, an assumption must be made about the SPT N-value that is 

representative of the engineered fill. 

FHWA (1987) used a SPT N-value of 32 blows per foot corrected for overburden pressure as 

a representative value for estimating settlement in structural fills. This value of SPT N-value 

corresponds to a relative density, Dr, of approximately 85 percent at an overburden stress of 

about 1 tsf (100 kPa) (FHWA, 1987); this is confirmed by the data in Figure 5-23. Based on 

Figure 5-33 or Equation 5-21, this value of Dr is at approximately 97% relative compaction 

based on Modified Proctor compaction energy (ASTM D 1557). Under such compacted 

conditions, and in the absence of other SPT data in structural fills, the settlement of a footing 

supported on structural fill can be estimated by using an assumed corrected SPT N-value 

(N160) of 32. However, a relative compaction of 95% based on Modified Proctor compaction 

energy is often used. For this case, a corrected SPT N-value (N160) of 23 is more 

appropriate. 

8.7 FOOTINGS ON INTERMEDIATE GEOMATERIALS (IGMs) AND ROCK 

The assumption made in this chapter is that intermediate geomaterials (IGMs) are stiff and 

strong enough that bearing capacity and settlement considerations will generally not govern 

the design of a spread footing supported on such a material. If a settlement estimate is 

necessary for shallow foundations supported on an IGM or rock, a method based on elasticity 

theory is probably the best approach. As with any of the methods for estimating settlement 

that use elasticity theory, the accuracy of the values estimated for the elastic parameter(s) 

required by the method is a major factor in determining the reliability of the predicted 

settlements. 

Equation 8-19 may be used to compute the settlement of a shallow spread footing founded on 

rock based on Young’s modulus of the intact rock. In this equation, the stress applied at the 

top of the rock surface can be calculated by using the stress distribution methods presented in 

Chapter 2. 

Cd ∆p Bf (1 − ν2 ) δv = 8-19

Em 

where: δv = vertical settlement at surface 

Cd = shape and rigidity factors (Table 8-13) 

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∆p = change in stress at top of rock surface due to applied footing load 

Bf = footing width or diameter 

ν = Poisson’s ratio (refer to Table 5-22 in Chapter 5) 

Em = Young’s modulus of rock mass (see Section 5.12.1 in Chapter 5) 

The elastic modulus of IGMs and some rocks may be measurable by in situ testing with 

equipment such as the pressuremeter (FHWA 1989a), the dilatometer (FHWA 1992b), and 

plate load tests or flat jacks. ASTM standards are available for each of these in situ tests and 

they provide details regarding performance and the interpretation of the test data. The 

method for determining elastic modulus based on RMR discussed in Chapter 5. 

To preserve the stability of footings on IGMs or rock, the geotechnical engineer must 

evaluate the potential for a global stability failure and the potential of limitations of the 

allowable bearing capacity because of the presence of rock mass discontinuities. The bearing 

capacity of IGMs derived from sedimentary rock can dramatically decrease when the IGM is 

exposed to weathering and moisture. 

Table 8-13 

Shape and rigidity factors, Cd, for calculating settlements of points on loaded areas at 

the surface of a semi-infinite elastic half space (after Winterkorn and Fang, 1975) 

Shape Center Corner 

Middle of 

Short Side 

Middle of 

Long Side Average 

Circle 1.00 0.64 0.64 0.64 0.85 

Circle (rigid) 0.79 0.79 0.79 0.79 0.79 

Square 1.12 0.56 0.76 0.76 0.95 

Square (rigid) 0.99 0.99 0.99 0.99 0.99 

Rectangle (length/width): 

1.5 1.36 0.67 0.89 0.97 1.15 

2 1.52 0.76 0.98 1.12 1.30 

3 1.78 0.88 1.11 1.35 1.52 

5 2.10 1.05 1.27 1.68 1.83 

10 2.53 1.26 1.49 2.12 2.25 

100 4.00 2.00 2.20 3.60 3.70 

1000 5.47 2.75 2.94 5.03 5.15 

10000 6.90 3.50 3.70 6.50 6.60 

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8.8 ALLOWABLE BEARING CAPACITY CHARTS 

The concept of an allowable bearing capacity chart was discussed in Section 8.3. The curves 

shown in Figure 8-10 can be obtained by performing computations for allowable bearing 

capacity and settlement for a range of values of footing widths by using the procedures 

described in Sections 8.4 to 8.7. This section presents an example bearing capacity chart and 

a step-by-step procedure to use such a chart for the sizing of footings. 

Example 8-3: The abutments of a bridge will be founded on spread foundations similar to 

the configuration shown in Figure 8-4. The length, Lf, of the abutment footing 

is 130 ft. The minimum depth of embedment, Df, of the footing base is 5 ft. 

The geotechnical engineer developed a bearing capacity chart based on sitespecific subsurface data. This chart is shown in Figure 8-22. Determine the 

footing width, Bf, such that the settlement of the footing is less than or equal 

to 1 in. 

Chart based on 

Lf =130 ft, Df =5 ft 

Figure 8-22. Example allowable bearing capacity chart. 

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Solution: 

Step 1: 

Assume a footing width, Bf, and compute the equivalent net uniform (Meyerhof) bearing 

pressure, qeu, at the base of the footing. The equivalent net uniform bearing pressure, qeu, is 

obtained by dividing the resultant vertical load, R, by the effective area, A', of the footing as 

follows: 

qeu = R/A' 

The resultant vertical load, i.e., the vertical component of the resultant load, should be 

determined by using the unfactored dead load, plus the unfactored component of live and 

impact loads assumed to extend to the footing level (Section 4.4.7.2 of AASHTO, 2002). 

The effective area, A', is determined as follows based on Equation 8-7, 8-8 and 8-9: 

A' = B'fL'f = (Bf -2eB) (Lf -2eL) 

where eB and eL are the eccentricities of the resultant load, R, in the Bf and Lf directions, 

respectively, as indicated in Figure 8-16. The eccentricities, eB and eL should be such that 

they are less than Bf/6 and Lf/6, respectively to ensure that no uplift occurs anywhere within 

the base of the footing. In cases where there is no load eccentricity, the effective length, L'f, 

and the effective width, B'f, are equal to the actual length, Lf, and actual width, Bf, 

respectively. 

For the example problem stated above, assume for the sake of illustration that the computed 

equivalent net uniform bearing pressure, qeu, at the base of the footing is 2.75 tsf for a 

retaining wall footing that is 130 ft long (Lf = L'f), has an effective width, B'f, of 18 ft, and is 

embedded 5 ft. 

Step 2: 

Since the minimum required allowable bearing capacity has to be at least equal to the net 

equivalent uniform bearing pressure, qeu, draw a horizontal line on the chart corresponding to 

the value of qeu. Thus, for the example problem, draw a horizontal line WX on the chart 

corresponding to a value of 2.75 tsf as shown in Figure 8-22. This horizontal line will 

intersect the curves of equal settlement, e.g., S=0.75 in, S = 1.0 in and so on as shown in 

Figure 8-22. 

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Step 3: 

Draw a vertical line YZ for the effective footing width, B'f, of 18 ft. Like the horizontal line, 

WX, the vertical line, YZ, will intersect the curves of equal settlement, e.g., S=0.75 in, S = 

1.0 in as shown in Figure 8-22. 

 

Step 4: 

From the point of intersection of the vertical line, YZ, with the appropriate acceptable 

settlement curve (1.00-in for this example) draw a horizontal line to the Y-axis to determine 

the allowable bearing capacity. By drawing the horizontal line, AC, it can be determined that 

the allowable bearing capacity corresponding to an effective footing width of 18 ft is 

approximately 3.2 tsf (see Point C in Figure 8-22). This value is greater than the qeu value of 

2.75 tsf and therefore the footing whose effective width, B'f, is 18 ft is acceptable. 

An alternative way to evaluate the acceptability of a footing size is to determine the 

estimated settlement corresponding to the computed equivalent net uniform bearing pressure, 

qeu, and compare it with the acceptable settlement. From the bearing capacity chart for the 

example problem, it can be seen that at an effective footing width, B'f, of 18 ft and a qeu value 

of 2.75 tsf, the estimated settlement will be approximately 0.88 in (see Point D that falls 

between the S=0.75 in and S=1.00 in curves in Figure 8-22). This value of estimated 

settlement is less than the limiting settlement of 1 in and is therefore acceptable. 

Step 5: 

Repeat Steps 1 to 4 as necessary to optimize the footing design or to resize the footing based 

on the “available” allowable bearing capacity. In this example, the “available” allowable 

bearing capacity for an 18 ft wide footing is 3.2 tsf which is greater than the required value 

of 2.75 tsf. Thus, it is possible that the footing width can be reduced. During the 

optimization process, linear interpolation within the limits of the data presented in the chart 

is acceptable. However, extrapolation of data is not advisable. 

8.8.1 Comments on the Allowable Bearing Capacity Charts 

•	 A factor of safety, FS, against ultimate bearing capacity (shear) failure is included in the 

computations that yield the steeply rising line on the left side of the chart, i.e., the line 

that is based on bearing capacity considerations. Since the settlement based allowable 

bearing capacity curves plot on the right side of the bearing capacity line, the actual 

factor of safety against shear failure will be higher than the assumed minimum FS. 

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•	 The effective footing width, B’f, on the X-axis of the charts represents the least lateral 

effective dimension of the footing. The footing size determined from the chart is a 

function of the depth of embedment of the footing, Df, and the length of the footing, Lf. 

The depth of embedment, Df, is the vertical distance between the lowest finished 

permanent ground surface above the footing to the base of the footing. Each bearing 

capacity chart is developed for a given footing length, Lf, and a minimum depth of 

embedment, Df. Therefore, these quantities must be clearly labeled on the chart as shown 

in Figure 8-22. If the actual dimensions of Df and/or Lf vary by more than ±10% from 

those noted on the charts then a new chart should be developed for the actual values of Df 

and Lf. 

•	 Finally, each bearing capacity chart should be specific to a given foundation element and 

should be developed based on location-specific geotechnical data. Consequently the 

charts should not be used for foundations at locations other than at which they are 

applicable. 

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Soils and Foundations – Volume II 8 - 63 December 2006 
8.9 EFFECT OF DEFORMATIONS ON BRIDGE STRUCTURES 

Bridge foundations and other geotechnical features such as approach embankments should be 

designed so that their deformations (settlements and/or lateral movements) will not cause 

damage to the bridge structure. Uneven displacements of bridge abutments and pier 

foundations can affect the quality of ride and the safety of the traveling public as well as the 

structural integrity of the bridge. Such movements often lead to costly maintenance and 

repair measures. Therefore, it is important that the geotechnical specialist as well as the 

structural engineer fully understand the effect of deformations of geotechnical features on 

bridge structures. 

FHWA (1985) and Duncan and Tan (1991) studied tolerable movements for bridges and 

found that “foundation movements would become intolerable for some other reason before 

reaching a magnitude that would create intolerable rider discomfort.” The “other” reasons 

might include reduction of clearance at overpasses and drainage considerations, as discussed 

later. Therefore, if movements are within a tolerable range with regard to structural distress 

for the bridge superstructure, they will also be acceptable with respect to user comfort and 

safe vehicle operation. The severity of the consequences of uneven movements of bridge 

structures, superstructure as well as substructure, increases with the magnitude of the 

settlements and lateral movements. Both of these components of bridge movements are 

discussed below. 

A. Settlement 

Settlement can be subdivided into the following three components, which are illustrated in 

Figure 8-23 (Duncan and Tan, 1991): 

1.	 Uniform settlement: In this case, all bridge support elements settle equally. Even 

though the bridge support elements settle equally, they can cause differential 

settlement with respect to the approach embankment and associated features such as 

approach slabs and utilities that are commonly located in or across the end-spans of 

bridges. Such differential settlement can create several problems. For example, it 

can reduce the clearance of the overpass, create a bump at the end of the bridge, 

change grades at the end of the bridge causing drainage problems, and distort 

underground utilities at the interfaces of the bridge and approaches. 

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Tilt (Rotation) 

Differential 

Settlement 

Differential 

Settlement 

SL 

SL 

SL 

Uniform Settlement 

Figure 8-23. Components of settlement and angular distortion in bridges 

(after Duncan and Tan, 1991). 

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Although uniform settlements may be computed theoretically, from a practical 

viewpoint it is not possible for the bridge structure to experience truly uniform 

settlement due to a combination of many factors including, but not limited to, the 

variability of loads and soil properties 

2.	 Tilt or rotation: Tilt or rotation occurs mostly in single span bridges with stiff 

superstructures. Tilt or rotation may not cause distortion of the superstructure and 

associated damage, but due to its differential movement with respect to the facilities 

associated with approach embankments, tilt or rotation can create problems similar to 

those of uniform settlement that were discussed above, e.g., a bump at the end of the 

bridge, drainage problems, and damage to underground utilities. 

3. Differential settlement: Differential settlement directly results in deformation of the 

bridge superstructure. As shown in Figure 8-23, two different patterns of differential 

settlement can occur. These are: 

a.	 Regular pattern: In this case, the settlement increases progressively from the 

abutments towards the center of the bridge 

b.	 Irregular pattern: In this case, the settlement at each support location varies 

along the length of the bridge. 

Both of the above patterns of settlement lead to angular distortion, which is defined as the 

ratio of the difference in settlement between two points divided by the distance between the 

two points. For bridge structures, the two points to evaluate the differential settlement are 

commonly selected as the distance between adjacent support elements, SL, as shown in 

Figure 8-23. Depending on the type of connections between the superstructure and support 

columns (pinned or fixed) and the locations of expansion and construction joints along the 

bridge deck (mid-span or elsewhere), the irregular pattern of differential settlement has the 

potential to create greater structural distress than the regular pattern of differential settlement. 

The distress may occur due to increased internal stresses associated with flexure and/or shear 

of the bridge superstructure and is generally manifested by cracks in the bridge deck and/or 

girders at support locations. 

In addition to the problems they create in the bridge superstructure, differential settlements 

can create the same problems as uniform settlements discussed earlier, i.e., problems with 

bumps at the junctures with approach slabs, problems with drainage, problems with clearance 

at underpasses, etc. 

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B. Horizontal Movements 

Horizontal movements cause more severe and widespread problems than do equal 

magnitudes of vertical settlement. The types of problems that arise as a result of differential 

horizontal movements between bridge decks and abutments, or between adjacent spans of 

bridges, include the following (Duncan and Tan, 1991): 

•	 Shearing of anchor bolts, 

•	 Excessive opening of expansion joints, 

•	 Reduced effectiveness of expansion joints when clearance is reduced, 

•	 Complete closing of expansion joints and jamming of bridge decks into abutments or 

adjacent spans, 

•	 Shifting of abutments when expansion joints jam, 

•	 Severe damage to abutment walls, approach slabs or bridge decks due to excessive 

loads when expansion joints jam, 

•	 Distortion and damage to bearing devices, 

•	 Excessive tilting of rockers, 

•	 Damage to rail curbs, sidewalks and parapets. 

C. Reliability of Estimation of Movements 

All analytical methods used for estimating movements are based on certain assumptions. 

Therefore, there is an inherent uncertainty associated with the estimated values of 

movements. The uncertainty of estimated differential settlement is larger than the 

uncertainty of the estimated settlement at the two support elements used to calculate the 

differential settlement, e.g., between abutment and pier, or between piers. For example, if 

one support element settles less than the amount estimated while the other support element 

settles the amount estimated, the actual differential settlement will be larger than the 

difference between the two values of estimated settlement at the support elements. Duncan 

and Tan (1991) suggest the following assumptions to estimate the likely value of differential 

settlement: 

•	 The settlement of any support element could be as large as the value calculated by 

using conservative procedures, and 

•	 At the same time, the settlement of the adjacent support element could be zero. 

Use of these conservative assumptions would result in an estimated maximum possible 

differential settlement equal to the largest settlement calculated at either end of any span. 

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Soils and Foundations – Volume II 8 - 67 December 2006 
8.9.1 Criteria for Tolerable Movements of Bridges 

8.9.1.1 Vertical Movements 

The FHWA (1985) study used the following definition of intolerable movement: 

“Movement is not tolerable if damage requires costly maintenance and/or 

repairs and a more expensive construction to avoid this would have been 

preferable.” 

This definition is somewhat subjective based on the cost and practical problems involved in 

the repair and maintenance or use of an alternative more expensive construction technique. 

FHWA (1985) studied data for 56 simple span bridges and 119 continuous span bridges and 

chose to express the definition for tolerable movement quantitatively in terms of limiting 

angular distortion as shown in Table 8-14. 

Table 8-14 

Tolerable movement criteria for bridges (FHWA, 1985; AASHTO 2002, 2004) 

Limiting Angular Distortion, δ/SL Type of Bridge 

0.004 Multiple-span (continuous span) bridges 

0.005 Single-span bridges 

Note: δ is differential settlement, SL is the span length. The quantity, δ/SL, is 

dimensionless and is applicable when the same units are used for δ and SL, i.e., 

if δ is expressed in inches then SL should also be expressed in inches. 

For example, the criteria in Table 8-14 suggest that for a 100 ft (30 m) span, a differential 

settlement of 4.8 inches (120 mm) is acceptable for a continuous span and 6 inches (150 mm) 

is acceptable for a simple span. 

Such relatively large values of differential settlements create concern for structural designers, 

who often arbitrarily limit the criteria to one-half to one-quarter of the values listed in Table 

8-14. While there are no technical reasons for structural designers to set such arbitrary 

additional limits for the criteria listed in Table 8-14, there are often practical reasons based 

on the tolerable limits of deformation of other structures associated with a bridge, e.g., 

approach slabs, wingwalls, pavement structures, drainage grades, utilities on the bridge, 

deformations that adversely affect quality of ride, etc. Thus, the relatively large differential 

settlements based on Table 8-14, should be considered in conjunction with functional or 

performance criteria not only for the bridge structure itself but for all of the associated 

facilities. The following steps are suggested in this regard: 

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Soils and Foundations – Volume II 8 - 68 December 2006 
Step 1: Identify all possible facilities associated with the bridge structure, and the tolerance 

of those facilities to movements. 

Step 2: Due to the inherent uncertainty associated with estimated values of settlement, 

determine the differential settlement by using the conservative assumptions 

described earlier. It is important that the estimation of differential settlement is 

based on a realistic evaluation of the sequence and magnitude of the loads as 

described in Section 8.9.2. 

Step 3: Compare the differential settlement from Step 2 with the various tolerances 

identified in Step 1 and in Table 8-14. Based on this comparison identify the 

critical component of the facility. Review this critical component to check if it can 

be relocated or if it can be designed to more relaxed tolerances. Repeat this process 

as necessary for other facilities. In some cases, a simple re-sequencing of the 

construction of the facility based on the construction sequence of the bridge may 

help mitigate the issues associated with intolerable movements. 

The above approach will help to develop project-specific limiting angular distortion criteria 

that may differ from the general guidelines listed in Table 8-14. 

8.9.1.2 Horizontal Movements 

Based on a survey of bridges, FHWA (1985) found that horizontal movements less than 1 in 

(25 mm) were almost always reported as being tolerable, while horizontal movements greater 

than 2 in (50 mm) were quite likely to be considered to be intolerable. Based on this 

observation, FHWA (1985) recommended that horizontal movements be limited to 1.5 in (38 

mm). The data presented by FHWA (1985) showed that horizontal movements tended to be 

more damaging when they were accompanied by settlement than when they were not. The 

estimation of magnitude of horizontal movements should take into account the movements 

associated with considerations of slope instability and lateral squeeze as discussed in Chapter 

6 and 7, respectively. 

Abutments are often designed for active lateral earth pressure conditions, which require a 

certain amount of movement (see Chapter 9). Depending on the configuration of the bridge 

end spans and expansion joints, horizontal movements of an abutment can be restrained, 

however, such restraint can lead to an increase in the lateral earth pressures above the active 

earth pressures normally used in design. Design of expansion joints should allow for 

sufficient movement to keep earth pressures at or close to their design values and still allow 

the joints to perform properly under all temperature conditions. 

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8.9.2 Loads for Evaluation of Tolerable Movements Using Construction Point 

Concept 

Most designers use the criteria described in Section 8.9.1 as if a bridge structure is 

instantaneously wished into place, i.e., all the loads are applied at the same time. In reality, 

loads are applied gradually as construction proceeds. Consequently, settlements will also 

occur gradually as construction proceeds. There are several critical construction points that 

should be evaluated separately by the designer. Table 8-15 illustrates this critical 

construction concept for a bridge abutment footing that was constructed as part of a 2-span 

bridge in the southwest United States. The prestressed concrete beam bridge is 64.4 ft (19.6 

m) wide and 170 ft (52 m) long. The bridge is continuous with mechanically stabilized earth 

(MSE) walls wrapped around both of the abutments. The abutments are fixed for shear 

transfer through semi-integral diaphragms connected to spread footings on top of the MSE 

walls. 

Even though the total settlement cited in Table 8-15 is 7.5 inches, in reality only 2.0 in is 

significant because it occurs progressively during the first 10 years the bridge is in service. 

(Note that immediately after construction the net settlement was estimated to be only 0.5 in 

even though the total settlement computed at this stage is 5.0 in) 

The pier for this bridge is supported by a group of pipe piles and was estimated to experience 

a settlement of approximately 0.5 in. To compute the worst angular distortion, it was 

assumed that the pier would not experience settlement while the abutment would experience 

the full estimated settlement. Thus, the angular distortion criterion where 0 in settlement is 

assumed at the pier yields the following results for an 85 ft span (1/2 of the 170 ft long 

bridge): 

• With Construction Point Concept 

Angular Distortion, A = (2.0 in – 0.0 in)/(85 ft x 12 in/ft) = 2.0 in/1,020 in = 0.002 

In this case, A is one-half of the limiting angular distortion of 0.004 as per Table 8­

14. Therefore, the settlements are acceptable. 

• Without Construction Point Concept 

Angular Distortion, A = (7.5 in – 0.0 in)/(85 ft x 12 in/ft) = 7.5 in/1,020 in = 0.0073 

Since A > 0.004, the angular distortion is deemed intolerable. 

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Table 8-15 

Example of settlements evaluated at various critical construction points 

Construction Point 

Estimated Net 

Applied Stress1 

(psf) 

Settlement 

(inches)2 

Net Settlement 

(inches) 

I. Embankment only 2,770 3.4 -

II. MSE Wall + Spread footing 

(no deck) 6,020 5.0 1.6 (during 

construction) 

III. MSE Wall + Spread footing + 

Deck (DL + LL) 6,520 5.5 

0.5 

(= 5.5 – 5.0) 

IV. MSE Wall + Spread Footing + 

Deck (DL+LL) + Creep3 6,520 7.5 

2.0 

(= 7.5 – 5.5) 

Notes: 

1. The 2 ft depth of embedment for the MSE wall was taken into account while 

estimating the net applied stress from new construction. 

2. Settlement analyses were performed by using Schmertmann’s method (1978) that 

allows for estimation of long-term (creep) settlement. In this project, relatively dry, 

low plastic fine grained soils were encountered that could possibly deform for some 

time after construction. 

3. A time period of 1.5 months was assumed for each Point II and III analyses. For 

this duration, the creep component of the deformation was less than 5% of the 

settlements reported above for Point II and III. Conservatively, a time period of 10 

years was assumed for the creep deformations for Point IV, after which it was 

assumed that no significant creep deformations would occur. Note, that the net 

settlement of 2.0 inches between construction Point III and IV is attributed entirely 

to creep settlement. 

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In this example, if the designer did not take into account the various construction points 

when evaluating settlement, then not only would the angular distortion criteria listed in Table 

8-15 not be met but it would also likely lead to implementation of costly and unnecessary 

ground improvement measures. This approach was used successfully for 55 bridges 

constructed as part of the I25/I40 (“BIG I”) traffic interchange in Albuquerque, NM. This 

critical construction point approach permitted the use of true bridge abutments, i.e., spread 

footings on top of MSE walls, on 28 of the 55 bridges on the BIG I project, which resulted in 

significant cost savings for the New Mexico Department of Transportation (NMDOT). The 

project was completed in 2001 and all of the bridges have performed well to date (2006). 

A key point in evaluating settlements at critical construction points is that the approach 

requires close coordination between the structural and geotechnical specialists. In the case of 

the BIG I project, the structural specialist performed a realistic evaluation of the loads and 

construction sequence and communicated them to the geotechnical specialist, who then 

evaluated the settlements for those loads. As demonstrated by the above example, this 

approach resulted in a realistic evaluation of the deformation of the bridge structure. This 

critical construction point approach can also often help in making other decisions such as the 

need for costly ground improvement measures. 

8.10 SPREAD FOOTING LOAD TESTS 

Spread footing load tests can be used to verify both bearing capacity and settlement 

predictions. Briaud and Gibbens (1994) present the results of predicted and measured 

behavior of five spread footings on sand. Full scale tests have been done on predominantly 

granular soils. An example is the I-359 project in Tuscaloosa, Alabama where dead load was 

placed on 12 ft x 12 ft (3.7 m x 3.7 m) footings to create a foundation contact pressure of 

over 4 tsf (383 kPa). A settlement of 0.1 in (2.5 mm) was recorded when the footing 

concrete was placed. The greatest settlement recorded after application of the load was also 

approximately 0.1 in (2.5 mm). Spread footing load tests can help develop confidence in the 

use of such foundations for transportation structures. 

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8.11 CONSTRUCTION INSPECTION 

Construction inspection requirements for shallow foundations are similar to those for other 

concrete structures. In some cases, agencies may have inspector checklists for construction 

of shallow foundations. Table 8-16 provides a summary of construction inspection check 

points for shallow foundations. Throughout construction, the inspector should check 

submittals for completeness before transmitting them to the engineer. 

8.11.1 Structural Fill Materials 

Fill requirements should be strictly adhered to because the fill must perform within expected 

limits with respect to strength and, more importantly, within tolerance for differential 

settlement. Sometimes the area for construction of the fill is small, such as behind abutment 

and wingwalls. In such situations, the use of hand compactors or smaller compaction 

equipment may be necessary. 

When the construction of structural fills that will support shallow foundations is being 

monitored, particular attention should be paid to the following items: 

•	 The material should be tested for gradation and durability at sufficient frequency to 

ensure that the material being placed meets the specification. 

•	 The specified level of compaction must be obtained in the fill. Testing, if applicable, 

should be performed in accordance with standard procedures and at the recommended 

intervals or number of tests per lift. 

If a surcharge fill is required for pre-loading, it should be verified that the unit weight of the 

surcharge fill meets the value assumed in the design. 

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Table 8-16 

Inspector responsibilities for construction of shallow foundations 

CONTRACTOR SET UP 

•

•

•

•

•

•

Review plans and specifications. 

Review contractor’s schedule. 

Review test results and certifications for pre-approved materials, e.g., cement, coarse and 

fine aggregate. 

Confirm that the contractor’s stockpile and staging area are consistent with locations 

shown on plans. 

Discuss anticipated ground conditions and potential problems with the contractor. 

Review the contractor’s survey results against the plans. 

EXCAVATION 

•

•

•

•

•

•

•

Verify that excavation slopes and/or structural excavation support is consistent with the 

plans. 

Confirm that limits of any required excavations are within right-of-way limits shown on 

the plans. 

Confirm that all unsuitable materials, e.g., sod, snow, frost, topsoil, soft/muddy soils, are 

removed to the limits and depths shown on the plans and the excavation is backfilled with 

properly compacted granular material. The in-place bearing stratum of soil or rock 

should be checked to verify the in-situ condition and the degree of improvement 

achieved by the contractor’s preparation approach. Some soil types can become 

remolded and weakened from disturbance. If the conditions deviate from those 

anticipated in the geotechnical report and/or the plans and specifications, the 

geotechnical engineer should be consulted to determine if additional measures are 

necessary. 

Confirm that leveling and proof-rolling of the foundation area is consistent with the 

requirements of the specifications. Probing is recommended for verification of subgrade. 

Confirm that contractor’s excavation operations do not result in significant water ponding. 

Confirm that existing drainage features, utilities, and other features are protected. 

Identify areas not shown on the plans where unsuitable material exists and notify 

engineer. 

SHALLOW FOUNDATION 

•

•

•

•

•

•

•

•

•

Approve footing foundation condition before concrete is poured. 

Confirm reinforcement strength, size, and type consistent with the specifications. 

Confirm consistency of the contractor’s outline of the footing (footing size and bottom of 

footing depth) with the plans. 

Confirm location and spacing of reinforcing steel consistent with the plans. 

Confirm water/cement ratio and concrete mix design consistent with the specifications. 

Record concrete volumes poured for the footing. 

Confirm appropriate concrete curing times and methods as provided in the specifications. 

Confirm that concrete is not placed on ice, snow, or otherwise unsuitable ground. 

Confirm that concrete is being placed in continuous horizontal layers and that the time 

between successive layers is consistent with the specifications. 

POST INSTALLATION 

• Verify pay quantities. 

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8.11.2 Monitoring 

The elevations of constructed foundations should be checked before and after the structural 

load is applied. The measurements made at those times will serve as a baseline for the longterm monitoring of the bridge. Subsequently, additional survey measurements should be 

made to confirm satisfactory performance or to identify whether potentially harmful 

settlements are occurring. It may be important to check the completion of fill settlements 

before foundation construction if the fill was constructed over soft compressible soils. As 

indicated in Chapter 7, settlement plates, horizontal inclinometers, or other types of 

instrumentation are typically installed in such cases. The lateral displacement potential can 

be greater than the vertical movements; therefore, if conditions warrant, monitoring may also 

include complete survey coordinates and possibly more accurate instrumentation. 

Monitoring may also be necessary to evaluate the impact of the new construction on 

neighboring facilities or the ground surface. Such concerns could be monitored with simple 

survey tag lines with benchmarks and monitoring hubs and telltales to measure lateral 

deviations and vertical subsidence/heave. Greater reliability may require more sophisticated 

instrumentation, such as inclinometers, strain gages, extensometers and tiltmeters. Surveys 

of the pre-construction condition of neighboring structures should be conducted, particularly 

in congested urban areas. The instrumentation program should be developed with a 

consideration of the anticipated performance, risks and potential consequences. Parameters 

should be identified that are critical to project success and appropriate instrumentation 

selected. A key to successful use of instrumentation is to measure, plot and interpret the data 

in a timely manner to be able to take corrective measures, if needed. 

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[THIS PAGE INTENTIONALLY BLANK] 
CHAPTER 9.0 

DEEP FOUNDATIONS 

Foundation design and construction involves assessment of factors related to engineering and 

economics. As discussed in Chapter 8, the selection of the most feasible foundation system 

requires consideration of both shallow and deep foundation types in relation to the characteristics 

and constraints of the project and site conditions. Situations commonly exist where shallow 

foundations are inappropriate for support of structural elements. These situations may be related 

either to the presence of unsuitable soil layers in the subsurface profile, adverse hydraulic 

conditions, or intolerable movements of the structure. Deep foundations are designed to transfer 

load through unsuitable subsurface layers to suitable bearing strata. Typical situations that 

require the use of deep foundations are shown in Figure 9-1 and briefly discussed below. 

•	 Figure 9-1(a) shows the most common case in which the upper soil strata are too 

compressible or too weak to support heavy vertical loads. In this case, deep foundations 

transfer loads to a deeper dense stratum and act as toe bearing foundations. In the absence 

of a dense stratum within a reasonable depth, the loads must be gradually transferred, 

mainly through soil resistance along shaft, Figure 9-1(b). An important point to remember 

is that deep foundations transfer load through unsuitable layers to suitable layers. The 

foundation designer must define at what depth suitable soil layers begin in the soil 

profile. 

•	 Deep foundations are frequently needed because of the relative inability of shallow 

footings to resist inclined, lateral, or uplift loads and overturning moments. Deep 

foundations resist uplift loads by shaft resistance, Figure 9-l(c). Lateral loads are resisted 

either by vertical deep foundations in bending, Figure 9-l(d), or by groups of vertical and 

battered foundations, which combine the axial and lateral resistances of all deep 

foundations in the group, Figure 9-l(e). Lateral loads from overhead highway signs and 

noise walls may also be resisted by groups of deep foundations, Figure 9-1(f). 

•	 Deep foundations are often required when scour around footings could cause loss of 

bearing capacity at shallow depths, Figure 9-l(g). In this case the deep foundations must 

extend below the depth of scour and develop the full capacity in the support zone below 

the level of expected scour. FHWA (2001c) scour guidelines require the geotechnical 

analysis of bridge foundations to be performed on the basis that all stream bed materials in 

the scour prism have been removed and are not available for bearing or lateral support. 

Costly damage and the need for future underpinning can be avoided by properly designing 

for scour conditions. 

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Figure 9-1. Situations in which deep foundations may be needed (Vesic, 1977; FHWA, 

2006a). 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 2 December 2006 
•	 Soils subject to liquefaction in a seismic event may also dictate that a deep foundation be 

used, Figure 9-1(h). Seismic events can induce significant lateral loads to deep 

foundations. During a seismic event, liquefaction-susceptible soils offer less lateral 

resistance as well as reduced shaft resistance to a deep foundation. Liquefaction effects on 

deep foundation performance must be considered for deep foundations in seismic areas. 

•	 Deep foundations are often used as fender systems to protect bridge piers from vessel 

impact, Figure 9-1(i). Fender system sizes and group configurations vary depending upon 

the magnitude of vessel impact forces to be resisted. In some cases, vessel impact loads 

must be resisted by the bridge pier foundation elements. Single deep foundations may also 

be used to support navigation aids. 

•	 In urban areas, deep foundations may occasionally be needed to support structures adjacent 

to locations where future excavations are planned or could occur, Figure 9-1(j). Use of 

shallow foundations in these situations could require future underpinning in conjunction 

with adjacent construction. 

•	 Deep foundations are used in areas of expansive or collapsible soils to resist undesirable 

seasonal movements of the foundations. Deep foundations under such conditions are 

designed to transfer foundation loads, including uplift or downdrag, to a level unaffected 

by seasonal moisture movements, Figure 9-1(k). 

9.1 TYPES OF DEEP FOUNDATIONS AND PRIMARY REFERENCES 

There are numerous types of deep foundations. Figure 9-2 shows a deep foundation 

classification system based on type of material, configuration, installation technique and 

equipment used for installation. This chapter discusses the driven pile and drilled shaft 

foundation types based on the information in the following primary references: 

FHWA (2006a) Design and Construction of Driven Pile Foundations - Vol. I and II, Report No. 

FHWA-NHI-05-042 and FHWA-NHI-05-043, Authors: Hannigan, P.J., G.G. Goble, G. 

Thendean, G.E. Likins and F. Rausche., Federal Highway Administration, U.S. Department of 

Transportation. 

FHWA (1999). Drilled Shafts: Construction Procedures and Design Methods. Report No. 

FHWA-IF-99-025, Authors: O’Neill, M. W. and Reese, L. C. Federal Highway Administration, 

U.S. Department of Transportation. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 3 December 2006 
 

Drilled 

Shaft 

Micropile Auger cast 

Tapered 

Precast Tip 

Unfilled 

Concrete Piles 

and Shafts 

Composite Piles 

Deep Foundations 

Fundex, Tubex 

or Groutinjected Tubex 

Driven w/ Mandrel Driven/Pushed w/o Mandrel Drilled / Bored 

Pipe 

Cased 

Shell 

Cased 

Micropile Drilled 

Shaft 

Pipe Monotube 

Timber Pipe -

Shell 

Steel Piles Timber Piles 

H Pipe

Precast 

Prestressed Reinforced 

Filled 

Open 

End 

Closed 

End 

Pretension 

Posttension 

Jointed NonJointed 

Cast-in-Place 

Cased Uncased 

Cylinder 

Drilled / Bored 

Helical 

Screw 

Compacted 

Figure 9-2. Deep foundation classification system (after FHWA, 2006a). 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 4 December 2006 
Micropiles and auger-cast piles are rapidly gaining in popularity as viable types of deep 

foundations for transportation structures. These types of piles are not addressed in this chapter. 

Guidance for these types of piles can be found in the following FHWA manuals. 

FHWA (2005a). “Micropile Design and Construction,” Report No. FHWA NHI-05-039, Authors: 

Sabatini, P.J., Tanyu, B., Armour., P., Groneck, P., and Keeley, J., National Highway Institute, 

Federal Highway Administration, U.S. Department of Transportation. 

FHWA (2006c) “Geotechnical Engineering Circular No. 8, Continuous Flight Auger Piles,” 

Authors: Brown, D. and Dapp, S., Federal Highway Administration, U.S. Department of 

Transportation. 

9.1.1 Selection of Driven Pile or Cast-in-Place (CIP) Pile Based on Subsurface Conditions 

For many years the use of a deep foundation has meant security to many designers. For 

example, the temptation to use driven piles under every facility is great because detailing of 

plans is routine, quantity estimate is neat, and safe structural support is apparently assured. 

Often, designers do not consider other pile alternatives such as cast-in-place (CIP) piles. Figure 

9-2 shows a variety of CIP pile types. The most common CIP pile type is the drilled shaft which, 

as indicated earlier, is the only CIP pile type discussed in this chapter. The selection of 

appropriate pile types for any project should include a consideration of subsurface conditions as 

the first step. Table 9-1 provides a discussion of driven pile versus drilled shafts for various 

subsurface conditions. Sections 9.2 to 9.9 discuss the details of the driven pile foundation 

systems while Sections 9.10 to 9.14 discuss the CIP pile types with emphasis on drilled shafts. 

9.1.2 Design and Construction Terminology 

Just as with the design of other geotechnical features, there is a specific terminology associated 

with design of various deep foundations. Examples of terminology are “static pile capacity,” 

“ultimate pile capacity,” “allowable pile capacity,” “driving capacity,” “restrike capacity,” “shaft 

resistance in piles,” “side resistance in drilled shafts,” “toe resistance for piles,” “base or tip 

resistance for drilled shafts,” etc. This terminology has been ingrained in the technical literature, 

FHWA manuals, various text books and AASHTO. Herein, the terminology in various primary 

references listed above will be used for driven piles and drilled shafts. The first time a specific 

phrase or term appears in the text, it will be highlighted in bold text. 

For all deep foundations, the capacity of the foundation is a function of the geotechnical and the 

structural aspects. The geotechnical aspect is a function of the resistance from the ground while 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 5 December 2006 
the structural aspect is a function of the structural section and the structural properties of the pile. 

In this chapter, the primary emphasis is on the geotechnical aspects of the deep foundations. 

Structural aspects are discussed only to the extent that they may be relevant, e.g., the structural 

capacity of a pile relative to the driving stresses induced during the driven pile installation 

process. 

Table 9-1 

Pile type selection based on subsurface and hydraulic conditions 

Typical Problem Recommendations 

Boulders overlying 

bearing stratum 

Use heavy nondisplacement driven pile with a reinforced tip or manufactured point and include contingent predrilling item in contract. 

Depending on the size of the boulders, large diameter drilled shaft may 

be feasible. 

Loose cohesionless 

soil 

Use tapered pile to develop maximum skin friction. For drilled shafts, 

side-support in form of casing or slurry will be required making it costlier 

than the driven pile option 

Negative shaft 

resistance 

Use smooth steel pile to minimize drag adhesion, and avoid battered 

piles. Minimize the magnitude of drag force when possible. In case of 

drilled shafts use casing to minimize drag load. 

Deep soft clay Use rough concrete pile to increase adhesion and rate of pore water 

dissipation. Drilled shaft is possible but side-support in form of casing or 

slurry will be required making it costlier than driven pile option. 

Artesian Pressure Do not use mandrel driven thin-wall shells as generated hydrostatic 

pressure may cause shell collapse; pile heave common to closed-end 

pipe. In case of drilled shaft, a slurry drilling will be required. 

Scour Do not use tapered piles unless large part of taper extends well below 

scour depth. Design permanent pile capacity to mobilize soil resistance 

below scour depth. Large drilled shaft is likely a better option compared 

to a group of piles. 

Coarse Gravel 

Deposits 

Use precast concrete piles where hard driving expected in coarse soils. 

DO NOT use H-piles or open end pipes as nondisplacement piles will 

penetrate at low blow count and cause unnecessary overruns. Drilled 

shaft is likely a better option for coarse gravel deposit. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 6 December 2006 
9.2 DRIVEN PILE DESIGN-CONSTRUCTION PROCESS 

The driven pile design and construction process has aspects that are unique in all of structural 

design. Because the driving characteristics are related to pile capacity for most soils, they can be 

used to improve the accuracy of the pile capacity estimate. In general, the various methods of 

determining pile capacity from dynamic data such as driving resistance with wave equation 

analysis and dynamic measurements are considerably more accurate than the static analysis 

methods based on subsurface exploration information. It must be clearly understood that the 

static analysis based on the subsurface exploration information usually has the function of 

providing an estimate of the pile length prior to field installation. The final driving 

criterion is usually a blow count that is established after going to the field and the 

individual pile penetrations may vary depending on the soil variability. Furthermore, pile 

driveability is a very important aspect of the process and must be considered during the 

design phase. 

The key point to understand in a driven pile design is that the pile should be designed such 

that it (a) can be driven to the design depth without damage, and (b )sustain the loads with the 

design factor of safety during the service life of the structure. If the design is completed and the 

piles cannot be driven, large costs can be generated. It is absolutely necessary that the design 

and construction phases be linked in a way that does not exist elsewhere in construction. 

The driven pile design-construction process is outlined in the flow chart of Figure 9-3. This flow 

chart will be discussed block by block using the numbers in the blocks as a reference and it will 

serve to guide the designer through all of the tasks that must be completed. 

Block 1: Establish Global Project Performance Requirements 

The first step in the entire process is to determine the general structure requirements. 

1.	 Is the project a new bridge, a replacement bridge, a bridge renovation, a retaining wall, a 

noise wall, or sign or light standard? 

2.	 Will the project be constructed in phases or all at one time? 

3.	 What are the general structure layout and approach grades? 

4.	 What are the surficial site characteristics? 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 7 December 2006 
 

 

 

1 

Establish global project 

performance requirements 

2 

Define project 

geotechnical site conditions 

3 Determine preliminary 

substructure loads and load 

combinations at foundation level 

Design Phase 

4 Develop and execute subsurface 

exploration and laboratory 

testing program for feasible 

foundation systems 

5 Evaluate information and
 

determine foundation systems for 

further evaluation
 

6 Deep Foundations Shallow Foundations See Figure (See Chapter 8) 8-10 

7 Cast-In-Place (CIP) Piles Select alternate driven pile See Figure (See Section 9.10) foundations types and sections for 9-47 

further evaluation 

Continued on Next Page 

Figure 9-3. Driven pile design and construction process (after FHWA 2006a). 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 8 December 2006 
 

Select static analysis method 

and calculate ultimate axial 

capacity vs depth 

8 

Identify most economical 

driven pile types from plots 

of ultimate capacity vs depth and 

cost per ton (MN) vs depth 

Size and estimate cost of 

pile cap for trial groups 

Continued on Next Page 

9 

Driveability of pile 

types to target penetration 

depth(s) and ultimate capacity 

10 

Select 1 or 2 pile types, 

ultimate capacities and pile 

penetration depths for trial 

pile group sizing 

11 

Iterate and 

Return to 

Block 7, as 

necessary 

No 

Yes 

Evaluate group axial, lateral, 

and rotational capacities, 

settlement, and performance of 

trial pile group configurations 

12 

13 

Summarize total cost of 

candidate pile types, group 

configurations and pile caps 

14 

Select and optimize final pile 

type, ultimate capacity group 

configuration, and construction 

control method 

15 

Figure 9-3 (Continued). Driven pile design and construction process (after FHWA 2006a). 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 9 December 2006 
Does optimized Design Meet 

Performance, Constructability 

and Driveability 

Prepare plans and 

specifications including field 

capacity determination procedure 

Adjust driving criteria 

or design 

17 

Perform wave equation 

analysis of contractor’s 

equipment submission, accept 

or reject 

19 

Yes 

22 

Construction control. 

drive production piles, resolve 

any pile installation problems 

23 

Post-construction 

evaluation and refinement 

for future designs 

24 

16 

Return to 

Block 11 

No 

Construction Phase 

20 Set preliminary driving 

criteria 

18 Contractor 

selected 

21 Drive test piles and 

evaluate capacity 

Figure 9-3 (Continued). Driven pile design and construction process (after FHWA 2006a). 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 10 December 2006 
5.	 Is the structure subjected to any special design events such as seismic, scour, downdrag, 

debris loading, vessel impact, etc.? If there are special design events, the design 

requirements should be reviewed at this stage so that these can be factored into the site 

investigation. 

6.	 What are the approximate foundation loads? What are the deformation or deflection 

requirements (total settlement, differential settlement, lateral deformations, tolerances)? 

7.	 Are there site environmental issues that must be considered in the design (specific 

limitation on noise, vibrations, etc.)? 

Block 2: Define Project Geotechnical Site Conditions 

A great deal can be learned about the foundation requirements with even a very general 

understanding of the site geology. For small structures, this may involve only a very superficial 

investigation such as a visit to the site. The foundation design for very large structures may 

require extensive geologic studies and review of geologic maps. Based on the geologic studies, 

the project team should consider possible modifications in the structure that may be desirable for 

the site under consideration 

Frequently there is information available on foundations that have been constructed in the area. 

This information can be of assistance in avoiding problems. Both subsurface exploration 

information and foundation construction experience should be collected prior to beginning the 

foundation design. Unfortunately, this step is not often done in practice. 

Block 3: Determine Preliminary Substructure Loads and Load Combinations at the 

Foundation Level 

Substructure loads and reasonable vertical and lateral deformation requirements should be 

established at this time. This issue was considered in Block 1. The result of that effort has 

probably matured in the intervening time which might be quite long for some projects and is now 

better defined. It is imperative that the foundation specialist obtain a completely defined and 

unambiguous set of foundation loads and performance requirements in order to proceed through 

the foundation design process. Accurate load information and performance criteria are essential 

in the development and implementation of an adequate subsurface exploration program for the 

planned structure. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 11 December 2006 
Block 4: Develop and Execute Subsurface Exploration Program for Feasible 

Foundation Systems 

Based on the information obtained in Blocks 1-3, it is possible to make decisions regarding the 

necessary information that must be obtained for the feasible foundation systems at the site. The 

subsurface exploration program and the associated laboratory testing must meet the needs of the 

design problem that is to be solved at a cost consistent with the size and importance of the 

structure. The results of the subsurface exploration program and the laboratory testing are used 

to prepare a subsurface profile and identify critical cross sections. These tasks are covered in 

greater detail in Chapters 3, 4, and 5. 

Block 5: Evaluate Information and Select Candidate Foundation Systems 

The information collected in Blocks 1-4 must be evaluated and candidate foundation systems 

selected for further consideration. The first question to be decided is whether a shallow or a deep 

foundation is required. This question will be answered based primarily on the strength and 

compressibility of the site soils, the proposed loading conditions, scour depth, the project 

performance criteria and the foundation cost. If settlement and scour are not a problem for the 

structure, then a shallow foundation will probably be the most economical solution. Ground 

improvement techniques in conjunction with shallow foundations should also be evaluated. 

Shallow and deep foundation interaction with approach embankments must also be considered. 

If the performance of a shallow foundation exceeds the limitations imposed by the structure 

performance criteria, a deep foundation must be used. The design of ground improvement 

techniques is not covered in this manual and can be found in FHWA (2006b). Information on 

design considerations for shallow foundations can be found in Chapter 8. 

Block 6: Deep Foundations 

The decision on deep foundation type is now between driven piles and other deep foundation 

systems. These other deep foundation systems are primarily drilled shafts, but would also 

include micropiles, auger cast piles, and other drilled-in deep foundation systems as shown in 

Figure 9-2. The questions that must be answered in deciding between driven piles and other 

deep foundation systems will center on the relative costs of available, possible systems. 

Foundation support cost can be conveniently calculated based on a cost per unit of load carried. 

In addition, constructability must be considered. Design guidance on drilled shafts can be found 

in Section 9.10 of this chapter. Guidance for other deep foundation systems such as micro-piles 

and auger cast piles can be found in the references listed in Section 9.1. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 12 December 2006 
 

Block 7: Select Candidate Driven Pile Types for Further Evaluation 

At this point on the flow chart, the primary concern is for the design of a driven pile foundation. 

The pile type must be selected consistent with the applied load per pile. Consider this problem. 

The general magnitude of the column or pier loads is known from the information obtained in 

Blocks 1 and 3. However, a large number of combinations of pile capacities and pile types can 

satisfy the design requirements. Should twenty, 225 kip (1000 kN) capacity piles be used to 

carry a 4,500 kip (20,000 kN) load, or would it be better to use ten, 450 kip (2,000 kN) capacity 

piles? This decision should consider both the structural capacity of the pile and the realistic 

geotechnical capacities of the pile type for the soil conditions at the site, the cost of the available 

alternative piles, and the capability of available construction contractors to drive the selected 

pile. Of course, there are many geotechnical factors that must also be considered. At this point 

in the design process, 2 to 5 candidate pile types and/or sections that meet the general project 

requirements should be selected for further evaluation. Pile type and selection considerations are 

covered in Section 9.3. 

At this stage the loads must also be firmly established. In Block 1, approximate loads were 

determined, which were refined in Block 3. At the early stages of the design process the other 

aspects of the total structural design were probably not sufficiently advanced to establish the 

final design loads. By the time that Block 6 has been reached, the structural engineer should 

have finalized the various loads. One common inadequacy that is sometimes discovered when 

foundation problems arise is that the foundation loads were never really accurately defined at the 

final stage of the foundation design. 

If there are special design events to be considered, they must be included in the determination of 

the loads. Vessel impact will be evaluated primarily by the structural engineer and the results of 

that analysis will give pile loads for that case. There may be stiffness considerations in dealing 

with vessel impact since the design requirement is basically a requirement that some vessel 

impact energy be absorbed by the foundation system. 

Scour presents a different requirement. The loads due to the forces from the stream must be 

determined as specified in the AASHTO (2002), Section 3.18. The requirements of this 

AASHTO section should be included in the structural engineer’s load determination process. 

The depth of scour must also be determined as directed in AASHTO (2002), Section 4.3.5. In 

the design process, it must be assured that the pile will still have adequate capacity after scour. 

In many locations in the country, seismic loads will be an important contributor to some of the 

critical pile load conditions. Since the 1971 San Fernando Earthquake, significant emphasis has 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 13 December 2006 
 

been placed on seismic design considerations in the design of highway bridges. The AASHTO 

Standard Specifications for Highway Bridges has been substantially expanded to improve the 

determination of the seismic loads. Usually the structural engineer will determine the seismic 

requirements. Frequently the behavior of the selected pile design will affect the structural 

response and hence the pile design loads. In this case, there will be another loop in the design 

process that includes the structural engineer. The geotechnical engineer should review the 

seismic design requirements in Division I-A of AASHTO (2002) for a general understanding of 

the design approach. 

Block 8: Select Static Analysis Method and Calculate Ultimate Capacity vs Depth 

A static analysis method(s) applicable to the pile type(s) under consideration and the soil 

conditions at the site should now be selected. Static analysis methods are covered in detail in 

Section 9.4. The ultimate axial capacity versus depth should then be calculated for all candidate 

pile types and sections. 

Block 9: Identify Most Economical Candidate Pile Types and/or Sections 

The next step is to develop and evaluate plots of the ultimate axial static capacity versus pile 

penetration depth and the pile support cost versus pile penetration depth for each candidate pile 

type and/or section. The support cost, which is the cost per ton (kN) supported, is the ultimate 

capacity at a given penetration depth divided by the pile cost to reach that penetration depth. The 

pile cost can be calculated from the unit cost per ft (m) multiplied by the pile length to the 

penetration depth. These plots should be evaluated to identify possible pile termination depths to 

obtain the lowest pile support cost. This process is briefly discussed in Section 9.3. 

Block 10: Calculate Driveability of Candidate Pile Types 

Candidate pile types should now be evaluated for driveability. Can the candidate pile type 

and/or section be driven to the required capacity and penetration depth at a reasonable pile 

penetration resistance (blow count) without exceeding allowable driving stresses for the pile 

material? This analysis is performed by using the wave equation theory. All of the necessary 

information is available except the hammer selection. Since the hammer to be used on the job 

will be known only after the contractor is selected, possible hammers must be identified to make 

sure that the pile is driveable to the capacity and depth required. 

Pile driveability, wave equation analysis and allowable pile driving stresses are discussed in 

Section 9.9. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 14 December 2006 
If candidate pile types or sections do not meet driveability requirements they are dropped from 

further evaluation or modified sections must be chosen and evaluated. For H-piles and pipe piles 

it may be possible to increase the pile section without increasing the soil resistance to driving. 

For concrete piles an increase in section usually means a larger pile size. Therefore, an increase 

in soil resistance must also be overcome. Hence, some section changes may cause the design 

process to revisit Block 8. If all candidate pile types fail to meet driveability requirements, the 

design process must return to Block 7 and new candidate pile types must be selected. 

Block 11: Select 1 or 2 Final Candidate Pile Types for Trial Group Sizing 

The most viable candidate pile types and/or sections from the cost and driveability evaluations in 

Blocks 9 and 10 should now be evaluated for trial group sizing by using the final loads and 

performance requirements. Multiple pile penetration depths and the resulting ultimate capacity 

at those depths should be used to establish multiple trial pile group configurations for each 

candidate pile type. These trial configurations should then be carried forward to Block 13. 

Block 12: Evaluate Capacity, Settlement, and Performance of Trial Groups 

The trial group configurations should now be evaluated for axial group capacity, group uplift, 

group lateral load performance, and settlement. These computations and analysis procedures are 

described in Section 9.6. 

Block 13: Size and Estimate Pile Cap Cost for Trial Groups 

The size and thickness of the pile cap for each trial group should be evaluated, and the resulting 

pile cap cost estimated. It is not necessary to design the cap reinforcement at this time only to 

determine cap size. Pile cap cost is a key component in selecting the most cost effective pile 

type and should not be overlooked. 

Block 14: Summarize Total Cost of Final Candidate Piles 

The total cost of each candidate pile should now be determined. A given pile type may have 

several total cost options depending upon the pile penetration depths, ultimate capacities, group 

configurations, and pile cap sizes carried through the design process. The cost of any special 

construction considerations and environmental restrictions should also be included in the total 

cost for each candidate pile. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 15 December 2006 
 

Block 15: Select and Optimize Final Pile Type, Capacity, and Group Configuration 

Select the final pile foundation system including pile type, section, length, ultimate capacity and 

group configuration for final design. A complete evaluation of lateral and rotational resistance 

of the group should be performed. The design should be optimized for final structure loads, 

performance requirements, and construction efficiency. 

Block 16: Does Optimized Design Meet All Requirements? 

The final pile type, section, capacity and group configuration optimized in Block 15 should be 

evaluated so that all performance requirements have been achieved. If the optimization process 

indicates that a reduced pile section can be used, the driveability of the optimized pile section 

must be checked by a wave equation driveability analysis. This analysis should also consider 

what influence the group configuration and construction procedures (e.g., cofferdams, etc.) may 

have on pile installation conditions. 

Block 17: Prepare Plans and Specifications, Set Field Capacity Determination 

Procedure 

When the design has been finalized, plans and specifications can be prepared and the procedures 

that will be used to verify pile capacity can be defined. It is important that all of the quality 

control procedures are clearly defined for the bidders to avoid claims after construction is 

underway. In the past a pile load specified on the basis of dynamic formulae was a design or 

working load since a factor of safety is contained in the formula. Modern methods for 

determining pile capacity always use ultimate loads with a factor of safety (or in LRFD a 

resistance factor) selected and applied. This modern approach should also be made clear in the 

project specifications so that the contractor has no question regarding the driving requirements. 

Procedures should be in place that address commonly occurring pile installation issues such as 

obstructions and driveability. 

Block 18: Contractor Selection 

After the bidding process is complete, a contractor is selected. The contractor should be 

qualified and experienced in the installation of driven piles for the type of structure being built. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 16 December 2006 
Block 19: Perform Wave Equation Analysis of Contractor’s Equipment Submission 

At this point the engineering effort shifts to the field. The contractor will submit a description of 

the pile driving equipment that he intends to use on the project for the engineer’s evaluation. 

Wave equation analyses are performed to determine the driving resistance that must be achieved 

in the field to meet the required capacity and pile penetration depth. Driving stresses are 

determined and evaluated. If all conditions are satisfactory, the equipment is approved for 

driving. Some design specifications make this information advisory to the contractor rather than 

mandatory. Section 9.8 provides additional information in this area. 

On smaller projects, a dynamic formula may be used to evaluate driveability. In this case, the 

modified Gates Formula should be used. If a dynamic formula is used, then driveability and 

hammer selection will be based on the driving resistance given by the formula only, since 

stresses are not determined. Dynamic formula usage is covered in Section 9.9. 

Block 20: Set Preliminary Driving Criteria 

Based on the results of the wave equation analysis of Block 19 (or on smaller projects the 

modified Gates Formula) and any other requirements in the design, the preliminary driving 

criteria can be set. 

Block 21: Drive Test Pile and Evaluate Capacity 

The test pile(s), if required, are driven to the preliminary criteria developed in Block 19. Driving 

requirements may be defined by penetration depth, driving resistance, dynamic monitoring 

results or a combination of these conditions. The capacity can be evaluated by driving resistance 

from wave equation analysis, the results of dynamic monitoring, static load test, the modified 

Gates Formula, or a combination of these. Dynamic monitoring is described in Section 9.9. 

Static load test procedures are discussed in greater detail at the end of this chapter. 

Block 22: Adjust Driving Criteria or Design 

At this stage the final conditions can be set or, if test results from Block 21 indicate the capacity 

is inadequate, the driving criteria may have to be changed. In a few cases, it may be necessary to 

make changes in the design that will return the process as far back as Block 8. 

In some cases, it is desirable to perform preliminary field testing before final design. When the 

job is very large and the soil conditions are difficult, it may be possible to achieve substantial 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 17 December 2006 
cost savings by having results from a design stage test pile program, including actual driving 

records at the site, as part of the bid package. 

Block 23: Construction Control 

After the driving criteria are set, the production pile driving begins. Quality control and 

assurance procedures have been established and are applied. Problems may arise and must be 

handled as they occur in a timely fashion. 

Block 24: Post-Construction Evaluation and Refinement of Design 

After completion of the foundation construction, the design should be reviewed and evaluated for 

its effectiveness in satisfying the design requirements and also its cost effectiveness. 

9.3 ALTERNATE DRIVEN PILE TYPE EVALUATION 

The selection of appropriate driven pile types for any project involves the consideration of 

several design and installation factors including pile characteristics, subsurface conditions and 

performance criteria. This selection process should consider the factors listed in Table 9-1, 

Table 9-2 and Table 9-3. Table 9-2 summarizes typical pile characteristics and uses. Table 9-3 

presents the placement effects of pile shape characteristics. 

Table 9-2 

Typical piles and their range of loads and lengths 

Type of Pile Typical Axial Design Loads Typical Lengths 

Timber 20-110 kips (100 – 500 kN) 15-120 ft (5-37 m)* 

Precast / 

Prestressed 

Reinforced 

Concrete 

90-225 kips (400-1,000 kN) for 

reinforced 

90-1000 kips (400-4,500 kN) for 

prestressed 

30-50 ft (10-15m) for reinforced 

50-130 ft (15-40m) for 

prestressed 

Steel H 130-560 kips (600-2,500 kN) 15-130 ft (5-40 m) 

Steel Pipe (without 

concrete core) 180-560 kips (800-2,500 kN) 15-130 ft (5-40 m) 

Steel Pipe (with 

concrete core) 560-3400 kips (2,500-15,000 kN) 15-130 ft (5-40 m) 

* 15-75 ft (5-23 m) for Southern Pine; 15-120 ft (5-37 m) for Douglas Fir 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 18 December 2006 
Table 9-3 

Pile type selection pile shape effects 

Shape 

Characteristics Pile Types Placement Effects 

Displacement Steel Pipe 

(Closed end), 

Precast Concrete 

• Increase lateral ground stress 

• Densify cohesionless soils, remolds and weakens 

cohesive soils temporarily 

• Set-up time may be 6 months in clays for pile groups 

Nondisplacement Steel H, Steel 

Pipe (Open end) 

• Minimal disturbance to soil 

• Not suited for friction piles in coarse granular soils. 

Piles often have low driving resistances in these 

deposits making field capacity verification difficult 

thereby often resulting in excessive pile lengths. 

Tapered Timber, 

Monotube, 

Tapertube, Thinwall shell 

• Increased densification of soils with less disturbance, 

high capacity for short length in granular soils 

In addition to the considerations provided in the Tables 9-1, 9-2 and 9-3, the problems posed by 

the specific project location and topography must be considered in any pile selection process. 

Following are some of the problems usually encountered: 

1. Noise and vibration from driven pile installation may affect pile type selection, and 

require special techniques such as predrilling and/or vibration monitoring of adjacent 

structures. 

2. Remote areas may restrict driving equipment size and, therefore, pile size. 

3. Local availability of certain materials and the capability of local contractors may have 

decisive effects on pile selection. 

4. Waterborne operations may dictate use of shorter pile sections due to pile handling 

limitations. 

5. Steep terrain may make the use of certain pile equipment costly or impossible. 

9.3.1 Cost Evaluation of Alternate Pile Types 

Often several different pile types meet all the requirements for a particular structure. In 

such cases, the final choice should be made on the basis of a cost analysis that assesses the 

over-all cost of the foundation alternatives. This requires that candidate pile types be 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 19 December 2006 
carried forward in the design process for determination of the pile section requirements for 

design loads and constructability. The cost analysis for the candidate pile types should 

include uncertainties in execution, time delays, cost of load testing programs, as well as the 

differences in the cost of pile caps and other elements of the structure that may differ among 

alternatives. For major projects, alternate foundation designs should be considered for 

inclusion in the contract documents if there is a potential for cost savings. 

For driven pile foundation projects, the total foundation cost can be separated into three major 

components as follows: 

• The pile cost 

• The pile cap cost, and 

• The construction control method cost 

For most pile types, the pile cost can usually be assumed as linear with depth based on unit price. 

However, this may not be true for very long concrete piles or long, large section steel piles. 

These exceptions may require the cost analysis to reflect special transportation, handling, or 

splicing costs for concrete piles or extra splice time and cost for steel piles. Table 9-4 presents 

cost savings recommendations to be considered during the evaluation of pile foundations. 

Expressing the cost of candidate pile types in terms of dollars per ton capacity would allow 

comparison of alternative pile types in a rational manner. Details of this approach, i.e., 

expressing costs in $/ton, are presented in FHWA (2006a). 

9.4 COMPUTATION OF PILE CAPACITY 

Once the allowable structural load has been determined for prospective pile alternates, the pile 

length required to support that load must be determined. For many years this length 

determination was considered part of the "art of foundation engineering." In recent years more 

rational analytic procedures have been developed. Static analyses provide a useful design tool to 

select the most economical pile alternates. The methods that follow are established procedures 

that account for the variables in pile length determination. The "art" remains in selecting 

appropriate soil strength values for the conditions and ascertaining the effects of pile installation 

on these values. For the typical project two static analyses will be required; the first to determine 

the length required for permanent support of the structures, and the second to determine the soil 

resistance to be overcome during driving to achieve the estimated length. It must be stressed that 

each new site represents a new problem with unique conditions. Experience with similar sites 

should not replace but should refine the rational analysis methods presented herein. This section 

discusses the concept of static capacity of the pile based on a rational approach. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 20 December 2006 
Table 9-4. Cost savings recommendations for pile foundations (FHWA, 2006a) 

Factor Inadequacy of Older Methods Cost Saving Recommendations 

A. Design 

structural load capacity of piles. 

1. Allowable pile material stresses 

may not address site-specific 

 considerations. 

1. 2. 3. 

Use realistic allowable stresses for pile 

materials in conjunction with adequate 

construction control procedures, (i.e., load testing, dynamic pile monitoring and wave equation). 

 Determine potential pile types and carry candidate 

pile types forward in the design process. 

 Optimize pile size for loads. 

1. Rational  A and B  foundati2. Significa

achieved type and loads widriveabi

B. Design 

geotechnical capacity of soil and rock to carry load transferred by piles. 

1. 2. 3. 

Inadequate subsurface explorations and 

laboratory testing. 

Rules of thumb and prescribed values 

used in lieu of static design may result in overly conservative designs. 

High potential for change 

orders and claims. 

1. 2. 3. 4. 

Perform thorough subsurface exploration 

including in-situ and laboratory testing to determine design parameters. 

Use rational and practical methods of design. 

Perform wave equation driveability analysis. Use design stage pile load testing on large pile driving projects to determine load capacities (load tests during design stage). 

1. 2.

Reductio

justified uncertai

capacitie

Rational lead to ssmaller 

C. Alternate 

foundation design. 

1. Alternate foundation designs are 

rarely used even when possibilities of 

cost savings exist by allowing alternates in contract documents. 

1. For major projects, consider inclusion of alternate 

foundation designs in the contract documents if estimated costs of feasible foundation alternatives are within 15 percent of each other. 

1. Alternat

more coto lower 

D. Plans and 

specifications. 

1.2. 

 Unrealistic specifications. 

Uncertainties due to inadequate subsurface explorations force the contractors to inflate bid prices. 

1. 2. 

Prepare detailed contract documents based on 

thorough subsurface explorations, understanding of contractors' difficulties and knowledge of pile techniques and equipment. Provide subsurface information to the contractor. 

1. 2. 

Lower bcontractavailablPotentia

 reduced  specifica

E. Construction 

determination of pile load capacity during installation. 

1. Often used dynamic formulas such as 

Engineering News formula are unreliable. Correlations between load capacities determined from Engineering News formula and static load tests indicate safety factors ranging from less than 1 (i.e. failure) to about 20 (i.e. excessive foundation cost). 

1. 2. 3. 

Eliminate use of dynamic formulas for 

construction control as experience is gained with the wave equation analysis. 

Use wave equation analysis coupled 

with dynamic monitoring for construction control 

and load capacity evaluation. Use pile load tests on projects to substantiate capacity predictions by wave equation and dynamic monitoring. 

1. 2. 3. 

Reduced 

allow shsmaller 

Pile dam

driving c

 dynamic 

Increase

 risk resu construc

FHWA NHI-06-089 Soils and Foundations – Volume II 9 - 21 
The static capacity of a pile can be defined as the sum of soil/rock resistances along the pile 

shaft and at the pile toe available to support the imposed loads on the pile. Static analyses are 

performed to determine the ultimate capacity of an individual pile and of a pile group as well as 

the deformation response of a pile group to the applied loads. The ultimate capacity of an 

individual pile and of a pile group is defined as the smaller of: 

(1) the capacity of the surrounding soil/rock medium to support the loads transferred from the 

pile(s) or, 

(2) the structural capacity of the pile(s). 

Soil-structure interaction analysis methods are used to determine the deformation response of 

piles and pile groups to lateral loads; such methods can also be used for deformation evaluation 

under vertical loads. The results from these analyses as well as the results of static analysis of 

pile group settlement are compared to the performance criteria established for the structure. 

The ultimate geotechnical pile capacity, Qu, of a pile in homogeneous soil may be expressed as 

follows in terms of the shaft (commonly knows as “skin”) resistance, Rs, toe resistance, Rt, 

and the weight, W, of the pile: 

Qu = Rs + Rt – W	 9-1 

In most cases, such as H-Piles and open ended pipe piles, the weight W is small compared to the 

shaft and toe resistance and is neglected. However, the weight of pipe piles, particularly large 

diameter pipes, filled with concrete may be significant and may be included in the analysis. In 

this chapter, the W term is neglected. Equation 9-1, without the W term, may also be expressed 

in the form 

Qu = fs As + qt At 9-2

where fs is the unit shaft resistance over the shaft surface area, As, and qt is the unit toe 

resistance over the pile toe area, At. The above equations for pile bearing capacity assume that 

both the pile toe and the pile shaft have moved sufficiently with respect to the adjacent soil to 

simultaneously develop the ultimate shaft and toe resistances. Generally, the displacement 

needed to mobilize the shaft resistance is smaller than that required to mobilize the toe 

resistance. This simple rational approach has been commonly used for all piles except very large 

diameter piles where such an approach may not be valid. 

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Figure 9-4 illustrates typical load transfer profiles for a single pile. The load transfer distribution 

can be obtained from a static load test where strain gages or telltale rods are attached to a pile at 

different depths along the pile shaft. Figure 9-4 shows the measured ultimate axial load, Qu, in 

the pile plotted against depth. The shaft resistance transferred to the soil is represented by 

Rs, and Rt represents the resistance at the pile toe. In Figure 9-4(a), the load transfer 

distribution for a pile with no shaft resistance is illustrated. In this case the full axial load at the 

pile head is transferred to the pile toe. In Figure 9-4(b), the axial load versus depth for a uniform 

shaft resistance distribution typical of a cohesive soil is illustrated. Figure 9-4(c) presents the 

axial load in the pile versus depth for a triangular shaft resistance distribution typical of 

cohesionless soils. 

9.4.1 Factors of Safety 

The results of static analyses yield a geotechnical ultimate pile capacity, Qu. The allowable 

geotechnical soil resistance (geotechnical pile design load), Qa, is selected by dividing the 

geotechnical ultimate pile capacity, Qu, by a factor of safety as follows. 

Q Q	 a = u 9-3

Factor of Safety 

The range of the factor of safety, FS, has depended primarily upon the reliability of the particular 

method of static analysis with consideration of the following items: 

1. The level of confidence in the input parameters. The level of confidence is a function of 

the type and extent of the subsurface exploration and laboratory testing of soil and rock 

materials. 

2. Variability of the soil and rock. 

3. Method of static analysis. 

4. Effects of and consistency of the proposed pile installation method. 

5. Level of construction control (static load test, dynamic analysis, wave equation analysis, 

Gates dynamic formula). 

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Soils and Foundations – Volume II 9 - 23 December 2006 
Figure 9-4. Typical load transfer profiles (FHWA, 2006a). 

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Soils and Foundations – Volume II 9 - 24 December 2006 
 

A large number of static analysis methods are documented in the literature with specific 

recommendations on the factor of safety to be used with each method. These recommended 

factors of safety have routinely disregarded the influence of the construction control method used 

to complement the static analysis computation. As part of the overall design process, it is 

important that the foundation designer qualitatively assess the validity of the chosen design 

analysis method and the reliability of the geotechnical design parameters. 

While the range of static analysis factors of safety in the past was from 2 to 4, most of the static 

analysis methods recommended a factor of safety of 3. As foundation design loads increased 

over time, the use of higher factors of safety often resulted in pile installation problems. In 

addition, experience has shown that construction control methods have a significant influence on 

pile capacity. Therefore, the factor of safety used in a static analysis calculation should be 

based upon the construction control method specified. Provided that the procedures 

recommended in this manual are used for the subsurface exploration and analysis, the factors of 

safety in Table 9-5 are recommended based on the specified construction control method. The 

factor of safety for other test methods not included in Table 9-5 should be determined by the 

individual designer. 

Table 9-5. Recommended factor of safety based on construction control method 

Construction Control Method Factor of Safety 

Static load test with wave equation analysis 2.00 

Dynamic testing with wave equation analysis 2.25 

Indicator piles with wave equation analysis 2.50 

Wave equation analysis 2.75 

Gates dynamic formula 3.50 

The pile design load should be supported by soil resistance developed only in soil layers that 

contribute to long term load support. The soil resistance from soils subject to scour, or from soil 

layers above soft compressible soils should not be considered. The following example problem 

will be used to clarify the use of the factor of safety in static pile capacity calculations for 

determination of the pile design load as well as for determination of the soil resistance to pile 

driving. 

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Soils and Foundations – Volume II 9 - 25 December 2006 
Consider a pile to be driven through the soil profile described in Figure 9-5. The proposed pile 

type penetrates through a sand layer subject to scour in the 100-year flood into an underlying 

very soft clay layer unsuitable for long term support and then into competent support materials. 

The soil resistances from the scour-susceptible sand layer and soft clay layer do not contribute to 

long term load support and should not be included in the soil resistance for support of the design 

load. In this example, static load testing with wave equation analysis will be used for 

construction control. Therefore, a factor of safety of 2.0 should be applied to the ultimate soil 

resistance calculated in suitable support layers in the static analysis. It should be noted that this 

approach is for scour conditions under the 100-year or overtopping flood events and that a 

different approach would apply for the superflood or 500-year event. For a superflood, a 

minimum factor of safety of 1.0 is used. This minimum factor of safety is determined by 

dividing the maximum pile load by the sum of the shaft and toe resistances available below scour 

depth. 

Figure 9-5. Soil profile for factor of safety discussion (FHWA, 2006a). 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 26 December 2006 
In the static analysis, a trial pile penetration depth is chosen and an ultimate pile capacity, Qu, is 

calculated. This ultimate capacity includes the soil resistance calculated from all soil layers 

including the shaft resistance in the scour susceptible layer, Rs1, the shaft resistance in the 

unsuitable soft clay layer, Rs2 as well as the resistance in suitable support materials along the pile 

shaft, Rs3, and at the pile toe resistance, Rt. 

Qu = Rs1 + Rs2 + Rs3 + Rt 

The design load, Qa, is the sum of the soil resistances from the suitable support materials divided 

by a factor of safety, FS. As noted earlier, a factor of safety of 2.0 is used in the equation below 

because of the planned construction control with static load testing. Therefore, 

Qa = (Rs3 + Rt) / (FS=2) 

The design load may also be expressed as the sum of the ultimate capacity minus the calculated 

soil resistances from the scour susceptible and unsuitable layers divided by the factor of safety. 

In this alternative approach, the design load is expressed as follows: 

Qa = (Qu - Rs1 - Rs2) / (FS=2) 

The result of the static analysis is then the estimated pile penetration depth, D, the design load 

for that penetration depth, Qa, and the calculated ultimate capacity, Qu. 

For preparation of construction plans and specifications, the calculated geotechnical ultimate 

capacity, Qu, is specified. Note that if the construction control method changes after the design 

stage, the required ultimate capacity and the required pile penetration depth for the ultimate 

capacity will also change. This is apparent when the previous equation for the design load is 

expressed in terms of the ultimate capacity as follows: 

Qu = Rs1 + Rs2 +(Qa)(FS=2) 

A static analysis should also be used to calculate the soil resistance to driving, SRD, that must 

be overcome to reach the estimated pile penetration depth necessary to develop the ultimate 

capacity. This information is necessary for the designer to select a pile section with the 

driveability to overcome the anticipated soil resistance and for the contractor to properly size 

equipment. Driveability aspects of design are discussed in Section 9.9. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 27 December 2006 
In the SRD calculation, a factor of safety is not used. The soil resistance to driving is the sum of 

the soil resistances from the scour susceptible and unsuitable layers plus the soil resistance in the 

suitable support materials to the estimated penetration depth. 

SRD = Rs1 +Rs2 + Rs3 + Rt 

Soil resistances in this calculation should be the resistance at the time of driving. Hence time 

dependent changes in soil strengths due to soil setup or relaxation should be considered (see 

Table 5-8 in Chapter 5 for brief explanation of these terms and Section 9.5.5 for more 

discussion). For the example presented in Figure 9-5, the driving resistance from the unsuitable 

clay layer would be reduced by the sensitivity of the clay. Therefore, Rs2 would be Rs2 / 2 for a 

clay with a sensitivity of 2. The soil resistance to driving to depth D would then be as follows 

SRD = Rs1 +Rs2/2 + Rs3 + Rt 

This example problem considers only the driving resistance at the final pile penetration depth. In 

cases where piles are driven through hard or dense layers above the estimated pile penetration 

depth, the soil resistance to penetrate these layers should also be calculated. Additional 

information on the calculation of time dependent soil strength changes is provided in Section 9.9 

of this chapter. 

The concepts discussed above are illustrated numerically in Example 9-1: 

Example 9-1:	 Find the ultimate capacity and driving capacity for the pile from the data listed 

in the profile. The hydraulic specialist determined that the sand layer is 

susceptible to scour. The geotechnical specialist determined that the soft clay 

layer is unsuitable for providing resistance. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 28 December 2006 

 

Pile 

Gravel Rs3 = 60 tons 

Rt = 40 tons 

Soft Clay Rs2 = 20 tons 

Sensitivity = 4 

Sand Rs1 = 20 tons 
Solution: 

Ultimate capacity = Rs3 + Rt 

 = 60 tons + 40 tons = 100 tons 

Driving capacity = Rs1 + (Rs2/Sensitivity) + Rs3 + Rt 

20 tons = 20 tons + + 60 tons + 40 tons = 125 tons

4 

9.5 DESIGN OF SINGLE PILES 

Numerous static analysis methods are available for calculating the ultimate capacity of a single 

pile. The following sections of this chapter will present recommended analysis methods for piles 

in cohesionless, cohesive, and layered soil profiles. For additional methods based on N-values, 

and cone penetration test results the reader is referred to FHWA (2006a). Regardless of the 

method used to evaluate the static capacity of a pile, it must be understood that the factor of 

safety is not based on the method of analysis but on the construction control as discussed in 

Section 9.4. Furthermore, the pile length determined from a static analysis is just an estimate 

prior to going into the field. 

9.5.1 Ultimate Geotechnical Capacity of Single Piles in Cohesionless Soils 

The geotechnical ultimate capacity of a single pile in a cohesionless soil is the sum of shaft and 

toe resistances (Qu = Rs + Rt). The calculation assumes that the shaft resistance and toe bearing 

resistance can be determined separately and that these two factors do not affect each other. The 

Nordlund method is recommended herein for computation of ultimate capacity of single piles in 

cohesionless soils. 

9.5.1.1 Nordlund Method 

The Nordlund method (1963) is based on field observations and considers pile taper and soil 

displacement in calculating the shaft resistance. The method also accounts for the differences in 

soil-pile coefficient of friction for different pile materials. The method is based on the results of 

several load test programs in cohesionless soils. Several pile types were used in these test 

programs including timber, H, closed end pipe, Monotubes and Raymond step-taper piles. These 

piles, which were used to develop the method's design curves, had pile widths generally in the 

range of 10 to 20 inches (250 to 500 mm). The Nordlund Method tends to overpredict pile 

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Soils and Foundations – Volume II 9 - 29 December 2006 
capacity for piles with widths larger than 24 inches (600 mm) and all sizes of open-ended pipe 

piles. 

