Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Synthesis and Evaluation of the 

Service Limit State of Engineered 

Fills for Bridge Support

PUBLICATION NO. FHWA-HRT-15-080 FEBRUARY 2016
FOREWORD

Engineered fills, including compacted granular fill and reinforced soil, are a cost-effective 

alternative to conventional bridge foundation systems; however, limited guidance exists on 

estimating the settlement and lateral deformation of these features under service conditions. 

Additionally, the stress distribution within these features is not well understood, leading to 

uncertainty in performance. To address these gaps, the Federal Highway Administration initiated 

a study to evaluate the service limit state (SLS) design and analysis of engineered fills for bridge 

support. This synthesis report is the product of an extensive literature search on current practices,

available load tests, and numerical modeling results. It presents factors impacting the service 

limit of engineered fills and also provides a preliminary analysis on the reliability of existing

prediction methods. The summarization of this work will assist in the continued development of 

research efforts to establish SLS design guidance for the use of engineered fills. This report will 

be of interest to engineers involved with bridge foundation research and design. 

Jorge E. Pagán-Ortiz

Director, Office of Infrastructure

Research and Development

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation 

in the interest of information exchange. The U.S. Government assumes no liability for the use 

of the information contained in this document. This report does not constitute a standard, 

specification, or regulation.

The U.S. Government does not endorse products or manufacturers. Trademarks or 

manufacturers’ names appear in this report only because they are considered essential to the 

objective of the document.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality information to serve 

Government, industry, and the public in a manner that promotes public understanding. Standards 

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its 

information. FHWA periodically reviews quality issues and adjusts its programs and processes to 

ensure continuous quality improvement.
TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.

FHWA-HRT-15-080

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

4. Title and Subtitle

Synthesis and Evaluation of the Service Limit State of 

Engineered Fills for Bridge Support

5. Report Date

February 2016

6. Performing Organization Code

7. Author(s)

Xiao, M., Qiu, T., Khosrojerdi, M., Basu, P., and Withiam, J.L. 

8. Performing Organization Report No. 

9. Performing Organization Name and Address

The Larson Transportation Institute

The Pennsylvania State University

201 Transportation Research Building

University Park, PA 16802

D’Appolonia Engineering Division of Ground Technology, Inc.

275 Center Road #2

Monroeville, PA 15146

10. Work Unit No.

11. Contract or Grant No.

DTFH61-14-C-00012

12. Sponsoring Agency Name and Address

Office of Infrastructure Research and Development

Federal Highway Administration

6300 Georgetown Pike

McLean, VA 22101-2296

13. Type of Report and Period Covered

Technical

14. Sponsoring Agency Code

15. Supplementary Notes

The Contracting Officer’s Representative (COR) was Jennifer Nicks, HRDI-40. Additional Federal Highway 

Administration technical consultants included Naser Abu-Hejleh, Michael Adams, and Khalid Mohamed. 

16. Abstract

This report synthesizes the current service limit state (SLS) design and analyses of engineered fills for bridge 

support used as shallow foundations. The SLS for settlement and deformations of bridge supports are 

summarized. Extensive literature reviews were conducted to synthesize the effects of various parameters on the 

SLS of engineered fills. The reliability of current prediction methods for deformations of bridge supports on 

granular soils are presented and evaluated using measured deformation data in the literature. Based on the 

literature review and synthesis, knowledge gaps and data needs for bridge supports with engineered fills 

were identified. 

17. Key Words

Engineered fills, Settlement, Deformations, Service limit state, 

Bridge abutment, Shallow foundation, Geosynthetic reinforced 

soil, Mechanically stabilized earth, Reinforced soil foundation

18. Distribution Statement

No restrictions. The report will be available 

to the public at FHWA: 

www.fhwa.dot.gov/research or NTIS: 

www.ntis.gov.

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

151

22. Price

N/A

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

SI* (MODERN METRIC) CONVERSION FACTORS 

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol 

LENGTH

in inches 25.4 millimeters mm 

ft feet 0.305 meters m 

yd yards 0.914 meters m 

mi miles 1.61 kilometers km 

AREA 

in2 square inches 645.2 square millimeters mm2

ft2 square feet 0.093 square meters m2

yd2 square yard 0.836 square meters m2

ac acres 0.405 hectares ha

mi2 square miles 2.59 square kilometers km2

VOLUME 

fl oz fluid ounces 29.57 milliliters mL 

gal gallons 3.785 liters L 

ft3 cubic feet 0.028 cubic meters m3 

yd3 cubic yards 0.765 cubic meters m3 

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

MASS oz ounces 28.35 grams g

lb pounds 0.454 kilograms kg

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

TEMPERATURE (exact degrees) o

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

C 

or (F-32)/1.8 

ILLUMINATION 

fc foot-candles 10.76 lux lx

fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS 

lbf poundforce 4.45 newtons N 

lbf/in2 poundforce per square inch 6.89 kilopascals kPa 

APPROXIMATE CONVERSIONS FROM SI UNITS 

Symbol When You Know Multiply By To Find Symbol 

LENGTH mm millimeters 0.039 inches in 

m meters 3.28 feet ft 

m meters 1.09 yards yd 

km kilometers 0.621 miles mi 

AREA mm2 square millimeters 0.0016 square inches in2 

m2 square meters 10.764 square feet ft2 

m2 square meters 1.195 square yards yd2 

ha hectares 2.47 acres ac

km2 square kilometers 0.386 square miles mi2 

VOLUME 

mL milliliters 0.034 fluid ounces fl oz 

L liters 0.264 gallons gal 

m3 cubic meters 35.314 cubic feet ft3 

m3 cubic meters 1.307 cubic yards yd3 

MASS 

g grams 0.035 ounces oz

kg kilograms 2.202 pounds lb

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

TEMPERATURE (exact degrees) o

C Celsius 1.8C+32 Fahrenheit oF 

ILLUMINATION 

lx lux 0.0929 foot-candles fc 

cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS 

N newtons 0.225 poundforce lbf 

kPa kilopascals 0.145 poundforce per square inch lbf/in2

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

(Revised March 2003)
iii

TABLE OF CONTENTS

CHAPTER 1. OVERVIEW OF BRIDGE SUPPORTS USING ENGINEERED FILLS...... 1

1.1 INTRODUCTION AND SCOPE OF WORK................................................................ 1

1.2 SUMMARY OF ENGINEERED FILLS ........................................................................ 1

1.3 BRIDGE SUPPORTS USING UNREINFORCED ENGINEERED FILLS............... 5

1.4 BRIDGE SUPPORTS USING MSE ............................................................................... 6

1.5 BRIDGE SUPPORTS USING GRS................................................................................ 7

CHAPTER 2. CURRENT SLS DESIGN PROCEDURES AND CRITERIA ...................... 11

2.1 AASHTO LOAD AND RESISTANCE FACTOR DESIGN (LRFD) BRIDGE 

DESIGN SPECIFICATIONS ............................................................................................... 11

2.2 BRIDGE SUPPORTS USING MSE ............................................................................. 11

2.3 BRIDGE SUPPORTS USING GRS.............................................................................. 12

2.4 CURRENT SLS CRITERIA FOR BRIDGE SUPPORTS.......................................... 13

Criteria for Settlement of Shallow Foundations of Bridges...............................................13

Tolerable Horizontal Deformation Criteria for Bridge Supports.......................................14

Tolerable Deformation Criteria for Reinforced Bridge Supports......................................15

CHAPTER 3. LITERATURE REVIEW OF PREVIOUS WORK IN ENGINEERED 

FILLS FOR BRIDGE SUPPORTS........................................................................................... 17

3.1 OVERVIEW OF LOAD DEFORMATION DATA CATALOG OF 

ENGINEERED FILLS FOR BRIDGE SUPPORTS......................................................... 17

3.2 SYNTHESIS OF FACTORS AFFECTING SETTLEMENT OF SHALLOW 

FOUNDATIONS................................................................................................................... 18

Effect of Relative Density of Soil on Settlement of Shallow Foundations........................18

Effect of N on Settlement of Shallow Foundations ...........................................................19

Effect of L and Tf of Reinforcement on Settlement of Shallow Foundations....................25

Effect of B on Settlement of Shallow Foundations............................................................29

Effect of Embedment Depth of Top Reinforcement Layer on Settlement of Shallow 

Foundations........................................................................................................................30

Effect of Vertical Spacing of Reinforcement (Sv) Layers on Settlement of Shallow 

Foundations........................................................................................................................32

Effect of Covering Ratio (CR) of Metallic Strip Reinforcement on Settlement of 

Shallow Foundations..........................................................................................................33

3.3 SYNTHESIS OF LOAD DEFORMATION RELATIONSHIPS OF BRIDGE 

ABUTMENTS AND PIERS................................................................................................. 34

Effect of Soil Parameters on Load Deformation Relationships.........................................34

Effect of Reinforcement Characteristics on Load Deformation Relationships .................46

Effect of Facing Blocks on Load Deformation Relationships...........................................58

Effect of Prestraining on Load Deformation Relationships...............................................59

3.4 EFFECTS OF TRANSIENT LOADS ON DEFORMATIONS OF BRIDGE 

SUPPORTS ON GRANULAR SOILS................................................................................ 62

3.5 DETERMINATION OF STRESS DISTRIBUTIONS IN GRANULAR SOILS 

UNDER SHALLOW FOUNDATIONS.............................................................................. 63
iv

CHAPTER 4. EVALUATION OF PREDICTION METHODS FOR 

DEFORMATIONS OF BRIDGE SUPPORTS ON GRANULAR SOILS ............................ 65

4.1 METHODS FOR IMMEDIATE SETTLEMENT OF SHALLOW 

FOUNDATIONS OF BRIDGES ON GRANULAR SOILS ............................................. 65

Modified Schmertmann Method........................................................................................65