According to the Nordlund method, the geotechnical ultimate capacity, Qu, of a pile in 

cohesionless soil is the sum of the shaft resistance, Rs and the toe resistance, Rt. Nordlund 

suggests the shaft resistance is a function of the following variables: 

1. The friction angle of the soil. 

2. The friction angle on the sliding surface between pile material and soil, i.e., the interface 

friction angle 

3. The taper of the pile. 

4. The effective unit weight of the soil. 

5. The pile length. 

6. The minimum pile perimeter. 

7. The volume of soil displaced. 

The Nordlund equation for computing the geotechnical ultimate capacity of a pile is as follows 

(see Figure 9-6 for illustration of variables): 

d=D sin (δ ∑ +ω) Qu = Kδ CF p t N' 

d Cd ∆ d + α q At pt 9-4 

cos ω d=0 

where: d = depth. 

D = embedded length of the pile. 

Kδ = coefficient of lateral earth pressure at depth d. 

CF = correction factor for Kδ when δ ≠ φ. 

pd = effective overburden pressure at the center of depth increment ∆d. 

δ = interface friction angle between pile and soil. 

ω = angle of pile taper from vertical. 

φ = soil friction angle. 

Cd = pile perimeter at depth d. 

∆d = length of pile segment. 

αt = dimensionless factor dependent on pile depth-width relationship. 

N'q = bearing capacity factor. 

At = pile toe area. 

pt = effective overburden pressure at the pile toe. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 30 December 2006 
Figure 9-6. Nordlund’s general equation for ultimate pile capacity (after Nordlund, 1979). 

For a pile of uniform cross section (ω=0) and embedded length D, driven in soil layers of the 

same effective unit weight and friction angle, the Nordlund equation becomes: 

 ' Qu = Kδ CF pd sin δ Cd D + αt Nq At pt 9-5 

The soil friction angle φ influences most of the calculations in the Nordlund method. In the 

absence of laboratory test data, φ can be estimated from corrected SPT N1 values. Therefore, 

Equation 3-3 in Chapter 3 should be used for correcting field N values. The corrected SPT N160 

values may then be used in Table 8-1 of Chapter 8 to estimate the soil friction angle, φ. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 31 December 2006 
Nordlund (1979) updated the method but did not place a limiting value on the shaft resistance. 

However, Nordlund recommended that the effective overburden pressure at the pile toe, pt, used 

for computing the pile toe resistance be limited to 3 ksf (150 kPa). 

STEP BY STEP PROCEDURE FOR USING NORDLUND METHOD 

Steps 1 through 6 are for computing the shaft resistance and steps 7 through 9 are for computing 

the pile toe resistance. 

STEP 1	 Delineate the soil profile into layers and determine the φ angle for each layer. 

a. Construct po diagram using procedure described in Chapter 2. 

b. Using Figure 3-24, correct SPT field N values for overburden pressure and obtain 

corrected SPT N160 values. Delineate soil profile into layers based on corrected 

SPT N160 values. 

c. Determine φ angle for each layer from laboratory or in-situ test data. 

d. In the absence of laboratory or in-situ test data, determine the average corrected 

SPT N160 value, N1, for each soil layer and estim  ̄ ate φ angle from Table 8-1 in 

Chapter 8. 

STEP 2	 Determine δ, the interface friction angle between the pile and soil based on displaced 

soil volume, V, and the soil friction angle, φ. 

a. Compute volume of soil displaced per unit length of pile, V. 

b. Enter Figure 9-7 with V and determine δ/φ ratio for pile type under consideration. 

Note that δ/φ may be greater than 1.0 for taper piles to account for the 

development of passive resistance along the length of the pile due to pile taper. 

c. Calculate δ from δ/φ ratio. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 32 December 2006 
STEP 3 Determine the coefficient of lateral earth pressure, Kδ, for each φ angle. 

a. Determine Kδ for φ angle based on displaced volume, V, and pile taper angle, ω, 

by using either Figure 9-8, 9-9, 9-10, or 9-11 and the appropriate procedure 

described in Step 3b, 3c, 3d, or 3e. 

b. If the displaced volume is 0.1, 1.0 or 10.0 ft3

/ft, which corresponds to one of the 

curves provided in Figures 9-8 through 9-11, and the φ angle is one of those 

provided, Kδ can be determined directly from the appropriate figure. 

c. If the displaced volume is 0.1, 1.0 or 10.0 ft3

/ft, which corresponds to one of the 

curves provided in Figures 9-8 through 9-11, but the φ angle is other than those 

provided, use linear interpolation to determine Kδ for the required φ angle. Tables 

9-6a and 9-6b also provide interpolated Kδ values at selected displaced volumes 

versus φ angle for uniform piles (ω = 0). 

d. If the displaced volume is other than 0.1, 1.0 or 10.0 ft3

/ft, which corresponds to 

one of the curves provided in Figures 9-8 through 9-11, and the φ angle 

corresponds to one of those provided, use log linear interpolation to determine Kδ

for the required displaced volume. Tables 9-6a and 9-6b also provide interpolated 

Kδ values at selected displaced volumes versus φ angle for uniform piles (ω = 0). 

e. If the displaced volume is other than 0.1, 1.0 or 10.0 ft3

/ft, which correspond to 

one of the curves provided in Figures 9-8 through 9-11, and the φ angle is other 

than one of those provided, first use linear interpolation to determine Kδ for the 

required φ angle at the displaced volume curves provided for 0.1, 1.0 or 10.0 

ft3

/ft. Then use log linear interpolation to determine Kδ for the required 

displaced volume. Tables 9-6a and 9-6b also provide interpolated Kδ values at 

selected displaced volumes versus φ angle for uniform piles (ω = 0). 

STEP 4 Determine the correction factor, CF, to be applied to Kδ if δ ≠ φ. 

Use Figure 9-12 to determine the correction factor for each Kδ. Enter figure with φ

angle and δ/φ value to determine CF. 

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STEP 5 Compute the average effective overburden pressure at the midpoint of each soil 

layer, pd (ksf). 

Note:A limiting value is not applied to pd. 

STEP 6 Compute the shaft resistance in each soil layer. Sum the shaft resistance from each 

soil layer to obtain the ultimate shaft resistance, Rs (kips). For a pile of uniform 

cross-section embedded in a uniform soil profile 

R s = K δ CF p d sin δCd D 9-6 

For H-piles in cohesionless soils, the "box" area should generally be used for shaft 

resistance calculations, i.e., the pile perimeter Cd should be considered as two times 

flange width plus two times the section height. Additional discussion on the 

behavior of open pile sections is presented in Section 9.5.4. 

STEP 7 Determine the αt coefficient and the bearing capacity factor, N'q, from the φ angle 

near the pile toe. 

a. Enter Figure 9-13(a) with φ angle near pile toe to determine αt coefficient based 

on pile length to diameter ratio. 

 

b. Enter Figure 9-13(b) with φ angle near pile toe to determine, N' q. 

c. If φ angle is estimated from SPT data, compute the average corrected SPT N160 

value over the zone from the pile toe to 3 diameters below the pile toe. 

STEP 8 Compute the effective overburden pressure at the pile toe, pt (ksf). 

Note:The limiting value of pt is 3 ksf (150 kPa). 

STEP 9 a. Compute the ultimate toe resistance, Rt (kips). 

Rt = αt N'q At pt 9-7a 

 

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Soils and Foundations – Volume II 9 - 34 December 2006 
b. Compute the maximum ultimate toe resistance, Rt (max) 

Rt (max)= qL At 9-7b

qL value is obtained as follows: 

1. Enter Figure 9-14 with φ angle near pile toe determined from laboratory or insitu test data. 

2. Enter Figure 9-14 with φ angle near the pile toe estimated from Table 8-1 in 

Chapter 8 and the average corrected SPT N1 near toe as described in Step 7. 

c. Use lesser of the two Rt values obtained from Equations 9-7a and 9-7b. 

For steel H and unfilled open end pipe piles, use only steel cross section area at pile 

toe unless there is reasonable assurance and previous experience that a soil plug will 

form at the pile toe. The assumption of a soil plug would allow the use of a box area 

at H pile toe and total pipe cross section area for open end pipe pile. Additional 

discussion on the behavior of open pile sections is presented in Section 9.5.4. 

STEP 10 Compute the ultimate geotechnical pile capacity, Qu (kips). 

Qu = Rs + Rt 

STEP 11 Compute the allowable geotechnical soil resistance, Qa (kips). 

Q Q a = u

Factor of Safety 

 The factor of safety used in the calculation should be based upon the construction 

control method to be specified. Recommended factors of safety based on 

construction control method are listed in Table 9-5. 

The concepts discussed above are illustrated numerically in Example 9-2. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 35 December 2006 
Figure 9-7. Relationship of δ/φ and pile soil displacement, V, for various types of piles (after 

Nordlund, 1963).
 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 36 December 2006 
Pile Taper 

Figure 9-8. Design curves for evaluating Kδ for piles when φ = 25° (after Nordlund, 1963). 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 37 December 2006 
Pile Taper 

Figure 9-9. Design curves for evaluating Kδ for piles when φ = 30° (after Nordlund, 1963). 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 38 December 2006 
Pile Taper 

Figure 9-10. Design curves for evaluating Kδ for piles when φ = 35° (after Nordlund, 1963). 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 39 December 2006 
Pile Taper 

Figure 9-11. Design curves for evaluating Kδ for piles when φ = 40° (after Nordlund, 1963). 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 40 December 2006 
Figure 9-12. Correction factor, CF for Kδ when δ ≠ φ (after Nordlund, 1963). 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 41 December 2006 
 

 

Table 9-6(a)
 

Design table for evaluating Kδ

 for piles when T = 0E and V = 0.10 to 1.00 ft3/ft (FHWA, 2006a) 

φ 

Displaced Volume –V (ft3

/ft) 

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 

25 0.70 0.75 0.77 0.79 0.80 0.82 0.83 0.84 0.84 0.85 

26 0.73 0.78 0.82 0.84 0.86 0.87 0.88 0.89 0.90 0.91 

27 0.76 0.82 0.86 0.89 0.91 0.92 0.94 0.95 0.96 0.97 

28 0.79 0.86 0.90 0.93 0.96 0.98 0.99 1.01 1.02 1.03 

29 0.82 0.90 0.95 0.98 1.01 1.03 1.05 1.06 1.08 1.09 

30 0.85 0.94 0.99 1.03 1.06 1.08 1.10 1.12 1.14 1.15 

31 0.91 1.02 1.08 1.13 1.16 1.19 1.21 1.24 1.25 1.27 

32 0.97 1.10 1.17 1.22 1.26 1.30 1.32 1.35 1.37 1.39 

33 1.03 1.17 1.26 1.32 1.37 1.40 1.44 1.46 1.49 1.51 

34 1.09 1.25 1.35 1.42 1.47 1.51 1.55 1.58 1.61 1.63 

35 1.15 1.33 1.44 1.51 1.57 1.62 1.66 1.69 1.72 1.75 

36 1.26 1.48 1.61 1.71 1.78 1.84 1.89 1.93 1.97 2.00 

37 1.37 1.63 1.79 1.90 1.99 2.05 2.11 2.16 2.21 2.25 

38 1.48 1.79 1.97 2.09 2.19 2.27 2.34 2.40 2.45 2.50 

39 1.59 1.94 2.14 2.29 2.40 2.49 2.57 2.64 2.70 2.75 

40 1.70 2.09 2.32 2.48 2.61 2.71 2.80 2.87 2.94 3.0 

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Soils and Foundations – Volume II 9 - 42 December 2006 
 

Table 9-6(b)
 

Design table for evaluating Kδ for piles when T = 0E and V = 1.0 to 10.0 ft3

/ft (FHWA, 2006a) 

φ 

Displaced Volume –V (ft3

/ft) 

1.0 2.0 .3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 

25 0.85 0.90 0.92 0.94 0.95 0.97 0.98 0.99 0.99 1.00 

26 0.91 0.96 1.00 1.02 1.04 1.05 1.06 1.07 1.08 1.09 

27 0.97 1.03 1.07 1.10 1.12 1.13 1.15 1.16 1.17 1.18 

28 1.03 1.10 1.14 1.17 1.20 1.22 1.23 1.25 1.26 1.27 

29 1.09 1.17 1.22 1.25 1.28 1.30 1.32 1.33 1.35 1.36 

30 1.15 1.24 1.29 1.33 1.36 1.38 1.40 1.42 1.44 1.45 

31 1.27 1.38 1.44 1.49 1.52 1.55 1.57 1.60 1.61 1.63 

32 1.39 1.52 1.59 1.64 1.68 1.72 1.74 1.77 1.79 1.81 

33 1.51 1.65 1.74 1.80 1.85 1.88 1.92 1.94 1.97 1.99 

34 1.63 1.79 1.89 1.96 2.01 2.05 2.09 2.12 2.15 2.17 

35 1.75 1.93 2.04 2.11 2.17 2.22 2.26 2.29 2.32 2.35 

36 2.00 2.22 2.35 2.45 2.52 2.58 2.63 2.67 2.71 2.74 

37 2.25 2.51 2.67 2.78 2.87 2.93 2.99 3.04 3.09 3.13 

38 2.50 2.81 2.99 3.11 3.21 3.29 3.36 3.42 3.47 3.52 

39 2.75 3.10 3.30 3.45 3.56 3.65 3.73 3.80 3.86 3.91 

40 3.00 3.39 3.62 3.78 3.91 4.01 4.10 4.17 4.24 4.30 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 43 December 2006 
9.16(a) 9-13(a)

9-13(b) 

Figure 9-13. Chart for estimating αt coefficient and bearing capacity factor N'q (FHWA, 

2006a). 

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Soils and Foundations – Volume II 9 - 44 December 2006 
Figure 9-14. Relationship between maximum unit pile toe resistance and friction angle for 

cohesionless soils (after Meyerhof, 1976). 

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Soils and Foundations – Volume II 9 - 45 December 2006 
Example 9-2: Determine the ultimate geotechnical pile capacity, Qu, for the 1 sq ft precast 

concrete pile Qu
 

γ′ = 62.5 pcf 

φ = 30°

c = 0 

40′ Silty Sand 

Since ω= 0, use Equation 9-5 

Qu = Kδ CF pd sin δ Cd D + At αt pt N′q 

where the following terms are known from 

the problem

At = 1 sq.ft 

pt = 40 γ′ = 2,500 psf 

pd = 20 γ′ = 1,250 psf 

ω = 0°, D = 40 ft, Cd = 4 ft 

Solution: 

Find Shaft Resistance, RS:
 

Use Figures 9-7, 9-9, and 9-12 with φ = 30°
 

From Figure 9-7 – For V = 1 ft3

/ft, and curve “c” for precast concrete piles;
 

δ = 0.76, Since φ = 30°, δ = 22.8° φ

From Figure 9-9 – For ω = 0, V = 1 ft3

/ft; Kδ = 1.15 

δ From Figure 9-12 – For = 0.76 ; CF = 0.9 

φ

Rs = Kδ CF pd sin δ Cd D Equation 9-6 

Rs = (1.15)(0.9)(1,250 psf)(sin 22.8o)(4 ft) (40 ft) = 80,216 lbs 

Rs = 40.1 tons 

Find Toe Resistance, Rt: 

Use Figure 9-13(b) to find N′q and αt for φ = 30°

D N′q = 30; αt = 0.5 (for = 40) B 

Rt = At αt p ′ 2

t N q = (1 ft )(0.5)(2,500 psf) 30 = 37,500 lbs = 18.75 tons Equation 9-7a 

Check limiting point resistance from Figure 9-14, qL ≈ 10 ksf ≈ 5 tsf 

Rt = q 2

L At = (5 tsf)(1 ft ) = 5 tons ∴ Rt = 5 tons Equation 9-7b 

Compute Ultimate Capacity, Qu: 

Qu = Rs + Rt = 40.1 + 5 = 45.1 tons 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 46 December 2006 
9.5.2 Ultimate Geotechnical Capacity of Single Piles in Cohesive Soils 

The ultimate geotechnical capacity of a pile in cohesive soil may also be expressed as the sum of 

the shaft and toe resistances or Qu = Rs + Rt. The shaft and toe resistances can be calculated 

from static analysis methods using soil boring and laboratory test data in either total stress or 

effective stress methods. The α-method is a total stress method that uses undrained soil shear 

strength parameters for calculating static pile capacity in cohesive soil. The α-method will be 

presented in Section 9.5.2.1. The effective stress method, or β-method, uses drained soil strength 

parameters for capacity calculations. Since the effective stress method may be used for 

calculating static pile capacity in cohesive as well as cohesionless soils, this method will be 

presented in Section 9.5.2.2. Alternatively, in-situ CPT test results can also be used to calculate 

pile capacity in cohesive soils from cone sleeve friction and cone tip resistance values. CPTbased methods as well as other methods are discussed in FHWA (2006a). 

The shaft resistance of piles driven into cohesive soils is frequently as much as 80 to 90% of the 

total capacity. Therefore, it is important that the shaft resistance of piles in cohesive soils be 

estimated as accurately as possible. 

9.5.2.1 Total Stress – α-method 

For piles in clay, a total stress analysis is often used where ultimate capacity is calculated from 

the undrained shear strength of the soil. This approach assumes that the shaft resistance is 

independent of the effective overburden pressure and that the unit shaft resistance can be 

expressed in terms of an empirical adhesion factor times the undrained shear strength. 

Shaft Resistance 

The unit shaft resistance, fs, is equal to the adhesion, ca, which is the shear stress between the pile 

and soil at failure. This may be expressed in equation form as: 

in which α is an empirical factor applied to the average undrained shear strength, cu, of 

undisturbed clay along the embedded length of the pile. The coefficient α depends on the nature 

and strength of the clay, magnitude of load, pile dimension, method of pile installation, and time 

effects. The values of α vary within wide limits and decrease rapidly with increasing shear 

strength. 

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Soils and Foundations – Volume II 9 - 47 December 2006 

fs = ca = α cu 9-8
The adhesion factor, α, is a function of the soil stratigraphy and pile embedment. Three common 

cases are as follows: 

• Case 1: Piles driven into stiff clays through overlying sands or sandy gravels 

• Case 2: Piles driven into stiff clays through overlying soft clays 

• Case 3: Piles driven into stiff clays without overlying different strata 

Figure 9-15 presents the adhesion factor, α, versus the undrained shear strength of the soil as a 

function of unique soil stratigraphy and pile embedment for Case 1 and Case 2. The adhesion 

factor from these soil stratigraphy cases should be used only for determining the adhesion in a 

stiff clay layer in that specific condition as follows: 

•	 Case 1: The top graph in Figure 9-15 may be used to select the adhesion factor when 

piles are driven through a sand or sandy gravel layer and into an underlying stiff clay 

stratum. This case results in the highest adhesion factors as granular material is dragged 

into the underlying clays. The greater the pile penetration into the clay stratum, the less 

influence the overlying granular stratum has on the adhesion factor. Therefore, for the 

same undrained shear strength, the adhesion factor decreases with increased pile 

penetration into the clay stratum. 

•	 Case 2: The bottom graph in Figure 9-15 should be used to select the adhesion factor 

when piles are driven through a soft clay layer overlying a stiff clay layer. In this case, 

the soft clay is dragged into the underlying stiff clay stratum thereby reducing the 

adhesion factor of the underlying stiff clay soils. The greater the pile penetration into the 

underlying stiff clay soils, the less the influence the overlying soft clays have on the stiff 

clay adhesion factor. Therefore, the stiff clay adhesion factor increases with increasing 

pile penetration into the stiff clay soils. 

Figure 9-16 presents the adhesion factor, α, versus the undrained shear strength of the soil for 

piles driven in stiff clays without any different overlying strata, i.e., Case 3. In stiff clays, a gap 

often forms between the pile and the soil along the upper portion of the pile shaft. In this case, 

the shallower the pile penetration into a stiff clay stratum the greater the effect the gap has on the 

shaft resistance that develops. Hence, the adhesion factor for a given shear strength is reduced at 

shallow pile penetration depths and increased at deeper pile penetration depths. 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 48 December 2006 
 

(a) 

(b) 

Figure 9-15. Adhesion values for driven piles in mixed soil profiles, (a) Case 1: piles driven 

through overlying sands or sandy gravels, and (b) Case 2: piles driven through overlying 

weak clay (Tomlinson, 1980). 

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Soils and Foundations – Volume II 9 - 49 December 2006 
Figure 9-16. Adhesion values for driven piles in stiff clays without different overlying strata 

(Case 3) (Tomlinson, 1980). 

The following should be considered by the designer while using Figures 9-15 and 9-16: 

•	 For a soil profile consisting of clay layers of significantly different consistencies such as 

soft clays over stiff clays, adhesion factors should be determined for each individual clay 

layer. 

•	 In clays with large shrink-swell potential, static capacity calculations should ignore the 

shaft resistance from the adhesion in the shrink-swell zone. During dry times, shrinkage 

will create a gap between the clay and the pile in this zone, therefore the shaft resistance 

should not be relied upon for long term support. 

•	 In cases where either Figures 9-15b or 9-16 could be used, the inexperienced user should 

select and use the smaller value obtained from either figure. All users should confirm the 

applicability of a selected design chart in a given soil condition with local correlations 

between static capacity calculations and static load tests results. 

•	 In the case of H piles in cohesive soils, the shaft resistance should not be calculated from 

the surface area of the pile, but rather from the sub-divided perimeter area of the four sides. 

The shaft resistance for H-piles in cohesive soils consists of the sum of the adhesion, ca, 

times the flange surface area along the exterior of the two flanges, plus the undrained shear 

strength of the soil, cu, times the section height surface area of the two remaining sides. 

This computation can be approximated by determining the adhesion and multiplying the 

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Soils and Foundations – Volume II 9 - 50 December 2006 
adhesion by the H-pile "box perimeter" area. Further discussion on this topic is included in 

Section 9.5.4. 

Toe Resistance 

The unit toe resistance in a total stress analysis for homogeneous cohesive soil is as follows: 

qt = cu Nc 9-9

The term Nc is a dimensionless bearing capacity factor that depends on the pile diameter and the 

depth of embedment and cu is the undrained shear strength of the material at and below the toe of 

the pile. The bearing capacity factor, Nc, is usually taken as 9 for deep foundations. 

It should be remembered that the movement required to mobilize the toe resistance is several 

times greater than that required to mobilize the shaft resistance. At the movement required to 

fully mobilize the toe resistance, the shaft resistance may have decreased to a residual value. 

Therefore, the contribution of the toe resistance to the ultimate pile capacity in cohesive soils is 

sometimes ignored except in hard cohesive deposits such as glacial tills. 

STEP BY STEP PROCEDURE FOR - "α-METHOD" 

STEP 1	 Delineate the soil profile into layers and determine the adhesion, ca, from Figure 9­

15 and 9-16 as appropriate. for each layer. 

Enter the appropriate figure with the undrained shear strength of the soil, cu, and 

determine adhesion or adhesion factor based on the ratio of the embedded pile length 

in clay, D, and the pile diameter, b. Use the D/b curve for the appropriate soil and 

embedment condition. 

STEP 2	 For each soil layer, compute the unit shaft resistance, fs in ksf (kPa). 

fs = ca = α cu

 where: ca = adhesion and α = adhesion factor. 

STEP 3	 Compute the shaft resistance in each soil layer and the ultimate shaft resistance, Rs, in 

kips (kN), from the sum of the shaft resistance from each layer. 

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Rs = fs As 9-10

 

where: As = pile-soil surface area in ft2

 (m2) = (pile perimeter) x (length). 

STEP 4 Compute the unit toe resistance, qt in ksf (kPa). 

qt = 9 cu 

where: cu = undrained shear strength of soil at the pile toe in ksf (kPa) 

STEP 5 Compute the ultimate toe resistance, Rt in kips (kN). 

Rt = qt At 9-11

where: A 2

t = Area of pile toe in ft2

 (m ). 

STEP 6 Compute the ultimate geotechnical pile capacity, Qu in kips (kN). 

Qu = Rs + Rt 

STEP 7 Compute the allowable geotechnical soil resistance, Qa in kips (kN). 

Q Q = u

a Factor of Safety 

 The factor of safety in this static calculation should be based on the specified 

construction control method as described in Section 9.4 of this chapter. Factors of 

safety for various construction control methods are listed in Table 9-5. 

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Soils and Foundations – Volume II 9 - 52 December 2006 
9.5.2.2 Effective Stress – β-method 

Static capacity calculations in cohesionless, cohesive, and layered soils can also be performed by 

using an effective stress based method. Effective stress based methods were developed to model 

the long term drained shear strength conditions. Therefore, the effective soil friction angle, φ', 

should be used in parameter selection. 

In an effective stress analysis, the unit shaft resistance is calculated from the following 

expression: 

fs = β po 9-12

where: β = Bjerrum-Burland beta coefficient = Ks tan δ. 

po = average effective overburden pressure along the pile shaft, in ksf (kPa). 

Ks = earth pressure coefficient. 

δ = interface friction angle between pile and soil. 

The unit toe resistance is calculated from:

 qt = Nt pt	 9-13 

where: Nt = toe bearing capacity coefficient. 

pt = effective overburden pressure at the pile toe in ksf (kPa). 

Recommended ranges of β and Nt coefficients as a function of soil type and φ' angle from 

Fellenius (1991) are presented in Table 9-7. Fellenius (1991) notes that factors affecting the β

and Nt coefficients consist of the soil composition including the grain size distribution, 

angularity and mineralogical origin of the soil grains, the original soil density and density due to 

the pile installation technique, the soil strength, as well as other factors. Even so, β coefficients 

are generally within the ranges provided and seldom exceed 1.0. 

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Soils and Foundations – Volume II 9 - 53 December 2006 
Table 9-7 

Approximate range of β and Nt coefficients (Fellenius, 1991) 

Soil Type φ' β Nt 

Clay 25 – 30 0.23 - 0.40 3 - 30 

Silt 28 – 34 0.27 - 0.50 20 - 40 

Sand 32 – 40 0.30 - 0.60 30 - 150 

Gravel 35 – 45 0.35 - 0.80 60 - 300 

For sedimentary cohesionless deposits, Fellenius (1991) that states Nt ranges from about 30 to a 

high of 120. In very dense non-sedimentary deposits such as glacial tills, Nt can be much higher, 

but it can also approach the lower bound value of 30. In clays, Fellenius (1991) notes that the 

toe resistance calculated by using an Nt of 3 is similar to the toe resistance calculated from an 

analysis where undrained shear strength is used. Therefore, the use of a relatively low value of 

the Nt coefficient in clays is recommended unless local correlations suggest higher values are 

appropriate. 

Graphs of the ranges in β and Nt coefficients versus the range in φ' angle as suggested by 

Fellenius are presented in Figure 9-17 and 9-18, respectively. These graphs may be helpful in 

selection of β or Nt. The inexperienced user should select conservative β and Nt coefficients. As 

with any design method, the user should also confirm the appropriateness of a selected β or Nt 

coefficient in a given soil condition with local correlations between static capacity calculations 

and static load tests results. 

It should be noted that the effective stress method places no limiting values on either the shaft or 

toe resistance. 

STEP BY STEP PROCEDURE FOR THE EFFECTIVE STRESS METHOD 

STEP 1 Delineate the soil profile into layers and determine φ' angle for each layer. 

a. Construct po diagram by using previously described procedures in Chapter 2. 

b. Divide soil profile throughout the pile penetration depth into layers and determine 

the effective overburden pressure, po, in ksf (kPa) at the midpoint of each layer. 

c. Determine the φ' angle for each soil layer from laboratory or in-situ test data. 

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Figure 9-17. Chart for estimating β coefficient as a function of soil type φ' (after Fellenius, 

1991). 

FHWA NHI-06-089 9 – Deep Foundations 

Soils and Foundations – Volume II 9 - 55 December 2006 
Figure 9-18. Chart for estimating Nt coefficients as a function of soil type φ' angle (after 

Fellenius, 1991). 

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Soils and Foundations – Volume II 9 - 56 December 2006 
d. In the absence of laboratory or in-situ test data for cohesionless layers, determine 

the average corrected SPT N1 value for each layer and estimate φ' angle from 

Table 8-1 in Chapter 8. 

STEP 2 Select the β coefficient for each soil layer. 

a. Use local experience to select β coefficient for each layer. 

b. In the absence of local experience, use Table 9-7 or Figure 9-17 to estimate the β

coefficient from the φ' angle for each layer. 

STEP 3 For each soil layer compute the unit shaft resistance, fs in ksf (kPa). 

fs = β po 

STEP 4 Compute the shaft resistance in each soil layer and the ultimate shaft resistance, Rs in 

kips (kN) from the sum of the shaft resistance from each soil layer. 

Rs = Σ fs As 

where: A rface area in ft2

 (m2 s = pile-soil su ) = (pile perimeter) x (length). 

STEP 5	 Compute the unit toe resistance, qt in ksf (kPa). 

qt = Nt pt 

a. Use local experience to select Nt coefficient. 

b. In the absence of local experience, estimate Nt from Table 9-7 or Figure 9-18 

based on φ' angle. 

c. Calculate the effective overburden pressure at the pile toe, pt in ksf (kPa). 

STEP 6 Compute the ultimate toe resistance, Rt in kips (kN). 

Rt = qt At
 

where: At = area of the pile toe in m2

 (ft2). 

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STEP 7 Compute the ultimate geotechnical pile capacity, Qu in kips (kN). 

Qu = Rs + Rt 

STEP 8 Compute the allowable geotechnical soil resistance, Qa in kips (kN). 

Qu Q = a Factor of Safety 

The factor of safety in this static calculation should be based on the specified 

construction control method as described in Section 9.4 of this chapter. 

Recommended factors of safety based on construction control methods are listed in 

Table 9-5 

The concepts discussed above are illustrated numerically in Example 9-3. 

Example 9-3: Determine the required pile length to resist a 40 tons load with a safety factor of 

2. Assume no toe resistance for the 1 ft2

 precast concrete pile. Site specific tests 

have indicated that the adhesion may be assumed equal to cohesion. 

γt2 = 130 pcf 

c2 = 1,100 psf, φ2 = 0 

γt1 = 120 pcf 

c1 = 500 psf, φ1 = 0 

Qall = 40 tons 

D1 = 10 ft 

D2 = ? 

Solution: 

Qu = Rs1 + Rs2 (Note: No toe resistance, i.e. 9 cu At = 0) 

Qu = ca1 As1 + ca2 As2 

Qu = ca1 Cd1 D1 + ca2 Cd2 D2 

where Cd1 and Cd2 are pile perimeters within depths D1 and D2 

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Cd1 = Cd2 = 4 × 1 ft = 4 ft 

From the problem statement, for site-specific conditions, adhesion = cohesion. Therefore, 

ca1 = c1 = 500 psf 

ca2 = c2 = 1,100 psf 

Qu = 40 tons × FS = 40 tons x 2 = 80 tons 

80 tons = (500 psf)(4 ft)(10 ft) + (1,100 psf)(4 ft)D2 

80 tons = 20,000 lbs + 4,400 D2 lbs/ft 

80 tons = 10 tons + 2.2 D2 tons/ft 

Solve for D2, 

80 tons − 10 tons D2 = ≈ 32 ft 

2.2 tons / ft 

∴Total pile length required = 32 ft + 10 ft ≈ 42 ft 

9.5.3 Ultimate Geotechnical Capacity of Single Piles in Layered Soils 

The ultimate capacity of piles in layered soils can be calculated by combining the methods 

previously described for cohesionless and cohesive soils. For example, a hand calculation 

combining the Nordlund method from Section 9.5.1.1 for cohesionless soil layers with the α

method from Section 9.5.2.1 for cohesive soil layers could be used. The effective stress method 

as described in Section 9.5.2.2 could also be used for layered soil profiles. 

­

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9.5.4 Plugging of Open Pile Sections 

Open pile sections include open end pipe piles and H-piles. The use of open pile sections has 

increased, particularly where special design events dictate large pile penetration depths. When 

open pile sections are driven, they may behave as low displacement piles and "cookie cut" 

through the soil, or act as displacement piles if a soil plug forms near the pile toe. It is generally 

desired that open sections remain unplugged during driving and plugged under static loading 

conditions. 

Stevens (1988) reported that plugging of pipe piles in clays does not occur during driving if pile 

accelerations along the plug zone are greater than 22g. Holloway and Beddard (1995) reported 

that hammer blow size influenced the dynamic response of the soil plug. With a large hammer 

blow, the plug "slipped" under the dynamic event whereas under a lesser hammer blow the pile 

encountered toe resistance typical of a plugged condition. From a design perspective, these cases 

indicate that pile penetration of open sections can be facilitated if the pile section is designed to 

accommodate a large pile hammer. Wave equation analyses can provide calculated accelerations 

at selected pile segments. 

Static pile capacity calculations must determine whether an open pile section will exhibit 

plugged or unplugged behavior. Studies by O'Neill and Raines (1991), Raines, et al. (1992), as 

well as Paikowsky and Whitman (1990) suggest that plugging of open pipe piles in medium 

dense to dense sands generally begins at a pile penetration-to-pile-diameter ratio of 20, but can 

occur in cases where the ratio is as high as 35. For pipe piles in soft to stiff clays, Paikowsky 

and Whitman (1990) reported plugging occurs at penetration-to-pile-diameter ratios of 10 to 20. 

The above studies suggest that plugging in any soil material is probable under static loading 

conditions once the penetration-to-pile-diameter ratio exceeds 20 in dense sands and clays, or 20 

to 30 in medium sands. An illustration of the difference in the soil resistance mechanism that 

develops on a pipe pile with an open and plugged toe condition is presented in Figure 9-19. 

Paikowsky and Whitman (1990) recommend that the static capacity of an open end pipe pile be 

calculated from the lesser of the following equations: 

Plugged Condition: Q u = f so A s + q t At 9-15a 

Unplugged Condition: Qu = f so As + f si Asi + qt Ap - wp 9-15b 

where: Qu = ultimate pile capacity in kips (kN). 

fso = exterior unit shaft resistance in ksf (kPa). 

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D
 

f

so
 f

so f

si 

qt qt qt 

b 

(a) Open Toe Condition (b) Plugged Toe Condition 

Figure 9-19. Plugging of open end pipe piles (after Paikowsky and Whitman, 1990). 

Figure 9-20. Plugging of H-piles (FHWA, 2006a). 

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As = pile exterior surface area in ft2

 (m2) 

fsi = interior unit shaft resistance in ksf (kPa) 

Asi = pile interior surface area in ft2

 (m2) 

qt = unit toe resistance in ksf (kPa) 

At = toe area of a plugged pile in ft2

 (m2) 

Ap = cross sectional area of an unplugged pile in ft2

 (m2) 

wp = weight of the plug in kips (kN) 

Static pile capacity calculations for open end pipe piles in cohesionless soils should be performed 

by using the Paikowsky and Whitman (1990) equations. Toe resistance should be calculated by 

using the Tomlinson limiting unit toe resistance of 105 ksf (5000 kPa), once Meyerhof's limiting 

unit toe resistance, determined from Figure 9-14, exceeds 105 ksf (5000 kPa). For open end 

pipe piles in predominantly cohesive soils, the Tomlinson equation should be used. 

The soil stresses and displacements induced by driving an open pile section and a displacement 

pile section are not the same. Hence, a lower unit toe resistance, qt, should be used for 

calculating the toe capacity of open end pipe piles compared to a typical closed end condition. 

The value of the interior unit shaft resistance in an open end pipe pile is typically on the order of 

1/3 to 1/2 the exterior unit shaft resistance, and is influenced by soil type, pile diameter, and pile 

shoe configuration. These factors will also influence the length of the soil plug that may 

develop. 

For open end pipe piles in cohesionless soils, Tomlinson (1994) recommends that the static pile 

capacity be calculated using a limiting value of 105 ksf (5000 kPa) for the unit toe resistance, 

regardless of the pile size or soil density. Tomlinson states that higher unit toe resistances do not 

develop, because yielding of the soil plug rather than bearing capacity failure of the soil below 

the plug governs the capacity. 

For open end pipe piles driven in stiff clays, Tomlinson (1994) recommends that the static pile 

capacity for cohesive soils be calculated as follows when field measurements confirm a plug is 

formed and carried down with the pile: 

Q u =0.8 ca As + 4.5 cu At 9-16 

where: Qu = ultimate pile capacity in kips (kN) 

ca = pile adhesion from Figure 9-15 in ksf (kPa) 

As = pile-soil surface area in ft2

 (m2) 

cu = average undrained shear strength at the pile toe in ksf (kPa) 

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At = toe area of a plugged pile in ft2

 (m2) 

The plugging phenomenon in H-piles can be equally difficult to analyze. However, the distance 

between flanges of an H-pile is smaller than the inside diameter of most open end pipe piles. 

Therefore, it can usually be assumed that an H-pile will be plugged under static loading 

conditions and the “box” area of the pile toe can be used for static calculation of the toe capacity 

in cohesionless and cohesive soils, i.e., area = flange width x section height. The toe capacity for 

H-piles driven to rock is usually governed by the pile structural strength. In that case, the toe 

capacity is calculated based on the steel cross sectional area, and should not include the area of a 

soil plug, if any. 

For H-piles in cohesionless soils, arching between the flanges can usually be assumed, and the 

"box" perimeter can be used for shaft resistance calculations, i.e., perimeter = 2 x flange width + 

2 x section height. In most cohesive soils, the shaft resistance is calculated from the sum of the 

adhesion, ca, along the exterior of the two flanges plus the undrained shear strength of the soil, 

cu, times the section height surface area of the two remaining sides of the "box" due to soil-tosoil shear along these two faces. Figure 9-20 illustrates that calculation of shear resistance for Hpiles in stiff clays can still be problematic. Sheared clay lumps can develop above the plug zone, 

in which case the shaft resistance may develop only along the exterior surfaces of the flanges in 

the sheared lump zone. 

The above discussions highlight the point that a higher degree of uncertainty often exists for 

static pile capacity calculations of open pile sections than for displacement piles. Soil plug 

formation and plug response is often different under static and dynamic loading. Such 

differences can complicate pile capacity evaluations of open pile sections with all dynamic 

methods (wave equation, dynamic testing, and dynamic formulas). Therefore, a static load test is 

recommended to verify calculated capacity for large diameter open end pipe piles, greater than 

18 in (450 mm), or for H-piles designed to carry their load primarily in shaft resistance. 

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9.5.5 Time Effects on Pile Capacity 

The soil is greatly disturbed when a pile is driven into the soil. As the soil surrounding the pile 

recovers from the installation disturbance, a time dependent change in pile capacity often occurs. 

Frequently piles driven in saturated clays, and loose to medium dense silts or fine sands gain 

capacity after driving has been completed. This phenomenon is called soil setup. Occasionally 

piles driven into dense saturated fine sands, dense silts, or weak laminated rocks such as shale, 

will exhibit a decrease in capacity after the driving has been completed. This phenomenon is 

called relaxation. Case history discussions on soil setup and relaxation may be found in 

Fellenius, et al. (1989), and Thompson and Thompson (1985), respectively. 

9.5.5.1 Soil Setup 

When saturated cohesive soils are compressed and disturbed due to pile driving, large excess 

pore water pressures develop. These excess pore water pressures are generated partly from the 

shearing and remolding of the soil and partly from radial compression as the pile displaces the 

soil. The excess pore water pressures cause a reduction in the effective stresses acting on the 

pile, and thus a reduction in the soil shear strength. The reduction in soil shear strength results in 

a reduced pile capacity during driving, and for a period of time afterwards. 

After driving, the excess pore water pressures will dissipate primarily through radial flow of the 

pore water away from the pile. With the dissipation of pore water pressures, the soil 

reconsolidates and shear strength increases. This increase in soil shear strength results in an 

increase in the static pile capacity and is called soil setup. A similar decrease in resistance to 

pile penetration with subsequent soil setup may occur in loose to medium dense, saturated, fine 

grained sands or silts. The magnitude of the gain in capacity depends on soil characteristics, pile 

material and pile dimensions. 

Because the pile capacity may increase after the end of driving, pile capacity assessments should 

be made from static load testing or restriking performed after equilibrium conditions in the soil 

have been re-established. The time for the return of equilibrium conditions is highly variable and 

depends on soil type and degree of soil disturbance. Piezometers installed within three diameters 

of the pile can be used to monitor pore pressure dissipation with time. Effective stress static pile 

capacity calculation methods can be used to evaluate the increase in capacity with time once pore 

pressures are quantified. 

Static load testing or restrike testing of piles in fine grained soils should not be conducted until 

after pore pressures dissipate and return to equilibrium. In the absence of site-specific pore water 

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pressure data from piezometers, it is suggested that static load testing or restrking of piles in 

clays and other predominantly fine grained soils be delayed for at least two weeks after driving 

and preferably for a longer period. In sandy silts and fine sands, pore pressures generally 

dissipate more rapidly. In these more granular deposits, five days to a week is often a sufficient 

time delay. 

FHWA (1996) calculated general soil setup factors based on the predominant soil type along the 

pile shaft. The soil setup factor was defined as the failure load from a static load test divided by 

the end-of-drive wave equation capacity. These results are presented in Table 9-20. The data 

base for this study was comprised of 99 test piles from 46 sites. The number of sites and the 

percentage of the data base in a given soil condition is included in the table. While these soil setup factors may be useful for preliminary estimates, soil setup is better estimated based on sitespecific data gathered from pile restriking, dynamic measurements, static load testing, and local 

experience. 

Komurka, et al., (2003) summarized the current practice in estimating and measuring soil setup 

in a report to the Wisconsin Highway Research Program. This report summarizes the 

mechanisms associated with soil setup development and reviews several empirical relationships 

for estimating set-up. 

Table 9-8 

Soil setup factors (after FHWA, 1996) 

Predominant Soil 

Type Along Pile 

Shaft 

Range in 

Soil Set-up 

Factor 

Recommended 

Soil Set-up 

Factors* 

Number of Sites 

and (Percentage 

of Data Base) 

Clay 1.2 - 5.5 2.0 7 (15%) 

Silt - Clay 1.0 - 2.0 1.0 10 (22%) 

Silt 1.5 - 5.0 1.5 2 (4%) 

Sand - Clay 1.0 - 6.0 1.5 13 (28%) 

Sand - Silt 1.2 - 2.0 1.2 8 (18%) 

Fine Sand 1.2 - 2.0 1.2 2 (4%) 

Sand 0.8 - 2.0 1.0 3 (7%) 

Sand - Gravel 1.2 - 2.0 1.0 1 (2%) 

* Confirmation with local experience recommended 

9.5.5.2 Relaxation 

The ultimate capacity of driven piles can also decrease with time following driving. This is 

known as relaxation and it has been observed in dense, saturated, fine grained soils such as 

non-cohesive silts and fine sands, as well as in some shales. In these cases, the driving process is 

believed to cause the dense soil near the pile toe to dilate, thereby generating negative excess 

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pore water pressures, i.e., suction. In accordance with the principle of effective stress, the 

negative pore water pressures temporarily increase the effective stresses acting on the pile, 

resulting in a temporarily higher soil strength and driving resistance. When these negative 

excess pore water pressures dissipate, the effective stresses acting on the pile decrease, as does 

the pile capacity. Relaxation in weak laminated rocks has been attributed to a release of lockedin horizontal stresses (Thompson and Thompson, 1985). 

Because the pile capacity may decrease due to relaxation after the end of driving, pile capacity 

assessments from static load testing or restrking should be made after equilibrium conditions in 

the soil have been re-established. In the absence of site-specific pore water pressure data from 

piezometers, it is suggested that static load testing or restrking of piles in dense silts and fine 

sands be delayed for five days to a week after driving, or longer if possible. In relaxation-prone 

shales, it is suggested that static load testing or restrike testing be delayed a minimum of two 

weeks after driving. 

Published cases of the relaxation magnitude of various soil types are quite limited. However, 

data from Thompson and Thompson (1985) as well as Hussein, et al. (1993) suggest relaxation 

factors for piles founded in some shales can range from 0.5 to 0.9. The relaxation factor is 

defined as the failure load from a static load test divided by the pile capacity at the end of initial 

driving. Relaxation factors of 0.5 and 0.8 have also been observed in two cases where piles were 

founded in dense sands and extremely dense silts, respectively. The importance of evaluating 

time dependent decreases in pile capacity for piles founded in these materials cannot be over 

emphasized. 

9.5.6 Additional Design and Construction Considerations 

The previous sections of this chapter addressed routine static analysis procedures for pile 

foundation design. However, the designer should be aware of additional design and construction 

considerations that can influence the reliability of static analysis procedures in estimating pile 

capacity. These issues include effects of predrilling or jetting, construction dewatering and soil 

densification on pile capacity. Pile-driving-induced vibrations can also influence the final design 

and results of static calculations if potential vibration levels dictate changes in pile type or 

installation procedures. These topics are outside the scope of this manual and the reader is 

referred to FHWA (2006a) for guidance. 

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9.5.7 The DRIVEN Computer Program 

The FHWA developed the computer program DRIVEN in 1998 for calculation of static pile 

capacity. The DRIVEN program can be used to calculate the capacity of open and closed end 

pipe piles, H-piles, circular or square solid concrete piles, timber piles, and Monotube piles. The 

program results can be displayed in both tabular and graphical form. Analyses may be 

performed in either English or SI units and can be switched between units during analyses 

(FHWA, 1998b). The DRIVEN manual and software Version 1.2, released in March 2001, can 

be downloaded from www.fhwa.dot.gov/bridge/geosoft.htm. 

In the DRIVEN program, the user inputs the soil profile consisting of the soil unit weights and 

strength parameters including the percentage strength loss during driving. For the selected pile 

type, the program calculates the pile capacity versus depth for the entire soil profile using the 

Nordlund and α-methods in cohesionless and cohesive layers, respectively. User-input 

percentage soil strength losses during driving are used to calculate the ultimate pile capacity at 

the time of driving as well as during restrike. 

The DRIVEN program includes several analysis options that facilitate pile design. These options 

include: 

•	 Soft compressible soils: The shaft resistance from unsuitable soil layers defined by the 

user is subtracted from the calculation of ultimate pile capacity. 

• Scourable soils: Based on a user-input depth, the calculated shaft resistance from 

scourable soils due to local scour is subtracted from the 

calculation of ultimate pile capacity. In the case of channel 

degradation scour, the reduction in pile capacity from the loss of 

shaft resistance in the scour zone as well as the influence of the 

reduced effective overburden pressure from soil removal on the 

capacity calculated in the underlying layers is considered. 

• Pile Plugging: DRIVEN handles pile plugging based on the recommendations 

presented in Section 9.5.4 of this manual. 

The initial DRIVEN program screen is the Project Definition Screen illustrated in Figure 9-21. 

In this screen the user inputs the project information as well as the number of soil layers. Inputs 

for three water table elevations are provided. The water table at the time of drilling is used for 

correction of SPT N values for overburden pressure if that option is selected by the user. The 

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water table at the time of restrike / driving affects the effective overburden pressure in the static 

capacity calculations at those times. The static calculation at the time of driving includes soil 

strength losses. The restrike static calculations include the long term soil strength. The water 

table at the ultimate condition is used in the calculation of effective overburden pressure for the 

static capacity calculation under an extreme event. 

The Soil Profile screen for a two layer soil profile is shown in Figure 9-22. A mouse click on the 

Select Graph Option will bring up the Cohesive Soil Layer Properties screen shown in Figure 9­

23. The user can then select how the adhesion is calculated. The general adhesion option 

attributed to “Tomlinson 1979” in Figure 9-23 is based upon the data presented in Figure 9-16, 

i.e., piles without different overlying strata. The bottom option in the Cohesive Soil Layer 

Properties screen shown in Figure 9-23 allows the user to enter an adhesion value of their choice. 

This bottom option may be useful with the data presented in Figures 9-15 and 9-16 or site data 

from specific load test.. 

The Soil Profile screen for a two layer profile with cohesionless soil properties is presented in 

Figure 9-24. The user can input the same or different soil friction angles to be used in the shaft 

resistance and end bearing calculations in the layer. The user can also input SPT N values and 

let the program compute the soil friction angle from a correlation developed by Peck, et al. 

(1974) as shown in Figure 9-25. However, it is recommended that the user manually select the 

soil friction angle rather than use this program option as factors influencing the N value - φ angle 

correlation such as SPT hammer type and sample recovery are not considered by the program. 

Both cohesive and cohesionless soil profile screens request the user to provide the percentage 

strength loss of the soil type during driving. This is sometimes difficult for the user to quantify. 

Insight into appropriate values of driving strength loss can be gathered from the soil setup factors 

presented in Section 9.5.5. The percent driving strength loss needed for input into DRIVEN can 

be then be calculated from: 

% Driving Strength Loss = 1 – [1 /setup factor] 

After the soil input has been entered, the user must select a pile type from a drop down menu 

located on the Soil Profile screen. A pile detail screen will appear for the pile type selected 

requesting additional information on the depth to the top of the pile and the pile properties. 

These DRIVEN screens are presented in Figure 9-26. 

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Figure 9-21. DRIVEN Project Definition screen. 

Figure 9-22. DRIVEN Soil Profile screen – cohesive soil. 

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Figure 9-23. DRIVEN Cohesive Soil Layer Properties screen. 

Figure 9-24. DRIVEN Soil Profile screen – cohesionless soil. 

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Figure 9-25. DRIVEN Cohesionless Soil Layer Properties screen. 

Figure 9-26. DRIVEN Soil Profile screen - Pile type selection drop down menu and pile 

detail screen. 

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Once all soil and pile information is entered, the user can review the static capacity calculations 

in tabular or graphical form by a mouse click on the appropriate icon in the program toolbar. 

The toolbar icons for tabular and graphical output are identified in Figure 9-27. The OutputTabular screen is shown in Figure 9-28. A summary of the input data and the results of the 

analysis will be printed if the user clicks on the report button. Analysis output can also be 

presented graphically as shown in Figures 9-28 and 9-29 for driving and restrike static analyses, 

respectively. The ultimate capacity versus depth from shaft resistance, toe resistance, and the 

combined shaft and toe resistance can be displayed by clicking on “skin friction,” “end bearing,” 

and “total capacity” on the Plots menu of the Output-Graphical screen, capacity changes with 

time or from extreme events can be reviewed by clicking on “restrike,” “driving,” and “ultimate” 

on the Plot Set menu of the Output-Graphical screen. 

The program also generates the soil input file required for a driveability study in the commonly 

used GRLWEAP wave equation program. The GRLWEAP file created by DRIVEN is 

compatible with the Windows versions of GRLWEAP. However, the DRIVEN file must be 

identified as a pre 2002 input file in the current version of GRLWEAP. 

Additional DRIVEN program capabilities are described in the DRIVEN Program User’s Manual 

by FHWA (1998b). 

Create 

GRLWEAP Driveability 

Analysis File 

Go To 

Tabular 

Output 

Go To 

Graphical 

Output 

Figure 9-27. DRIVEN toolbar output and analysis options. 

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Figure 9-28. DRIVEN Output Tabular screen. 

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Figure 9-29. DRIVEN Output-Graphical screen for end of driving. 

Figure 9-30. DRIVEN Output -Graphical screen for restrike. 

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9.5.8 Ultimate Capacity of Piles on Rock and in Intermediate Geomaterials (IGMs) 

Pile foundations on rock are normally designed to carry large loads. For pile foundations driven 

to rock, which include steel H-piles, pipe piles or precast concrete piles, the exact area in contact 

with the rock, the depth of penetration into rock, as well as the quality of rock are largely 

unknown. Therefore, the determination of load capacity of driven piles on rock should be made 

on the basis of driving observations, local experience and load tests. 

Rock Quality Designation (RQD) values can provide a qualitative assessment of rock mass as 

discussed in Chapter 3. Except for soft weathered rock, the structural capacity of toe bearing pile 

will generally be less than the capacity of rock of fair to excellent quality as described in Figure 

3-17 in Chapter 3. The structural capacity, which is based on the allowable design stress for the 

pile material, will therefore govern the pile capacity in many cases. 

Small diameter piles supported on fair to excellent quality rock may be loaded to their allowable 

structural capacity. Piles supported on soft weathered rock, such as shale or other types of very 

poor or poor quality rock, should be designed based on the results of pile load tests. Similarly, 

for driven piles that penetrate into soft rocks or IGMs, the ultimate capacity may include the 

contribution of shaft resistance if a static load test is performed to verify the magnitude of the 

shaft resistance. 

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9.6 DESIGN OF PILE GROUPS 

The previous sections of this chapter dealt with design procedures for single piles. However 

piles for almost all highway structures are installed in groups due to the heavy foundation loads. 

This section of the chapter will address the foundation design procedures for evaluating the axial 

compression capacity of pile groups as well as the settlement of pile groups under axial 

compression loads. The axial compression capacity and settlement of pile groups are interrelated 

and are therefore presented in sequence. 

The efficiency of a pile group in supporting the foundation load is defined as the ratio of the 

ultimate capacity of the group to the sum of the ultimate capacities of the individual piles 

comprising the group. This may be expressed in equation form as: 

Qug ηg = 9-17 nQu 

where: ηg = pile group efficiency 

Qug = ultimate capacity of the pile group 

n = number of piles in the pile group 

Qu = ultimate capacity of each individual pile in the pile group 

If piles are driven into compressible cohesive soil or into dense cohesionless material underlain 

by compressible soil, then the ultimate axial compression capacity of a pile group may be less 

than that of the sum of the ultimate axial compression capacities of the individual piles. In this 

case, the pile group has a group efficiency of less than 1. In cohesionless soils, the ultimate axial 

compression capacity of a pile group is generally greater than the sum of the ultimate axial 

compression capacities of the individual piles comprising the group. In this case, the pile group 

has a group efficiency greater than 1. 

The settlement of a pile group is likely to be many times greater than the settlement of an 

individual pile carrying the same per pile load as each pile in the group. Figure 9-31(a) 

illustrates that for a single pile, only a relatively small zone of soil around and below the pile toe 

is subjected to vertical stress. Figure 9-31(b) illustrates that for a pile group, a much larger zone 

of soil around and below the pile group is stressed. The settlement of the pile group may be 

large depending on the compressibility of the soils within the stressed zone. 

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Figure 9-31. Stress zone from single pile and pile group (after Tomlinson, 1994). 

Figure 9-32. Overlap of stress zones for friction pile group (after Bowles, 1996). 

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The soil supporting a pile group is also subject to overlapping stress zones from individual piles 

in the group. The overlapping effect of stress zones for a pile group supported by shaft 

resistance is illustrated in Figure 9-32. 

9.6.1 Axial Compression Capacity of Pile Groups 

9.6.1.1 Cohesionless Soils 

In cohesionless soils, the ultimate group capacity of driven piles with a center to center spacing 

of less than 3 pile diameters is greater than the sum of the ultimate capacity of the individual 

piles. The greater group capacity is due to the overlap of individual soil compaction zones 

around each pile, which increases the shaft resistance due to soil densification. Piles in groups at 

center to center spacings greater than three times the average pile diameter generally act as 

individual piles. 

Design recommendations for estimating group capacity for driven piles in cohesionless soil are 

as follows: 

1. The ultimate group capacity for driven piles in cohesionless soils not underlain by a weak 

deposit may be taken as the sum of the individual ultimate pile capacities, provided jetting or 

predrilling was not used in the pile installation process. Jetting or predrilling can result in 

group efficiencies less than 1. Therefore, jetting or predrilling should be avoided whenever 

possible or controlled by detailed specifications when necessary. 

1. If a pile group founded in a firm bearing stratum of limited thickness is underlain by a weak 

deposit, then the ultimate group capacity is the smaller value of either the sum of the ultimate 

capacities of the individual piles, or the group capacity against block failure of an equivalent 

pier, consisting of the pile group and enclosed soil mass punching through the firm stratum 

into the underlying weak soil. From a practical standpoint, block failure in cohesionless soils 

can only occur when the center to center spacing of the piles is less than 2 pile diameters, 

which is less than the minimum center to center spacing of 2.5 diameters allowed by the 

AASHTO code (2002). The method shown for cohesive soils presented in the Section 9.6.1.3 

may be used to evaluate the possibility of a block failure. 

3. Piles in groups should not be installed at center to center spacings less than 3 times the 

average pile diameter. A minimum center to center spacing of 3 diameters is recommended to 

optimize group capacity and minimize installation problems. 

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9.6.1.2 Cohesive Soils 

In the absence of negative shaft resistance, the group capacity in cohesive soil is usually 

governed by the sum of the ultimate capacities of the individual piles, with some reduction due 

to overlapping zones of shear deformation in the surrounding soil. Negative shaft resistance is 

described in Section 9.8 and often occurs when soil settlement transfers load to the pile. The 

AASHTO (2002) code states that the group capacity is influenced by whether or not the pile cap 

is in firm contact with the ground. If the pile cap is in firm contact with the ground, the soil 

between the piles and the pile group act as a unit. 

The following design recommendations are for estimating ultimate pile group capacity in 

cohesive soils. The lesser of the ultimate pile group capacity, calculated from Steps 1 to 4, 

should be used. 

1. For pile groups driven in clays with undrained shear strengths of less than 2 ksf (95 kPa) and 

for the pile cap not in firm contact with the ground, a group efficiency of 0.7 should be used 

for center to center pile spacings of 3 times the average pile diameter. If the center to center 

pile spacing is greater than 6 times the average pile diameter, then a group efficiency of 1.0 

may be used. Linear interpolation should be used for intermediate center to center pile 

spacings. 

2. For pile groups driven in clays with undrained shear strengths less than 2 ksf (95 kPa) and for 

the pile cap in firm contact with the ground, a group efficiency of 1.0 may be used. 

3. For pile groups driven in clays with undrained shear strength in excess of 2 ksf (95 kPa), a 

group efficiency of 1.0 may be used regardless of the pile cap - ground contact. 

4. Calculate the ultimate pile group capacity against block failure by using the procedure 

described in Section 9.6.1.3. 

5. Piles in groups should not be installed at center to center spacings less than 3 times the 

average pile diameter and not less than 3 ft (1 m). 

It is important to note that the driving of pile groups in cohesive soils can generate large excess 

pore water pressures. The excess pore water pressures can result in short term group efficiencies 

on the order of 0.4 to 0.8 for 1 to 2 months after installation. As these excess pore water 

pressures dissipate, the pile group efficiency will increase. Figure 9-33 presents observations on 

the dissipation of excess pore water pressure versus time for pile groups driven in cohesive soils. 

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Depending upon the group size, the excess pore water pressures typically dissipate within 1 to 2 

months after driving. However, in very large groups, full excess pore water pressure dissipation 

may take up to a year. 

If a pile group will experience the full group load shortly after construction, the foundation 

designer must evaluate the reduced group capacity that may be available for load support. In 

these cases, piezometers should be installed to monitor pore pressure dissipation with time. 

Effective stress capacity calculations can then be used to determine if the increase in pile group 

capacity versus time during construction meets the load support requirements. 

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Figure 9-33. Measured dissipation of excess pore water pressure in soil surrounding full 

scale pile groups (after O’Neill, 1983). 
 

 

 

9.6.1.3 Block Failure of Pile Groups 

Block failure of pile groups is generally a design consideration only for pile groups in soft 

cohesive soils or in cohesionless soils underlain by a weak cohesive layer. For a pile group in 

cohesive soil as shown in Figure 9-34, the ultimate capacity of the pile group against a block 

failure is provided by the following expression: 

Qug = 2D (B + Z) cu1 + B Z cu2 Nc 9-18

where: Qug = ultimate group capacity against block failure 

D = embedded length of piles 

B = width of pile group 

Z = length of pile group 

cu1 = weighted average of the undrained shear strength over the depth of pile 

embedment for the cohesive soils along the pile group perimeter 

cu2 = average undrained shear strength of the cohesive soils at the base of the pile 

group to a depth of 2B below pile toe level 

Nc = bearing capacity factor 

Figure 9-34. Three dimensional pile group configuration (after Tomlinson, 1994). 

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If a pile group will experience the full group load shortly after construction, the ultimate group 

capacity against block failure should be calculated by using the remolded or a reduced shear 

strength rather than the average undrained shear strength for cu1. 

The bearing capacity factor, Nc, for a rectangular pile group is generally 9. However, for pile 

groups with relatively small pile embedment depths and/or relatively large widths, Nc should be 

calculated from the following equation where the terms D, B and Z are as shown in Figure 9-34. 

= 5 1 + ⎛

⎜

⎝

D ⎛

⎜

⎝

⎞

⎟

⎠

B ⎞

⎟

⎠ Nc 1 +
 ≤ 9 9-19

5 B
 5Z
 

In the evaluation of possible block failure of pile groups in cohesionless soils underlain by a 

weak cohesive deposit, the weighted average unit shaft resistance for the cohesionless soils 

should be substituted for cu1 in calculating the ultimate group capacity. The pile group base 

strength determined from the second part of the ultimate group capacity equation should be 

calculated by using the strength of the underlying weaker layer. 

9.6.2 Settlement of Pile Groups 

Pile groups supported in and underlain by cohesionless soils will produce only elastic or 

immeidate settlements. This means that the settlements will occur almost immediately as the 

pile group is loaded. Pile groups supported in and underlain by cohesive soils may produce both 

elastic settlements that will occur almost immediately and consolidation settlements that will 

occur over a period of time. In highly over-consolidated clays, the majority of the foundation 

settlement will occur almost immediately. Consolidation settlements will generally be the major 

source of foundation settlement in normally consolidated clays. 

Methods for estimating settlement of pile groups are provided in the following sections. 

Methods for estimating single pile settlements are not provided in this document because piles 

are usually installed in groups. 

9.6.2.1 Elastic Compression of Piles 

The methods for computing pile group settlement discussed in the following sections consider 

soil settlements only and do not include the settlement caused by elastic compression of pile 

material due to the imposed axial load. Therefore, the elastic compression should also be 

computed and added to the group settlement estimates of soil settlement to obtain the total 

settlement. The elastic compression can be computed by the following expression: 

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Q L

∆ = a	 9-20 

A E 

 

 

 

 

 

where: ∆ = elastic compression of pile material in inches (mm)

 Qa = design axial load in pile in kips (kN) 

L = length of pile in inches (mm)

 A = pile cross sectional area in in2

 (mm2) 

E = modulus of elasticity of pile material in ksi (kPa) 

The modulus of elasticity for steel piles is 30,000 ksi (207,000 MPa). For concrete piles, the 

modulus of elasticity varies with concrete compressive strength and is generally on the order of 

4,000 psi (27,800 MPa). The elastic compression of short piles is relatively small and can often 

be neglected in design. 

9.6.2.2 Settlement of Pile Groups in Cohesionless Soils 

Meyerhof (1976) recommended the settlement of a pile group in a homogeneous sand deposit not 

underlain by a compressible soil be conservatively estimated by the following expressions in 

U.S. units: 

 

4 p 8 p B I f B If For silty sand, use: s = f f	 9-21 s = 

N' N'

where: s = estimated total settlement in inches 

pf = design foundation pressure in ksf = group design load divided by group area 

B = width of pile group in ft 

N' = average corrected SPT N160 value within a depth B below pile toe 

If = influence factor for group embedment = 1- [ D / 8 B ] ≥ 0.5 

D = pile embedment depth in ft 

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9.6.2.3 Settlement of Pile Groups in Cohesive Soils 

Terzaghi and Peck (1967) proposed that pile group settlements could be evaluated using an 

equivalent footing situated at a depth of D/3 above the pile toe. This concept is illustrated in 

Figure 9-35. For a pile group consisting of only vertical piles, the equivalent footing has a plan 

area (B)(Z) that corresponds to the perimeter dimensions of the pile group as shown in Figure 9­

34. The pile group load over this plan area is then the bearing pressure transferred to the soil 

through the equivalent footing. The load is assumed to spread within the frustum of a pyramid of 

side slopes at 30o and to cause uniform additional vertical pressure at lower levels. The pressure 

at any level is equal to the load carried by the group divided by the plan area of the base of the 

frustum at that level. Once the equivalent footing dimensions have been established then the 

settlement of the pile group can be estimated by using the procedures described in Chapter 8 

(Shallow Foundations). 

Rather than fixing the equivalent footing at a depth of D/3 above the pile toe for all soil 

conditions, the depth of the equivalent footing should be adjusted based upon soil stratigraphy 

and load transfer mechanism to the soil. Figure 9-36 presents the recommended location of the 

equivalent footing for the following load transfer and soil resistance conditions: 

a) toe bearing piles in hard clay or sand underlain by soft clay 

b) piles supported by shaft resistance in clay 

c) piles supported in shaft resistance in sand underlain by clay 

d) piles supported by shaft and toe resistance in layered soil profile 

Note that Figures 9-35 and 9-36 assume that the pile group consists only of vertical piles. If a 

group of piles contains battered piles, then they should be included in the determination of the 

equivalent footing width only if the stress zones from the battered piles overlap with those from 

the vertical piles. 

9.7 DESIGN OF PILES FOR LATERAL LOAD 

The interaction of a pile-soil system subjected to lateral load has long been recognized as a 

complex function of nonlinear response characteristics of both pile and soil. The theory and 

design method for analyzing laterally loaded piles is beyond the scope of this document. 

Guidance on lateral load analysis is provided in FHWA (1994). The program LPILE is 

commonly used to evaluate the behavior of single piles under lateral loads. FHWA (2006a) 

discusses the use of LPILE program for piles subjected to lateral loads. 

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Figure 9-35. Equivalent footing concept (after Duncan and Buchignani, 1976). 

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Figure 9-36. Stress distribution below equivalent footing for pile group (FHWA, 2006a). 

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9.8 DOWNDRAG OR NEGATIVE SHAFT RESISTANCE 

When piles are installed through a soil deposit undergoing consolidation, the resulting relative 

downward movement of the soil around piles induces "downdrag" forces on the piles. These 

"downdrag" force is also called negative shaft resistance. Negative shaft resistance is the reverse 

of the usual positive shaft resistance developed along the pile surface that allows the soil to 

support the applied axial load. The downdrag force increases the axial load on the pile and can 

be especially significant on long piles driven through compressible soils. Therefore, the 

potential for negative shaft resistance must be considered in pile design. Batter piles should be 

avoided in soil conditions where relatively large soil settlements are expected because of the 

additional bending forces imposed on the piles, which can result in pile deformation and damage. 

Settlement computations should be performed to determine the amount of settlement the soil 

surrounding the piles is expected to undergo after the piles are installed. The amount of relative 

settlement between soil and pile that is necessary to mobilize negative shaft resistance is about 

0.4 to 0.5 inches (10 to 12 mm). At that amount of movement, the maximum value of negative 

shaft resistance is equal to the soil-pile adhesion. The negative shaft resistance can not exceed 

this value because slip of the soil along the pile shaft occurs at this value. It is particularly 

important in the design of friction piles to determine the depth at which the pile will be 

unaffected by negative shaft resistance. Only below that depth can positive shaft resistance 

provide support to resist vertical loads. 

The most common situation where large negative shaft resistance develops occurs when fill is 

placed over a compressible layer immediately prior to, or shortly after piles are driven. This 

condition is shown in Figure 9-37(a). Negative shaft resistance can also develop whenever the 

effective overburden pressure is increased on a compressible layer through which a pile is driven 

as for example in the case of lowering of the ground water table as illustrated in Figure 9-37(b). 

NCHRP (1993) presents the following criteria for identifying when negative shaft resistance may 

occur. If any one of these criteria is met, negative shaft resistance should be considered in the 

design. The criteria are: 

1. The total settlement of the ground surface will be larger than 4 in (100 mm). 

2. The settlement of the ground surface after the piles are driven will be larger than 0.4 in 

(10 mm). 

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New

Fill

Bridge Deck

Soft Soil Consolidating

Due to Fill Weight

New 

Fill 

Bridge Deck 

Soft Soil Consolidating 

Due to Fill Weight 

Bearing Stratum 

Figure 9-37(a). Common downdrag situation due to fill weight (FHWA, 2006a). 

Soft Soil Consolidating

Due to Recent Placement

or Ground Water Lowering

Soft soil consolidation due 

to ground water lowering 

Bearing Stratum 

Figure 9-37(b). Common downdrag situation due to ground water lowering (FHWA, 

2006a). 

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3. The height of the embankment to be placed on the ground surface exceeds 6.5 ft (2 m). 

4.	 The thickness of the soft compressible layer is larger than 30 ft (10 m). 

5. The water table will be lowered by more than 13 ft (4 m). 

 6. The piles will be longer than 80 ft (25 m). 

For pile groups, the total downdrag load should not be calculated by summation of the downdrag 

load on each pile in the group. Rather, the downdrag load should be computed based on the 

perimeter surface area of the group block. 

FHWA (2006a) presents several different methods for determining negative shaft resistance. In 

situations where the negative shaft resistance on piles is relatively large such that a reduction in 

the pile design load is impractical, negative shaft resistance forces can be handled or reduced by 

using one or more of the following techniques: 

•	 Reduce soil settlement, e.g. by preloading the soil 

•	 Use lightweight fill material 

•	 Use a friction reducer such as bitumen and plastic wrap. These reducers are prone to being 

scrapped off during driving and are not considered to be reliable. 

•	 Increase allowable pile-stress 

•	 Prevent direct contact between soil and pile, e.g., pile sleeves 

The above options for reducing negative shaft resistance are discussed in FHWA (2006a). 

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9.9 CONSTRUCTION OF PILE FOUNDATIONS 

Construction control of pile operations is a much more difficult proposition than for spread 

footings. During footing placement an inspector can easily examine a prepared footing area and 

observe the concrete footing being poured to assure a quality foundation. Piles derive their 

support below ground. Direct quality control of the finished product is not possible. Therefore, 

substantial control must be maintained over the peripheral operations leading to the incorporation 

of the pile into the foundation. In general terms, control is exercised in two areas; the pile 

material, and the installation equipment. These items are interrelated since changes in one may 

affect the others. It is mandatory that pile foundation installation be considered during design to 

insure that the piles shown on the plans can be installed. This section discusses the installation 

and construction monitoring aspects of driven pile foundations. 

9.9.1 Selection of Design Safety Factor Based on Construction Control 

The topic of selection of a suitable design safety factor based on construction control was 

discussed in Section 9.4. It is reiterated that the factor of safety used should be based on the 

construction control method used for capacity verification. The factor of safety applied to the 

design load should increase with the increasing unreliability of the method used for 

determining ultimate pile capacity during construction. The recommended factors of safety 

on the design load for various construction control methods were presented in Table 9-5. The 

factor of safety for other test methods not included in Table 9-5 should be determined by the 

individual designer. 

9.9.2 Pile Driveability 

Greater pile penetration depths are increasingly being required to satisfy performance criteria in 

special design events such as scour, vessel impact, ice and debris loading, and seismic events. 

Therefore, the ability of a pile to be driven to the required depth has become increasingly more 

important and must be evaluated in the design stage. Pile driveability refers to the ability of a 

pile to be driven to a desired depth and/or capacity. All of the previously described static 

analysis methods are meaningless if the pile cannot be driven to the required design depth 

without sustaining damage. The limit of pile driveability is the maximum soil resistance a 

pile can be driven either without sustaining damage or a refusal driving resistance with a 

properly sized driving system. 

Primary factors controlling the ultimate geotechnical capacity of a pile are the pile details (type 

and length), subsurface data, and the method of installation. Table 9-9 highlights these factors 

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and the items to be included in the plans and specifications that are the design engineer's 

responsibility. Also included in Table 9-9 are the items to be checked for quality assurance that 

are the construction engineer's responsibility. Since the pile type, length and method of 

installation can be specified, it is often erroneously assumed that the pile can be installed as 

designed to the estimated depth. However, the pile must have sufficient driveability to overcome 

the soil resistance encountered during driving in order to reach the estimated or specified depth. 

If a pile section does not have a driveability limit in excess of the soil resistance to be overcome 

during driving, it will not be driveable to the desired depth. The failure to evaluate pile 

driveability is one of the most common deficiencies in driven pile design practice. 

In evaluating the driveability of a pile, the soil disturbance during installation and the time 

dependent soil strength changes should be considered. Both soil setup and relaxation have been 

described earlier in this chapter. For economical pile design, the foundation designer must match 

the soil resistance to be overcome at the time of driving with the pile impedance, the pile 

material strength, and the pile driving equipment. These factors are discussed in the following 

section. 

9.9.2.1 Factors Affecting Driveability 

A pile must satisfy two aspects of driveability. First, the pile must have sufficient stiffness to 

transmit driving forces large enough to overcome soil resistance. Second, the pile must have 

sufficient structural strength to withstand the driving forces without damage. 

The primary controlling factor on pile driveability is the pile impedance, which is defined as 

EA/C, where E is the elastic modulus of pile material, A is the cross-sectional area of the pile 

and C is the wave propagation velocity of pile material. Since E and C are constant for a given 

type of pile, only increasing the pile cross sectional area, A, will improve the pile driveability. 

For steel H-piles, the designer can improve pile driveability by increasing the H-pile section 

without increasing the H-pile size. The driveability of steel pipe piles can be improved by 

increasing the pipe wall thickness. For open ended pipe piles, an inside-fitting cutting shoe can 

improve driveability by delaying the formation of a soil plug and thereby reducing the soil 

resistance to be overcome. Most concrete piles are solid cross sections. Therefore, increasing 

the pile area to improve driveabilty is usually accompanied by an increase in the soil resistance 

to driving. 

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Table 9-9. Responsibilities of design and construction engineers 

Item Design Engineer's 

Responsibilities 

Construction Engineer's 

Responsibilities 

Pile Details Include in plans and specifications: 

a. Material and strength: concrete, 

steel, or timber. 

b. Cross section: diameter, tapered 

or straight, and wall thickness. 

c. Special coatings for corrosion or 

downdrag. 

d. Splices, toe protection, etc. 

e. Estimated pile tip elevation. 

f. Estimated pile length. 

g. Pile design load and ultimate 

capacity. 

h. Allowable driving stresses. 

Quality control testing or certification of 

materials. 

Subsurface Include in plans and specifications: Report major discrepancies in soil 

Data a. Subsurface profile. 

b. Soil resistance to be overcome to 

reach estimated length. 

c. Minimum pile penetration 

requirements. 

d. Special notes: boulders, artesian 

pressure, buried obstructions, 

time delays for embankment fills, 

etc. 

profile to the designer. 

Installation Include in plans and specifications: 

a. Method of hammer approval. 

b. Method of determining ultimate 

pile capacity. 

c. Compression, tension, and lateral 

load test requirements (as needed) 

including specification for tests 

and the method of interpretation 

of test results. 

d. Dynamic testing requirements (as 

needed). 

f. Limitations on vibrations, noise, 

and head room. 

g. Special notes: spudding, 

predrilling, jetting, set-up period, 

etc. 

a. Confirm that the hammer and driving 

system components agree with the 

contractor's approved submittal. 

b. Confirm that the hammer is 

maintained in good working order 

and the hammer and pile cushions are 

replaced regularly. 

c. Determination of the final pile length 

from driving resistance, estimated 

lengths and subsurface conditions. 

d. Pile driving stress control. 

e. Conduct pile load tests. 

f. Documentation of field operations. 

g. Ensure quality control of pile splices, 

coatings, alignment and driving 

equipment. 

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A lesser factor influencing pile driveability is the pile material strength. The influence of pile 

material strength on driveability is limited, since strength does not alter the pile impedance. 

However, a pile with a higher pile material strength can tolerate higher driving stresses that may 

allow a larger pile hammer to be used. Use of larger hammer may allow a slightly higher 

capacity to be obtained before driving refusal or pile damage occurs. 

Other factors that may affect pile driveability include the characteristics of the driving system 

such as ram weight, stroke, and speed, as well as the actual system performance in the field. The 

dynamic soil response can also affect pile driveability. Soils may have higher damping 

characteristics or elasticity than assumed, both of which can reduce pile driveability. These 

factors are discussed in Section 9.9.3 and 9.9.6. 

Even if the pile structural capacity and geotechnical capacity both indicate a high pile capacity 

could be used, a high pile capacity may still not be obtainable because driving stresses may 

exceed allowable driving stress limits. A pile cannot be driven to an ultimate static capacity that 

is as high as the structural capacity of the pile because of the additional dynamic resistance or 

damping forces generated during pile driving. The allowable static design stresses in pile 

materials specified by various codes generally represent the static stress levels that can be 

consistently developed with normal pile driving equipment and methods. Maximum allowable 

design and driving stresses are presented in Section 9.9.7. 

9.9.2.2 Driveability Versus Pile Type 

Driveability should be checked during the design stage of all driven piles. It is particularly 

important for closed end steel pipe piles where the impedance of the steel casing may limit pile 

driveability. Although the designer may attempt to specify a thin-wall pipe without mandrel in 

order to save material cost, a thin wall pile may lack the driveability to develop the required 

ultimate capacity or to achieve the necessary pile penetration depth. Wave equation analyses 

should be performed in the design stage to select the pile section and wall thickness. 

Steel H-piles and open-end pipe piles, prestressed concrete piles, and timber piles are also 

subject to driveability limitations. This is particularly true as allowable design stresses increase 

and as special design events such as scour require increased pile penetration depths. The 

driveability of long prestressed concrete piles can be limited by the pile's tensile strength. 

The following sections discuss the various aspects related to pile driveability. First, the pile 

driving equipment and operation (Section 9.9.3) is introduced followed by the fundamental pile 

driving formula (Section 9.9.4), basics of the dynamic analysis of pile driving (Section 9.9.5), 

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use of wave equation methodology to perform dynamic analysis of pile driving (Section 9.9.6), 

discussion of driving stresses (Section 9.9.7), and some useful guidelines to assess the results of 

wave equation analysis in terms of pile driveability (Section 9.9.8). General pile construction 

monitoring considerations are discussed in Section 9.9.10 followed by a brief description of the 

elements of dynamic pile monitoring in Section 9.9.11. 

9.9.3 Pile Driving Equipment and Operation 

Proper inspection of pile driving operations requires that the inspector have a basic 

understanding of pile driving equipment. Estimation of "as driven pile capacity" is usually based 

on the number of hammer blows needed to advance the pile a given distance. Each hammer 

blow transmits a given amount of energy to the pile. The total number of blows is the total 

energy required to move the pile a given distance. This energy can then be related to soil 

resistance and supporting capacity. However, pile inspection entails more than counting blows 

of the hammer. 

The energy transmitted to the pile by a given hammer can vary greatly depending on the 

equipment used by the contractor. Energy losses can occur by poor alignment of the driving 

system, improper or excessive cushion material, improper appurtenances, or a host of other 

reasons. As the energy losses increase, additional blows are required to move the pile. The 

manufacturer's rated hammer energy is based on minimal energy losses. Assumptions that the 

hammer is delivering its rated energy to the pile can prove dangerous if substantial energy is lost 

in the driving system. Artificially high blow counts can result in acceptance of driven pile 

lengths, which are shorter than that necessary for the required pile capacity. 

Important elements of the driving system include the leads, the hammer cushion, the helmet, 

and for concrete piles, the pile cushion. Typical components of a pile driving system are shown 

in Figure 9-38. The leads are used to align the hammer and the pile such that every hammer 

blow is delivered concentrically to the pile system. The helmet holds the top of the pile in proper 

alignment and prevents rotation of the pile during driving. Typical components of a helmet are 

shown in Figure 9-39. The hammer and the helmet “ride” in the leads so that hammer - pile 

alignment is assured. 

All impact pile driving equipment, except some gravity hammers should be equipped with a 

suitable thickness of hammer cushion material. The function of the hammer cushion is to 

prevent damage to the hammer or pile and insure uniform energy delivery per blow to the pile. 

Hammer cushions must be made of durable manufactured materials provided in accordance with 

the hammer manufacturer's guidelines. All wood, wire rope and asbestos hammer cushions are 

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specifically disallowed and should not be used. The thicker the hammer cushion, the less the 

amount of energy transferred to the pile. Mandatory use of a durable hammer cushion material, 

which will retain uniform properties during driving, is necessary to relate blow count to pile 

capacity accurately. Non-durable materials, which deteriorate during driving, cause erratic 

energy delivery to the pile and prevent the use of blow counts to determine pile capacity. 

Figure 9-38. Typical components of a pile driving system. 

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Note: The helmet shown is for nomenclature only. Various sizes and types are available to drive H, pipe, 

concrete (shown) and timber piles. A system of inserts or adapters is utilized up inside of the helmet to 

change from size to size and shape to shape. 

Figure 9-39. Typical components of a helmet. 

The heads of concrete piles must be protected by a pile cushion made of hardwood or plywood. 

The minimum thickness of pile cushion placed on the pile head should not be less than four 

inches. A new pile cushion should be provided for each pile. 

A non-routine element called a follower may be used in the driving system, particularly for piles 

driven below water. Followers cause substantial and erratic reduction in the hammer energy 

transmitted to the pile due to the follower is flexibility, poor connection to the pile head, frequent 

misalignment, etc. Reliable correlation of blow count with pile capacity is impossible when 

followers are used. Special monitoring with devices such as the Pile Driving Analyzer (PDA) 

(FHWA, 2006a) should be specified when followers are used. 

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9.9.4 Dynamic Pile Driving Formulae 

In the 1800s, the fundamental pile driving formula was established to relate dynamic driving 

forces to available pile bearing capacity. The formula was based on a simple energy balance 

between the kinetic energy of the ram at impact and the resulting work done on the soil, i.e., a 

distance of pile penetration against a soil resistance. The concept assumed a pure Newtonian 

impact with no energy loss. The fundamental formula was expressed as follows: 

WORK DONE ON SOIL = KINETIC ENERGY INPUT 

where: W = weight of the ram in pounds 

H = distance of ram fall in feet 

R = total soil resistance against the pile (driving capacity) in pounds 

S = pile penetration per blow (set) in inches 

En = driving energy (ft-lbs), which is converted to in-lbs for unit consistency by 

multiplying by 12. 

An inherent difficulty in the pile driving operation is that only a portion of the ram's kinetic 

energy actually causes penetration of the pile. Studies indicate that typically only 30 to 65 

percent of the rated energy is passed through to the pile. Much of the energy is lost in either heat 

(soil friction, hammer mechanism, pile material, etc.) or strain (elastic compression of the 

cushion, the pile and the surrounding soil). For example, if the elastic shortening of the pile (∆L) 

is RL/AE, where L = the effective length of the pile in inches, A = the cross sectional area of the 

pile in in2

, and E = modulus of elasticity of the pile material in lbs/in2, then the average 

shortening along the length of the pile would be ∆L/2 and the energy lost due to elastic 

compression of the pile would be R(∆L/2) or R2

L/2AE. Therefore, if all losses are ignored 

except those due to elastic compression of the pile, then Equation 9-22 can be re-written as: 

RS = WH = 12 En 9-22

2 R L RS =12 E − 9-23a n 2AE 

If the pile is driven through reasonably uniform soil the effective length, L, is the full length of 

pile penetration. If the pile is driven through relatively firm soil into a weaker substratum, the 

effective length is generally taken as the length from the head of the pile to the depth of the weak 

substratum. 

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If k is defined as RL/2AE then Equation 9-23a can be re-written as: 

RS = 12 En - Rk 9-23b 

When Equation 9-23b is solved for total soil resistance (R) the result is the Engineering News 

pile driving formula: 

12 En R = 9-24 S + k 

The Engineering News (EN) pile driving formula was first published in the Engineering News in 

the year 1888. The EN formula is commonly, but incorrectly termed the ENR formula since the 

publishers of the Engineering News merged with the McGraw-Hill Publishing Company in 1917 

to produce the Engineering News-Record. The EN formula was developed for wood piles driven 

by a drop hammer. As expressed by Equation 9-24, the EN formula is for driving resistance. 

Subsequently, in an attempt to develop a relationship between driving resistance and bearing 

capacity, the equation was modified to provide the safe load that a pile could withstand to the 

input energy and set per blow. The basic assumption in the modification of the original EN 

formula is that the safe working load (P) is one-sixth of the driving resistance. Therefore, the 

basic EN formula as we know it today is: 

R 2E

P = = n 9-25 

6 S + k 

 

 

 

where: En = driving energy (ft-lbs). 

S = pile penetration per blow (set) in inches. 

k = constant based on hammer type = 0.1 for single acting steam hammer 

and 1 for drop hammer. 

According to Hough (1957), the basic assumption that the safe working load (P) is one-sixth of 

the driving resistance is not the same as applying a factor of safety of 6 to the ultimate bearing 

capacity under static load. The real factor of safety for the EN formula may be considerably 

more or even less than 6 under certain conditions 

Most engineers are not aware (1) that the EN formula was originally developed for timber piles, 

or (2) that the EN formula has a built-in factor of safety of 6. Sowers (1979) states the following 

about the EN formula: 

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"The EN formula was derived from observations of the driving of wood piles in sand 

with free-falling drop hammers. Numerous pile load tests show that the real factor of 

safety of the formula can be as low as 2/3 and as high as 20. For wood piles driven 

with free-falling drop hammers and for lightly loaded short piles driven with a steam 

hammer, the EN formulas give a crude indication of pile capacity. For other 

conditions they can be very misleading." 

In 1988 the Washington State DOT published a study (WSDOT, 1988) based on high quality pile 

load test data that showed the EN formula to be the least reliable of the 10 dynamic formulae that 

were analyzed. Subsequent studies by FHWA as part of the Demonstration Project 66 (precursor 

of the FHWA (2006a) manual) confirmed the unreliability of the EN formula, particularly for 

higher pile loads where actual safety factors are too frequently less than 1.0. 

The WSDOT and FHWA studies resulted in both organizations replacing EN in their 

specifications with the Gates dynamic formula. However, the Gates dynamic formula, which 

was originally developed based on correlations with static load test data, is usually restricted to 

piles that have driving capacities less than 600 kips. The Gates formula, was modified by 

FHWA for driving capacity as shown below: 

R u =1.75 Er l og10 (10N b ) -100	 9-26a 

where: Ru = the ultimate pile capacity (kips) 

Er = the manufacturer's rated hammer energy (ft-lbs) at the field observed 

ram stroke

 Nb = the number of hammer blows per 1 inch at final penetration 

The number of hammer blows per foot of pile penetration required to obtain the ultimate pile 

capacity is calculated as follows: 

 N/ft = 12 (10x

) 

9-26b 

 

 

where: x = [(Ru + 100)/(1.75 E r )] -1 

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9.9.5 Dynamic Analysis of Pile Driving 

An examination of the pile driving process discloses that the concept of a Newtonian impact 

does not apply. When viewed in slow motion, the ram does not immediately rebound from the 

pile after impact. The ram transfers force to the pile head over a finite period of time that 

depends on the properties of the hammer-pile-soil system. A force pulse is created that travels 

down the pile in a wave shape. The amplitude of the wave will decay due to system damping 

properties before reaching the pile tip. The force in the wave, which reaches the tip, will "pull" 

the pile tip into the soil before the wave is reflected back up the pile. After reflection, an amount 

of permanent "set" of the pile tip will remain. This process is crudely shown in Figure 9-40 for 

the hammer-pile-soil system. 

Figure 9-40. Hammer-pile-soil system. 

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The analysis of the force pulse wave is commonly known as the wave equation analysis 

(WEA). In a WEA a number of variables such as pile length and flexibility are accounted for in 

addition to the variations in the contractor's driving system and the project soils. Therefore, 

WEA represents a significant improvement over dynamic formulas. The approach was 

developed by E.A.L. Smith (1960), and after the rationality of the approach had been recognized, 

several researchers developed a number of computer programs. For example, the Texas 

Department of Highways supported research at the Texas Transportation Institute (TTI) in an 

attempt to determine driving stresses and reduce concrete pile damage by using a realistic 

analysis method. FHWA sponsored the development of both the TTI program (Hirsch, et al., 

1976) and WEAP (Goble and Rausche, 1976). FHWA supported the development of WEAP to 

obtain analysis results backed by measurements taken on construction piles during installation 

for a variety of hammer models. WEAP was updated several times under FHWA sponsorship 

until 1986 (Goble and Rausche, 1986). Later, additional options, improved data files, refined 

mathematical representations and modern user conveniences were added to this program on a 

proprietary basis, and the program is now known as GRLWEAP (Pile Dynamics, Inc. 2005). 

TNOWAVE is a similar program developed in the Netherlands since 1970s and is popular in 

Europe and elsewhere. Similar computer programs based on the method of characteristics have 

been developed such as PDPWAVE (Bielefeld and Middendorp, 1992). 

The wave equation approach has been subjected to a number of checks and correlation studies. 

Studies on the performance of WEAP have produced publications demonstrating that program's 

performance and utility (e.g., Blendy 1979, Soares, et al. 1984, Rausche, et al., 2004). In the 

WEA approach, it is recognized that each element in the hammer-pile-soil system affects the pile 

penetration and stresses caused in the pile. A few characteristics of each element are discussed 

below before the WEA methodology is discussed in detail. 

1. Hammer 

•	 Pile hammers can be categorized into two main types: impact hammers and vibratory 

hammers. There are numerous types of impact hammers having variations in the types 

of power source, configurations, and rated energies. 

•	 Mechanical efficiency determines what percentage of rated energy is transmitted by the 

ram. Typical values of mechanical efficiency for hammers in good condition are 50% 

for double or differential acting air hammers, 67% for single acting air/steam hammers, 

80% for diesel hammers, and 80 to 95% for hydraulic hammers. 

 

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•	 Force wave shape characteristics are different for different hammer types. The shape 

affects pile stress and pile penetration. 

2. Pile and Appurtenances (Cushions, Helmets, etc.) 

•	 The stiffness of appurtenances such as the hammer cushion is defined by the cross 

sectional area times the modulus of elasticity divided by the thickness. The stiffness has 

a major effect on both blow count and stress transfer to the pile. These elements must not 

degrade during driving as observed blow count will decrease and pile stresses increase. 

•	 As noted in Section 9.9.2.1, pile impedance affects pile driveability. The cross sectional 

area of the pile does not control pile driveability. As an example, an HP 14x117 has a 

cross-sectional area of 34.4 in2

 (0.22 m2) and an impedance of 61.4 k-s/ft (900 kN-s/m). 

A 12 in square concrete pile has a cross-sectional area of 144 in2

 (0.93 m2)and an 

impedance of 57.9 k-s/ft (845 kN-s/m). Hence, the H pile has better driveability even 

though it has approximately 25% of the cross-sectional area of the concrete pile. 

3. Soil 

•	 Soil strength may be permanently or temporarily changed during driving. Piles being 

driven into soil that contains large percentages of fines may require restrikes to estimate 

long term capacity due to effects of set-up or relaxation. 

•	 The damping properties of the soil surrounding the pile can have a dramatic effect on the 

observed blow count. An increase in damping decreases driveability. Damping 

parameters can be estimated by soil type or from basic index test data. Consideration of 

the dynamic aspects of the field pile driving operation is necessary so that the driving 

characteristics can be related to the static pile capacity. Foundation designers should 

routinely consider the potential for dynamic effects such as set-up and include provisions 

for field observations such as restrikes. In addition, construction control of pile driving 

should account for basic dynamic parameters that influence blow count and pile stress. 

Some of these parameters can be controlled by specification; others require use of a pile 

wave equation analysis. 

 

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9.9.6 Wave Equation Methodology 

The wave equation analysis (WEA) is a tool to understand the variable involved in pile driving. 

In a WEA, the hammer, helmet, and pile are modeled by a series of segments each consisting of 

a concentrated mass and a weightless spring. A schematic of the wave equation hammer-pile-soil 

model is presented in Figure 9-41. The hammer and pile segments are approximately 3 ft in 

length. Spring stiffness and mass values are calculated from the cross sectional area, modulus of 

elasticity, and specific weight of the corresponding pile section. Hammer and pile cushions are 

represented by additional springs whose stiffnesses are calculated from area, modulus of 

elasticity, and thickness of the cushion materials. In addition, coefficients of restitution (COR) 

are usually specified to model energy losses in cushion materials and in all segments that can 

separate from their neighboring segments by a certain slack distance. The COR is equal to unity 

for a perfectly elastic collision that preserves all energy and is equal to zero for a perfectly plastic 

condition that loses all deformation energy. The usual condition of partially elastic collisions is 

modeled with an intermediate COR value. 

The soil resistance along the embedded portion of the pile and at the pile toe is represented by 

both static and dynamic components. Therefore, both a static and a dynamic soil resistance force 

acts on every embedded pile segment. The static soil resistance forces are modeled by elastoplastic springs and the dynamic soil resistance by dashpots. The displacement at which the soil 

changes from elastic to plastic behavior is referred to as the soil "quake,” q. The dynamic soil 

resistance is proportional to a damping factor, J, times the pile velocity times the assigned static 

soil resistance. The parameters q and J are shown in lower left hand corner of Figure 9-41. In 

simple terms, q, is a parameter used in determination of static resistance while J is a parameter 

used in determination of dynamic resistance. 

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Figure 9-41. Typical Wave Equation models (FHWA 2006a). 

FHWA NHI-06-089 Soils and Foundations – Volume II 9 - 104 
 

9.9.6.1 Input to Wave Equation Analysis 

In a typical wave equation analysis, parameters defining the hammer, pile (plus appurtenances), 

and soil systems are needed. The confidence level that can be assigned to the output is directly 

related to how well the project-specific input parameters are known. The basic input parameters 

are discussed below. 

•	 Hammer Data: Hammer input properties are usually well known from a manufacturers’ 

database. In a driveability analysis, hammer types are selected based on the soil 

resistance to be overcome. In construction monitoring analysis the contractor submits 

the intended driving system for review and approval. If a satisfactory driving system is 

submitted and approved, then the only major concern in construction is that the hammer 

is in good working condition as was assumed for the input. 

•	 Driving System or Appurtenance Data: The driving system or appurtenance data 

consists of information on hammer cushion, helmet including striker plate, inserts, 

adapters, etc. and pile cushion in case of concrete piles. The properties of cushions, for 

both hammer and pile, are especially critical. Only manufactured materials whose 

properties remain reasonably constant during driving can be used with confidence. The 

actual cushion thickness used in the field must be checked and discrepancies reported so 

that the wave equation analysis can be modified. 

•	 Pile Data: Required pile data consists of total length, cross-sectional area, elastic 

modulus and weight, all as a function of depth. This is the pile profile. The wave 

analysis cannot predict pile length. This fact is commonly misunderstood by 

engineers. Pile length is determined by static analysis procedures and then used as input 

to pile wave analyses. One exception is a “driveability analysis” where pile behavior is 

assessed at various depths. The cross sectional area of the pile is frequently varied in 

design analyses to determine which section is both driveable and cost effective. 

Increasing the pile section has the effect of improving driveability as well as reducing 

pile stresses. 

•	 Soil Data: Soil data input requires both an understanding of site-specific soil properties 

and the effects of pile driving on those properties. Dynamic properties such as damping 

and quake are roughly correlated with soil type. These properties are best determined 

by experienced geotechnical specialist. The driving soil resistance and its distribution 

are determined from the static analysis. The driving soil resistance may be substantially 

greater than the design load times the safety factor; particularly for piles in scour 

situations. Also the dynamic effects of pile driving on soil resistance must be 

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considered by an experienced geotechnical specialist to determine set-up or relaxation 

values for ultimate soil resistance. These dynamic effects are frequently overlooked, 

which can result in large variations between estimated and actual pile lengths. 

9.9.6.2 Output Values from Wave Equation Analysis 

The results of a wave equation analysis include the predicted blow count, pile stresses, and 

delivered hammer energy for an assigned driving soil resistance, Rult, and for given hammer, 

driving system (appurtenance), pile and soil conditions. Each wave equation analysis is for the 

specific pile length that was considered in the analysis. A summary table of the results 

obtained from a wave equation analysis is shown in Table 9-10. The data shown in Table 9-10 

was generated for a specific site where a pile length of 50 ft (15 m) was being analyzed. 

Table 9-10 

Summary of example results from wave equation analysis 

Rult kips Blow Count 

BPF 

Stroke 

(EQ) ft 

Tensile 

Stress ksi 

Compressive 

Stress ksi 

Transfer Energy 

ft-kip 

35.0 7 3.27 -0.73 1.68 13.6 

80.0 16 3.27 -0.32 1.71 13.6 

140.0 30 3.27 -0.20 1.73 13.0 

160.0 35 3.27 -0.14 1.73 13.0 

195.0 49 3.27 -0.00 1.75 12.8 

225.0 63 3.27 0.0 1.96 12.7 

280.0 119 3.27 0.0 2.34 12.6 

350.0 841 3.27 0.0 2.75 12.5 

Note that for each driving resistance (Rult), a value of blow count, hammer stroke, tensile stress, 

compressive stress, and transferred energy has been computed. The data is also commonly shown 

in graphical form as noted in Figure 9-42. 

9.9.6.3 Pile Wave Equation Analysis Interpretation 

The data in Table 9-10, when plotted as shown in Figure 9-42, presents the predicted relationship 

between pile hammer blow count and other variables for the situation when the pile is embedded 

50 ft (15 m) in the ground. The plot, which relates the ultimate capacity to penetration 

resistance, is known as a bearing graph. The data in Table 9-10 is interpreted in the field by 

comparing them with the measured blow count at a pile penetration of 50 ft (15 m) as follows. 

When the pile reaches 50 ft (15 m), if the blow count is 49, the driving resistance is 195 kips 

(867 kN), the stroke is 3.27 ft (0.99 m), the tensile stress is zero ksi, the compressive stress is 

1.75 ksi (12,069 kPa), and transferred energy is 12.8 ft-kips (17.3 m-kN). If the blow count had 

been 63 the driving resistance would have been predicted to be 225 kips (1,000 kN), etc. 

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Rult 

Rult 

Stroke 

Compressive stress 

Tensile stress 

Figure 9-42. Summary of stroke, compressive stress, tensile stress, and driving capacity vs. 

blow count (blows/ft) for air-steam hammer. 

 

Note that Table 9-10 is an example for an air-steam hammer and the stroke is constant for all 

blow counts. Diesel hammers operate at different strokes depending on the pile-soil properties. 

A pile wave summary table for a diesel hammer will display a predicted combination of blow 

count and stroke that is necessary to achieve the driving capacity. In fact, there are numerous 

combinations of blow count and stroke that correspond to a particular driving resistance. These 

combinations may be computed and plotted for a selected driving resistance. A typical plot of 

diesel hammer stroke versus blow count is shown in Figure 9-43 for a constant resistance of 240 

kips (1,067 kN). 

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Compressive stress 

Tensile stress 

Stroke 

Figure 9-43. Graph of diesel hammer stroke versus blow count for a constant pile capacity. 

A wave equation bearing graph is substantially different from a similar graph 

generated from a dynamic formula. The wave equation bearing graph is associated 

with a single driving system, hammer stroke, pile type, soil profile, and a particular pile 

length. If any one of the above items is changed, the bearing graph will also change. 

9.9.7 Driving Stresses 

In almost all cases, the highest stress levels occur in a pile during driving. High driving stresses 

are necessary to cause pile penetration. The pile must be stressed to overcome the ultimate soil 

resistance, plus any dynamic resistance forces, in order to be driven to the design depth and load. 

The high strain rate and temporary nature of the loading during pile driving allow a substantially 

higher driving stress limitation than for the static design case. Wave equation analyses can be 

used for predicting driving stresses prior to installation. During installation, dynamic testing can 

be used to monitor driving stresses. 

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The stresses predicted by the wave equation analysis should be compared to safe stress levels. 

This comparison is usually performed for the tensile and compressive stress shown at the 

computed driving resistance for the estimated pile length. Table 9-11 presents a summary of 

design and driving stresses for various types of driven piles. 

9.9.8 Guidelines for Assessing Pile Driveability 

The last operation in pile design is to insure that the pile can be driven to the estimated length 

without damage. For this purpose a trial wave equation analysis is done with an appropriately 

sized hammer. Figure 9-44 can be used to choose a reasonable hammer for wave analysis. In 

general, the suggested hammer energies in Figure 9-44 are less than the optimum energy 

necessary to drive the appropriate pile cross section. Judgment should be used in selecting the 

hammer size. If initial wave equation analysis yield high blow counts and low stresses the 

hammer size should be increased. 

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 Rated Hammer Energy, ft-lbs 

Figure 9-44. Suggested trial hammer energy for wave equation analysis. 

During design, a wave equation analysis should be performed to determine if a reasonable range 

of hammer energies can drive the proposed pile section without exceeding the allowable driving 

stresses listed in Table 9-11 and a reasonable range of hammer blows, i.e., 30 to 144 bpf for 

friction piles and higher blows of short duration for end bearing piles. This concept is illustrated 

numerically by Example 9-4. 
 

 

 

 

 

 

 

 

 

 

 

 

 

Table 9-11. Maximum allowable stresses in pile for top driven piles (after AASHTO, 2002; 

FHWA, 2006a)
 

Pile Type 

Maximum Allowable Stresses 

(fy = yield stress of steel; f' c = 28-day compressive strength of concrete; fpe = pile 

prestress) 

Steel H-Piles 

Design Stress 

0.25 fy 

0.33 fy If damage is unlikely, and confirming static and/or dynamic load tests 

are performed and evaluated by engineer. 

Driving Stress 

0.9 fy 

32.4 ksi (223 MPa) for ASTM A-36 (fy = 36 ksi; 248 MPa) 

45.0 ksi (310 MPa) for ASTM A-572 or A-690, (fy = 50 ksi; 345 MPa) 

Unfilled Steel 

Pipe Piles 

Design Stress 

0.25 fy 

0.33 fy If damage is unlikely, and confirming static and/or dynamic load tests 

are performed and evaluated by engineer. 

Driving Stress 

0.9 fy 

27.0 ksi (186 MPa) for ASTM A-252, Grade 1 (fy = 30 ksi; 207 MPa) 

31.5 ksi (217 MPa) for ASTM A-252, Grade 2 (fy = 35 ksi; 241 MPa) 

40.5 ksi (279 MPa) for ASTM A-252, Grade 3 (fy = 45 ksi ; 310 MPa) 

Concrete filled 

steel pipe piles 

Design Stress 

0.25 fy (on steel area) plus 0.40 f'c (on concrete area) 

Driving Stress 

0.9 fy 

27.0 ksi (186 MPa) for ASTM A-252, Grade 1 (fy = 30 ksi; 207 MPa) 

31.5 ksi (217 MPa) for ASTM A-252, Grade 2 (fy = 35 ksi; 241 MPa) 

40.5 ksi (279 MPa) for ASTM A-252, Grade 3 (fy = 45 ksi ; 310 MPa) 

Precast 

Prestressed 

Concrete Piles 

Design Stress 

0.33 f'c - 0.27 fpe (on gross concrete area) ; f'c minimum of 5.0 ksi (34.5 MPa) 

fpe generally > 0.7 ksi (5 MPa) 

Driving Stress 

Compression Limit < 0.85 f'c - fpe (on gross concrete area) 

Tension Limit (1) < 3 (f'c )1/2 +fpe (on gross concrete area) US Units*

 < 0.25 (f' c )1/2 +fpe (on gross concrete area) SI Units * 

Tension Limit (2) < fpe (on gross concrete area) 

(1) - Normal Environments ; (2) - Severe Corrosive Environments 

*Note: f'c and fpe must be in psi and MPa for US and SI equations, respectively. 

Conventionally 

reinforced 

concrete piles 

Design Stress 

0.33 f'c (on gross concrete area) ; f'c minimum of 5.0 ksi (34.5 MPa) 

Driving Stress 

Compression Limit < 0.85 f'c ; Tension Limit < 0.70 fy (of steel reinforcement) 

Timber Pile 

Design Stress 

0.8 to 1.2 ksi (5.5 to 8.3 MPa) for pile toe area depending upon species 

Driving Stress 

Compression Limit < 3 σa 

Tension Limit < 3 σa 

σa - AASHTO allowable working stress 

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Example 9-4: Determine if the 14 inch square concrete pile can be driven to a driving capacity of 

225 kips by using the wave equation output summary provided. Assume the 

concrete compressive strength, f'c, is 4000 psi and the pile prestress, fpe, is 700 psi. 

Wave equation output summary 

Rult kips Blow Count 

BPF 

Stroke (EQ) 

ft 

Tensile Stress 

ksi 

Compressive 

Stress ksi 

Transfer 

Energy ft-kip 

35.0 7 3.27 -0.73 1.68 13.6 

80.0 16 3.27 -0.32 1.71 13.6 

140.0 30 3.27 -0.20 1.73 13.0 

160.0 35 3.27 -0.14 1.73 13.0 

195.0 49 3.27 -0.00 1.75 12.8 

225.0 63 3.27 0.0 1.96 12.7 

280.0 119 3.27 0.0 2.34 12.6 

350.0 841 3.27 0.0 2.75 12.5 

Solution: 

Acceptable driveability depends on achieving the desired driving capacity at hammer blows 

between 30 and 144 bpf without exceeding the allowable compressive and tensile driving stress. 

1. At Rult = 225 kips, blow count = 63 bpf O.K.(between 30 and 144) 

2.	 The allowable driving stresses based on Table 9-11, for prestressed precast concrete piles 

are calculated as follows: 

• Compressive stress allowed = 0.85 f'c - fpe = 0.85 (4,000 psi) – 700 psi = 2,700 psi, 

•	 Actual maximum compressive stress up to 225 kips from wave equation output 

summary is 1.96 ksi or 1,960 psi ≤ 2,700 psi allowed value. O.K. 

• Tensile stress allowed = 3 (f' )1/2 1/ c +fpe = 3 (4,000 psi) 2 + 700 psi = 890 psi 

• Actual maximum tensile stress up to 225 kips from wave equation output summary is 

0.730 ksi or 730 psi ≤ 890 psi allowed value. O.K. 

Therefore, the analyzed pile-hammer system can be approved. 

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9.9.9 Pile Construction Monitoring Considerations 

The approval of a contractor's driving equipment is an example of design and construction 

coordination. It is recommended to use the wave equation analysis to determine if the 

contractor's equipment is adequate to drive the pile to the estimated length without pile damage. 

The steps in this procedure are as follows: 

1. The pile specifications should include a statement similar to: 

"All pile driving equipment to be furnished by the contractor shall be subject to the approval 

of the engineer. Prerequisite to such approval, the contractor shall submit the following: 

a.	 A completed pile and driving equipment data form (Figure 9-45) for each hammer 

proposed for the project. 

b. A wave equation analysis performed by a professional engineer for each proposed 

hammer at least to the soil resistance value listed on the plans. 

Contractor notification of acceptance or rejection of the hammer will be made within 14 

days of receipt of the data form and wave equation analysis." 

In this case the contractor is charged with performing the wave equation analysis. In some 

cases, the owner may perform the analysis. 

2. The designer should also receive a copy of the data form and the results of wave equation 

analysis. An independent wave equation analysis should be performed to verify the 

submitted results and in some cases to establish driving criteria for the piles. The designer 

should check the results for reasonableness. For example, 30 to 144 blows per foot are 

considered reasonable for friction piles. Greater blow counts can be permitted for end 

bearing piles since the duration of high blow counts is short. Then the stresses at that blow 

count are checked to determine if the values are below the allowable driving stress of the 

pile material. If these items are satisfied, the equipment can be approved and the 

information sent to the construction engineer. The results of the wave equation analysis 

may be transmitted to the field with a recommendation to reject or approve the hammer. 

3. The procedure for the changing of approved hammers during the contract is the same. 

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Contract No.: Structure Name and/or No.: 

Project: 

Pile Driving Contractor or Subcontractor: 

County:

 (Piles driven by) 

Manufacturer: Model No.: ______________ 

Hammer Type: ____________________ Serial No.: _________________ 

Manufacturers Maximum Rated Energy:____ ___________________(Joules) (ft-k)

 Hammer Stroke at Maximum Rated Energy: ____________________________ (meters) (ft) 

Range in Operating Energy: _________________ to _____________ (Joules) (ft-k) 

Range in Operating Stroke: _________________ to ______________ (meters) (ft) 

Ram Weight: (kips) (kN) 

Modifications: _ 

Striker Weight: _______________ (kips) (kN) Diameter: _________________(in) (mm) 

Plate Thickness: _______________ (in) (mm) 

Material #1 Material #2 

(for Composite Cushion) 

Name: _______________________ Name: 

Hammer Area: _________________(in2) (cm2) Area: _____________________ (in2) (mm2) 

Cushion Thickness/Plate: ________(in) (mm) Thickness/Plate: _____________ (in) (mm) 

No. of Plates: ______________ No. of Plates: ______________________ 

Total Thickness of Hammer Cushion: ___________________________ (in) (mm) 

Helmet 

(Drive Head) Weight: including inserts (kips) (kN) 

Pile Material: __________________________________________________________ 

Cushion Area: ________________(in2) (cm2) Thickness/Sheet: ______________(in) (mm) 

No. of Sheets: _____________ 

Total Thickness of Pile Cushion: _______________ (in) (mm) 

Pile Type: _________________________________________________________ 

Wall Thickness: ______________(in) (mm) Taper: _______________________ 

Cross Sectional Area: ________ (in2) (mm2) Weight/ft (m): __________________ 

Pile 

Ordered Length: (ft) (m) 

Design Load: (kips) (kN) 

Ultimate Pile Capacity: (kips) (kN) 

 Description of Splice: 

Driving Shoe/Closure Plate Description: 

Submitted By: ____________ Date: 

Telephone No.: ___________________ Fax No.: 

Figure 9-45. Pile and driving equipment data form (after FHWA, 2006a). 

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During production operations, the engineer will check if the necessary blow count is attained at 

the estimated length shown on the pile driving information form. The resistance is generally 

acceptable if the blow count is within 10 percent of that expected, or if the expected blow count 

is achieved within 5 ft (1.5 m) of the estimated length. The construction engineer should be 

aware that blow counts greater than expected will cause an increase in pile stress. If necessary 

an upper blow count limit may need to be established to prevent damage. 

If either radically different blow counts (greater or less) than those predicted from wave equation 

analysis or damage are observed during the driving process, the foundation designer should be 

contacted immediately. The phone number of the foundation designer should be on the 

information form. 

It should be realized that pile driving is not by any means an exact science and actual blow 

counts and pile lengths may be expected to vary somewhat even in the same footing. The 

objective of construction monitoring of pile driving is to ensure that the pile is capable of 

supporting the design load safely. This means that the pile is not damaged and adequate soil 

resistance is mobilized for support. Both these items can be checked from the wave equation 

analysis output. 

The use of wave equation analysis for construction monitoring provides the engineer with a 

method to predict the behavior of the driven piles during installation. While this prediction is 

superior to previous methods of estimating driveability, the optimal method of determining pile 

driveability is to obtain dynamic measurements during pile installation. Dynamic test methods 

commonly employ accelerometers and strain gages attached to the pile during driving to measure 

real time strains and accelerations produced during the driving process. Field computers use 

these measurements to develop driving variables, which the inspector can use to: 

• Monitor hammer and driving system performance, 

• Evaluate driving stresses and pile integrity, and, 

• Verify pile capacity 

Additional details of the dynamic test procedure are discussed in the following section. 

9.9.10 Dynamic Pile Monitoring 

Dynamic test methods use measurements of strain and acceleration taken near the pile head as a 

pile is driven or restruck with a pile driving hammer. These dynamic measurements can be used 

to evaluate the performance of the pile driving system, calculate pile installation stresses, assess 

pile integrity, and estimate static pile capacity. Dynamic test results can be further evaluated by 

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using signal matching techniques to determine the relative distribution of soil resistance along 

the pile, as well as representative dynamic soil properties for use in wave equation analyses. 

This section provides a brief discussion of the equipment and methods of analysis associated 

with dynamic measurements. 

A typical dynamic monitoring system consists of a minimum of two strain transducers and two 

accelerometers bolted to diametrically opposite sides of the pile to monitor strain and 

acceleration and account for nonuniform hammer impacts and pile bending. Because of 

nonuniform impacts and bending, the use of two diametrically opposite mounted strain 

transducers is essential for a valid test. The reusable strain transducers and accelerometers are 

generally attached two to three diameters below the pile head. Almost any driven pile type 

(concrete, steel pipe, H, Monotube, timber, etc.) can be tested with the pile preparation for each 

pile type varying slightly. 

As the pile is struck by a pile hammer, the strains and accelerations detected by the 

corresponding gages on the pile are converted into forces and velocities. Typical force and 

velocity traces generated during dynamic measurements are shown in Figure 9-46. These traces 

are processed to obtain an estimate of the static pile capacity at the time of testing and for pile 

design. The additional information obtained and displayed includes compressive and tensile 

stresses in the pile, transferred energy to the pile, and the force and velocity at the top of the pile 

throughout the duration of the hammer impact. An experienced operator can use this data to 

evaluate the performance of the pile driving system and the condition of the pile. The results of 

the dynamic monitoring are enhanced by the post-testing evaluation in which signal matching is 

used with computer analysis to verify the correctness of assumed dynamic inputs including 

damping, quake and load transfer distribution. 

ASTM D 4945 contains a detailed description of the equipment requirements and test procedure 

for dynamic pile load testing. 

9.9.10.1 Applications 

Dynamic pile monitoring costs much less and requires less time than static pile load testing. 

Important information can be obtained regarding the behavior of both the pile-soil system and 

the pile driving system that is not available from a static pile load test. Determination of driving 

stresses and pile integrity with dynamic test methods has facilitated the use of fewer, higher 

capacity piles in foundations through better pile installation control Some of the applications of 

dynamic pile testing are discussed below (FHWA, 2006a). 

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Figure 9-46. Typical force and velocity traces generated during dynamic measurements. 

• Static Pile Capacity

 a. Evaluation of static pile capacity at the time of testing. Soil setup or relaxation 

potential can be also assessed by restriking several piles and comparing restrike 

capacities with end-of-initial driving capacities. 

b. Assessments of static pile capacity versus pile penetration depth can be obtained by 

testing from the start to the end of driving. This can be helpful in profiling the depth to 

the bearing stratum and thus the required pile lengths. 

 

c. Signal matching computer analysis can provide refined estimates of static capacity, 

assessment of soil resistance distribution, and soil quake and damping parameters for 

input into a wave equation analysis. 

• Hammer and Driving System Performance 

a. Calculation of energy transferred to the pile for comparison with the manufacturer's 

rated energy and wave equation predictions which indicate hammer and drive system 

performance. Energy transfer can also be used to determine effects of changes in 

hammer cushion or pile cushion materials on pile driving resistance. 

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b. Determination of drive system performance under different operating pressures, strokes, 

or changes in hammer maintenance by comparative testing of hammers, or of a single 

hammer over an extended period of use. 

c. Identification of hammer performance problems, such as preignition problems with 

diesel hammers or preadmission problems in air/steam hammers. 

d. Determination of whether soil behavior or hammer performance is responsible for 

changes in observed driving resistances. 

•	 Driving Stresses and Pile Integrity

 a. Calculation of compression and tension driving stresses. In cases with driving stress 

problems, this information can be helpful when evaluating adjustments to pile 

installation procedures are being evaluated. Calculated stresses can also be compared 

to specified driving stress limits. 

b.	 Determination of the extent and location of pile structural damage. With dynamic pile 

monitoring costly extraction may not be necessary to confirm or quantify damage 

suspected from driving records. 

c.	 Stress distribution throughout pile by using signal matching computer analysis. 

9.9.10.2 Interpretation of Results and Correlation with Static Pile Load Tests 

The results of dynamic pile monitoring should be interpreted by an experienced geotechnical 

specialist who has had the opportunity to observe and evaluate the results from many 

dynamically test piles and can detect the signs, not always readily apparent, of unusual soil-pile 

response, pile damage, erratic hammer operation or testing equipment malfunction. It is 

important that the geotechnical specialist performing the evaluation should have attained an 

appropriate level of expertise through qualifying examinations by providers of dynamic testing 

services. 

Interpretation of the results of dynamic pile measurements also requires an awareness of the 

differences in behavior of dynamically and statically loaded piles. Improper correlations of 

dynamic and static pile loads test may be caused by the following: 

•	 Incorrectly assumed soil damping, quake and load transfer parameters. This source of 

discrepancy can be minimized by performing a post-test computerized analysis to match 

 

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measured and computed relationships between force and velocity to determine the most 

appropriate parameters. 

•	 Time-related changes in pile capacity. Depending on soil type and pile characteristics, the 

capacity of a pile may increase or, less commonly, decrease with time. The principal causes 

are time-related changes of pore water pressure in cohesive soils and stress relaxation in 

cohesionless soils. The effects can be assessed by “restriking” the pile at various time 

intervals after driving and comparing the observed “restrike” capacity to the driving capacity 

obtained during the initial drive. The pile capacity should be determined during the first few 

“good” hammer blows during re-strike. When comparing the results of dynamic testing 

against those of a static pile load test, at least one dynamic test should be performed after 

completion of static testing. 

•	 Inadequate pile tip displacement. Pile tip displacement during dynamic testing may be 

inadequate to mobilize full end bearing. Frictional resistance between a pile and the 

surrounding soil is mobilized at a fraction of the pile movement necessary to mobilize full 

end bearing resistance. A penetration resistance of 10 blows/inch (10 blows/25.4 mm) or 

higher, may produce insufficient strain in the soil to mobilize full end resistance. This results 

in an underestimate of the end bearing capacity. For many types of piles, the estimate can be 

improved by performing a force-velocity match both for the initial drive and for the restrike 

data. The tip capacity derived from the initial drive is combined with skin resistance from 

the restrike to obtain the total pile capacity. However, this method may not be applicable for 

open-ended pipe, H-piles, and precast cylinder piles. In the case of these types of piles, only 

the structural area of the pile can mobilize the toe bearing during installation. This value of 

toe bearing may be significantly less than the value that may be experienced in the static load 

test, since the soil in the static load test will adhere to the pile with time and create a plug. 

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9.10 CAST-IN-PLACE (CIP) PILES 

There are a variety of cast-in-place (CIP) piles as shown in Figure 9-2. In contrast to the driven 

piles wherein piles manufactured in a factory are driven in the ground, in the case of CIP piles, 

the load resisting element is constructed in a pre-drilled hole. The load resisting element is often 

a combination of steel and CIP concrete. As shown previously in Figure 9-2, there are a variety 

of CIP piles, e.g., drilled shafts, micropiles, auger cast piles, etc. 

The design and construction process for CIP piles is shown in Figure 9-47. This process is 

similar to that for driven piles shown in Figure 9-3 for Blocks 1 to 18. It is in the construction 

phase where there are major differences between the driven piles and CIP piles. Blocks 19 to 24 

are briefly discussed below: 

Block 19: Review Contractor’s Installation Procedures 

The potential that the CIP piles will perform as designed is heavily dependent on the techniques 

employed by the contractor during construction. For example, soil excavation technique will not 

be suitable for excavation in IGMs or rocks. The contractor should be required to submit a 

detailed CIP pile construction procedure that will be reviewed by the geotechnical engineer. 

Block 20: Set Preliminary Installation Criteria 

Based on the evaluation of the contractor’s proposed installation procedures with respect to 

project installation criteria and any other requirements in the design and specifications, the 

preliminary approval of the contractor’s equipment and procedures can be given. If the 

contractor’s installation procedures are not acceptable, then the process returns to Block 19. 

Block 21: Install Test Piles and Evaluate Constructability 

Usually, the first CIP pile on a project is considered to be a “test” pile wherein the contractor’s 

proposed equipment and installation procedures are evaluated in the field. Often, where prior 

experience is not available, the first pile is required to be installed as a sacrificial pile at a 

location away from the footprint of the production piles. The constructability evaluation of the 

test pile is critical. Non-destructive (integrity) tests are recommended at this stage to evaluate 

the quality of the constructed product. 

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Establish global project 

performance requirements 

1 

Define project 

geotechnical site conditions 

2 

Determine preliminary 

substructure loads and load 

combinations at foundation level 

3 

Develop and execute subsurface 

exploration and laboratory 

testing program for feasible 

foundation systems 

4 

Evaluate information and 

determine foundation systems for 

further evaluation 

5 

Deep Foundations 6 Shallow Foundations 

(See Chapter 8) 

Select alternate CIP pile 

foundations types and sections for 

further evaluation 

7 Driven Piles 

(See Section 9.2) See Figure 

9-3 

Continued on Next Page 

Design Phase 

See Figure 

8-10 

Figure 9-47. Cast-in-Place (CIP) pile design and construction process (modified after FHWA 

2006a). 

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Soils and Foundations – Volume II 9 - 120 December 2006
 
 

 

 

Select static analysis method 

and calculate ultimate axial 

capacity vs depth 

8 

Identify most economical 

CIP pile types from plots of 

ultimate capacity vs depth and 

cost per ton (MN) vs depth 

Size and estimate cost of 

CIP pile cap for trial groups 

Continued on Next Page 

9 

Constructability evaluation of 

CIP pile types to target depth(s) 

10 

Select 1 or 2 CIP pile types, 

for trial pile group sizing 

11 

Evaluate group axial, lateral, 

and rotational capacities, 

settlement, and performance of trial 

CIP Pile Group Configurations 

12 

13 

Summarize total cost of CIP 

pile types, group 

configurations and pile caps 

14 

Select and optimize final pile 

type, ultimate capacity group 

configuration, and construction 

control method 

15 

Figure 9-47 (Continued). Cast-in-Place (CIP) pile design and construction process (modified after 

FHWA 2006a). 

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Does optimized design meet 

performance and 

constructability requirements? 

Prepare plans and 

specifications 

Adjust construction 

procedures or design 

17 

Review contractor’s CIP pile 

installation procedures. Accept 

or Reject 

19 

Yes 

22 

Construction control. 

Install production piles, perform 

integrity tests and resolve 

any construction problems 

23 

Post-construction. 

Evaluation and refinement 

for future designs 

24 

16 

Return to 

Block 11 

No 

Construction Phase 

20 Set preliminary installation 

criteria based on contractor’s 

approved installation plan 

18 Contractor 

selected 

21 

Observe construction of test 

CIP pile(s), perform integrity 

tests and evaluate 

constructablity 

Figure 9-47 (Continued). Cast-in-Place (CIP) pile design and construction process (modified after 

FHWA 2006a).
 

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Block 22: Adjust Construction Procedures 

In this step, an adjustment in the contractor’s construction procedures may be required prior to 

construction of the production piles. If significant adjustments are necessary, then another test 

pile may be warranted. 

Block 23: Construction Control 

After the test CIP pile has been successfully constructed, the same construction procedures are 

applied for the production piles unless different subsurface conditions are encountered that may 

warrant alternative construction techniques. In this case another test pile may be required. 

Quality control and assurance procedures including integrity tests are implemented as discussed 

in Section 9.14. Problems may arise and must be handled in a timely fashion as they occur. 

Block 24: Post-Construction Evaluation and Refinement of Design 

After completion of the foundation construction, the project should be reviewed and evaluated 

for its effectiveness in satisfying the project requirements and also its cost effectiveness. The 

evaluation should be performed from the viewpoint of refining the construction and design 

procedures as appropriate for future projects. 

9.11 DRILLED SHAFTS 

A drilled shaft is a form of cast-in-place (CIP) pile. A drilled shaft is a machine- and/or handexcavated shaft in soil or rock that is filled with concrete and reinforcing steel, with the primary 

purpose of providing structural support. A drilled shaft is usually circular in cross section and 

may be belled at the base to provide greater bearing area. A typical drilled shaft is shown in 

Figure 9-48. Other terminology commonly used to describe a drilled shaft includes: drilled pier, 

drilled caisson, bored pile and cast-in-drilled hole (CIDH). Rectangular drilled shafts are called 

barrettes. 

Vertical load is resisted by the drilled shaft in base bearing and side friction. Horizontal load is 

resisted by the shaft in horizontal bearing against the surrounding soil or rock. 

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Figure 9-48. A typical drilled shaft and terminology (after FHWA, 1999). 

9.11.1 Characteristics of Drilled Shafts 

The following special features distinguish drilled shafts from driven pile foundations: 

1. The drilled shaft is constructed in a drilled hole, unlike the driven pile. 

2. Wet concrete is cast and cures directly against the soil in the borehole. Temporary steel 

casing may be necessary for stabilization of the open hole and may or may not be extracted. 

3. The construction method for drilled shafts is adapted to suit the subsurface conditions. 

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9.11.2 Advantages of Drilled Shafts 

Following are the advantages of drilled shafts. 

a. Construction equipment is normally mobile and construction can proceed rapidly. 

b. The excavated material and the drilled hole can often be examined to ascertain whether 

or not the soil conditions at the site agree with the estimated soil profile. For endbearing situations, the soil beneath the tip of the drilled shaft can be probed for cavities 

or for weak soil. 

c. Changes in geometry of the drilled shaft may be made during the course of the project 

if the subsurface conditions so dictate. 

d. The heave and settlement at the ground surface due to installation will normally be 

very small. 

e. The personnel, equipment, and materials for construction is usually readily available. 

f. The noise level from the equipment is less than for some other methods of 

construction. 

g. The drilled shaft is applicable to a wide variety of subsurface conditions. For example, 

it is possible to drill through a layer of cobbles and into hard rock for many feet. It is 

also possible to drill through frozen ground. 

h. A single drilled shaft can sustain very large loads so that a pile cap may not be needed. 

i. Databases that contain documented load-transfer information are available. These 

databases allow confident designs of drilled shafts to be made in which load-transfer 

both in end bearing and in side resistance can be considered. 

j. The shaft occupies less area than the footing and thus can be built closer to railroads, 

existing structures and constricted areas. 

k. Drilled shafts may be more economical than spread footing construction, especially 

when the foundation support layer is deeper than 10' below the ground or at water 

crossings. 

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9.11.2.1 Special Considerations for Drilled Shafts 

a. Construction procedures are critical to the quality of the drilled shaft. Knowledgeable 

inspection is required. 

b. Drilled shafts are not normally used in deep deposits of soft clay or in situations where 

artesian pressures exist. 

c. Static load tests to verify the ultimate capacity of large diameter shafts are very costly. 

9.11.3 Subsurface Conditions and Their Effect on Drilled Shafts 

Subsurface investigation for drilled shaft designs must include an assessment of the potential 

methods of shaft construction as well as a determination of soil properties. The standard method 

for obtaining soil characteristics is similar to pile foundations and involves laboratory testing of 

undisturbed samples and the use of in situ techniques including the standard penetration test. 

Constructability is difficult to assess from routine geotechnical investigations. Critical items 

such as hole caving, dewatering, rock drilling and obstructions can best be examined by drilling 

a full diameter test shaft hole during the exploration or design phase of the project. These test 

holes are usually done by local drilled shaft contractors under a short form contract. Prospective 

bidders should be invited to observe the construction of the test hole. A detailed log should be 

made of the test hole including items such as type of drilling rig, rate of drilling, type of drill 

tools and augers used, etc. Such information should be made available for bidders. 

Subsurface Conditions Affecting Construction 

a. The stability of the subsurface soils against caving or collapse when the excavation is 

made will determine whether or not a casing is necessary. The dry method of 

construction can be used only where the soils will not cave or collapse. The casing 

method must be used if there is danger of caving or collapse. 

b. The existence of groundwater at the site must be determined and what rate of flow can 

be expected into a shaft excavation. This knowledge will permit selection of 

appropriate slurry type and dosage to support the sides and the bottom of the shaft 

during drilling and subsequent placement of reinforcing cage and concrete. The 

groundwater can be regional groundwater or perched water. 

c. Any artesian water conditions must be clearly identified in the contract documents. 

Artesian water flowing could spoil the concrete placement, or cause collapse or 

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heaving at the excavation. Flowing water can create similar problems during concrete 

placement as it can leach the cement grout out of the concrete mix. Conventional 

slurry-assisted drilling alone may not be adequate in cases where artesian pressure is 

encountered and casing may be required. 

d. The presence of cobbles or boulders can cause difficulties in drilling. It is sometimes 

not easy to extract large pieces of rock, especially with smaller diameter shafts. 

e. The presence of existing foundations or structures. 

f.	 The presence of landfill that could contain material that cannot be easily excavated, 

such as an old car body. 

g.	 The presence of rock may require more sophisticated drilling methods. 

h.	 The presence of a weak stratum just below the base of the drilled shaft. For this 

situation drilling may have to be extended below the weak stratum. 

9.12 ESTIMATING AXIAL CAPACITY OF DRILLED SHAFTS 

The procedures for estimation of drilled shaft capacity have improved significantly over the past 

decade. The major reason for this improvement is a database that has been developed on load 

transfer in skin friction and in end bearing based on load tests in a broad range of geomaterials. 

It is now well established that drilled shafts can carry a substantial portion of applied loads in 

skin friction. As with pile foundations, the ultimate skin friction is mobilized at a relatively 

small downward movement of the shaft relative to the soil. End bearing resistance is developed 

in relation to the amount of deflection at the tip. 

Separate analyses are required to determine skin friction and end bearing contributions in 

different soil types and rock. Details of these analyses can be found in FHWA (1999). The basic 

formulation for drilled shaft capacity in soils and rocks, excerpted from FHWA (1999), is 

presented herein. The discussions in this manual regarding drilled shaft axial capacity are 

limited to drilled shafts of uniform cross-section, with vertical alignment, concentric axial 

loading, and a relatively horizontal ground surface. The reader is referred to FHWA (1999) for 

procedures to incorporate the effects of enlarged base, group action, and sloping ground. 

The ultimate axial capacity (Qult) of the drilled shaft is determined as follows for compression 

and uplift loading, respectively: 

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Qu = Qs + Qt – W 9-34a 

Qu ≤ 0.7Qs + W 9-34b 

 

where: Qu = total ultimate axial capacity of the foundation 

Qs = ultimate skin (side) capacity 

Qt = ultimate tip (base or end) capacity 

W = weight of the shaft. 

Note that in contra-distinction to the ultimate capacity equation for driven piles (see Equation 9­

1), the weight term is included for the drilled shaft since the weight of a shaft is usually much 

larger than that of a pile. The shaft weight can therefore act as a load in the downward direction 

or act as a resistance in uplift. 

Similar to the driven piles, the allowable geotechnical soil resistance, Qa, is determined as 

follows: 

 

Qu Q = 9-35 a FS 

where FS = factor of safety which typically varies between 2 to 3. If load tests are not performed 

then the shaft should be designed for a minimum factor of safety of 2.5 (AASHTO, 2002). This 

minimum recommended factor of safety is based on an assumed normal level of field quality 

control during shaft construction as per the requirements of FHWA (2002d). If a normal level of 

field quality control as required by FHWA (2002d) cannot be assured, larger minimum factors of 

safety such as 3.0 are recommended. If a site-specific load test is performed, consideration may 

be given to reducing the factor of safety from 2.5 to 2.0. 

Shafts in cohesive soils may be designed by total and effective stress methods of analysis, for 

undrained and drained conditions, respectively. Shafts in cohesionless soils should be designed 

by effective stress methods of analysis for drained loading conditions. Formulations for both 

cohesive and cohesionless soils using allowable stress design (ASD) are presented herein based 

FHWA (1999) and AASHTO (2002). For LRFD based formulations the reader is referred to 

AASHTO (2004 with 2006 Interims). 

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9.12.1 Side Resistance in Cohesive Soil 

For cylindrical shafts in cohesive soils loaded under undrained loading conditions, the ultimate 

side resistance may be estimated by using the following expression: 

N 

Qs = πD∑αisui∆zi 9-36 

i=1 

Where, D is the diameter of the shaft and αi and sui are the adhesion factor and undrained shear 

strength, respectively, in a layer ∆zi. The adhesion factor, α, is given as follows. 

α = 0.55 for s p u a ≤ 1.5 9-37a

α = 0.55 − 0.1(su p a −1.5) for 1.5 < su p a ≤ 2.5 9-37b

where pa= atmospheric pressure (=1.06 tsf = 2.12 ksf=14.7 psi =101kPa). The units of sui and pa 

should be dimensionally consistent. 

The ultimate unit load transfer in side resistance at any depth fsi is given as follows: 

fsi = αi sui 9-38 

As illustrated in Figure 9-49, the top and bottom 5-ft of the shaft should not be included in the 

development of the ultimate skin resistance. Environmental, long-term loading or construction 

factors may dictate that a depth greater than the top 5-ft should be ignored in estimating Qs. 

Figure 9-49. Portions of drilled shafts not considered in computing ultimate side resistance 

(FHWA, 1999). 

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Effective stress methods for computing Qs described in Section 9.10.2.3 may be used for the 

following cases: 

•	 For shafts in cohesive soils under drained loading conditions, and 

•	 In the zones where time-dependent changes in soil shear strength may occur, e.g., swelling of 

expansive clay or downdrag from a consolidating clay. 

9.12.1.1 Mobilization of Side Resistance in Cohesive Soil 

Figure 9-50 presents the load-transfer characteristics for side resistance in cohesive soils. The 

curves presented indicate the proportion of the ultimate side resistance (Qs) mobilized at various 

magnitudes of settlement. It can be seen that the full ultimate side resistance is mobilized at 

displacements of 0.2% to 0.8% of the shaft diameter. Thus, for a 4-ft diameter shaft in cohesive 

soil, full side resistance will be mobilized at vertical displacements in the range of 1/8” to 3/8” (3 

mm to 10 mm). 

Figure 9-50. Load-transfer in side resistance versus settlement for drilled shafts in cohesive 

soils (FHWA, 1999). 

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9.12.2 Tip Resistance in Cohesive Soil 

For axially loaded shafts in cohesive soil subjected to undrained loading conditions, the ultimate 

tip resistance of drilled shafts may be estimated by using the following relationship: 

Qt = qt At = NcsutAt 9-39 

Where qt is the unit tip resistance, Nc is a bearing capacity factor, sut is the undrained shear 

strength of the soil at the tip of the shaft and At is the tip area of the shaft. Values of the bearing 

capacity factor, Nc, may be determined by using the following relationship. 

Nc = 6.0[1+0.2(z/D)]; Nc ≤ 9 9-40 

 

where z is the depth of the penetration of the shaft and D is the diameter of the shaft. The units 

of z and D should be consistent. 

The limiting value of unit end bearing (qt = Ncsut) is 80 ksf. The value of 80 ksf is not a 

theoretical limit but a limit based on the largest measured values. A higher limiting value may 

be used if it is based on the results of a load test, or previous successful experience in similar 

soils under similar loading conditions. 

The value of sut should be determined from the results of in-situ and/or laboratory testing of 

undisturbed samples obtained within a depth of 2.0 diameters below the tip of the shaft. If the 

soil within 2.0 diameters of the tip has sut < 0.5 ksf, the value of Nc should be multiplied by 0.67. 

9.12.2.1 Mobilization of Tip Resistance in Cohesive Soil 

Figure 9-51 presents the load-transfer characteristics for tip resistance in cohesive soils. The 

curves presented indicate the proportion of the ultimate tip resistance (Qt) mobilized at various 

magnitudes of settlement. It can be seen that the ultimate tip resistance, Qt, is fully mobilized at 

displacements of 2% to 5%. Thus, for a 4-ft diameter shaft in cohesive soil, full tip resistance 

will be mobilized at vertical displacements in the range of 1” to 2.5” (25 mm to 65 mm). 

Conversely, if the shaft settles less than these values, then full tip resistance may not be 

mobilized. For example, if the shaft settles only 1% of the shaft diameter then approximately 

60% of the tip resistance will be mobilized as indicated by the trendline shown in Figure 9-51. 

For smaller tolerable settlements, the mobilized tip resistance will be similarly smaller. If one 

limits the deformation to between 0.2% and 0.8% to be consistent with full mobilization of side 

resistance in cohesive soil, then from Figure 9-51, it can be seen that only approximately 10 to 

50% of the tip resistance will be available based on the trendline. 

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Figure 9-51. Load-transfer in tip resistance versus settlement for drilled shafts in cohesive 

soils (FHWA, 1999). 

The above examples of shaft settlements clearly demonstrate the need to perform detailed 

settlement analyses by using Figure 9-50 and 9-51 to estimate the shaft resistance based on 

consistent deformations. For shafts in cohesive soil under drained loading conditions, Qt, may be 

estimated by using the procedure described in Section 9.12.3.1 for cohesionless (drained) soils. 

9.12.3 Side Resistance in Cohesionless Soil 

For cylindrical shafts in cohesionless soil or for effective stress analysis of cylindrical shafts in 

cohesive soils under drained loading conditions, the ultimate side resistance of axially loaded 

drilled shafts may be estimated by using the following equation: 

N 9-41 

Qs = πD∑βi po∆zi 

i=1 

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where: βi = 1.5 − 0.135 zi with 1.2 > βi > 0.25 9-42 
 

In above equations D is the shaft diameter, N is the number of layers used in the analysis, zi is 

the depth in feet to the center of the ith layer and po is the effective overburden pressure at the 

center of the ith layer. The ultimate unit load transfer in side resistance at any depth fsi is given 

as follows: 

fsi = βi po 9-43 

The limiting value of fsi for shafts in cohesionless soils is 4 ksf (191 kPa). 

9.12.3.1 Mobilization of Side Resistance in Cohesionless Soil 

Figure 9-52 presents the load-transfer characteristics for side resistance in cohesionless soils. 

The curves presented indicate the proportion of the ultimate side resistance (Qs) mobilized at 

various magnitudes of settlement. It can be seen that the full ultimate side resistance, Qs, is fully 

mobilized at displacements of 0.1% to 1.0% of the shaft diameter. Thus, for a 4-ft diameter shaft 

in cohesionless soil, full side resistance will be mobilized at vertical displacements in the range 

of 0.05” to 0.5” (1.3 to 13 mm). 

9.12.4 Tip Resistance in Cohesionless Soil 

For axially load drilled shafts in cohesionless soils or for effective stress analysis of axially 

loaded drilled shafts in cohesive soils, the ultimate tip resistance may be estimated by using the 

following equation: 

Qt = qt At 9-44 

The value of qt may be determined from the results of standard penetration testing using N60 

blow count readings within a depth of 2B below the tip of the shaft as follows: 

 For N60 ≤ 75: qt = 1.2N60 in ksf 9-45a 

 For N60 > 75: qt = 90 ksf 9-45b 

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Figure 9-52. Load-transfer in side resistance versus settlement for drilled shafts in 

cohesionless soils (FHWA, 1999). 

9.12.4.1 Mobilization of Tip Resistance in Cohesionless Soil 

Figure 9-53 presents the load-transfer characteristics for tip resistance in cohesionless soils. The 

curves presented indicate the proportion of the ultimate tip resistance (Qt) mobilized at various 

magnitudes of settlement. It can be seen that the ultimate tip resistance, Qt, is fully mobilized at 

displacements of approximately 5%. Thus, for a 4-ft diameter shaft in cohesive soil, full tip 

resistance will be mobilized at vertical displacements of approximately 2.4-inches. Conversely, 

if the shaft settles less than this value, then full tip resistance may not be mobilized. For example 

if the shaft settles only 1% of the shaft diameter then approximately 30% of the tip resistance 

will be mobilized as indicated by the trendline shown in Figure 9-53. For smaller settlements, 

the mobilized tip resistance will be similarly smaller. If one limits the deformation to between 

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0.1% and 1% to be consistent with full mobilization of side resistance in cohesionless soils, then 

from Figure 9-53, it can be seen that only approximately 5 to 30% of the tip resistance will be 

available based on the trendline. 

Compared to similar examples for cohesive soils, it can be seen that deformation compatibility is 

more critical in cohesionless soils due to the relatively large deformation of 5% of shaft diameter 

that is required to mobilize full tip resistance. This reinforces the need to perform detailed 

settlement analyses by using Figure 9-52 and 9-53 to estimate the shaft resistance based on 

consistent deformations. 

Figure 9-53. Load-transfer in tip resistance versus settlement for drilled shafts in 

cohesionless soils (FHWA, 1999). 

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9.12.5 Determination of Axial Shaft Capacity in Layered Soils or Soils with Varying 

Strength with Depth 

The design of shafts in layered soil deposits or soil deposits having variable strength with depth 

requires evaluation of soil parameters characteristic of the respective layers or depth. The side 

resistance, Qs, in such soil deposits may be estimated by dividing the shaft into layers according 

to soil type and properties, determining Qs, for each layer, and summing the values for each layer 

to obtain the total load Qs. If the soil below the shaft tip is of variable consistency, Qt, may be 

estimated using the strength properties of the predominant soil strata within a depth of 2 shaft 

diameters below the shaft tip. While summing the resistances, particular attention must be paid 

to deformation compatibility. 

For shafts extending through soft compressible layers to firm soil or rock, consideration should 

be given to the effects of negative skin friction due to the potential consolidation settlement of 

soils surrounding the shaft. Where the shaft tip would bear on a thin firm soil layer underlain by 

a softer soil unit, the shaft should be extended through the softer soil unit to eliminate the 

potential for a punching shear failure into the softer deposit. 

9.12.6 Group Action, Group Settlement, Downdrag and Lateral Loads 

These topics are similar to those for pile foundations. Their detailed discussion is beyond the 

scope of this manual. The reader is referred to FHWA (1999) for discussion of these topics. 

The concepts regarding axial capacity of drilled shafts in cohesionless or drained cohesive soils 

are illustrated numerically by Example 9-5. The concepts regarding axial capacity of drilled 

shafts in layered soils are illustrated numerically by Example 9-6. 

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Example 9-5:	 Size a shaft to resist 170 tons of vertical design load in the soil profile shown 

below. Assume a factor of safety (FS) of 2.5. 

N60-values 

N60 = 11 

N60 = 14 

N60 = 14 

N60 = 22 

N60 = 12 

52.0 

N60 = 19 

N60 = 21 

N60 = 37 

Solution: 

The ultimate geotechnical axial load = (FS) (Design Load) = (2.5) (170 tons) = 425 tons. 

Assume a straight-sided drilled shaft with a diameter of 3-ft and a length of 60-ft. Thus, π(D) = 

9.42-ft 

N / Use Equation 9-41 to determine ultimate skin resistance, Qs = πD∑γi zi

βi∆zi 

i=1 

Depth 

Interval, 

∆z, ft 

Surface Area 

per depth 

interval, 

∆z(π)(D), ft2 

Average effective 

vertical (overburden) 

stress, po =γ

/

zi 

tsf 

β 

i i −=β z0.1351.5 

with 1.2 0.25 βi >>

∆Qs 

Tons 

0 – 4 37.7 0.115 1.20 5.20 

4 – 30 245.0 0.572 0.94 131.70 

30 – 60 282.7 1.308 0.59 218.20 

QS 355.10 

Base resistance (N60=21 at 60-ft). Using Equation 9-45a qt = 1.2N 60 = 25.2 ksf = 12.6 tsf 

A 2

t = 7.07 ft Therefore, Qt = (7.07 ft2

) (12.6 tsf) = 89.1 tons 

Thus, ultimate geotechnical axial resistance, Qult is given by: 

Qu = 355.1 + 89.1 = 444.2 tons ≈ 440 tons > 425 tons Okay. 

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Example 9-6:	 Determine the shaft length to resist 150 tons of vertical design load in the 

mixed (clay on sand) soil profile shown below. Assume a safety factor of 2.5. 

Assume a total unit weight of 125 pcf for clay and 115 pcf for sand. Water 

table is at a depth of 17-ft. Assume depth of zone of seasonal moisture change 

to be 5-ft. Once the shaft is sized for ultimate load, check the deformation 

under design load of 150 tons. 

N60 = 20 

N60 = 25 

N60 = 50 

Solution: 

For a factor of safety of 2.5, the ultimate axial load is computed to be (2.5)(150 tons) = 375 tons. 

For a straight-sided shaft with a diameter of 3.0-ft and a depth of penetration of 50-ft, π(D) =
 

9.42-ft 

Use Equation 9-36 and 9-41, 

 

N
 

Qs = πD∑αisui∆zi
 

i=1
 

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N / Qs = πD∑γi zi

βi∆zi 

i=1 
 

 

 

 

Soil Depth 

Interval, 

∆z, ft 

Surface Area 

per depth 

interval, 

∆z(π)(D), ft2 

Shear Strength or Average 

effective vertical 

(overburden) stress, 

tsf 

α or β ∆Qs 

Tons 

Clay 0 – 5 -- -- 0.00 0 

Clay 5-32 254.5 0.80 (shear strength) α =

0.55* 

112.0 

Sand 32-50 169.6 {(17 ft x 125 pcf) + 

(32ft -17 ft)(125 pcf-62.4 pcf) 

+9ft(115 pcf - 62.4 pcf)}/2,000 

=3537.4 psf/2,000 = 1.769 tsf 

β =

0.64** 

192.0 

* From Equation 9-37a 

** From Equation 9-42, i i −=β z0.1351.5 

At mid-depth of sand layer, zi = 32 ft + (50 ft – 32 ft)/2 = 41 ft 

 At zi = 41 ft, 0.6441ft0.1351.5 i −=β ≈

QS 304.0 

Base resistance (N60=25 at 50 ft) 

Use Equation 9-45a 

qt = 1.2N 60 = 1.2 (25) = 30 ksf = 15 tsf 

At = 7.07 ft2 

Qt = (7.07 ft2

) (15.0 tsf) = 106 tons 

Total ultimate axial resistance, Qult is given by: 

Qu = 304.0 + 106.0 = 416.0 tons > 375 tons Okay. 

Check of settlement under design load (150 tons)
 

Because most of the load in side resistance and all of the end bearing are derived from sand, 

Figures 9-52 and 9-53 will be used to estimate settlement. A settlement near the upper bound in 

both figures will be selected as a conservative estimate. 

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A settlement of 0.15 percent of the diameter is selected for the average settlement of the sides, or 

0.06-inch. That would indicate that about 138 tons is carried in side resistance, and about 12 

tons is carried in bearing, assuming that the shaft is essentially incompressible. 

Comment: The settlement solution appears to be reasonable. 

9.12.7 Estimating Axial Capacity of Shafts in Rocks 

Drilled shafts are commonly socketed into rock to limit axial displacements, increase load 

capacity and/or provide fixity for resistance to lateral loading. 

Typically, axial compression load is carried solely by the side resistance on a shaft socketed into 

rock until a total shaft vertical displacement on the order of 0.4 inches occurs, i.e., elastic 

compression of the concrete plus downward movement of the shaft under load. At this 

displacement, the ultimate side resistance in rock, Qsr, is mobilized and slip occurs between the 

concrete and rock. As a result of this slip, any additional load is transferred to the tip. 

The design procedures assume the socket is constructed in reasonably sound rock that is not 

significantly affected by construction, i.e., the rock does not rapidly degrade upon excavation 

and/or exposure to air or water, and is cleaned prior to concrete placement, i.e., the rock surface 

is free of soil and other debris. If the rock is degradable, consideration of special construction 

procedures, larger socket dimensions, or reduced socket capacities should be considered. 

9.12.7.1 Side Resistance in Rocks 

For drilled shafts socketed into rock, shaft resistance may be evaluated as follows (Horvath and 

Kenney, 1979): 

Q = πDr L q 9-46 sr r sr 

0.5 0.5 ' ⎛ q ⎞ ⎛ f ⎞

u ⎜ c qsr = 0.65(αE )(pa )

⎜

⎜ ⎟⎟ < 0.65(pa ) ⎟ 9-47 

p ⎜ p ⎟ ⎝ a ⎠ ⎝ a ⎠

where: Dr = diameter of rock socket (ft) 

Lr = length of rock socket (ft) 

qsr = unit skin resistance of rock (tsf) 

qu = uniaxial compressive strength of rock (tsf) 

pa = atmospheric pressure =1.06 tsf 

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 αE = EM/Ei = reduction factor to account for jointing in rock as provided in 

Table 5-23 in Chapter 5, where EM is the elastic modulus of the rock mass 

and Ei is the elastic modulus of intact rock 

 f′c = 28-day compressive strength of concrete (tsf) 

Equation 9-46 applies to the case where the side of the rock socket is considered to be smooth or 

where the rock is drilled using a drilling slurry. Significant additional shaft resistance may be 

achieved if the borehole is specified to be artificially roughened by grooving. Methods to 

account for increased shaft resistance due to borehole roughness are provided in FHWA (1999). 

Equation 9-46 should be used only for intact rock. When the rock is highly jointed, the 

calculated qsr should be reduced to arrive at a final value for design. The procedure is as follows: 

Step 1.	 Evaluate the ratio of rock mass modulus to intact rock modulus (i.e., Em/Ei) by 

using Table 5-23 in Chapter 5. 

Step 2.	 Evaluate the reduction factor, αE = EM/Ei, by using Table 5-23. 

Step 3. Calculate qsr according to Equation 9-47. 

9.12.7.2 Tip Resistance in Rocks 

If the rock below the base of the drilled shaft to a depth of 1.0 diameter is either intact or tightly 

jointed, i.e., there are no compressible materials or gouge-filled seams, and the depth of the 

socket is greater than 1.5 diameters, then the tip resistance of the rock may be evaluated as 

follows (FHWA, 1999): 

Q = A q	 9-48 tr t tr 

qtr = 2.5 qu	 9-49 

 

 

where: At = tip area of rock socket 

qtr = unit tip resistance, which is evaluated in terms of qu, where qu = unconfined 

compressive strength of intact rock (tsf) 

If the rock below the base of the shaft is jointed and the joints have random orientation, then the 

reader should refer to the procedures in FHWA (1999). 

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9.12.8 Estimating Axial Capacity of Shafts in Intermediate GeoMaterials (IGMs) 

Intermediate geomaterials (IGMs) are the transitory materials between soils and rocks. IGMs are 

defined by FHWA (1999) as follows: 

•	 Cohesive IGM – clay shales or mudstones with an undrained shear strength, su, of 2.5 to 25 

tsf, and 

•	 Cohesionless – granular tills or granular residual soils with N60 greater than 50 blows/ft. 

For detailed information regarding the estimation of shaft resistances in IGM’s, the reader should 

consult FHWA (1999). 

9.13 CONSTRUCTION METHODS FOR DRILLED SHAFTS 

There are three basic methods for construction of drilled shafts. These are (a) dry method, (b) 

wet method and (c) casing method. Each of these methods is briefly presented below. 

1. Dry Method 

The dry method is applicable to soils above the water table that will not cave or slump when 

the hole is drilled to its full depth. A soil that meets this specification is a homogeneous 

stiff clay. The dry method can be employed in some instances with sands above the water 

table if the sands have some cohesion, or if they will stand for a period of time because of 

apparent cohesion. 

The dry method can be used for soils below the water table if the soils are low in 

permeability so that only a small amount of water will seep into the hole during the time the 

excavation is open. 

The dry method consists of drilling a hole using an auger or bucket drill without casing, 

cleaning the bottom of the excavation, placing a rebar cage and then filling the hole with 

concrete. The 4 steps involved in construction of a drilled shaft by the dry method are 

shown in Figure 9-54. 

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 (a) (b) (c) (d) 

Figure 9-54. Steps in construction of drilled shafts by the dry method (a) drill, (b) clean, (c) 

position reinforcement cage, and (d) place concrete. 

2. Wet Method 

Bentonite or polymer slurry is introduced into the excavation to prevent caving or 

deformation of loose or permeable soils. The wet method is commonly used while drilling 

under the groundwater level. Drilling by use of an auger or clamshell mounted on a kelly 

bar continues through the slurry. When the desired depth is reached, the excavation is 

cleaned and the rebar cage is lowered into the slurried hole. Concrete is then tremie-poured 

into the hole. Slurry is displaced by the heavier concrete and collected at the surface in a 

sump. The slurry may again be used in another hole. Figure 9-55 shows the 5-step process 

of shaft construction using wet method. 

3. Casing Method 

The casing method is applicable to sites where soil conditions are such that caving or 

excessive deformation will occur when a hole is excavated. An example of such a site is a 

clean sand below the water table. This method employs a cylindrical steel casing inside the 

excavation to support the caving soil. The excavation is made by driving, vibrating, or 

pushing a heavy casing to the proposed founding level and by removing the soil from within 

the casing either continuously as excavation proceeds or in one sequence after the casing 

has reached the desired depth. Slurry may be required if the excavation is advanced below 

the ground water table. The excavation is cleaned and the rebar cage is lowered into the 

excavation. Concrete is then placed, by tremie if the excavation is slurried, and the casing 

removed. The casing is sometimes permanently left in place. Figure 9-56 shows the 5-step 

process of shaft construction using the casing method. 

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 (a) (b) (c) (d) (e) 

Figure 9-55. Steps in construction of drilled shafts by the wet method (a) start drilling and 

introduce slurry (bentonite or polymer) in the excavation PRIOR to encountering the 

known piezometric level, (b) continue drilling with slurry in the excavation, (c) clean the 

excavation and slurry, (d) position reinforcement cage, and (e) place concrete by tremie.

 (a) (b) (c) (d) (e) 

Figure 9-56. Steps in construction of drilled shafts by the casing method (a) start drilling 

and introduce casing in the excavation PRIOR to encountering the known piezometric level 

and/or caving soil, (b) advance the casing through the soils prone to caving, (c) clean the 

excavation, (d) position reinforcement cage, and (e) place concrete and remove the casing if 

it is temporary. 

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It is critical that the correct construction method be chosen for a given project. Unlike driven 

piles, which are assembled under controlled conditions and then driven into the ground, drilled 

shafts are “manufactured” on-site. Thus, the quality of the constructed drilled shaft will be only 

as good as the quality of the construction processes. In particular, the side and tip resistances are 

directly affected by the construction processes. While each of the steps in Figures 9-54 to 9-56 

are important, the most important step is related to cleaning of the shaft excavation. There 

are many considerations involved in the proper cleaning of shafts that are beyond the scope 

of this manual. Figure 9-57a shows a photograph of a shaft in which the excavation was not 

cleaned properly, while Figure 9-57b shows a photograph of a shaft where the cleaning was 

adequate. These photographs clearly illustrate the need for proper cleaning of the shaft 

excavation. A detailed discussion of the drilled shaft construction and inspection processes 

including procedures to assure adequate cleaning can be found in FHWA (1999) and FHWA 

(2002d). 

(a) (b) 

Figure 9-57. Photographs of exhumed shafts (a) shaft where excavation was not 

adequately cleaned, (b) shaft where excavation was properly cleaned (FHWA, 2002d). 

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9.14 QUALITY ASSURANCE AND INTEGRITY TESTING OF DRILLED SHAFTS 

Unlike piles, which are manufactured in a factory (e.g., steel pipe piles) or a casting yard (e.g., 

precast concrete piles), drilled shafts are “manufactured” at the site. Anomalies often develop 

during the construction of drilled shafts as shown in Figure 9-57a. An anomaly is a deviation 

from an assumed uniform geometry of the shaft and/or from the required physical properties of 

the shaft. Typical anomalies may include necking or bulbing, “soft bottom” conditions, voids or 

soil intrusions, poor quality concrete, debonding, lack of concrete cover over the reinforcement 

steel and honey-combing. Non-destructive test (NDT) methods are used for Quality Assurance 

(QA) integrity testing of drilled shaft foundations to identify anomalies. 

NDT testing techniques can be categorized as external and internal. External NDT techniques 

are used at the surface of the concrete structure when access to the interior of the concrete is not 

available. Examples of external NDT techniques include Sonic Echo (SE), Impulse Response 

(IR) or Ultra-seismic (US). Internal NDT techniques are used when testing equipment can 

access the interior of a concrete structure through either cast-in-place access tubes or cored 

access paths, or through cast-in-place equipment within the concrete (e.g., strain gages). 

Commonly used internal NDT techniques include standard Cross-hole Sonic Logging 

(CSL) with zero-offset measurements and Gamma-Gamma Density Logging (GDL). Both 

of these techniques are described below. Other more specialized internal NDT techniques 

include the Neutron Moisture Logging (NML) and Temperature Logging (TL). All of the NDT 

methods are discussed in FHWA (2003). Summaries of the methods are given in FHWA (1999), 

FHWA (2002d) and by Samtani, et al. (2005). 

9.14.1 The Standard Crosshole Sonic Logging (CSL) Test 

In the standard CSL test method, an ultrasonic transmitter or source and receiver probes are first 

lowered to the bottom of a pair of water-filled pre-installed access tubes as shown in Figure 9-58. 

It is common industry practice to locate the access tubes inside the reinforcing cage. The two 

probes are then pulled up simultaneously such that the probes are level with each other, i.e., zerooffset. The travel time of the ultrasonic wave between the tubes is recorded along with the 

amplitude of the signal as a function of every inch of depth. This test procedure is repeated for 

all possible paired combination of access tubes along the outer perimeter as well as across the 

inner diagonal of the shaft as shown in the inset Plan View in Figure 9-58. Typically, one tube 

per foot diameter of the shaft is installed for CSL tests. Thus, for 6-ft diameter shaft, 6 tubes are 

used. The minimum number of tubes should be 3. 

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Figure 9-58. Schematic of CSL Test (Samtani, et al., 2005). 