Hough Method ...................................................................................................................66

Peck and Bazaraa method ..................................................................................................67

Burland and Burbidge Method...........................................................................................68

D’Appolonia Method.........................................................................................................68

4.2 LONG-TERM SETTLEMENT OF SHALLOW FOUNDATIONS ON 

GRANULAR SOILS............................................................................................................. 68

4.3 VERTICAL DEFORMATION OF GRS ABUTMENTS ........................................... 70

4.4 LATERAL DISPLACEMENT OF GRS WALLS AND ABUTMENTS................... 70

FHWA Method ..................................................................................................................71

Geoservices Method...........................................................................................................72

Colorado Transportation Institute (CTI) Method ..............................................................72

Jewell-Milligan Method.....................................................................................................72

Wu Method ........................................................................................................................73

Adams Method...................................................................................................................74

4.5 EVALUATION OF THE DEFORMATION PREDICTION METHODS ............... 74

Immediate Settlement ........................................................................................................75

Vertical Deformations of GRS Walls and Abutments.......................................................88

Lateral Displacements of GRS Walls and Abutments.......................................................91

CHAPTER 5. NUMERICAL AND CONSTITUTIVE MODELS FOR 

COMPACTED FILL AND REINFORCED SOIL FOR BRIDGE SUPPORTS................ 109

5.1 MODELING OF COMPACTED SOILS ................................................................... 109

5.2 MODELING REINFORCED SOIL AS A SINGLE COMPOSITE 

MATERIAL......................................................................................................................... 110

5.3 MODELING OF REINFORCEMENTS .................................................................... 111

5.4 MODELING OF SOIL-REINFORCEMENT INTERACTIONS............................ 112

5.5 NUMERICAL MODELING OF STRUCTURES SUPPORTED BY 

ENGINEERED SOILS....................................................................................................... 113

5.6 NUMERICAL MODELING OF LONG-TERM BEHAVIOR OF GRS

STRUCTURES.................................................................................................................... 116

5.7 SIMILARITIES AND DIFFERENCES BETWEEN PIER AND ABUTMENT 

FOUNDATION DEFORMATION MODELS................................................................. 117

CHAPTER 6. CONCLUSIONS............................................................................................... 119

6.1 CONCLUSIONS ........................................................................................................... 119

6.2 KNOWLEDGE GAPS AND DATA NEEDS FOR BRIDGE SUPPORTS 

USING ENGINEERED FILLS ......................................................................................... 119

REFERENCES.......................................................................................................................... 121
v

LIST OF FIGURES

Figure 1. Illustration. Engineered fill details of structural approach road and bridge 

foundation ....................................................................................................................................... 6

Figure 2. Illustration. True MSE abutment types ........................................................................... 7

Figure 3. Illustration. Typical cross-section of GRS bridge abutment ........................................... 8

Figure 4. Illustration. Annotations of parameters of a shallow foundation on reinforced soil....... 9

Figure 5. Graph. Load-settlement results on unreinforced and reinforced sand........................... 18

Figure 6. Graph. Load-settlement results for different relative densities..................................... 19

Figure 7. Graph. Load-settlement results for strip footing for u/B = h/B = 0.333, b/B = 10 ........ 20

Figure 8. Graph. Load-settlement results for square footing for u/B = h/B = 0.333, b/B = 6....... 20

Figure 9. Graph. Load-settlement results for square footing on unreinforced and reinforced 

soil with polypropylene (PP) geogrid layers................................................................................. 21

Figure 10. Graph. Load-settlement results for sandy soil for u/B = 0.4, h/B = 0.33, 

and b/B = 4.................................................................................................................................... 22

Figure 11. Graph. Load-settlement results for 1.18-inch (30-mm)-diameter circular footing ..... 23

Figure 12. Graph. Effect of number of geogrids on the load required for a settlement of 

0.02 inch (0.5 mm)........................................................................................................................ 24

Figure 13. Graph. Load-settlement results for different numbers of metallic reinforcement....... 24

Figure 14. Graph. Load-settlement results for different widths of geonet (N = 4, d = 2B) .......... 25

Figure 15. Graph. Stress-strain relationship of reinforced soil..................................................... 26

Figure 16. Graph. Stress-strain relationship of the mini-pier experiments................................... 27

Figure 17. Graph. Load-settlement results for different reinforcement lengths (N = 3)............... 29

Figure 18. Graph. Load-settlement results in reinforced sand (DR = 75 percent)......................... 30

Figure 19. Graph. Load-settlement results of model footings on clay subgrade reinforced 

with geogrid ................................................................................................................................. 31

Figure 20. Graph. Load-settlement results for different depth of top layer of metallic 

reinforcement (N = 3) ................................................................................................................... 32

Figure 21. Graph. Load-settlement results for square footing tests with three layers of 

geogrids placed at different vertical spacing ................................................................................ 33

Figure 22. Graph. Load-settlement results for different CRs of reinforcement 

(L = 2B, N = 3).............................................................................................................................. 34

Figure 23. Graph. Load-deformation behavior from PTs on GRS piers using five types 

of DC backfills.............................................................................................................................. 36

Figure 24. Graph. Effects of backfill internal on vertical displacement at abutment seat 

(reinforcement spacing = 7.87 inches (20 cm)) ............................................................................ 37

Figure 25. Graph. Effects of backfill internal (reinforcement spacing = 7.87 inches 

(20 cm)) on horizontal displacement at abutment seat ................................................................. 38

Figure 26. Graph. Effects of backfill internal (reinforcement spacing = 7.87 inches 

(20 cm)) on the maximum lateral displacement of the facing ...................................................... 38

Figure 27. Graph. Influence of apparent c and on lateral displacement of the wall.................. 39

Figure 28. Graph. Influence of backfill apparent c and values on maximum 

reinforcement loads in wall models at EOC ................................................................................. 40

Figure 29. Graph. Horizontal displacements at wall face............................................................. 41

Figure 30. Graph. Maximum lateral displacement versus geosynthetic stiffness for soils 1–4.... 43

Figure 31. Graph. Maximum lateral displacement versus geosynthetic stiffness for soils 5–8.... 44
vi

Figure 32. Graph. Maximum lateral displacement versus geosynthetic stiffness for soils 9–12.. 45

Figure 33. Graph. Maximum lateral displacement versus geosynthetic stiffness for 

soils 13–16 .................................................................................................................................... 46

Figure 34. Graph. Effect of bearing bed reinforcement for TF-7 and TF-8 ................................. 47

Figure 35. Graph. Measured lateral deformation at 3,600 psf (172.5 kPa) applied pressure for 

TF-7 (no bearing bed reinforcement) and TF-8 (two courses of bearing bed reinforcement)...... 47

Figure 36. Graph. Load-deformation behaviors for GSGC tests.................................................. 49

Figure 37. Graph. Lateral deformation of test specimens at 12,531 psf (600 kPa) and the 

ultimate applied pressure .............................................................................................................. 49

Figure 38. Graph. Effect of geosynthetic stiffness (reinforcement spacing = 7.87 inches 

(20 cm)) on vertical displacement at abutment seat...................................................................... 50

Figure 39. Graph. Effect of geosynthetic spacing on vertical displacement at abutment seat ..... 51

Figure 40. Graph. Effect of geosynthetic stiffness (reinforcement spacing = 7.87 inches 

(20 cm)) on horizontal displacement at abutment seat ................................................................. 51

Figure 41. Graph. Effect of geosynthetic stiffness (reinforcement spacing = 7.87 inches 

(20 cm)) on the maximum lateral displacement of the facing ...................................................... 52

Figure 42. Graph. Effect of geosynthetic spacing on horizontal displacement at 

abutment seat ................................................................................................................................ 53

Figure 43. Graph. Effect of geosynthetic spacing on the maximum lateral displacement 

of the facing .................................................................................................................................. 53

Figure 44. Graph. Central settlement of the foundation versus applied load ............................... 54

Figure 45. Graph. Wall face displacement at applied pressure of 3,969.1 lb/ft2 (190 kN/m2) 

for non-woven and woven reinforcement..................................................................................... 54

Figure 46. Graph. Relative horizontal displacement of wall facing recorded at EOC ................. 55

Figure 47. Graph. Influence of soil-reinforcement interface stiffness value on lateral 

displacement of the wall ............................................................................................................... 56

Figure 48. Graph. Effect of ER on the maximum vertical displacement of MSE abutments 

with metal strips............................................................................................................................ 57

Figure 49. Graph. Load-settlement results for the foundation on top of MSE abutment ............. 58

Figure 50. Graph. Stress-strain response for different piers......................................................... 59

Figure 51. Graph. Load-settlement curves for the pier................................................................. 60

Figure 52. Graph. Lateral displacement measured by LVDT....................................................... 60

Figure 53. Graph. Lateral deformation profiles of the west abutment.......................................... 61

Figure 54. Graph. Lateral deformation profiles of the east abutment........................................... 62

Figure 55. Equation. Immediate settlement of spread footing based on modified 

Schmertmann method ................................................................................................................... 66

Figure 56. Equation. Correction factor to consider foundation embedment depth....................... 66

Figure 57. Equation. Correction factor to consider creep............................................................. 66

Figure 58. Equation. Immediate settlement of each soil layer based on the Hough method........ 67

Figure 59. Equation. Immediate settlement of footing based on Peck and Bazaraa method........ 67

Figure 60. Equation. SPT blow count corrected for overburden pressure less than or equal 

to 1,566 lb/ft2 (75 kPa).................................................................................................................. 67

Figure 61. Equation. SPT blow count corrected for overburden pressure greater than 

1,566 lb/ft2 (75 kPa)...................................................................................................................... 68

Figure 62. Equation. Immediate settlement of a footing based on Burland and Burbidge 

method........................................................................................................................................... 68
vii

Figure 63. Equation. Immediate settlement of a footing based on D’Appolonia method ............ 68

Figure 64. Equation. Settlement due to creep............................................................................... 69

Figure 65. Equation. Creep rate of shallow foundations .............................................................. 69

Figure 66. Equation. Time-dependent settlement of footings in sand .......................................... 70

Figure 67. Equation. Vertical displacement of a GRS abutment with a strip footing .................. 70

Figure 68. Equation. Displacement coefficient of a reinforced soil wall ..................................... 71

Figure 69. Equation. Maximum lateral deformation of a GRS wall with inextensible 

reinforcement (i.e., metallic reinforcement) ................................................................................. 71

Figure 70. Equation. Maximum lateral deformation of a GRS wall with extensible 

reinforcement (i.e., geosynthetic reinforcement).......................................................................... 71

Figure 71. Equation. Maximum horizontal displacement of a GRS wall or abutment 

based on Geoservices method....................................................................................................... 72

Figure 72. Equation. Maximum lateral displacement of a GRS wall or abutment based 

on CTI method .............................................................................................................................. 72

Figure 73. Equation. Lateral displacement of a GRS wall or abutment with flexible facing....... 73

Figure 74. Equation. Lateral movement of a GRS wall with modular block facing .................... 73

Figure 75. Equation. Lateral movement of a GRS wall with modular block facing 

(no friction between wall and soil) ............................................................................................... 74

Figure 76. Equation. Lateral displacement of GRS abutments in response to a vertical load...... 74

Figure 77. Equation. Lateral strain of GRS abutments in response to a vertical load .................. 74

Figure 78. Equation. Arithmetic mean value ................................................................................ 75

Figure 79. Equation. Standard deviation....................................................................................... 75

Figure 80. Equation. COV ............................................................................................................ 75

Figure 81. Graph. Frequency of occurrence histogram of for immediate settlements 

of shallow foundations using the modified Schmertmann method............................................... 78

Figure 82. Graph. Probability plot for measured and predicted settlements using the 

modified Schmertmann method.................................................................................................... 78

Figure 83. Graph. Frequency of occurrence histogram of for immediate settlements

of shallow foundations using the Hough method ......................................................................... 80

Figure 84. Graph. Probability plot for measured and predicted settlement using the 

Hough method............................................................................................................................... 80

Figure 85. Graph. Frequency of occurrence histogram of for immediate settlements of 

shallow foundations using the Peck and Bazaraa method ............................................................ 82

Figure 86. Graph. Probability plot for measured and predicted settlement using the Peck 

and Bazaraa method...................................................................................................................... 82

Figure 87. Graph. Frequency of occurrence histogram of for immediate settlements of 

shallow foundations using the Burland and Burbidge method ..................................................... 84

Figure 88. Graph. Probability plot for measured and predicted settlement using the 

Burland and Burbidge method...................................................................................................... 84

Figure 89. Graph. Frequency of occurrence histogram of for immediate settlements of 

shallow foundations using the D’Appolonia method.................................................................... 86

Figure 90. Graph. Probability plot for measured and predicted settlement using the 

D’Appolonia method .................................................................................................................... 86

Figure 91. Equation. Elastic modulus of GRS composite ............................................................ 88

Figure 92. Equation. Elastic modulus of GRS composite (modified equation)............................ 88

λλ

λλ

λλ

λλ

λλ
viii

Figure 93. Graph. Frequency of occurrence histogram of of vertical displacement of 

abutments and GRS walls............................................................................................................. 90

Figure 94. Graph. Probability plot for measured and predicted vertical displacement of 

abutments and GRS walls............................................................................................................. 90

Figure 95. Graph. Frequency of occurrence histogram of for the lateral displacement 

of GRS walls and abutments using the FHWA method ............................................................... 92

Figure 96. Graph. Probability plot for measured and predicted lateral displacement of 

GRS walls using the FHWA method............................................................................................ 93

Figure 97. Graph. Frequency of occurrence histogram of for the lateral displacement of 

GRS walls and abutments using the Geoservices method............................................................ 95

Figure 98. Graph. Probability plot for measured and predicted lateral displacement of 

GRS walls using the Geoservices method .................................................................................... 96

Figure 99. Graph. Frequency of occurrence histogram of for the lateral displacement 

of GRS walls and abutments using the CTI method..................................................................... 98

Figure 100. Graph. Probability plot for measured and predicted lateral displacement of 

GRS walls using the CTI method ................................................................................................. 99

Figure 101. Graph. Frequency of occurrence histogram of for the lateral displacement

of GRS walls and abutments using the Jewell-Milligan method................................................ 101

Figure 102. Graph. Probability plot for measured and predicted lateral displacement of 

GRS walls using the Jewell-Milligan method ............................................................................ 101

Figure 103. Graph. Frequency of occurrence histogram of for the lateral displacement

of GRS walls and abutments using the Wu method ................................................................... 104

Figure 104. Graph. Probability plot for measured and predicted lateral displacement 

of GRS walls using the Wu method............................................................................................ 104

Figure 105. Graph. Frequency of occurrence histogram of for the lateral displacement

of GRS walls and abutments using the Adams method.............................................................. 106

Figure 106. Graph. Probability plot for measured and predicted lateral displacement 

of GRS walls using the Adams method ...................................................................................... 106

λλ

λλ

λλ

λλ

λλ

λλ

λλ
ix

LIST OF TABLES

Table 1. FHWA materials and construction requirements for engineered granular fills................ 2

Table 2. General considerations for select structural backfill......................................................... 3

Table 3. Criteria for settlement of shallow foundations of bridges .............................................. 13

Table 4. WSDOT settlement criteria for bridge piers and abutments........................................... 14

Table 5. Properties of test sands ................................................................................................... 23

Table 6. Geotextile properties....................................................................................................... 25

Table 7. Placed geogrid strength................................................................................................... 27

Table 8. Summary of the maximum displacements of the front wall facing and of the 

settlements of the bridge abutment footing................................................................................... 28

Table 9. GRS pier materials and results recorded from vertical deformation survey................... 35

Table 10. Parametric study on aggregate size............................................................................... 36

Table 11. GRS retaining wall dimensions.................................................................................... 41

Table 12. Representative soil parameters ..................................................................................... 42

Table 13. Test conditions and results summary of GSGC tests.................................................... 48

Table 14. Soil and foundation parameters for the case histories .................................................. 76

Table 15. Predicted and measured immediate settlements of shallow foundations using the 

modified Schmertmann method.................................................................................................... 77

Table 16. Predicted and measured immediate settlements of shallow foundations using the 

Hough method............................................................................................................................... 79

Table 17. Predicted and measured immediate settlements of shallow foundations using the 

Peck and Bazaraa method ............................................................................................................. 81

Table 18. Predicted and measured immediate settlements of shallow foundations using the 

Burland and Burbidge method...................................................................................................... 83

Table 19. Predicted and measured immediate settlements of shallow foundations using the 

D’Appolonia method .................................................................................................................... 85

Table 20. Summary of the statistical analyses of the five prediction methods for immediate 

settlement of shallow foundations on granular soil, results from this study................................. 87

Table 21. Summary of the statistical analyses of the five prediction methods for immediate 

settlement of shallow foundations on granular soil, results from Gifford .................................... 87

Table 22. Abutment and GRS wall parameters in case histories.................................................. 88

Table 23. Predicted and measured vertical displacements of abutments and GRS walls............. 89

Table 24. Abutment and GRS wall parameters in case histories.................................................. 91

Table 25. Predicted and measured maximum lateral displacements of GRS walls at EOC 

using the FHWA method .............................................................................................................. 92

Table 26. Predicted and measured lateral displacements of GRS walls and abutments 

using the Geoservices method ...................................................................................................... 94

Table 27. Predicted and measured maximum lateral displacements of GRS walls using 

the CTI method ............................................................................................................................. 97

Table 28. Predicted and measured lateral displacements of GRS walls and abutments 

using the Jewell-Milligan method............................................................................................... 100

Table 29. Predicted and measured lateral displacements of GRS walls and abutments 

with modular block facing using the Wu method....................................................................... 102

Table 30. Predicted and measured lateral displacements of GRS walls and abutments 

using the Adams method............................................................................................................. 105
x

Table 31. Summary of the statistical analyses of the six prediction methods for lateral 

displacements of GRS abutments and walls............................................................................... 107
xi

LIST OF ABBREVIATIONS AND SYMBOLS

Abbreviations

3D three-dimensional

AASHTO American Association of State Highway and Transportation Officials

ADOT Arizona Department of Transportation

CR covering ratio

CMU Concrete Masonry Unit

COV coefficient of variation

CTI Colorado Transportation Institute

DC Defiance County, OH

EOC end of construction 

FE finite element

FEA finite element analysis

FEM finite element method

FHWA Federal Highway Administration

GRS geosynthetic reinforced soil

GSGC generic soil geosynthetic composite

IBS integrated bridge system

LRFD load and resistance factor design

LTDS long-term design strength

LVDT linear voltage displacement transducer

MSE mechanically stabilized earth

NHI National Highway Institute 

PET polyester

POT potentiometer

PI Plasticity Index

PP polypropylene

PT performance test

RC relative compaction

RSF reinforced soil foundation

SHRP Strategic Highway Research Program
xii

SLS service limit state

SPT standard penetration test

SRW segmental retaining wall

TF Turner-Fairbank

TFHRC Turner-Fairbank Highway Research Center

ULS ultimate limit state

UX uniaxial

WSDOT Washington State Department of Transportation

WWM welded wire mesh

Symbols

a footing offset from the edge of the wall face (i.e., setback distance)