 

The measured travel time, t, between two tubes with a known center to center distance, d, is 

expressed in terms of velocity as: V =d/t. This computed velocity, V, is compared with the 

theoretical compressional wave velocity, VC, in concrete. The theoretical ultrasonic wave 

velocity in competent concrete with unconfined compressive strength, fc, in the range from 3,000 

to 5,000 psi is approximately 10,000 to 11,500 ft/sec, respectively (Samtani et al., 2005). As a 

comparison, the sonic velocity in water and air is approximately 5,000 ft/sec and 1,000 ft/sec, 

respectively. The computed velocity is compared with the theoretical velocity and expressed in 

terms of velocity reductions, VR = (1-V/VC)(100)%. A qualitative rating is assigned to the 

concrete based on VR, as follows: 

VR Rating 

0-10% Good 

10-20% Questionable 

>20% Poor 

The ratings are partially based on the estimated reduction in strength of concrete in anomalous 

zones. For example, if VR=10% at a given location in a shaft, then the fc at that location is 

approximately 65% of the nominal 28-day f′c value of the concrete in that shaft. Similarly, a 

concrete with VR=20% implies that f′c at that location is 40% of the 28-day strength. 

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With the exception of voids and possibly honeycombs, the locations of poor concrete can be 

confirmed by checking the signal amplitudes. Weaker concrete absorbs the energy of the sonic 

wave more than sounder concrete and this phenomenon is reflected in lower signal amplitudes. 

Thus, if the measurements in the shaft indicate lower velocity and lower signal amplitudes then 

they typically point to anomalous zones due to soil intrusions or poor quality concrete. An 

example single plot display format that includes velocity and signal amplitude profiles is shown 

in Figure 9-59. In this particular case, it can be seen that a soft bottom condition in the shaft is 

reflected at the very bottom of the profile by a drastic change in both in the velocity and 

amplitude profiles. 

Figure 9-59. Single plot display format for the CSL data for shaft with five tubes 

(Samtani, et al., 2005). 

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If the tubes debond from the concrete, i.e., there is a small air gap between the outer surface of 

the tube and the concrete of the shaft, then the CSL test will record a partial or complete loss of 

signal depending on the extent of the debonding around the perimeter of the tube at that location. 

Debonding can occur with Schedule 40 PVC access tubes particularly near the ground surface or 

above the groundwater table where temperature gradients are generally greater. For Schedule 40 

PVC tubes, the debonding may occur within a week after placement of concrete as the concrete 

sets and tends to shrink away from the tubes. Thus, if Schedule 40 PVC tubes are used, then it is 

generally recommended to perform the CSL tests within 2 to 3 days after concrete placement. A 

thicker wall PVC tube, such as a Schedule 80 tube, may help extend this timeframe because it is 

able to withstand the higher temperature gradients better than a thinner PVC tube. Longer time 

frames can be achieved by the use of steel tubes that experience minimal to no debonding. 

Therefore, many owners tend to specify steel tubes to alleviate the debonding problems. 

However, in doing so, the owners are giving up an advantage of the PVC tubes in that they can 

serve as access paths to repair the shafts should an anomaly be identified by the CSL test since 

the PVC tubes can be cut open at any depth by use of a high velocity water jet, commonly known 

as the “water knife.” Use of a water knife is much more difficult, if not impossible, in steel due 

to the practical limitation of generating a very high water velocity at depth within the access 

tubes. 

Cross-hole Sonic Logging Tomography (CSLT) using multi-offset CSL method is a logical 

newer extension of the CSL technique and is starting to gain acceptance. The Perimeter Sonic 

Logging (PSL) is yet another new variation in which zero-offset or multi-offset CSL may be 

performed in PVC tubes attached to the outside of the reinforcing cage. Samtani, et al. (2005) 

and FHWA (2003) provide summaries of these methods 

9.14.2 The Gamma Density Logging (GDL) Test 

A typical field setup for the GDL test is shown in Figure 9-60. In this test a weak Cesium-137 

(radioactive) source emits gamma rays into the surrounding medium. A small fraction of the 

gamma ray photons are reflected back to the probe due to Compton scattering. The intensity of 

the reflected photons is recorded by a NaI scintillation crystal as counts per second (cps). The 

measured count rate (cps) depends on the electron density of the surrounding medium, which is 

proportional to the mass per unit volume. The instrument is calibrated by placing the probe in an 

environment of known density in order to convert the measured count rate (cps) into the units of 

density or unit weight, e.g. lb/ft3

 (pcf). 

In the GDL test, the radius of the investigation is largely governed by 1⁄2 of the source-detector 

spacing. Good concrete conditions will result in a near continuous alignment of the data. 

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Anomalous zones due to soil intrusions, poor concrete or voids are characterized by low density 

which leads to a high count rate. 

A typical GDL log is shown in Figure 9-61. In a GDL log, the measured gamma ray intensity 

count rate (cps) is presented in terms of unit weight (pcf). In Figure 9-61, the results are plotted 

in 4 separate sub-plots from the tested access tubes. Each individual sub-plot depicts the GDL 

results from a 14-inch source-detector separation (corresponding to about 5- to 6-inch radius of 

investigation) presented in a magnified density scale of 130-180 pcf. Also, in each sub-plot, the 

mean as well as the minus 2 (-2) and minus three (-3) standard deviation (SD) from mean curves 

are displayed as vertical guidelines. Depths, in feet, are measured from the top of the shaft and 

are shown on the vertical axis. 

Figure 9-60. Schematic of GDL Test (Samtani, et al., 2005). 

The results of GDL tests are used to define “questionable” concrete conditions as a zone with 

reduction in unit weight between -2SD and -3SD and “poor” concrete conditions as a zone with 

reduction in unit weight of greater than -3SD from the mean (M). These criteria are based on the 

observation that a cps data set approximates a standard normal distribution probability function 

in which 99.73% of the data is within M±3SD. Therefore, when data points are identified 

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beyond 3SDs, they are considered to represent an anomaly. While these definitions are generally 

accepted, it is not widely recognized that the computation of M and SD varies during 

presentation of the results by various testers/agencies. Some testers or agencies define the M and 

SD with respect to a given tube while others may define these quantities based on all tubes 

within a shaft, i.e. ignore the variation of steel density and hole geometry, or all tubes from a 

group of shafts that may form a single overall foundation element for a superstructure. 

Obviously, the definition of the concrete quality will be different based on the definition of the 

M and SD. Therefore, the user should be careful with the interpretation of the GDL test data. 

Unlike the CSL test, the GDL is not affected much by debonding of the tubes from the concrete. 

Therefore, a PVC tube is generally used, although steel can also be used with GDL testing. It 

must be recognized, however, that the thicker or denser the tube material, the lower the measured 

counts per second (cps) since the tube itself will absorb some of the electrons. Therefore, the 

user of the data should review the calibration data and check whether the tube type used during 

calibration is consistent with that used in the actual shaft and the density of the shaft 

reinforcement. 

Figure 9-61. Single plot display format for the GDL data for shaft with four tubes 

(Samtani, et al., 2005). 

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9.14.3 Selecting the Type of Integrity Test for Quality Assurance 

Most agencies use either the CSL or GDL test method to evaluate the structural integrity of a 

constructed shaft. As shown in Figure 9-58, the CSL test evaluates the area of the shaft between 

the tubes. Since the tubes are commonly located on the inside of the cage, this means that only 

the portion of the shaft within the reinforcing cage is evaluated. On the other hand, the GDL test 

evaluates a portion of the shaft immediately surrounding a tube. In other words, GDL evaluates 

a zone inside and outside the reinforcing cage as shown in Figure 9-60. Due to the different 

portions of the shaft evaluated by the CSL and GDL tests, it is recommended that both tests be 

performed to assure an evaluation of the concrete inside and outside the reinforcing cage. 

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9.15 STATIC LOAD TESTING OF DEEP FOUNDATIONS 

Static load testing of deep foundations is the most accurate method of determining load capacity. 

Depending upon the size of the project, static load tests may be performed either during the 

design stage or the construction stage. Conventional load test types include the axial 

compression, axial tension or lateral load tests. 

The purpose of this section is to provide an overview of static testing and its importance as well 

as to describe the basic test methods and interpretation techniques. For additional details on load 

testing for deep foundations, the reader is referred to FHWA (1992c) and ASTM D 1143. It may 

be noted that ASTM D 1143 was not re-approved in 2006. Therefore, as of the publication date 

of this manual, there is no accepted ASTM standard for static load tests. However, for the 

purposes of this manual, the latest ASTM D 1143 prior to 2006 is adequate from the viewpoint 

of the basic aspects of load testing. 

9.15.1 Reasons for Load Testing 

1. To minimize risks to the structure by confirming the suitability of the deep foundation to 

support the design load with an appropriate factor of safety. 

2. It is the most positive way for determining the capacity of deep foundations. 

3. To develop information for use in the design and/or construction of a deep foundation. 

4. Implementation of new static or dynamic analysis methods or procedures. 

5. Calibrations of new design procedures such as the Load and Resistance Factor Design 

(LRFD). 

9.15.2 Advantages of Static Load Testing 

The advantages of performing static load tests are summarized as follows: 

1. A static load test allows a more rational design. Confirmation of pile-soil capacity through 

static load testing is considerably more reliable than capacity estimates from static capacity 

analyses and dynamic formulas. 

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2. An improved knowledge of deep foundation-soil behavior is obtained that may allow a 

reduction in deep foundations lengths or an increase in the design load, either of which 

may result in potential savings in foundation costs. 

3. With the improved knowledge of deep foundation-soil behavior, a lower factor of safety 

may be used on the design load. A factor of safety of 2.0 is generally applied to design 

loads confirmed by load tests as compared to a factor of safety of 3.5 used on design loads 

in the Modified Gates dynamic formula. Hence, a cost savings potential again exists 

(Refer to Table 9-5). 

4. The ultimate geotechnical capacity determined from load testing allows confirmation that 

the design load may be adequately supported at the planned foundation penetration depth. 

Engineers are sometimes hesitant to recommend a static load test because of cost concerns or 

potential time delays in design or construction. While the cost of performing a static load test 

should be weighed against the anticipated benefits, cost alone should not be the determining 

factor. 

Delays to a project in the design or construction stage usually occur when the decision to 

perform static load tests is added late in the project. Such delays can be minimized by 

determining early in the project whether a static load test program should be performed. In the 

construction stage, delays can be minimized by clearly specifying the number and locations of 

static load tests to be performed as well as the time necessary for the engineer to review the 

results. In addition, the specifications should state that the static test must be performed prior to 

ordering pile lengths or commencing production driving. In this way, the test results are 

available to the design and construction engineer early in the project so that the maximum 

benefits can be obtained. At the same time the contractor is also aware of the test requirements 

and analysis duration and can schedule the project accordingly. 

9.15.3 When to Load Test 

The following criteria, adapted and modified from FHWA (1992c), summarize conditions when 

pile load testing can be effectively utilized: 

1. When substantial cost savings can be realized. This is often the case on large projects 

involving either friction piles to prove that lengths can be reduced or end bearing piles 

to prove that the design load can be increased. Testing can also be justified if the 

savings obtained by using a lower factor of safety equals or exceeds the testing cost. 

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2. When a safe design load is uncertain due to limitations of an engineer's experience base 

or due to unusual site or project conditions. 

3. When subsurface conditions vary considerably across the project, but can be delineated 

into zones of similar conditions. Static tests can then be performed in representative 

areas to delineate foundation variation. 

4. When a significantly greater load is contemplated relative to typical design loads and 

practice. 

5. When time dependent changes in deep foundation capacity are anticipated as a result of 

soil setup or relaxation. 

6. Verification of new design or testing methods. 

7. When new, unproven deep foundation types and/or pile installation procedures are 

utilized. 

8. When existing deep foundations will be reused to support a new structure with heavier 

design loads. 

9. When a reliable assessment of uplift capacity or lateral behavior is important. 

10. When, during construction, the estimated ultimate capacity determined by using 

dynamic formulas or dynamic analysis methods differs from the estimated capacity at 

that depth determined by static analysis. For example, H-piles that "run" when driven 

into loose to medium dense sands and gravels. 

11. Calibrations of new design procedures such as the Load and Resistance Factor Design 

(LRFD). 

Experience has also shown that load tests will typically confirm that pile lengths can be reduced 

at least 15 percent versus the lengths that would be required by the Engineering News (EN) 

formula on projects where piles are supported predominantly by shaft resistance. This 15 percent 

pile length reduction was used to establish the following “rule of thumb” formula to compute the 

total estimated pile length that the project must have to make the load test cost effective based 

purely on material savings alone. 

 

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 9-50 cost of load test Total estimated pile length in feet on project ≥(0.15) (cost / ft of pile) 

The above formula may not be valid for drilled shafts since the EN formula is not applicable. 

9.15.4 Effective Use of Load Tests 

9.15.4.1 Design Stage 

The best information for design of a deep foundation is provided by the results of a load testing 

program conducted during the design phase. The number of static tests, types of piles/shafts to 

be tested, method of driving and test load requirements, method of shaft excavation should be 

selected by the geotechnical and structural engineers responsible for design. A cooperative effort 

between the two is necessary. The following are the advantages of load testing during the design 

stage. 

a. Allows load testing of several different pile/shaft types and lengths resulting in the 

design selection of the most economical pile/shaft foundation. 

b. Confirm driveability to minimum penetration requirements and suitability of foundation 

capacity at estimated pile penetration depths. 

c. Establishes preliminary driving criteria for production piles. 

d. Pile driving information released to bidders should reduce their bid "contingency." 

e. Confirm the excavation and excavation support methods for drilled shafts. 

e. Reduces potential for claims related to pile driving problems or shaft excavation 

methods. 

f.	 Allows the results of the load test program to be reflected in the final design and 

specifications. 

9.15.4.2 Construction Stage 

Load testing at the start of construction may be the only practical time for testing on smaller 

projects that can not justify the cost of a design stage program. Construction stage static tests are 

invaluable to confirm that the design loads are appropriate and that the pile installation procedure 

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is satisfactory. Driving of test piles and load testing is frequently done to determine the pile 

order length at the beginning of construction. These results refine the estimated pile lengths 

shown on the plans and establish minimum pile penetration requirements. 

9.15.5 Prerequisites for Load Testing 

In order to plan and implement a static load testing program adequately, the following 

information should be obtained or developed. 

1. A detailed subsurface exploration program at the test location. 	 A load test is not a 

substitute for a subsurface exploration program. 

2. Well defined subsurface stratigraphy including engineering properties of soil materials and 

identification of groundwater conditions. 

3. Static pile capacity analyses to select pile type(s) and length(s) as well as to select 

appropriate location(s) for load test(s). 

4. For drilled shafts, caliper-logging to determine the exact dimensions of the shaft 

excavation. Caliper-logging is required because the actual dimensions of excavations in 

geomaterials can vary significantly from the diameter of the drilling tool due to a variety 

of geologic factors or drilling considerations. Calipers are available in either mechanical 

or electronic configurations. Determination of the exact dimensions of the excavation is 

the key to proper interpretation of the load test results. 

5. For drilled shafts, integrity testing should be performed prior to the load test to determine 

whether the shaft needs to be structurally repaired so that it has enough structural 

capacity to sustain the test loads. 

9.15.6 Developing a Static Load Test Program 

The goal of a static load test program should be clearly established. The type and frequency of 

tests should be selected to provide the required knowledge for final design purposes or 

construction verification. A significantly different level of effort and instrumentation is required 

if the goal of the load test program is simply to confirm the ultimate pile capacity or if detailed 

load-transfer information is desired for final design. The following items should be considered 

during the planning stage of the load test program so that the program provides the desired 

information. 

 

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1. The capacity of the loading apparatus (reaction system and jack) should be specified so 

that the test pile(s) may be loaded to plunging failure. A loading apparatus designed to 

load a pile to only twice the design load is usually insufficient to obtain plunging failure. 

Hence, the true factor of safety on the design load cannot be determined, and the full 

benefit from performing the static test is not realized. 

2. Specifications should require use of a load cell and spherical bearing plate as well as dial 

gages with sufficient travel to allow accurate measurements of load and movement at the 

pile head. Where possible, deformation measurements should also be made at the pile toe 

and at intermediate points to allow for an evaluation of shaft and toe bearing resistance. 

3. The load test program should be supervised by a person experienced in this field of work. 

4. A test pile installation record should be maintained with installation details appropriately 

noted. Too often, only the hammer model and driving resistance are recorded on a test pile 

log. Additional items such as hammer stroke (particularly at final driving), fuel setting, 

accurately determined final set, installation aids used and depths at which they are used, 

predrilling, driving times, stops for splicing, etc., should be recorded. 

5. Use of dynamic monitoring equipment on the load test pile is recommended for estimates 

of pile capacity at the time of driving, evaluation of drive system performance, calculation 

of driving stresses, and subsequent refinement of soil parameters for wave equation 

analysis. 

9.15.7 Compression Load Tests 

Deep foundations are most often tested in compression, but they can also be tested in tension or 

for lateral load capacity. Figure 9-62 illustrates the basic mechanism of performing a 

compression pile load test. This mechanism normally includes the following steps: 

1. The pile is loaded incrementally from the pile head according to some predetermined 

loading sequence, or it can be loaded at a continuous, constant rate. 

2. Measurements of load, time, and movement at the pile head and at various points along the 

pile shaft are recorded during the test. 

3. A load movement curve is plotted. 

 

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4. The failure load and the movement at the failure load are determined by one of several 

methods of interpretation. 

5. The movement is usually measured only at the pile head. However, the pile can be 

instrumented to determine movement anywhere along the pile. Telltales (solid rods 

protected by tubes) shown in Figure 9-62 or strain gages may be used to obtain this 

information. 

Figure 9-62. Basic mechanism of a compression pile load test (FHWA, 2006a). 

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9.15.7.1 Compression Test Equipment 

ASTM D1143 recommends several alternative systems for (1) applying compressive load to the 

pile, and (2) measuring movements. Most often, compressive loads are applied by hydraulically 

jacking against a beam that is anchored by piles or ground anchors, or by jacking against a 

weighted platform. A schematic of a typical compression load test setup is presented in Figure 

9-63. The primary means of measuring the load applied to the pile should be with a calibrated 

load cell. The jack load should also be recorded from a calibrated pressure gage, such as the 

Bourdon gage shown in Figure 9-63. To minimize eccentricities in the applied load, a spherical 

bearing plate should be included in the load application arrangement. 

Axial pile or shaft head movements are usually measured by dial gages or LVDT's that measure 

movement between the pile head and an independently supported reference beam. ASTM 

requires the dial gages or LVDT's have a minimum of 2 inches (50 mm) of travel and a precision 

of at least 0.01 inches (0.25 mm). It is preferable to have gages with a minimum travel of 3 

inches (75 mm) and with a precision of 0.001 inches (0.025 mm) particularly when testing long 

piles that may undergo large elastic deformations under load. A minimum of two dial gages or 

LVDT's mounted equidistant from the center of the pile and diametrically opposite to each other 

should be used. Two backup systems consisting of a scale, mirror, and wire system should be 

provided with a scale precision of 0.01 inches (0.25 mm). The backup systems should also be 

mounted on diametrically opposite pile faces. Both the reference beams and backup wire 

systems are to be independently supported with a clear distance of not less than 8 ft (2.5 m) 

between supports and the test pile. A remote backup system consisting of a survey level should 

also be used in case reference beams or wire systems are disturbed during the test. 

ASTM D 1143 specifies that the clear distance between a test pile and reaction piles be at least 5 

times the maximum diameter of the reaction pile or test pile, whichever has the greater diameter 

if not the same pile type, but not less than 7 ft (2 m). If a weighted platform is used, ASTM D 

1143 requires the clear distance between the cribbing supporting the weighted platform and the 

test pile exceed 5 ft (1.5 m). 

Photographs of the load application and movement monitoring components are presented in 

Figures 9-64 and 9-65. A typical compression load test arrangement using reaction piles is 

presented in Figure 9-66 and a weighted platform arrangement is shown in Figure 9-67. 

Additional details on load application as well as head load and movement measurements may be 

found in ASTM D1143 as well as in FHWA (1992c). 

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Figure 9-63. Typical arrangement for applying load in an axial compressive test (FHWA, 

1992c). 

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Reaction Beam 

Spherical Bearing 

Plates 

Load Cell 

Hydraulic Jack 

Strain Gage 

Readout Unit 

Jack Pressure Gage 

Jack Pump 

Figure 9-64. Load test load application and monitoring components (FHWA, 2006a). 

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LVDT 

Dial 

Gage 

Magnetic 

Base 

Smooth 

Surface 

Reference 

Beam 

Figure 9-65. Load test movement monitoring components (FHWA, 2006a). 

 

Figure 9-66. Typical compression load test arrangement with reaction piles (FHWA, 

2006a). 

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Figure 9-67. Typical compression load test arrangement using a weighted platform 

(FHWA, 2006a). 

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9.15.7.2 Recommended Compression Test Loading Method 

It is extremely important that standardized load testing procedures are followed. Several 

loading procedures are detailed in ASTM D 1143. The quick load test method is 

recommended. This method replaces traditional methods where each load increment was 

held for extended periods of time. The quick test method requires that load be applied in 

increments of 10 to 15% of the pile design load with a constant time interval of 22 minutes 

or as otherwise specified between load increments. Readings of time, load, and gross 

movement are to be recorded immediately before and after the addition of each load 

increment. This procedure is to continue until continuous jacking is required to maintain the 

test load or the capacity of the loading apparatus is reached, whichever occurs first. Upon 

reaching and holding the maximum load for 5 minutes, the pile is unloaded in four equal load 

decrements, each of which is held for 5 minutes. Readings of time, load, and gross 

movement are once again recorded immediately after, 22 minutes after, and 5 minutes after 

each load reduction, including the zero load. 

9.15.7.3 Presentation and Interpretation of Compression Test Results 

The results of load tests should be presented in a report conforming to the requirements of 

ASTM D 1143. A load-movement curve similar to the one shown in Figure 9-68 should be 

plotted for interpretation of test results. 

The literature abounds with different methods of defining the failure load from static load 

tests. Methods of interpretation based on maximum allowable gross movements, which do 

not take into account the elastic deformation of the pile shaft, are not recommended. These 

methods overestimate the allowable capacities of short piles and underestimate the allowable 

capacities of long piles. Methods that account for elastic deformation and are based on a 

specified failure criterion provide a better understanding of pile performance and provide 

more accurate results. 

AASHTO (2002) and FHWA (1992c) recommend pile compression test results be evaluated 

by using an offset limit method as proposed by Davisson (1972). The “double-tangent” is 

more commonly used for drilled shafts. These methods are shown in Figure 9-68 and are 

discussed in the following sections. 

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Load 

Load-settlement curve 

from load test 

Failure Load 

Parallel Line 

Elastic 

Compression 

Line, ∆=PL/AE 

Settlement 

0.15+b/120 

(a) 

Load 

Failure 

Load 

Tangent Lines 

Settlement 

Legend: 

(b) 

Figure 9-68. Presentation of typical static pile load-movement results, (a) Davisson’s 

method, (b) Double-tangent method. 

 

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9.15.7.4 Plotting the Failure Criteria 

Figure 9-68a shows the load-movement curve from a typical pile load test. To facilitate the 

interpretation of the test results, the scales for the loads and movements are selected so that 

the line representing the elastic deformation ∆ of the pile is inclined at an angle of about 20E

from the load axis. The elastic deformation ∆ is computed from: 

 

QL ∆ = 9-51

AE 

Where: ∆ = elastic deformation in inches (mm) 

Q = test load in kips (kN) 

L = pile length in inches (mm) 

A = cross sectional area of the pile in in2 (m2

) 

E = modulus of elasticity of the pile material in ksi (kPa) 

9.15.7.5 Determination of the Ultimate (Failure) Load 

For pile diameters less than 24 in (610 mm), the ultimate or failure load Qf of a pile is that 

load which produces a movement of the pile head equal to: 

 ⎛ b ⎞ In US Units sf = ∆ + ⎜0.15+ ⎟ 9-52 ⎝ 120 ⎠

 

 

where: sf = settlement at failure in inches 

b = pile diameter or width in inches 

∆ = elastic deformation of total pile length in inches 

A failure criterion line parallel to the elastic deformation line is plotted as shown in Figure 9­

68a. The point at which the observed load-movement curve intersects the failure criterion is 

by definition the failure load. If the load-movement curve does not intersect the failure 

criterion line, the pile has an ultimate capacity in excess of the maximum applied test load. 

For pile diameters greater than 24 in (610 mm), additional pile toe movement is necessary to 

develop the toe resistance. For pile diameters greater than 24 in (610 mm), the failure load 

can be defined as the load that produces at movement at the pile head equal to: 

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 ⎛ b ⎞ In US Units sf = ∆ + ⎜ ⎟ 9-53 ⎝ 30 ⎠

 

For drilled shafts, the failure load is commonly determined based on the “double-tangent” 

method shown in Figure 9-68b. Alternatively, the failure load is often defined as the test 

load corresponding to 5% of the shaft diameter because such a movement represents a large 

movement given that the drilled shafts are often much larger in diameter than driven piles. 

9.15.7.6 Determination of the Allowable Geotechnical Load 

The allowable geotechnical load is usually determined by dividing the ultimate load, Qu, by a 

suitable factor of safety. A factor of safety of 2.0 is recommended by AASHTO (2002) and 

is often used. However, larger factors of safety may be appropriate under the following 

conditions: 

a. Where soil conditions are highly variable. 

b. Where a limited number of load tests are specified. 

c. For friction piles in clay, where group settlement may control the allowable load. 

d. Where the total movement that can be tolerated by the structure is exceeded. 

e. For piles installed by means other than impact driving, such as vibratory driving or 

jetting. 

9.15.7.7 Load Transfer Evaluations 

FHWA (1992c) provides a method for evaluation of the soil resistance distribution from 

telltales embedded in a load test pile. The average load in the pile, Qavg, between two 

measuring points can be determined as follows: 

 1 - R2 Q	 = A E R 9-54 avg ∆ L 

Where: ∆L = length of pile between two measuring points under no load condition 

A = cross sectional area of the pile 

E = modulus of elasticity of the pile 

R1	 = deflection readings at upper of two measuring points 

R2	 = deflection readings at lower of two measuring points 

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If the R1 and R2 readings correspond to the pile head and the pile toe respectively, then an 

estimate of the shaft and toe resistances may be computed. For a pile with an assumed 

constant uniform soil resistance distribution, Fellenius (1990) states that an estimate of the 

toe resistance, Rt, can be computed from the applied pile head load, Qh by the following 

equation. 

R t =2 Qavg - Qh 9-55 

The applied pile head load, Qh, is chosen as close to the failure load as possible. For a pile 

with an assumed linearly increasing triangular soil resistance distribution, the estimated toe 

resistance may be calculated by using the following equation: 

R = 3 t Q avg h - 2 Q 9-56

The estimated shaft resistance can then be calculated from the applied pile head load minus 

the toe resistance. 

During driving, residual loads can be locked into a pile that does not completely rebound 

after a hammer blow, i.e., return to a condition of zero stress along its entire length. This 

mechanism is particularly true for flexible piles, piles with large frictional resistances, and 

piles with large toe quakes. Load transfer evaluations performed by using telltale 

measurements described above assume that no residual loads are locked in the pile during 

driving. Therefore, the load distribution calculated from the above equations would not 

include residual loads. If measuring points R1 and R2 correspond to the pile head and pile toe 

of a pile that has locked-in residual loads, the calculated average pile load would also include 

the residual loads. This inclusion of residual loads would result in a lower toe resistance 

being calculated than actually exists as depicted in Figure 9-69. Additional details on telltale 

load transfer evaluation, including residual load considerations, may be found in Fellenius 

(1990). 

When detailed load transfer data is desired, telltale measurements alone are insufficient since 

residual loads cannot be directly accounted for. Dunnicliff (1988) suggests that weldable 

vibrating wire strain gages be used on steel piles and sister bars with vibrating wire strain 

gages be embedded in concrete piles for detailed load transfer evaluations. A geotechnical 

instrumentation specialist should be used to select the appropriate instrumentation to 

withstand pile handling and installation, to determine the redundancy required in the 

instrumentation system, to determine the appropriate data acquisition system, and to reduce 

and report the data acquired from the instrumentation program. 

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Figure 9-69. Example of residual load effects on load transfer evaluation (FHWA, 

2006a). 

A sister bar vibrating wire strain gage for embedment in concrete or concrete filled pipe piles 

is shown in Figure 9-70 and an arc-weldable vibrating wire strain gage attached to a steel Hpile is presented in Figure 9-71. When detailed load-transfer data is desired, a data 

acquisition system should be used. 

Figure 9-70. Sister bar vibrating wire gages for concrete embedment (FHWA, 2006a). 

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Figure 9-71. Arc-weldable vibrating wire strain gage attached to H-pile. (Note: 

protective channel cover shown on left) (FHWA, 2006a). 

9.15.8 Other Compression Load Tests 

Two methods of load testing were introduced in recent years that have been used to varying 

degrees by highway agencies for testing drilled shafts. These methods are the Osterberg 

Cell® and the Statnamic® methods, both of which are proprietary methods. Both of these 

techniques can routinely be used for test loads in range of 10,000 to 15,000 kips. The 

Osterberg Cell® test can apply loads up to 50,000 kips. Both, driven piles and cast-in-place 

piles, e.g., drilled shafts, can be tested by these methods. Although the details of each 

method are beyond the scope of this manual, a brief description follows on each method. 

Additional details are presented in primary references for this chapter (FHWA, 2006a; 

FHWA, 1999). 

9.15.8.1 The Osterberg Cell® Method 

Instead of using a conventional jack, reaction frame and reaction anchor system, the axial 

loading test can be performed by applying the load with an expendable jack and load cell cast 

within the test shaft. This jack - load cell is called an Osterberg Cell® after its inventor, Jorj 

Osterberg and the test in which the Osterberg Cell® is used is commonly known as the OCell® test. A schematic of the O-Cell® test in comparison with a static load test with a 

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reaction frame is shown in Figure 9-72. Figure 9-73 shows some details for the O-Cell ® test. 

Figure 9-74 shows a photograph of an O-cell. Figure 9-75 shows a photograph of an O-Cell® 

assembly attached to a reinforcing cage just prior to the cage being placed into a drilled shaft 

excavation. 

Figure 9-72. Comparison of reaction mechanism between Osterberg Cell® and Static 

test. 

The principle of operation is very simple. The Osterberg Cell® consists essentially of two 

plates (pistons) of a prescribed diameter between which there is an expandable chamber that 

can hold pressurized fluid, usually oil or water. The upper and lower plates on the cell can be 

field welded to steel plates, usually at least 2 in (50 mm) thick, whose diameters are 

approximately equal to that of the test shaft. The chamber is pressurized by pumping from a 

reservoir on the ground surface. The unique feature of this device is that the pistons being 

pressurized have standard diameters that are approximately the full diameter of the cell, 

which may be up to 32 in (800 mm). Therefore, the pressurized fluid is acting on a very 

large area, unlike a conventional ram in which the area of the piston is usually small. This 

characteristic allows the Osterberg Cell® to apply very large loads with relatively low 

hydraulic pressures. Standard models with a diameter of 32 in (800 mm) are capable of 

applying loads of up to 3,000 tons (26.7 MN). Smaller sizes are also available from the 

supplier with consequently smaller capacities. The Osterberg Cell® is manufactured in a 

variety of sizes for both drilled shaft installations and driven pile installations as shown in 

Tables 9-12 and 9-13, respectively. 

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Figure 9-73. Some details of the O-Cell® test (after www.bridgebuildermagazine.com). 

Figure 9-74. Photograph of an O-Cell® . 

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O-cells® between 

two steel plates 

CSL tubes 

Cage 

Centralizers 

Instrumentation 

(strain gages) 

Figure 9-75. O-Cell® assembly attached to a reinforcing cage with other 

instrumentation. 

Table 9-12. Osterberg Cells® for drilled shafts 

Size Diameter 

Inches 

Height 

Inches 

Capacity 

Tons 

Weight 

Pounds 

5 5.25 5.18 75 32 

9 9.00 10.75 200 190 

13 13.00 11.65 400 300 

21 21.25 11.65 1,200 800 

26 26.25 11.65 1,800 1,230 

34 34.25 12.37 3,000 2,015 

Note: 1 in = 25.4 mm; 1 ton = 8.9 kN 

Table 9-13. Osterberg Cells® for driven piles 

Size – Inches Capacity – Tons Stroke - Inches Description of Pile 

14 200 6 Round-steel pipe 

14 300 6 Square-precast Concrete 

18 900 8 Round-steel pipe 

30 950 9 Square-precast Concrete 

Note: 1 in = 25.4 mm; 1 ton = 8.9 kN 

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The load being applied to the drilled shaft is usually monitored by measuring the pressure in 

the fluid being applied by the pump. The Osterberg Cell® will therefore need to be calibrated 

in a testing machine prior to installation to obtain a relationship between the measured 

pressure and the load applied by the cell. Ordinarily, a calibration is provided by the 

supplier. Note that in practice the hydraulic pressure will usually be measured at the ground 

surface, but the cell is situated at some distance below the ground surface, e.g., about 110 ft 

(33.5 m) for the Osterberg Cell® assembly shown in Figure 9-75. Therefore, the actual 

pressure at the level of the cell is the pressure that is measured plus the vertical distance from 

the pressure gauge to the middle of the cell times the unit weight of the cell fluid. This 

correction needs to be made before load versus movement is plotted. Movement can be 

measured at the top of the cell through telltales attached to the top of the cell that are 

monitored by movement sensors, e. g., dial gauges suspended from stable reference beams on 

the ground surface. Similarly, movement can be measured at the top of the test shaft by 

means of movement sensors suspended from stable reference beams. Movement of the 

bottom plate can be determined by measuring the movement of the top of the Osterberg Cell® 

with telltales and then measuring the relative movement between the upper and lower ends of 

the cell by means of sacrificial electronic movement sensors attached between the top and 

bottom plates. 

The O-Cell® test has some limitations in that the total failure load of the foundation element 

cannot usually be measured; only the failure load of the friction above the cell or the 

resistance below the cell are measured. 

The Osterberg Cell®

 has been used in a variety of soil and rock conditions. The cell has been 

used to determine the bond stress in rock sockets and in dense glacial tills. In addition, a 

variety of strain gage devices have been used in conjunction with the O-Cell®

 test to develop 

a distribution of resistance along the foundation element. Such measurements can also be 

obtained below an Osterberg Cell®

 installed at the mid-height of a shaft by extending 

instrumented rebar below the base of the cell. 

The cost of a single O-cell®

 test, including the Osterberg Cell® itself, instrumentation and 

shaft construction, is often in the range of 50 to 60 per cent of the cost of performing a 

conventional static load test for situations, such as shafts of small capacity, in which 

conventional static load tests can be used, although the percentage varies considerably from 

site to site. 

By using multiple Osterberg Cells® in a given shaft, it is possible to mobilize up to 25,000 

tons of combined side and base resistance. The O-Cell® test has not been standardized by 

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AASHTO or ASTM as of 2006. Additional information on the O-Cell® test can be found at 

www.loadtest.com. 

9.15.8.2 The Statnamic® Test Method 

The Statnamic®

 test method is a proprietary method developed by the Berminghammer 

Foundation Corporation (www.berminghammer.com). A new ASTM draft standard, entitled 

“Standard Test Method for Piles under Rapid Axial Compressive Load,” has been proposed 

but had not been approved as of 2006. 

A Statnamic® loading test also can be performed without the need for an expensive reaction 

system. An advantage of this type of test relative to the O-Cell® test is that it does not 

require the loading device to be cast into the shaft. Therefore, the Statnamic® loading test 

can be performed on a drilled shaft for which a loading test was not originally planned. 

The principle of the Statnamic® test is shown in Figure 9-76. Dead weights are placed upon 

the surface of the test shaft. Beneath the dead weights is a small volume of propellant and a 

load cell. The propellant is ignited and accelerates the masses upward. As this occurs a 

reaction force equal to the masses times their acceleration is produced against the head of the 

shaft, as indicated in Figure 9-76. This force, which increases with time up to one to two 

hundred milliseconds, causes the shaft to displace downward. As the ignition of the 

propellant stops, the reaction force rapidly decreases and the shaft rebounds. The 

displacement of the shaft head is measured by means of a laser beam from a source located 

some distance away from the test shaft. The laser beam is targeted on the shaft head. The 

load can be graphed against both time and displacement instantaneously. 

For reasons of safety the reaction masses are contained within a metal sheath that is also 

filled with an energy absorbing material, such as dry gravel, that will cushion the impact of 

the masses as they fall back upon the head of the drilled shaft. A photograph of a Statnamic® 

test arrangement, with the gravel-filled sheath surrounding the reaction masses is shown in 

Figure 9-77 just after igniting the propellant. 

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Figure 9-76. Schematic of Statnamic® test 

Figure 9-77. Photograph of Statnamic® test arrangement showing masses being 

accelerated inside gravel-filled sheath. 

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Since there are dynamic components to the resistance of the drilled shaft, some interpretation 

of the data is necessary, as illustrated in the bottom part of Figure 9-76. Since the load 

produced at the head of the shaft by igniting the propellant is applied much more slowly than 

the load applied by the blow of a pile-driving hammer, it can usually be assumed that the 

length of the stress wave that is imparted to the drilled shaft is much longer than the length of 

the shaft itself and that the shaft is therefore penetrating into the soil or rock as a rigid body. 

It may not be possible to make this simplifying assumption if the test shaft is extremely long. 

However, if rigid body motion is assumed, the load acting on the head of the shaft can be 

reasoned to be the sum of (1) the total static soil resistance (base and sides), (2) damping 

forces produced by the relative velocity between the shaft and the soil/rock, and (3) the mass 

of the drilled shaft itself times its acceleration. In the Statnamic® test, if the load 

corresponding to a zero slope on the load-settlement relation measured near the beginning of 

rebound, as illustrated in Figure 9-76, is selected as the analysis point, then component (2), 

above, will be zero, since the velocity of the shaft will be zero, and the total static resistance 

of the drilled shaft, RT, can be approximated by : 

⎛

⎜

⎜

⎝

⎞

⎟

⎟

⎠

as RT = Fso − Ws 

g 

9-57 

where, Fso = the force measured by the load cell at the point at which the slope of the 

rebound curve is zero, identified by the arrow in Figure 9-68 

Ws = total weight of the drilled shaft 

as = acceleration of the drilled shaft corresponding to Fso, which can be measured 

with an accelerometer at the head of the shaft 

g = acceleration of gravity. 

Note that as will not be zero despite the fact that the velocity of the test shaft is momentarily 

zero at Fso. If the test shaft is long, a stress wave analysis may be necessary to obtain an 

accurate estimate of resistance. 

Statnamic® devices have been constructed that are capable of applying head loads of up to 

approximately 3600 tons (32 MN). The cost of a Statnamic® test will usually be 

approximately the same as the cost of an O-Cell® test of the same magnitude. 

Further technical information on the Statnamic® test method can be found in the Proceedings 

of the First International Statnamic Seminar, Vancouver, British Columbia, 1995. Copies 

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can be obtained from Berminghammer Foundation Equipment Company, Wellington Street 

Marine Terminal, Hamilton, Ontario L8L 4Z9, Canada. The reader is also referred to FHWA 

(2006a) for further information on the load test interpretation. 

9.15.9 Limitations of Compression Load Tests 

Compression load tests can provide a wealth of information for design and construction of 

pile foundations and are the most accurate method of determining pile capacity. However, 

static load test results cannot be used to account for long-term settlement, downdrag from 

consolidating and settling soils, or to represent pile group action adequately. Other 

shortcomings of static load tests include cost, the time required to setup and complete a test, 

and the minimal information obtained on driving stresses or extent of potential pile damage. 

Static load test results can also be misleading on projects with highly variable soil conditions. 

9.15.10 Axial Tension and Lateral Load Tests 

Load tests can also be performed such that uplift and lateral loading conditions are simulated. 

Such load tests are described in FHWA (1999) and FHWA (2006a). 

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[THIS PAGE INTENTIONALLY BLANK] 
CHAPTER 10.0 

EARTH RETAINING STRUCTURES 

Earth retaining structures or systems are used to hold back earth and maintain a difference in 

the elevation of the ground surface as shown in Figure 10-1. The retaining wall is designed 

to withstand the forces exerted by the retained ground or “backfill” and other externally 

applied loads, and to transmit these forces safely to a foundation and/or to a portion of the 

restraining elements, if any, located beyond the failure surface. 

Figure 10-1. Schematic of a retaining wall and common terminology. 

In general, the cost of constructing a retaining wall is usually high compared with the cost of 

forming a new slope. Therefore, the need for a retaining wall should be assessed carefully 

during preliminary design and an effort should be made to keep the retained height as low as 

possible. 

In highway construction, retaining walls are used along cuts or fills where space is 

inadequate for construction of cut slopes or embankment slopes. Bridge abutments and 

foundation walls, which must support earth fills, are also designed as retaining walls. 

Typical applications for earth retaining structures in highway construction include: 

• new or widened highways in developed areas; 

• new or widened highways at mountain or steep slopes; 

• grade separation; 

• bridge abutments, wing walls and approach embankments; 

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• culvert walls; 

• tunnel portals and approaches; 

• flood walls, bulkheads and waterfront structures; 

• cofferdams for construction of bridge foundations; 

• stabilization of new or existing slopes and protection against rockfalls; and 

• groundwater cut-off barriers for excavations or depressed roadways. 

Figure 10-2 provides schematic illustrations of several retaining wall systems traditionally 

used in highway applications. A great number of wall systems have been developed in the 

past two decades by specialty contractors who have been promoting either a special product 

or a specialized method of construction, or both. Due to the rapid development of these 

diversified systems and their many benefits, the design engineer is now faced with the 

difficult task of having to select the best possible system; design the structure; and ensure its 

proper construction. 

An important breakthrough in the design of earth retaining structures (ERS) that occurred in 

this era was the recognition that the earth pressure acting on a wall is a function of the type of 

wall and the amount and distribution of wall movement. Classical earth pressure theories, 

which were developed by Coulomb (1776) and Rankine (1857), were formalized for use by 

Caquot and Kerisel (1948) and others. Sophisticated analyses of soil-structure interaction 

and wall/soil movements began in the 1960s with the development of finite difference and 

finite element analytical procedures. The simultaneous advancement of geotechnical 

instrumentation equipment and monitoring procedures made the “observational method” of 

design (Peck, 1969) popular and cost effective. 

Since 1970 there has been a dramatic growth in the number of methods and products for 

retaining soil. O’Rourke and Jones (1990) describe two trends in particular that have 

emerged since 1970. First, there has been an increasing use of reinforcing elements, either 

by incremental burial to create reinforced soils (MSE walls), or by systematic in situ 

installation to reinforce natural soils or even existing fills (soil nailing); see Figure 10-2b. 

Mechanically stabilized earth and soil nailing have changed the ways we construct fill or cut 

walls, respectively, by providing economically attractive alternatives to traditional designs 

and construction methods. Second, there has been an increasing use of polymeric products to 

reinforce the soil and control drainage. Rapid developments in polymer manufacturing have 

supplied a wide array of geosynthetic materials. The use of these products in construction 

has encouraged a multitude of different earth retention schemes. 

The rapid development of these new trends and the increased awareness of the impact of 

construction on the environment, have led to the emergence of the concept of “earth walls.” 

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In this concept, the soil supports itself or is incorporated into the structure and assumes a 

major structural or load carrying function. With this concept, structural member 

requirements of the system are reduced, or eliminated altogether. Examples of recently 

developed earth walls include the soil-reinforcement systems discussed above, as well as 

systems involving chemical treatment of the in-situ soil such as jet grouting or deep soil 

mixing. 

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(a) Externally Stabilized Systems 

(b) Internally Stabilized Systems 

Figure 10-2. Variety of retaining walls (after O’Rourke and Jones, 1990) 
10.01 Primary References: 

The two primary references for earth retaining structures are: 

FHWA (2005b). Earth Retaining Structures - DRAFT. Report No. FHWA-SA-05-046, 

Authors: Tanyu, B.F., Sabatini, P.J. and Berg, R.R., Federal Highway Administration, U.S. 

Department of Transportation. 

AASHTO (2004 with 2006 Interims). AASHTO LRFD Bridge Design Specifications, 3rd 

Edition, American Association of State Highway and Transportation Officials, Washington, 

D.C. 

10.1 CLASSIFICATION OF EARTH RETAINING STRUCTURES 

Earth retaining systems may be classified according to: 

• load support mechanism, i.e., externally or internally stabilized walls; 

• construction method, i.e., fill or cut walls; and 

• system rigidity, i.e., rigid or flexible walls. 

Every retaining wall can now be classified by using these three factors. For example, a 

sheet-pile wall would be classified as an externally-stabilized cut wall that is relatively 

flexible. A mechanically stabilized earth (MSE) wall is an internally stabilized fill wall that 

is relatively flexible. Further description of these classifications is provided subsequently. 

10.1.1 Classification by Load Support Mechanism 

The stability component of walls can be organized according to two principal categories: 

externally and internally stabilized systems (O’Rourke and Jones, 1990) as shown in Figure 

10-3. An externally stabilized system uses an external structural wall against which 

stabilizing forces are mobilized. An internally stabilized system involves reinforcements 

installed within the retained soil mass and extending beyond the potential failure plane. 

Hybrid systems combine elements of both internally and externally supported walls. 

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Figure 10-3. Classification of earth retaining systems (after O’Rourke and Jones, 1990)

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Virtually all traditional types of walls may be regarded as externally stabilized systems 

(Refer to Figure 10-2a). Gravity walls, in the form of cantilever structures or gravity 

elements (e.g., bins, cribs and gabions), support the soil and, through their weight and 

stiffness, resist sliding, overturning, and shear. Bracing systems, such as cross-lot struts and 

rakers, provide temporary support for in situ structural and chemically stabilized walls. 

Ground anchors provide support through their pullout capacity in stable soils outside of the 

zone of potential failure. 

It is in the area of internally stabilized systems that relatively new concepts have been 

introduced (Refer to Figure 10-2b). Shear transfer to mobilize the tensile capacity of closely 

spaced reinforcing elements embedded in the retained soil mass has enabled retaining 

structures to be constructed without an external structural wall element. The shear transfer 

mechanism allows a composite system of reinforcing elements and soil to serve as the 

primary structural entity. A facing is required on an internally stabilized system, however, its 

purpose is to prevent raveling and deterioration rather than to provide primary structural 

support. 

10.1.2 Classification by Construction Method 

Earth retaining structures (ERS) can also be classified according to the method required for 

their construction, i.e., fill construction or cut construction. Fill wall construction refers to a 

wall system in which the wall is constructed from the base of the wall up to the top, i.e., 

“bottom-up” construction. Cut wall construction refers to a wall system in which the wall is 

constructed from the top of the wall down to the base concurrent with excavation operations, 

i.e., “top-down” construction. The classification of each wall system according to its 

construction method is also presented in Figure 10-3. 

It is important to recognize that the “cut” and “fill” designations refer to how the wall is 

constructed, not necessarily the nature of the earthwork associated with the project. For 

example, a prefabricated modular gravity wall, which may be used to retain earth for a major 

highway cut, is considered a fill wall because its construction is not complete until the 

backfill has been placed from the “bottom-up” after the excavation for the cut has reached its 

final grade. 

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10.1.3 Classification by System Rigidity 

The rigidity or flexibility of a wall system is fundamental to the understanding of the 

development of earth pressures, discussed in Section 10.2. In simple terms, a wall is 

considered to be rigid if it moves as a unit in rigid body rotation and/or translation and does 

not experience bending deformations. Most gravity walls can be considered rigid walls. 

Flexible walls are those that undergo bending deformations in addition to rigid body motion. 

Such deformations result in a redistribution of lateral pressures from the more flexible to the 

stiffer portions of the system. Virtually all wall systems, except gravity walls, may be 

considered to be flexible. 

10.1.4 Temporary and Permanent Wall Applications 

Permanent wall systems are generally considered to have a service life of 75 to 100 years. 

However, the ERS listed in Figure 10-3 are technically feasible for both temporary and 

permanent applications. In most cases, however, certain systems may not be cost-effective 

for temporary applications. Temporary walls generally have less restrictive requirements on 

material durability, design factors of safety, performance, and overall appearance than do 

permanent walls. Also, walls that can be constructed rapidly are often used for temporary 

applications. For example, MSE walls with segmental, precast facings are not typically used 

for temporary applications since the cost of the facing components and the select backfill 

may be more than 50 percent of the total cost of the wall. 

The service life of temporary earth support systems is based on the time required to support 

the ground while the permanent systems are installed. This document has adopted the 

AASHTO guidance which considers temporary systems to be those that are removed upon 

completion of the permanent systems. The time period for temporary systems is commonly 

stated to be 18 to 36 months, but may be shorter or longer based on actual project conditions. 

Temporary systems may be divided into “support of excavation” (SOE) temporary systems 

and “critical” temporary systems. In general the owner will determine which temporary 

systems are to be designated as critical. That decision is often based on the owner’s need to 

restrict lateral movement of the support system to minimize ground movements behind the 

support system. In general, specific components or design features for temporary systems 

may be designed to the same or similar criteria as used for permanent systems. Conversely, 

SOE systems are commonly designed to less restrictive criteria than permanent systems. The 

owner commonly assigns the responsibility for design and performance of SOE systems to 

the contractor. The design of SOE systems is often based more on system stability than on 

minimizing ground movements. 

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10.1.5 Wall Selection Considerations 

Given the wide variety of retaining walls as shown in Figure 10-3, it is important to select a 

wall that is most economical for the application being considered. The wall selection process 

should include consideration of various factors such as (1) ground type, (2) groundwater, (3) 

construction considerations, (4) speed of construction, (5) right of way, (6) aesthetics, (7) 

environmental concerns, (8) durability and maintenance, (9) tradition and (10) local 

contracting practices. A detailed discussion of these wall selection factors is outside the 

scope of this manual. The reader is referred to FHWA (2005b) where a systematic wall 

selection process considering these factors is described. 

10.2 LATERAL EARTH PRESSURES 

Some of the basic concepts of lateral earth and water pressures were discussed in Chapter 2. 

It is recommended that the reader should review Section 2.9 before proceeding further in this 

Chapter. Here the principles of lateral earth pressure are explained on the basis of 

deformation. A total lateral pressure diagram consistent with the assumed deformations is 

developed for use in assessing the forces acting on the wall from the backfill or retained 

ground. This section focuses primarily on theoretical earth pressure diagrams, which are 

most commonly used in the design of rigid gravity structures, nongravity cantilevered walls, 

MSE walls, and anchored walls with stiff structural facings such as diaphragm walls. 

A wall system is designed to resist lateral earth pressures and water pressures that develop 

behind the wall. Earth pressures develop primarily as a result of loads induced by the weight 

of the backfill and/or retained in-situ soil, earthquake ground motions, and various surcharge 

loads. For purposes of earth retaining system design, three different types of lateral earth 

pressure are usually considered: (1) at-rest earth pressure; (2) active earth pressure; and (3) 

passive earth pressure. These conditions are shown in Figure 10-4 relative to lateral 

deformation of the walls. The conditions are defined as follows: 

•	 At-rest earth pressure is defined as the lateral earth pressure that exists in level ground 

for a condition of no lateral deformation. 

•	 Active earth pressure is developed as the wall moves away from the backfill or the 

retained soil. This movement results in a decrease in lateral pressure relative to the 

at-rest condition. A relatively small amount of lateral movement is necessary to reach 

the active condition. 

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Figure 10-4. Effect of wall movement on wall pressures (after Canadian Geotechnical 

Society, 1992). 

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•	 Passive earth pressure is developed as the wall moves towards the backfill or the 

retained soil. This movement results in an increase in lateral pressure relative to the 

at-rest condition. The movements required to reach the passive condition are 

approximately ten times greater than those required to develop active earth pressure. 

Each of these earth pressure conditions can be expressed in general form by: 

ph = Kpo	 10-1 

where ph is the lateral earth pressure at a given depth behind the wall, po, is the vertical stress 

at the same depth, and K is the earth pressure coefficient that has a value related to the at-rest 

condition (Ko), active conditions of movement, (Ka), or passive conditions of movement, 

(Kp). 

As shown in Figure 10-4, the magnitudes of these earth pressure coefficients follow the 

relationship of Kp > Ko > Ka. The relationship between the magnitude of retaining wall 

movement, in this case rotation, Y/H, into or away from the retained material about its toe, 

and the horizontal pressure exerted by the soil is presented in Figure 10-4, with angular 

movement along the x axis and the mobilized coefficient of lateral earth pressure on the y 

axis. Figure 10-4 can also be used to estimate the state of stress for walls with uniform 

horizontal translation equal to Y. As illustrated in this figure, significantly larger lateral 

displacements are required to mobilize the passive resistance than those required to develop 

active pressures. The maximum values of Ka and Kp correspond to fully mobilized pressures 

that represent active and passive failure conditions, respectively. 

When the estimated wall movement is less than the value required to fully mobilize 

active or passive pressure, the earth pressure coefficient can be adjusted proportionally 

based on the graphical relationship presented in Figure 10-4. 

10.2.1 At-Rest Lateral Earth Pressure 

The at-rest earth pressure represents the lateral effective stress that exists in a natural soil in 

its undisturbed state. For cut walls constructed in near normally consolidated soils, the atrest earth pressure coefficient, Ko, can be approximated by the equation (Jaky, 1944): 

Ko = 1 − sin φ′	 10-2 

where φ′ is the effective (drained) friction angle of the soil. The magnitude of the at-rest 

earth pressure coefficient is primarily a function of soil shear strength and degree of 

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overconsolidation, which, as indicated in Chapter 7, may result from natural geologic 

processes for retained natural ground or from compaction effects for backfill soils. 

In overconsolidated soils, Ko can be estimated as (Schmidt, 1966): 

Ko = (1 − sin φ′)(OCR)Ω 10-3 

where Ω is a dimensionless coefficient, which, for most soils, can be taken as sin φ′ (Mayne 

and Kulhawy, 1982) and OCR is the overconsolidation ratio. 

Usually, Equations 10-2 and 10-3 for the at-rest earth pressure coefficient are sufficiently 

accurate for normally to lightly overconsolidated soils provided the overconsolidation ratio 

has been evaluated from laboratory consolidation testing. For moderately to heavily 

overconsolidated clays, or where a more accurate assessment is required, laboratory triaxial 

tests on undisturbed samples and in-situ testing such as pressuremeter testing may be used. 

For normally consolidated clay, Ko is typically in the range of 0.55 to 0.65; for sands, the 

typical range is 0.4 to 0.5. For lightly overconsolidated clays (OCR ≤ 4), Ko may reach a 

value up to 1; for heavily overconsolidated clays (OCR > 4), Ko values may be greater than 2 

(Brooker and Ireland, 1965). For heavily overconsolidated soils, values for Ko can be very 

large. A relatively stiff wall would be required to resist the large forces resulting from the 

lateral earth pressures in this case. For walls constructed in such soils, consideration should 

be given to performing pressuremeter tests, which provide a direct measure of lateral 

pressures in the ground. 

In the context of wall designs consisting of steel soldier beams or sheet-pile wall elements, 

design earth pressures based on at-rest conditions are not typically used since at-rest earth 

pressures imply that the wall system undergoes no lateral deformation. This condition may 

be appropriate for heavily preloaded, stiff wall systems, but designing to a requirement of 

zero wall movement for flexible wall systems is not practical. 

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10.2.2 Active and Passive Lateral Earth Pressures 

As discussed in Chapter 2, in stability analyses active and passive earth pressures are 

developed as a result of soil displacement within a failure zones developed behind the wall 

(active) or in front of the wall (passive) assuming that the wall displaces outward. For the 

purpose of illustration Figure 10-5 shows the two conditions with respect to wall movement 

relative to the backfill only. In one case the wall moves away from the backfill (active case) 

in the other case the wall moves into the backfill (passive case) As shown in the figure, the 

failure zone for both cases is typically bounded by the back face of the wall and a failure 

surface through the retained soil mass along which the soil has attained limiting equilibrium. 

In addition to the effect of lateral movements on the values of Ka and Kp shown in Figure 10­

4, the magnitude of the active and passive earth pressure coefficients are functions of the soil 

shear strength, the backfill geometry, i.e., horizontal backfill surface or sloping ground 

surface above the wall, the orientation of the surface where the wall contacts the backfill or 

retained soil, i.e., vertical or inclined, and the friction and cohesive forces that develop on 

this surface as the wall moves relative to the retained ground. 

Active and passive earth pressure coefficients based on a plane wedge theory, which 

considers the effect of wall friction, sloping backfill and sloping wall face, was first proposed 

by Coulomb (1776) and are shown in Figure 10-5. The pressures calculated by using these 

coefficients are commonly known as the Coulomb earth pressures. Since Coulomb’s method 

is based on limit equilibrium of a wedge of soil, only the magnitude and direction of the earth 

pressure is found. Pressure distributions and the location of the resultant are assumed to be 

triangular. 

For simple cases involving vertical walls retaining homogeneous soil with a level ground 

surface, without friction between the soil and the wall face, and without the presence of 

groundwater, the formulas for computing the earth pressure coefficients can be simplified 

considerably by substituting, δ = θ = β = 0 in Coulomb’s equations, as shown in Figure 10-5. 

For such simplified cases, Ka and Kp can be expressed by Equations 10-4 and 10-5, 

respectively: 

1 − sin φ′ 2 K a = = tan (45 − φ′ 2) 10-4 1 + sin φ′

1 + sin φ′ 2 K p = = tan (45+ φ′/ 2 ) 10-5 1 − sin φ′

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Wall Movement 

Wall Movement 

γ, φ

γ, φ

Figure 10-5. Coulomb coefficients Ka and Kp for sloping wall with wall friction and 

sloping cohesionless backfill (after NAVFAC, 1986b). 

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These simplified equations were also derived independently by Rankine (1857). Hence, the 

earth pressures computed by using these equations are commonly known as the Rankine 

earth pressures. 

For a cohesionless soil with a groundwater table, the effective lateral earth pressure acting on 

the wall at any depth, z, below the surface is a function of the pore water pressure u as 

follows, 

pa ′ = Ka (γz - u) 10-6 

pp′ = Kp (γz - u) 10-7 

10.2.3 Effect of Cohesion on Lateral Earth Pressures 

For a cohesive soil defined by effective stress strength parameters φ′ and c′, the active and 

passive earth pressure coefficients are: 

 

′ 2 2c 2 Ka = tan (45 − φ′/ 2) − tan (45 − φ′/ 2) 10-8 

p′

o 

2 2c′ 2 Kp = tan (45 + φ′/ 2) + tan (45 + φ′/ 2) 10-9 

p′

o 

Figure 10-6(a) presents active and passive pressure distributions for cohesionless soils (c' = 

0) while Figure 10-6(b) shows similar pressure distributions for c'-φ' soils. 

For a c'-φ' soil with a groundwater table, the effective lateral earth pressure acting on the wall 

at any depth, z, below the surface is, 

pa ′ = Ka (γz - u) - 2c′ Ka 10-10 

pp′ = Kp (γz - u) + 2c′ Kp 10-11 

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2c′√Ka 

z 

p′

p p′

u a u u p′

p p′

a

u

2c′√Kp

z

z

u p′

p p′

a 

u 

2c′√Kp 

z 

z z

(a) (b) 

Figure 10-6. (a) Wall pressures for a cohesionless soil, and (b) Wall pressures for soil 

with a cohesion intercept – with groundwater in both cases (after Padfield and Mair, 

1984) 

Theoretically, in soils with cohesion, the active earth pressure behind the wall becomes 

negative from the ground surface to a critical depth z where γz is less than 2c′ K . a This

critical depth is referred to as the “tension crack.” The active earth pressure acting against 

the wall within the depth of the tension crack is assumed to be zero. Unless positive drainage 

measures are provided, water infiltration into the tension crack may result in hydrostatic 

pressure on the retaining structure. 

Use of values of c′ for the retained soil, greater than say, 100 psf (5 kPa), results in a 

significant depth of theoretical negative active earth pressure. Therefore, it is important 

either to: 

•	 reduce c′ towards the surface, which may be realistic for many clays in view of 

weathering; 

or 

•	 assume that the effective pressure on the wall at any depth should not be less than 30z 

psf where z = depth in ft (5z kN/m2

 (z = depth in m). 

In all cases where water is present in the soil, full hydrostatic pressure is added to the 

lateral earth pressure computed by Equations 10-8 to 10-11 to obtain the total lateral 

pressure that will be experienced by a retaining wall. 

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Active wedge1

Passive wedge

 

Wall Movement

1 Active Wedge2 

2 Passive Wedge3 

Note: (1) Assume wall moves as a rigid body to the left. 

(2) Active wedge moves downward relative to wall 

(3) Passive wedge moves upward relative to wall. 

Figure 10-7. Wall friction on soil wedges (after Padfield and Mair, 1984) 

10.2.4 Effect of Wall Friction and Wall Adhesion on Lateral Earth Pressures 

In practice, walls are not smooth. As indicated previously, wall friction and wall adhesion 

modify the stress distribution near a wall. Therefore, wall friction, δ, and wall adhesion, cw, 

should both be considered as proportions of φ′, and c′ or su, respectively. For a rigid wall 

moving away from the retained soil, the frictional forces exerted by the wall on the soil are in 

the sense shown in Figure 10-7. The active wedge moves down with respect to the wall, 

while the passive wedge moves upwards. 

An important exception to this mechanism is when the wall acts as a significant load-bearing 

element, when large vertical loads are applied to the top of the wall, or when an inclined 

ground anchor is stressed to an appreciable load and the vertical component of the load acts 

downward. In such cases, the wall has to move down relative to the soil on both sides of the 

wall in order to mobilize the required skin friction to support the load. Therefore, the friction 

acts to increase the pressures on both the active and passive sides, because it acts on the soil 

wedges in a downward direction. This effect, however, is neglected because limiting or 

failure conditions are considered in calculation of overall stability and the directions in which 

the frictional forces act should be taken as shown in Figure 10-7. 

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Wall friction, δ, and wall adhesion, cw, have an important effect on soil pressures. Equations 

10-10 and 10-11 can be written to account for those effects in a more general as follows: 

pa ′ = Ka(γz - u) - Kacc′ 10-12 

pp′ = Kp(γz - u) + Kpcc′ 10-13 

where Ka and Kp depend on δ and Kac and Kpc depend on δ and cw, and pa ′ and pp′ are the 

components of effective pressure normal to the wall. Where c′ is incorporated into the soil 

strength characterization, approximate values of Kac and Kpc should be calculated from the 

following expressions: 

wa )c/c1(K2K ac += ′ 10-12a 

wp )c/c1(K2K pc += ′ 10-13a 

Different values of δ are given by several sources. As shown in Table 10-1, values of δ

depend on soil type and the wall material. The maximum wall friction suggested for design 

is: 

Active: δ = 2/3 φ′

Passive: δ = 1/2 φ′

Where a cohesion intercept is used as part of the characterization of strength in terms of 

effective stress, a maximum wall adhesion of cw = 0.5c′ could be used, but in view of the 

inevitable remolding of the clay close to the wall by any construction process, it is 

recommended that no wall adhesion be allowed in the design. 

The values of wall friction provided above and in Table 10-1 are maximum values for design. 

These values can be adopted in most cases, but the design engineer should consider any 

circumstances where the values might be affected by the relative movement of the soil and 

the wall. For example, on the active side, reduced values should be used if there is a 

tendency for the wall to move downwards, e.g., for load-bearing walls or walls supported by 

prestressed ground anchors. For walls retaining soft cohesive soils or granular soils that will 

be subjected to significant vibration, e.g., walls near railway tracks or machine foundations, δ

should be assumed to be zero in the design. 

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Table 10-1 

Wall friction and adhesion for dissimilar materials (after NAVFAC, 1986b) 

Interface Materials Friction 

Factor, tan o 

Friction 

angle, o de~rees 

Mass concrete on the following foundation materials: 

Clean sound rock 0.70 35 

Clean gravel, gravel sand mixtures, coarse sand 0.55 to 0.60 29 to 31 

Clean fine to medium sand, silty medium to coarse sand, silty or clayey gravel 0.45 to 0.55 24 to 29 

Clean fine sand, silty or clayey fme to medium sand 0.35 to 0.45 19 to 24 

Fine sandy silt, nonplastic silt 0.30 to 0.35 17 to 19 

Very stiff and hard residual or preconsolidated clay 0.40 to 0.50 22 to 26 

Medium stiff and stiff clay and silty clay (Masonry on foundation 

materials has same friction factor) 

0.30 to 0.35 17 to 19 

Steel sheet piles against the following soils: 

Clean gravel, gravel-sand mixtures, well-graded rock fill with spalls 0.40 22 

Clean sand, silty sand-gravel mixtures, single size hard rock fill 0.30 17 

Silty sand, gravel or sand mixed with silt or clay 0.25 14 

Fine sandy silt, nonplastic silt 0.20 11 

Formed concrete or concrete sheet piling against the following soils: 

Clean gravel, gravel-sand mixture, well-graded rock fill with spalls 0.40 to 0.50 22 to 26 

Clean sand, silty sand-gravel mixture, single size hard rock fill 0.30 to 0.40 17 to 22 

Silty sand, gravel or sand mixed with silt or clay 0.30 17 

Fine sandy silt, nonplastic silt 0.25 14 

Various structural materials: 

Masonry on masonry, igneous and metamorphic rocks: 

Dressed soft rock on dressed soft rock 0.70 35 

Dressed hard rock on dressed soft rock 0.65 33 

Dressed hard rock on dressed hard rock 0.55 29 

Masonry on wood (cross grain) 0.50 26 

Steel on steel at sheet pile interlocks 0.30 17 

Interface Materials (Cohesion) Adhesion c. (kPa) 

Very soft cohesive soil (0- 12 kPa) 0- 12 

Soft cohesive soil (12- 24 kPa) 12-24 

Medium stiff cohesive soil (24 - 48 kPa) 24-36 

Stiff cohesive soil (48- 96 kPa) 36-45 

Very stiff cohesive soil (96- 192 kPa) 45-62 

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The effect of wall friction on the Rankine and Coulomb methods of earth pressure 

computation is as follows: 

1. The Rankine method cannot take account of wall friction. Accordingly, Ka is 

overestimated slightly and Kp is under-estimated, thereby making the Rankine 

method conservative for most applications. 

2. The Coulomb theory can take account of wall friction, but the results are unreliable 

for passive earth pressures for wall friction angle values greater than φ′/3 because the 

failure surface is assumed to be a plane. The failure wedges assumed in the Coulomb 

analysis take the form of straight lines as shown in Figure 10-8. This may be 

contrasted with the curved shapes of failure surface observed in model tests. The 

curvature results from the disturbing influence of wall friction on the stress field near 

the wall. The error in the Coulomb solutions results in Ka being underestimated 

slightly and Kp being overestimated very significantly for large values of φ′. 

If the angle of wall friction δ is small, the failure surface is almost linear. For large values of 

δ, the failure surface is curved and can be approximated by a log-spiral. The deviation of the 

curved surface from a planar surface is minor for the active case but significant for the 

passive case as shown in Figure 10-8. For most applications, the effect of wall friction on 

active earth pressures is relatively small and is often neglected. 

For the passive case, however, large values of δ cause downward tangential shear forces to 

act on the passive wedge of soil adjacent to the wall, increasing its resistance to upward 

movement. This increased resistance to upward movement causes a curved failure surface to 

occur in the soil, as shown in Figure 10-8b. The soil fails on this curved surface of least 

resistance and not on the Coulomb plane, which would require greater lateral driving force. 

Hence, passive pressures computed on the basis of the plane wedge theory are always greater 

than those calculated on the basis of a log-spiral failure surface and may be on the unsafe 

side since passive earth pressure forces are generally resisting forces in stability analyses. 

Based on the above discussions, it is recommended that the log-spiral theory be used for the 

determination of the passive earth pressure coefficients. Charts for two common wall 

configurations, sloping wall with level backfill and vertical wall with sloping backfill based 

on the log-spiral theory are presented in Figures 10-9 and 10-10 (Caquot and Kerisel, 1948; 

NAVFAC, 1986b). For walls that have a sloping backface and sloping backfill, the passive 

earth pressure coefficient can be calculated as indicated in Figure 10-5 by using δ= φ′/3. 

FHWA NHI-06-089 10 – Earth Retaining Structures 

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Analysis 

“Actual” Failure Surface 

Failure Surface by Coulomb 

(a) Active Case (φ′ = 30°, δ = 30°) 

(b) Passive Case (φ′ = 30°, δ = 30°) 

Figure 10-8. Comparison of plane and log-spiral failure surfaces (a) Active case and (b) 

Passive case (after Sokolovski, 1954) – Note: Depiction of gravity wall is for illustration 

purpose only. 

 

For the active case, the resultant load predicted by using coefficients based on the plane 

wedge theory is within 10 percent of that obtained with the more exact log-spiral theory. 

Hence, for the active case, Coulomb’s theory can be used to calculate the earth pressure 

coefficient (Refer to Figure 10-5). 

For some wall types, such as cantilever retaining walls and an MSE walls, the “interface” 

where the earth pressures are computed is within the retained soils along a vertical plane 

passing through the heel of the base slab. In such cases, there is soil-to-soil contact and the 

resultant may be oriented at the angle of mobilized friction. The angle of mobilized friction 

depends on the factor of safety used for the angle of internal friction. For these cases, it is 

generally conservative to assume that the earth pressure is parallel to the slope of the backfill. 

FHWA NHI-06-089 10 – Earth Retaining Structures 

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Figure 10-9. Passive coefficients for sloping wall with wall friction and horizontal 

backfill (Caquot and Kerisel, 1948; NAVFAC, 1986b). 

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Figure 10-10: Passive coefficients for vertical wall with wall friction and sloping backfill 

(Caquot and Kerisel, 1948; NAVFAC, 1986b). 

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10.2.5 Theoretical Lateral Earth Pressures in Stratified Soils 

For stratified or non-homogeneous soils, the theoretical earth pressures are assumed to be 

distributed as shown in Figure 10-11 where the discontinuities in the earth pressure diagram 

occur at the boundary between soil strata having different unit weights and shear strength 

parameters. Unless the computed earth pressures vary widely with depth, the total applied 

lateral force determined from the computed pressure diagram may be redistributed to a 

corresponding simplified equivalent triangular pressure diagram as indicated in Figure 10-11. 

For complex cases such as layered soils, irregular backfill, irregular surcharges, wall friction, 

and sloping groundwater level, pressures can be determined by graphical solutions. Among 

the many graphical solutions are Culmann’s method (1866) and the Trial Wedge method. 

These procedures can be found in Bowles (1996) or NAVFAC (1986b). The Trial Wedge 

method has the advantage of including cohesion as a soil parameter in the analysis. 

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B′

CB′DE 

•	 Use buoyant unit weight for soils below water table. 

•	 Add water pressure as appropriate to obtain total lateral pressure. 

•	 The simplified distribution may not be justified for all soil conditions. Use judgment to 

determine validity of such simplified distributions. 

Figure 10-11. Pressure distribution for stratified soils. 
10.2.6 Semi Empirical Lateral Earth Pressure Diagrams 

The earth pressure distributions discussed in the previous sections are strictly applicable to 

rigid wall systems, i.e., walls that translate and/or rotate as a unit and do not experience 

bending deformations. Most gravity walls can be considered rigid walls. 

If a wall system undergoes bending deformations in addition to rigid body motion then such 

a wall system is considered flexible. Virtually all wall systems, except gravity walls, may be 

considered to be flexible. The bending deformations result in a redistribution of the lateral 

pressures from the more flexible to the stiffer portions of the system. Thus, in these walls the 

final distribution and magnitude of the lateral earth pressure may be considerably different 

from those used for rigid walls. For example, soldier-pile and lagging walls with multiple 

levels of support are usually designed by using empirical earth pressure distributions based 

on observed data. The shape of these empirical earth pressure distributions may vary from 

rectangular to trapezoidal. The magnitude of the pressures may also vary depending on the 

soil type. 

Other factors that may influence the development of earth pressures are the type of 

construction, e.g., “bottom-up” or “top-down,” the wall support mechanism, e.g., tie-backs, 

struts, rakers, soil nails, reinforcing elements, single or multiple levels of support, etc., the 

geometry of the retained soil, e.g., silo pressure, the superimposed or surcharge loads, e.g., 

strip, line, concentrated, or equipment loads, and the type of analysis, e.g., static or seismic. 

In addition, for cases of soil reinforced by inclusions such as MSE walls or soil-nailed walls, 

different types of earth pressure distributions are used to evaluate the internal and external 

stability of the wall system. The empirical earth pressure distributions are generally related 

to the basic earth pressure coefficients Ka, Kp and Ko, which, as indicated previously, are a 

function of the shear strength of the soil. 

10.2.7 Lateral Earth Pressures in Cohesive Backfills 

Most DOTs involved in the design and procurement of fill wall systems, such as MSE walls, 

have well-defined backfill material requirements. In general, specifications for wall backfill 

require high-quality, granular, relatively free-draining backfills. However, in some cases a 

poorer quality on-site backfill material may be used, especially for temporary systems. 

These poorer quality backfills are generally more fine-grained and not free-draining. 

Methods to calculate earth pressures in clayey soils were described previously. In this 

section cautions are provided regarding the use of fine-grained cohesive backfill soils. 

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Lateral pressures can be caused by the volume expansion of ice in fine-grained soils such as 

fine sand, silt and clay. Lateral pressures due to volume expansion of the retained soil may 

achieve relatively high values that are difficult to predict. Since structures are usually not 

designed to withstand frost-generated stresses, provisions should be made so that frostrelated stresses will not develop behind the structure or be kept to a minimum. The use of 

one or more of the following measures may be necessary: 

•	 Isolate the backfill from underground sources of water either by providing a 

permeable drainage system or an impervious barrier; 

•	 Use pervious backfill and provide weep holes in the structure; 

•	 Provide an impervious soil layer near the ground surface, and grade the ground 

behind the wall to drain surface water away from the wall. 

Expansive clays can cause very high lateral pressures on the back of a retaining structure and 

should therefore be avoided whenever possible. In cases where expansive clays are present 

behind a wall, swelling pressures should be evaluated based on laboratory tests so that the 

wall can be designed properly to withstand these swelling pressures, which can be significant 

Alternatively, one of the following measures can be taken: 

•	 A granular filter material can be provided between the clay backfill and the back of 

the wall. This material will drain the groundwater away from the expansive soil and, 

at the same time act as a buffer zone between the expansive soil and the structure. 

•	 The expansive soil can be treated with lime to reduce or even eliminate its swelling 

potential, if the soil does not contain gypsum. Expansive soils that contain gypsum 

should not be treated with lime because the combination of the minerals in expansive 

soils with gypsum and water may lead to the formation of ettringite, which has a 

much higher swelling potential than the untreated expansive soils. 

The following is noted by Duncan, et al. (1990) concerning the use of clayey soils as backfill 

for fill wall applications: 

•	 Clayey backfills generally have lower drained shear strength than cohesionless soils. 

Low drained shear strength results in: (1) larger lateral earth pressures against the 

back of the wall; (2) lower frictional resistance along the reinforcement for MSE 

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walls that employ frictional reinforcement; and (3) lower bearing value for MSE 

walls that employ passive reinforcement. 

•	 Clayey backfills are more plastic and contain more fines than cohesionless soils. 

Higher plasticity results in: (1) poor drainage and the potential for the development of 

water pressures behind the wall; (2) the potential for freezing of retained water and 

development of ice pressures on the back of the wall; and (3) greater potential for 

corrosion of metallic reinforcements for MSE walls. 

•	 Clayey backfills have the potential to undergo creep deformations that can lead to 

higher earth pressures and greater wall face deformations than will occur with soils 

that do not exhibit significant creep potential. Earth pressures used for design of 

gravity walls employing clayey backfills should be based on past performance and 

field experience, as wall design methods do not consider the effects of creep. 

Despite these problems, silts and clays may be used as backfill soils provided suitable design 

procedures are employed, including conservative estimates of lateral earth pressures, and 

construction control measures are incorporated into the contract documents. When silts and 

clays are used as backfills, walls may need to be designed for pressures between active and 

at-rest conditions. For soils that are deemed to have high swell potential, an earth-pressure 

coefficient as great as 1.0 may be used for design (Canadian Geotechnical Society, 1992). In 

all cases, water pressures and appropriate surcharge loads also need to be added to these earth 

pressures. 

In general, any permanent fill wall system that incorporates silty or clayey backfills must 

have an appropriately designed subsurface and surface drainage system to minimize pore 

pressure build-up and soil saturation. Such wall systems should also include periodic 

measurements of wall face movements. 

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10.3 LATERAL PRESSURES DUE TO WATER 

In retaining wall design, it is general practice to provide drainage paths, commonly known as 

“weep holes,” through the earth retaining structure, or use other methods to drain 

groundwater that may otherwise collect behind the structure. The purpose of these drainage 

features is to prevent the development of water pressure on the structure. Occasionally, 

however, it may not be feasible or desirable to drain the water from behind the structure. For 

example, maintenance of existing ground water levels may be desirable to safeguard against 

potential settlement of adjacent structures or to prevent contaminated groundwater from 

entering the excavation. In such instances, the earth retaining structure must be designed for 

both lateral earth pressure and water pressure. 

Computation of active lateral earth pressures for the case of a uniform backfill and static 

groundwater is illustrated in Figure 10-12. In this case, the water pressure represents a 

hydrostatic condition since there is no seepage or flow of water through the soil. The lateral 

earth pressure below the water level is based on the effective vertical stress, p′o, times the 

active lateral earth pressure coefficient. The lateral pressure due to the water is added to the 

active lateral earth pressure to obtain the total lateral pressure on the wall. By analogy to 

lateral earth pressure coefficients, the lateral water pressure coefficient = 1.0. The lateral 

pressure computations should consider the greatest unbalanced water head anticipated to act 

on the wall, since this generally results in the largest total lateral load. 

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γ
 

Figure 10-12. Computation of lateral pressures for static groundwater case. 
For cases where seepage may occur through or beneath the earth retaining structure, the 

resulting seepage gradients will result in an increase or reduction in the water pressure 

depending on the direction of the seepage path. For such cases, flow net procedures can be 

used to compute the lateral pressure distribution due to water. 

The concepts of lateral earth pressures and lateral pressures due to water are illustrated in 

Example 10-1. 

Example 10-1: For the wall configuration shown below, construct the lateral pressure 

diagram. Assume the face of the wall to be smooth (δ = 0, cw = 0). 

φ = 30o 

γsat = 120 pcf 

φ = 30o 

γ = 115 pcf 6 ft 

12 ft 

Solution: 

Use the Coulomb method (Figure 10-5) for φ = 30o , β = 10o , θ = 0, and δ = 0: 

Ka = 0.374 

The pressures at various depths can then be calculated as shown in a tabular format as 

follows. Based on the values in the table, the lateral pressure diagrams due to earth and 

water can be constructed as shown below. The total lateral pressure diagram is the sum of 

the two lateral pressure diagrams shown in the figure accompanying this example. 