B width of foundation 

b length of reinforcement layers below foundation

b width of facing block

bq,vol width of the load along the top of the wall (including the setback)

c cohesion

C1 correction factor for strain relief due to soil excavation for foundation 

embedment used in Schmertmann method

C2 correction factor to consider creep as the time-dependent increase in 

settlement for t number of years after construction used in Schmertmann 

method

d depth of bearing bed reinforcement

dmax maximum aggregate size

Df depth of embedment of foundation

DL lateral displacement of GRS abutments in response to a vertical load

DR soil relative density

Dv vertical settlement in the GRS abutment

D10 particle diameter at which 10 percent of the sample is finer, by mass

EGRS Young’s elastic modulus of GRS composition

ER elastic modulus of reinforcement

Es elastic modulus of soil

h spacing of reinforcement layers

H height of abutment/pier
xiii

Hi thickness of each soil layer

kb interface stiffness between backfill soil and reinforcement layers

Kh horizontal earth pressure coefficient

Kreinf stiffness of reinforcement

L length of foundation/reinforcement layers within pier or abutment

Las distance between adjacent supports

Ltotal total length of foundation

n time dependency exponent in time-dependent settlement equation

N number of reinforcement layers

N0 total number (population) of values

N60 standard penetration number that is corrected based on the field conditions

(N1)60 corrected SPT blow count

N-value blow count for an SPT sampler to penetrate the second and third 6 inches 

into the subsoil

p footing bearing pressure

q applied pressure

qc static cone resistance of cone penetration test

R2 coefficient of determination

Sv vertical spacing between reinforcement

s/B ratio of settlement of foundation to its width

Tf tensile strength

t time

tR thickness of reinforcement

u embedment depth of top geogrid layer

z standard normal variable

Z depth from the crest of wall

zi depth of influence zone

h lateral displacement of a GRS wall or abutment with flexible facing

H100 differential settlement 100 ft (30.5 m) within pier or abutment and 

between piers

i lateral movement of a GRS wall with modular block facing

net uniform pressure applied at the foundation depth used in Schmertmann 

method

p
xiv

bulk unit weight of facing (such as modular block)

unit weight of soil

strain limit

arithmetic mean of 

sampled value

friction angle

friction angle of soil based on direct shear test

dilation angle of soil

friction angle between modular block facing elements

lateral deformation of a GRS wall or abutment

maximum lateral deformation of a GRS wall or abutment

relative displacement coefficient 

initial average effective stress of the subdivided soil layer

σσ standard deviation

arithmetic mean of bias value

bias value (ratio of the measured value to the predicted value)

b

s

εd

λλ

λλii λλ

ds

h

max

R

σ0

′

λλ
1

CHAPTER 1. OVERVIEW OF BRIDGE SUPPORTS USING ENGINEERED FILLS

1.1 INTRODUCTION AND SCOPE OF WORK

This report focuses on the service limit states (SLSs) of deformations and stresses of engineered 

fills used as bridge supports for abutments and piers. The engineered fills focus on compacted 

granular engineered fills of mineral origin and reinforced soil systems. The SLSs ensure the 

durability and serviceability of a bridge and its components under typical everyday loads, 

traditionally termed “service loads.”(1) In this report, “service limit” refers to the vertical and 

lateral deformations of bridge supports.

The use of engineered fills with and without layered reinforced soil systems is an economical 

solution to reduce deformations and improve bearing resistance of shallow foundations for 

bridge supports. Notable studies of spread footings on engineered fills published by the Federal 

Highway Administration (FHWA) concluded that this technique was a suitable alternative to 

deep foundations.

(2,3) Engineered fills can be used to support bridge abutments and piers with 

various configurations. In bridge abutments, the engineered fills can be compacted granular fills

or compacted granular fills with metallic or geosynthetic reinforcement, while in bridge piers, 

the engineered fills can be compacted granular fills or compacted granular fills with geosynthetic 

reinforcement. Bridge supports using reinforced engineered fills contribute to better 

compatibility of deformation between the components of bridge systems, thus minimizing the 

effects of differential settlements and the occurrence of undesirable “bumps” between the bridge 

deck and the approach embankment transitions.

(4) Recent FHWA national surveys revealed that 

State transportation departments have safely and economically constructed highway bridges 

supported on spread footings bearing on competent and improved natural soils as well as 

engineered granular and mechanically stabilized earth (MSE) fills.

(5)

Despite these advantages, many transportation agencies do not consider shallow foundation 

alternatives, even when appropriate, for a variety of reasons, including concerns related to 

meeting serviceability requirements (e.g., vertical and lateral deformations). Due to the large size 

of spread footings for highway bridges, soil bearing failure is not likely.

(6) Therefore, the 

performance of spread footings in highway bridge design is evaluated primarily on the basis of 

vertical displacement (i.e., settlement and how differential settlements affect angular 

distortion).(7) SLS for shallow foundations often controls the design of bridge foundations; 

however, little guidance on SLS has been provided for engineered fills.

(8) According to the 

American Association of State Highway and Transportation Officials (AASHTO) Manual for 

Bridge Evaluation, SLS relates to stress, deformation, and cracking.

(9) The Strategic Highway 

Research Program 2 (SHRP2) report, Bridges for Service Life Beyond 100 Years: Service Limit 

State Design presents the existing limit states and tolerances of bridge components set forth by 

various agencies in the United States and internationally.

(10)

1.2 SUMMARY OF ENGINEERED FILLS

FHWA defines engineered granular fill as high-quality granular soil selected and constructed to 

meet certain material and construction specifications (also called “compacted structural fill” and 

“compacted granular soil”).

(5) Engineered fill may be reinforced with geosynthetics or metal 
2

strips. The high quality refers to gradation, soundness, compaction level, durability, and 

compatibility. Such specifications are further described in table 1 and table 2. 

A number of State transportation departments, including the Washington State Department of 

Transportation (WSDOT), the New Mexico Department of Transportation, and the Minnesota

Department of Transportation, have successfully utilized compacted engineered granular 

fills.

(5) For example, based on a survey of 148 bridges in Washington, FHWA concluded that 

spread footings on engineered fill can provide a satisfactory alternative to deep foundations, 

especially if high-quality fill materials are constructed over competent foundation soil.

(2)

National Cooperative Highway Research Program Report No. 651 reported higher resistance 

factors for the compacted granular fill than natural granular soil because of better control for 

compacted fill.

(11) Nevertheless, concerns exist regarding the use of spread footing bearing on 

engineered granular and MSE fills. A number of State transportation departments have allowed 

and constructed spread footings on natural soils but not on engineered granular and MSE fills 

due to the concerns related to the quality and uniformity of compacted fill materials as well as 

costly design and construction of bridge footings on MSE walls.

(5) Table 1 lists the FHWA 

material and construction requirements for engineered granular fills.

(12)

Table 1. FHWA materials and construction requirements for engineered granular fills.

(12)

Soil Properties

Requirements

U.S. Sieve Size

Percentage Passing 

(percent)

Gradation (AASHTO T27)(13)

4 inches 100

#40 (0.0165 inch) 0–70

#200 (0.0029 inch) 0–15

1 inch = 25.4 mm

Additional general considerations in selecting structural backfills are as follows:(6)

Plasticity Index (PI) (AASHTO T90): PI < 6 percent.(14)

Soundness: Based on AASHTO T104.(15)

Compaction level: Compaction level is 100 percent of maximum dry density based on 

standard Proctor test per AASHTO T99; moisture content should be ±2 percent of 

optimum moisture content.(16)

Table 2 provides general considerations in selecting structural backfills, as highlighted in

FHWA’s Soils and Foundations Reference Manual: Volume I.

(6)
3

Table 2. General considerations for select structural backfill.

(6)

Consideration Comments

Lift thickness Limit to 6 to 8 inches so compaction is possible with small equipment.

Topsize (largest 

particle size)

Limit to less than three-fourths of lift thickness.

Gradation/percent

fines

Use well-graded soil for ease of compaction. Typical gradation is 

as follows:

4-inch sieve = 100 percent passing by weight.

#40 sieve (0.0165 inch) = 0 to 70 percent passing by weight.

#200 sieve (0.0029 inch) = 0 to 15 percent passing by weight.

The limitation on percent fines (particles smaller than #200 sieve) is to 

prevent piping and allow gravity drainage. For rapid drainage, 

consideration may be given to limiting the percent fines to 5 percent.

PI PI should not exceed 10 to control long-term deformation.

Durability This consideration attempts to address breakdown of particles and 

resultant settlement. The material should be substantially free of shale 

or other soft, poor-durability particles. Where the agency elects to test 

for this requirement, a material with a magnesium sulfate soundness 

loss exceeding 30 should be rejected.

AASHTO T99 

density control(16)

Small equipment cannot achieve AASHTO T180 densities.

Minimum of 100 percent of standard Proctor maximum density is 

required.(17)

Compatibility Particles should not move into voids of adjacent fill or drain material.

1 inch = 25.4 mm

The FHWA report, Soils and Foundations Reference Manual: Volume II, recommends that 

compacted structural fills used for supporting spread footings should be a select and specified 

material that includes sand- and gravel-sized particles.

(18) Furthermore, the fill should be 

compacted to a minimum relative compaction (RC) of 95 percent based on the modified Proctor 

compaction energy, and structural fill should extend for the entire embankment below 

the footing. 

In the United States, the concept and principles of MSE technology were introduced in 1969.

(19)

There are two basic types of soil reinforcements in MSE structures: inextensible (metallic) and 

extensible (polymeric). Metallic reinforcement has been primarily used as the reinforcement of 

soils. The first reported MSE abutment in the United States was constructed in 1974 in 

Lovelock, NV, to support a precast bridge span of 70 ft (21 m).

(20) MSE structures built with 

inextensible reinforcement, such as discrete metallic strips or welded wire mats, have a unique 

combination of precast panels, reinforcement, and connection details.

(21) For bridge supports 

using extensible geosynthetics, Adams is among the first to report on the performance of a 

pre-strained geosynthetic reinforced soil (GRS) bridge pier, which demonstrated the feasibility of 

such a technique in bridge supports. (22) Since then, many full-scale studies on GRS as bridge 

supports and many bridge abutments built using such technologies continued to recognize its 

advantage over conventional bridge supports. (See references 5 and 23–29.) Moreover, 
4

engineered fills have been used for bearing of bridge abutments in other countries and have 

also proven to be effective.

(30,31) These previous studies have shown that engineered fills 

offer advantages of improved performance and savings in labor costs, equipment, and time. 

Cost savings could total up to 65 percent compared to conventional deep foundations for 

bridge systems.

(18)

For GRS abutments, backfill selection is important because it is a major structural component for 

the abutment. FHWA’s Geosynthetic Reinforced Soil Integrated Bridge System Interim 

Implementation Guide provides recommendations for the gradations for well-graded and opengraded backfills used for GRS abutments.

(32) “Open-graded material” refers to a gradation where 

skips between the sieve gradations have been deliberately achieved so that the voids are not 

filled with intermediate-size particles. The main criteria are: (1) there is a minimum friction 

angle ( ) of 38 degrees, (2) the maximum grain size is between 0.5 and 2 inches (13 and

51 mm), (3) PI should be less than or equal to 6, (4) the mass percentage of soils finer than 

#200 sieve should be less than 12 percent, and (5) the backfill shall be substantially free of shale 

or other poor durability particles, and the material shall have a magnesium sulfate loss of less 

than 30 percent after four cycles (or a sodium value less than 15 percent after five cycles). 

In addition to the gradation requirement, backfill selection depends on the following factors:

(32)

Ability to ensure compaction.

Open-graded backfill is recommended for an abutment located in a flood zone to 

facilitate the flow of water out of the abutment.

Open-graded fine aggregates (i.e., about 0.5 inch (12.7 mm)) are easier to spread, level, 

and compact than well-graded fill.

Angular particles are recommended to maximize the shear strength and minimize the 

compressibility of the GRS mass.

FHWA indicated that for GRS abutments, reinforced soil foundation (RSF), and approach-way 

backfills for GRS integrated bridge systems (GRS-IBSs), the backfill of well-graded aggregates

must be properly compacted to a minimum of 95 percent of maximum dry density according to 

AASHTO T99.

(32,16)

As of 2012, all GRS-IBS projects had selected open-graded gravel due to its relative ease of 

construction and drainage characteristics. The various counties and agencies that are building 

GRS-IBS have selected locally available structural backfills for their projects.

(21) Adams et al. 

provided the fill gradations of five GRS-IBS projects; the majority of the grains were in the 

range of 0.375 to 1 inch (9.5 to 25.4 mm), but their size distributions varied.

(21) It is noted that 

how the different grain sizes affect the load-deformation behavior remains to be studied.

Using different types of engineered fills for bridge support has its benefits and limitations. One 

benefit is that contractors and bridge owners have wider choice and availability of backfill 

materials; this will result in savings in cost and labor.
5

The limitations include the following:

Currently, granular soils and aggregates are mainly used as engineered fills for bridge 

support, while the performance of other types of engineered fills, such as those with 

higher fine content, remain uncertain.

When higher fines content exists in fills supporting bridge substructures, segregation can 

occur, and drainage of backfill can be compromised. This directly affects the stability and 

compressibility of the foundation and bridge structure.

Strength, compressibility, and index properties of other types of engineered fills may not 

meet the requirements for bridge supports, thus making them less desirable than other 

fill types.

1.3 BRIDGE SUPPORTS USING UNREINFORCED ENGINEERED FILLS

Special details and specifications are necessary when constructing a compacted structural fill to 

support a bridge foundation such as an abutment. Figure 1 shows the recommended details for 

construction of a structural approach embankment and bridge foundation. The material

specifications are chosen so that the engineered fill material is capable of being compacted to a 

firm, non-yielding condition to support a bridge abutment spread footing. FHWA’s Geotechnical 

Engineering Circular No. 6: Shallow Foundations recommends that structural fill for highway 

embankment material should not include unsuitable or deleterious material such as peat, muck, 

wood, organic waste, coal, charcoal, or any other material that would perform poorly in an 

embankment.(12)
6

1 ft = 0.305 m

Figure 1. Illustration. Engineered fill details of structural approach road and bridge 

foundation.

(33)

1.4 BRIDGE SUPPORTS USING MSE

Since the first MSE abutment was constructed in the United States in 1974, MSE technology has 

been used in bridge-supporting structures such as bridge abutments, and both metallic and 

geosynthetic reinforcements have been used.(34) MSE abutments are MSE retaining walls 

subjected to much higher area loads that are located close to the wall face. Using MSE structures 

as direct support for bridge abutments can be a significant simplification in the design and 

construction of current bridge abutment systems and may lead to faster construction of highway 

bridge infrastructure. When a bridge beam is supported on a spread footing that bears directly on 

top of an MSE structure, this configuration is known as true MSE abutment, as shown in 

figure 2. To prevent overstressing the soil from the excess load exerted on a true MSE abutment, 

the beam seat is sized so that the centerline of bearing is at least 3.05 ft (1 m) behind the MSE 
7

wall face, and the service bearing pressure on the reinforced soil is no more than 4 kip/ft2

(192 kPa).(34) Anderson and Brabant reported that there are approximately 600 MSE abutments 

(300 bridges) built annually in the United States, of which 25 percent are true MSE 

abutments.(34)

Note: This figure was created by FHWA after Anderson and Brabant.(34)

Figure 2. Illustration. True MSE abutment types.

MSE abutments may result in construction cost savings where deep foundations are not needed. 

Additionally, the use of true bridge abutments can result in significant cost savings.(34) True 

bridge abutments also have significant advantages over conventional abutments. The proverbial 

bump at the end of the bridge is alleviated because the footing settles along with the MSE wall in 

contrast to a deep foundation that does not settle at the same rate. Additionally, approach slabs 

are not necessary because of the elimination of conditions that would lead to the bump at the 

end of the bridge, and the elimination of approach slabs results in significant cost savings.(7)

While there are proven advantages of MSE abutments, there are some limits for their 

applicability, as with any technology. A study by Purdue University and the Indiana Department 

of Transportation revealed that MSE structures on shallow foundations should not be used as 

direct bridge abutments when soft soil layers, such as normally consolidated clays, are present 

near the surface where significant deformation and differential settlement are expected.(4) In such 

conditions, a design configuration including piles should be used. In more competent foundation 

profiles, MSE walls can be used for direct support of bridge abutments.

1.5 BRIDGE SUPPORTS USING GRS

GRS technology consists of closely spaced layers of geosynthetic reinforcement and compacted 

granular fill material. GRS has been used for a variety of earthwork applications since the U.S. 

Forest Service first used it to build walls for roads in steep mountain terrain in the 1970s.

(21) The 

spacing of GRS reinforcement should not exceed 12 inches (304.8 mm) and is typically 8 inches 

(203.2 mm).

(21) As shown in figure 3, GRS-IBS typically includes an RSF, a GRS abutment, and 
8

a GRS integrated approach to transition to the superstructure. The RSF is composed of granular 

fill material that is compacted and encapsulated with a geotextile fabric. The application of GRS

has several advantages: the system is easy to design and economically construct; it can be built in 

variable weather conditions with readily available labor, materials, and equipment; and it can 

easily be modified in the field.

(21) Figure 4 shows an illustration of RSF and the common 

parameters used in RSF in this report.

1 inch = 25.4 mm

Figure 3. Illustration. Typical cross-section of GRS bridge abutment.

(21)
9

Figure 4. Illustration. Annotations of parameters of a shallow foundation on 

reinforced soil.

Where:

B = Width of foundation.

b = Length of reinforcement layers below foundation.

N = Number of reinforcement layers.

u = Embedment depth of top geogrid layer.

h = Spacing of reinforcing layers.

d = Depth of bearing bed reinforcement.

Df = Depth of embedment of foundation.

N=1

N=2

N=3

b

d

B u

h

h

Footing

Reinforcement Layer

Df

11

CHAPTER 2. CURRENT SLS DESIGN PROCEDURES AND CRITERIA

2.1 AASHTO LOAD AND RESISTANCE FACTOR DESIGN (LRFD) BRIDGE DESIGN 

SPECIFICATIONS(8)

The AASHTO LRFD Bridge Design Specifications incorporates limit state design in LRFD.

(8)

A “limit state” is a condition beyond which a bridge component ceases to satisfy the criteria for 

which it was designed. All possible structural and geotechnical failure modes for foundations 

that can lead to bridge failure are grouped into three distinct structural and geotechnical limit 

states: SLS, strength limit state, and extreme event limit state.