Effective Lateral Earth Pressures, p'a 

z, ft po, psf pa = Ka po , psf 

0 0 0 

6 (115 pcf) (6 ft) = 690.0 psf 0.374(690.0 psf) = 258.1 psf 

18 690 psf +(120 pcf-62.4 pcf)(12 ft) = 1381.2 psf 0.374(1381.2 psf) = 516.6 psf 

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Hydrostatic Pressure, u = Kw uw 

z, ft zw, ft uw = zw γw, psf Lateral water pressures, u psf 

0 0 0 = 0 

6 0 0 = 0 

18 12 12 ft (62.4 pcf) = 748.8 psf 1.0(748.8 psf) = 748.8 psf 

φ = 30o 

γsat = 120 pcf 

φ = 30o 

γ = 115 pcf 6 ft 

12 ft 

258.1 psf 

516.6 psf 748.8 psf 

(a) (b)

(a) Lateral effective earth pressure diagram and (b) Lateral water pressure diagram. 

10.4 LATERAL PRESSURE FROM SURCHARGE LOADS 

10.4.1 General 

Surcharge loads on the backfill surface near an earth retaining structure also cause lateral 

pressures on the structure. Typical surcharge loadings may result from railroads, highways, 

sign/light structures, electric/telecommunications towers, buildings, construction equipment, 

and material stockpiles. 

The loading cases of particular interest in the determination of lateral pressures are: 

• uniform surcharge; 

• point loads; 

• line loads parallel to the wall; and 

• strip loads parallel to the wall. 

Figure 10-13 shows examples of retaining walls with surcharge loads. 

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(b) 

Figure 10-13: (a) Retaining wall with uniform surcharge load and (b) Retaining wall 

with line loads (railway tracks) and point loads (catenary support structure). 

(a) 

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10.4.2 Uniform Surcharge Loads 

Surcharge loads are vertical loads applied at the ground surface, which are assumed to result 

in a uniform increase in lateral pressure over the entire height of the wall. The increase in 

lateral pressure for a uniform surcharge loading can be written as: 

∆ph = Kqs 10-14 

where: ∆ph is the increase in lateral earth pressure due to the vertical surcharge load, qs. 

applied at the ground surface, and K is an appropriate earth pressure coefficient. Examples 

of surcharge loads for highway wall system applications include: (1) dead load surcharges 

such as that resulting from the weight of a bridge approach slab or concrete pavement; (2) 

live load surcharges such as that due to traffic loadings; and (3) surcharges due to equipment 

or material storage during construction of the wall system. 

When traffic is expected to come to within a distance from the wall face equivalent to onehalf the wall height, the wall should be designed for a live load surcharge. For temporary 

walls that are not considered critical, actual surcharge loads may be evaluated and considered 

in the design instead this prescriptive value. Both temporary and permanent wall designs 

should account for unusual surcharges such as large material stockpiles. Calculated lateral 

pressures resulting from these surcharges should be added explicitly to the design lateral 

earth pressure diagram. Surcharge loads from existing buildings need to be considered if 

they are within a horizontal distance from the wall equal to the wall height. 

10.4.3 Point, Line, and Strip Loads 

Point loads, line loads, and strip loads are vertical surface loadings that are applied over 

limited areas as compared to surcharge loads. As a result, the increase in lateral earth 

pressure used for wall system design is not constant with depth as is the case for uniform 

surcharge loadings. These loadings are typically calculated by using equations based on 

elasticity theory for lateral stress distribution with depth (Figure 10-14). Examples of such 

loads include heavy cranes (temporary) or walls (permanent). Lateral pressures resulting 

from these surcharges should be added explicitly to other lateral pressures. 

A numerical problem solved by use of Figure 10-14 is presented in Example 10-2. 

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Figure 10-14. Lateral pressure due to surcharge loadings (after USS Steel, 1975) 

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Example 10-2: Construct the lateral pressure diagram due to a line load of 700 lb/ft 

located 15 ft behind the top of a 30 ft high unyielding wall shown below. 

30 ft 

15 ft 

700 lb/ft 

Geometry of the Example Problem 10-2 

Solution: 

The procedure to calculate the lateral pressures due to a line load is given in Figure 10-14. 

From this figure the lateral pressure can be found as follows: 

15ft 

m = = 0.5 > 0.4 

30ft 

For m > 0.4 , the lateral pressure is given by: 

For m = 0.5, Ql=700 lb/ft and H = 30 ft, the lateral pressure is given by: 

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⎡

⎞ m 2 ⎤ ⎛ Q n P = 1 ⎢ h 1.28⎜ ⎟

)

⎥

⎝ H ⎠⎢ 2 2 n 2 ⎥ ⎣(m + ⎦

⎡ lb/ft ⎞ ⎡ ⎤ ⎛ 700 0.5 2 n ⎤ 0.25n P = 1.28 ⎜ ⎟ ⎢ ⎥ → P = 29.9⎢

( )

⎥ h ⎜ ⎟ h ⎝ 30ft ⎠ ⎢ 2 ⎥ ⎢⎣(0.5 2 2 + n 2 ) ⎦⎥ 2 ⎣ 0.25 + n ⎦
Lateral pressures computed at various depths by using the above formula and the chart for 

line loads in Figure 10-14 are tabulated below. 

Computation of Lateral Earth Pressures Due To Line Load 

= z / Hn Depth below top of wall (ft) Ph (psf) 

0 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

0 

3 

6 

9 

12 

15 

18 

21 

24 

27 

30 

0.00 

11.0 

17.8 

19.4 

17.8 

14.9 

12.0 

9.5 

7.5 

6.0 

4.8 

The information in the table is used to construct the curve of depth vs. lateral pressure shown 

below. 

Lateral Pressure, psf 

0.0 5.0 10.0 15.0 20.0 

0 

3 

6 

9 

12 

15 

18 

21 

24 

27 

30 

Depth below ground surface, ft 

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10.5 WALL DESIGN 

There are many different types of walls as shown in Figure 10-3. All walls have to be 

evaluated for stability with respect to different modes of deformation. There are four basic 

modes of instability from a geotechnical viewpoint. These are (a) sliding, (b) limiting 

eccentricity or overturning, (c) bearing capacity, and (d) global stability. The four modes of 

instability are shown in Figure 10-15. Since these modes of instability assume that the wall 

is intact, the evaluation of these modes is commonly referred to as the “external stability” 

analysis. All four modes may or may not be applicable to all wall types. Furthermore, 

depending on the wall type and its load support mechanism (refer to Section 10.1), there may 

be additional instability modes, such as pullout, tension breakage, bending and shear. The 

evaluation of these additional modes of instability are commonly referred to as “internal 

stability” analyses. 

 (a) Sliding (b) Limiting Eccentricity (Overturning) 

(c) Bearing Capacity (d) Deep-seated (global) Stability 

Figure 10-15. Potential failure mechanisms for rigid gravity and semi-gravity walls. 

The external stability analysis is best illustrated by using the concept of gravity and semigravity walls. Table 10-2 summarizes the major design steps for cast-in-place concrete 

(CIP) gravity and semi-gravity walls. 

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Table 10-2 

Design steps for gravity and semi-gravity walls 

Step 1. Establish project requirements including all geometry, external 

loading conditions such as (temporary, permanent, and seismic, 

performance criteria, and construction constraints. 

Step 2. Evaluate site subsurface conditions and relevant properties of in 

situ soil and rock and wall backfill. 

Step 3. Evaluate soil and rock parameters for design and establish factors 

of safety. 

Step 4. Select initial base dimension of wall for evaluation of external 

stability. 

Step 5. Select lateral earth pressure distribution. Add appropriate water, 

surcharge, and seismic pressures and develop total lateral pressure 

diagram for design. 

Step 6. Evaluate bearing capacity. 

Step 7. Evaluate limiting eccentricity (overturning) and sliding. 

Step 8. Check overall stability and revise wall design if necessary. 

Step 9. Estimate maximum lateral wall movement, tilt, and wall 

settlement. Revise design if necessary. 

Step 10. Design wall drainage systems. 

10.5.1 Steps 1, 2, and 3 – Establish Project Requirements, Subsurface Conditions, 

Design Parameters 

It is assumed that Steps 1, 2 and 3 are completed and a CIP wall has been deemed 

appropriate. Soil and/or rock parameters for design have been established. In general, the 

required parameters for in situ soil and rock are the same as those required for a spread 

footing, in particular, foundation shear strength for bearing resistance and compression 

parameters of the foundation materials to allow for computations of wall settlement. For 

gravity walls that require deep foundation support, the soil/rock parameters are the same as 

those required for the design of a driven pile or drilled shaft foundation. 

The drainage and shear strength characteristics of the wall backfill soil are assessed as part of 

Step 3. Guidelines for wall backfill material gradation and drainage behind gravity retaining 

walls can be found in the AASHTO (2002). Whenever possible, the backfill material should 

be free draining, nonexpansive, and noncorrosive. All backfill material should be free of 

organic material. The backfill gradation should follow the guidelines presented in Table 10­

3. 

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Table 10-3 

Suggested gradation for backfill for cantilever 

semi-gravity and gravity retaining walls 

 Sieve Size Percent Passing 

3 in. (76.2 mm) 100 

No. 4 (4.75 mm) 35 – 100 

No. 30 (0.6 mm) 20 – 100 

No. 200 (0.075 mm) 0 – 15 

10.5.2 Step 4 – Select Base Dimension Based on Wall Height 

Figure 10-16 shows typical dimensions for a semi-gravity cantilever retaining wall and for a 

counterfort wall. These dimensions were developed based on a range of backfill properties, 

geometries, and stable foundation soils and can be used for preliminary design. However, 

the final external stability calculations should be performed based on the geometry 

requirements and specific conditions of the project, e.g., limited right-of-way. Similar 

guidelines exist for other wall types and can be found in FHWA (2005b). 

10.5.3 Step 5 – Select Lateral Earth Pressure Distribution 

Lateral earth pressures for design of CIP walls are determined by using the procedures 

presented previously. Generally, Coulomb theory is used to compute earth pressures either 

directly on the back face of the wall, as is the case with a gravity wall, or on a vertical plane 

passing through the heel of the base slab, as is the case with a semi-gravity wall. Both of 

these concepts are illustrated in Figure 10-17. 

The procedures described in Figure 10-17 are used to calculate the earth pressure loading for 

the wall subject to the following considerations: 

•	 Use at-rest earth pressures for walls where rotation and displacement are restrained, 

e.g., rigid gravity retaining walls resting on rock or batter piles, unyielding walls such 

as culverts, tunnels and rigid abutment U-walls such as the CIP abutment with 

integral wingwalls shown in Figure 10-18. 

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(a) 

(b) 

Figure 10-16. Typical dimensions (a) Cantilever wall, (b) Counterfort wall (Teng, 1962). 

[1 m = 3.28 ft; 25.4 mm= 1in] 

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DEFINITIONS 

B = width of the base of the footing 

tan δb = friction factor between soil and base (see 

Table 10-1 for guidance) 

W = weight at the base of wall. Includes weight 

of wall for gravity walls. Includes weight of 

the soil above footing for cantilever and 

counterfort walls 

c = cohesion of the foundation soil 

ca = adhesion between concrete and soil 

δ = angle of wall friction 

Pp = passive resistance 

LOCATION OF RESULTANT, R 

Based on moments about toe (assuming Pp=0) 

Wa + Pvg − Phb d = W + Pv 

CRITERIA FOR ECCENTRICITY, e 

B 

e = d − ; e ≤ B/6 for soils; e ≤ B/4 for rocks

2 

FACTOR OF SAFETY AGAINST SLIDING 

(W + Pv ) tan δb + ca B FS = ≥ 1.5(min) s Ph 

APPLIED STRESS AT BASE (qmax, qmin, qeq) 

(W + Pv ) ⎛ 6e ⎞ q max = ⎜1 + ⎟ B ⎝ B ⎠
 

(W + P ) v ⎛ 6e ⎞ qmin = ⎜1 − ⎟ B ⎝ B ⎠

Equivalent uniform (Meyerhof) applied stress, qeq, is 

given as follows: 

(W + P ) v qeq = where B′ = B − 2e

B′

Use uniform stress, qeq, for soils and settlement 

analysis; use trapezoidal distribution with qmax and 

qmin for rocks and structural analysis 

DEEP-SEATED (GLOBAL) STABILITY 

Evaluate global stability using guidance in Chapter 6 

(Slope Stability) 

Figure 10-17. Design criteria for cast-in-place (CIP) Concrete retaining walls 

(after NAVFAC, 1986b). 

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Figure 10-18. CIP abutment with integral wingwalls 

•	 Use the average of the at-rest and active earth pressures for CIP semi-gravity walls 

that are founded on rock or restrained from lateral movements, e.g., by the use of 

batter piles, and are less than 15 ft (5 m) in height. 

•	 Use active earth pressures for CIP semi-gravity walls founded on rock or restrained 

from lateral movements that are greater than 15 ft (5 m) in height. 

•	 Use the procedures described previously to compute pressure due to water and lateral 

earth pressures due to compaction and/or surcharges. Add these pressures to lateral 

earth pressure due to retained soil. 

•	 Passive resistance in front of the wall should not be used in the analyses unless the 

wall extends well below the depth of frost penetration, scour or other types of 

disturbance such as a utility trench excavation in front of the wall. Development of 

the passive earth pressure in the soil in front of the wall requires a relatively large 

rotation or outward displacement of the wall; accordingly, the passive earth pressure 

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is neglected for walls with deep foundations and for other cases where the wall is 

restrained from rotation or displacement. 

Figure 10-17 shows general loading diagrams for rigid gravity and semi-gravity walls. 

Loadings due to earth pressures behind the wall and for resultant vertical pressures at the 

base of the wall are shown. 

If adequate drainage measures are provided, the hydrostatic pressure due to groundwater 

behind the wall generally need not be considered. However, hydrostatic pressure must be 

considered for portions of the wall below the level of the weep holes unless a deeper drainage 

system is provided behind the base of the wall. The wall must be designed for the full 

hydrostatic pressure when it is necessary to maintain the groundwater level behind the wall. 

In addition to the lateral earth pressure, the wall must be designed for lateral pressure due to 

surcharge loads (see Section 10.4). For stability analyses of CIP gravity walls, the surcharge 

loads are generally assumed to be applied starting directly behind the top of the wall, unless 

specific conditions dictate otherwise. For CIP semi-gravity walls, the surcharge loads are 

generally assumed to be located behind the heel of the wall, and conservatively neglected 

within the width of the base slab since they contribute to overturning and sliding resistance. 

However, the surcharge loads within the width of the base slab are considered for the 

structural design of the wall stem. 

10.5.4 Step 6 – Evaluate Bearing Capacity 

10.5.4.1 Shallow Foundations 

The computed vertical pressure at the base of the wall footing must be checked against the 

ultimate bearing capacity of the soil. The generalized distribution of the bearing pressure at 

the wall base is illustrated in Figure 10-17. Note that the bearing pressure at the toe is greater 

than that at the heel. The magnitude and distribution of these pressures are computed by 

using the applied loads shown in Figure 10-17. The equivalent uniform bearing pressure, qeq, 

should be used for evaluating the factor of safety against bearing capacity failure. The 

procedures for determining the allowable bearing capacity of the foundation soils can be 

found in Chapter 8 (Spread Foundations) of this manual. Generally, a minimum factor of 

safety against bearing capacity failure of 3.0 is required for the spread footing foundation. 

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10.5.4.2 Deep Foundations 

CIP walls founded on a deep foundation may be subject to potentially damaging ground and 

structural displacements at sites underlain by cohesive soils. Such damage may occur if the 

weight of the backfill material exceeds the bearing capacity of the cohesive subsoils causing 

plastic displacement of the ground beneath the retaining structure and heave of the ground 

surface in front of the wall. When the cohesive soil layer is located at or below the base of 

the wall, the factor of safety against this type of bearing capacity failure can be approximated 

by the following equation (Peck, et al., 1974): 

5c FS = 10-15 (γ H + q) 

where H is the height of the fill, γ is the unit weight of fill, c is the shear strength of the 

cohesive soil and q is the uniform surcharge load. 

The computed factor of safety should not be less than 2.0 for the embankment loading. 

Below this value progressive lateral movements of the retaining structure are likely to occur 

(Peck, et al., 1974). As the factor of safety decreases, the rate of movement will increase 

until failure occurs at a factor of safety of unity. For CIP walls founded on vertical piles or 

drilled shafts, this progressive ground movement would be reflected by an outward 

displacement of the wall. CIP walls founded on battered piles typically experience an 

outward displacement of the wall base and a backward tilt of the wall face (Figure 10-19). 

Figure 10-19. Typical Movement of pile-supported cast-in-place (CIP) wall with soft 

foundation. 

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10.5.5 Step 7 – Evaluate Overturning and Sliding 

Figure 10-17 presents criteria for the design of CIP walls against sliding and eccentricity. 

The base dimensions of a CIP wall are determined by satisfying the following criteria: 

• Sliding: FS ≥ 1.5 

Sliding resistance along the base of the wall is evaluated by using the same 

procedures as for spread footing design (Refer to Chapter 8.0). Note that any passive 

resistance provided by soil at the toe of the wall by embedment is ignored due to the 

potential for the soil to be removed through natural or manmade processes during the 

service life of the structure. Also, the live load surcharge is not considered as a 

stabilizing force over the heel of the wall when sliding resistance is being checked. 

If adequate sliding resistance cannot be achieved, design modifications may include: 

(1) increasing the width of the wall base; (2) using an inclined wall base or battering 

the wall to decrease the horizontal load; (3) incorporating deep foundation support; 

(4) constructing a shear key; and (5) embedding the wall base to a sufficient depth so 

that passive resistance can be relied upon. 

If the wall is supported by rock, granular soils or stiff clay, a key may be installed 

below the foundation to provide additional resistance to sliding. The method for 

calculating the contribution of the key to sliding resistance is shown in Figure 10-20. 

Note: See Figure 10-17 for list of symbol definitions. 

Figure 10-20. Resistance against sliding from keyed foundation. 

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•	 Eccentricity, e, at base: ≤ B/6 in soil 

 ≤ B/4 in rock 

The eccentricity criterion essentially requires that the safety factor of the wall against 

overturning is approximately of 2.0 for soils and 1.5 for rocks. If the eccentricity is 

not within the required limits then it implies inadequate resistance to overturning and 

consideration should be given to either increasing the width of the wall base or 

providing a deep foundation. 

10.5.6 Step 8 – Evaluate Global Stability 

Where retaining walls are underlain by inadequate foundation materials, the overall stability 

of the soil mass must be checked with respect to the most critical failure surface. As shown 

in Figure 10-21, both circular and non-circular slip surfaces must be considered. A minimum 

factor of safety of 1.5 is desirable. If global stability is found to be a problem, deep 

foundations or the use of lightweight backfill may be considered. Alternatively, measures 

can be taken to improve the shear strength of the weak soil stratum. Other wall types, such 

as an anchored soldier pile and lagging wall or tangent or secant pile wall, should also be 

considered in this case. 

Figure 10-21. Typical modes of global stability (after Bowles, 1996) 

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10.5.7 Step 9 – Evaluate Settlement and Tilt 

Foundation settlement can be computed by the methods discussed in Chapter 8 (Spread 

Foundations). CIP walls can generally accommodate a differential settlement of up to about 

1/500 measured as the ratio of differential settlement of two points along the wall to the 

horizontal distance between the points. In general, tolerable total settlements of CIP walls 

are limited to 1 inch as a means to control differential settlement. If the computed settlement 

and tilt exceed acceptable limits, the wall dimensions can be modified to shift the resultant 

force closer to the center of the base and thereby reduce the load eccentricity and differential 

settlement. In some cases, use of lightweight backfill material may solve the problem. The 

use of deep foundations can also be considered. 

Unless CIP walls are provided with a deep foundation, a small amount of wall tilting should 

be anticipated. It is therefore advisable to provide the face of the wall with a small inward 

batter to compensate for the forward tilting. Otherwise, a small amount of forward tilting 

may give the illusion that the wall is unstable. 

In cases where the foundation materials are stiffer or firmer at the toe of the base than at the 

heel, the resulting settlement may cause the wall to rotate backwards towards the retained 

soil. Such wall movements could substantially increase the lateral pressures on the wall 

since the wall is now pushing against the soil i.e., generating a passive pressure condition. 

Such wall movements can be avoided by reproportioning the wall, supporting the wall on a 

deep foundation, or treating the foundation soils. 

10.5.8 Step 10 – Design Wall Drainage Systems 

Water can have detrimental effects on earth retaining structures. Subsurface water and 

surface water can cause damage during and/or after construction of the wall. Control of 

water is a key component of the design of earth retaining structures. 

A subsurface drainage system serves to prevent the accumulation of destabilizing hydrostatic 

pressures, which may develop as a result of groundwater seepage and/or infiltration of 

surface water. Subsurface drainage is addressed in Section 10.5.8.1. There may be several 

soil zones behind an earth retaining structure. Groundwater flow from one zone to another, 

and then to a drain and outlet feature, should be unimpeded. If impeded, water will backup at 

the interface of the two adjacent zones thereby increasing hydrostatic pressures and 

decreasing the stability of the wall structure. Soil filtration and permeability requirements 

must be met between the two adjacent zones of different soils to prevent impeded flow. Soil 

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and geotextile filter design and water collection components are discussed in Section 

10.5.8.2. 

Surface water runoff can destabilize a structure under construction by inundating the backfill. 

Surface water can also destabilize a completed structure by erosion or by infiltrating into the 

backfill. Design for surface water runoff is discussed in Section 10.5.8.3. 

In most cases, and especially for fill walls, it is preferable to provide backfill drainage rather 

than design the wall for the large hydrostatic water pressure resulting from a saturated 

backfill. Saturation of the backfill may result from either a high static water table, from 

direct and/or indirect rainfall infiltrations, or from other wetting conditions, e.g., ruptured 

water lines, etc. 

10.5.8.1 Subsurface Drainage 

Potential sources of subsurface water are surface water infiltration and groundwater as 

illustrated in Figure 10-22. Groundwater present at an elevation above the base of the wall 

may have flowed into the backfill from an excavation backcut. Ground water may also be 

present beneath the bottom of the wall. A groundwater surface beneath a wall may rise into 

the structure, depending on the hydrogeology of the site. Surface water may infiltrate into 

the wall backfill from above, or from the front face of the wall for the case of flowing water 

in front of the structure (after Collin, et al., 2002). 

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Surface Water 

Infiltration 

Drainage 

aggregate 

Reinforced Fillrced Fillrced Fill Retained Fill 

Groundwater 

Drainage Aggregate Aggregate Aggregate 

Foundation Soil

Figure 10-22. Potential sources of subsurface water. 
 

 

Drainage system design depends on wall type, backfill and/or retained soil type, and 

groundwater conditions. Drainage system components such as granular soils, prefabricated 

drainage elements and filters, are usually sized and selected based on local experience, site 

geometry, and estimated flows, although detailed design is only occasionally performed. 

Drainage systems may be omitted if the wall is designed to resist full water pressure. 

Drainage measures for fill wall systems, such as CIP walls, and cut wall systems typically 

consist of the use of a free-draining material at the back face of the wall, with “weep holes” 

and/or longitudinal collector drains along the back face as shown in Figure 10-23. The 

collector drains may be perforated pipes or gravel drains. This minimum amount of drainage 

should be sufficient if the wall backfill is relatively free-draining and allows the entire 

backfill to serve as a drain. It may be costly to fully backfill with free-draining or relatively 

free-draining material for some project applications therefore, it may be necessary to 

construct other types of drainage systems. 

Fill wall drains may be placed (1) immediately behind the concrete facing or wall stem; (2) 

between wall backfill and embankment fill; (3) along a backcut; and (4) as a blanket drain 

beneath the wall. Examples of drains behind a wall stem are shown in Figure 10-24. The 

drainage system shown in the figure primarily serves to collect surface water that has 

infiltrated immediately behind the wall and transport it to an outlet. The system may also 

serve to drain the wall backfill, if the backfill soil is relatively free-draining. 

Backfill Soil

Drainage

Blanket

Longitudinal

Drain Pipe

Backfill Soil

Prefabricated

Drainage

Element

Weephole

Backfill Soil

Drainage

Blanket

Longitudinal

Drain Pipe

Backfill Soil 

Drainage 

Blanket 

Longitudinal 

Drain Pipe 

Backfill Soil

Prefabricated

Drainage

Element

Weephole

Backfill Soil 

Prefabricated 

Drainage 

Element 

Weephole 

Figure 10-23. Typical retaining wall drainage alternatives. 

A drain behind the wall backfill should be used when the backfill is not relatively freedraining. Such a drain may be located as noted in (2) or (3) above, and as illustrated in 

Figure 10-24. A granular blanket drain with collection pipes and outlets should be used 

beneath fill wall structures where a high or seasonally high groundwater table exists. 

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Collection and Drain Pipes

Wall Backfill Retained Backfill

Face chimney drain

Outlet Pipe

Weephole

Chimney drain Face chimney drain 

Collection and Drain Pipes 

Outlet Pipe 

Wall Backfill Retained Backfill 

Weephole 

Chimney drain 

Foundation Soil 

Figure 10-24. Drains behind backfill in cantilever wall in a cut situation. 

10.5.8.2 Drainage System Components 

Drainage systems for fill walls may include: 

•	 column(s) or zone(s) of free-draining gravel or coarse sand to collect water seepage 

from the backfill; 

•	 perforated pipe(s) to collect water in the granular column(s) or zone(s); 

• conveyance piping; 

• outlet(s); and 

•	 filter(s) between backfill soil(s) and granular column(s) or zone(s). 

Longitudinal pipes transport collected water to outlet pipes that discharge at appropriate 

points in front of and/or below the wall. Outlets may be via weep holes through the wall 

facing that discharge in front of the structure to grade; via conveyance piping to storm sewers 

as is common in urban applications, or via conveyance piping to a slope beneath the wall 

structure. Weep holes generally consist of 11⁄2 - 3 in (40 - 75 mm) diameter holes that extend 

through the wall facing and are closely spaced horizontally along the wall, typically less than 

10 ft (3 m) apart. If weep holes are used with a counterfort wall, at least one weep hole 

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should be located between counterforts. A screen and/or filter are used to prevent soil piping 

through a weep hole. 

The collection and conveyance pipes need to be large enough and sufficiently sloped to 

effectively drain water by gravity flow from behind the wall while maintaining sufficient 

pipe flow velocity to prevent sediment buildup in the pipe. Use of 3 to 4 in (75 to 100 mm) 

diameter pipes is typical and practical. The diameter is usually much greater than that 

required for theoretical flow capacity. Procedures for the design of pipe perforations, such as 

holes or slots, is provided in Section 5.2 of Cedergren (1989). Pipe outlets to slope areas 

beneath wall structures should be detailed similar to pavement drain outlets. If the outlet is 

to a grass area, it should have a concrete apron, a vertical post marking its location (for 

maintenance), and a screen to prevent animal ingress. 

Filters are required for water flowing between zones of different soils. A filter must prevent 

piping of the retained soil while providing sufficient permeability for unimpeded flow. The 

filter may be a soil or a geotextile. A geotextile is not required if the two adjacent soils meet 

certain soil filtration criteria. An open-graded aggregate will generally not allow the 

development of a soil filter at its interface with the backfill soil. In this case a geotextile filter 

will be required. 

Geocomposite drains may be used in lieu of clean gravel or coarse sand and a geotextile. A 

geocomposite, or prefabricated, drain consists of a geotextile filter and a water collection and 

conveyance core. The cores convey the water and are generally made of plastic waffles, 

three-dimensional meshes or mats, extruded and fluted plastic sheets, or nets. A wide variety 

of geocomposites are readily available. However, the filtration and flow properties, detailing 

requirements, and installation recommendations vary and may be poorly defined for some 

products. 

The flow capacity of geocomposite drains can be determined by using the procedures described 

in ASTM D 4716. Long-term compressive stresses and eccentric loadings on the geocomposite 

core should be considered during design and selection. The geotextile of the geocomposite 

should be designed to meet filter and permeability requirements. 

Installation details, such as joining adjacent sections of the geocomposite and connections to 

outlets, are usually product-specific. Product-specific variances should be considered and 

addressed in the design, specification, detailing and construction phases of a project. Post 

installation examination of the drainage core/path with a camera scope should be considered for 

critical applications. 

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10.5.8.3 Surface Water Runoff 

Surface drainage is an important aspect of ensuring wall performance and must be addressed 

during design. Appropriate measures to prevent surface water from infiltrating into the wall 

backfill should be included in the design of all earth retaining structures. 

During construction of a fill wall, the backfill surface should be graded away from the wall 

face at the end of each day of construction to prevent water from ponding behind the wall 

and saturating the soil. Surface water running onto a partially completed backfill can carry 

fine-grained soils into the backfill work area and locally contaminate a free-draining granular 

backfill with fines. If a fine-grained soil is being utilized for the backfill, saturation can 

cause movements of the partially constructed wall facing. 

Finish grading at the top of a wall structure should provide positive drainage away from the 

wall, when possible, to prevent or minimize infiltration of surface water into the backfill. If 

the area above the wall is paved, a curb and gutter is typically used to direct the flow away from 

the wall. Concrete-, asphalt- or vegetation-lined drainage swales may be used where a 

vegetated finished grade slopes to the wall. Water runoff over the top of a wall where the 

backfill slopes towards it can lead to erosion and undercutting of the wall and can cause 

staining of the wall face as soil is carried with the water. Construction of a collection swale 

close to the wall will help to prevent runoff from going over the top of the wall. Runoff flow 

will concentrate at grading low points behind the face. Ponding of runoff behind the wall 

leads to undesirable infiltration of water into the backfill. 

Collection and conveyance swales should prevent overtopping of the wall for the design 

storm event. Extreme events (e.g., heavy rainfalls of short duration) have been known to 

cause substantial damage to earth retaining structures due to erosion and undercutting, 

flooding, and/or increased hydrostatic pressures both during and after construction. This is 

particularly true for sites where surface drainage flows toward the wall structure and where 

finer-grained backfills are used. 

Site drainage features are designed for an assumed or prescribed design storm event, such as, 

the 25 year storm event. However, extreme events can occur that result in short duration 

flows, e.g., 1 to 3 hours, that significantly exceed the design capacity of the stormwater 

management system. When such events occur, site flooding can cause overtopping of the 

wall, erosion and undercutting, and an increase in hydrostatic forces within and behind the 

reinforced soil mass. 

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If surface water flows toward an earth retaining structure, the water is likely to be picked up 

in a gutter or other collection feature. Such features are often sized based upon the design 

storm event. The site layout and wall structure should include features for handling flows 

greater than the design event as is typically done in the design of an overflow spillway for a 

dam. The wall designer should address potential excess flows and coordinate work with 

other project designers. Consideration should be given to incorporating details of overflow 

features, such as a spillway, into the wall design for sites where surface water flows towards 

the wall structure. 

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10.6 EXTERNAL STABILITY ANALYSIS OF A CIP CANTILEVER WALL 

The following example problem is used to illustrate the procedure for performing an external 

stability analysis of a CIP cantilever retaining wall. 

Example 10-3. 

Analyze the CIP cantilever wall shown below for factors of safety against sliding, 

overturning and bearing capacity failure. The backfill and foundation soils consist of clean, 

fine to medium sand, and the groundwater table is well below the base of the wall. 

2.3 2.3 8.5 

2.3 ft 

18 ft 

1.5 ft 

2.3 ft 

1.6 ft 

5 f

φb t = 38o 

γt = 120 pcf 

φ = 30o 

γt = 115 pcf 

γconc = 150 pcf 

Geometry and parameters for example problem. 

Solution 

Step 1: Determine the total height of soil exerting pressure. 

H = thickness of base slab + height of stem + (width of heel slab) tan (backslope angle) 

H = 2.3 ft + 18 ft + 8.5 ft (tan 10o

) 

= 21.8 ft 

Step 2: Compute the coefficient of active earth pressure by using the equation of Ka in 

Figure 10-5 for a vertical backface (θ=0). 

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2

where: 

φ = internal friction angle of soil = 30o
 

 

β= angle of backfill slope = 10o
 

δ= angle of wall friction = β = 10o
 

For the example problem: 

cos 2 30°

cos φ Ka = 2 ⎡ sin(φ + δ) sin(φ − β) ⎤

cos δ⎢1 + ⎥

cos δcos(−β ⎣ ) ⎦

Ka = 2 ⎡ sin(30° + 10°) sin(30° −10°) ⎤ cos10°⎢1 + ⎥ cos10° cos(− ⎣ 10°) ⎦
 

Ka = 0.35
 

Step 3. Compute the magnitude of the resultant of active pressure, Pa, per foot of wall 

into the plane of the paper. 

1 P = Ka γH 2

a 2
 

1 = (0.35)(115pcf )(21.8ft) 2 = 9,564.2lb / ft 2 

Step 4. Resolve Pa into horizontal and vertical components: 

Ph = Pa cos β Pv = Pa sin β
 

= (9,564.2 lb/ft) cos 10o 

 = (9,564.2 lb/ft ) sin 10o
 

= 9,418.9 lb/ft = 1,660.8 lb/ft 

Moment arm of Ph about point A = (2.3 ft + 18 ft + 1.5 ft)/3 = 21.8/3 = 7.27 ft = b 

Moment arm of Pv about point A = 2.3 ft + 2.3 ft + 8.5 ft = 13.1 ft = g 

Step 5: Determine weights and sum moments about the toe of the wall (point A). 

The weights of various areas and the moments due to the weights shown in the geometry of 

the example problem are set out in the following table. The unit weight of concrete is 

assumed to be 150 pcf and the weight of the soil above the footing toe is neglected. 

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Area Weight, lb/ft Moment arm about A, ft Moment about A, lb.ft/ft 

1 (1.6ft) (18 ft) (150 pcf) = 4,320 2.3 ft+0.7 ft+(1.6/2) ft = 3.80 (4,320 lb) (3.80 ft) = 16,416.0 

2 (0.5) (0.7 ft) (18 ft) (150 pcf) = 945 2.3 ft+ (2/3) (0.7) ft = 2.77 (945 lb) (2.77 ft) = 2,617.7 

3 (13.1 ft) (2.3 ft) (150 pcf) = 4,519.5 13.1/2 ft = 6.55 (4,519.5 lb) (6.55 ft) = 29,602.7 

4 (8.5 ft) (18 ft) (115 pcf) = 17,595 2.3 ft+ 2.3 ft+(8.5/2) ft = 8.85 (17,595 lb) (8.85 ft) = 155,715.8 

5 (0.5) (8.5 ft) (1.5 ft) (115 pcf) = 733.1 2.3 ft+2.3 ft+(2/3)(8.5) ft = 10.27 (733.1lb) (10.27 ft) = 7,528.9 

Total W = 28,112.6 Mw = 211,881.1 

Step 6: Check factor of safety against sliding; neglect passive resistance of embedment depth 

soil (Refer to Figure 10-20) 

(W + PV ) tan δb FSs = Ph
 

where: 

W = weight of concrete and soil on the base of the wall footing AB 

δb = friction angle between concrete base and foundation soil 

Use δb = (3/4) φb = (3/4) (38o) = 28.5o, for friction angle between concrete and clean, 

fine to medium sand (see NAVFAC, 1986b). This value of δb is within the range of 

values listed in Table 10-1 for clean fine to medium sand. 

Step 7: Check the limiting eccentricity and factor of safety against bearing failure. 

(1) Compute the location of resultant at distance d from point A. 

(28,112.6 lb/ft + 1,660.8lb/ft)tan28.5° 16,165.6 lb/ft FSs = = =1.72 O.K. 

9,418.9 lb/ft 9,418.9 lb/ft 

∑ M R − ∑ M

d 0 = ∑V
 

M W − Ph b + P d = v g

W + PV 

21,1881.1lb.ft/ft + (1,660.8lb/ft)(13.1ft) − (9,418.9 lb/ft)(7.27ft) d = 28,112.6lb/ft + 1,660.8lb/ft
 

where: W + PV = ΣV 

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16,5162.2 lb.ft/ft d =	 = 5.55 ft 

29,773.4 lb/ft 

(2) Compute the eccentricity of the load about the center of base. 

B 13.1ft 

e = − d = − 5.55ft = 1.0ft 

2 2
 

B 13.1ft
 e = 1.0ft < = = 2.18 ft O.K. 

6	 6 

(3) Compute the maximum and minimum pressures under the wall footing. 

∑ V ⎛ 6e ⎞

q max,min = ⎜1± ⎟ B ⎝ B ⎠
 

29,773.4 lb/ft ⎛ 6(1.0 ft) ⎞
 = ⎜ ⎟ ⎜1 ± ⎟ 13.1ft ⎝ 13.1ft ⎠
 

= 2,272.7 psf (1.46 or 0.54)
 

i.e., 	 qmax = 3,318.1psf 

 qmin = 1,227.3 psf 

(4) Estimate ultimate bearing capacity. 

Use the procedures presented in Chapter 8 (Shallow Foundations). Assume that for a 

footing with eccentric and inclined loading the ultimate bearing capacity computed by the 

geotechnical specialist is: 

qult =20,000 psf 

(5) Check factor of safety against bearing capacity failure. 

q ult 20,000 psf FS bc = = = 6.03 > 3.0 O.K.

q max 3,318.1psf

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SUMMARY
 

Factor of safety against sliding FSs = 1.72 

Eccentricity e = 1.0 ft < B/6 

Factor of safety against bearing failure FSbc = 6.03 

In addition, the factor of safety against global failure and wall settlement including tilting and 

lateral squeeze should be evaluated to complete the analysis. 

10.7 CONSTRUCTION INSPECTION 

FHWA (2005b) discusses construction considerations for many of the walls presented in 

Figure 10-3. Construction considerations for CIP walls only are presented in this manual. In 

general, the construction inspection requirements for CIP walls are similar to those for other 

concrete structures. In some cases, state agencies may have inspector checklists for this type 

of construction. Table 10-4 provides a summary of typical construction inspection 

requirements for CIP retaining walls. 

Table 10-4 

Inspector responsibilities for a typical CIP gravity and semi-gravity wall project 

CONTRACTOR SET UP 

Review plans and specifications 

Review the contractor’s schedule 

Review test results and certifications for preapproved materials, e.g., cement, coarse and fine 

aggregate. 

Confirm that the contractor’s stockpile and staging area are consistent with locations shown on 

the plans 

Discuss anticipated ground conditions and potential problems with the contractor 

Review the contractor’s survey results against the plans 

EXCAVATION 

Verify that excavation slopes and/or structural excavation support is consistent with the plans 

Confirm that limits of any required excavations are within right-of-way limits shown on plans 

Confirm that all unsuitable materials, e.g., sod, snow, frost, topsoil, soft/muddy soil are 

removed to the limits and depths shown on the plans and that the excavation is backfilled with 

granular material and properly compacted 

Confirm that leveling and proof-rolling of the foundation area is consistent with requirements 

of the specifications 

Confirm that the contractor’s excavation operations do not result in significant water ponding 

Confirm that existing drainage features, utilities, and other features are protected 

Identify areas not shown on the plans where unsuitable material exists and notify the engineer 

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FOOTING 

Approve condition of footing foundation soil/rock before concrete is poured 

Confirm reinforcement strength, size, and type consistent with the specifications 

Confirm the consistency of the contractor’s outline of the footing (footing size and bottom of 

footing depth) with the plans 

Confirm the location and spacing of reinforcing steel consistent with the plans 

Confirm water/cement ratio and concrete mix design consistent with the specifications 

Record concrete volumes poured for the footing 

Confirm appropriate concrete curing times and methods as provided in the specifications 

Confirm that concrete is not placed on ice, snow, or otherwise unsuitable ground 

Confirm that concrete is being placed in continuous horizontal layers and that the time 

between successive layers is consistent with the specifications 

STEM 

Confirm the placement of weep hole inserts (number, elevation, and specific locations) with 

the plans if weep holes are used, 

Confirm that concrete is poured in section lengths consistent with the specifications 

Record concrete volumes used to form the stem 

Confirm that all wall face depressions, air pockets, gaps, rough spots, etc. are repaired 

Confirm that storage of reinforcing bars is consistent with the specifications, e.g.-use of 

platform or supports. 

Perform preliminary check of condition of epoxy-coated reinforcing bars 

Confirm that forms are clean and appropriately braced during concrete pour operations 

Confirm that all reinforcing bars are held securely in place and are being rigidly supported at 

the face of forms and in the bottom of wall footings 

Confirm that construction joints are being made only at locations shown on the plans or 

otherwise at locations approved by the engineer 

DRAINAGE SYSTEMS AND BACKFILL 

Confirm that installation of the drainage system is consistent with the specifications and plans 

Confirm that the backfill material being used is approved by the engineer 

Confirm that placement of the backfill is performed in lifts consistent with the specifications 

Confirm that minimum concrete strength is achieved before backfill is placed and compacted 

against back of wall 

Confirm that the backfill placement method used by the contractor does not cause damage to 

prefabricated drainage material or drain pipes 

Confirm that earth cover over drainage pipes is sufficient to prevent damage from heavy 

equipment. The minimum cover based on ground pressure from equipment should be 

provided in the specifications. 

Perform required backfill density tests at the frequencies specified, especially for areas that are 

compacted with lightweight equipment, e.g., areas just behind the wall. 

Check that the drainage backfill just behind weep holes is the correct gradation and that it is 

properly installed 

POST INSTALLATION 

Verify pay quantities 

 Note: Throughout the project, check submittals for completeness before transmitting them to the engineer.
 

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[THIS PAGE INTENTIONALLY BLANK] 
CHAPTER 11.0 

GEOTECHNICAL REPORTS 

Upon completion of the subsurface exploration and laboratory testing program, the 

geotechnical specialist will compile, evaluate, and interpret the data and perform engineering 

analyses for the design of foundations, cut slopes, embankments, and other required facilities. 

Additionally, the geotechnical specialist will be responsible for producing a report that 

presents the subsurface information obtained from the site investigations and provides 

specific design and construction recommendations. The geotechnical analyses and design 

procedures to be implemented for the various types of highway facilities are addressed in 

various other FHWA publications. This chapter provides guidelines and recommendations 

for developing a geotechnical report. 

11.01 Primary References 

FHWA (1988). Checklist and Guidelines for Review of Geotechnical Reports and 

Preliminary Plans and Specifications. Report No. FHWA ED-88-053, Federal 

Highway Administration, U.S. Department of Transportation, Revised 2003. 

Geotechnical Engineering Notebook. FHWA Geotechnical Guidelines GT1–GT16. 

http://www.fhwa.dot.gov/engineering/geotech/index.cfm. 

11.1 TYPES OF REPORTS 

Generally, one or more of three types of reports will be prepared: A geotechnical 

investigation report; a geotechnical design report and/ or a geoenvironmental report. Several 

disciplines within an agency may contribute to the development of the geotechnical report. 

The preparer and the choice of the report depends on the requirements of the highway agency 

(owner) and the agreement between the geotechnical specialist and the facility designer. The 

need for multiple types of reports on a single project depends on the project size, phasing and 

complexity. Regardless, all the typical sections of a report outlined herein must be included. 

All consultant produced work should be in conformance with the reporting guidelines for the 

agency. 

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11.1.1 Geotechnical Investigation Reports 

Geotechnical investigation reports present site-specific data and have three major 

components: 

1. Background Information: The initial sections of the report summarize the 

geotechnical specialist's understanding of the facility for which the report is being 

prepared and the purposes of the subsurface exploration. This section includes 

information on loads, deformations and additional performance requirements. This 

section also presents a general description of site conditions, geology and geologic 

features, drainage, ground cover and accessibility, and any peculiarities of the site 

that may affect the design and construction. 

2. Work Scope: The second part of the investigation report documents the scope of the 

exploration program and the specific procedures used to perform this work. These 

sections identify the types of exploration methods used; the number, location and 

depths of borings, exploration pits and in-situ tests; the types and frequency of 

samples obtained; the dates of subsurface exploration; the subcontractors used to 

perform the work; the types and number of laboratory tests performed; the testing 

standards used; and any variations from conventional procedures. 

3. Data Presentation: This portion of the report, generally contained in appendices 

with a complementary narrative of explanation, presents the data obtained from the 

field and laboratory exploration program. The appendices typically include final logs 

of all borings, exploration pits, and piezometer or well installations, water level 

readings, data plots from each in-situ bore hole, summary tables and individual data 

sheets for all laboratory tests performed, rock core photographs, geologic mapping 

data sheets and summary plots, subsurface profiles developed from the field and 

laboratory test data, as well as statistical summaries. The geotechnical investigation 

report often includes copies of existing information such as boring logs or laboratory 

test data from previous investigations at the project site. 

The intent of a geotechnical investigation report is to document the investigation performed 

and present the data obtained. The report should include a summary of the subsurface and 

lab data. Interpretations and recommendations on the index and design properties of soil and 

rock should also be included. The geotechnical investigation report typically does not 

include detailed design analyses and recommendations, but it should include a narrative that 

summarizes and provides an interpretation of the subsurface data. The geotechnical 

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Soils and Foundations – Volume II 11 - 2 December 2006 
investigation report is sometimes used when the subsurface explorations are subcontracted to 

a geotechnical consultant, but the data interpretation and design tasks are performed by the 

owner’s or the prime consultant’s in-house geotechnical staff. An example Table of Contents 

for a geotechnical investigation report is presented in Figure 11-1. 

11.1.2 Geotechnical Design Reports 

A geotechnical design report typically provides an assessment of existing subsurface 

conditions at a project site, presents, describes and summarizes the procedures and findings 

of all geotechnical analyses performed, and provides appropriate recommendations for 

design and construction of foundations, earth retaining structures, embankments, cuts, and 

other required facilities. Unless a separate geotechnical investigation report was developed 

previously, the geotechnical design report will also include documentation of any subsurface 

explorations and laboratory investigations performed and a presentation of the results of 

those investigations as described in Section 11.1.1. An example Table of Contents for a 

geotechnical design report is presented in Figure 11-2. 

Since the scope, site conditions, and design/construction requirements of each project are 

unique, the specific contents of a geotechnical design report must be tailored for each project. 

In order to develop this report, the author must possess detailed knowledge of the facility. In 

general, however, the geotechnical design report must address all the geotechnical issues that 

may be anticipated on a project. The report must identify each soil and rock unit of 

engineering significance, and must provide recommended design parameters for each of 

these units. To this end, all factual data must be synthesized and analyzed to justify the 

recommended index and design properties. Groundwater conditions are particularly 

important for both design and construction and, accordingly, they need to be carefully 

assessed and described. For every project, the subsurface conditions encountered in the site 

investigation need to be compared with the geologic setting in order to understand the nature 

of the deposits better and to predict the degree of variability between exploration locations. 

Each geotechnical design issue must be addressed in accordance with the methodology 

described in the various chapters of this manual. The results of these studies need to be 

discussed concisely and clearly in the report. Of particular importance is an assessment of 

the impact of existing subsurface conditions on construction operations, phasing and timing. 

Properly addressing any construction issues in the report that are related to subsurface 

conditions can preclude change-of-conditions claims. Examples include but are not limited 

to: 

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 1.0 INTRODUCTION 

2.0 SCOPE OF WORK 

3.0 SITE DESCRIPTION 

4.0 SITE CONDITIONS, GEOLOGIC SETTING, AND TOPOGRAPHIC INFORMATION 

5.0 FIELD INVESTIGATION PROGRAM AND IN-SITU TESTING 

6.0 DISCUSSION OF LABORATORY TESTING 

7.0 SUMMARY OF SUBSURFACE CONDITIONS AND SOIL PROFILES 

8.0 DISCUSSION OF FINDINGS, CONCLUSIONS, AND RECOMMENDATIONS 

8.1 GENERAL 

8.1.1 Subgrade and Foundation Soil/Rock Types 

8.1.2 Soil/Rock Properties 

8.2 GROUND WATER CONDITIONS/ OBSERVATIONS 

8.3 SPECIAL TOPICS (e.g., dynamic properties, seismicity, environmental). 

8.4 CHEMICAL ANALYSIS 

9.0 FIELD PERMEABILITY TESTS 

10.0 REFERENCES 

LIST OF APPENDICES

 Appendix A - Boring Location Plan and Subsurface Profiles 

Appendix B - Test Boring Logs and Core Logs With Core Photographs 

Appendix C - Cone Penetration Test Soundings 

Appendix D - Flat Plate Dilatometer, Pressuremeter, Vane Shear Test Results

 Appendix E - Geophysical Survey Data 

Appendix F - Field Permeability Test Data and Pumping Test Results 

Appendix G - Laboratory Test Results 

Appendix H - Existing Information 

LIST OF FIGURES 

LIST OF TABLES 

Figure 11-1. Example Table of Contents for a Geotechnical Investigation Report. 

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1.0 INTRODUCTION 

1.1 Project Description (includes facility description, loads and performance 

requirements) 

1.2	 Scope of Work
 

2.0 GEOLOGY 

2.1	 Regional Geology

 2.2	 Site Geology 

3.0 EXISTING GEOTECHNICAL INFORMATION 

4.0 SUBSURFACE EXPLORATION PROGRAM 

4.1 Subsurface Exploration Procedures 

4.2	 Laboratory Testing 

5.0 SUBSURFACE CONDITIONS 

5.1	 Topography

 5.2 Stratigraphy

 5.3 Soil Properties 

5.4 Groundwater Conditions 

6.0 RECOMMENDATIONS FOR BRIDGE FOUNDATIONS 

6.1 Design Alternatives 

6.2	 Group Effects 

6.3 Foundation Settlement 

6.4	 Downdrag 

6.5 Lateral Loading 

6.6	 Construction Considerations 

6.7 Pile Testing 

7.0 RECOMMENDATIONS FOR EARTH RETAINING STRUCTURES 

7.1 Suitable Types 

7.2 Design and Construction Considerations 

8.0 ROADWAY RECOMMENDATIONS 

8.1	 Embankments and Embankment Foundations 

8.2	 Cuts 

8.3	 Pavement 

9.0 SEISMIC CONSIDERATIONS 

9.1 Seismicity
 

9.2 Seismic Hazard Criteria 

9.3	 Liquefaction Potential 

10.0 CONSTRUCTION RECOMMENDATIONS 

LIST OF REFERENCES 

LIST OF FIGURES 

APPENDICES 

Appendix A Boring Logs 

Appendix B Laboratory Test Data 

Appendix C Existing Subsurface Information 

Figure 11-2. Example Table of Contents for a Geotechnical Design Report. 

FHWA NHI-06-089 11 – Geotechnical Reports 

Soils and Foundations – Volume II 11 - 5 December 2006 
•	 vertical and lateral limits for recommended excavation and replacement of any 

unsuitable shallow surface deposits such as peat, muck and top soil; 

•	 excavation and cut requirements, i.e., safe slopes for open excavations or the need for 

sheeting or shoring; 

•	 anticipated fluctuations of the groundwater table along with the consequences of a 

high groundwater table on excavations; 

•	 effect of boulders on pile drivability or drilled shaft drilling, and rock hardness on 

rippability. 

Recommendations should be provided for the solution of anticipated problems. The above 

issues are but a few of those that need to be addressed in a geotechnical design report. To aid 

engineers with a quantitative review of geotechnical reports, FHWA has prepared review 

checklists and technical guidelines (FHWA, 2003b). One of the primary purposes of the 

FHWA guidelines is to provide transportation agencies and consultants with minimum 

standards/criteria for the geotechnical information that FHWA recommends be included in 

geotechnical reports as well as plans and specification packages. Technical guidelines for 

“minimum” site investigation information common to all geotechnical reports for any type of 

geotechnical feature and basic information and recommendations for specific geotechnical 

features are provided in the checklists and technical guidelines (FHWA, 2003b). Checklists 

are presented in the form of a question and answer format for specific geotechnical features 

such as: 

•	 centerline cuts and embankments; 

•	 embankments over soft ground; 

•	 landslide corrections; 

•	 retaining walls; 

•	 structural foundations such as spread footings, driven piles and drilled shafts; 

•	 borrow material sites. 

11.1.3 GeoEnvironmental Reports 

When the subsurface exploration indicates the presence of contaminants at the project site, 

the geotechnical specialist may be requested to prepare a geoenvironmental report in which 

the findings of the investigation are presented and discussed, and recommendations made for 

the remediation of the site. 

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Soils and Foundations – Volume II 11 - 6 December 2006 
The preparation of such a report usually requires the geotechnical specialist to work with a 

team of experts, since many aspects of the contamination or the remediation may be beyond 

his/her expertise. A representative team preparing a geoenvironmental report may be 

composed of chemists, geologists, hydrogeologists, environmental scientists, toxicologists, 

air quality and regulatory experts, as well as one or more geotechnical specialists. The report 

should contain all of the components of the geotechnical investigation report, as discussed 

above. Additionally, the geoenvironmental report will have a clear and concise discussion of 

the nature and extent of contamination, the risk factors involved, if applicable, a contaminant 

transport model, and the source of the contamination , if known, e.g., landfill, industrial 

waste water line, broken sanitary sewer, above-ground or underground storage tanks, 

overturned truck or train derailment, etc. 

The team may also be required to present solutions to remediate the site. Depending upon 

the nature and amount of contaminant and its location within the geologic profile and its 

potential impact on the environment, remediation measures may include removal of the 

contaminated material, pumping and treatment of the contaminated groundwater, installation 

of slurry cut-off walls, abandonment of that portion of the right-of-way, deep soil mixing, 

biorestoration, and electrokinetics. The geoenvironmental report should also address the 

regulatory issues pertinent to the specific contaminants found and the proposed site 

remediation methods. 

11.2 DATA PRESENTATION 

11.2.1 Boring Logs 

Boring logs, rock coring, soundings, and exploration logging should be prepared in 

accordance with the procedures and formats discussed in Chapters 3 through 5. Test boring 

logs and exploration test pit records can be prepared by using software capable of storing, 

manipulating, and presenting geotechnical data in simple one-dimensional profiles, or 

alternatively two-dimensional graphs of the subsurface profiles, or three-dimensional 

representations. These and other similar software allow for the orderly storage of project 

data for future reference. The website: http://www.ggsd.com lists over 40 separate software 

packages available for the preparation of soil boring logs. 

Many new software programs offer a menu-based boring log drafting program. The 

computer-aided drafting tools let users create custom boring log formats that can include 

graphic logs, monitoring well details, and data plots. Custom designed legends explaining 

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graphic symbols and containing additional notes can be added to boring logs for greater 

clarity. These legends can include a library of soil types, sampler and well symbols as well 

as other nomenclature used on the boring logs. Geological profiles can be generated by the 

program and may be annotated with text and drawings. 

Similarly, the results of various in-situ tests performed by using cones, pressuremeters and 

vanes, can be presented by the use of available commercial software. Links to many 

geotechnical software programs may be found at: http://www.usucger.org 

Alternatively, it is convenient for the in-situ test data to be reduced directly and simply by 

using a spreadsheet format such as EXCEL and QUATTRO PRO. In many ways, the 

spreadsheet is a superior approach as it allows the engineer to tailor the interpretations 

individually to account for specific geologic settings and local formations. The spreadsheet 

also permits creativity and uniqueness in the graphical presentation of the results, thereby 

enhancing the abilities and resources available to the geotechnical personnel. Since soils and 

rocks are complex materials with enumerable variants and facets, a site-specific tailoring of 

the interpreted profiles and properties is prudent. 

11.2.2 Boring Location Plans 

A boring location plan should be provided for reference on a regional or local scale. County 

or city street maps or USGS topographic quad maps are ideally suited for this purpose. 

Topographic information at 20 ft (6 m) contour line intervals is now downloadable from the 

internet (e.g., www.usgs.gov). Topographic maps for the entire United States can also be 

purchased from commercial suppliers. 

The locations of all field tests, sampling, and exploratory studies should be shown clearly on 

a scaled plan of the specific site under investigation. Preferably, the plan should be a 

topographic map with well-delineated elevation contours and a properly-established 

benchmark. The direction of magnetic or true north should be shown. Figure 11-3 shows an 

example of a boring location plan. The fence baseline defines the line along which a vertical 

profile of subsurface conditions will be developed based on information from adjacent boring 

logs. If multiple types of exploratory methods are used, the legend on the site test location 

plan should clearly show the different types of soundings. 

A geographic information system (GIS) can be utilized on the project to locate the test 

locations with reference to existing facilities on the premises including any and all 

underground and above-ground utilities, as well as roadways, culverts, buildings, or other 

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Soils and Foundations – Volume II 11 - 8 December 2006 
structures. Recent advances have been made in portable measuring devices that utilize global 

positioning systems (GPS) to permit quick, approximate determinations of coordinates of test 

locations and installations. 

Figure 11-3. Example boring location plan for retaining walls RW-11 and RW-12 

retaining an on-ramp to a freeway. 

11.2.3 Subsurface Profiles 

Geotechnical reports are normally accompanied by the presentation of subsurface profiles 

developed from the field and laboratory test data. Longitudinal profiles are typically 

developed along the roadway or bridge alignment, and a limited number of transverse 

profiles may be included for key locations such as at major bridge foundations, cut slopes or 

high embankments. Such profiles provide an effective means of summarizing pertinent 

subsurface information. The subsurface profiles, coupled with judgment and an 

understanding of the geologic setting, aid the geotechnical specialist in his/her interpretation 

of subsurface conditions between the investigation sites. 

For the development of a two-dimensional subsurface profile, the profile baseline, typically 

the roadway centerline, needs to be defined on the boring location plan, and the relevant 

borings projected to this line. Figure 11-4 shows the subsurface profile along the “Fence 

Baseline” between retaining walls RW-11 and RW-12 shown in Figure 11-3. Judgment 

should be exercised in the selection of the borings since projection of the borings, even for 

short distances, may result in a misleading representation of the subsurface conditions in 

some situations. The subsurface profile should be presented at a scale appropriate to the 

depth and frequency of the borings and soundings and the overall length of the cross-section. 

An exaggerated scale of 1(V):10(H) or 1(V):20(H) is typically used. 

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Soils and Foundations – Volume II 11 - 9 December 2006 
Figure 11-4. Subsurface profile along the baseline between retaining walls RW-11 and RW-12 shown in 

FHWA NHI-06-089 Soils and Foundations – Volume II 11 - 10 
The subsurface profile can be presented with reasonable accuracy and confidence at the 

locations of the borings. However, owners and designers generally expect the geotechnical 

specialist to present a continuous subsurface profile that shows an interpretation of the 

location, extent and nature of subsurface formations or deposits between borings. At a site 

where rock or soil profiles vary significantly between boring locations, the value of such 

presentations become questionable. The geotechnical specialist must be very cautious in 

presenting such data. Such presentations should include clear and simple caveats explaining 

that the profiles, as presented, cannot be relied upon fully to represent actual subsurface 

conditions between investigation locations. Should there be a need to provide more reliable 

continuous subsurface profiles, the geotechnical specialist should increase the frequency of 

borings and/or utilize geophysical methods to determine the continuity of subsurface 

conditions, or lack thereof. 

11.3 TYPICAL SPECIAL CONTRACT NOTES 

The geotechnical specialist should include in the geotechnical design report any special notes 

that should be placed in the contract plans or special provisions. The purpose of such special 

notes is to bring the contractor's and/or project engineer's attention to certain special 

requirements of the design or construction. Example special notes relating to pile driving, 

drilled shaft, and embankment construction are as follows: 

1.	 "Difficult driving of piles may be encountered and mechanical equipment may be 

necessary to remove consolidated material or boulders from the location of piles. 

This may be accomplished by various types of earth augers, well drilling equipment, 

or other devices to remove the consolidated material to permit piles to be driven to 

the desired depth or rated resistance without damage." 

 

2.	 "If any obstructions to pile driving are encountered ten (10) feet or less from the 

bottom of the footing, the contractor shall, if so ordered by the engineer, pull the 

partially driven pile or piles, remove the obstruction, and backfill the hole with 

approved suitable material, which shall be thoroughly compacted to the satisfaction of 

the engineer. However, no partially driven pile shall be removed until the engineer is 

satisfied that the contractor has made every effort to drive the pile through the 

obstruction. Payment for excavation will be made at the unit price bid for the 

structure excavation item and for the temporary sheeting under Item when 

sheeting is used. No other extra payment will be made for this work." 

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Soils and Foundations – Volume II 11 - 11 December 2006 
3.	 "The ordered length of pile shall be measured below the cut-off elevation shown on 

the plans. Any additional lengths of pile or splices above the cut-off elevation 

necessary to facilitate the contractor's operation shall be at his own expense." 

4.	 "Piles for are driven because of possible future scour of the stream bed and 

shall be driven to the minimum lengths shown on the plans regardless of the 

resistance to driving. The actual driving resistance is estimated to be tons." 

5.	 "Piles will be acceptable only when driven to pile driving criteria established by the 

Chief Bridge Engineer. Prerequisite to establishing these criteria, the contractor shall 

submit, to the Chief Bridge Engineer, and others as required, Form 'Pile and 

Driving Equipment Data'. All information listed on Form shall be provided 

within fourteen (14) days after the award of the contract. Each separate combination 

of pile and pile driving equipment proposed by the contractor will require the 

submission of a corresponding Form ." 

6.	 "Piles for the existing structure shall be removed where they interfere with the pile 

driving for the new structure." 

7.	 "It shall be the contractor's responsibility to place the cofferdams for so that 

they will not interfere with the driving of batter piles. Pay lines for the cofferdams 

shall be as shown on the plans." 

8.	 "The general subsurface conditions at the site of this structure are as shown on 

Drawing No. ." 

9.	 "Pile driving will not be allowed at the abutments until fill settlement is complete. 

Estimated settlement time is months after placement of the foot 

surcharge." 

10. “The bottom of all drilled shafts shall be cleaned with a mechanical cleanout bucket 

before the concrete is placed in the shaft. A minimum of passes of the 

cleanout bucket is recommended. For dry shafts, the bottom of the shaft shall be 

cleaned such that no more than inches of excavated spoil and no more than 

xxxxx inches of water remain at the bottom of the shaft prior to concreting. If wet 

(slurry) construction processes are used, then the sand content prior to concreting 

shall not be greater than % by volume. In the event that wet (slurry) 

construction processes are used, the Engineer shall be contacted for further criteria.” 

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11. “Temporary surface casing is recommended to aid in alignment of drilled shafts as 

well as to prevent surface sloughing or raveling and to ensure personnel safety. A 

minimum ft long temporary surface casing with at least ft stick-up 

above the ground surface is recommended. The diameter of the surface casing shall 

not be more than be inches larger than the nominal diameter of the shaft. 

12. “Poorly graded sands and gravels were encountered during the design stage 

investigations. These soils are prone to caving and may cause large fluid losses 

during slurry-assisted drilled shaft construction. Therefore, localized caving should 

be anticipated during drilled shaft construction. These local caving zones may be up 

to ft thick and can occur at various depths.” 

13. "The contractor shall coordinate the project construction schedule to allow 

installation of embankment monitoring instrumentation by the Agency forces." 

"Instrumentation damaged by the contractor’s personnel shall be repaired or replaced 

at the contractor's expense. All construction activity in the area of any damaged 

instrument shall cease until the damage has been corrected." 

14. "The contractor's attention is directed to the soil sample gradation test results, which 

are shown on Drawing No. . Soil sample gradation test results have been 

furnished to assist the contractor in determining dewatering procedures, if necessary." 

15. "The actual soil resistance to be overcome to reach estimated pile tip elevation is as 

shown below for each abutment and pier. The contractor shall size his pile driving 

equipment to install piles to the estimated length without damage." 

16. "The south embankment shall be constructed to final grade and a month waiting 

period observed before pile driving begins. The actual length of the waiting period 

may be reduced by the Engineer based on an analysis of settlement platform and 

piezometer data." 

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11.4 SUBSURFACE INFORMATION MADE AVAILABLE TO BIDDERS 

The finished boring logs and/or generalized soil profile should be made available to bidders 

and included with the contract plans. Other subsurface information, such as soil and rock 

samples and results of field and laboratory testing, should also be made available for 

inspection by bidders. The invitation for bids should indicate the type of information 

available and when and where it may be inspected. The highway agency should have a 

system for documenting what information each contractor inspects. Such documentation can 

be of major importance in the event of later claim actions. 

The information developed during the subsurface exploration is very useful in the selection 

of effective construction procedures and for estimating construction costs. Such information 

is, therefore, of value to knowledgeable contractors bidding on the project. There has been 

much disagreement among owners and engineers as to what information should be made 

available to bidders, and how. The legal aspects are conflicting. In general, the owner's best 

interests are served by releasing pertinent information prior to the bid. Indeed, some courts 

have opined that failure to reveal information can weaken the owner's position in the event of 

dispute. On the other hand, some engineers are fearful that the release of information will 

imply guarantees on their part that the information is fully representative of the actual 

conditions that will be encountered. 

One of the best surveys of the problem was prepared by Standing Subcommittee No. 4 of the 

U.S. National Committee on Tunneling Technology. The Subcommittee was composed of 

engineers and attorneys having experience dealing with owners, engineering firms, and 

contracting organizations. 

The following is excerpted from their recommendations: 

"In sum, all subsurface data obtained for a project, professional interpretations 

thereof, and the design considerations based on these data and interpretations 

should be included in the bidding documents or otherwise made readily 

available to prospective contractors. Fact and opinion should be clearly 

separated. 

The bidder should be entitled to rely on the basic subsurface data, with no 

obligation to conduct his own subsurface survey. 

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Soils and Foundations – Volume II 11 - 14 December 2006 
It is considered, however, that specific disclaimers of responsibility for 

accuracy are appropriate, with respect to the following categories: 

•	 Information obtained by others, perhaps at other times and for other 

purposes, which is being furnished prospective bidders in order to 

comply with the legal obligation to make full disclosure of all available 

data. 

•	 Interpretations and opinions drawn from basic subsurface data, because 

equally competent professionals may reasonably draw different 

interpretations from the same basic data." 

Additional information on this topic is included in Geotechnical Guideline No. 15 – 

Geotechnical Differing Site Conditions of FHWA’s Geotechnical Engineering Notebook. 

11.5 LIMITATIONS (DISCLAIMERS) 

Soil and rock exploration and testing have inherent uncertainties. Thus users of the data who 

are unfamiliar with the variability of natural and manmade deposits should be informed in the 

report of the limitations inherent in the extrapolation of the limited subsurface information 

obtained from the site investigation. This notification often takes the form of “Disclaimer” 

clauses. The validity that courts give disclaimer clauses varies from state to state. However, 

the courts generally give much more validity to "specific" versus "general" disclaimer 

clauses. "General" disclaimer clauses are the types that say, in effect - subsurface 

information was gathered for use in design. However, the contractor should not rely on this 

information in preparing his bid. It is no big surprise, therefore, that judges give little 

validity to such general disclaimer clauses since common sense dictates that if the subsurface 

information is good enough to base the design on, then the contractor should be able to place 

some reliance on the information in preparing his bid. Dr. Ralph Peck, a noted geotechnical 

specialist, put it succinctly when asked his opinion concerning general disclaimer of 

subsurface information on a recent large Interstate project. He stated, "If the state or 

engineers it has engaged to develop the contract documents have accepted certain 

information as the basis for those documents, that information should not be disclaimed." 

As mentioned previously, the courts have generally upheld the use of "specific" disclaimer 

clauses. The use of specific disclaimer clauses is strongly recommended over the use of 

general disclaimer clauses. An example of a specific disclaimer would be a statement such 

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Soils and Foundations – Volume II 11 - 15 December 2006 
as – “the boring logs are representative of the conditions at the location where the boring was 

made but conditions may vary between borings.” 

The following are examples of good "specific" disclaimer clauses used by one highway 

agency. These disclaimer clauses are placed on the interpreted soil profile that is included in 

the contract plans: 

General Notes 

1.	 The explorations were made between and by . 

2.	 General soil and rock (where encountered) strata descriptions and indicated 

boundaries are based on an engineering interpretation of all available subsurface 

information by the Agency Name and may not necessarily reflect the actual 

variation in subsurface conditions between borings and samples. Data and field 

interpretation of conditions encountered in individual borings are shown on the 

subsurface exploration logs. 

3.	 The observed water levels and/or conditions indicated on the subsurface profiles are 

as recorded at the time of exploration. These water levels and/or conditions may vary 

considerably, with time, according to the prevailing climate, rainfall or other factors 

and are otherwise dependent on the duration of and methods used in the explorations 

program. 

4.	 Sound engineering judgment was exercised in preparing the subsurface information 

presented hereon. This information was prepared and is intended for State design and 

estimate purposes. Its presentation on the plans or elsewhere is for the purpose of 

providing intended users with access to the same information available to the State. 

This interpretation of subsurface information is presented in good faith and is not 

intended as a substitute for personal investigation, independent interpretations or 

judgment of the contractor. 

5.	 All structural details shown hereon are for illustrative purposes only and may not be 

indicative of the final design conditions shown in the contract plans. 

6.	 Footing elevations shown are as indicated at the time of this drawing's preparation. 

FHWA NHI-06-089 11 – Geotechnical Reports 

Soils and Foundations – Volume II 11 - 16 December 2006 
Other examples of site-specific disclaimers are as follows: 

•	 “The boring logs for BAF-1 through BAF-4 are representative of the conditions at the 

location where each boring was made, but conditions may vary between borings.” 

•	 “Although boulders in large quantities were not encountered on this site, in the 

borings that are numbered BAF-1 through BAF-4, previous projects in this area have 

found large quantities of boulders. Therefore, the contractor should be expected to 

encounter substantial boulder quantities in excavations. The contractor should 

include any perceived extra costs for boulder removal in this area in his bid price for 

Item xxx.” 

The reader is referred to a document entitled “Important Information About Your 

Geotechnical Engineering Report,” which is published by ASFE, The Association of 

Engineering Firms Practicing In The Geosciences (www.asfe.org). This document presents 

suggestions for writing a geotechnical report and observations to help reduce the 

geotechnical-related delays, cost overruns and other costly headaches that can occur during a 

construction project. 

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[THIS PAGE INTENTIONALLY BLANK] 
CHAPTER 12.0 

REFERENCES 

AASHTO (1988). Manual on Subsurface Investigations. American Association of State

Highway and Transportation Officials, Washington, D.C. 

AASHTO (1994). AASHTO LRFD Bridge Design Specifications, 1st Edition. American

Association of State Highway and Transportation Officials, Washington, D.C. 

AASHTO (1996). Standard Specifications for Highway Bridges. American Association of

State Highway and Transportation Officials, Washington, D.C. 

AASHTO (2002). Standard Specifications for Highway Bridges. American Association of

State Highway and Transportation Officials, Washington, D.C. 

AASHTO (2004 with 2006 Interims). AASHTO LRFD Bridge Design Specifications. 3rd

 

Edition, American Association of State Highway and Transportation Officials, 

Washington, D.C. 

AASHTO (2006). Standard Specifications for Transportation Materials and Methods of 

Sampling and Testing, Parts I and II. American Association of State Highway and 

Transportation Officials, Washington, DC. 

ACI (1956). Building Code Requirements for Reinforced Concrete, ACI 318-56. American 

Concrete Institute, Detroit, MI. 

ACI (1963). Building Code Requirements for Reinforced Concrete, ACI 318-63. American 

Concrete Institute, Detroit, MI. 

ACI (1968). Building Code Requirements for Reinforced Concrete, ACI 318-68. American 

Concrete Institute, Detroit, MI. 

ACI (2002). Building Code Requirements for Structural Concrete, ACI 318-02. American 

Concrete Institute, Detroit, MI. 

API-RP-2A (1993). Recommended Practice for Planning, Designing and Constructing Fixed 

Offshore Platforms - Load and Resistance Factor Design. American Petroluem Institute 

– Recommended Practices. 

FHWA NHI-06-089 12 - References
 

Soils and Foundations – Volume II 12 - 1 December 2006
 
 

 

 

ASCE (1993). Unsaturated Soils, Editors: Houston, S. L. and Wray, W. K., Geotechnical 

Special Publication No. 39, American Society of Civil Engineers, Reston, VA. 

ASCE (1994). Predicted and Measured Behavior of Five Spread Footings on Sand. Editors: 

Briaud, J-L, and Gibbens, R. M. Geotechnical Special Publication No. 41, American 

Society of Civil Engineers (co-sponsored by the Federal Highway Administration). 

ASCE (1997). Unsaturated Soil Engineering Practice, Editors: Houston, S. L. and Fredlund, 

D. G., Geotechnical Special Publication No. 68, American Society of Civil Engineers, 

New York, NY. 

ASTM (1988). Vane Shear Strength Testing in Soils: Field and Laboratory Studies. 

American Society for Testing and Materials, Committee D-18 on Soil and Rock For 

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Powers, J. P. (1992). Construction Dewatering: New Methods and Applications. 2nd, John 

Wiley & Sons, NY. 

Raines, R. D., Ugaz, O. G., and O’Neill, M. W. (1992). "Driving Characteristics of OpenToe Piles in Dense Sand." American Society of Civil Engineers, Journal of 

Geotechnical Engineering, 118 (No. 1), 72-88. 

Rankine, W. J. M. (1857). "On the Stability of Loose Earth." Proceedings of the Royal 

Society of London, London, 185-187. 

Rausche, F., Liang, L., Allin, R., and Rancman, D. (2004). “Applications and Correlations of 

the Wave Equation Analysis Program GRLWEAP.” Proceedings of the 7th 

International Conference on the Application of Stresswave Theory to Piles, Petaling 

Jaya, Selangor, Malaysia, 2004. 

Reese, L. C., Isenhower, W. M., and Wang, S-T. (2006). Analysis and Design of Shallow and 

Deep Foundations. John Wiley & Sons, NY. 

ReSSA (2001). ADAMA Engineering (www.GeoPrograms.com), Newark, DE. 

FHWA NHI-06-089 12 - References
 

Soils and Foundations – Volume II 12 - 15 December 2006
 
 

 

Roberts, F.L., Kandhal, P.S., Brown, E.R., Lee, D.Y., and Kennedy, T.W. (1996). Hot Mix 

Asphalt Materials, Mixture Design, and Construction. National Asphalt Pavement 

Association Education Foundation. Lanham, MD. 

Robertson, P. K., Campanella, R. G., Gillespie, D., and Greig, J. (1986). "Use of Piezomenter 

Cone Data." Geotechnical Special Publication No. 6, Use of In-Situ Tests in 

Geotechnical Engineering, American Society of Civil Engineers, New York, N.Y., 

1263-1280. 

Robertson, P. K., and Campanella, R. G. (1983). "Interpretation of Cone Penetration Tests." 

Canadian Geotechnical Journal, 20(4), 718-754. 

Samtani, N.C., Jalinoos, F., and Poland, D. M. (2005). “Integrity Testing of Drilled Shafts – 

Existing and New Techniques.” Proceedings of the GEO3

 Conference, ADSC, Dallas, 

TX. 

Schmertmann, G. R., Chouery-Curtis, V. E., Johnson, R. D., and Bonaparte, R. (1987). 

“Design Charts for Geogrid-Reinforced Soil Slopes.” Proceedings Geosynthetics ’87 

Conference., IFAI, Industrial Fabric Association International, New Orleans, 108-120. 

Schmertmann, J. H. (1955). "The Undisturbed Consolidation Behavior of Clay." 

Transactions, ASCE, Vol. 120, 1201-1233. 

Schmertmann, J. H., Hartman, J. P., and Brown, P. R. (1978). "Improved Strain Influence 

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Schmidt, B. (1966). "Discussion of, Earth Pressure At-Rest Related to Stress History." 

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Schroeder, W. L. (1980). Soils in Construction. 2nd Edition, John Wiley & Sons, NY. 

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FHWA NHI-06-089 12 - References
 

Soils and Foundations – Volume II 12 - 16 December 2006
 
 

Skempton, A. W. (1953). "The Collodial Activity of Clays." Proceedings 3rd International 

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Soares, M., de Mello, J. and de Matos, S. (1984). “Pile Driveability Studies, Pile Driving 

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Sowers, G. F. (1979). Introductory Soil Mechanics and Foundations: Geotechnical 

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Soils and Foundations – Volume II 12 - 17 December 2006
 
 

Terzaghi, K., and Peck, R. (1967). Soil Mechanics in Engineering Practice. 2nd Edition, John 

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Terzaghi, K., Peck, R. B., and Mesri, G. (1996). Soil Mechanics in Engineering Practice. 3rd 

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Properties of Residual Soil." Quarterly Journal of Engineering Geology & 

Hydrogeology, 21(1), 69-84. 

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Vesic, A. S. (1977). Design of Pile Foundations. NCHRP Report 42, Transportation 

Research Board, National Research Council, Washington, D.C. 

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Westergaard, H. M. (1938). A Problem of Elasticity Suggested by a Problem in Soil 

Mechanics: Soft Material Reinforced by Numerous Strong Horizontal Sheets. Harvard 

University, Cambridge, MA. 

Winterkorn, H. F., and Fang, H. (1975). Foundation Engineering Handbook. 2nd Edition, 

Van Nostrand Reinhold, New York, NY. 

Woodward, R. J., Gardner, W. S., and Greer, D. M. (1972). Drilled Pier Foundations. 

McGraw-Hill, NY. 

Wright, S. G., Arcement, B., and Benson, C. H. (2003). “Comparison of Maximum Density 

of Cohesionless Soils Determined Using Vibratory and Impact Compaction Methods.” 

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Mechanics and Geotechnical Engineering, Cambridge, MA, 1709-1715. 

WSDOT (1988). Comparison of Methods for Estimating Pile Capacity. Report No. WA-RD 

163.1, Authors: Fragasny, R. J., Higgins, J. D., and Argo, D. E., Washington State 

Department of Transportation, Olympia. 

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FHWA NHI-06-089 12 - References
 

Soils and Foundations – Volume II 12 - 19 December 2006
 
 

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APPENDIX A 

APPLE FREEWAY PROJECT 

FHWA NHI-06-089 Appendix A– Apple Freeway
 

Soils and Foundations – Volume II December 2006 
 

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FHWA NHI-06-089 Appendix A– Apple Freeway
 

Soils and Foundations – Volume II December 2006 
 

APPENDIX A 

APPLE FREEWAY PROJECT 

GENERAL NOTES 

This appendix presents the geotechnical engineering considerations and calculations for a 

fictitious bridge project from conception to completion in a serialized illustrative workshop 

design problem. The appendix is divided into several sections. Each section corresponds to a 

specific phase in the design and construction monitoring process. The section numbering 

system is as follows: 

A.# 

where A denotes appendix designation and # denotes the section number in the manual. Thus, 

Section A.2 relates to the second section in the appendix. Within each section, the numbering 

system for pages, figures, tables, etc. is in accordance with the following format: 

A.# - * 

where # denotes the section number in the appendix and * denotes the page number, figure 

number and so on in that section. Thus, for example, “Figure A.2-4” refers to the fourth figure 

in the second section, and “A.2-4” at the bottom of the page refers to the fourth page in the 

second section. 