(8) The SLSs are defined as the 

limit states related to stress, deformation, and cracking under regular operating conditions. In 

SLSs, failure may be defined as exceeding the tolerable displacement. For example, the 

foundations must have adequate structural and geotechnical stiffness to keep the bridge 

displacements less than the bridge tolerable displacements. The failure modes in strength limit 

states are related to the strength and stability of the foundations under loads and conditions 

applied continuously or frequently during the bridge design life. The failure modes in extreme 

event limit states are related to the strength and stability of the foundations under loads and 

conditions applied during certain events that have a return period greater than the bridge design 

life. LRFD of spread footings at all limit states is prescribed in the AASHTO LRFD Bridge 

Design Specifications.

(8) SLS design (Article 10.6.2) covers the settlement and overall stability of 

spread footings, and Article 10.6.2.4 describes the methods that should be used to estimate 

settlement of spread footings of bridges on cohesionless and cohesive soils.(8)

Although not explicitly prescribed in the current AASHTO LRFD Bridge Design Specifications, 

the SLS design of engineered fills follows the same acceptance criterion used for bridge 

foundations.

(8) Namely, the estimated movement must not exceed the tolerable movement. Thus, 

current practice uses a variety of empirical, semi-empirical, and numerical modeling approaches 

to estimate fill deformation, and tolerable movement criteria are based on the permissible 

deformation of a bridge abutment, approach slab, pavement, or other structural feature in or 

on the fill.

2.2 BRIDGE SUPPORTS USING MSE

Guidelines for the static design of MSE walls have been published by AASHTO and FHWA. 

(See references 8 and 35–37.) A study by Koerner and Soong compared three static MSE design 

methods: the modified Rankine method, the FHWA method, and the National Concrete Masonry 

Association method.

(38,39) They found that the FHWA method provided a factor of safety value 

between those by the other two methods. Guidelines for the design of MSE as true bridge 

abutments are also available that limit MSE settlement to 0.5 inch (13 mm) if service loads are 

kept below 27.84 psi (192 kPa), but details on the parameters impacting the deformation 

response are still lacking.

(21,32,37) In addition, the parameters used (e.g., , cohesion (c), etc.) may 

vary depending on the measurement technique and the design method selected, which may have 

an impact on the SLS analysis.

The FHWA National Highway Institute (NHI) reference manual, Mechanically Stabilized Earth 

Walls and Reinforced Soil Slopes Design and Construction Guidelines, provides a design method 
12

for MSE bridge abutments.

(36) In addition, the FHWA NHI manual, Design of Mechanically 

Stabilized Earth Walls and Reinforced Soil Slopes—Volume I, suggests that the following

conditions be implemented in the design of MSE abutments:(37)

The tolerable angular distortions (i.e., limiting differential settlement) between abutments 

or between piers and abutments should be limited to 0.005Las for simple-span bridges 

and 0.004Las for continuous-span bridges, where Las is the distance between 

adjacent supports.

A minimum offset of 3.05 ft (1 m) from the front of the facing to the centerline of the 

bridge bearing is required.

A clear distance of 6 inches (150 mm) between the back face of the facing units and front 

edge of footing is required.

The abutment should be placed on a 3.05-ft (1-m)-thick bed of compacted coarse 

aggregate where significant frost penetration is anticipated.

The bearing capacity on the reinforced volume should be limited to 4,000 lb/ft2

(192 kPa).

The maximum horizontal force at each reinforcement level should be used for the design 

of connections to the facing units.

The density, length, and cross-section of reinforcements of the abutment should be 

extended to wing walls for a horizontal distance of 0.5H, where H is the height of the 

abutment wall.

The seismic design forces should also include seismic forces transferred from the bridge 

through bearing supports that do not slide freely (e.g., elastomeric bearings).

2.3 BRIDGE SUPPORTS USING GRS

FHWA’s Geosynthetic Reinforced Soil Integrated Bridge System Interim Implementation Guide

provides the current design procedure for GRS abutments.

(32) The guide notes that the design 

methods are appropriate for GRS structures (an abutment and wing walls) with a vertical or near 

vertical face and at a height that does not exceed 30 ft (9.15 m). The bearing stress on the GRS 

abutment is limited to a service load of 4,000 lb/ft2 (192 kPa). The guide recommends that 

engineers should limit bridge spans to approximately 140 ft (42.7 m) since the SLS performances 

(such as thermal-induced movements) of longer spans on GRS-IBS were not as well 

understood.

(32) GRS abutment capacities are dependent on a combination of the strength of the 

fill material and the strength of the reinforcement when built in accordance with the two rules of 

GRS construction: (1) good compaction (95 percent of maximum dry unit weight, according to 

AASHTO T99 for well-graded aggregate backfill) of high-quality granular fill and (2) closely 

spaced layers of reinforcement (less than or equal to 12 inches (304.8 mm)).(16)
13

Basic design guidelines for GRS foundations are available that outline recommended spacing 

along with length and depth of reinforcement layers for pier foundations and abutment 

supports.

(32,40) The work is largely based on load tests on reinforced soil shallow foundations and 

performance tests (PTs) on abutment supports.

(41,22,42) However, the design guidelines are limited 

to the conditions and parameters under which testing has occurred. While recent FHWA research 

has added to the database and provided recommendations on methods to limit deformations to a 

target value, quantifying the vertical and lateral deformations is still empirically based.

(42)

2.4 CURRENT SLS CRITERIA FOR BRIDGE SUPPORTS

In general, foundation movement criteria should be consistent with the function and type of 

structure, anticipated service life, and consequences of unacceptable movements on structure 

performance. Specifications and reports published by FHWA, AASHTO, and some State 

transportation departments provide criteria for the settlement of shallow foundations of bridges 

and vertical and horizontal deformations of bridge abutments and piers. The following section 

summarizes the current SLS criteria for bridge supports using shallow foundations.

Criteria for Settlement of Shallow Foundations of Bridges

According to section 11 in AASHTO LRFD Bridge Design Specifications, “Abutments, piers, and 

walls shall be investigated for excessive vertical and lateral displacement, and overall stability, at 

the service limit state.”(8) The vertical settlements of bridge foundations can be expressed in 

terms of angular distortion, which is defined as the differential settlement divided by span 

length. Uneven displacements of bridge abutments and pier foundations can affect the ride 

quality, functioning of deck drainage, and the safety of the traveling public as well as the 

structural integrity and aesthetics of the bridge. Such movements often lead to costly 

maintenance and repair measures.

(10) Table 3 shows the criteria from various reports. 

Three different reports show the same criteria for the angular distortion for continuous span 

bridges, while the criteria for the angular distortion for simple span bridges vary.

Table 3. Criteria for settlement of shallow foundations of bridges.

Aspects Used for 

Settlement 

Evaluation

Source

Moulton et al. and 

Elias et al.(43,36) Moulton et al.(44)

AASHTO LRFD Bridge 

Design Specifications(8)

(based on Moulton et al., 

DiMillio, and Barker et 

al.(44,2,45))

Maximum angular 

distortion for 

continuous span 

bridges

0.004 0.004 0.004

Maximum angular 

distortion for simple

span bridges

0.005 0.007 0.008

WSDOT provided the differential settlement criteria and the associated action based on the total 

settlement. Table 4 lists the settlement criteria for pier and abutment.(46)
14

Table 4. WSDOT settlement criteria for bridge piers and abutments.

(46)

Total Settlement at 

Pier or Abutment

( H)

Differential Settlement 

100 ft within Pier or 

Abutment and between Piers

( H100) Action

H 1 inch H100 10.75 inches Design and construct the bridge 

foundation, since criteria are met.

1 inch < H 4 inches 0.75 inches < H100 3 inches Ensure structure can tolerate 

settlement.

H > 4 inches H100 > 3 inches Obtain approval* prior to proceeding 

with design and construction.

1 ft = 0.305 m

1 inch = 25.4 mm

*Approval of WSDOT State Geotechnical Engineer and WSDOT Bridge Design Engineer required.

Chapter 10 of Arizona Department of Transportation’s (ADOT) Bridge Design Guidelines states

the following:

“The bridge designer should limit the total settlement of a foundation per 30 m 

(100 ft) span to 13 mm (0.5 in). Linear interpolation should be used for other span 

lengths. Higher total settlement limits may be used when the superstructure is 

adequately designed for such settlements. The designer shall also check other 

factors such as rideability and aesthetics. Any total settlement that is higher than 

2.5 in, per 30 m (100 ft) span, must be approved by the ADOT Bridge Group.”(47)

Through tolerable movement analysis of 148 highway bridges supported by spread footings on 

compacted fill throughout Washington, an FHWA report concluded that these bridges have easily 

tolerated differential settlement of 1 to 3 inches (25.4 to 76.2 mm) without serious distress.

(2)

Based on field studies of 314 bridges and theoretical analyses, Moulton et al. found that the 

bridges that performed acceptably had average settlement of 2 inches (50.8 mm).(43)

Tolerable Horizontal Deformation Criteria for Bridge Supports

Horizontal deformations cause more severe and widespread problems for highway bridge 

structures than do equal magnitudes of vertical movement.

(10) The data presented by 

Moulton et al. also show that horizontal movements resulted in more damage when accompanied 

by settlement than when occurring alone.

(44) Tolerance of the superstructure to horizontal 

(lateral) movement depends on bridge seat or joint widths, bearing type(s), structure type, and 

load distribution effects. Moulton et al. found that horizontal movements less than 1 inch 

(25.4 mm) were almost always tolerable, while horizontal movements greater than 2 inches

(50.8 mm) were typically considered to be intolerable.

(44) Wahls states, “Horizontal movements 

in excess of 2 inches (50 mm) appear likely to cause structural distress.”(48) Moulton et al. 

recommends that horizontal movements be limited to 1.5 inches (38.1 mm).

(40) Similarly, surveys 

of the performance of bridges by Bozozuk, Walkinshaw, and Wahls also indicate that horizontal 

abutment movements less than 1.5 inches (38.1 mm) can usually be tolerated by bridge 

superstructures without significant damage.(49–51)

D D
15

On the other hand, abutments are often designed for active lateral earth pressure conditions, 

which require a certain amount of movement. 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. Samtani and Nowatzki recommends that, “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.”(Chapter 8, pp. 69)(18)

Tolerable Deformation Criteria for Reinforced Bridge Supports

MSE walls can tolerate larger total and differential vertical deflections than rigid walls. The 

amount of total and differential vertical deflections that can be tolerated depends on the wall 

facing material, configuration, and timing of facing construction.

(8) AASHTO states that 

abutments should not be constructed on MSE walls if the anticipated angular distortion is greater 

than 50 percent of the values recommended by Moulton et al. as shown in table 3.

(52,44) For GRS 

abutment, the vertical strain should be limited to 0.5 percent unless the engineer decides to 

permit additional deformation, and the lateral strain should be limited to 1 percent.

(32)

17

CHAPTER 3. LITERATURE REVIEW OF PREVIOUS WORK IN ENGINEERED 

FILLS FOR BRIDGE SUPPORTS

3.1 OVERVIEW OF LOAD DEFORMATION DATA CATALOG OF ENGINEERED 

FILLS FOR BRIDGE SUPPORTS

Various factors may affect the behavior of bridge supports using engineered fills. They include

the following:

Backfill soil types, unit weight, and strength parameters.

Geosynthetic type and ultimate tensile strength (Tf).

Reinforcement spacing, total depth of reinforcement placement (N), and horizontal length 

(extent) of reinforcement.

Bridge support geometry.

Foundation shape and size.

GRS foundation soil type, density, strength parameters, and reinforcement.

Natural soil type, unit weight, and strength parameters beneath the GRS foundation.

Loading condition.

Ambient temperature range.

Effect of transient load versus static load on SLS of bridge supports.

The performance of bridge supports using engineering fills can be characterized by

the following:

Load bearing resistance (a check corresponding to ultimate limit state (ULS)).

Immediate and long-term vertical and horizontal deformations of the reinforced and 

foundation soils (components of SLS design).

In this chapter, the factors that affect the behaviors of shallow foundations are synthesized based 

on the published results in the literature. They include factors affecting the settlement of shallow 

foundations with and without reinforcement and factors affecting vertical and lateral 

deformations of bridge piers and abutments using engineered fills. Further, the effects of 

transient loads on deformations of bridges supports on granular soils and the determination of 

stress distributions in granular soils under shallow foundations are reviewed. Based on the 

literature review, a load-deformation data catalog was compiled into an unpublished Microsoft®

Excel spreadsheet.
18

3.2 SYNTHESIS OF FACTORS AFFECTING SETTLEMENT OF SHALLOW 

FOUNDATIONS 

Effect of Relative Density of Soil on Settlement of Shallow Foundations

Fragaszy and Lawton performed a series of laboratory model tests designed to determine the 

influence of soil relative density (DR) on the load-settlement behavior of reinforced sand.

(53) The 

uniformly graded native sand was reinforced with three layers of aluminum foils in all tests. As

figure 5 shows, in all cases, the ultimate bearing capacity increased with increasing DR. 

Additionally, the load-settlement behavior of the strip footings on reinforced soil was stiffer than 

those bearing on unreinforced soil at the same relative density. The results show that with a

10 percent increase in DR, at 14.5 psi (100 kPa) pressure, the settlement of the foundation 

decreased by about 20 percent. By reinforcing the soil, the ultimate bearing capacity of the 

foundation increased at least 60 percent at a ratio of settlement of foundation to its width (s/B) of 

10 percent. Note that the increase in confinement with the addition of reinforcement layers 

suppressed the dilative behavior, as observed through the suppressed peak in load-settlement 

response. Basudhar et al. conducted an experimental study on circular footings resting on sand 

reinforced with geotextiles.

(54) They concluded that the immediate settlement of the foundation 

decreased with an increase in DR (see figure 6).

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Fragaszy and Lawton.(53)

Figure 5. Graph. Load-settlement results on unreinforced and reinforced sand.

0

5

10

15

20

25

0 50 100 150 200 250 300 350 400

Normalized Settlement s/B (%)

Bearing Pressure (kPa)

Dr=51% (Unreinforced Soil)

Dr=51% (Reinforced Soil)

Dr=61% (Unreinforced Soil)

Dr=61% (Reinforced Soil)

Dr=70% (Unreinforced soil)

Dr=70% (Reinforced Soil)

Dr=80% (Unreinforced Soil)

Dr=80% (Reinforced Soil)

Dr=90% (Unreinforced Soil)

Dr=90% (Reinforced Soil)
19

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Basudhar et al.(54)

Figure 6. Graph. Load-settlement results for different relative densities.

Effect of N on Settlement of Shallow Foundations

Omar et al. conducted a series of laboratory model tests on strip and square foundations 

supported by sand reinforced with geogrid layers.

(55) As their results in figure 7 and figure 8

show, for similar values of applied load, the settlement of footings bearing on reinforced soil was 

lower than that on unreinforced soil. For tests with a strip foundation, when N increased from 1 

to 3, the ultimate bearing load doubled, while the settlement at its respective ultimate load also 

almost doubled. At each applied pressure, the amount of settlement decreased with increasing N.

for N greater than or equal to 4, the settlement at ultimate bearing load remained practically 

constant, indicating there is an optimum N beyond which the settlement at ultimate bearing load 

has insignificant improvement. It should be considered that based on the study by Omar et al.,

the effective depth of reinforcement is about 2B for strip foundations.

(55) Therefore, in their

experiment, by having u/B = h/B = 0.33 (the notations are shown in figure 4), reinforcements 

with N greater than or equal to 7 are placed out of the influence zone.

0

5

10

15

20

25

0 50 100 150 200

Footing Settlement (mm)

Vertical Stress (kPa)

Dr=45%

Dr=73%

Dr=84%
20

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Omar et al.(55)

Figure 7. Graph. Load-settlement results for strip footing for u/B = h/B = 0.333, b/B = 10.

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Omar et al.(55)

Figure 8. Graph. Load-settlement results for square footing for u/B = h/B = 0.333, b/B = 6.

Chen et al. investigated the behavior of square foundations on geosynthetic-reinforced clayey 

soil with a PI of 15 percent using laboratory model footing tests.(56) The model footings used in 

the tests were steel plates with dimensions of 5.98 by 5.98 by 1 inch (152 by 152 by 25.4 mm) 

(width by length by thickness). The model tests were conducted in a 4.92- by 2.98- by 2.98-ft

(1.5- by 0.91- by 0.91-m) (length by width by depth) steel test box. The testing procedure was 

0

5

10

15

20

0 50 100 150 200 250 300 350 400

Footing Settlement (mm)

Bearing Pressure at the Footing Base (kPa)

N=1

N=2

N=3

N=4

N=5

N=6

N=7

0

1

2

3

4

5

6

0 50 100 150 200 250

Footing Settlement (mm)

Bearing Pressure at the Footing Base (kPa)

N=1

N=2

N=3

N=4

N=5

N=6
21

performed according to the ASTM D 1196-93, where the load increments were applied and 

maintained until the rate of settlement was less than 0.001 inch/min (0.03 mm/min) for 3 min 

consecutively.(57) The results, plotted in figure 9, show that by increasing N, the amount of 

settlement at each applied pressure decreased up to N = 4. For N greater than or equal to 4, 

settlement of square foundations did not increase with additional reinforcement layers. This 

again indicates there is an optimum N beyond which the settlement has insignificant 

improvement. It should be noted that based on Chen et al., the effective depth of reinforcement 

is about 1.5B for geogrid reinforced clay.(56) Therefore, in the experiment by Chen et al., by 

having u/B = h/B = 0.33, reinforcements with N greater than or equal to 7 are placed out of the 

influence zone.(56)

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Chen et al.(56)

Figure 9. Graph. Load-settlement results for square footing on unreinforced and 

reinforced soil with polypropylene (PP) geogrid layers.

Das et al. conducted laboratory model tests to investigate the ultimate bearing capacity of surface 

strip foundations on geogrid reinforced sand and clay.

(58) Each foundation was made of an 

aluminum plate with dimensions of 3 by 12 inches (76.2 by 304.8 mm) (B × L). Bearing capacity 

tests were conducted in two boxes, each with internal dimensions of 3.61 by 0.98 by 2.95 ft 

(1.1 by 0.3 by 0.9 m) (length by width by depth). The results show that the inclusion of geogrid 

reinforcement increased the load per unit area that could be carried by a foundation at any given 

settlement level. This is true for the tests in both sand and clay. As figure 10 shows, the 

foundation settlement decreased with the increase of reinforcement layer until N = 5. When 

N was greater than 5, the foundation settlement no longer decreased with an increase of the 

reinforcement layers. The results may be due to the fact that additional reinforcement layers 

were placed below the effective depth of reinforcement that was about 2B for strip footing in 

sandy soil.

0

10

20

30

40

50

0 500 1000 1500 2000

Footing Settlement (mm)

Bearing Pressure at the Footing Base (kPa)

Unreinforced

N=1

N=2

N=3

N=4

N=5
22

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Das et al.(58)

Figure 10. Graph. Load-settlement results for sandy soil for u/B = 0.4, h/B = 0.33,

and b/B = 4.

Basudhar et al. conducted an experimental study on circular footings resting on sand reinforced 

with geotextiles.