As an aid to following the design process, a summary of relevant concepts and/or procedures is 

presented at the beginning of each section with cross reference to the appropriate chapter(s) in 

the text of the manual. Equations used in the computations are also cross referenced to the 

equation number listed in the text of the manual. 

To simplify hand calculations, the unit weight of water, γw, of 60 pcf has been used in some of 

the calculations. In actual calculations for any given project, the user should use the more 

common value of γw = 62.4 pcf unless higher values are justified, e.g., in brackish water. 

FHWA NHI-06-089 General Notes 

Soils and Foundations – Volume II A - 1 December 2006 
SECTION A.1 

INTRODUCTION AND SCOPE OF WORK
 

A.1-1 RELEVANT CONCEPTS AND PROCEDURES 

•	 Description of the project. 

•	 Development of a scope of work 

A.1-2 DESCRIPTION OF THE PROJECT 

Figure A.1-1 shows the layout of a two-span bridge that carries Interstate 0 (I-0) over the 

Apple Freeway, which is a divided freeway. The center pier of the I-0 bridge will be in the 

median between the northbound (NB) and southbound (SB) freeway. The approaches to 

the bridge will be constructed on embankment fills. The fills will have an end-slope 

spilling through the abutment locations at a grade of 2H:1V (H: Horizontal, V: Vertical) as 

shown in Figure A.1-1. 

A.1-3 SCOPE OF WORK 

The scope of the work includes the following: 

•	 Setup and perform the field investigations. The field investigations should include 

SPTs in drilled holes and CPTs to obtain continuous stratigraphic profiles. Develop 

idealized subsurface profile based on visual description of soils and information from 

CPT sounding profiles. 

•	 Setup and perform laboratory investigations including consolidation and strength tests. 

•	 Perform slope stability analyses for the 2H:1V end-slopes. Evaluate the end-slopes for 

both circular and block failure mechanisms. 

•	 Perform immediate and consolidation settlement analyses and lateral squeeze 

computations for embankment fills. If warranted, perform ground improvement as 

necessary to mitigate large long-term settlements. Evaluate two alternatives (a) 

surcharging and (b) surcharging with wick-drains. 

•	 Evaluate and analyze spread shallow foundations at both abutment and pier locations. 

Determine the allowable bearing capacity, anticipated settlement and settlement rates. 

•	 Evaluate and analyze driven pile foundations at both abutments and pier locations. 

Evaluate driving resistance for pile foundation alternative. Estimate the possible 

abutment lateral movement due to lateral squeeze of soils. 

•	 Perform wave equation analyses for pile foundations as part of construction monitoring 

and QA/QC. 

•	 Prepare a memorandum report summarizing the above work. 

FHWA NHI-06-089 Introduction and Scope of Work 

Soils and Foundations – Volume II A.1 - 1 December 2006 
Figure A.1-1. Apple Freeway plan and section. 

FHWA NHI-06-089 Introduction and Scope of Work 

Soils and Foundations – Volume II A.1 - 2 December 2006 
 

[THIS PAGE INTENTIONALLY BLANK]
 
 

 

 

 

 

 

 

 

 

Subsurface 

Explorations 

Basic Soil Properties Visual description 

Classification tests 

Subsurface profile 

Laboratory Testing po diagram 

Test request 

Consolidation results 

Strength results 

Slope 

Stability 

Design soil profile 

Circular arc analysis 

Sliding block analysis 

Approach Roadway 

Deformations 

Design soil profile 

Magnitude of settlement 

Rate of settlement 

Surcharge 

Vertical drains 

Lateral squeeze 

Spread Footing 

Design 

Design soil profile 

Pier bearing capacity 

Pier settlement 

Abutment settlement 

Surcharge 

Vertical drains 

Driven Pile Design Design soil profile 

Static analysis – pier

 Pipe pile 

H - pile 

Static analysis – abutment 

Pipe pile 

 H-pile 

Driving resistance 

Lateral movement - abutment 

Construction 

Monitoring 

Wave equation 

Hammer approval 

Embankment instrumentation 

Terrain reconnaissance 

Site inspection 

Subsurface explorations 

Figure A.2-1 . Overview of the geotechnical work to be performed. 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 1 December 2006 
SECTION A.2 

SUBSURFACE EXPLORATIONS 

A.2-1 RELEVANT CONCEPTS AND PROCEDURES (Refer to Figure A.2-1) 

•	 Terrain reconnaissance and site inspection – Chapter 3 

•	 Preparation of a field exploration program – Chapter 3 

•	 Subsurface borings for SPT sampling – Chapter 3 

•	 Subsurface soundings for CPT logging – Chapter 3 

A.2-2 DETAILED PROCEDURES 

Given:	 Examination of USGS topo and geology maps and USDA soil map showed 

structure to be located in a delta landform. Field inspection showed wet area 

with cattails in vicinity of east abutment. 

Required:	 Plan subsurface exploration program and prepare boring request. 

Solution Procedure: 

Step 1:	 Prepare terrain reconnaissance and site inspection 

•	 Locate structure on USGS topo map or other maps available from local 

agencies that show greater surface detail to obtain preliminary estimates of 

boring locations and site access by drilling equipment. 

•	 Visit the site to verify conditions. 

Step 2:	 Prepare preliminary field exploration program (see Figure A.2-2) 

•	 Identify types of subsurface borings and establish location of each. 

•	 Specify borings with disturbed SPT sampling (DH BAF) at each abutment 

and intermediate support 

•	 Specify CPT soundings (CPT BAF) immediately next to the drill hole in 

which the SPTs were performed. 

•	 Specify hand auger holes (EA) in wet area within east approach fill limits 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 2 December 2006 
CPT-BAF-2 CPT-BAF-4 

CPT-BAF-3 CPT-BAF-1 

Figure A.2-2 . Proposed site exploration – Preliminary. 

Step 3: Establish criteria for determining boring depth 

•	 SPT holes to depth where the minimum average SPT-N equals 20 for 20-ft 

depth or 10-ft into bedrock, whichever depth is less. 

•	 Based on the observations from terrain reconnaissance, use a 20-ton CPT 

rig which should be sufficient to explore the soft and/or organic soils 

•	 Hand auger holes to a maximum depth of 10-ft or at least 3-ft below bottom 

of unstable soils (soft and/or organic soils), whichever depth is less. 

Step 4: Establish sampling criteria 

•	 East and west abutments: disturbed SPT every 5-ft. 

•	 Pier footing: continuous SPT samples to depth of 15-ft, then 5-ft intervals 

since spread footings may be considered 

•	 Wet area: obtain representative samples from each auger hole. 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 3 December 2006 
•	 CPTs: perform with a piezocone to permit pore water pressure 

measurements 

Step 5:	 Identify and address other important considerations. 

•	 Since area is a delta landform, granular deposits overlying clay may be 

encountered. If so, an undisturbed drill hole (UDH) will be required. The 

location, depth, and sampling details will be selected based on the results of 

the three SPT boring. Notify the drillers of possibility of UDH and field 

vane shear so necessary equipment can be taken to site. 

•	 Long-term water level reading should be taken in one hole. 

•	 Obtain all required right-of-way (ROW) and entry permits. Consult with 

state and local departments of environmental quality for any environmental 

permits if required. 

•	 Arrange for traffic control on Apple Freeway 

Step 6:	 Prepare preliminary field exploration request (see Figure A.2-3). 

Step 7:	 Perform field exploration and prepare final field exploration layout (see 

Figure A.2-4) 

•	 Perform three (3) SPT drill hole (DH) borings (DH BAF-1, DH BAF-2, DH 

BAF-3) 

•	 Perform four (4) CPT probes (CPT BAF-1, CPT BAF-2, CPT BAF-3 and 

CPT BAF-4) 

•	 Perform one (1) undisturbed drill hole (UDH) borings (UDH BAF-4) 

•	 Perform nine (9) hand-augured holes (EA1 to EA9) on a rectangular grid 

pattern at the east abutment site 

•	 Logs of borings, CPT soundings and hand-augured holes are included 

herein. 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 4 December 2006 
FHWA NHI-06-089 Subsurface Explorations 

Soils and Foundations – Volume II A.2 - 5 December 2006 

Figure A.2-3 . Typical preliminary exploration request.

SUBSURFACE EXPLORATION REQUEST 

 August 1, 2006 

Subject: Request for Subsurface Exploration 

 Interstate Structure over the Apple Freeway 

From: Foundation Engineer 

To: Regional Office 

In accordance with project authorization from the Chief Engineer dated January 16, 2006, a subsurface 

exploration program has been prepared for the subject structure. We request that your office advance a 

21⁄2 - inch diameter cased drill hole and a CPT sounding at each of the following locations: 

 

 Baseline 

Hole No. 

DH-BAF-1 

Station

90 + 77 

 Offset (ft) 

50' Rt 

DH-BAF-2 92 + 00 50' Lt 

DH-BAF-3 93 + 27 50' Rt 

 

The locations may be field adjusted along the footing line shown on the attached drawing if necessary. 

Each boring shall extend to a depth where the blow count per foot on the sample spoon exceeds 20 for a 

20-feet depth. If rock is encountered above this depth, 10 feet of rock core shall be cored and extracted. 

Spoon samples shall be taken at intervals of 5-feet except for the top 15-feet of BAF-2 where continuous 

spoon samples are required. On completion of BAF-2 a perforated plastic pipe shall be inserted before 

extracting the casing to permit long-term water level observation. It is anticipated that soft clay soils may 

be encountered at this site. If so, an additional 4-inch diameter cased hole (UDH) may be required to 

extract undisturbed tube samples and/or perform in situ vane shear tests. Before the drill crew 

demobilizes, the driller should telephone the results of the first three SPT borings to the project engineer, 

Mr. Richard Cheney at 202-555-0355. At that time, a decision on the details of the UDH will be issued. 

The CPT soundings shall be performed by using CPTu equipment that includes a piezocone to permit 

continuous pore water pressure measurements. The CPT truck should provide a minimum reaction of 20 

tons. A CPT sounding shall be performed in the immediate vicinity of each of the drilled holes. 

A wet area of potentially unstable soil (soft and/or organic soils) exists in the area of the proposed east 

approach embankment. Please define the depth of this deposit beneath the limits of the east approach 

embankment back to Baseline station 93 + 50 with hand auger exploration. Perform at least 9 hand auger 

holes in that area on a rectangular grid pattern and show the locations on the final exploration layout plan. 

The present schedule for structure design requires that all samples and subsurface logs be received in the 

main office by November 1, 2006. 

Attachment: Proposed preliminary site exploration plan (Figure A.2-2).
CPT-BAF-2 CPT-BAF-4 

CPT-BAF-3 CPT-BAF-1 

Figure A.2-4. Final field exploration layout. 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 6 December 2006 
A.2-3 SUMMARY OF THE SITE EXPLORATION PHASE FOR THE APPLE 

FREEWAY DESIGN PROBLEM 

1.	 Terrain Reconnaissance 

•	 Delta landform - possible clay deposit buried 

2.	 Site Inspection 

•	 Unsuitable soils near east approach embankment 

•	 Easy access for drilling equipment and CPT rig. 

3.	 Subsurface Borings 

•	 Hand auger holes define limits and depth of unsuitable organic deposit. 

•	 SPT drill holes show sand over clay over gravel and rock. 

•	 CPT soundings indicate that the clay layer may have thin silt seams in it (this would 

possibly help in reducing consolidation time) 

•	 Undisturbed samples and vane shear tests taken in clay. 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 7 December 2006 
Figure A.2-5. Field log for boring DH BAF-1 (0-35 ft). 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 8 December 2006 
Figure A.2-5 (Continued). Field log for boring DH BAF-1 (35-60 ft). 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 9 December 2006 
Figure A.2-6. Field log for boring DH BAF-2 (0-35 ft). 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 10 December 2006 
Figure A.2-6 (Continued). Field log for boring DH BAF-2 (35-60 ft). 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 11 December 2006 
Figure A.2-7. Field log for boring DH BAF-3 (0-35 ft). 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 12 December 2006 
Figure A.2-7 (Continued). Field log for boring DH BAF-3 (35-69 ft). 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 13 December 2006 
Figure A.2-8. Field log for boring DH BAF-4 (0-35 ft). 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 14 December 2006 
Figure A.2-8 (Continued). Field log for boring DH BAF-4 (35-65 ft). 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 15 December 2006 
Figure A.2-9. CPT sounding from CPT-BAF-1 in vicinity of DH BAF-1. 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 16 December 2006 
Figure A.2-10. CPT sounding from CPT-BAF-2 in vicinity of DH BAF-2. 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 17 December 2006 
Figure A.2-11. CPT sounding from CPT-BAF-3 in vicinity of DH BAF-3. 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 18 December 2006 
Figure A.2-12. CPT sounding from CPT-BAF-4 in vicinity of UDH BAF-4. 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 19 December 2006 
Figure A.2-13. Hand Auger Hole Logs - East Abutment Area. 

FHWA NHI-06-089 Subsurface Explorations
 

Soils and Foundations – Volume II A.2 - 20 December 2006 
 

 

 

 

 

 

 

 

 

 

 

 

Subsurface Terrain reconnaissance 

Explorations Site inspection 9

Laboratory testing 

Slope 

Stability 

Approach roadway 

Deformations 

Spread footing design 

Driven pile design 

Construction 

monitoring 

Subsurface explorations 

Basic soil 

properties 

po diagram 

Test request 

Consolidation results 

Strength results 

Design soil profile 

Circular arc analysis 

Sliding block analysis 

Design soil profile 

Magnitude of settlement 

Rate of settlement 

Surcharge 

Vertical drains 

Lateral squeeze 

Design soil profile 

Pier bearing capacity 

Pier settlement 

Abutment settlement 

Surcharge 

Vertical drains 

Design soil profile 

Static analysis – pier 

 Pipe pile 

H - pile 

Static analysis – abutment 

Pipe pile 

H - pile 

Driving resistance 

Lateral movement - abutment 

Wave equation 

Hammer approval 

Embankment instrumentation 

Visual description 

Classification tests 

Subsurface profile
 

Figure A.3-1. Overview of the geotechnical work to be performed. 

FHWA NHI-06-089 Basic Soil Properties 

Soils and Foundations – Volume II A.3 - 1 December 2006
 
SECTION A.3 

BASIC SOIL PROPERTIES 

A.3-1 RELEVANT CONCEPTS AND PROCEDURES (Refer to Figure A.3-1) 

•	 Visual description of soils – Chapter 4.1 

•	 Classification tests – Chapter 4.2 

•	 Engineering characteristics of main soil types – Chapter 4.3 

•	 Idealized soil profile – Chapter 4.7 

In this section the process of estimating the engineering characteristics of the main soil types 

based on visual descriptions (logs) and classification tests (field and laboratory) is illustrated. 

The boring logs, CPT soundings and laboratory moisture content test data presented in 

Appendix A.2-1 are used to illustrate how an idealized soil profile is established for analysis 

and design. Note that the idealized profile is not suitable for bidding purposes 

A.3-2 DETAILED PROCEDURES 

Given:	 Boring logs with SPT-N, logs of CPT soundings, and laboratory moisture 

content test data. 

Required:	 Develop a preliminary idealized soil profile for analysis and design. 

Solution Procedure: 

Step 1: Locate the borings in plan (Refer to Figure A.3-2). 

•	 Distinguish between SPT borings (target symbols), CPT soundings (large 

solid circles), and hand-auger borings (small solid circles). 

•	 Use appropriate designations to identify each probe (Refer to Section A.2-

2 – Step 2). 

Step 2: Show corresponding elevation view of borings, soundings and auger holes 

(Refer to Figure A.3-3). 

•	 Plot the variation of field SPT-N values and laboratory moisture content 

test data with depth. 

•	 SPT values are boxed and designated by the symbol “N”. 

•	 Corresponding moisture contents are listed to the right of the SPT-N 

values and are designated by the symbol “W.” 

•	 Make sure the designation used to identify each probe is consistent with 

FHWA NHI-06-089 Basic Soil Properties 

Soils and Foundations – Volume II A.3 - 2 December 2006
 
that shown in Figure A.3-2. 

• Plot the observed water levels in the borings and the date observed. 

Step 3: Develop a preliminary idealized soil profile by interpolating between 

borings to identify zones where soils may have similar characteristics. 

•	 Use SPT-N values and visual descriptions made by field personnel as the 

initial criteria for distinguishing between different types of soil. 

•	 Include soil descriptions on the elevation drawings. 

•	 Perform a preliminary classification of the soils according to the Unified 

Soil Classification System (USCS) or some other system commonly used 

in region. The preliminary classification according to visual-manual 

procedures (ASTM D2488) will be verified or changed based on the 

results of the laboratory testing phase of the geotechnical investigation. In 

lieu of the soil descriptions, USCS symbols may be included on the 

profile. 

•	 Show the idealized profile on the elevation drawing in terms of zones, 

with the top and bottom of each zone clearly marked in each boring. The 

lines between borings are solely for the purpose of the design and should 

not be shown on bid documents since such well-defined boundaries may 

not exist in reality. 

•	 Compare the preliminary idealized soil profile with CPT soundings and 

adjust as necessary. 

FHWA NHI-06-089 Basic Soil Properties 

Soils and Foundations – Volume II A.3 - 3 December 2006
 
CPT-BAF-2 CPT-BAF-4 

CPT-BAF-3 CPT-BAF-1 

Figure A.3-2. Location Plan – SPT Borings, CPT Soundings and Hand-Auger Holes. 

Figure A.3-3. Designer’s interpretation of preliminary idealized soil profile through 

Section A-A. 

FHWA NHI-06-089 Basic Soil Properties 

Soils and Foundations – Volume II A.3 - 4 December 2006
 
A.3-3 SUMMARY OF SOIL CHARACTERISTICS FROM RESULTS OF FIELD 

INVESTIGATIONS AND THEIR USE IN DEVELOPING AN IDEALIZED 

SOIL PROFILE 

1.	 Boring location (plan and elevation) prepared by designer 

•	 SPT-N and depth to ground water table are shown on longitudinal and 

transverse sections cut through selected boring locations shown on plan. 

2.	 Visual description of materials encountered during drilling performed by field 

personnel 

•	 Predominant soil types are sand, silty clay and sandy gravel. 

•	 Rock 

3.	 Visual-manual procedures used by field personnel to classify soils 

•	 Preliminary classifications are sand (SW), silty clay (CL), and sandy gravel 

(GW) according to the Unified Soil Classification System 

4.	 Moisture content determined in the laboratory. 

•	 Values of moisture content are shown on the sections next to SPT-N values. 

5.	 Preliminary idealized soil profile developed based on information shown on the 

sections. 

•	 Subsurface variation of soil layers and ground water estimated between 

borings. 

•	 Idealized profile expressed in terms of zones with boundaries shown at boring 

locations only. 

•	 Profile may differ in transverse and longitudinal directions. 

•	 Preliminary profile compared to CPT soundings to refine characteristics of 

soils identified. For example, CPT soundings indicate that the silty clay layer 

may contain distinct seams of silt. The presence of such seams may help to 

reduce consolidation time. 

FHWA NHI-06-089 Basic Soil Properties 

Soils and Foundations – Volume II A.3 - 5 December 2006
 
[THIS PAGE INTENTIONALLY BLANK] 
 

 

 

 

 

 

 

 

 

Subsurface Terrain reconnaissance 

Explorations 

Subsurface explorations 

Site inspection 9

Basic soil properties Visual description 

Classification tests 9

Slope 

Stability 

Approach Roadway 

Deformations 

Spread footing design 

Driven pile design 

Construction 

monitoring 

Subsurface profile 

po diagram

Laboratory Test request

testing Consolidation results 

Strength results 

Design soil profile 

Circular arc analysis 

Sliding block analysis 

Design soil profile 

Magnitude of settlement 

Rate of settlement 

Surcharge 

Vertical drains 

Lateral squeeze 

Design soil profile 

Pier bearing capacity 

Pier settlement 

Abutment settlement 

Surcharge 

Vertical drains 

Design soil profile 

Static analysis – pier 

 Pipe pile 

H - pile 

Static analysis – abutment 

Pipe pile 

H - pile 

Driving resistance 

Lateral movement - abutment 

Wave equation 

Hammer approval 

Embankment instrumentation 

Figure A.4-1. Status of geotechnical work. 

FHWA NHI-06-089 Laboratory Testing
 

Soils and Foundations – Volume II A.4 - 1 December 2006 
SECTION A.4 

LABORATORY TESTING 

A.4-1 RELEVANT CONCEPTS AND PROCEDURES (Refer to Figure A.4-1) 

•	 Construction of the po diagram – Example 2-1. 

•	 Preparation of a soil mechanics laboratory test request. 

•	 Presentation of typical consolidation test results – Chapter 5.4. 

•	 Presentation of typical strength test results – Chapter 5.5. 

In this section the construction of a po diagram based on the Apple Freeway soil profile is 

demonstrated. A laboratory test request for consolidation and strength tests is presented. 

The numerical results of such tests are included in tabular form at the end of the chapter. The 

results are also presented in graphical form to show the variation of maximum past effective 

stress (pc) and undrained shear strength (su) with depth. 

A.4-2 DETAILED PROCEDURES 

Given:	 Preliminary idealized soil profile as determined in Section A.3 and total (γt) 

and dry (γd) unit weights of soils in the profile as determined from laboratory 

tests (Refer to Chapter 2) 

Required: 

•	 Construct the po diagram (Refer to Figure A.4-2). The po diagram represents the 

variation of the effective geostatic vertical stress (po) with depth. Typically, the 

variation of the total geostatic vertical stress (pt) with depth is also shown on the po 

diagram to illustrate the effect of the groundwater table on the effective stress 

distribution. The difference between the two curves is the hydrostatic pore water 

pressure (pw) (Refer to Chapter 2) 

•	 Prepare laboratory test request for consolidation and strength testing (Refer to Figure 

A.4-3). 

•	 Superimpose on the po diagram a plot of the maximum past effective stress (pc) as 

determined from the results of consolidation tests (Refer to Figure A.4-4 and Table 

A.4-3). 

•	 Prepare a plot of undrained shear strength (su) with depth based on the results of vane 

shear tests, unconsolidated -undrained (UU) and consolidated-undrained (CU) triaxial 

tests (Refer to Figure A.4-5 and Table A.4-4) 

FHWA NHI-06-089 Laboratory Testing
 

Soils and Foundations – Volume II A.4 - 2 December 2006 
Solution: 

Step 1: Construct the po diagram at boring UDH BAF – 4. 

•	 UDH BAF – 4 is the boring where the samples for strength and 

consolidation tests were obtained. 

•	 Table A.4-1 shows the unit weights of the soils in the idealized profile as 

determined in the laboratory. 

•	 The computations for po, pt, and pw at soil layer and ground water table 

boundaries are shown in Table A.4-2. (Refer to Chapter 2 and Example 2-

1) 

Step 2: Based on the effective geostatic vertical pressure (po) at each depth specify 

test parameter for consolidation and strength tests. 

•	 Specify loads, test duration and loading pattern for consolidation tests 

(Refer to Figure A.4-3) 

•	 Specify confining pressure for UU tests corresponding to total in situ 

geostatic vertical stress at the depth from which each sample was retrieved 

(Refer to Figure A.4-3) 

•	 Specify three consolidation pressures for each CU test starting with po at 

the depth from which each sample was retrieved (Refer to Figure A.4-3). 

Step 3: Use the results laboratory tests to determine design parameters. 

•	 From consolidation test results determine the maximum past effective 

stress (pc), the compression index (Cc), the recompression index (Cr) and 

the coefficient of consolidation (cv) for samples retrieved at various depths 

(Refer to Table A.4-3). 

•	 Plot the values of maximum past effective stress (pc) as estimated from the 

results of the consolidation tests on the po diagram to determine the stress 

history of the compressible layer (Refer to Figure A.4-4). Since the OCR 

(pc/po) >1, the soil is overconsolidated (Refer to Chapter 5.4) 

•	 From UU tests determine the undrained shear strength (su) directly as onehalf the undrained shear strength (Refer to Table A.4-4). 

•	 From CU tests determine the undrained shear strength (su) as one-half the 

undrained shear strength for each sample consolidated under a confining 

pressure equal to po at the depth from it was retrieved (Refer to Table A.4-

4). 

•	 From vane shear tests determine the undrained shear strength directly as 

one-half the measured undrained shear strength for both undisturbed and 

FHWA NHI-06-089 Laboratory Testing
 

Soils and Foundations – Volume II A.4 - 3 December 2006 
remolded conditions (Refer to Table A.4-4). 

•	 Plot the results of the vane shear tests (V), UU tests (U) and CU tests (C) 

versus depth in the clay layer (Refer to Figure A.4-5). Select 1,100 psf as 

the design value since it is (a) close to the middle of the consolidating clay 

layer and (b) it is a lower bound value. 

A.4-3 Summary of Laboratory Testing and Illustration of the Use of Laboratory Test 

Results to Obtain Values for Geotechnical Design Parameters 

1.	 Construct po diagram 

•	 Show increase of total and effective vertical geostatic pressures with depth 

•	 Show effect of groundwater table and hydrostatic pore water pressure 

2.	 Prepare soil mechanics laboratory test request 

•	 Assign consolidation test pressures and load times. 

•	 Assign confining pressures for UU strength test to simulate variation of total 

geostatic pressures with depth. 

•	 Assign range of consolidation pressures for CU test performed on samples 

retrieved from various depths to simulate effective stresses states ranging from 

initial value to final value due to the embankment. 

3.	 Consolidation test results 

•	 Determine compression and recompression indices, maximum past effective 

stress, overconsolidation ratio (OCR), and coefficient of consolidation at 

various depths within the silty clay deposit. 

4.	 Strength test results 

•	 Determine variation of undrained shear strength with depth (confining 

pressure) from results of vane shear tests. 

•	 Determine variation of undrained shear strength with depth (confining 

pressure) from results of UU tests. 

•	 Determine variation of undrained shear strength with depth (confining 

pressure) from results of CU tests. 

•	 Compare differences of undrained shear strength obtained from the three tests 

and select a design value based on anticipated loading conditions. 

FHWA NHI-06-089 Laboratory Testing
 

Soils and Foundations – Volume II A.4 - 4 December 2006 
Figure X.4-2: Pressure Diagram (p0 and pt) 

psf 

(3x110) 600

po 

pt 

Figure A.4-2. The po diagram for boring UDH BAF – 4 

(Note: Ground water was encountered at a depth of 6 ft in UDH BAF-4). 

FHWA NHI-06-089 Laboratory Testing
 

Soils and Foundations – Volume II A.4 - 5 December 2006 
Figure A.4-3. Laboratory test request. 

FHWA NHI-06-089 Laboratory Testing
 

Soils and Foundations – Volume II A.4 - 6 December 2006 
Table A.4-1 

Unit weights of soils in idealized profile (Boring UDH BAF-4) 

(Assume unit weight of water = 60 pcf) 

Soil stratum Inclusive 

Depth (ft.) 

Total unit 

weight (γt) pcf 

Saturated unit 

weight (γsat) pcf 

Buoyant unit 

weight (γb) pcf 

Organics 0 - 3 90 - -

Sand 3 - 10 110 110 50 

Silty clay 10 - 45 125 125 65 

Table A.4-2 

Computations for construction of po diagram (Boring UDH BAF-4) 

(The ground water table [GWT] is located at a depth of 6-ft below the surface) 

Depth (ft) 

to a 

boundary 

Total (pt) geostatic vertical 

pressure (psf) 

Effective (po) geostatic 

vertical pressure (psf) 

Hydrostatic (pw) pore water 

pressure (psf) 

3 3-ft x 90 pcf = 270 psf 3-ft x 90 pcf = 270 psf pt - po = 0 (above GWT) 

6 270 psf + 3 ft x 110 pcf = 

600 psf 

270 psf + 3 ft x 110 pcf 

= 600 psf 

pt - po = 0 (at GWT) 

10 600 psf + 4 ft x 110 pcf = 

1,040 psf 

600 psf + 4 ft x 50 pcf = 

800 psf 

1,040 psf – 800 psf = 240 psf 

or 

4 ft x 60 pcf = 240 psf 

45 1,040 psf + 35 ft x 125 pcf = 

5,415 psf 

800 psf + 35-ft x 65 pcf 

= 3,075 psf 

5,415 psf – 3,075 psf = 2,340 psf 

or 

39-ft x 60 pcf = 2,340 psf 

Table A.4-3 

Consolidation test results summary (Boring UDH BAF-4) 

Depth, ft Tube No. w % po, psf eo pc, psf Cr Cc 

cv 

ft2/day 

11 T3 33 800 0.91 6,500 0.033 0.35 0.6 

16 T4 35 1150 0.89 6,000 0.031 0.32 0.4 

21 T5 31 1450 0.96 4,800 0.040 0.36 0.8 

26 T6 36 1790 1.01 4,200 0.035 0.34 0.6 

31 T7 38 2130 0.98 3,400 0.037 0.34 0.8 

40 T9 37 2720 1.02 3,800 0.032 0.35 0.4 

FHWA NHI-06-089 Laboratory Testing
 

Soils and Foundations – Volume II A.4 - 7 December 2006 
 

 

 

 

 

 

 

 

 

 

 

Table A.4-4 

Shear strength test results summary (Boring UDH BAF-4) 

Undrained Shear Strength – psf 

Depth, 

ft 

Tube 

No. 

w 

% 

su from UU 

tests 

(U) 

su @ po from 

CU tests 

(C) 

su from vane shear tests (V) 

Undisturbed Remolded 

13 34 1,150 550 

16 T4 34 1,050 1,150 

18 36 1,100 600 

21 T5 35 950 1,250 

23 38 1,050 500 

26 T6 39 975 1,200 

28 37 1,125 550 

31 T7 40 1,000 1,250 

37 35 1,250 600 

40 T9 38 800 1,300 

FHWA NHI-06-089 Laboratory Testing
 

Soils and Foundations – Volume II A.4 - 8 December 2006 
pc 

po 

Figure A.4-4. Plot of estimated preconsolidation pressure, pc, on a po plot. 

FHWA NHI-06-089 Laboratory Testing
 

Soils and Foundations – Volume II A.4 - 9 December 2006 
Figure A.4-5. Plot of variation of undrained shear strength with depth determined by 

various test methods (U = UU Test, C = CU Test, V = Undisturbed Vane Shear Test). 

 

FHWA NHI-06-089 Laboratory Testing
 

Soils and Foundations – Volume II A.4 - 10 December 2006 
 

 

 

 

 

 

 

 

 

Subsurface Terrain reconnaissance 

Explorations 

Subsurface explorations 

Site inspection 9

Basic Soil Properties 

Laboratory Testing 

Approach Roadway 

Deformations 

Spread Footing 

Design 

Driven Pile Design 

Construction 

Monitoring 

Visual description 

Subsurface Profile 

Classification tests 9

po diagram 

Consolidation results 

Test request 9

Strength results 

Design soil profile

Slope Circular arc analysis 

Stability Sliding block analysis 

Design soil profile 

Magnitude of settlement 

Rate of settlement 

Surcharge 

Vertical drains 

Lateral squeeze 

Design soil profile 

Pier bearing capacity 

Pier settlement 

Abutment settlement 

Surcharge 

Vertical drains 

Design soil profile 

Static analysis – pier 

 Pipe pile 

H – pile 

Static analysis – abutment 

Pipe pile 

H – pile 

Driving resistance 

Lateral movement - abutment 

Wave equation 

Hammer approval 

Embankment instrumentation 

Figure A.5-1. Status of geotechnical work. 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 1 December 2006 
SECTION A.5 

SLOPE STABILITY 

A.5-1 RELEVANT CONCEPTS AND PROCEDURES (Refer to Figure A.5-1) 

•	 Design factor of safety (FS) - Chapter 6.2. 

•	 Ordinary Method of Slices – hand solution - Chapter 6.4.3. 

•	 Bishop’s Method – computer solution - Chapter 6.4.4; Table 6-1. 

•	 Sliding (Rankine) Block Method – hand solution - Chapter 6.7. 

In this section the analysis and design of an embankment with respect to global stability 

considerations are illustrated. The Ordinary Method of Slices is used to perform a stability 

analysis of the I-0 embankment. The results of hand calculations are compared to the results 

of computer-generated solutions based on the Ordinary Method of Slices and Bishop’s 

Simplified Method. A sliding block analysis is performed and the possibility of lateral 

squeeze is examined. 

A.5-2 DETAILED PROCEDURES 

Given:	 The proposed embankment geometry as shown in Figure A.5-2 and the 

embankment and foundation soil properties at the east approach as provided in 

Table A.5-1. Assume that the shallow (≈ 3′) surface layer of organic material 

shown in the idealized soil profile (Figure A.4-2) has been removed and replaced 

with select material having the same properties as the embankment fill. 

Required: 

•	 Perform hand calculations based on the Ordinary Method of Slices to compute the 

minimum factor of safety of the I-0 approach embankment at the east abutment. 

•	 Compare the minimum factor of safety obtained from the hand calculations with 

the minimum factors of safety obtained from computer analyses based on the 

Ordinary Method of Slices and Bishop’s Method. 

•	 Perform hand calculations based on the sliding (Rankine) block method to 

compute the minimum factor of safety of the I-0 approach embankment at the east 

abutment and compare the result with the results obtained from the two circular 

arc type failure analyses. Determine critical failure mode. 

•	 Perform hand calculations to assess the potential for lateral squeeze of the 

embankment foundation soils at this location. 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 2 December 2006 
 

Table A.5-1 

Geotechnical engineering properties of embankment and foundation soils 

East Abutment - (Boring BAF-4)
 

Soil Type Cohesion 

(c) - psf 

Friction 

angle (φ′) 

γt 

(pcf) 

γsat 

(pcf) 

γb 

(pcf) 

Embankment fill 0 40o 130 

Sand 0 36o 110 110 50 

Silty clay 1,100 0 125 125 65 

Gravel 0 43o 130 130 70 

Solution: 

Step 1:	 As illustrated in Figure A.5-2, construct an idealized design profile to scale 

including the embankment and accounting for the assumption listed above. 

Figure A.5-2. Idealized design soil profile – East Abutment. 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 3 December 2006 

Step 2: Compute the FS against circular arc failure by a hand solution based on the 

Ordinary Method of Slices. 

•	 Chose a trial failure circle, i.e., select a center (Point O) of a circle having radius (R) 

that will subtend a failure arc through the soils shown in Figure A.5-3. Depending 

upon the soil profile, the critical circle may be “deep seated”, i.e., be tangent to a 

relatively strong stratum underlying a much weaker layer, or it may be a “toe circle”, 

i.e., the arc passes through the toe of the slope when the soil profile is virtually 

homogeneous. 
 

•	 For a complete hand solution many trail failure circles must be chosen to determine 

the minimum factor of safety. The circles typically cover a range of center points and 

radii. 

 

 fill slope. 

For deep clay sub soils the "critical" (Min. 

surface will generally pass deep into the 

clay layer. T he center of the critical 

usually lies above the 

R 

2:1 

R 

33' Fill 

7' Sand 

35' Clay 

Dense 

Gravel 

25' 

10' 

O 

midpoint 

of the fill slope. 

Figure A.5-3. Trial failure circle – Embankment fill - East Abutment. 

•	 For the purpose of illustrating the hand procedure here and for comparison with the 

computer solution later on, the coordinates of the Point O chosen in this example 

correspond to the coordinates for the circle yielding the minimum factor of safety as 

determined by the computer solution based on Bishop’s Method. 

•	 Depending upon the geometry of the cross section and the number of soil layers 

intersected by the failure arc, divide the soil mass above the arc of the failure circle 

into at least 10 and no more than 20 vertical slices For this example there are 16 

slices selected as shown in Figure A.5-4. 

•	 As shown in Figure A.5-5, determine the α – angles for each vertical slice, where α = 

the angle, as measured at Point O, between a vertical line through Point O and the 

radius that intersects the middle of the failure arc segment for a given slice. 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 4 December 2006 
O 

R 

R 

33' 

7' 

35' 

25' 

10' 

Fill 

Sand 

Clay 

6 45 3 2 1

7 

8 

9 

11

14 13 12 15 

16 

2:1

10 

33' 33' 33' 33' 33' 33' 

27' 

20' 

14' 9' 

5' 5' 5' 5' 5'

2' 2' 2' 2' 2' 2' 2' 2' 2'

5' 5' 5' 5' 5' 5' 5' 5' 5' 5' 5' 5' 

12' 

12' 

19' 

25' 

28' 30' 30'

25' 

19' 

12' 

12' 12' 12' 2'4' 15'

12' 

12' 

12' 

12' 

12' 

4' 12' 12' 13'

4' 

Dense 

Gravel 

Figure A.5-4. Vertical slices above assumed failure arc – East Abutment. 

(Not-to-scale) 

16 

O 

R 

R 

33' 

7' 

35' 

25' 

10' 

Fill 

Sand 

Clay 

6 45 3 2 1

7 

8 

9 

11

14 13 12 15 

2:1

10 

α=+60°

+54 +5 °

1

+43

°

°

+34°

+25°

+16°

+9°

+1°

−

7°

−15°

−24°

−32°

−42°

−49°

−53°

Dense 

α = 0° Gravel 

Figure A.5-5. Determination of α – Angles corresponding to each vertical slice above 

assumed failure arc – East Abutment. 

(Not-to-scale) 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 5 December 2006 
•	 Once the geometry and α – angle for each vertical slice have been determined, 

compute the resisting and driving forces for all slices by use of the following 

procedure as illustrated for Slice 7. Figure A.5-6 shows the geometry of the slice and 

the relevant soil properties. (Refer to equations 6-14 to 6-20). 

Figure A.5-6. Geometry and relevant soil properties for slice 7 (Not-to-scale). 

3⁄4 Calculate the total weight of the slice for a unit thickness into the plane of the 

paper by summing the contributions of the various soil strata lying above the 

failure arc. 

⎛ 27ft + 33ft ⎞ WT = (1ft)(12ft)⎜ ⎟(130 pcf ) + (1ft)(12ft)(7ft) (110pcf ) + ⎝ 2 ⎠

⎛ 28ft + 25ft ⎞ (1ft)(12ft)⎜ ⎟(125pcf ) = 95,790lbs ⎝ 2 ⎠

3⁄4 Calculate the tangential driving force, which is the component of the weight of the 

slice acting perpendicular to the radius (R). 

T = WT sin α = 95,790 lbs (sin 16°) = 26,403 lbs 

3⁄4 Calculate the shearing resistance along the length of arc subtended by the failure 

surface. Use the length of the chord (l) to approximate the arc length. In general, 

the shearing resistance consists of a frictional component and a cohesion 

component. For a unit thickness into the plane of the paper, the frictional 

component is given by: N′ tan φ = (WT cos α – ul) tan φ, where u = the average 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 6 December 2006 
pore water pressure acting along the chord length, l (Refer to Eq. 6-18). The 

cohesion component is given by cl where c = the cohesion for drained conditions 

and the undrained shear strength (su) for undrained conditions. Since undrained 

conditions are usually critical, the undrained shear strength (su) is generally used 

in the calculation. 

Since the bottom of Slice 7 is in clay where φ = 0, N tan φ = 0. Therefore, the 

total shearing resistance for a unit thickness into the plane of the paper is given by 

the cohesion component as follows: 

c l = (1,100 psf)(13 ft)(1 ft) = 14,300 lbs 

Therefore for Slice 7: 

 Driving Force = T = 26,403 lbs 

 Resisting Force =c l = 14,300 lbs 

•	 Slice 7 was used to illustrate the case where the failure surface passed through a 

purely cohesive material below the ground water table. Slice 15 is used to illustrate 

the procedure when the failure surface passes through a purely frictional material 

below the ground water table. Figure A.5-7 shows the geometry of Slice 15 and the 

relevant soil properties. 

3⁄4 As before, calculate the total weight of the slice for a unit thickness into the plane 

of the paper 

⎛10 ft + 5ft ⎞ WT = (1ft)(4 ft)⎜ ⎟(110 pcf ) = 3,300 lbs ⎝ 2 ⎠

3⁄4 As before, calculate the tangential driving force 

T = WT sin α = 3,300 lbs (sin (-49°)) = - 2,491 lbs 

Note: T is negative for this slice since the weight tends to RESIST sliding. 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 7 December 2006 
1=6.5’ 

" = - 49o 

Sand 

N = 36o 

mt = 110 pcf 

Figure A.5-7. Geometry and relevant soil properties for slice 15 (Not-to-scale). 

3⁄4 As before, calculate the shearing resistance along the length of arc subtended 

by the failure surface. Use the length of the chord (l) to approximate the arc 

length. 

Since the bottom of Slice 15 is in sand where c = 0, cl = 0. Therefore, the 

total shearing resistance for a unit thickness into the plane of the paper is 

given by the frictional component based on φ = 36° as follows: 

N = Wt cos α - ul 

N = (3,300 lbs)(cos (-49°)) – (1 ft)(5 ft/2) (6.5 ft) (60 pcf) 

N = 2,165 lbs – 975 lbs = 1,190 lbs 

N tan φ = 1,190 lbs (tan 36°) = 865 lbs 

Therefore, for Slice 15: 

Driving Force = T = -2,491 lbs 

Resisting Force = 865 lbs 

•	 Follow the procedures described above to calculate weights for each slice. For ease 

in computation use the tabular format illustrated in Table A.5-2. 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 8 December 2006 
 

 

 

 

 

 

 

 

 

 

 

Table A.5-2 

Tabular form for computing total weights of slices for a unit thickness into the plane of 

the paper 

Slice No. B (ft) hI (ft) γi (pcf) Wi (lbs/ft) ∑ Wi=WT (lbs) 

1 15 33/2 130 32,175 32,175 

2 2 33 130 8,580 

2/2 110 220 8,800 

3 4 33 130 17,160 

 (7+2)/2 110 1,980 19,140 

4 12 33 130 51,480

 7 110 9,240 

 12/2 125 9,000 69,720 

5 12 33 130 51,480

 7 110 9,240 

(19+12)/2 125 23,250 83,970 

6 12 33 130 51,480

 7 110 9,240 

(19+25)/2 125 33,000 93,720 

7 12 (27+33)/2 130 46,800

 7 110 9,240 

(25+28)/2 125 39,750 95,790 

8 12 (20+27)/2 130 36,660

 7 110 9,240 

(30+28)/2 125 43,500 89,400 

9 12 (14+20)/2 130 26,520

 7 110 9,240 

30 125 45,000 80,760 

10 12 (9+14)/2 130 17,940

 7 110 9,240 

(28+30)/2 125 43,500 70,680 

11 12 (9+3)/2 130 9,360 

7 110 9,240 

(25+28)/2 125 39,750 58,350 

12 13 10 110 14,300 

(19+25)/2 125 35,750 50,050 

13 12 10 110 13,200 

(12+19)/2 125 23,250 36,450 

14 12 10 110 13,200 

 12/2 125 9,000 22,200 

15 4 (5+10)/2 110 3,300 3,300 

16 4 5/2 110 1,100 1,100 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 9 December 2006 
•	 Follow the computational procedures described above and record the relevant soil and 

geometric properties and the calculated values of driving and resisting forces for each 

slice in a table. For ease in computation of the global factor of safety, use the tabular 

format illustrated in Table A.5-3. 

•	 Calculate the global factor of safety by using the equations shown in Table A.5-3. 

•	 Summarize the results of the Ordinary Method of Slices based on hand calculations 

by showing the critical failure circle and its associated minimum factor of safety 

graphically (Refer to Figure A.5-8). 

Step 3: Compute the FS against circular arc failure by computer solutions based on 

the Ordinary Method of Slices and the Bishop Simplified Method. 

•	 Summarize the results of the Ordinary Method of Slices (OMS) and Bishop’s 

Simplified Method based on a computer solution by showing the critical failure circle 

and its associated minimum factor of safety graphically (Refer to Figure A.5-9). Note 

that for the purpose of illustrating the difference between the FS for the two computer 

solutions, the coordinates of Point O and the radius of the failure arc, R, for the 

Ordinary Method of Slices computer solution correspond to those of the circle 

yielding the minimum factor of safety as determined by the computer solution based 

on Bishop’s Method. As noted previously, the same geometry was used for the 

Ordinary Method of Slices solution by hand calculations. 

•	 Figure A.5-10 illustrates the search routine used by the computer program to obtain 

the minimum FS. Contours of equal FS are shown with the minimum FS being the 

point at the center of the contours. The contours represent the results of many 

computer runs in which the center and radius of the failure circle were varied in a 

systematic way until the minimum FS was reached. The efficiency of the computer 

solution over the hand solution in terms of time and accuracy is obvious. 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 10 December 2006 
Table A.5-3 

Tabular form for computing factor of safety by Ordinary Method of Slices 

Slice 

No. 

WT 

(from Table 

l α c φ u ul WTcosα N′ = 

WTcosα-ul 

N′tanφ 

A.5-2) 

 (lbs) (ft) (deg) (psf) (deg) (psf) (lbs) (lbs) (lbs) (lbs) 

1 32,175 36 60 0 40 0 0 16,088 16,088 13,499 

2 8,800 3 54 0 36 0 0 5,173 5,173 3,758 

3 19,140 7 51 0 36 150 1,050 12,045 10,995 7,988 

4 69,720 17 43 1,100 0 - - - - 0 

5 83,970 15 34 1,100 0 - - - - 0 

6 93,720 15 25 1,100 0 - - - - 0 

7 95,790 13 16 1,100 0 - - - - 0 

8 89,400 13 9 1,100 0 - - - - 0 

9 80,760 12 1 1,100 0 - - - - 0 

10 70,680 12 -7 1,100 0 - - - - 0 

11 58,350 13 -15 1,100 0 - - - - 0 

12 50,050 14 -24 1,100 0 - - - - 0 13 36,450 14 -32 1,100 0 - - - - 0 14 22,200 16 -42 1,100 0 - - - - 0 15 3,300 6.5 -49 0 36 150 975 2,165 1,190 865 

16 1,100 6.5 -53 0 36 0 0 662 662 481 

Σ 26,591 

Σ ( W T cos α − ul ) tan φ + Σ cl Σ N ′ tan φ + Σ cl 26 ,591 lbs + 169 ,400 lbs FS = = = 

Σ W sin T α Σ W sin T α 144 ,154 lbs

L

WT 

α 

l 

egend: Refer to Figure 6-10 for definition of various slice quantities 

W

T = Total weight of Slice (soil + water) 

l

 = Base length of the slice

 c

 = Cohesion at base of slice 

φ = angle of internal friction u = pore water pressure at base of slice 

FHWA NHI-06-089 

Soils and Foundations – Volume II A.5 - 11 
Figure A.5-8. Graphical representation of solution for minimum Factor of Safety by 

Ordinary Method of Slices/Hand computation – East Abutment. 

F.S.OMS=1.37 

F.S.BISHOP=1.63 

Figure A.5-9. Graphical representation of solution for minimum Factor of Safety by 

Ordinary Method of Slices (OMS)/Computer solution and Bishop’s Method – East 

Abutment. 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 12 December 2006 
Figure A.5-10 

Illustration of search routine used by computer program to develop contours of equal 

FS that converge on the point of minimum FS and center of critical circle. 

Step 4: Compare the FS against circular arc failure computed by each of the three 

methods and select a design FS. 

 F.S. = 1.36 - Ordinary Method of Slices: Hand Solution 

F.S. = 1.37 - Ordinary Method of Slices: Computer Solution 

F.S. = 1.63 - Bishop’s Simplified Method: Computer Solution 

Use a minimum factor of safety for design F.S. (Bishop) = 1.63 

Step 5: Calculate FS against a Sliding Block Type Failure by Using Rankine Wedges 

and Sliding Block Analysis 

•	 Choose a trial block type failure surface along the top of clay layer as shown in 

Figure A.5-11. 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 13 December 2006 
 

5’ 

5’ 

Fill 

γt = 130 pcf 

N = 40o 

Sand 

γt = 110 pcf 

N = 36o 

Clay 

γt = 125 pcf 

N = 0o 

c = 1100 psf 

Pa 

ASSUMED 

FAILURE 

SURFACE 

cL 

L = 60’ 

2’ 

33’ 

35’ 

Passive 

Wedge 

Pp 

Central 

Block 

Active 

Wedge 

2’ 7’ 

2:1 

Figure A.5-11. Trial failure surface consisting of Active and Passive Rankine wedges 

and central sliding block. 

•	 Calculate active Rankine coefficient of lateral earth pressure (Ka) 

3⁄4 For fill (Soil Layer 1) 

K 2

a1=tan2

 (45° - 40°/2) = tan (25°) = 0.22 

3⁄4 For sand (Soil Layer 2) 

K =tan2 (45° - 36°/2) = tan2

a2 (27°) = 0.26 

•	 Calculate active lateral earth pressure (pa) (Units of kips are used to facilitate use of 

less digits in the calculations: 1 kip = 1,000 lbs; kip is abbreviated as k) 

3⁄4 At base of fill (Soil Layer 1) 

pa1 = γ1h1Ka1 = (0.130 kcf)(33 ft)(0.22) = 0.94 ksf 

3⁄4 At top of sand layer (Soil Layer 2) 

pa2 (top of sand) = γ1h1Ka2 = (0.130 kcf)(33 ft)(0.26) = 1.11 ksf 

3⁄4 At depth of 2 ft below top of sand layer (i.e. at water table elevation) 

pa3 = 1.11 ksf + (0.110 kcf)(2 ft)(0.26) = 1.17 ksf 

3⁄4 At base of sand layer 

pa4 = 1.17 ksf + (0.050 kcf*)(5 ft)(0.26) = 1.24 ksf 

(*buoyant unit weight below water table) 

•	 Calculate active Rankine force (Pa) for a unit thickness into the plane of the paper and 

plot force and active lateral earth pressure diagram as shown in Figure A.5-12 

3⁄4 Pa = (0.94 ksf)(33 ft)(1/2)(1 ft) + ((1.11 ksf + 1.17 ksf)/2)(2 ft)(1 ft) + ((1.17 

ksf + 1.24 ksf)/2)(5 ft)(1 ft) = 15.5 kips + 2.3 k + 6 k ≈ 24 k 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 14 December 2006 
 

 

Active Pressure 

Diagram 

5′

2′

33′

pa3 = 1.17 ksf 

p pa2 = 1.11 ksf a1 = 0.94 ksf 

Pa = 24k 

Fill 

γt = 130 pcf 

φ = 40°

Sand 

γt = 110 pcf, φ = 36°

2:1 

Pa4 = 1.24 ksf 

Figure A.5-12 

Active earth pressure diagram and resultant active Rankine force 

•	 Calculate passive Rankine coefficient of lateral earth pressure (Kp) 

3⁄4 For sand 

K = tan2 (4 /2) = tan2

p 5° + 36° (63°) = 3.85 

•	 Calculate passive lateral earth pressure (pp) 

3⁄4 At 5-ft below top of sand layer (i.e. at water table elevation)
 

pp1 = (0.110 kcf)(5 ft)(3.85) = 2.1 ksf 

3⁄4 At base of sand layer 

pp2 = 2.1 ksf + (0.050 kcf*)(5 ft)(3.85) = 3.1 ksf 

(*buoyant unit weight below water table) 

•	 Calculate passive Rankine force (Pp) for a unit thickness into the plane of the paper 

and plot force and passive lateral earth pressure diagram as shown in Figure A.5-13 

3⁄4 Pp = (2.1 ksf)(5 ft)(1/2)(1 ft) + ((2.1 ksf+3.1 ksf)/2)(5 ft)(1 ft) = 5.3 k + 13 k 

≈ 18 k 

•	 Calculate the resisting force of the central block for assumed failure plane along the 

top of the clay layer and the plot the force system as shown on Figure A.5-14. 

3⁄4 c = 1,100 psf = 1.1 ksf 

3⁄4 L = 60 ft 

3⁄4 cL = (1.1 ksf)(60 ft)(1 ft) = 66k 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 15 December 2006 
 

2:1 

pp1 = 2.1 ksf 

Passive Pressure Diagram 

pp2 = 3.1 ksf 

5′

5′ Sand

Fill 

Pp = 18k 

Figure A.5-13. Passive earth pressure diagram and resultant passive Rankine force. 

•	 Calculate the FS against sliding failure 

P + CL 

 

•	 Compare FS against sliding failure (3.5) vs. minimum FS against circular arc failure 

(1.63). 

•	 Conclusion: circular arc failure is more critical and governs the design. 

Horizontal Resisting Forces F.S. = p 	 = Horizontal Driving Forces PA 

18	 

K + 66 K 84 K

= = = K 3.5 

24K 24

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 16 December 2006 

Active 

Wedge 2:1 

PASSIVE 

WEDGE 

Central Pa = 24k 

Block 

Pp = 18k Sand 

Clay 

cL = 66k	 γt = 125 pcf 

φ = 0 deg 

c = 1,100 pcf 

Figure A.5-14. Force system acting on central block. 
A.5-3 SUMMARY OF THE APPROACH USED TO DETERMINE 

EMBANKMENT STABLITY FOR THE APPLE FREEWAY DESIGN 

PROBLEM 

1.	 Construct an idealized design profile to scale. 

•	 Use idealized soil profile from Boring UDH BAF-4 

•	 Include 33-ft high embankment at east abutment. 

•	 Estimate geotechnical properties of soil layers from results of field and 

laboratory tests. 

2.	 Perform hand calculations to determine FS against circular arc failure by using the 

Ordinary Method of Slices. 

•	 For illustration use center and radius of circle from computer solution that 

provided minimum FS by Bishop Simplified Method 

•	 Divide the soil mass above the arc of the failure circle into at least 10 and no 

more than 20 vertical slices. 

•	 Set up a table to aid in the performance of the calculations. 

•	 Fill the table with soil properties and geometric data for each slice. 

•	 Illustrate calculations performed for Slice 7 – arc segment in clay. 

•	 Illustrate calculations performed for Slice 15 – arc segment in sand. 

•	 Calculate the FS for the assumed center and radius. 

3.	 Compute the FS against a circular arc failure by using computer solutions based on 

the Ordinary Method of Slices and the Bishop Simplified Method. 

4.	 Compare the FS against a circular arc failure computed by each of the three methods 

and select the minimum FS. 

•	 Note that only the computer solution by Bishop’s Modified Method provides a 

minimum FS against circular arc failure. The values obtained from the 

Ordinary Method of Slices hand calculations and computer solution may not 

be the minima for that method since the center and radius of the circle used 

here to illustrate the method are those that provided the minimum FS by 

Bishop Simplified Method computer solution. 

5.	 Calculate the FS against a sliding block type failure by using Rankine wedges and 

sliding block analysis. 

1.	 Calculate the active and passive coefficients of lateral earth pressure for each 

soil layer by using Rankine equations. 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 17 December 2006 
2.	 Calculate the active and passive lateral earth pressure distributions taking into 

account changes in soil layering and the presence of ground water. 

3.	 Calculate the active (driving) and passive (resisting) forces due to the Rankine 

wedges. 

4.	 Assume that sliding occurs along the top of the clay layer and calculate the 

resisting force of the central block. 

5.	 Calculate the FS against a sliding block type failure and compare it to the 

minimum FS against a circular arc failure. Select the lower of the two as the 

design FS. 

FHWA NHI-06-089 Slope Stability 

Soils and Foundations – Volume II A.5 - 18 December 2006 
 

 

 

 

 

 

 

 

 

 

Subsurface 

Explorations 

Basic Soil Properties 

Laboratory Testing 

Slope 

Stability 

Spread Footing 

Design 

Driven Pile Design 

Construction 

Monitoring 

Terrain reconnaissance 

Site inspection 

Subsurface explorations 

9

Visual description 

Classification tests 

Subsurface profile 

9

po diagram 

Test request 

Consolidation results 

Strength results 

9

Design soil profile 

Circular arc analysis 

Sliding block analysis 

9

Approach 

Roadway 

Deformations 

Design soil profile 

Magnitude and rate of 

settlement 

Surcharge 

Vertical drains 

Lateral Squeeze 

Design soil profile 

Pier bearing capacity 

Pier settlement 

Abutment settlement 

Surcharge 

Vertical drains 

Design soil profile 

Static analysis – pier 

 Pipe pile 

H - pile 

Static analysis – abutment 

Pipe pile 

H - pile 

Driving resistance 

Lateral movement - abutment 

Wave equation 

Hammer approval 

Embankment instrumentation 

Figure A.6-1. Status of geotechnical work. 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 1 December 2006 
SECTION A.6 

APPROACH ROADWAY DEFORMATIONS 

A.6-1 RELEVANT CONCEPTS AND PROCEDURES (Refer to Figure A.6-1) 

•	 General procedure to determine pressure distribution with depth due to approach 

embankment; Chapter 7.3 

•	 Immediate settlement – computation of magnitude; Chapter 7.4. 

•	 Consolidation settlement – computation of magnitude; Chapter 7.5. 

•	 Consolidation settlement – computation of time rate; Chapter 7.5.3. 

•	 Treatment by surcharging to accelerate consolidation settlement and reduce time; 

Chapter 7.7 

•	 Treatment by Wick Drains without surcharge to accelerate consolidation settlement 

and reduce time; Chapter 7.7 

•	 Estimating horizontal movement due to lateral squeeze of embankment foundation 

soils; Chapter 7.6 

In this section the computation of the magnitude of immediate settlement of a sand layer and 

the magnitudes and rates of consolidation settlement of an organic layer and a clay layer due 

to the construction of an embankment fill are illustrated. The options of surcharging and 

vertical drains with and without surcharge are also examined as a means of treatment to 

accelerate consolidation settlement and reduce time. 

A.6-2 DETAILED PROCEDURES 

Given: 

•	 The subsurface profile and soil properties shown in Figure A.6-2 for the east 

abutment embankment of the Apple Freeway Bridge. 

•	 The consolidation test results presented in Table A.6-1. 

•	 Assume that N-values in the profile are N60 values. 

Required: 

•	 Perform hand calculations to compute the pressure distribution with depth due to the 

embankment fill. 

•	 Perform hand calculations to compute the magnitude of the anticipated consolidation 

settlement due to the embankment fill. 

•	 Perform hand calculations to compute the time required for the settlement to occur 

without treatment by surcharging or vertical drains and plot the time vs. settlement 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 2 December 2006 
curve. 

•	 Evaluate the stability of the 30 ft embankment fill with the addition of 10 ft of 

surcharge treatment. 

•	 Examine the effect of treatment by surcharging on settlement and time (including 

cost analysis). 

•	 Examine the effect of treatment by vertical wick drains without surcharge on 

settlement and time (including cost analysis). 

•	 Estimate the amount of horizontal deformation due to lateral squeeze of the 

embankment foundation soils 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 3 December 2006 

Fill 

2:1 30′

γ = 130 pcf 

φ = 40°

c = 0 

Organic γ = 90 pcf; w = 120%; Gs = 1.6 5′

Sand γ = 110 pcf; N60 = 17 

γb = 50 pcf; c′ = 90 

3′

7′

35′

Clay 

γb = 65 pcf 

Cc = 0.35 

Cr = 0.035 

cv = 0.6 ft2

/day 

w = 35% 

Gs = 2.78 

Incompressible 

Figure A.6-2. Design subsurface profile and soil properties at east embankment location. 
 

A.6-3 SOLUTION TO DETERMINE THE MAGNITUDE OF AND TIME FOR THE 

ANTICIPATED SETTLEMENT DUE TO THE EMBANKMENT FILL 

Step 1: Obtain soil consolidation characteristics (from laboratory tests). 

Table A.6-1 

Consolidation test results summary (Hole BAF-4) 

Depth Tube pc (psf) Cc Cr cv (ft2/day) 

11 T3 6,500 0.35 0.033 0.6 

16 T4 6,000 0.32 0.031 0.4 

21 T5 4,800 0.36 0.040 0.8 

26 T6 4,200 0.34 0.035 0.6 

31 T7 3,400 0.34 0.037 0.8 

40 T9 3,800 0.35 0.032 0.4 

eo (average) = 0.97 

Step 2: Plot overburden pressure (Figure A.4-2) and preconsolidation pressure 

(Table A.6-1) with Depth as shown in Figure A.6-3. 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 4 December 2006 

Pressure (psf) 

1000 2000 3000 4000 5000 6000 

Depth (ft) 

0 

10 

20 

30 

40 

pc po 

Figure A.6-3. Variation of overburden pressure and preconsolidation pressure with 

depth. 
Step 3: Determine the distribution of pressure increase with depth due to the 

embankment pressure (pf) at end of construction: 

•	 Obtain embankment geometry. Use the same geometry (plan and section) 

from Example 7-1 in Chapter 7. 

•	 Embankment top width = 100 ft 

•	 Side and end slopes = 1V on 2H 

•	 Top of end slope from toe = 60 ft 

•	 Embankment height = 30 ft 

•	 Embankment load (at longitudinal centerline) = Hemb × γemb = 30 ft × 130 pcf = 

3,900 psf 

•	 Use Figure A.6-4 to obtain pressure coefficient K (left ordinate) for b= 

⎛100 ft 60ft ⎞ ⎜ + ⎟ = 80 ft and a distance from midpoint of end slope = 0.375b. ⎝ 2 2 ⎠

•	 Abutment center located 30 ft from midpoint of end slope →

30 ft ( ) b = 0.375b

80 ft 

•	 Use a series of charts corresponding to different depths expressed as a 

percentage of bf (right ordinate) to obtain a distribution of pressure 

coefficients with depth. 

•	 Compute pressure change ∆p = K × embankment load at various depths 

expressed as a percentage of bf. The results of these computations are 

presented in Table A.6-2. 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 5 December 2006 
Point Where Design Problem 

Settlement Needed 

b = 80 ft 

h = 30 ft 

Figure A.6-4. Pressure distribution chart used to estimate the change in pressure at 

depths below the end of an embankment fill. 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 6 December 2006 
Table A.6-2 

Summary of pressure increments at various depths due to embankment fill 

Depth (ft) ′′K′′ - from Figure A.6-4 ∆p = ′′K′′ × 3,900 psf 

Distributed pressure (psf) 

0.2 bf = 16 ft 1.00 3,900 

0.4 bf = 32 ft 0.88 3,432 

0.6 bf = 48 ft 0.78 3,042 

0.8 bf = 64 ft 0.70 2,730 

1.0 bf = 80 ft 0.60 2,340 

Step 4: Calculate the final pressure (pf = po + ∆p) at various depths and plot the 

overburden pressure (po), preconsolidation pressure (pc), and pf with depth 

as shown in Figure A.6-5 

po

 pc 

pf 

3 ft 

10 ft 

18 ft 

28 ft 

Figure A.6-5. Variation of overburden pressure (po), preconsolidation pressure (pc) and 

final pressure due to embankment (pf) with depth. 

In settlement analyses, use pressures measured at the center of a layer or a partial layer. 

Thick layers should be subdivided (i.e., if a layer is 20 ft thick compute settlement in 10 ft 

increments) unless the slope of po, pc, or pf are slowly converging straight lines. Dashed 

horizontal lines in Figure A.6-5 show the increments selected here for analysis. 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 7 December 2006 
Step 5: Compute settlement in each layer (or partial layer). 

•	 Layer 1 – Organic (0 ft to 3 ft) – use equation for consolidation settlement 

(Refer to Chapter 7.5). As indicated in the logs of Borings BAF-3 and BAF-4 

where this material was encountered, no tube samples were obtained for 

consolidation testing. Therefore, the stress history of the layer cannot be 

determined from test results. However, based on the description of the 

material given in the boring logs and from experience with surface and nearsurface organic soils, the organic layer is assumed to be normally consolidated 

for the computation presented here as shown in the sketch of the generic 

consolidation curve below. As is generally the case with these soils in 

practice, for the Apple Freeway Bridge the organic layer will be removed and 

replaced with compacted select material before the embankment fill is 

constructed. Settlement of 3-ft of compacted select material is considered to 

be negligible. The situation presented here illustrates the importance of 

sampling and testing all soils that have the potential to cause problems during 

and after construction. 

C c pf ∆H = H log 1 + e o po 

 H = 3 ft – 0 ft = 3 ft 

3ft The mid-thickness depth of the Organic Layer is =1.5ft 

2 

 Cc = 0.0115w = 0.0115 (120) = 1.38 - (Refer to Table 5-5 of Chapter 5) 

 From Figure 5-9 of Chapter 5, Cc ≈ 1.0 

 

 Therefore use Cc (average) = 1.2 

 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 8 December 2006 

po = pc pf 

e 
w × G 120 ×1.6 e0 = s = = 1.9 

%Sat. 100
 

⎛ 1.2 ⎞ 4,100 psf ∆H = 3ft⎜ ⎟ log	 * Remember (po ≥ 200psf) ⎝1 + 1.9 ⎠ 200 psf * 

 ∆H =1.63ft =19.54 in 

 This enormous amount of settlement corresponds to more than 50% of the 

original thickness of the organic layer, which is one of the reasons why such 

materials, when located at or close to the surface, should be removed and 

replaced with compacted select material. 

•	 Layer 2 – Sand (3 ft to 10 ft) – use equation for immediate settlement (Refer to 

Chapter 7.4). 

1 p ∆H = H log f 

C′ po
 

 H = 10 ft - 3 ft = 7 ft 

7 ft The mid-thickness depth of the Sand Layer is 3ft + = 6.5ft 

2 

 To find C′ use N60 = 17 (Refer to Boring BAF–3 at depth = 7 ft) 

N160 	 = 2 @ p o = 500 psf (Refer to Eq. 3-3 in Chapter 3) N 60 

 

 Therefore N160 = 34 

 C′ = 90 (Refer to Figure 7-7 in Chapter 7 – interpolate between silty sand & 

fine to coarse sand) 

⎛ 1 ⎞ 4470 psf ∆H = (7 ft)⎜ ⎟log ⎝ 90 ⎠ 570 psf
 

 ∆H = 0.069ft = 0.83in
 

•	 Layer 3 – Clay – Sub-layer 1 (10 ft to 18 ft) – use equation for consolidation 

settlement (Refer to Chapter 7.5). As shown in Figure A.6-5, the clay layer is 

over-consolidated since pc > po and remains so during application of the entire 

load increment within this depth range as shown in the sketch of the generic 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 9 December 2006 
 

consolidation curve below, i.e., pf < pc. (Refer to Chapter 7.5.2) 

p0 pf pc

e 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 10 December 2006 

Cc pf ∆H = H log 1 + e o po 

 H = 18 ft – 10 ft = 8 ft 

8 ft The mid-thickness depth of Clay Sub-layer 1 is 10ft + =14 ft 

2 

 From consolidation test data: 

Cr (average) = 0.035 

eo (average) = 0.97 

⎛ 0.035 ⎞ 4,920 psf ∆H = (8ft)⎜ ⎟log ⎝1 + 0.97 ⎠ 1,020 psf 

 ∆H = 0.097ft = 1.17in 

•	 Layer 3 – Clay - Sub-layer 2 (18 ft to 28 ft) - use equation for consolidation 

settlement (Refer to Chapter 7.5). The thickness of this sub-layer of the clay 

stratum was chosen because of the sharp break in the slope of the pc vs. depth 

curve at 28-ft (Refer to Figure A.6-5). As shown in Figure A.6-5, the clay 

layer is over-consolidated within this depth range since pc > po, but at the middepth the load increment causes pf > pc. Therefore the settlement for this sublayer must be calculated in two steps as shown in the following sketch of the 

generic consolidation curve, one step for the pressure increment from po to pc 

for which Cr applies, and the other for the pressure increment from pc to pf for 

which Cc applies. (Refer to Chapter 7.5) 
 p pf c po 

e 

C p C p ∆H = H r log c + H c log f

1 + eo p o 1 + e o pc 

 H = 28 ft – 18 ft = 10 ft 

10 ft Mid-thickness depth of Clay Sub-layer 2 is at 18 ft + = 23ft 

2 

 From consolidation test data: 

Cr (avg.) = 0.035 

Cc (avg.) = 0.35 

eo (avg.) = 0.97 

⎛ 0.035 ⎞ 4,450 psf ⎛ 0.35 ⎞ 5,300 psf ∆H = (10ft)⎜ ⎟log + 10ft⎜ ⎟log ⎝1 + 0.97 ⎠ 1,630 psf ⎝1 + 0.97 ⎠ 4,450 psf 

 ∆H = 0.077 ft + 0.135ft = 0.93in +1.62in = 2.55in 

•	 Layer 3 – Clay - Sub-layer 3 (28 ft to 45 ft) - use equation for consolidation 

settlement (Refer to Chapter 7.5). The thickness of this sub-layer of the clay 

stratum represents the depth from the sharp beak in the pc vs. depth curve at 28­

ft to the bottom of the clay stratum (Refer to Figure A.6-5). As shown in 

Figure A.6-5, the clay layer is over-consolidated within this depth range since 

pc > po, but at the mid-depth the load increment causes pf > pc. Therefore the 

settlement for this sub-layer, as was the case for Sub-layer 2, must be 

calculated in two steps as shown in the following sketch of the generic 

consolidation curve, step one for the pressure increment from po to pc for which 

Cr applies, and the other for the pressure increment from pc to pf for which Cc 

applies. (Refer to Chapter 7.5) 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 11 December 2006 
 

 

 

p pc pf o 

e 

 

 

Cr pc Cc pf ∆H = H log + H log 1 + eo po 1 + eo pc 

H = 45 ft – 28 ft = 17 ft 

17 ft The mid-thickness depth of Clay Sub-layer 3 is 28 ft + = 36.5ft 

2 

 From consolidation test data: 

Cr (average) = 0.035 

Cc (average) = 0.35 

eo (average) = 0.97 

⎛ 0.035 ⎞ 3,600 psf ⎛ 0.35 ⎞ 5,800 psf ∆H = (17 ft)⎜ ⎟log + (17 ft)⎜ ⎟log ⎝1 + 0.97 ⎠ 2,460 psf ⎝1 + 0.97 ⎠ 3,600 psf 

∆H = 0.050ft + 0.63ft = 0.60in + 7.51in = 8.11in 

Table A.6-3 

Summary of layer and sub-layer settlements due to embankment fill 

and computation of total settlement 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 12 December 2006 

Layer Settlement (in)

Layer 1 – Organic (0 ft to 3 ft) 

- replaced with compacted select material ≈ 0 

Layer 2 – Sand (3 ft to 10 ft) 0.83 in 

Layer 3 – Clay (10 ft to 45 ft) 

 Sub-layer 1 - (10 ft to 18 ft) 1.17 in 

 Sub-layer 2 - (18 ft to 28 ft) 2.55 in 

 Sub-layer 3 - (28 ft to 45 ft) 8.11 in 

∆H Total 12.66 in 
 

Step 6: Compute Time for Settlement to Occur in Clay (Layer 3) 

• Layer 1 – Select backfill material no settlement expected. 

• Layer 2 – 0.83 inch settlement occurs immediately in sand. 

• Layer 3 – ∆H Total (Layer 3) = 1.17 in + 2.55 in + 8.11 in = 11.83 in 

Time required for a specified percentage of total settlement to occur is computed 

T H2

v from: t = d where: 

cv 

Hd = longest drainage path (ft) = 1⁄2 thickness of clay layer since permeable 

layers exist above and below. Therefore, for the clay layer 

35ft Hd = =17.5ft 

2 

cv = 0.6 ft2

/day 

Tv = time factor corresponding to a specified average percent 

consolidation (U) - (Refer to Table 7-4 in Chapter 7 or calculate by using 

Equation 7-8 in the Chapter 7) 

 Table A.6-4 provides a convenient template for performing computations to 

obtain settlement vs. time values for arbitrarily chosen values of average 

percent consolidation. 

Table A.6-4 

Template to compute values of consolidation settlement (∆H) in clay layer at various times 

(t) after application of embankment load 

Average % 

Consol. (U) 

∆H (in) = 

(U)( ∆H Total 

(Layer 3) 

Time Factor (T) 

From Table 7-4 

v 

2 

d 

c 

H t (days) 

20 2.4 0.031 510.4 16 

50 5.9 0.197 101 

70 8.3 0.403 206 

90 10.6 0.848 432 

The time-settlement plot can now be constructed for all soil layers. 

Remember to include 0.83 inch sand settlement, which occurs immediately as 

load is applied. Therefore ∆HTotal = 12.66 in 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 13 December 2006 
Step 7: Plot Settlement vs. Time Curve – (include ∆H Sand = 0.83 in) 

t100 for sand + t90 for 11.43 in clay @ 432 days 

Figure A.6-6. Settlement vs. Time after construction of 30-ft embankment fill. 

The designer must insure that 90% consolidation is achieved before construction of the 

abutment foundation begins. If the waiting period is too long, as it is in this case for the 

Apple Freeway (432 days ≈ 14 months), the choices of treatment are: 

1.	 Surcharge. 

2. Vertical drains 

It should be noted that the decision on the choice of treatments will be made before 

construction of the embankment fill begins. That decision will influence the construction 

procedure, e.g., if surcharging is chosen, the surcharge will be placed as part of the 

embankment fill and removed afterward. 

A.6-4 CONSIDERATION OF SURCHARGE OPTION TO ACCELERATE 

CONSOLIDATION SETTLEMENT AND REDUCE TIME REQUIRED FOR 

SETTLEMENT DUE TO THE EMBANKMENT FILL 

Assume: 

•	 10-ft high compacted surcharged (γ = 130 pcf). Therefore, the total change in 

pressure (∆ptotal) at the surface is now due to the embankment fill (∆pfill) plus the 

surcharge (∆ps) = (30-ft)(130 pcf) + (10-ft)(130 pcf) = 5,200 psf. 

•	 The pressure increase at various depths below the surface is calculated as before, but 

with the value of the change in pressure at the surface = 5,200 psf. Since the 

dimensions of the embankment, except for the height, are the same as before, the 

values of “K” are unchanged. The results of these computations are presented in 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 14 December 2006 
Table A.6-5. 

•	 Additional immediate settlement of sand due to the surcharge is negligible. 

•	 eo remains 0.97 although the actual value is less due to compression under the 

previous load. 

Step 1: Obtain pressure increase with depth (use previous “K” value) 

Table A.6-5 

Pressure increments at various depths due to embankment fill + surcharge 

Depth (ft) ′′K′′ - from Figure A.6-4 ∆ptotal = ′′K′′ × 5,200 psf 

Distributed pressure (psf) 

0.2b = 16 ft 1.00 5,200 

0.4b = 32 ft 0.88 4,580 

0.6b = 48 ft 0.78 4,060 

Step 2: Calculate the new final pressure (pf + ps = po + ∆ptotal) at various depths and 

plot the overburden pressure (po), preconsolidation pressure (pc), and the 

new final pressure due to the embankment plus the surcharge (pf + ps) with 

depth. 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 15 December 2006 

3⁄4

3⁄4

3⁄4

3⁄4

3⁄4

3⁄4

Pressure (PSF) 

pf + ps 

pc 

po 

Figure A.6-7. Variation of overburden pressure (po), preconsolidation pressure (pc) and 

final pressure due to embankment + surcharge (pf + ps) with depth. 
Step 3: Compute Settlement in Layer 3 

The Layer 1 organics were replaced by compacted select fill, therefore any settlement 

of this layer will be negligible even with the 10 ft surcharge. As indicated previously, 

additional settlement of Layer 2 due to an additional 10 ft of surcharge fill will also 

be negligible. Therefore, Layer 3 is the only layer that will settle more than originally 

calculated due to the additional 10 ft of surcharge. As was done originally, subdivide 

Layer 3 into three partial layers or sub-layers for computational purposes. 

•	 Layer 3 – Clay – Sub-layer 1 (10 ft to 18 ft) – use equation for consolidation 

settlement (Refer to Chapter 7.5). As shown in Figure A.6-5, the clay layer is 

over-consolidated since pc > po , but at the mid-depth the load increment due 

to the additional 10 ft of surcharge causes pf + ps > pc. Therefore the 

settlement for this sub-layer must now be calculated in two steps as shown in 

the following sketch of the generic consolidation curve, one step for the 

pressure increment from po to pc for which Cr applies, and the other for the 

pressure increment from pc to (pf + ps) for which Cc applies. (Refer to Chapter 

7.5) 

pf + pS po pf pc

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 16 December 2006 

C C ∆H = H r p log c + H c p log f + ps

1 + e p 1 o o + e o pc 

⎛ 0.035 ⎞ 5,730 psf ⎛ 0.35 ⎞ 6,220 psf ∆H = (8ft)⎜ ⎟log + (8ft)⎜ ⎟log ⎝1 + 0.97 ⎠ 1,020 psf ⎝1 + 0.97 ⎠ 5,730 psf 

∆H = 0.11ft + 0.05ft = 0.16ft 

∆H =1.32 in + 0.61in =1.93in 
•	 Layer 3 – Clay - Sub-layer 2 (18 ft to 28 ft) - use equation for consolidation 

settlement (Refer to Chapter 7.5). The thickness of this sub-layer of the clay 

stratum was chosen because of the sharp break in the slope of pc vs depth curve 

at 28-ft (Refer to Figure A.6-5). As shown in Figure A.6-5, the clay layer is 

over-consolidated within this depth range since pc > po, but at the mid-depth the 

load increment including the 10-ft surcharge causes pf + ps > pc. Therefore the 

settlement for this sub-layer must be calculated in two steps as shown in the 

following sketch of the generic consolidation curve, one step for the pressure 

increment from po to pc for which Cr applies, and the other for the pressure 

increment from pc to (pf + ps) for which Cc applies. (Refer to Chapter 7.5) 

pf + ps p pf c po 

Cr pc Cc pf + ps ∆H = H log + H log 1 + e p 1 + e p o o o c 

⎛ 0.035 ⎞ 4,450 psf ⎛ 0.35 ⎞ 6,500 psf ∆H = (10 ft)⎜ ⎟log + 10 ft⎜ ⎟log ⎝1 + 0.97 ⎠ 1,630 psf ⎝1 + 0.97 ⎠ 4,450 psf 

∆H = 0.08ft + 0.29 ft = 0.37 ft
 

∆H = 0.93in + 3.51in = 4.44 in
 

•	 Layer 3 – Clay - Sub-layer 3 (28 ft to 45 ft) - use equation for consolidation 

settlement (Refer to Chapter 7.5). The thickness of this sub-layer represents the 

depth from the sharp break in the pc vs. depth curve at 28-ft to the bottom of the 

clay stratum (Refer to Figure A.6-5). As shown in Figure A.6-5, the clay layer 

is over-consolidated within this depth range since pc > po, but at the mid-depth 

the load increment including the 10-ft surcharge causes pf + ps > pc. Therefore 

the settlement for this sub-layer, must also be calculated in two steps as shown 

in the following sketch of the generic consolidation curve, step one for the 

pressure increment from po to pc for which Cr applies, and the other for the 

pressure increment from pc to (pf + ps) for which Cc applies. (Refer to Chapter 

7.5). 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 17 December 2006 
 

po pf pf p + ps c 

Cr pc Cc pf + ps ∆H = H log + H log 1 + e p 1 + e p o o o c 

 

 

⎛ 0.035 ⎞ 3,600 psf ⎛ 0.35 ⎞ 6,920 psf ∆H = (17 ft)⎜ ⎟log + (17 ft)⎜ ⎟log ⎝1 + 0.97 ⎠ 2,460 psf ⎝1 + 0.97 ⎠ 3,600 psf 

∆H = 0.05ft + 0.86ft = 0.91ft
 

∆H = 0.60in + 10.32 in =10.89 in
 

Table A.6-6 

Summary of sub-layer settlements in clay due to embankment fill + surcharge and 

computation of total settlement of clay - Layer 3 

Layer Embankment Only Embankment + Surcharge Surcharge 

10 ft to 18 ft 1.17 in 1.93 in 0.76 in 

18 ft to 28 ft 2.55 in 4.44 in 1.89 in 

28 ft to 45 ft 8.11 in 10.89 in 2.78 in 

Total ∆H = 11.83 in 17.26 in 5.43 in 

Tv H2 

Step 4: Obtain Time-Settlement Relationship: t = d 

cv 

Table A.6-7 

Template to compute values of consolidation settlement (∆H) in clay layer at various times 

(t) after application of embankment and surcharge loads
 

Average % 

Consol. (U) ∆H (in) = 

(U)( ∆H Total - Layer 3) 

Time Factor (T) 

From Table 6-3 

v 

2 

d 

c 

H t (days) 

20 3.5 in 0.031 510.4 16 

50 8.6 in 0.197 101 

70 12.1 in 0.403 206 

90 15.5 in 0.848 432 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 18 December 2006 
Step 5: Plot Settlement vs. Time Curve – (include ∆H Sand = 0.83 in) 

Figure A.6-8. Settlement vs. Time after construction of 30 ft embankment fill with and 

without surcharge. 

Step 6: Determine time of waiting period with surcharge to obtain equivalent 

settlement to that of proposed embankment. 

 Enter the settlement vs. time plot for 30 ft fill with 10 ft surcharge with 12.66 

inches (total [immediate + consolidation] settlement expected for 30 ft fill). 

Extend the line across to the “30’ Fill + 10’ Surcharge” curve and read the waiting 

period time in days on the time axis, i.e. 195 days or 6.5 months. 

Step 7: Recommend instrumentation for monitoring settlement and pore water 

pressures – (Table A.6-8) 

Table A.6-8 

Recommend instrumentation for monitoring settlement and excess pore water pressures at 

East Abutment
 

Instrument Station Depth Below Ground 

Settlement plate 90 + 00 At ground surface 

Settlement plate 93 + 50 At ground surface 

Settlement plate 96 + 50 At ground surface 

Piezometers 93 + 50 20 ft, 28 ft, 36 ft 

Piezometers 96 + 50 20 ft, 28 ft, 36 ft 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 19 December 2006 
 

 

Step 8:	 Recheck stability of 30 ft fill with 10 ft surcharge – Refer to procedure in 

Section A.5 

10′ Surcharge 

35′

25′

Sand 

2:1 

10′

33′

7′

Fill 

Clay 

Dense Gravel 

Figure A.6-9. Trial failure circle – embankment fill + surcharge - East Abutment. 

Safety Factor with surcharge = 1.33.
 

Safety Factor without surcharge = 1.63. 

Conclusion: the safety factor in both cases is greater than 1.30, which is minimum
 

recommended for bridge approach stability for the temporary case of surcharge. 

Step 9: Prepare cost estimate for surcharge 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 20 December 2006 

Top Width = 60′ min. 

10′ 1: 1.5

30′ 1:2 

Figure A.6-10. Idealized cross section of embankment fill + surcharge. 
•	 Assume 500 linear feet behind top of end slope to be surcharged at each approach, 

therefore total length of surcharge = 1,000 feet. 

•	 Assume average width of surcharge = 80 feet including side slopes. 

•	 Calculate surcharge quantity (Vsur) as: 

1,000 ft 80ft ×10ft × = 3 29,630 yd 
 

27 ft3 /yd3
 

•	 Unit cost to place and remove surcharge = $4.00 /yd3

, therefore total cost is as 

follows: 

Total cost = 29,630 yd3 × $4.00 /yd3 ≈ $120,000 

[THIS IS AN EXAMPLE. ALWAYS CHECK THE LOCAL UNIT PRICES] 

A.6-5 CONSIDERATION OF WICK DRAIN OPTION (NO SURCHARGE) TO 

ACCELERATE CONSOLIDATION SETTLEMENT AND REDUCE TIME 

REQUIRED FOR SETTLEMENT DUE TO THE EMBANKMENT FILL 

Step 1: Choose reasonable spacing of wick drains – assume equivalent wick drain 

diameter of 0.5 ft and try 7.5-ft center to center triangular spacing. 

•	 Recent designs for wick drains have used equivalent diameters of 0.5 ft, i.e., 

dw = 0.5 ft 

•	 For triangular spacing: 

de = 1.05 × s = 1.05 × 7.5 ft = 7.875 ft 

η = de/dw = 7.875 ft / 0.5 ft = 15.75 ft ≈ 16 ft 

Step 2: Compute settlement-time-relationship 

•	 cv = cr = 0.6 ft2

/day 

•	 Arbitrarily select a reasonable range of values of time (days) and calculate the 

corresponding time factors for vertical (Tv) and radial (Tr) drainage as 

follows: 

Tr = t ch/d 2

e = t (days) 0.6 ft2

/day/(7.875 ft)2
 

T 2 2 2 v = t cv/Hd = t (days) 0.6 ft /day/(17.5 ft)

Hd = 1⁄2 H = 17.5 ft (Refer to previous calculation for vertical drainage only) 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 21 December 2006 
•	 Calculate the values of average percent consolidation (Uv) corresponding to 

the calculated values of time factor (Tv) by: 

Uv = (4 Tv /π)

1/2 

•	 Estimate the values of average percent consolidation (Ur) corresponding to the 

calculated values of time factor (Tr) for η = 16 from the curves in Figure 4 in 

FHWA (1986). 

•	 Calculate average percent consolidation for combined drainage (Uc) by: 

Uc = 1 - [(1 - Ur)(1 -Uv)] 

 where Urand Uv are in decimals. 

•	 Calculate values of consolidation settlement ∆H (inches) in clay Layer 3 due 

to combined vertical and radial drainage corresponding to the arbitrarily 

assumed values of time –use template shown in Table A.6-10 to aid in the 

calculation. 

Table A.6-10 

Template to compute values of consolidation settlement (∆H) in clay -Layer 3 at various 

times (t) after application of embankment load (wick drains with no surcharge) due to 

combined vertical and radial drainage 

Time after 

loading t 

(days) 

Time 

factorTv 

Average % 

Consolidation 

Uv 

Time 

factorTr 

Average % 

Consolidation 

Ur 

Combined 

Average % 

Consolidation 

Uc% 

Layer 3 

∆H (in) 

10 0.020 16 0.097 34 44 5.2 

20 0.039 22 0.193 57 66 7.8 

30 0.059 27 0.290 71 79 9.3 

40 0.078 32 0.387 81 87 10.3 

50 0.098 35 0.484 85 90 10.6 

60 0.118 39 0.580 92 95 11.2 

70 0.137 42 0.677 94 97 11.4 

80 0.157 45 0.774 97 98 11.6 

90 01.76 47 0.871 99 99 11.8 

Step 3: Plot settlement-time-curve for wick drains – Refer to Figure A.6-11. 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 22 December 2006 
Time (days) 

100 200 300 400 

0.83 

5 

10 

0 

Wick 7.5′ spacing

Settlement(inches) 

Figure A.6-11. Time versus settlement after completion of embankment fill for wick 

drain treatment without surcharge. 

Step 4: Prepare cost estimate for wick drains 

•	 Assume: 

1.	 500 linear feet of drains at both approaches, therefore total length = 1,000 

linear feet. 

2.	 Width of drain treatment midslope to midslope = 160 linear ft 

3.	 Length of each drain = 45 ft 

4.	 Unit cost per wick drain: $1.00/ft (THE USER SHOULD CALL THE 

LOCAL CONTRACTORS FOR LATEST COSTS) 

•	 Consider Wick Drains - 7.5 ft center to center. 

Treated area/drain = 0.866 S2

 = 0.866(7.5 ft)2 = 49 ft2/drain 

No. of drains = (160 ft)(1,000 ft)/49 ft2

/drain = 3,265 drains 

Linear feet of drain = (3,265 drains) 45 ft/drain = 146,925 ft 

Cost = (146,925 ft)($1.00/ft) + $25,000 (Mobilization) = $172,000 

Step 5: Prepare settlement–time curves for (a) 30-ft embankment fill, (b) 30-ft 

embankment fill with 10-ft surcharge (c) 30-ft fill embankment with vertical 

drains (wick) without surcharge (Refer to Figure A.6-12) 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 23 December 2006 
Time (days) 

100 200 300 400 

20 

12.66 inches 

30′ Fill w/Vertical Drains 

0.83 

5 

10 

0 

30′ Fill 

30′ Fill + Surcharge 

∆H′′

15 

Figure A.6-12. Summary of time-settlement curves for baseline case (30-ft embankment 

fill) and various treatment options. 

Step 6: Prepare table showing summary of results for base-line case (embankment 

fill only) and various treatment options in terms of waiting period and extra 

costs of treatment. Refer to Table A.6-12 

Table A.6-12 

Summary of results for base-line case (embankment fill only) and various treatment 

options
 

Treatment Time for at Least 90% 

Consolidation (Months) 

Extra Cost 

Fill only 14 Base line 

Fill with 10-ft of surcharge 6.5 $120,000 

Fill with Wick Drains 2 $172,000 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 24 December 2006 
A.6-6 CHECK FOR LATERAL SQUEEZE OF CLAY 

Step 1 Determine whether or not lateral squeeze will occur. 

Lateral squeeze causes pile supported abutments to rotate into embankment or 

spread footing abutments to move laterally. Lateral squeeze occurs if (see 

Chapter 7.6): 

γfill Hfill > 3 x cohesion 

For East Abutment: 

γfill Hfill = 130 pcf x 30 ft > 3 x 1,100 psf 

3,900 psf > 3,300 psf, therefore: 

•	 lateral squeeze may occur. 

•	 consider waiting period to dissipate settlement of fill. 

•	 do not construct abutments until settlement dissipates, i.e. until the average 

percent consolidation (U) ≥ 90%. 

Step 2 Estimate amount of horizontal movement of abutment due to lateral squeeze 

of clay - Layer 3. 

 Assume baseline case – 30-ft embankment fill only 

Rule of thumb: 

Horizontal Movement = 0.25 ∆H of embankment (in clay) 

 = 0.25 × 11.83 in 

Horizontal Movement = 3 in 

Recommend no spread footing construction or pile driving until settlement is at 

least 90% complete, i.e., at time = t90. 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 25 December 2006 
A.6-7 SUMMARY OF THE APPROACH ROADWAY STABILITY – FOR DETAILS 

REFER TO SECTION A.5-4 OF PREVIOUS PROBLEM 

1.	 Develop a design soil profile 

• Soil layer unit weights and strength estimated. 

2.	 Circular Arc Analysis 

•	 Approach embankment safety factor 1.63 against circular failure. 

3.	 Sliding and Block Analysis 

• Approach embankment safety factor 3.5 against sliding failure. 

4.	 Lateral Squeeze 

• Possible abutment rotation problem. 

A.6-8 SUMMARY OF EMBANKMENT SETTLEMENT ANALYSES AT EAST 

ABUTMENT 

1.	 Construct an idealized design profile to scale. 

•	 Use idealized soil profile from Boring UDH BAF-4 

•	 Include 30-ft high embankment at east abutment (assume 3 ft organic layer at 

the surface is replaced by compacted select material). 

•	 Estimate consolidation properties of clay layer from results of field and 

laboratory tests. 

2.	 Determine overburden pressure (po), change in pressure due to embankment fill (∆p), 

and maximum past pressure (pc) , all as a function of depth. 

•	 Plot pressure distributions with depth and determine stress history of impacted 

layers. 

3.	 Calculate settlement of each layer impacted by 30-ft embankment fill 

•	 Compacted select fill (Layer 1 organic replacement material ) - negligible 

settlement 

•	 Sand (Layer 2) - 0.8 inches of immediate settlement 

•	 Clay (Layer 1) - 11.83 inches of consolidation settlement. 

•	 Total of 12.6 inches of settlement predicted. 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 26 December 2006 
4.	 Calculate time required for 90% of primary consolidation to occur and plot settlement 

vs. time curve including immediate settlement of sand layer. 

•	 t90 = 432 days. (organic material replaced) 

5.	 Consider surcharge option to accelerate consolidation settlement and reduce time 

required for settlement due to the embankment fill. 

•	 Calculate the new final pressure due to the embankment plus the surcharge (pf 

+ ps) and plot values of (pf + ps), the overburden pressure (po), and the 

preconsolidation pressure (pc) with depth. 

•	 Calculate settlement in Layer 3. 

•	 Calculate and plot settlement-time relationship. 

•	 Determine waiting time with 10-ft of surcharge to obtain settlement equivalent 

to that of proposed embankment. 

•	 t90 = 432 days. (organic material replaced) 

•	 Recheck stability of 30 ft fill with 10 ft surcharge – FS = 1.33. 

•	 Prepare cost estimate for surcharge - cost = $120,000. 

6.	 Consideration of vertical drain option (wick drains - no surcharge) to accelerate 

consolidation settlement and reduce time required for settlement due to the 

embankment fill. 

•	 Choose reasonable spacing of drains. 

•	 Calculate and plot settlement-time-curve for combined vertical and radial 

drainage. 

•	 Determine waiting times to obtain settlement equivalent that of proposed 

embankment. 

•	 t90 ≈ 50 days for wick drains (organic material replaced). 

•	 Prepare cost estimate for vertical drains - cost = $172,000 (wick drains). 

FHWA NHI-06-089 Approach Roadway Deformations 

Soils and Foundations – Volume II A.6 - 27 December 2006 
[THIS PAGE INTENTIONALLY BLANK] 
 

 

 

 

 

 

 

 

 

Subsurface 

Explorations 

Basic Soil Properties 

Laboratory Testing 

Slope 

Stability 

Approach Roadway 

Deformations 

Driven Pile Design 

Construction 

Monitoring 

9

9

9

9

9

Design soil profile 

Pier bearing capacity 

Spread Footing Pier settlement 

Design	 Abutment settlement 

Surcharge 

Vertical drains 

Design soil profile 

Static analysis – pier 

 Pipe pile 

H - pile 

Static analysis – abutment 

Pipe pile 

H - pile 

Driving resistance 

Lateral movement - abutment 

Wave equation 

Hammer approval 

Embankment instrumentation 

Terrain reconnaissance 

Site inspection 

Subsurface explorations 

Visual description 

Classification tests 

Subsurface profile 

po diagram 

Test request 

Consolidation results 

Strength results 

Design soil profile 

Circular arc analysis 

Sliding block analysis 

Design soil profile 

Magnitude and rate of 

settlement 

Surcharge 

Vertical drains 

Lateral Squeeze 

Figure A.7-1. Status of geotechnical work. 

FHWA NHI-06-089 Spread Footing Design 

Soils and Foundations – Volume II A.7 - 1 December 2006 
SECTION A.7 

GEOTECHNICAL DESIGN OF SPREAD FOOTING 

A.7-1 RELEVANT CONCEPTS AND PROCEDURES (Refer to Figure A.7-1) 

•	 General procedure to calculate ultimate bearing capacity of a rectangular footing 

in a layered subsurface profile; Chapter 8 

•	 Procedure based on 2:1 geometric attenuation of applied pressure with depth to 

determine pressure distribution with depth due to rectangular footing; Chapter 2. 

•	 Immediate and consolidation settlement of rectangular footing – computation of 

magnitude; Chapter 7 and Chapter 8 

•	 Consolidation settlement - rectangular footing – computation of time rate; Chapter 

7. 

•	 Effect of pre-construction treatment by surcharging or vertical drains on 

consolidation settlement of rectangular footing; Chapter 7. 

In this section the geotechnical design process for spread footings for the pier and abutment 

foundations is illustrated. The computation procedures for the evaluation of ultimate bearing 

capacity are presented. The assessment of allowable bearing capacity is discussed with the 

context of settlement criteria. Settlement analysis for both immediate and consolidation 

settlement are performed to illustrate the effect of footing geometry on the magnitude of 

those settlements. The effect of pre-treatment by surcharging or vertical drains on both the 

magnitude of settlement and time required for full consolidation settlement is illustrated. 

A.7-2 DETAILED PROCEDURES 

Given: 

•	 The footing geometry and subsurface conditions shown in Figure A.7-2 for the 

center pier of the Apple Freeway Bridge. 

•	 The results of Standard Penetration tests (SPT-N blow counts) performed in 

Boring BAF – 2 as shown in Figure A.7-2. 

•	 The footing geometry and subsurface conditions shown in Figure A.6-2 for the 

east embankment of the Apple Freeway Bridge. 

•	 Values of relevant soil as provided in the previous example (Refer to Section A.6) 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 2 December 2006 
Required: 

•	 Compute the ultimate bearing capacity of a rectangular footing at the pier location 

and apply an appropriate factor of safety to obtain the allowable bearing pressure. 

•	 Compute the pressure transmitted to the underlying clay layer by the footing and 

compare that pressure to the allowable clay bearing capacity. 

•	 Compute the magnitudes of the anticipated immediate and consolidation 

settlement due to the rectangular footing at the pier location. 

•	 Compute the ultimate bearing capacity of a rectangular footing founded within the 

embankment at the East Abutment and apply an appropriate factor of safety to 

obtain the allowable bearing pressure 

•	 Compute the magnitudes of the anticipated immediate and consolidation 

settlement due to the rectangular footing founded within the embankment at the 

East Abutment. Taking into account pretreatment by wick drains (Refer to 

Section A.6-5). 

•	 Compute the time required for the settlement of the footing to occur. Take into 

account pretreatment by wick drains and continuing consolidation due to the 

embankment fill. 

•	 Plot settlement-time curves for both the pier and embankment footings. 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 3 December 2006 

SPT-N 

7′

4 

6 

11 

21 

22 

40 

37 

33 

BAF - 2 

Clay 

15′ 10′

4′

Sand 

Figure A7-2. Footing geometry and subsurface conditions for center pier of the Apple 

Freeway Bridge including SPT-N blow counts from Boring BAF-2. 
 

A.7-3 COMPUTE ULTIMATE AND ALLOWABLE BEARING CAPACITY OF 

PIER FOOTING 

•	 Define geometry of the problem. 

3⁄4 Footing embedment below final grade (Df) = 4 feet. 

3⁄4 Footing width (Bf) = 1/3 pier height = 7 feet 

3⁄4 Footing length (Lf) = 100 feet 

3⁄4 Depth to ground water below base of footing (Dw) = 6 feet. 

•	 Identify characteristics of geometry that are relevant to solution. 

3⁄4 Lf / Bf = 100 ft / 7 ft > 10, therefore consider the footing to be continuous. 

3⁄4 If (Dw < 1.5Bf + Df), the effect of ground water table must be considered. Check: 

6 ft < 1.5 (7 ft), therefore ground water table must be considered. 

3⁄4 Use SPT-N values to estimate internal friction angle (φ) of the sand. 

Step 1: Find average corrected SPT-N blow count (N160) below footing (Refer to 

Section 3-7 of text) and estimate internal friction angle (φ) of soil. 

Table A-7.1 

Determination of SPT-N values corrected for hammer energy and depth 

Depth 

(ft) 

po 

(psf) 

po 

(tsf) 

N 

(bpf) 

Hammer 

Efficiency (Ef) 

Ef / 60 N60 

(bpf) CN 

N160 

(bpf) 

5 550 0.275 11 65 1.083 12 1.43 17 

7 770 0.385 21 65 1.083 23 1.32 30 

8 880 0.440 22 65 1.083 24 1.28 31 

10 1100 0.550 40 65 1.083 43 1.20 52 

12 1195 0.598 37 65 1.083 40 1.17 47 

14 1290 0.645 33 65 1.083 36 1.15 41 

Average corrected blow count = 36 

•	 For average corrected blow count assume internal friction angle of sand φ ≈ 36o 

(Refer to Table 8-3 in Chapter 8) 

Step 2: Determine ultimate capacity (qult). 

•	 Equation 8-6 in the text can be re-written as follows since cohesion = 0. 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 4 December 2006 

 

0 

qult = c Nc sc bc + q Nq CWq sq bq dq + 0.5 γ Bf Nγ CWγ sγ bγ
 
3⁄4 By using the appropriate equations in Table 8-4 of the text the shape factors are: 

sq = 1.05 

sγ = 0.97 

3⁄4 Since the base of the footing is horizontal, the base inclination factors bq and bγ

both = 1.0 

3⁄4 The surcharge parameter q = γt Df = 110 pcf (4 ft) = 440 psf 

3⁄4 By using the Table 8-5 in the text, the groundwater correction factors are: 

CWq = 1.0 (i.e., the groundwater level is below the base of the footing) 

CWγ = 0.786 (i.e., the groundwater level is within 1.5Bf of the bottom of the 

footing.) 

3⁄4 From Table 8-6 in the text, the depth correction factor for Df / Bf = 4 ft / 7 ft = 

0.57 is estimated as: 

dq ≈ 1.15 

3⁄4 The bearing capacity factors for φ = 36o are estimated from Table 8-1 in the text 

as: 

 Nq = 37.8 

 Nγ = 56.3 

Therefore, the ultimate bearing capacity of the pier footing in sand is calculated as: 

qult = (440 psf)(37.8)(1.0)(1.05)(1.0)(1.15) + 0.5(110 pcf)(7 ft)(56.3)(0.786)(0.97)(1.0) 

qult = 20,083 psf + 16,526 psf = 36,609 psf 

Step 3: Determine allowable bearing capacity (use FS = 3) 

36,609 psf qall = = 12,203 psf = 6.1 tsf ≈ 6 tsf

3 

A7-4 CHECK PRESSURE TRANSMITTED TO CLAY LAYER AND COMPARE 

IT TO THE ALLOWABLE BEARING CAPACITY OF THE CLAY 

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Soils and Foundations – Volume II A.7 - 5 December 2006 

 

 

 

 

12,203 

2/1 2/1 

7′ 11′
 

Clay Layer 
Step 1 Determine pressure on clay layer (Refer to Section A.6-3 of text) 

⎛ 7 ft ⎞ •	 Footing pressure transmitted to clay surface (pclay) = ⎜ ⎟ ⎜ ⎟(12,203psf ) = 4,746

⎝ 7 ft +11ft ⎠

psf 

Step 2 Check bearing capacity of virtual footing on top of clay layer 

 For the virtual (transferred) footing: 

3⁄4 Footing embedment below final grade (Dtf) = 4 ft + 11 ft = 15 ft 

3⁄4 Footing width (Btf) = 7 ft +11 ft = 18 ft 

3⁄4 Footing length (Ltf) = 100 ft + 11 ft = 111 ft 

3⁄4 Ground water is 5 ft above the base of virtual footing 

Equation 8-6 in the text can be re-written as follows for a purely cohesive soil ( φ = 0) for 

which Nγ = 0. 

0 

qult clay = c Nc sc bc + q Nq CWq sq bq dq + 0.5 γ Btf Nγ CWγ sγ bγ 

3⁄4 By using the appropriate equations in Table 8-4 of the text the shape factors are: 

sq = 1.00 

sc = 1.03 

3⁄4 Since the base of the footing is horizontal, the base inclination factors bq and bγ

both = 1.0 

3⁄4 The surcharge parameter q = 110 pcf (10 ft) + 50 pcf(5 ft) = 1,350 psf 

3⁄4 By Table 8-5 in the text, the groundwater correction factors are: 

CWq = 0.5 (i.e., the groundwater level is at or above the footing base). 

3⁄4 From Table 8-6 in the text, the depth correction factor for Dtf / Btf = 15 ft/ 18 ft = 

0.83 is estimated as: 

dq ≈ 1.18 

3⁄4 The bearing capacity factors for φ = 0o are estimated from Table 8-1 in the text as: 

 Nq = 1.0 

 Nc = 5.14 

Therefore, the ultimate bearing capacity of the virtual footing on clay is calculated as: 

qult.clay = (1,100 psf)(5.14)(1.03)(1.0) + (1,350) psf(1.0)(0.83)(1.0)(1.0)(1.18) = 

qult.clay = 5,824 psf + 1,322 psf = 7,146 psf 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 6 December 2006 
 

 

Step 3: Determine allowable bearing capacity of virtual footing on clay (use FS = 3) 

7,146 psf qall clay = = 2,382 psf 3 

Since qall clay < pclay, the actual footing pressure needs to be reduced since qall clay 

controls bearing capacity of pier footing founded on the layered system. 

Step 4: Transfer qall clay up to the base of the pier footing to determine the limiting 

allowable bearing capacity qall max of the pier footing founded on sand. 

qall max = ?? 

2/1 2/1 

7′ 11′

qall = 2,382 Clay Layer 

⎛ 7 ft + 11ft ⎞
 qall max = qall clay ⎟

⎟ ⎜⎜

7 ft ⎝ ⎠

⎛18 ft ⎞

qall max = 2,382 psf ⎟

⎟ ⎜⎜ = 6,125 psf 7 ft ⎝ ⎠

qall max ≈ 6,125 psf ≈ 3.1 tsf 

•	 Check with bridge designer to see if 3.1 tsf is a realistic pressure. 

•	 Designer estimates a maximum un-factored structural load of 2,200 tons, and a 

minimum footing width of 7 ft 

2,200 tons •	 The estimated maximum footing pressure (qfts )= = 3.14 tsf

7ft ×100ft 

•	 Since the estimated maximum footing pressure is virtually identical to the 

estimate allowable bearing capacity, the footing size is acceptable for the load and 

use applied pressure (q) = 3 tsf for settlement analysis. 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 7 December 2006 
A7-5 CALCULATE SETTLEMENT OF PIER FOOTING FOUNDED WITHIN A 

TWO-LAYER SYSTEM 

Step 1: Find pressure distribution by 2 on 1 construction (Refer to Chapter A.6-3 of 

text for procedure and Table A.7-2 below for results) 

6,000 psf 1 

2 

x 

7 ft

∆P = (6,000 psf) 7 ft + x 

Table A.7-2 

Computation of pressure change at various depths due to 

pressure applied by footing 

Depth x 

(feet) k = 

x7 ft 

7 ft 

+

∆p = k (6,000 psf) 

(psf) 

3.5 0.67 4,000 

7 0.50 3,000 

10.5 0.40 2,400 

14 0.33 2,000 

21 0.25 1,500 

28 0.20 1,200 

35 0.17 1,000 

Step 2: Calculate the final pressure (pf = po + ∆p) at various depths and plot the 

overburden pressure (po), preconsolidation pressure (pc), and pf with depth 

as shown in Figure A.7-3 

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Soils and Foundations – Volume II A.7 - 8 December 2006 
po 

pf 

pc 

Figure A.7-3. Variation of overburden pressure (po), preconsolidation pressure (pc) and 

final pressure due to pier footing (pf) with depth. 

Step 3: Calculate immediate settlement of the pier due to compression of the sand 

layer from 4 ft to 15 ft 

Settlement computation by Hough’s Method 

•	 Thickness of sand layer beneath pier footing = 15 ft - 4 ft = 11 ft 

•	 Calculate immediate settlement (Refer to Chapter 7.4.1 in text) 

•	 For (N160) average = 36, C′ = 90 (Refer to Figure 7-7 of text –use curve for “wellgraded fine to medium silty sand”). 

•	 Calculate settlement for po = 1,050 psf and pf = 4,350 psf. 

∆H = 0.90 in 

1 p ∆H = f H log C′ po 

⎛ 1 ⎞ 4,350 psf ⎛12 in ⎞ ∆H = 11ft⎜ ⎟log ⎜ ⎟ ⎝ 90 ⎠ 1,050 psf ⎝ ft ⎠

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 9 December 2006 
Settlement Computation by Schmertmann’s method (Chapter 8.5 in the text) 

•	 Begin by drawing the strain influence diagram. The Lf/Bf ratio for the footing is: 

100 ft/7 ft = 14.3 

Determine the value of the strain influence factor at the base of the footing, IZB, as 

follows: 

IZB = 0.2 for plane strain case (Lf/Bf ≥ 10) 

•	 Determine the maximum depth of influence, DI, as follows: 

DI = 4Bf for Lf/Bf >10 

DI = 4 x 7 ft = 28 ft 

•	 Determine the depth to the peak strain influence factor, DIP, as follows: 

DIP = Bf for Lf/Bf > 10 

DIP = 7 ft 

•	 Determine the value of the maximum strain influence factor, IZP, as follows: 

∆p = 6,000 psf − 4 ft (110 pcf )=5,560 psf = 5.56 ksf
 pop =10 ft (110 pcf ) +1ft(110pcf − 62.4pcf ) =1,147.6 psf =1.15 ksf
 

•	 Draw the IZ vs. depth diagram as shown below. The hatched portions show portions 

of the strain influence diagram within the sand layer and the clay layer. The 

immediate settlement will occur only in the sand layer. Therefore, the portion of the 

strain influence diagram in the clay layer will not be considered in the computation of 

the immediate settlement. 

0.5 ⎛ ⎞ ⎜	 ∆p ⎟ I	 ZP = 0.5 + 0.1⎜ ⎟ ⎜ p ⎟ ⎝	 op ⎠

5,560psf IZP =0.5+ 0.1 =0.72 

1,147.6psf 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 10 December 2006 
Influence Factor (Iz) 

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 

0 

4 

Sand 

Layer 

Depth below footing (ft)

8 

12 

16 

20 

Clay 

Layer 

24 

28 

• Determine value of elastic modulus Es from Table 5-16 in Chapter 5. 

For “clean fine to medium sands with slightly silty sands” Es = 7N160 tsf. Since the 

elastic modulus Es is based on correlations with N160-values obtained from Table 5­

16, calculate the X multiplication factor as follows: 

X = 1.75 for Lf/Bf ≥ 10 

Thus, XEs = 1.75 (7) (36) = 441 tsf. 

• Divide the sand layer into convenient sublayers using the guidelines in Chapter 

8.5.1.2. Using those guidelines, the sand layer below the footing is divided into 1 ft 

and 2 ft sublayers. Using the sublayers determine the settlement by setting up a table 

as follows: 

FHWA NHI-06-089 Spread Footing Design 

Soils and Foundations – Volume II A.7 - 11 December 2006 
 

Layer Hc

 (inches) 

N160 Es

(tsf) 

XEs

(tsf) 

Z1

(ft) 

IZ at Zi c 

s 

Z

i H

XE 

I H =

(in/tsf) 

1 12 36 252 441 0.5 0.237 0.00645 

2 24 36 252 441 2.0 0.349 0.01897 

3 12 36 252 441 3.5 0.460 0.01252 

4 24 36 252 441 5.0 0.571 0.03110 

5 24 36 252 441 7.0 0.720 0.03918 

6 24 36 252 441 9.0 0.651 0.03543 

7 12 36 252 441 10.5 0.600 0.01633 

Σ Hi= 0.15998 

• Determine embedment factor (C1) and creep factor (C2) as follows: 

a) Embedment factor 

⎛ p ⎞	 ⎛ × ⎞ C =1− 0.5 ⎜ o ⎟ 4 ft 110 pcf 

1	 =1 − 0.5 ⎜ ⎟ = 0.960 ⎜ ∆p ⎟ ⎜ ⎟ ⎝ 5,560 psf ⎝ ⎠ ⎠

b) Creep Factor
 

⎛ t(years)⎞ C2 =1+ 0.2 log10 ⎜ ⎟ ⎝ 0.1 ⎠
 

For end of construction t(yrs) = 0.1 yr (1.2 months) 

⎛ 0.1⎞ C2 =1+ 0.2 log10 ⎜ ⎟ =1.0 ⎝ 0.1⎠

• Determine the settlement at end of construction as follows: 

Si =C1C2∆p∑ Hi 

⎛	 ⎞

( )( )⎜ 5,560psf	 ⎟ 	 ⎛ in ⎞ S i	 = 0.960 1.0 ⎜ ⎟⎜0.15998 ⎟ ⎜ psf tsf 2,000 ⎟⎝ ⎠ ⎝ tsf ⎠
 

S i = 0.43inches

Note: The settlement computed by Hough’s method was 0.90 inches which is 

approximately 2 times more than that computed above by Schmertmann’s 

method. This difference is similar to that found by FHWA (1987) and 

discussed in Chapter 8.5.1 in the text. 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 12 December 2006 
Step 4: Calculate settlement of the pier due to consolidation of the clay layer. Use 

equation for consolidation settlement (Refer to Chapter 7.5) and consider two 

sublayers; sublayer 1 from 15 ft to 32 ft and sublayer 2 from 32 ft to 40 ft 

•	 Thickness of clay Sub-layer 1 = 32 ft - 15 ft = 17 ft 

3⁄4 As shown in Figure A.7-3, the clay in Sub-layer 1 is over-consolidated since po < 

pc and the load increment results in pf which is also less than pc within this depth 

range. Therefore, calculate settlement for the pressure increment from po = 1,900 

psf to pf = 3,520 psf and use the recompression index Cr. 

0.035 3,520 psf ⎛12 in ⎞ ∆H = 17 ft log ⎜ ⎟ 1 + 0.97 1,900 psf ⎝ ft ⎠

∆H = 0.97 in 

•	 Thickness of clay Sub-layer 2 = 40 ft - 32 ft = 8 ft 

3⁄4 As shown in Figure A.7-3, the clay in Sub-layer 2 is over-consolidated within this 

depth range since pc > po, but at the mid-depth the load increment causes pf > pc. 

Therefore the settlement for this sub-layer must be calculated in two steps, one 

step for the pressure increment from po to pc for which Cr applies, and the other 

for the pressure increment from pc to pf for which Cc applies. (Refer to Chapter 

7.5.2) 

3⁄4 Calculate settlement of clay Sub-layer 2 for the pressure increment from po = 

2,710 psf to pc = 3,450 psf. 

0.035 3,450 psf ⎛12 in ⎞ ∆H = 8ft log ⎜ ⎟ 1 + 0.97 2,710 psf ⎝ ft ⎠

 ∆H = 0.18 in 

C p ∆H = r f H log 1 + e	 o po 

C ∆H = H r pc log 1 + e	 o po 

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Soils and Foundations – Volume II A.7 - 13 December 2006 
3⁄4 Calculate settlement of clay Sub-layer 2 for the pressure increment from pc = 

3,450 psf to pf = 3,840 psf. 

 Cc pf ∆H = H log 1 + e	 o c p

 0.35	 3,840 psf ⎛12 in ⎞ ∆H = 8ft log ⎜ ⎟ 1 + 0.97 3,450 psf ⎝ ft ⎠
 

 ∆H = 0.80 in 

Step 5: Summarize settlement contributions from sand and clay layers (Refer to Table 

A.7-3) 

Table A.7-3 

Summary of settlement of pier footing
 

Layer Settlement (in) 

Sand (4 ft to 15 ft) 0.90 in 

Clay – Sub-layer 1 (15 ft to 32 ft) 0.97 in 

Clay – Sub-layer 2 (32 ft to 40 ft) 0.98 in 

Total settlement = 2.85 in 

Total settlement of clay layer = 1.95 in 

Step 6: 	 Compute time for settlement due to pier footing to occur in clay layer 

•	 Obtain time for various percentages of settlement as shown in Table A.7-4 by 

using Table 7-4 in Chapter 7.5.3.1 in the text and the following equations 

3⁄4 Hd = 1⁄2 H = 1⁄2 (40 ft – 15 ft) =12.5 ft 

3⁄4 cv = 0.6 ft2/day 

3⁄4 (Hd )2/cv = (12.5 ft)2 / (0.6 ft2/day) = 260 days 

3⁄4 For time (t) use Equation 7-8 of text 

T H2

t = d cv 

Table A.7-4 provides a convenient template for performing computations to obtain 

settlement vs. time values for arbitrarily chosen values of average percent consolidation. 

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Soils and Foundations – Volume II A.7 - 14 December 2006 
Table A.7-4 

Template to compute values of consolidation settlement (∆H) in clay layer at various times 

(t) after application of pier footing load (refer to section A.6) 

Average % 

Consol. (U) 

∆H (in) = 

(U)( ∆H Total Clay 

Layer) 

Time Factor (T) 

(from Table 7-4 

in text) v 

2 

d 

c 

H t (days) 

20 0.39 0.031 260 8 

50 0.98 0.197 51 

70 1.37 0.403 104 

90 1.76 0.848 220 

Step 7: Plot settlement-time curve for the pier including immediate settlement of sand 

as shown in Figure A.7-4. 

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Soils and Foundations – Volume II A.7 - 15 December 2006 

Time (days) 

50 100 150 200 250 

∆ H = 2.85′′
 

∆ H

1′′

2′′

3′′

Figure A.7-4. Settlement-time curve for pier including immediate settlement of sand. 
A.7-6 CALCULATE SETTLEMENT OF EAST ABUTMENT FOOTING FOUNDED 

WITHIN A TWO-LAYER SYSTEM 

•	 Define geometry of the problem and state relevant assumptions. 

3⁄4 Footing embedment below final grade of embankment fill (Df) = 10 ft 

3⁄4 Footing width (Bf) = 1/3 pier height = 7 ft 

3⁄4 Footing length (Lf) = 100 ft 

3⁄4 Depth to ground water below base of footing (Dw) = 25 ft 

3⁄4 Internal consolidation of embankment fill under its own weight is negligible. 

3⁄4 Organic layer is excavated and replaced with 3-feet of compacted select fill. 

P 

10 ft 

γ = 130 pcf 

23 ft 

Figure A.7-5. Footing geometry for embankment footing. 

Step 1: Determine net footing pressure at footing embedment depth due to soil 

removal for footing excavation. 

o	 p = the net pressure applied at the footing level. Assume that the abutment 

will be constructed after the embankment fill is in place. 

o p = 6,300 psf – (10 ft)130 pcf) = 5,000 psf 

Step 2: Calculate change in pressure due to embankment footing by 2:1 construction. 

Consider layer mid-depths corresponding to those considered in calculation of 

po and pf in Section 6 for embankment settlement. (Refer to Figure A.6-5 

Refer to Table A.7-5 below for results) 

7’ wide 

P 1

x 2 ′	 7 ft

∆P = P 

7 ft + x ft 

• pabut = pf + ∆pabut where
 

pf = po + change in pressure due to embankment load (Refer to Table A.6-2)
 

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Soils and Foundations – Volume II A.7 - 16 December 2006 
 

Table A.7-5 

Computation of pressure change due to pressure applied by abutment footing and pabut
 

at various depths the embankment 

Layer Thickness 

(feet) 

Depth x from 

top of sand to 

layer mid-point 

(ft) 

Depth z 

to 

midpoint 

(feet) 

x7ft 

7ft k 

+ = ∆pabut = 

k (5,000 psf) 

(psf) 

pf 

(psf) 

pabut 

(psf) 

Sand 7 3.5 26.5 0.21 1,050 4,470 5,520 

Clay 

Sublayer 1 8 11.0 34.0 0.17 850 4,920 5,770 

Clay 

Sub 

layer 2 27 28.5 51.5 0.12 600 5,650 6,250 

Step 3: Plot the pressure distributions with depth of the overburden pressure (po), 

preconsolidation pressure (pc), final pressure due to embankment fill only 

(pf), and the final pressure due to embankment fill plus abutment footing 

(pabut) as shown in Figure A.7-6 

Step 4: Calculate immediate settlement of the abutment footing due to compression 

of the sand layer (3 ft to 10 ft). 

• Thickness of sand layer beneath pier footing = 10 ft - 3 ft = 7 ft 

• Calculate immediate settlement (Refer to Chapter 7) 

⎛ 1 ⎞ 5,520 psf ∆H = 7 ft⎜ ⎟log ⎝ 90 ⎠ 4,470 psf 

∆H = 0.0071 ft ∼ 0.09 in 

Note: Schmertmann’s method can also be used. This was demonstrated earlier. 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 17 December 2006 

1 p ∆H = H	 log abut

C′ pf 
Figure A.7-6. Pressure distributions with depth at East Abutment for the overburden 

pressure (po), preconsolidation pressure (pc), final pressure due to embankment fill only 

(pf), and the final pressure due to embankment fill plus abutment footing (pabut). 

pf 

po 

pabut 

pc 

4920 5770 

5650 6250

5520 4470 

Gravel Layer 

Clay 

Sand 

Pressure (psf) 

0 1000 2000 3000 4000 5000 6000

Depth (ft) 

10 

20 

30 

40 

50 

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Soils and Foundations – Volume II A.7 - 18 December 2006 
 

Step 5: Calculate settlement of the abutment footing due to consolidation of the clay 

layer. Use equation for consolidation settlement (Refer to Chapter 7.5) and 

consider two partial layers, Sub-layer 1 from 10 ft to 18 ft and Sub-layer 2 

from 18 ft to 45 ft. 

•	 Thickness of clay Sub-layer 1 = 18 ft - 10 ft = 8 ft 

3⁄4 As shown in Figure A.7-6, the clay in Sub-layer 1 was over-consolidated prior to 

the construction of the embankment fill since po < pc and remained so during and 

after consolidation under the embankment fill since pf is also < pc. Figure A.7-6 

further shows that Sub-layer 1 will continue to be over-consolidated during and 

after consolidation under the abutment footing, i.e., pabut is also < pc within this 

depth range. Therefore, calculate settlement due to the abutment footing for the 

pressure increment from pf = 4,920 psf to pabut = 5,770 psf and use the 

recompression index Cr= 0.035. 

C p ∆H = H r log abut

1 + eo pf 

0.035 5,770 psf ∆H = 8ft log 1 + 0.97 4,920 psf 

∆H = 0.0098 ft ∼ 0.12 in 

•	 Thickness of clay Sub-layer 2 = 45 ft - 18 ft = 27 ft 

3⁄4 As shown in Figure A.7-6, the clay in Sub-layer 2 was also over-consolidated 

prior to the construction of the embankment fill since po < pc. However, during 

consolidation under the embankment fill, the pressure increment at every depth in 

Sub-layer 2 caused the final pressure pf to become > pc. It was for this reason that 

the total consolidation settlement for this Sub-layer under the embankment fill 

had to be calculated by the use of a two-step procedure. In the first step the 

settlement was calculated as the pressure increased from po to pc; in the second 

step the settlement was calculated as the pressure increased from pc to pf. As 

described in Step 5 of Section A.6-3, Cr was used in the first step and Cc in the 

second. Therefore, unless the abutment footing is built after 100% consolidation 

of the clay layer under the embankment load has occurred, the clay will be underconsolidated at the time of construction of the footing, i.e., settlement due to the 

abutment footing will be accompanied by continued settlement due to the 

embankment. Therefore, calculate settlement due to the abutment footing for the 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 19 December 2006 
 

pressure increment from pf = 5,650 psf to pabut = 6,250 psf and use the 

compression index Cc = 0.35. 

 Cc pabut ∆H = H log 1 + eo	 pf 

 0.35	 6,250 psf ∆H = 27 ft log 1 + 0.97 5,650 psf
 

∆H = 0.21 ft ∼ 2.50 in 

Step 6: Summarize contributions to settlement under abutment footing loads from 

sand and clay layers (Refer to Table A-7.6) 

Table A.7-6 

Summary of settlement of pier footing
 

Layer Settlement (in) 

Sand (3 ft to 10 ft) 0.09 in 

Clay – Sub-layer 1 (10 ft to 17 ft) 0.12 in 

Clay – Sub-layer 2 (17 ft to 45 ft) 2.50 in 

Total settlement due to abutment footing= 2.71 in 

Total settlement of clay layer due to abutment footing= 2.62 in 

Step 7:	 Compute Time for Settlement Due to Abutment Footing to Occur in Clay 

Layer 

•	 Obtain time for various percentages of settlement as shown in Table A.7-4 by 

using Table 7-4 in Chapter 7.5.3.1 in the text and the following equations 

3⁄4 Hd = 1⁄2 H = 1⁄2 (45 ft – 10 ft) =17.5 ft 

3⁄4 cv = 0.6 ft2/day 

3⁄4 (H 2

d ) /cv = (17.5 ft)2

 / (0.6 ft2/day) = 510 days 

3⁄4 For time (t) use Equation 7-8 of text 

T H2

t = d cv 

Table A.7-7 provides a convenient template for performing computations to obtain 

settlement vs. time values for arbitrarily chosen values of average percent consolidation. 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 20 December 2006 
Table A.7-7 

Template to compute values of consolidation settlement (∆H) in clay layer at various times 

(t) after application of abutment footing load (refer to section A.6) 

Average % 

Consol. (U) 

∆H (in) = 

(U)( ∆H Total Clay 

Layer) 

Time Factor (T) 

v 

2 

d 

c 

H t (days) 

20 0.52 0.031 510 16 

50 1.31 0.197 100 

70 1.83 0.403 206 

90 2.36 0.848 432 

Step 9:	 Plot settlement-time curve for the pier including immediate settlement of sand 

as shown in Figure A.7-7. 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 21 December 2006 

Time (days) 

100 200 300 400 500 

0 

1 

∆

2

 H (in) 

∆ H total abut = 2.62 in 

Figure A.7-7. Settlement-Time curve for abutment footing. 
A.7-7 EVALUATE THE EFFECT OF PRE-TREATMENT ON THE SETTLEMENT 

OF EAST ABUTMENT FOOTING 

•	 As indicated in Step 6 of Section A.7-6 above, the settlement due to the abutment 

footing will occur while the settlement remaining due to embankment load continues. 

Therefore the actual settlement of is the sum of these two components of settlement. 

For example, if the abutment footing were built immediately after placement of the 

embankment fill (t = 0) without pre-treatment by surcharging and/or vertical drains, 

the total consolidation settlement of the abutment footing would be: 

 ∆H total (emb + abut) = ∆H total emb + ∆H total abut = 12.66 in + 2.62 in = 15.28 in 

•	 However, pretreatment by surcharges and/or vertical drains can be used to accelerate 

consolidation of the clay layer under the embankment load so that when the abutment 

footing is built at a later time, e.g., at a time when the t90 for the embankment fill 

without treatment is reached, the total settlement due to the abutment footing (∆H total 

(emb + abut)) will be only slightly larger than the settlement due to the abutment footing 

alone (∆H total abut). 

•	 For the case of pre-treatment by wick drains, Figure A.7-8 shows that the t90 

settlement of 11.43 inches due to the 30 ft of embankment fill without treatment is 

reached after approximately 50 days. If the abutment footing is constructed at that 

time, only about 1.23 inches of settlement due to the embankment alone remains. 

Therefore, the abutment footing will undergo a total settlement of 1.23 in + 2.62 in = 

3.85 in as compared to 15.28 in it would have undergone had the pre-treatment not 

been used and the abutment footing built immediately after construction of the 

embankment. 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 22 December 2006 
100 200 300 400 Time – days 

Begin abutment footing construction. Thirty days after completion of the footing, 0.25 

inches of settlement remain for the 30 ft of fill to reach ∆ at t90 without treatment 

∆Htotal abut = 2.62 in 

12.66 in = ∆ for 30 ft of fill at t90 without treatment 

0 

∆ H (in) 

15 

10 

5 

15.28 in = ∆H total (emb + abut) for 30 ft of fill at t90 without treatment 

Assume wick drains installed 

Figure A.7-8. Settlement –Time curve for abutment footing built 6 months after 

completion of embankment fill with vertical drain pre-treatment.
 

•	 For the case of pre-treatment by 10 ft of surcharge, Figure A.7-9 shows that the t90 

settlement of 13.7 inches due to 30 ft of embankment fill plus surcharge is reached after 

approximately 240 days. 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 23 December 2006 
 

 

 

Time – Days 

∆H – Total 

0 

0.83 

5 

10 

15 

100 200 300 400 500 

30 ft Fill + 

10 ft Surcharge 

13.7 in @ t90 

*Assume 10 ft 

Surcharge Used 

15.25 in = Total ∆H 

240 days 400 days 

Figure A.7-9. Settlement –Time curve for 30 ft of embankment fill plus 10 ft surcharge. 

* Surcharge must be left in place for 13 months to dissipate all embankment and abutment ∆H 

Summary of the Spread Footing Design Phase for Apple Freeway Design Problem 

•	 Design Soil Profile 

 Strength and consolidation values selected for all soil layers. Footing elevation and 

width chosen. 

•	 Pier Bearing Capacity

 Qallowable = 3 tsf 

•	 Pier Settlement
 

 Settlement = 2.67 in, t90 = 220 days. 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 24 December 2006 
•	 Abutment Settlement
 

 Settlement = 2.7 in, t90 = 432 days. 

•	 Vertical Drains

 t90 = 60 days - could reduce settlement to 0.25 in after abutment constructed and 

loaded. 

•	 Surcharge 

10 ft surcharge: t90 = 240 days 

 before abutment constructed. 

A.7-7 SUMMARY OF GEOTECHNICAL DESIGN OF PIER AND ABUTMENT 

SPREAD FOOTINGS 

1.	 Construct idealized design profile with footing geometry shown. 

•	 Use logs of appropriate borings 

•	 Include 30 ft high embankment at East abutment (assume 3 ft organic layer at 

the surface is replaced by compacted select material). 

•	 Estimate consolidation properties of clay layer at each location from results of 

field and laboratory tests. 

•	 Estimate internal friction angle of sand from SPT-N corrected blow counts (φ

≈ 36o) 

2.	 Determine overburden pressure at each location, change in pressure due to pier 

footing, change in pressure due to embankment fill at East abutment, change in 

pressure due to abutment footing, and maximum past pressure at each location, all as 

a function of depth. 

•	 Plot pressure distributions with depth and determine stress history of impacted 

layers at each location. 

3.	 Calculate ultimate and allowable bearing capacity of pier footing 

•	 Footing width = 7 ft 

•	 Footing length = 100 ft 

•	 Depth of embedment = 4 ft 

•	 qult = 33,000 psf 

•	 qall = 11,000 psf 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 25 December 2006 
4.	 Check pressure transmitted to clay layer and compare it to the allowable bearing 

capacity of the clay 

•	 qall max ≈ 3.1 tsf– use 3 tsf for settlement analysis 

5.	 Calculate settlement of pier footing founded within a two-layer system and plot 

settlement time relationship 

•	 Sand (4–15 ft) = 0.91 in 

•	 Clay (15–32 ft) = 0.97 in 

•	 Clay (32-40 ft) = 0.98 in 

•	 Total settlement = 2.85 in due to clay plus sand 

•	 Total settlement = 1.95 in due to clay alone 

•	 t90 = 220 days 

6.	 Calculate settlement of East abutment footing founded within the embankment and 

underlain by a two-layer system. Plot settlement time relationship 

•	 Sand (3-10 ft) = 0.09 in 

•	 Clay (10-17 ft) = 0.12 in 

•	 Clay (17-45 ft) = 2.50 in 

•	 Total settlement = 2.71 in - footing due to clay plus sand 

•	 Total settlement = 2.62 in - footing due to clay alone 

•	 Total settlement = 15.28 in - footing plus embankment due to clay 

 plus sand 

•	 t90 = 433 days for embankment alone without 

 pre-treatment 
 

7.	 Evaluate the effect of pre-treatment on the settlement-time relationship of the East 

abutment footing and embankment fill. 

•	 t90 = 60 days for embankment alone pre- treated 

 with vertical drains. 

•	 Total settlement = 0.25 in remaining due to embankment. 

•	 Abutment footing constructed at this time. 

•	 Total settlement = 0.25 in + 2.60 in = 2.85 in – footing plus embankment 

 due to clay alone after abutment footing constructed and 

 loaded. 

FHWA NHI-06-089 Spread Footing Design
 

Soils and Foundations – Volume II A.7 - 26 December 2006 
 

 

 

 

 

 

 

 

 

 

 

 

Subsurface 

Explorations 

Basic Soil Properties 

Laboratory Testing 

Slope 

Stability 

Approach Roadway 

Deformations 

Spread Footing Design 

Construction 

Monitoring 

Terrain Reconnaissance 

Site Inspection 

Subsurface Explorations 

9

Visual Description 

Classification Tests 

Subsurface Profile 

9

po Diagram
 

Consolidation Results 

Test Request 9

Strength Results 

Design Soil Profile 

Analysis Sliding Block Analysis 

Circular Arc 9

Design Soil Profile 

Settlement

Time – Rate 


 9

Surcharge 

Vertical Drains
 

Lateral Squeeze 

Design Soil Profile 

Pier Bearing Capacity 

Pier Settlement
 9

Abutment Settlement 

Surcharge 

Vertical Drains
 Design Soil Profile 

Static Analysis – Pier 

 Pipe Pile 

Driven Pile H – Pile 

Design Static Analysis – abutment

 Pipe Pile 

H – Pile 

Driving Resistance 

Abutment Lateral Wave Equation 

Hammer Approval Movement 

Embankment Instrumentation 

Figure A.8-1. Status of geotechnical work. 

FHWA NHI-06-089 Driven Pile Design 

Soils and Foundations – Volume II A.8 - 1 December 2006 
 

SECTION A.8 

DRIVEN PILE DESIGN 

A.8-1 RELEVANT CONCEPTS AND PROCEDURES (Refer to Figure A.8-1) 

• Refer to Chapter 9 for driven pile design 

In this Section, the Apple Freeway is used to illustrate the pile design for support 

of the pier and abutment. Although drilled shafts may also be a feasible deep 

foundation design alternate for this structure, only driven piles are discussed 

herein because they involve a lot more detail in design and construction. The 

computation process for static analysis to determine pile capacity by Nordlund 

Method is presented along with the computation of pile driving resistance. 

Given: The subsurface profile and soil properties shown below. 

Required: Determine the allowable pile capacity using static analysis. 

FHWA NHI-06-089 Driven Pile Design 

Soils and Foundations – Volume II A.8 - 2 December 2006 

 

 

 

East Abutment 

10′ 11′

15′

25′

10′ Gravel γ = 130 pcf 

φ = 43° 10′

35′

7′

23′

Sand γ =110 pcf 

φ = 36°

Fill γ = 130 pcf 

φ = 40o 

Clay γ = 125 pcf 

c = 1,100 psf 

(Assume Sensitivity = 2) 
A.8-2 CONSIDERATION FOR PILE TYPE SELECTION 

•	 Spread footings would be feasible at both the pier and abutment except for settlements 

due to consolidation of the clay deposit. To eliminate these settlements any pile type 

selected must achieve capacity below the bottom of the clay deposit. 

•	 End bearing will provide most of the ultimate resistance at either the pier or abutment 

location due to the minimal thickness of the gravel layer. 

•	 The maximum estimated design structural load of 2,200 tons can be supported by either 

the gravel or the rock layer. However pile driveability appears to be an issue in design. 

•	 Required loads, end bearing support, and difficult driving concerns would favor a 

straight-sided steel pile over either a timber or concrete or tapered pile. 

•	 Static analyses will be used to determine if a displacement pile with an end plate or a 

non-displacement pile will provide the best choice for both bearing and driveability. The 

designer selected a 12 inch diameter closed end pipe pile and a 12 inch H-pile for 

alternate evaluation at this site. The project’s structural engineer usually designs the pipe 

pile for a 70-ton design load and the H-pile for a 120-ton design load. 

Step 1: Plot po diagram. 

po @ pier 

po @ abut. 

70 

60 

50 

40 

30 

20 

10 

1,000 2,000 3,000 4,000 5,000 6,000 Pressure psf 

Depth (ft) 

FHWA NHI-06-089 Driven Pile Design 

Soils and Foundations – Volume II A.8 - 3 December 2006 
A.8-3 STATIC PILE ANALYSIS – PIER 

A. For 12 inch diameter pipe pile (closed end, 70 ton design) 

Step 2A: Compute shaft resistance. 

• Sand Layer (4 ft – 15 ft - Use Nordlund Method – Chapter 9.5.1.1) 

 D = 15 ft – 4 ft = 11 ft 

 δ = 0.6 (for closed end pipe pile from Figure 9-7 in Chapter 9) φ

 δ = (0.6)(36°) = 21.6°

 Kδ = 1.92 (for φ = 36o from Table 9-6(a) in Chapter 9) 

 Correction Factor, CF = 0.75 (from Figure 9-12 in Chapter 9) 

Cd = π d = π (1 ft) = 3.14 ft 

Rs (sand) 	 = Kδ (CF)(pd)(Cd)(sin δ)D (Equation 9-6 in Chapter 9) 

 = (1.92)(0.75)(1,050 psf)(3.14 ft)(sin 21.6o)(11 ft) 

Rs (sand) 	 = 19,225 lbs = 9.6 tons 

• Clay Layer (15 ft – 40 ft) 

Rs(clay) = caCdD 

ca (Adhesion) ≅ 1,100 psf (assume adhesion ≈ cohesion, i.e., α ≈ 1.0) 

Rs(clay) = 1,100 psf (3.14 ft) 25 ft = 86,350 lbs = 43.1 tons 

• *Gravel Layer (Try 4 ft Embedment i.e.. 40 ft – 44 ft) 

*Remember to reduce φ of 43° to maximum 36° value for hard, angular gravel skin 

friction. 

πd 2 3 = = 0.785ft 

4 ft

pile vol. V = foot
 

4 ft +15ft 

pd Avg. @ = 9.5 ft is 1,050 psf 2 

FHWA NHI-06-089 Driven Pile Design 

Soils and Foundations – Volume II A.8 - 4 December 2006 
 Rs = (Kδ)(CF)(pd)(Cd)(sin δ)D
 

 δ = 0.6
 φ

 δ = (0.6)(36°) = 21.6°

 Kδ = 1.92 (for φ = 36o from Table 9-6(a) in Chapter 9) 

CF = 0.7 (from Figure 9-12 in Chapter 9) 

po = 3,200 psf 

Rs(gravel) = (1.92)(0.7)(3,200 psf )(3.14 ft)(sin 21.6°)4 ft 

Rs(gravel) = 19,885 lbs = 9.9 tons 

Step 3A: Compute toe resistance. 

•	 Gravel Layer 

For φ = 43o, α ≈ 0.75 from Figure 9-13(a) in Chapter 9 

For φ = 43o, N′q = 300 from Figure 9-13(b) in Chapter 9 

 pt max.
 

a.	 Rt = Ap αt pt N′q (Equation 9-7a in Chapter 9) 

 = (0.785 ft2

)(0.75)(3,000 psf)(300) 

 Rt = 529,875 lbs = 265 tons 

b.	 Rt (max) = qL × Ap (Equation 9-7b in Chapter 9) 

 = (680 ksf)(0.785 ft2

) (qL=680 ksf for φ = 43o from Figure 9­

14 in Chapter 9) 

 Rt (max) = 533.8 kips = 267 tons 

 ∴Rt = 265 tons 

It is obvious that any embedment in gravel layer will produce capacities > 200 tons. 

Therefore, estimate pile length to top of gravel. 

Step 4A: Determine soil resistance to driving SRD for 70 ton load with SF = 2. 

Rs(clay) SRD = Rs(sand) + + (70 tons × 2) sensitivity 

FHWA NHI-06-089 Driven Pile Design 

Soils and Foundations – Volume II A.8 - 5 December 2006 
43.1tons = 9.6 tons + +140 tons (note sensitivity = 2 is given in 2 

problem statement) 

 SRD = 171. 1 tons 

B. For 12 inch H-Pile* (120 ton design load) 

 *Assume HP 12x84 pile section 

Step 2B: Compute Shaft Resistance 

(References to Figures and Tables are as in Step 2A above) 

Sand Layer (4 ft - 15 ft) 

24.6 0.17 ft 3

V =	 = 144 ft

 δ = 0.80 φ

 δ = (0.80)(36°) = 28.8°

 Kδ = 1.30 

CF = 0.92 

Cd = 4 ft 

4 ft +15ft 

pd Avg. @ = 9.5 ft is 1,050 psf 2 

Rs (sand) = (1.30)(0.92)(1,050 psf)(4 ft)(sin 28.8o

) (11 ft) 

Rs (sand) = 26,619 lbs ≈ 13.0 tons 

Clay Layer (15 ft - 40 ft) 

Rs(clay) = caCdD 

ca (Adhesion) ≅ 1,100 psf (assume adhesion ≈ cohesion, i.e., α ≈ 1.0) 

Rs(clay) = 1,100 psf (4 ft) 25 ft = 110,000 lbs = 55 tons 

FHWA NHI-06-089 Driven Pile Design 

Soils and Foundations – Volume II A.8 - 6 December 2006 
• *Gravel Layer (Try 4 ft Embedment, ie. 40 ft – 44 ft) 

*Use φMax = 36°

 qs = (Kδ)(CF)(P0)(Cd)(Sin δ)D 

24.6 V = = 0.17 CF 

144 Ft.

 δ = 0.80 φ

 δ = (0.80)(36°) = 28.8°

 Kδ = 1.30 

CF = 0.92 

Cd = 4 ft 

pd = 3,200 psf 

Rs(gravel) = (1.30)(0.92)(3,200 psf) (4 ft)(sin 28.8°) (4 ft) 

Rs(gravel) = 29,500 lbs ≈ 14.7 tons 

Step 3B: Compute toe resistance (Use φ = 43°) at 44 ft 

(References to Figures and Tables are as in Step 3A above) 

• Gravel Layer 

For φ = 43o, αt ≈ 0.75 from Figure 9-13(a) in Chapter 9 

For φ = 43o, N′q = 300 from Figure 9-13(b) in Chapter 9 

 pt max. 

c. Rt = Ap αt pt N′q (Equation 9-7a in Chapter 9) 

 24.6in 2

= (0.75)(3,000 psf )(300)
 2 

144in 

ft 2


 

 Rt = 115,313 lbs ≈ 57.7 tons 

FHWA NHI-06-089 Driven Pile Design 

Soils and Foundations – Volume II A.8 - 7 December 2006 
d.	 Rt (max) = qL × Ap (Equation 9-7b in Chapter 9) 

 2 (q =680 ksf for φ = 43o from Figure 9­ = ( ) 24.6in L

680ksf 2 14 in Chapter 9) 144in 

f 2

t 

 Rt (max) = 116.2 kips = 58.1 tons > 57.7 tons 

 ∴Rt = 57.7 tons 

• Total useable soil capacity below clay is = 14.7 tons + 57.7 tons = 72.4 tons 

• Total Required capacity is 240 Tons 

• Extending pile to 50 ft only increases Rs to 37 tons 

Conclusion: Pile must bear on rock to develop 240 tons capacity below clay layer. 

Therefore estimate pile length to rock. 

Step 4B: Determine soil resistance to driving SRD for 120 ton load with SF = 2. 

Rs (clay) SRD = R + s ) (sand + (120 tons × 2) sensitivity 

55 tons = 13.0 tons + + 240 tons (note sensitivity = 2 is given in 2 

problem statement) 

 SRD = 280.5 tons 

* Composed of 37 tons skin friction in the gravel and 203 tons in end bearing on rock. 

FHWA NHI-06-089 Driven Pile Design 

Soils and Foundations – Volume II A.8 - 8 December 2006 
STATIC PILE ANALYSIS - ABUTMENT @ STA 93 + 50 

A. For 12 inch Diameter Pipe Pile 

Step 2A & 3A:	 Based on computation at the pier, the pipe pile will develop the 140 ton 

ultimate load at the top of the gravel layer, ie. an estimated length of 65 ft. 

However the driving resistance will increase. 

Step 4A: Compute driving resistance. 

•	 Fill (Use φmax = 36°) 

qs = (Kδ)(CF)(po)(Cd)(sin δ) Cd D 

V = 0.785 ft3

/ft. 

 δ = 0.6 (for closed end pipe pile from Figure 9-7 in Chapter 9) φ

 δ = (0.6)(36°) = 21.6°

 Kδ = 1.92 (for φ = 36o from Table 9-6(a) in Chapter 9) 

 Correction Factor, CF = 0.75 (from Figure 9-12 in Chapter 9) 

Cd = π d = π (1 ft) = 3.14 ft 

pd = 1,650 psf 

Rs (fill) = Kδ (CF)(pd)(Cd)(sin δ)D (Equation 9-6 in Chapter 9) 

 = (1.92)(0.75)(1,650 psf)(3.14 ft)(sin 21.6o)(23 ft) 

Rs (fill) = 63,168 lbs ≈ 31.6 tons 

•	 Sand 

Rs(sand) = (1.92)(0.75)(3,330 psf)(3.14 ft))(sin 21.6°) (7 ft) 

Rs(sand) = 38,800 lbs ≈ 19.4 tons 

•	 Clay 

c C R a dD 	 s(clay) = sensitivity 

(1,100 psf )(3.14)(1ft)(35ft) R	 s(clay) = = 60,445lbs ≈ 30.2 tons

2 

FHWA NHI-06-089 Driven Pile Design 

Soils and Foundations – Volume II A.8 - 9 December 2006 
Soil Resistance to driving, SRD @ top of gravel= 31.6 tons + 19.4 tons +30.2 tons + 140 tons 

= 221.2 tons 

Step 5A: Check driving resistance in embankment. 

Assume pile tip embedded 23 ft 

Rs(fill) = 31.6 tons (from Step 4A) 

Rt = Apαt pd at 23′N′q 

 = (0.785 ft2

) (0.74) (2,990 psf) 170 

Rt = 147.6 tons < Rt (max) = 200 (0.785) = 157 tons 

 SRD(fill) = 31.6 tons + 147.6 tons = 179.2 tons 

 To overcome this SRD, pre-augering may be required through the fill 

B. 12 inch H – Pile (120 ton design) – assume HP 12×84 section 

Steps 2B & 2C: Estimate length to rock i.e., 75 ft, as pier computation showed H-pile must 

bear on rock to achieve designed ultimate capacity. 

Step 4B: Compute driving resistance. 

•	 Fill 

 V = 0.17 CF/Ft. 

 δ = 0.80 φ

 δ = (0.80)(36°) = 28.8°

φmax 

Kδ = 1.30 

CF = 0.92 

Rs(fill) = (1.30)(0.92)(1,495 psf)(4 ft)(sin 28.8°)(23 ft) 

Rs(fill) = 79,247 lbs ≈ 39.6 tons 

•	 Sand 

Rs(sand) = (1.30)(0.92)(3,303 psf)(4 ft)(sin 28.8°)(7 ft) 

FHWA NHI-06-089 Driven Pile Design 

Soils and Foundations – Volume II A.8 - 10 December 2006 
 Rs(sand) = 53,287 lbs ≈ 26.6 tons 

•	 Clay 

c C D R a d

s(clay) = sensitivity
 

(1,100 psf )(4ft)(35ft) R s(clay) =	 =77,000lbs = 38.5 tons

2 

• Gravel 

Rs(gravel) = (1.30)(0.92)(5,600 psf)(4 ft)(sin 28.8°)(10 ft) 

Rs(gravel) = 129,063 lbs ≈ 64.5 tons 

 Total Rs = Rs(fill) + Rs(sand) + Rs(clay) = Rs(gravel)

 

 Total Rs = 39.6 tons + 26.6 tons + 38.5 tons + 64.5 tons 

 Total Rs = 169.2 tons = 338.4 kips 

 SRD = 39.6 tons + 26.6 tons + 38.5 tons + [64.5 tons + 175.5 tons] 

 SRD = 344.7 tons = 689.4 kips 240 tons
 

 ∴(Total Rs)/SRD = 338.4 kips / 689.4 kips = 0.49 or 49% 

Step 5B: Check H – Pile driving resistance in embankment 

Assume pile tip embedded 23 ft 

Rs(fill) = 39.6 tons (from Step 4B) 

Rt = Apαt pd at 23′N′q 

24.6 in2

Rt = (0.74)(2,990 psf )170 

in 2 

144 

f 2

t 

Rt = 64,257 lbs ≈ 32.1 tons < qlim = (200)(0.17)=34 tons > 32.1 tons (use 32.1 tons) 

 SRD (fill) = 39.6 tons + 32.1 tons = 71.7 tons 

 To overcome this SRD, pre-augering may be required through the fill 

FHWA NHI-06-089 Driven Pile Design 

Soils and Foundations – Volume II A.8 - 11 December 2006 
Summary of the Pile Design Phase for the Apple Freeway Design Problem 

•	 Design Soil Profile
 

 Strength value selected for all layers.
 

•	 Static Analysis - Pier 

12 inch closed end pipe pile - 70 ton – 36 ft length required 

12 inch HP 12x84 - 120 ton – 46 ft length required. 

•	 Static Analysis Abutment 

12 inch closed end pipe pile- 70 ton – 65 ft length required 

12 inch HP 12 x 84- 120 ton – 75 ft length required. 

•	 Soil Driving Resistance 

 Driving Resistances computed for both pipe and H-piles to permit design check of 

pile section overstress. 

 Pipe pile will require pre-augering through embankment. 

•	 Abutment Lateral Movement 

From Step 2 in Section A.6-6, 3 inch possible horizontal movement even with a 

pile foundation unless recommended waiting period observed prior to pile driving. 

FHWA NHI-06-089 Driven Pile Design 

Soils and Foundations – Volume II A.8 - 12 December 2006 
 

 

 

 

 

 

 

 

 

Subsurface 

Explorations 

Basic Soil Properties 

Laboratory Testing 

Slope 

Stability 

Approach Roadway 

Settlement 

Spread Footing 

Design 

Driven Pile Design 

Construction 

Monitoring 

Terrain Reconnaissance 

Site Inspection 

Subsurface explorations 

Visual Description 

Classification Tests 

Subsurface Profile 

po Diagram 

Test Request 

Consolidation Results 

Strength Results 

Design Soil Profile 

Circular Arc 

Sliding Block Analysis 

Design Soil Profile 

Settlement 

Time – Rate 

Surcharge 

Vertical Drains 

Lateral Squeeze 

Design Soil Profile 

Pier Bearing Capacity 

Pier Settlement 

Abutment Settlement 

Vertical Drains 

Surface 

Design Soil Profile 

Static Analysis – Pier 

 Pipe Pile 

H – Pile 

Static Analysis – abutment 

Pipe Pile 

H – Pile 

Driving Resistance 

Abutment Lateral Movement 

9

9

9

9

9

9

9

9

Wave Equation 

Hammer Approval 

Embankment 

Instrumentation 

Figure A.9-1. Status of geotechnical work. 

FHWA NHI-06-089 Wave Equation Analysis
 

Soils and Foundations – Volume II A.9 - 1 December 2006
 
SECTION A.9 

CONSTRUCTION MONITORING OF DRIVEN PILES
 

In this Section the Apple Freeway Design Example is use to illustrate the wave equation 

analysis using a wave equation analysis program. The use of wave equation analysis for pile 

driveability analysis, checking suitability of contractors driving system, and determining pile 

driving criteria is addressed. A commonly used wave equation analysis program is the 

GRLWEAP. Other similar products such as TNOWave are also available as noted in 

Chapter 9. Herein, the program GRLWEAP will be used for the example problem. The use 

of GRLWEAP does not constitute an endorsement of the product by FHWA. 

Given: 	 Using the soil profile and pile driving resistance previously computed (Section 

A.8) 

Required:	 Complete wave equation analyses using the GRLWEAP program for the 

following: 

•	 Driveability of the proposed design pile section 

•	 Acceptance of contractors driving system 

•	 Production pile driving criteria 

Solution: 

Driveability of Proposed Design Pile Section 

Proposed pile section is a HP 12 × 84. The maximum driving resistance determined from 

static analyses is at the east abutment where the total driving resistance including 

embankment penetration is 689.4 kips. Perform wave equation analysis for the proposed pile 

section using the maximum driving resistances. 

Step 1: 	 Prepare Wave Equation Input: 

1.	 Select hammer (IHAMR) 

•	 Hammer size selected from Figure 9-44 in Chapter 9 using maximum driving 

resistance of 689.4 kips (345 tons). Minimum hammer energy = 57,000 ft-lbs. 

•	 Using GRLWEAP help screen, scan hammer library for hammers with sufficient 

energies. Select Delmag 30 – 13 hammer which has slightly more energy than 

required (66,000 ft-lbs) to insure efficient driving. 

2.	 Select uniform or non-uniform pile cross-section along the entire pile (NCROSS) 

 Select non-uniform option (1) because pile point will be used. Pile cross-section described 

on input screen NCROSS =1 as shown on “page 7” of the GRLINP input printoutogram. 

FHWA NHI-06-089 Wave Equation Analysis
 

Soils and Foundations – Volume II A.9 - 2 December 2006
 
FHWA NHI-06-089 Wave Equation Analysis 

Soils and Foundations – Volume II A.9 - 3 December 2006

3. Select percent pile skin friction (IPERC) 

• From static analysis, (skin friction resistance/total driving resistance) = 

(338/689)(100) = 49%. 

4. Select skin friction distribution (ITYS) 

• Use the actual skin friction distribution determined in the static analysis ultimate 

driving resistance computation (ITYS = 0). An analysis using the actual skin 

friction distribution is more realistic and accurate. From static analyses (see next 

page). 

5. Select helmet and hammer cushion information (helmet weight, hammer cushion area, 

elastic modulus and thickness). 

• Using GRLWEAP help screen, scan hammer library for Delmag Hammers using the 

proposed pile section. 

132.4

x = × 2 = 8.83

30

77

x′ = = 2.2

35

5,250 ⎛129 ⎞

x′′ = ⎜ ⎟ = ips 12.08

5,600 ⎝ 10 ⎠

5,950 ⎛129 ⎞

x′′′ = ⎜ ⎟ = 13.72

5,600 ⎝ 10 ⎠

6. Select Pile Top Information (length, x-section area, elastic modulus, specific weight, 

coefficient of restitution). 

• Using GRLWEAP help screen, obtain the x-sectional area and weight for the 

proposed HP12×84. 

7. Select soil parameters (quake and damping). 

• Using GRLWEAP help screen, select appropriate soil parameters. 

8. Select ultimate driving capacities to be analyzed. 

• Input a range of ultimate driving capacities around and including the maximum soil 

driving resistance (SRD) calculated from static analyses (689.4 kips). A range of 

capacities highlights trends within the graphical plots. 

x′′

x ′′′

x′

x 

129 k

77 kips

132.4 kips 

10′

35′

Rock 

Gravel 

Clay 

30 Fill & Sand ′
GRLINP Input Screens for HP 12×84 Driven through the Embankment Material – 

Ultimate Resistance 689.4 kips. 

FHWA NHI-06-089 Wave Equation Analysis
 

Soils and Foundations – Volume II A.9 - 4 December 2006
 
FHWA NHI-06-089 Wave Equation Analysis
 

Soils and Foundations – Volume II A.9 - 5 December 2006
 
FHWA NHI-06-089 Wave Equation Analysis
 

Soils and Foundations – Volume II A.9 - 6 December 2006
 
FHWA NHI-06-089 Wave Equation Analysis
 

Soils and Foundations – Volume II A.9 - 7 December 2006
 
Perform wave equation analysis for the submitted driving system. 

•	 Modify hammer data in the GRLWEAP input file previously used to analyze the HP 

12×84 pile section. Use the submitted driving system data, and the GRLWEAP 

driveability option. 

GRLINP Input Screens for GRLWEAP Driveability option. Screens not Shown Below 

are Unchanged from the Pile Section Analysis. 

Continue GRLINP Input Screens for GRLWEAP Driveability Options Analysis of Ice 

70S Driving System. 

FHWA NHI-06-089 Wave Equation Analysis
 

Soils and Foundations – Volume II A.9 - 8 December 2006
 
SUMMARY RESULTS OVER DEPTH FOR ICE 70S HAMMER 

FHWA NHI-06-089 Wave Equation Analysis
 

Soils and Foundations – Volume II A.9 - 9 December 2006
 
FHWA NHI-06-089 Wave Equation Analysis
 

Soils and Foundations – Volume II A.9 - 10 December 2006
 
GRLWEAP Output – plot 

FHWA NHI-06-089 Wave Equation Analysis
 

Soils and Foundations – Volume II A.9 - 11 December 2006
 
SUMMARY OF DRIVEABILITY ANALYSES FOR ICE 70S
 

Driving Stresses: 32.7 ≈ 32.4 ksi OKAY 

Driving stresses vary between 31.66 ksi (0.9 friction reduction) to 33.19 ksi (1.1 friction 

reduction), well below the yield strength of 36 ksi. Since, the maximum stresses occur when 

the pile has penetrated the rock and is at near refusal conditions, the piles should be capable 

of being seated into the rock without damage. 

Blow Count: 159 bpf ≈ 144 bpf OKAY 

The blow count is approximately 35 bpf at just above the rock line, and near refusal 150 - 

220 bpf in the rock layer. Therefore, the hammer should (if operating properly) penetrate 

quickly through the embankment and into the rock. 

HAMMER APPROVED 

 PRODUCTION PILE DRIVING CRITERIA FOR 

ICE 70S DRIVING SYSTEM 

Drive HP12x84 pile through the embankment material and into the rock. Pile driving shall 

be terminated when the combination of stroke and blow count indicates a driving capacity of 

690 kips. If pre-augering is used the driving capacity of 650 kips should be attained. 

FHWA NHI-06-089 Wave Equation Analysis
 

Soils and Foundations – Volume II A.9 - 12 December 2006
 

Stroke Vs. Blow Count Plot 
CONSTRUCTION CONTROL 

•	 Pile Driveability
 

 Driveability of HP 12 x 84 pile 

 Section verified for most difficult driving condition. 

•	 Driveability versus Depth 

 Driveability of HP 12 x 84 computed for full 75 feet depth. 

 Pile installation time expected to vary between 16 and 20 minutes 

 (no pre- augering). 

FHWA NHI-06-089 Wave Equation Analysis
 

Soils and Foundations – Volume II A.9 - 13 December 2006
 

SECTION A.10 

GEOTECHNICAL DESIGN SUMMARY REPORT 

A typical example of a Geotechnical Design Summary Report is presented in the following 

section with reference to the Apple Freeway Design Example. The report illustrates the 

inclusion of various items discussed in the preceding sections of this chapter and summarize 

the pertinent results and conclusions obtained from the various analysis/design stages in the 

preceding chapters. 

FHWA NHI-06-089 Geotechnical Design Summary Report
 

Soils and Foundations – Volume II A.10 - 1 December 2006 
WORKSHOP DESIGN PROBLEM - GEOTECHNICAL DESIGN SUMMARY REPORT 

December 15, 2006 

Geotechnical Design Summary Report 

To: Mr. A. J. Jones 

 Chief Engineer 

From:	 Mr. A. B. Smith 

 Chief Foundation Engineer 

Subject: Interstate 0 Structure over the Apple Freeway 

The Geotechnical Section has completed an analysis of the foundation conditions at the site 

of the subject structure. Our analysis is based on the following information: 

1. A 1-inch equals 20 feet plan and profile prepared by the Bridge Division and received in 

this office October 1, 2006. 

2. An interpretation of the boring logs and analysis of soil samples from three drill holes 

numbered BAF-1 thru 3, nine auger holes numbered EA-1 thru 9, one drill hole 

numbered BAF-4 from which undisturbed samples were taken, and four Cone 

Penetration Test (CPT) soundings numbered CPT BAF-1 through 4. 

3. Laboratory testing on undisturbed samples from BAF-4. 

Subsurface Conditions: 

The general subsurface conditions are shown on Drawing No. 5 GS 331. 

Foundation Recommendations: 

1. Elevation Assumptions 

The foundation recommendations are based on the following bottom of footing 

elevations: 

 

FHWA NHI-06-089 Geotechnical Design Summary Report
 

Soils and Foundations – Volume II A.10 - 2 December 2006 
 

 

 

West Abutment 1011 

Pier 992 

 East Abutment 1012 

Changes to footing elevations may affect the foundation recommendations and should be 

discussed with this office. 

2. Embankment Construction 

A. Unsuitable Subexcavation 

An approximate 1 to 3-foot thick organic layer exists between approximate stations 

92+70 to 94+00 in the area of the east approach embankment. This organic layer 

should be removed and replaced with granular embankment material in accordance 

with Bridge Design Data Sheet 80-1. 

B. Embankment Material and Placement 

The approach embankment shall be constructed of materials placed in accordance 

with Bridge Design Data Sheet 80-1. 

C. Embankment Settlement 

An estimated 12 inches of fill settlement will occur due to consolidation of the 

35-foot thick clay layer underlying the proposed 30-foot high east approach 

embankment. Estimated settlement time for 90 percent primary settlement is 14 

months. Settlement time can be reduced to, (1) 6 months by use of a 10-foot 

surcharge fill or (2) 2 months with wick drains at 7.5 foot center to center spacing. 

Estimated cost for each of these treatments is: 

Treatment Estimated Settlement Time Estimated Extra Cost 

Fill only 14 months $ ---

Fill w/10 foot surcharge 6 months 120, 000 

Fill w/wick drains 2 months 172,000 

FHWA NHI-06-089 Geotechnical Design Summary Report
 

Soils and Foundations – Volume II A.10 - 3 December 2006 
 

It is understood the construction schedule will not allow a 14-month waiting period 

but will allow up to an 8-month waiting period, therefore, the 10-foot surcharge 

treatment is recommended as the most cost-effective method to reduce settlement 

time. The surcharge should be placed full height for a length of 500 feet back of 

the bridge ends on both the east and west approach and sloped at 1 vertical to 1.5 

horizontal down to the embankment grade. 

D. Embankment Stability 

The estimated immediate end of construction factor of safety for the proposed 30' 

high east approach embankment is 1.63. The estimated immediate 

end-of-construction factor of safety for the proposed 30-foot fill plus 10 foot 

temporary surcharge is 1.33. Both factors of safety are adequate and no special 

approach embankment treatment is necessary. Long-term factor of safety will 

increase as consolidation of the foundation soils occur. The factor of safety for the 

west approach embankment will be higher as the fill height is 10' less. An analysis 

of highway borings confirms that no stability problems will occur due to the 500’ 

extension of the surcharge. 

E. Embankment Monitoring 

Fill settlement is recommended to be monitored with settlement plates and 

piezometers. Settlement plates should be installed at existing ground elevation at 

centerline stations 90+00, 93 + 50, and 96 + 50. Piezometers to monitor excess 

pore pressure buildup and dissipation in the clay subsoil are recommended at 

centerline stations 93 + 50 and 96 + 50. A total of three piezometers should be 

installed at each location - one each at 20, 28, and 36 foot depths. Instrumentation 

will be installed by State forces. 

3. Abutment Foundation 

A. Spread Footings 

The abutments may be supported on spread footings placed on compacted select 

material with a maximum allowable bearing capacity of 3 tons per square foot 

assuming a footing width of 7 feett is used. Changes to the footing width affect 

both bearing capacity and settlement and should be discussed with this office. The 

total settlement of the east and west abutments respectively will be 2.6 and 1.9 

FHWA NHI-06-089 Geotechnical Design Summary Report
 

Soils and Foundations – Volume II A.10 - 4 December 2006 
 

 

inches which occurs over respective time periods of 14 months and 7 months. 

About 60 percent of the settlement will occur in 2 months after structure 

construction. This settlement may be reduced by extending the surcharge period. 

For 90 percent consolidation the surcharge should remain in place a total of 8 

months; 2 months longer than required for embankment considerations. If vertical 

drains are installed during embankment construction, these drains will reduce the 

time for abutment settlement such that only 1⁄4” will remain 30 days after all 

abutment loads have been placed 

B. Piles 

Two pile types were analyzed at the abutment; a displacement pile (12" diameter 

closed end pipe) and a non-displacement pile (HP 12 x 84 pile). Displacement type 

piles are not recommended due to their inability to be driven through the fill and 

the uncertainty of obtaining penetration in the dense gravel stratum. 

Non-displacement H-piles are recommended. However, to insure that the pile can 

be driven to rock without damage, the section should not be less than a HP 12 x 84 

pile. A HP 12 x 84 pile driven to rock may be designed for a maximum load of 

120 tons. Tip reinforcement, such as APF 75500, should be used to prevent tip 

damage by boulders in the gravel stratum and to insure penetration to rock. 

Estimated pile lengths are 60 feet at the west abutment and 75 feet at the east 

abutment. 

At the abutments, negative skin friction may be expected if the piles are installed 

before fill settlement is complete. In addition lateral squeeze of the clay subsoil 

will occur as the clay consolidates. Therefore, to prevent increased vertical 

downdrag pile loads, bending of abutment piles and rotation of the abutment 

toward the fill, the abutment piling should not be installed until embankment 

settlement is complete. 

The actual driving resistance estimated to develop the design load for the H-pile at 

the estimated length is 345 tons at the east abutment and 290 tons at the west 

abutment. The contractor should size his equipment to achieve this resistance 

without damaging the pile. 

FHWA NHI-06-089 Geotechnical Design Summary Report
 

Soils and Foundations – Volume II A.10 - 5 December 2006 
 

 

 

4. Pier Foundation 

A. Spread Footings 

The pier may be supported on spread footings placed 4 feet below ground on 

natural undisturbed soil and designed for a maximum allowable bearing capacity of 

3 tons per square foot assuming a footing width of 7' is used. Changes in footing 

width should be discussed with this office. Approximately 2.8 inches of settlement 

is expected at this location over about 7 months with 1 inch occurring immediately 

and 2 inches occurring in less than 2 months. If a spread footing foundation is 

chosen, consideration should be given to increasing the structure clearance over the 

Apple Freeway to account for these settlements. Settlement along the footing axes 

will be uniform. However a short term differential settlement of 1.5” can be 

expected between the abutment and pier footings if spread footings are used. 

B. Piles 

A 12" diameter closed end pipe pile and a HP 12 x 84 pile were analyzed at the 

pier. The closed end pipe may be designed for 70 tons with a safety factor of 2 if 

driven into the dense gravel layer. The estimated length is 36 feet. However a 

minimum wall thickness of 0.375 inches should be used to prevent overstress 

during driving. A driving resistance of 170 tons is estimated to reach the estimated 

length. A conical reinforced point should be used to prevent tip damage due to 

boulders. The cost per ton on a per foot basis equals $11. 

A HP 12 x 84 pile may be designed for 120 tons with a safety factor of 2 if driven 

to rock. The estimated length is 46 feet. A driving resistance of 280 tons is 

estimated to obtain design resistance at the estimated length. A reinforced tip 

similar to APF 75500 should be used to prevent tip damage due to boulders. The 

cost per ton on a per foot basis equals $8. 

We recommend that H-piles be chosen if piles are used because of cost advantages 

and installation advantages. 

FHWA NHI-06-089 Geotechnical Design Summary Report
 

Soils and Foundations – Volume II A.10 - 6 December 2006 
5. Special Notes 

The following special notes are recommended to be included in the contract documents. 

1. The general subsurface conditions at this site are shown on Drawing No. 

5 GS 331. 

2. A 6-month waiting period will be imposed between completion of the 10-foot 

surcharge on the east embankment. The actual length of the waiting period may be 

reduced by the Engineer based on an analysis of settlement platform and 

piezometer readings. 

3. The contractor shall coordinate his construction schedule to allow installation of 

instrumentation by State forces. 

4. Instrumentation damaged by contractor personnel shall be repaired or replaced at 

the contractor's expense. All construction activity in the area of any damaged 

instrument shall cease until the damage has been corrected. 

If piles are used the additional special notes should be provided. 

5. Pile driving will not be allowed at the abutments until fill settlement is complete. 

Estimated maximum settlement time is 6 months after placement of the 10-foot 

surcharge. This time may be reduced based on interpretation by the State of 

settlement plate readings. 

6.	 Piles will be acceptable only when driven to pile driving criteria established by the 

Deputy Chief Engineer (Structures). Prerequisite to establishing these criteria, the 

contractor shall submit, to the Deputy Chief Engineer (Structures) and others as 

required, Form entitled, "Pile and Driving Equipment Data." All information listed 

on the Form shall be provided within 14 days after the award of the contract. Each 

separate combination of pile and pile driving equipment proposed by the contractor 

will require the submission of a corresponding Form. 

The actual driving resistance to install the 12 x 84 H-piles to the estimated lengths shown on 

the plans is estimated to be 280 tons at the pier, 345 tons at the east abutment and 290 tons at 

the west abutment. The contractor's equipment shall be capable of overcoming these 

resistances without inflicting pile damage. 

FHWA NHI-06-089 Geotechnical Design Summary Report
 

Soils and Foundations – Volume II A.10 - 7 December 2006 
General Notes 

The subsurface explorations shown hereon made between 5/1 and 5/12/92 by the regional soils section.1. General soil and rock (where encountered) strata descriptions and

indicated boundaries are based on an engineering interpretation of all available subsurface information by the Soil Mechanics Bureau and may not necessarily reflect the actual variation in subsurface conditions between borings and samples. Detailed data and field interpretation of conditions encountered inindividual borings are shown on the subsurface exploration logs. 

2. The observed water levels and/or conditions indicated on the subsurface 

profiles are as recorded at the time of exploration. These water levels and/or CPT-BAF-2 conditions may vary considerably, with time, according to the prevailing CPT-BAF-3 climate, rainfall or other factors and are otherwise dependent on the duration of 

and methods used in the explorations program. 

3. Sound engineering judgment was exercised in preparing the subsurface

information presented hereon. This information was prepared and is intendedfor State design and estimate purposes. Its presentation on the plans or else 

where is for the purpose of providing intended users with access to the same CPT-BAF-4 information available to the State. This subsurface information interpretation CPT-BAF-1 is presented in good faith and is not intended as a substitute for personal

investigation, independent interpretations or judgment of the contractor. 

4. All structure details shown hereon are for illustrative purposes only and may 

not be indicative of the final design conditions shown in the contract plans. 

5. Footing elevations shown are as indicated at the time of this drawing's 

preparation. 

CPT 

FHWA NHI-06-089 Geotechnical Design Summary Report
 

Soils and Foundations – Volume II A.10 - 8 December 2006 
 

APPENDIX B 

MOHR’S CIRCLE AND ITS 

APPLICATIONS IN GEOTECHNICAL 

ENGINEERING
 

FHWA NHI-06-089 Appendix B – Mohr’s Circle
 

Soils and Foundations – Volume II December 2006 
 

[THIS PAGE INTENTIONALLY BLANK] 

FHWA NHI-06-089 Appendix B – Mohr’s Circle
 

Soils and Foundations – Volume II December 2006 
APPENDIX B 

MOHR’S CIRCLE AND ITS APPLICATIONS IN GEOTECHNICAL 

ENGINEERING 

The relationship between the normal and shear stress acting on any plane within a solid mass 

(continuum) may be represented graphically by an extremely useful device known as Mohr’s 

Circle for Stress. It is named after the German engineer Otto Mohr who devised it in 1882. 

B.1 BASIC CONVENTIONS FOR PLOTTING A MOHR’S CIRCLE 

The basic conventions for plotting a Mohr’s circle are as follows: 

1.	 The normal stresses (σ) are plotted on the abscissa. In conventional solid mechanics, 

tensile stresses are considered positive (plotted to the right of the origin) and 

compressive stresses are considered negative (plotted to the left of the origin). 

 

2.	 The shear stresses (τ) are plotted on the ordinate. In both conventional solid 

mechanics and soil mechanics, positive shear stresses are plotted above the origin 

while negative shear stresses are plotted below the origin. This sign convention for 

plotting the shear stresses should not be confused with the sign convention for the 

shear stresses themselves. Although sign conventions for the shear stresses 

themselves vary from one text to another, in general positive shear causes clockwise 

rotation of the stress element and negative shear causes counterclockwise rotation of 

the stress element (as discussed in Section B.2). 

3.	 Positive angles on the circle are measured in the counterclockwise sense; negative 

angles are obtained in the clockwise sense. An angle of 2θ on the circle corresponds 

to an angle of θ on the element, where θ is defined as the angle between any two 

planes within the soil element (as discussed in Section B.2). 

B.2 MOHR’S CIRCLE CONSTRUCTION FOR GENERAL STRESS 

CONDITIONS 

Figure B-1(a) shows a solid element subjected to a normal stress (σ) and a shear stress ( τ ) 

on each of its four planes. The element can be considered to consist of a set of two mutually 

perpendicular planes – one horizontal, e.g., Plane Q, the other vertical, e.g., Plane P. Table 

B-1 presents a summary of the stresses acting on the four planes shown in Figure B-1(a) and 

their directions (sign) according to the conventions discussed in Section B.1. 

FHWA NHI-06-089 Appendix B – Mohr’s Circle
 

Soils and Foundations – Volume II B - 1 December 2006 
 

Figure B-1. Mohr’s circle for general stress conditions (Cernica, 1982). 

Table B-1 

Summary of stresses acting on the four planes shown in Figure B-1(a)
 

Plane Normal Stress Sign Shear Stress Sign 

P σx + τxy + 

Q σy + τyx -

R σx + τyx + 

S σy + τxy -

Note: In this table and Figure B-1, the sign convention is according to that commonly 

used in solid mechanics, i.e., tensile (normal) stresses are considered positive and are 

plotted to the right of the origin. In soil mechanics it is customary to indicate 

compressive stresses as positive because soil cannot sustain tensile stresses since it has 

virtually no strength in tension. The use of the soil mechanics convention will be 

illustrated in Sections B.3 and B.4. 

FHWA NHI-06-089 Appendix B – Mohr’s Circle
 

Soils and Foundations – Volume II B - 2 December 2006 
The following convention is used for the subscripts in Figure B-1: 

•	 For normal stresses, the subscript denotes the orientation of the stress with respect to 

an x-y coordinate system centered on the element where x is the horizontal axis and y 

is the vertical axis. Thus σy acts in the vertical direction on planes Q and S, both of 

which are horizontal planes. Since the element is in static equilibrium, the normal 

stresses acting on the two horizontal planes must be equal. The same logic applies to 

σx, which acts horizontally on vertical planes R and P. 

•	 For shear stress, there are two letters in the subscript. The first letter refers to the 

subscript of the normal stress acting on the same plane as the shear stress. The 

second letter refers to the direction in which the shear stress itself is acting. Thus, τyx 

acts on Plane Q where the normal stress is σy and it acts horizontally (x-direction). 

Since τyx causes counterclockwise rotation of the element, it is considered to be 

negative as per the sign convention discussed previously. Although it is not shown 

on the figure, the shear stress acting on Plane S is also τyx and it also causes 

counterclockwise rotation of the element. Since moment equilibrium must exist for 

the element to be in static equilibrium, τxy = τyx but the signs must be opposite. This 

can be verified by reference to Table B-1, which was derived from Figure B-1(a). 

For the purpose of illustration, assume σx > σy > 0 The Mohr circle for the stress element 

shown in Figure B-1(a) is then plotted as follows (Recall that Mohr’s circle is plotted on 

shear stress (τ) vs. normal stress (σ) coordinates where (τ) is the ordinate and (σ) is the 

abscissa.): 

1.	 Find the planes having the larger normal stress and determine its sign. In this case, σx 

acts on planes P and R and its sign is positive (tension). Determine the magnitude 

and sign of the shear stress acting on those planes; τxy is of known magnitude and it 

causes clockwise rotation of the element, therefore it is positive. Refer to Table B.1 

for confirmation. The normal and shear stresses on plane P (or R) represent a point 

on the τ-σ axis shown in Figure B-1(b). 

 

2.	 Plot the normal and shear stress values on plane P (or R) at the coordinate point D 

shown in Figure B-1(b). The reason the stresses on these two planes plot at the same 

point is that one plane is oriented 180-degrees from the other on the stress element, 

i.e., refer to Figure B-1(a) and rotate vertical plane P and its normal and shear stresses 

by 180-degrees to obtain vertical Plane R that has the same magnitude and direction 

FHWA NHI-06-089 Appendix B – Mohr’s Circle
 

Soils and Foundations – Volume II B - 3 December 2006 
(sign) of normal and shear stresses as plane P. Since an angle between two planes on 

the stress element (θ) plots as twice the angle on the Mohr’s circle (2θ), point D 

represents the stress conditions on both planes P and R since 2θ = 360-degrees. The 

same holds true for the stress conditions on planes S and Q. Note that the point plots 

in the first quadrant since both σx and τxy are positive as per the sign convention 

discussed previously. 

3.	 Find the planes perpendicular to planes P and R; those are planes Q and S. The lesser 

normal stress, σy, acts on those planes and it too is positive (tension). Determine the 

magnitude and sign of the shear stress acting on those planes; τyx is of known 

magnitude and it causes counterclockwise rotation of the element, therefore it is 

negative. Refer to Table B-1 for confirmation. The normal and shear stresses on 

plane Q (or S) represent a point on the τ-σ axis shown in Figure B-1(b). 

4.	 As in Step 2, plot the normal and shear stress values on plane Q (or S) at the 

coordinate point E shown in Figure B-1(b). The reason that both planes plot at the 

same point was explained previously in #2. Note that the point plots in the fourth 

quadrant since both σx is positive but and τyx is negative as per the sign convention 

discussed previously. 

5.	 The line ED represents the diameter of the Mohr’s circle. The center of the circle lies 

on the σ axis at point C, which is simply the average value of the normal stresses σx 

and σy. Use the center of the circle and the diameter to draw the full circle. 

A number of important stress conditions can be determined once the full Mohr’s circle is 

drawn. For example, the values of the major and minor principal stresses can be read directly 

from the circle. By definition, the major and minor principal stresses are normal stresses 

that occur on planes where the shear stress equals zero. The major principal stress is 

shown as σmax and the minor principal stress as σmin (point H) on Figure B-1(b). In soil 

mechanics, the major and minor principal stresses are called σ1 and σ3, respectively. 

Also, the magnitude of the maximum shear stress (τmax), which is equal to the radius of 

the circle, can be read directly from the circle at points F (or G) on Figure B-1(b). 

Alternatively, the radius of the circle can be calculated from triangle ACE shown in the 

figure. The orientation of the maximum shear stress with respect to the original plane can 

either be measured directly on the Mohr’s circle or easily calculated with the help of 

trigonometry. 

FHWA NHI-06-089 Appendix B – Mohr’s Circle
 

Soils and Foundations – Volume II B - 4 December 2006 
In general, the normal and shear stresses on any plane oriented at an angle θ from a plane of 

known stress conditions (2θ on the Mohr’s circle), e.g., planes P, Q, R, S, can either be read 

directly from the Mohr’s circle or easily calculated with the help of trigonometry. 

B.3 BASIC RELATIONSHIPS DERIVED FROM THE MOHR’S CIRCLE 

Figure B-2 shows a simplified version of Figure B-1(b). A number of basic relationships 

between stresses can be obtained from a Mohr’s circle. The following relationships can be 

observed directly from Figure B-2: 

1.	 As indicated previously, the maximum shear stress (τmax) is equal to the radius of 

the circle. Furthermore, since τmax is oriented at + or – 90o (2θ) from a principle 

stress on the Mohr’s circle, the maximum shear stress in the stress element acts on 

planes that make an angle (θ) of + or – 45o with the principal stress planes. 

 

2.	 For the stress conditions (σ, τ) at a point S on the circle, which correspond to the 

stress conditions on some plane in the soil element, the resultant stress (0S) has a 

magnitude of σ2 + τ2 as shown in Figure B-2. Furthermore, the angle of obliquity 

(α) of the resultant is equal to tan-1 (τ/σ). The angle of obliquity is the angle 

formed between the σ-axis and the line drawn from the point on the σ-axis where 

τ = 0 to any point on the Mohr’s circle. 

3.	 The maximum angle of obliquity (αf) is constructed by passing a line through the 

origin that is also tangent to the Mohr circle, such as line 0T in Figure B-2. The 

normal and shear stresses that correspond to point T on the circle represent the 

stresses on the plane of maximum obliquity. Note that the shear stress on this plane is 

less than τmax and that slippage occurs at the point of maximum obliquity and not at 

the angle where τmax occurs. Therefore αf assumes the more prominent position 

regarding slip failure. 

FHWA NHI-06-089 Appendix B – Mohr’s Circle
 

Soils and Foundations – Volume II B - 5 December 2006 
 

 

Figure B-2. Simplified version of Figure B-1(b) showing some basic relationships and 

characteristics of the Mohr’s Circle (Cernica, 1982). 

B.4 MOHR’S THEORY OF FAILURE – APPLICATION TO SOILS 

The following concise description of Mohr’s theory of failure is provided by Cernica (1982). 

“The shear strength of soil is generally regarded as the resistance to deformation by 

continuous shear displacement of soil particles along surfaces or rupture. That is, 

the shear strength of the soil is not regarded solely in terms of its ability to resist peak 

stresses, but it must be viewed in the context of deformation which may govern its 

performance. In that light, therefore, shear failure is necessarily viewed as the state 

of deformation when the functional performance of the soil mass is impaired. 

There are a number of different theories as to the nature and extent of the state of 

stress and deformation at the time of failure. Failure of a soil mass, particularly 

cohesionless soil which develops its strength primarily from solid frictional resistance 

between and interlocking of grains, appears to be best explained by Mohr’s rupture 

theory. According to Mohr’s theory, the shear stress in the plane of slip reaches, at 

the limit a maximum value which depends on the normal stress acting in the same 

planes and the properties of the material. This represents the combination of normal 

FHWA NHI-06-089 Appendix B – Mohr’s Circle 

Soils and Foundations – Volume II B - 6 December 2006 
 

 

 

and shear stresses which results in a maximum angle of obliquity αf .” (see Figure B2).” 

The combination of normal and shear stresses that results in the line inclined at the maximum 

angle of obliquity αf represents the stress conditions on the failure plane within the soil mass. 

The Mohr’s circle corresponding to failure conditions is called the “Mohr failure circle” 

and the straight line inclined at the maximum angle of obliquity αf is called the “Mohr 

failure envelope.” The combination of stresses at any other point on the Mohr’s circle 

defined by an obliquity angle smaller than αf represents stress conditions on a plane where 

failure has not occurred even though the soil mass has failed. Thus, for example, failure does 

not occur on the plane where the shear stress equals τmax. 

In reality, the relationship between normal stress and shear stress in soils is usually nonlinear, as shown in Figure B-3(a). In addition, depending upon the type of soil and the 

conditions of loading, a soil might exhibit shear strength when the normal stress = 0, as is 

also illustrated in Figure B-3(a). Fortunately, the curvature of the Mohr failure envelope is 

relatively small for most practical problems where the stress range of interest is fairly 

narrow. Thus, it is mathematically convenient to represent the Mohr envelope by a straight 

line, sloped at an angle φ, that intersects the τ-axis at a value of shear stress = c. This is 

shown in Figure B-3(b) where φ represents the internal friction angle of the soil and c 

represents its “cohesion.” The cohesion and friction angle are called the shear strength 

parameters of the soils. 

FHWA NHI-06-089 Appendix B – Mohr’s Circle 

Soils and Foundations – Volume II B - 7 December 2006 

τ = f(σ) τ = c+ σtanφ

Figure B-3. Shear strength according to Mohr (a) and Coulomb (b) (Cernica, 1982). 
The linear approximation was first proposed by Coulomb in 1776 in connection with his 

investigations of retaining walls. Therefore, the linear approximation to the Mohr failure 

envelope is called the “Mohr-Coulomb failure envelope” and constitutes the Mohr-Coulomb 

failure criterion. As shown in Figure B-3(b), the Mohr-Coulomb failure criterion can be 

expressed as: 

τ = c + σtan φ B-2a 

Equation B-2a is a general expression of the Mohr-Coulomb failure criterion that is 

applicable to all soils and conditions of loading. It can be easily modified to account of those 

cases. For example: 

• For cohesionless soils (c = 0) 

τ = σtan φ B-2b 

• For purely cohesive soils (φ = 0) 

τ = c B-2c 

• For use with effective stress parameters (c = c′ , φ = φ′)

τ′ = c′ + σ′tan φ′ B-2d 

Since many applications of soil mechanics to problems in practice involve knowledge of the 

principal stresses in the soil (e.g. lateral earth pressure theory and use of triaxial test results 

for slope stability analyses), it is useful to express the Mohr Coulomb failure criterion in 

terms of principal stresses rather than in the formats used in Equations B-2a to B-2d. Figure 

B-4 shows the Mohr coulomb strength envelope for one Mohr circle at failure. The principal 

stresses contain a subscript “f” to indicate that they are the principal stress acting at failure on 

the stress element shown in the insert. 

The following relationships can be derived from Figure B-4. 

R sin φ = B-3a

D 

FHWA NHI-06-089 Appendix B – Mohr’s Circle 

Soils and Foundations – Volume II B - 8 December 2006 
 

Figure B-4. Mohr coulomb failure envelope with one Mohr failure circle (Holtz and 

Kovacs, 1981). 

Substitution of the stresses corresponding to R and D into Eq. B-3a yields: 

Rearrangement of terms in Eq. B-3b and substitution of trigonometric identities yields: 

σ1f −σ3f 

2 sin φ = B-3b

σ 1f +σ3f + c cot φ 2 

(σ1f −σ3f 1f 3f ) = (σ +σ )sin φ + 2c cos φ B-3c

Solving Eq. B-3c for σ1f yields: 

Substitution of the identity cos φ = (1 – sin2 1⁄2 φ ) into Eq. B-3d yields: 

FHWA NHI-06-089 Appendix B – Mohr’s Circle 

Soils and Foundations – Volume II B - 9 December 2006 

⎡(1 + sin φ )⎤ ⎡ 2c cos φ ⎤

σ1f = σ3f + ⎢ ( ⎥ ⎢ ⎥ B-3d ⎣ 1-sin φ) ⎦ ⎣(1-sin φ)⎦
⎡(1 + sin φ )⎤ ⎡2c (1+ sin φ )⎤

σ1f = σ3f + ⎢ ⎢ ⎥ B-3e ⎣ (1-sin φ) ⎥

⎦ ⎢⎣ (1-sin φ) ⎦⎥

Equation B-3e represents the general relationship between the major (σ1) and minor (σ3) 

principal stresses in terms of the soil strength parameters c and φ. 

For cohesionless soils (c = 0), Eq. B-3e reduces to: 

σ1f (1 + sin φ ) = σ3f ( B-3f 1-sin φ)

The reciprocal of Eq. B-3f yields: 

σ3f (1-sin φ ) = σ ( B-3g

13f 1 + sin φ)

By the use of trigonometric identities Eq. B-3f can be re-written as: 

σ1f φ ⎞ = 2 ⎛ tan ⎜45° + ⎟ B-3h

σ3f ⎝ 2 ⎠

Similarly, Eq. B-3g can be re-written as: 

σ3f 2 ⎛ φ⎞ = tan ⎜45° − ⎟ B-3h

σ1f ⎝ 2 ⎠

Equation B-3h gives the coefficient of passive earth pressure, Kp, while Equation B-3i gives 

the coefficient of active earth pressure, Ka that were introduced in Chapter 2. Many concepts 

in geotechnical engineering can be similarly explained by used of Mohr’s circle. The most 

common use of Mohr’s circle is for interpretation of the results of shear strength tests 

discussed in Chapter 5. For use of Mohr’s circle in interpretation of shear strength tests, the 

reader is referred to well-known text books such as Holtz and Kovacs (1981) and Lambe and 

Whitman (1979). 

FHWA NHI-06-089 Appendix B – Mohr’s Circle 

Soils and Foundations – Volume II B - 10 December 2006 
 

APPENDIX C 

LOAD AND RESISTANCE 

FACTOR DESIGN (LRFD)
 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II December 2006 
 

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FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II December 2006 
 

APPENDIX C 

LOAD AND RESISTANCE FACTOR DESIGN (LRFD) 

C.1 INTRODUCTION 

In 1994, the AASHTO Subcommittee on Bridges adopted a Bridge Design Specification 

based on the use of the Load and Resistance Factor (LRFD) method (AASHTO, 1994). The 

geotechnical parts of the new specification had been developed by an NCHRP Research 

Project (NCHRP, 1991). The most recent version of the LRFD specifications is the 2004 

version of AASHTO. Most states are now in the process of implementing the LRFD 

specifications. 

The geotechnical portion of the LRFD specification has proven to be one of the most difficult 

to implement. This includes shallow and deep foundations, and earth retaining systems. In 

fact, the Section 10 of the LRFD specification, was significantly updated in 2006 Interims. 

In this Appendix, basic concepts of LRFD will be presented including a brief discussion on 

comparison of LRFD with allowable stress design (ASD) approach. The purpose here is to 

provide the necessary basis for preparing the geotechnical specialist to use this new method. 

The material presented in this Appendix has been adapted from similar material included in 

the FHWA (2006a) manual on driven pile foundations. 

C.1.1 Primary References 

The primary references for this Appendix are as follows: 

AASHTO (2002). Standard Specifications for Highway Bridges. 17th Edition, American 

Association of State Highway and Transportation Officials, Washington, D.C. 

AASHTO (2004 with 2006 Interims). AASHTO LRFD Bridge Design Specifications, 3rd 

Edition, American Association of State Highway and Transportation Officials, 

Washington, D.C. 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 1 December 2006 
 

 

C.2 CONCEPTS OF ASD AND LRFD 

To understand and appreciate LRFD approach, it is necessary to first briefly summarize the 

fundamental basis for allowable stress design (ASD) and then to review the history of the 

development of the LRFD and its early implementation. 

Allowable Stress Design (ASD) evolved from the development of methods of structural 

analysis during the nineteenth century. Prior to these developments, structures were designed 

based entirely on experience and of rules-of-thumb. The methods of structural analyses were 

developed based on the assumption that the structure behaved elastically and that they 

produced a rational evaluation of structural behavior that satisfied both equilibrium and 

compatibility. But, the analyses only explained structural behavior. It was desirable that a 

rational design approach be developed and it was logical to limit the calculated stresses in a 

structure to some fraction of the structural material strength. Gradually, structural loads 

appropriate for design were defined and then codified. So, if member stresses could be 

calculated it was logical to limit those stresses and values of allowable stresses were 

gradually accepted based on the experience that the structure did not fail. These limiting 

stress values became known “design stresses” or “allowable stresses.” For instance, the 

allowable stresses in steel beams in bending have been limited to between about 0.4 and 0.66 

times the steel yield strength. 

But, linear elastic behavior is not universally observed in all structural elements. For 

example, the failure strength of a column is related the slenderness ratio of the member and 

methods are available to confidently calculate the failure load. Similar considerations affect 

the design of other structural elements. The approach that came to be used in some 

applications during the development of ASD was to apply a “factor of safety” to the 

calculated ultimate member capacity. 

Once the structural analysis was performed based on linear elastic theory and an appropriate 

factor of safety, the forces at the foundation element were obtained. At this stage, it was 

realized that the foundation element is embedded in geomaterials (i.e., soils and rocks) which 

are inherently inelastic and use of linear elastic theory will not represent the strength of a soil 

structure. Therefore, to account for inherent uncertainties in the characterization of 

geomaterials, the use of the concept of factor of safety was extended to geomaterials as well 

and has become universal in geotechnical design. Rather than use of two factors of safety, 

one for structural analysis and one for geotechnical analysis, a single combined factor of 

safety was applied to account for all uncertainties and this was commonly applied in the 

geotechnical analysis. 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 2 December 2006 
 

 

 

The combined factors of safety were selected so that failures were very unlikely, based on 

experience, but the magnitudes of the factors of safety were based only on experience. The 

geotechnical engineer should understand that he/she does not “own” all of the factor of 

safety. It must be adequate to deal with the variability of the loads and the inadequacy of the 

analysis in addition to the strength variability. 

Until 1956, the analysis of a concrete section subject to bending was performed assuming 

that the compression stress in the concrete was linearly distributed on the cross section with 

the further assumption that concrete could carry no tension. Designs were limited by placing 

limits on the calculated stress in both the concrete in compression and in the steel in both 

tension and compression (if compression steel was present). In other words, the element 

strength was treated as if the materials were elastic and, to perform the analysis, the steel was 

then “transformed” into concrete based on the relative moduli of the two materials. The 

result of these assumptions produced quite conservative results, particularly if compression 

reinforcement was present as is always the case with columns. The time dependent 

deformation of concrete subjected to compression causes its effective modulus to be time 

dependent. Extensive research was performed in the first half of the twentieth century to 

understand what the actual stress distribution was and how it could be used in design. 

These fundamental probIems with the use of ASD caused the American Concrete Institute 

(ACI) in 1956 to adopt a new edition of their Building Code for the design of concrete 

structures and in that code an Appendix was included that used a strength design approach 

(ACI 1956) to replace the allowable stress method described above. The ultimate strength of 

the element in bending was calculated using a prescribed, nonlinear concrete stress 

distribution on the section at failure. The computational procedure was quite simple and the 

result was element strength not stress. The Appendix of ACI 318-56 achieved little use. 

The ACI Committee that prepared this method then took another major step. Instead of 

selecting a factor of safety for particular failure modes they broke the factor of safety into 

parts. They realized that the limiting value of ultimate load should depend on the variability 

of the particular load types. So they specified different “load factors” for the various types 

of loads and, indirectly, they applied an additional multiplier to provide structural safety for 

the strength variability of member types and failure modes. 

ACI 318-63, adopted in 1963, made extensive changes from the 1956 Code and the result 

had the form that we now know as LRFD (ACI 1963). 

Σγij Qij ≤ φk Rnk 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 3 December 2006 

C-1 
 

Where, γ is the load factor, Q is the load effect (this refers the element load calculated from 

the applied loads by a linear elastic structural analysis.) The subscripts i and j refer to the 

load condition (dead, live, wind, etc.) and the load combination, respectively. φ is the 

resistance factor for a given limit state (failure mode), Rnk is the nominal resistance in the 

kth limit state. The term nominal resistance was adopted to define the element strength 

determined by some specified method. (It should be noted that in the AASHTO LRFD 

Code the term nominal resistance is used instead of nominal strength.) The summation 

on the left side of Equation (1) is known as the factored load. A generally used name for the 

right side of the expression has not been accepted. The term factored resistance will be 

used here. 

The version of Equation (1) used in the AASHTO LRFD Design Specification is somewhat 

different. It has the following form: 

Σηγ ij Qij ≤ φk Rnk C-2 

where η is a factor related to the ductility, redundancy and operational importance. 

When ACI 318-63 was adopted, the load and resistance factors were generated based on 

judgment followed by extensive comparative designs. By 1965, the designers of concrete 

structures in the private sector had almost universally adopted the ACI LRFD Code. There 

were a few minor changes in the load factors in the next edition of the Code in 1968 (ACI 

1968) and the ASD section was dropped completely. The ACI LRFD Building Code was 

then essentially unchanged until 2002 (ACI 2002) when extensive changes were made 

primarily to the load and resistance factors. During this entire development period the design 

method was known as “Ultimate Strength Design.” 

The LRFD procedure adopted by ACI 318-63 was applicable to structural concrete elements 

for buildings only. It did not apply to the geotechnical aspects of foundation design. This 

produced a considerable anomaly for reinforced concrete building designers. For example, in 

the design process the geotechnical engineer recommended an allowable bearing pressure for 

a spread footing. The structural designer then had to size the footing using allowable loads – 

and that implied the use of a different set of loads - but perform the structural design of the 

reinforced concrete footing with factored loads. 

Driven pile cap design was even more absurd. The geotechnical engineer selected an 

ultimate pile capacity based on subsurface conditions. Most of the methods that are used to 

establish pile capacity produce ultimate capacity. As discussed in Chapter 9, those methods 

include wave equation analysis, dynamic testing or static load testing. The one exception is 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 4 December 2006 
 

the use of a dynamic formula and most formulas usually give allowable loads. The Gates 

Formula is an exception in that it produces a predicted ultimate load. The geotechnical 

engineer then selected a factor of safety to arrive at an allowable load. Again, the structural 

engineer had to use allowable loads to do the pile group selection and layout but then use 

factored loads to design the pile cap. Private sector designers have been dealing with this 

inconsistency for forty years. 

In 1969, Cornell published a paper in the ACI Journal (Cornell, 1969) showing that the load 

and resistance factors could be determined rationally using a probabilistic analysis. As input 

to that analysis the variability of both the loads and the resistance was required. The 

National Bureau of Standards (NBS) completed a research project to collect the necessary 

information for buildings and they generated the associated factors (Ellingwood, et al., 

1980). At that time the only LRFD Design Code in use was the ACI Code and the NBS 

factors were quite different than those contained in the ACI Code. These differences 

continued until 2002. 

Today, LRFD design specifications are available for both steel and concrete buildings. 

Beginning with the 2002 ACI Building Code the load factors for both steel and concrete 

structures became the same. All concrete buildings are designed using LRFD but in the case 

of steel buildings the implementation of LRFD is not complete and an ASD design 

specification is still available and widely used for steel structures. 

C.3 CALIBRATION OF PROBABILITY BASED LRFD 

The original work of Cornell (1969) produced a major research effort to develop a 

probabilistic approach to structural design based on the load and resistance factor concept. 

The fundamental concept held that, since neither the loads nor the resistance are 

deterministic, it is appropriate to treat both load and resistance as random variables and to 

develop an approach to the design of structures based on probability theory. The concept is 

illustrated in Figure C-1 where probability density functions (PDFs) are shown for both the 

load effect, Q, and the resistance, R. The area under the resistance curve between a and b 

represents the probability of the resistance being between a and b. The region where the two 

curves overlap represents cases of “failure.” Probability-based design is founded on the 

concept that the design be selected so that the probability of failure is equal to, or less than, 

some prescribed value. The limiting failure probability was originally established from 

laboratory test data on structural elements. 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 5 December 2006 
 

fR(R),fQ(Q 

) 

Rn R 

Load Effect 

Q 

Resistance (R) 

A 

a b R,Q

Figure C-1. Example of Probability Density Functions for both Load and Resistance. 

The load effect in Figure C-1 has been shown much narrower than the resistance for 

illustrative purposes, indicating that, in this case, the load has less variability than the 

resistance. The variability is defined by the standard deviation of the distribution. (The 

standard deviations are not shown in Figure C-1.) In Figure C-1, the mean values are 

denoted by Q and R . The nominal resistance, Rn is not necessarily the same as the mean 

resistance as illustrated in Figure C-1, but is the resistance that would be determined by the 

specified analysis method. 

If distributions are available for both the load effect and the resistance, then the probability of 

failure can be determined. One approach that has been used is to consider the combined 

probability density function for R-Q and this is illustrated in Figure C-2. Failure is defined 

when R-Q is less that zero and the region is shaded in Figure C-2. The probability of 

failure is the area of the shaded portion under the curve. The basis for design is to require 

that the mean of that distribution, R − Q , be greater than the value of R-Q = 0. The distance 

of that mean above zero is taken as a multiple, β, of the standard deviation of the distribution. 

β is known as the safety index or reliability index. There are other approaches to 

establishing a measure of safety. A more detailed discussion of probabilistic code calibration 

has been presented by Kulicki (1998). 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 6 December 2006 
 

R-Q

fR-Q

0 

R-Q

βσ 

R-Q

Figure C-2. Probability Density Function for R-Q. 

Existing structures that have performed satisfactorily have been analyzed to determine safety 

indices and from these analyses recommended values have been determined. Then, with 

knowledge of the load and the strength variabilities it is possible to select load and resistance 

factors to produce the required safety index. Structural engineers have established load 

factors for the various load types in the AASHTO Bridge Code and most of these values are 

probably not subject to change today. So the geotechnical resistance factors must be selected 

to achieve the required appropriate safety index. 

Geotechnical strength measurement is very difficult to describe statistically due to the lack of 

standardized procedures for material characterization of soils. But, load and resistance 

factors can be calibrated based on a direct comparison with existing design practice. Load 

factors have been selected for the AASHTO LRFD Bridge Code so resistance factors can be 

directly determined to produce designs similar to those obtained in current ASD practice. 

For example, the AASHTO Strength I case is considered since it is commonly critical in 

design. The equality condition is used to obtain a unique and limiting expression. The 

expression can be stated in a simplified fashion as 

γD QD + γL QL = φk Rnk 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 7 December 2006 

C-3 
 

where the subscript D refers to dead load and L refers to live load. Values are available for 

the dead and live load factors for Strength I in the AASHTO LRFD Bridge Code and 

Equation C-3 becomes 

1.25 QD + 1.75 QL = φk Rnk C-4 

The equivalent ASD relationship can be stated 

(QD + QL) FS = Rnk C-5

where FS is the ASD factor of safety. For the equality condition, Rnk can be eliminated from 

Equations C-4 and C-5 and this results in a single relationship for φk, in terms of FS and the 

QL/QD ratio. 

FS(1 + QL / QD ) φk = C-6 (1.25 + 1.75QL / QD ) 

Figure C-3 shows resistance factors for various factors of safety as a function of QL/QD ratio 

for the AASHTO LRFD Code. From Equation C-6 and Figure C-2, the importance of livedead load ratio becomes clear. For short span bridges the live load may be much larger than 

the dead load while for very long spans structures the live loads can be almost 

inconsequential. Regardless of the source of resistance factors they must be checked against 

existing ASD practice. For example, if the probability analysis produced smaller resistance 

factors than the equivalent ASD factors of safety this would imply an unnecessary increase in 

conservatism in the design. 

The factor η in Equation C-2 has been ignored in the above discussion. The primary concern 

with η in foundation design comes when only a very few deep foundation elements are used 

so that the foundation is non-redundant. While it is not so clear how redundancy can be 

determined since it is to some degree controlled by the superstructure geometry it can be 

critical and must be evaluated. Certainly a single deep foundation element will be nonredundant. Of course, most driven pile foundations will have enough piles to be redundant. 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 8 December 2006 
 

 

QL/QD

Figure C-3. Resistance factor as a function of QL/QD for various factors

 of safety for the AASHTO LRFD Bridge Code. 

C.4 LRFD DETAILS 

The issue of the verification of the safety safety of an LRFD-based design is now discussed. 

The question that will be considered is, “Does the structural element (pile) have adequate 

axial strength.” To answer this question it is best to consider some details. First, consider 

the determination of the loads that would be used in bridge design. There are five strength 

limit states, two extreme event limit states, four serviceability limit states and one fatigue 

limit state given in Table 3.4.1-1 of the AASHTO LRFD Bridge Code (AASHTO 2004 with 

2006 Interims). Here only the strength limit states will be considered for illustration 

purposes. The factored loads for those five cases are as shown in Table C-1. These load 

combinations have been somewhat simplified for this discussion. 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 9 December 2006 
 

 

 

Table C-1 

Strength Limit State Load Combination 

I γpD + 1.75 L + 1.0 WA + 1.0 FR 

II γpD + 1.35 L + 1.0 WA + 1.0 FR 

III γpD + 1.0 WA + 1.4 WS + 1.0 FR 

IV γp D + 1.0 WA + 1.0 FR (but for dead load due to structural 

components only 1.5 D) 

V γpD + 1.35 L + 1.0 WA + 0.4 WS + 1.0 WL + 1.0 FR 

Notations: 

γp – load factor for the various types of dead load. For the superstructure dead load γp is 

1.25, but other values are specified for other types of dead load. 

D – dead load. 

L – live load 

WA – water and stream load 

FR – friction load 

WS – wind load on the structure 

WL – wind load on the live load 

Since the load combinations have been somewhat simplified, the reader is encouraged to 

review Section 3 of the AASHTO LRFD Bridge Design Specifications (AASHTO 2004 with 

2006 Interims). Probably geotechnical engineers that are responsible for foundation design 

will not be required to determine the factored loads, but a general understanding of those 

loads provides a better understanding of the entire design process. While the above loads and 

load combinations have differences from that of previous AASHTO Specifications the 

general structure of the loads is unchanged. Since there may be several different sets of loads 

(for instance, maximum and minimum) for each of the strength limit states the final set of 

factored loads will usually be larger than the five given above and sometimes much larger, 

particularly if extreme event conditions must be considered. 

At this stage of the foundation design process, the factored loads will have been determined 

by the structural designer and with the exception of the downdrag case it is unlikely that 

these loads or load combinations will change in future AASHTO Codes. Therefore, the left 

side of Equation C-2 has now been determined. 

The right side of Equation C-2 is of greater concern for the geotechnical foundation designer 

who must determine values of φk, the resistance factor, and Rnk, the nominal strength. 

Values for φk must be defined by code. It has often been implied that resistance factors may 

be determined in the design process using a probability analysis. This is not realistic and 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 10 December 2006 
 

certainly not necessary for deep foundation design. At the present, the resistance factors are 

prescribed in AASHTO (2004 with 2006 Interims) and are not always unique. The reader is 

referred to Sections 10 and 11 of AASHTO 2006 Interims for selection of appropriate 

resistance factors and methods to determine the nominal strength, Rnk. 

C.5 THE DESIGN PROCESS 

The design process for LRFD will now be reviewed. The flow chart for LRFD-based design 

is given in Figure C-4. In Blocks 1 to 5, project requirements must be determined and the 

subsurface must be explored and evaluated to obtain the necessary geotechnical design 

quantities. In Blocks 6 and 7, an appropriate foundation type is selected. For illustration 

purposes herein, a driven pile type is selected. Then in Block 8 the factored loads are 

determined. After determining whether the pile is driven in soil or to rock (see Blocks 9 or 

11), the designer selects the resistance factor in Blocks 10 or 12 based on the capacity 

verification procedure and the quality control method that has been selected. In the ASD 

method, a factor of safety is selected based on the information in Table 4.5.6.2.1A of 

AASHTO (2002). The resistance factor for LRFD is given in the Tables 10.5.5.2.3-1, 

10.5.5.2.3-2 of AASHTO (2004 with 2006 Interims). Selection of the proper value for 

resistance factor from the LRFD Specification will not be discussed here. 

The rest of the flow chart is similar to the one for ASD. It can be seen that there is little 

difference in the design process for LRFD composed to ASD. 

C.6 A SIMPLE EXAMPLE 

A very simple numerical design example will be solved to illustrate the differences between 

ASD and LRFD. Only strength will be considered since those limitations are the only ones 

that are different for the two methods. The soil is a medium dense sand with an adjusted 

N160-value of 20 and a friction angle of 33 degrees. The site has some variability and in 

terms of low, medium and high variability, the site can be characterized as having medium 

variability. In this trial design, a closed end steel pile having a length of 66 ft (20 m) and a 

cross section 14 in x 5/16 in (356 mm x 8 mm) has been selected and a geotechnical analysis 

indicates a nominal axial resistance of 330 kips (1470 kN). The working load on the 

foundation will be taken as 500 kips (2,225 kN) dead load and 800 kips (3,560 kN) live load 

including impact. Assume one (1) static load test will be performed. 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 11 December 2006 
 

 

Establish Requirements for Structural 

Conditions and Site Characterization 

1 

Deep Foundation Shallow Foundation 

Driven Pile Other Deep Foundation Types 

Establish Factored Load 

and 

General Foundation Conditions 

Pile Driven to 

Rock or Dense Layer 

Select Pile Type, Length, 

Axial Capacity, Evaluation 

Method and 

Resistance Factor 

See Next Page 

Obtain General Site Geology 2 

Foundation Design Process 

Design Phase 

6 

Evaluate Information and Select Foundation System to 

Satisfy Requirements at a Minimum Cost 

5 

Develop and Execute Subsurface Exploration Program 4 

Collect Foundation Experience from the Area 3 

8 

7 

Select Pile Type and Length to 

Satisfy Design Requirements and Least Cost 

13 

Select the Axial Capacity Evaluation 

Method, Quality Control Procedures and 

Resistance Factor 

12 

Piles Driven in Soil 11 

Check the Other Limit States 14 

10 

9 

Design 

Not 

Discussed 

Here 

Figure C-4. Driven pile design and construction process by LRFD (FHWA, 2006a). 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 12 December 2006 
 

Prepare Plans and Specifications 

Set Field Capacity Determination Procedure 

Construction Control 

Drive Production Piles 

Resolve Pile Installation Problems and 

Construction Procedures 

Design 

Satisfactory 16 

Criteria 

Satisfactory 22 

Construction Phase 

No No

Yes 

No 

Calculate Driveability 15 

Set Preliminary Driving Criteria 20 

Perform Wave Equation Analysis of 

Contractor’s Equipment Submission 

Accept or Reject 

19 

Contractor Selection 18 

17 

23 

Drive Test Pile and Evaluate Capacity 21 

Yes 

Post-Construction Evaluation and 

Refinement of Design 

24 

Figure C-4. Driven pile design and construction process by LRFD (FHWA, 2006a) 

(Continued). 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 13 December 2006 
 

 

 C.6.1 ASD 

According to Table 3.22.1A of AASHTO (2002) for the service load Case I, the design load 

is 

500 kips + 800 kips = 1,300 kips (5,785 kN) 

First, assume that a static load test will be used in addition to a drivability analysis by wave 

equation with subsurface exploration and static analysis to verify the driving criteria. 

Therefore, the factor of safety specified in Table 4.5.6.2A of AASHTO (2002) is 2.0 and the 

required nominal axial resistance is 2,600 kips (11,570 kN). Now if the pile nominal 

resistance is 330 kips (1,470 kN), then the total required number of piles will be 

2,600 kips/330 kips = 7.8 piles, say 8 piles 

If dynamic measurement and analysis is used the specified factor of safety is 2.25 per 

AASHTO (2002), giving a required ultimate axial resistance of 1,300 kips x 2.25 = 2,925 

kips (13,016 kN). In this case the required number of piles will be 

2,925 kips/330 kips = 8.9 piles, say 9 piles 

C.6.2 LRFD 

First, determine the factored load. In this very simple example, only Strength I of Table 

3.4.1-1 of the AASHTO LRFD Bridge Code (AASHTO 2004 with 2006 Interims) will be 

considered. 

1.25 x 500 + 1.75 x 800 = 2,025 kips (9,007 kN) 

As per Table 10.5.5.2.3-2 of AASHTO (2004 with 2006 Interims), the specified resistance 

factor to be used for the case of one (1) on a site with medium variability is 0.70. Based on 

this resistance factor, the required nominal resistance is as follows: 

2,025 kips / 0.70 = 2,893 kips (12,868 kN) 

The required number of piles is 

2,892 kips / 330 kips = 8.8 piles, say 9.0 piles 

FHWA NHI-06-089 Appendix C – LRFD 

Soils and Foundations – Volume II C - 14 December 2006 
 

C.6.3 Comments 

This very simple example illustrates the difference between ASD and LRFD. Of course, 

only one failure mode limit state was considered. In a real design problem, several load 

combinations would be included, the loads would include overturning loads and all aspects of 

the problem would be much more complex. This simple example illustrates the difference 

between ASD and LRFD clearly and simply. No conclusions should be made regarding the 

fact that the LRFD design for this simple example was virtually the same as the ASD design. 

For other load combination, the design may be different. (In the latter case, Strength IV load 

combination would become critical and fewer piles would be required.) 

FHWA NHI-06-089 Appendix C – LRFD 

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APPENDIX D 

USE OF THE COMPUTER PROGRAM 

ReSSA
 

FHWA NHI-06-089 Appendix D – ReSSA 

Soils and Foundations – Volume II December 2006 
 

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FHWA NHI-06-089 Appendix D – ReSSA 

Soils and Foundations – Volume II December 2006 
 

APPENDIX D 

USE OF THE COMPUTER PROGRAM ReSSA 

D.1 INTRODUCTION 

The computer program Reinforced Slope Stability Analysis (ReSSA), version 2.0 was 

developed by ADAMA Engineering, Inc. (ADAMA), Newark, Delaware under contract to 

FHWA. The following description of the program is provided by ADAMA: 

“ReSSA(2.0) is an interactive program for analyzing rotational and 

translational stability of slopes. It was developed to allow for convenient 

integration of horizontally placed reinforcement, thus also enabling the 

analysis of mechanically stabilized earth slopes. The sole purpose of the 

ReSSA software is to assist experienced engineers in the analysis of 

reinforced and unreinforced earth slopes.” 

ReSSA(1.0), the first released version, is a user-friendly, Windows-based program that is 

provided free-of-charge (but in a limited number of licenses) to each state DOT for use on 

reinforced and slope stability analysis applications. ReSSA(2.0) has additional features that 

were added in response to users comments. For rotational (i.e., circular) failure modes, the 

program addresses moment equilibrium utilizing the Modified Bishop method of analysis. 

For translational (i.e., sliding) failure modes, the program addresses moment and force 

equilibrium utilizing the Spencer’s method of analysis. For reinforced soil slopes (RSS) in 

fill, the program incorporates the AASHTO/FHWA method of analysis (FHWA, 2001b). In 

these regards, it is recognized that ReSSA is not a comprehensive slope stability software 

package because it does not deal with general-shape slip surface. This limitation 

notwithstanding, ReSSA is an extremely powerful design and analysis software package that 

can address complex subsurface stratigraphic conditions and slope configurations. Given the 

potential application of ReSSA to DOT projects and to provide an introduction to the course 

participants regarding the utility of computer programs that have been developed to address 

slope stability problems, a summary of the use and capabilities of ReSSA is provided herein 

as part of the Soils and Foundations course. 

This appendix was prepared to provide a narrative summary of some of the specific features 

of ReSSA, as most of these capabilities are also included in other readily available 

commercial computer programs that are used for assessing slope stability. It is recognized 

that this document is provided in lieu of a hands-on demonstration of the program 

capabilities as part of the course. The instructor is available to demonstrate ReSSA if there is 

interest among individual participants. It is important to note, however, that this summary 

FHWA NHI-06-089 Appendix D – ReSSA 

Soils and Foundations – Volume II D - 1 December 2006 
 

was never intended to serve as or replace the Users Manual and the supporting technical 

documentation provided with the ReSSA program by ADAMA. 

The remainder of this appendix is organized to provide several screen shots from ReSSA and 

will demonstrate the use of the program to assess the calculated factor of safety of a 30 ft 

deep cut slope in a uniform deposit of clay. This problem was originally presented in the 

Reference Manual in Chapter 6 and was explicitly selected because the solution (i.e., the 

calculated factors of safety) was presented as an example problem in the Reference Manual 

to demonstrate the use of chart solutions. 

D.2 PREPARING FOR INPUT TO THE COMPUTER PROGRAM 

Before any slope stability analysis can be performed using a computer, it is essential that the 

user/designer prepare a hand sketch using an “unexaggerated” x-y scale (i.e., the same scale 

in the x and y directions). This sketch should show the geometry of slope, the subsurface 

stratigraphy, and the location of the water table. It will be necessary to assign coordinates to 

the various points on this sketch so that information regarding the geometry can be input to 

the computer. Remember that the computer will only solve the problem that the user asks it 

to solve, so the user needs to be sure that the geometry developed in the hand sketch matches 

the geometry presented on the computer screen. Once the hand sketch is developed, it is 

possible to now enter the information into the computer. This initial step of developing a 

hand sketch is absolutely essential, particularly for complex subsurface conditions. If the 

subsurface conditions change across the actual project site, it is necessary to develop multiple 

cross-sections for analysis so that the most critical cross-section can be identified and 

reported. 

D.3 WORKING WITH ReSSA 

When ReSSA is executed, an introductory screen is provided, identifying the copyright 

information. This is followed by a screen that flashes the ReSSA startup screen (Figure D1). Most important here is the “File” button on the taskbar. From here the user can start a 

new analysis or retrieve a previous project; this latter capability of being able to retrieve 

previous problems is one of the biggest advantages of computer programs. For our example, 

the Example 6-1 in Chapter 6 will be launched from this menu. What follows next is the 

Main Menu for ReSSA (Figure D-2), where the user will sequentially develop the problem 

and perform the stability analysis. 

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Figure D-1. ReSSA startup screen. 

Figure D-2. ReSSA main menu. 

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In ReSSA, the user has the following options: 

•	 Mode of Operation: User selects whether a “design” or “analysis” will be 

performed. For slope stability, we select “analysis.” For MSE slopes, the user can 

either use the “design” or “analysis” mode. In “design” mode, ReSSA determines the 

length of the reinforcement based on target factors of safety; this option is limited to 

simple slopes and should be used only as a first step. The user can switch from 

“design” to “analysis” and find the actual factors of safety corresponding to the 

computer generated reinforcement layout or any other layout specified by the user. 

•	 Geometry: User can select several different inputs modes in ReSSA. In general, the 

“simple” and “semi-complex” modes are used when performing parametric analyses 

to assess relative sensitivity of parameter (i.e., slope angle, strength, etc.) selection. 

For the vast majority of slope stability analyses, it is recommended (and often 

required) to select the “complex” method of data entry. 

•	 Reinforcement: ReSSA can perform an MSE slope analysis using either 

geosynthetic or metallic reinforcement. For unreinforced slope stability calculations, 

no reinforcement is used. At this step, the user selects one of the two reinforcement 

types and will later have the opportunity to overwrite this selection. This 

select/overwrite requirement is simply a procedural detail in ReSSA. 

The next step is the select the “Input Data” tab (Figure D-3), where the user has the 

opportunity to set up the slope stability analysis project and essentially convert the 

handwritten slope geometry to an electronic record. Importantly, if a previous version of the 

project is selected, it is possible to change select parameters from the previous selection and 

then proceed with analysis. Data are input using the following screens: 

•	 Units: User selects whether the input data are provided in English or SI units. It is 

important to recognize the specific units that are used and to be consistent throughout 

the analysis. 

•	 General Information: This screen (Figure D-4) allows user to input information 

about the specific analysis and can help distinguish between various computer runs. 

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Figure D-3. Data input screen from main menu. 

Figure D-4. General information screen. 

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•	 Slope Geometry: When the user selects the “Slope Geometry” tab, they are given 

the opportunity select the technique used to input the slope and subsurface geometry 

(Figure D-5). ReSSA also provides a “tip” to help the user in the data input process. 

Other computer programs have similar nuances that were incorporated by the 

developer to facilitate data input. The user next selects the number of input soil 

layers that will be used and then the “Define Geometry of Layers” tab. For the 

selected problem, Figure D-6 shows an example of the slope and subsurface profile 

that was previously input. The following information is presented on this figure: 

o	 Layer Number: For each layer, commencing at the ground surface, the user 

defines the geometry of the layer and the properties of the soils beneath the 

layer. When the geometry of a layer is entered, the user selects the next layer 

and repeats the geometry/properties data input. Once the geometry for the 

entire problem is entered, the user can return to these tabs and rapidly assess 

and modify any of the information. 

o	 Unit Weight: The total unit weight of the soil within the selected layer. 

o	 Friction Angle: The angle of internal friction for the soils within the selected 

layer. 

o	 Cohesion: The cohesion for the soils within the selected layer. 

o	 Table of X and Y Coordinates: Using the hand sketch as a guide, the user 

sequentially enters the coordinates of selected problem. At this stage, the user 

can observe the slope geometry being constructed. 

•	 Surcharge: The user has the opportunity to place point loads or line loads as 

surcharges anywhere on the top surface. The loads can be vertical or inclined with 

respect to the vertical. 

•	 Water Level: A single water table (or phreatic surface) can be considered in ReSSA. 

This surface can be horizontal or “sloped”, where the attitude of the surface is 

controlled by a series of line segments defined by their x and y coordinates. On this 

screen the user also has the opportunity to select whether a total or effective stress 

analysis will be performed. Guidelines for selection of the analysis type is beyond 

the scope of the course. 

•	 Tension Crack: ReSSA gives the opportunity for the user to select a tension crack at 

the ground surface. The user can indicate the location and depth of the crack, as well 

as whether water will be considered to act on the crack. For purposes of analysis, the 

shear strength of this zone is not considered. 

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Figure D-5. Screen used to define soil layer geometry. 

Figure D-6. Screen used to establish soil profile. 

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•	 Seismic Parameters: If a pseudo-static analysis is considered, the user can select the 

horizontal ground acceleration coefficient, Ao, as a specific percentage of the 

gravitational acceleration “g”. Procedures and guidelines for selecting an appropriate 

value of Ao is beyond the scope of this course. 

•	 Reinforcement: Finally, the type of reinforcement considered in the analysis is 

selected. The user will note that the option “No Reinforcement Used” is selected to 

overwrite the previous selection when unreinforced slopes are considered. 

At this point, the problem is ready to solve. It is recommended to double check all of the 

input screens to assure that the appropriate values and options are selected. Once this has 

been completed, the user will note that ReSSA offers the following three analysis options: 

•	 Rotational Failure Mode: This option is selected when performing a circular or 

rotational analysis in assessing global slope stability. Additional discussion follows. 

•	 Translational Failure Mode: This failure mode is limited to reinforced slopes and 

will not be used for general slope stability of unreinforced slopes. No additional 

discussion is presented in this document. 

•	 Three-Part Wedge Failure Mechanism: This option is selected to assess the 

potential for sliding along the base, also referenced as a “block sliding” mode. 

Additional discussion follows. 

Before an analysis can be performed, the user needs to select one of the two options. 

Regardless of the option selected, this first step of the analysis allows the user to select the 

controls that will be used to assess either rotational or sliding failure modes. For each of 

these, the user selects the “locations” where the analyses will be conducted. For the 

rotational failure mode, ReSSA accomplishes this by selecting a range of “Start” points at the 

top of the slope, the “Exit” points at the bottom of the slope, and the number of start and exit 

points within the selected range (Figure D-7). ReSSA makes it very easy for the user to 

select and modify the selected points by use of either: (i) coordinate selection; or (ii) drag and 

click using the mouse. For the three-part wedge failure mechanism, the user selects “boxes” 

in the subsurface where the base of the wedge will pass through (Figure D-8). Like the 

rotational failure mode, the box location can be selected using specific coordinates or by 

dragging the corners of the boxes using the mouse. The user can select a fairly wide range of 

potential surfaces in the initial runs and then “fine tune” the selection after preliminary 

review of the analysis results. 

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Figure D-7. Selection of Start and Exit analysis points (Rotational failure mode). 

Figure D-8. Selection of Boxes for Three-Part Wedge (Sliding Block analysis). 

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After all of this preliminary work has been completed, it is now possible to actually conduct 

the analysis. This is accomplished by simply hitting the “Run” button. In a few seconds, the 

calculated lowest factor of safety, the most critical failure surface, and the center of the 

critical circle for the specific user-selected controls are displayed (Figure D-9). At this point, 

the user can perform additional analyses by narrowing the selection windows, as displayed in 

Figures D-7 and D-8 to assure that the computer is converging on the correct critical surface. 

With regards to the rotational failure mode, ReSSA provides the user with several useful 

options to help assess the calculated results. The following three options presented in Figure 

D-10 are particularly helpful and can be accessed using the “Results” tab on the toolbar. 

•	 Display 10 Most Critical Circles: Although the program returns the analysis results 

for the single most critical calculation result, there is an option to display the surfaces 

that exhibit the 10 most critical (i.e., lowest calculated FS) surfaces. This option 

allows the user to assess whether there may be additional failure surfaces that need to 

be investigated. 

•	 FS Distribution: This option is particularly helpful and is displayed at the top of 

Figure D-10. It shows the lowest calculated factor of safety at each of the “Start” and 

“Exit” points selected by the user. As shown on this figure, the selected range of start 

and exit points should results in a local minimum calculated factor of safety (FS). If 

the distribution indicates multiple local low values or low values at the edge of one of 

the start/exit points, it is recommended that the user “fine tune” the analysis to assure 

that the most critical condition(s) are identified and assessed. 

•	 Display Safety Map: This option allows the user to observe all of the surfaces that 

were analyzed by the computer. Furthermore, using a user selected sensitivity scale 

bar, the calculation results are essentially “color coded” to indicate the relative 

sensitivity of the calculated FS. The safety map is a diagnostic tool that can indicate 

how efficient the reinforcement is utilized considering both its strength and length. 

Using other options of the taskbar the user can observe the number of slices used in the 

analysis and assess the orientation of calculated forces, etc. on each slice. Importantly, a 

tabulated summary of results can be obtained for review by the user. Finally, a summary 

report can be presented. It is recommended that once an analysis has been completed, the 

user print a hard copy of the report for the project files and to assure that the problem solved 

by the computer is, in fact, the one desired by the user. 

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Figure D-9. Critical failure surface (Rotational analysis). 

Figure D-10. Factor of safety distribution and Safety Map. 

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As can be seen in this narrative summary and the selected screen shots, ReSSA is a powerful 

analysis tool that can greatly aid the geotechnical specialist in assessing slope stability. One 

of the biggest advantages of ReSSA (and other computer programs) is that the “learning 

curve” for the program is not very steep, implying that users can be “up and running” fairly 

quickly. Most commercial programs are user-friendly and provide analysis/display options 

to help the user perform several “what-if” sensitivity analyses, which can be tremendously 

beneficial for a given project. In term of advice to the user, the authors recommend that they 

refer to the example programs provided by the software developers and try to re-create the 

published solutions. Most commercial slope stability software programs have extremely 

helpful example programs, Help Screens, and Users Manuals to help the user increase 

competence and confidence in assessing slope stability. 

Finally, it is always recommended that a selected solution be verified or validated using 

independent resources (i.e., other computer codes, chart solutions, etc.) and that final 

results be reviewed by an experienced peer and senior reviewer. 

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APPENDIX E 

USE OF THE COMPUTER PROGRAM 

FoSSA
 

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APPENDIX E 

USE OF THE COMPUTER PROGRAM FoSSA 

E.1 INTRODUCTION 

The computer program Foundation Stress and Settlement Analysis (FoSSA), version 2.0 was 

developed by ADAMA Engineering, Inc. (ADAMA), Newark, Delaware under contract to 

FHWA. The following description of the program is provided by ADAMA: 

“FoSSA(2.0) is an interactive program for computing the stress and 

settlement resulting from an embankment loading. It can consider the 

effects of staged construction and PVD’s.” 

FoSSA(1.0), the first released version, is a user-friendly, Windows-based program that is 

provided free-of-charge (but in a limited number of licenses) to each state DOT for their use 

to assess stress distribution and to calculate settlements beneath embankments. FoSSA(2.0) 

has additional features that were added in response to users comments. As indicated in the 

above description, FoSSA can also address partial consolidation under staged loading 

conditions and the beneficial effects of prefabricated vertical drains (PVDs). There is also a 

provision in FoSSA to address the stress distribution and settlement beneath multiple 

footings. As FoSSA is used in the Soils and Foundations course primarily to assess and 

understand the stress distribution beneath embankments, this narrative focuses on this 

component of the program. The other components (i.e., staged loading, PVDs, multiple 

footings) are considered beyond the scope of the course and will not be addressed. An 

excellent introduction regarding the program capabilities related to these other topics is 

provided on the opening screen taskbar titled ‘Help Topics” (Figure E-1). 

Figure E-1. Opening screen to learn capabilities of the program (Help Topics). 

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With regards to embankment stress distribution and settlement, FoSSA represents an 

advancement of the DOS-based program titled EMBANK (version 2.00), a program 

developed for FHWA by Prototype Engineering, Inc. in 1991. FoSSA can also be used to 

confirm the validity of the chart solutions regarding stress distribution beneath embankments 

attributed to the New York State DOT as presented in Figure 7-6 in the Reference Manual. 

This appendix was prepared to provide a narrative summary of some of the specific features 

of FoSSA. It is recognized that this document is provided in lieu of a hands-on 

demonstration of the program capabilities as part of the course. The instructor can 

demonstrate FoSSA if there is interest among individual participants. It is important to note, 

however, that this summary was never intended to serve as or replace the Users Manual and 

the supporting technical documentation provided with the FoSSA program by ADAMA. The 

remainder of this appendix is organized to provide several screen shots from FoSSA and will 

demonstrate the use of the program for the case of an embankment on clay deposit. 

E.2 PREPARING FOR INPUT TO THE COMPUTER PROGRAM 

Before the analysis can be performed using a computer, it is essential that the user/designer 

prepare a hand sketch using an “unexaggerated” x-y scale (i.e., the same scale in the x and y 

directions). This sketch should show the geometry of embankment, geometry of the loads, 

the subsurface stratigraphy, and the location of the water table. It will be necessary to assign 

coordinates to the various points on this sketch so that information regarding the geometry 

can be input to the computer. Remember that the computer will only solve the problem that 

the user asks it to solve, so the user needs to be sure that the geometry developed in the hand 

sketch matches the geometry presented on the computer screen. Once the hand sketch is 

developed, it is possible to now enter the information into the computer. This initial step of 

developing a hand sketch is absolutely essential, particularly for complex embankment 

geometries and subsurface conditions. If the subsurface conditions change across the actual 

project site, it is necessary to develop multiple cross-sections for analysis so that the most 

critical cross-section can be identified and reported. 

E.3 WORKING WITH FoSSA 

The opening screens for FoSSA are similar to the opening screens for the program ReSSA 

presented previously in Appendix D. Under the “File” tab on the initial screen, the user 

opens an existing file or selects “New.” At this step, the user has the option to: (i) re-run the 

program using an existing file; (ii) modify the input of an existing file and re-run the 

program; or (iii) establish a new program. For whichever option is selected, the next screen 

(Figure E-2) allows the user to select: (i) 2D geometry represented by a long rectangular 

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embankment of uniform cross section (i.e., plane strain); (ii) 3D geometry for representing 

relatively square embankment or footing loadings; or (iii) multiple foundations to simulate 

the interaction of foundation loading. Only the 2D case is discussed for the course. When 

the user selects “2D” and “Input Data,” Figure E-3 is presented. The user can “Select Units” 

and provide “General Information” in a manner similar to that used previously for ReSSA. 

Figure E-2. Launch screen for computing stress and settlement. 

Figure E-3. Input Data Menu (2D Geometry). 

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After the initial general information is provided, the problem geometry is ready to be input to 

the computer. As mentioned in Section E.2 earlier, it is imperative that the user first sketch 

the analysis cross-section by hand and assign coordinates to all of the relevant foundation and 

embankments layers. For this example problem, Figure E-3 indicates that the user can select 

an option to consider a “Simple” (i.e., horizontal subsurface stratigraphy that will used 

herein) or a “Complex” 3D geometry (i.e., plane strain geometry assuming soil layers of nonuniform thickness in the cross-section. For the purpose of this demonstration, select “Simple 

Geometry” which will then give the opportunity to develop the profile by selecting the 

“Foundation” and “Embankment” tabs. An example of a “Simple” stratigraphy is presented 

in Figure E-4, while an example of a “Complex” stratigraphy is provided in Figure E-5. Note 

that for the Simple stratigraphy, only the vertical elevation is required, while for the Complex 

model data for the subsurface are entered as lines exhibiting x-y coordinates similar to the 

procedure used in ReSSA (Appendix D). 

Figure E-4. Example problem with “Simple” horizontal geometry. 

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From Figure E-4 the user provides information regarding the geometry of the Foundation 

soils and the Embankment soils by accessing the relevant “Geometry” tabs. For the 

“Foundation” layer, there is a tab designated “Computations Manager” where input regarding 

the analysis are provided (Figure E-6). At this tab, the user can identify the following 

analysis conditions: (i) primary consolidation; (ii) effects of PVDs; (iii) calculation of 

increased shear strength due to consolidation; (iv) secondary consolidation; and (v) elastic or 

immediate settlement. 

By accessing the “Modify Input” button on this screen, the user is provided the opportunity 

to input the consolidation (and time rate of consolidation) properties of the foundation soils 

(Figure E-7). With regards to the “Embankment” layer, the “Geometry” tab allows the user 

to provide information regarding the geometry and properties of the embankment (Figure E8). In FoSSA, it is assumed that the embankment provides the loading for the foundation 

soils. Internal settlement of the embankment is explicitly not considered. From the “Input 

Data” button shown in Figure E-2, the user can also locate the water table using x and y 

coordinates (Figure E-9). 

Figure E-5. Example of 2D “Complex” subsurface stratigraphy. 

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Figure E-6. Computation Manager Tab for defining the analysis case. 

Figure E-7. Screen to provide foundation soil properties. 

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Figure E-8. Screen for embankment properties and geometry. 

Figure E-9. Input of water table. 

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At this point, the program goes back to the screen (Figure E-2) and is ready to “Compute 

Stress” or “Compute Settlement” that would be induced in the foundation soils by the 

overlying embankment. Under each computation section is the launch tab titled “Define 

Scope and Analysis of Run.” For the “Compute Stress” analysis, the user is directed to the 

taskbar, where there are several options to define the analysis limits and the results display 

format (Figure E-10). Of major importance are the “Define” task and the “Define Domain” 

option under this task (Figure E-11). At this screen, the user can select whether the analysis 

results (and display) will be presented along vertical or horizontal profiles, at a single point, 

or at selected grid points. The user selects the number of analysis and display points. 

Example outputs are presented in: (i) Figure E-12 for the vertical incremental stress 

distribution at 50 different depths beneath the centerline of the embankment to a depth of 400 

ft below the embankment; and (ii) Figure E-13 for the contour of vertical incremental stresses 

using an analysis grid. Figure E-14 shows the analysis grid used for the contours presented 

in Figure E-13. As shown in the lower right hand corner of Figures E-10 through E-14, the 

user has the option to display the incremental vertical, horizontal and/or shear stresses on the 

display. Finally, by selecting the “Results” tab on the Taskbar after a specific analysis is 

complete, a tabulated summary of results is produced for export to Excel. This tabulated 

summary can include the vertical overburden stress or all of the incremental stress 

calculation results not just the displayed results (Figure E-15). 

Figure E-10. Defining scope of stress analysis 

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Figure E-11. Defining scope of stress analysis using Define Domain on Taskbar. 

Figure E-12. Example output for vertical stress profile beneath centerline. 

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Figure E-13. Example contour plot of incremental vertical stress increase. 

Figure E-14. Example of analysis grid used to produce Figure E-13. 

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Figure E-15. Examples of results in a tabulated output format. 

With regards to settlement calculations, the user can launch the “Compute Settlement” 

analysis independent of the stress calculations on the screen shown in Figure E-9. The 

resulting display from the launch is shown on Figure E-16. Calculated settlements at the 

base of the embankment are calculated. The user has the option to define the horizontal 

limits of the presented results and the number of analysis points that will be displayed. After 

launching “Calculate Ultimate Settlement,” the user has the option to display results on a true 

axis or on an exaggerated vertical axis (Figure E-17). By accessing the “Results” option on 

the taskbar, a tabulated summary of results is presented in an Excel format similar to that 

previously shown in Figure E-15. Time rate of settlement calculations can also be 

performed, but are limited to a single horizontal location. After selecting the analysis 

location and performing an ultimate settlement calculation, the user launches the “Time Rate 

of Consolidation” button. The user selects either the time of the percent consolidation 

criteria for controlling the analysis, as displayed in the upper right hand corner, and then 

launches the analysis by selecting “Calculate” on the displayed screen. Results are presented 

as isochrones (Figure E-18). Results can also be presented in a tabulated format by selecting 

the “Tabulated Results for approximately “x days,” where x was previously selected by the 

user (Figure E-19). 

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Figure E-16. Resulting screen from Launch to compute settlement. 

Figure E-17. Settlement results presented on exaggerated vertical axis. 

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Figure E-18. Example of time rate of consolidation results. 

Figure E-19. Tabulated time rate of consolidation results. 

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FoSSA provides a significant advancement in capabilities relative to its predecessor (i.e., the 

DOS program EMBANK). As can be seen in this narrative summary and the selected screen 

shots, FoSSA is a powerful analysis tool that can greatly aid the geotechnical specialist in 

assessing stress distribution and settlement induced in foundation soils subjected to 

embankment loading. Like its sister program, ReSSA, the computer program FoSSA enjoys 

a fairly modest “learning curve,” in that the user can be “up and running” fairly quickly. 

FoSSA is user-friendly and provides analysis/display options to help the user perform several 

“what-if” sensitivity analyses, which can be tremendously beneficial for a given project. In 

term of advice to the user, the authors recommend that they refer to the example programs 

provided by the software developers and try to re-create the published solutions. FoSSA has 

an extremely helpful range of example problems, Help Screens, and Users Manual to help the 

user increase competence and confidence in using and understanding the program. 

Finally, it is always recommended that a selected solution be verified or validated using 

independent resources (i.e., hand calculations for approximate stress distribution and 

settlement or chart solutions) and that final results be reviewed by an experienced peer 

and senior reviewer. 

FHWA NHI-06-089 Appendix E – FoSSA 

Soils and Foundations – Volume II E - 14 December 2006