(54) They concluded that with an increase in N, the settlement gradually 

decreased in rate. As figure 11 shows, when N is greater than or equal to 2, the foundation 

settlement no longer decreased with an increase of the reinforcement layers, with the exception 

of the settlement at ultimate capacity. For the test with three layer of reinforcement, the 

geotextile was placed at depths of 0.25B, B, and 2B below the base of the footing. By 

considering the results presented in section, the effective depth of reinforcement was less than 2B

for square foundation; therefore, layer 3 and the additional layers were placed outside the 

influence zone and no longer affected the foundation settlement.

0

5

10

15

20

0 5 10 15 20 25 30

Footing Settlement (mm)

Bearing Pressure at the Footing Base (kPa)

Unreinforced

N=1

N=2

N=3

N=4

N=5

N=6
23

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Basudhar et al.(54)

Figure 11. Graph. Load-settlement results for 1.18-inch (30-mm)-diameter circular footing.

Phanikumar el al. performed a series of laboratory plate load tests on geogrid reinforced sand 

beds.(59) Properties of the test sands are presented in table 5. Figure 12 shows that at certain 

settlements, the bearing load needed to reach that settlement was also affected by N and 

soil types.

Table 5. Properties of test sands.

(59)

Property Fine Sand Medium Sand Coarse Sand

Dry unit weight (at DR = 50 percent) 

(kN/m3)

15.2 14.9 14.7

Maximum aggregate size (dmax) (mm) 0.425 2.36 4.75

Particle diameter at which 10 percent of 

the sample is finer, by mass (D10) (mm)

0.25 0.59 1.3

Internal * (degree) 32 35 40

Coefficient of uniformity 1.4 1.995 2.07

Coefficient of curvature 1.17 1.12 1.25

1 kN/m3 = 6.37 lbf/ft3

1 inch = 25.4 mm

*The internal of the test sands was determined by performing direct shear tests. The test sands were

compacted at their respective dry unit weights corresponding to a relative density of 50 percent.

0

5

10

15

20

0 20 40 60 80 100 120

Footing Settlement (mm)

Bearing Pressure at the Footing Base (kPa)

Unreinforced

N=1

N=2

N=3
24

1 lbf = 0.0044 kN

Note: This figure was created by FHWA after Phanikumar et al.(59)

Figure 12. Graph. Effect of number of geogrids on the load required for a settlement of 

0.02 inch (0.5 mm).

Results of the effect of different numbers of reinforcement on the behavior of foundation 

placed on reinforced sand with phosphor-bronze layers are plotted in figure 13.

(60) The results 

also show the decreasing trend of settlement with the increasing N at two ratios of reinforcement:

L versus B.

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Huang and Tatsuoka.(60)

Figure 13. Graph. Load-settlement results for different numbers of metallic reinforcement.

0

0.04

0.08

0.12

0.16

1 2 3 4

Load (kN)

N

Medium Sand

Fine sand

Coarse sand

0

2

4

6

8

10

12

14

16

0 50 100 150 200 250 300 350

Settlement (mm)

Applied Pressure (kPa)

N=1 (L/B=6)

N=2 (L/B=6)

N=3 (L/B=6)

N=1 (L/B=1)

N=2 (L/B=1)

N=3 (L/B=1)
25

Effect of L and Tf of Reinforcement on Settlement of Shallow Foundations

Results from laboratory model tests conducted by Latha and Somwanshi are plotted in 

figure 14.

(61) The results show that with an increase in b, the magnitude of ultimate bearing 

capacity of foundations on reinforced soil increased, and settlement decreased.

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Latha and Somwanshi.(61)

Figure 14. Graph. Load-settlement results for different widths of geonet (N = 4, d = 2B).

Elton and Patawaran conducted an experimental study on reinforced soil specimens to evaluate 

the effects of Tf of geotextiles on the stress-strain relationship of reinforced soil.(62) The 

properties of the six geotextile used in their experiments are presented in table 6. Figure 15

shows the unconfined compression test results. Three transducers on top of the steel loading 

plate measured vertical displacements. As the results show, the curve initially reached its peak 

strength at approximately 3 to 8 percent strain, had a decrease in some strength, and then 

gradually increased back to reach a second peak before finally decreasing sharply. The 

peak strength and the corresponding strain of the specimens increased as reinforcement 

strength increased.

Table 6. Geotextile properties.(62)

Property

Geotextile Type (G)

G4 G6 G8 G12 G16 G28

Mass per area (g/m2) 135.64 203.46 271.28 406.92 542.56 949.48

Wide-width machine 

direction strength (kN/m)

9.0 14.0 14.5 18.6 20.1 24.9

Wide-width cross-machine 

direction strength (kN/m)

14.4 19.3 19.8 20.3 22.9 21.7

1 g/m2 = 2.05 10-4 lb/ft2

1 kN/m = 68.5 lbf/ft

0

5

10

15

20

0 100 200 300 400 500 600 700

Normalized Settlement s/B (%) 

Bearing Pressure at the Footing Base (kPa)

unreinforced

b/B=4

b/B=5

b/B=5.93
26

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Elton and Patawaran.(62)

Figure 15. Graph. Stress-strain relationship of reinforced soil.

Adams and Collin conducted five laboratory experiments on reduced-scale piers as part of an

FHWA research project.

(41) Of the five experiments, one was unreinforced, and the others were 

reinforced with different reinforcement spacing and Tf. As the results in figure 16 show, the 

specimen with spacing of 0.66 ft (0.2 m) and lower wide width strength of 1,439 lbf/ft (21 kN/m)

could withstand higher stresses compared to the specimen with 1.31-ft (0.4-m) spacing and 

higher wide width strength of 4,797 lbf/ft (70 kN/m) at any given strain. Therefore, they 

concluded that the reinforcement spacing played a more important role than the 

reinforcement strength.

0

100

200

300

400

500

600

0 5 10 15 20 25 30

Stress (kPa)

Vertical Strain (Percent)

G4

G6

G8

G12

G16

G28
27

1 psi = 6.89 kPa

1 kN/m = 68.5 lbf/ft

1 ft = 0.305 m

Note: This figure was created by FHWA after Adams and Collin.(41)

Figure 16. Graph. Stress-strain relationship of the mini-pier experiments.

Abu-Hejleh et al. conducted an assessment of the new Founders/Meadows Bridge near Denver, 

CO, which was completed in July 1999.

(63,64) The study focused on the performance and behavior 

of the GRS system under service loads. Three sections of the GRS system were instrumented to 

measure movements of the front GRS wall, settlement of the bridge footing, and differential 

settlements between the bridge abutment and the approaching roadway. The backfill soil used in 

this project was a mixture of gravel (35 percent), sand (54.4 percent), and fine-grained soil 

(10.6 percent). The backfill soil was classified as well-graded silty sand per ASTM D 2487 and 

as stone fragments, gravel, and sand (A-1-B (0)) per AASHTO M145-91.

(65,66) The average unit 

weight and dry unit weight of the compacted backfill soil as measured during construction were

140.6 and 133.7 lb/ft3 (22.1 and 21 kN/m3

), respectively, and the water content was 5.6 percent. 

Results of large direct shear and large triaxial tests showed a of 47.7 and 39.5 degrees and c of 

16.06 and 5.73 psi (110.7 and 39.5 kPa), respectively, for the direct shear and triaxial tests. Three 

grades of geogrid reinforcements were used in this project: uniaxial (UX) 6 below the foundation 

and UX 3 and UX 2 behind the abutment wall. Table 7 summarizes the ultimate strength and the

long-term design strength (LTDS) for these geogrids.

Table 7. Placed geogrid strength.

(64)

Geogrid Type 

and Notation

Ultimate Strength 

(kN/m)

LTDS 

(kN/m)

UX 6 157.3 27

UX 3 64.2 11

UX 2 39.3 6.8

1 kN/m =68.5 lbf/ft

0

100

200

300

400

500

0 1 2 3 4 5 6 7

Stress (kPa)

Strain (Percent)

Unreinforced

T=70 kN/m, S=0.4 to 0.6 m

T=70 kN/m, S=0.4m

T=21 kN/m, S=0.2 m

T=70 kN/m, S=0.2m
28

Data were collected during construction of the GRS walls, during placement of the bridge 

superstructure, and during the 18 mo after opening the bridge to traffic. The results are presented 

in table 8 and show excellent performance of the GRS structure. The monitored overall 

displacements were smaller than those expected in the design and allowed by performance 

requirements, there were no signs for development of the bridge bump problem or of any 

structural damage, and post-construction movements became negligible within a year after 

opening the bridge to traffic. 

Table 8. Summary of the maximum displacements of the front wall facing and of the 

settlements of the bridge abutment footing.

Types of Maximum 

Movements

Induced 

Only by GRS

Wall 

Construction

Induced Only 

by Placement 

of Bridge 

Superstructure 

(115-kPa

Surcharge)

Induced Only While 

Bridge in Service 

(150-kPa Surcharge)

6 Mo 12 Mo 18 Mo

Maximum outward displacement 

of the front wall facing (mm)

12 10 8 12 13

Maximum settlement of the 

leveling pad supporting the front 

wall facing (mm)

8 7 4 5 5

Maximum bridge abutment 

footing settlement (mm)

13 7 11 10

Percent maximum settlement of 

bridge abutment of wall height 

(percent)

0.29 0.17

1 kPa = 0.145 psi

1 inch = 25.4 mm

Note: This table was created by FHWA after Abu-Hejleh et al.(64) Blank cells indicate no value was recorded.

Huang and Tatsuoka used different types of metal strips to reinforce the soil beneath a shallow 

foundation.

(60) Figure 17 shows the results from laboratory model tests reinforced with phosphorbronze strips. The results show that with an increase in L, the magnitude of the settlement in each 

applied load decreased. However, this decrease was not proportional to the increase in L. For 

example, under 4,177 psf (200 kPa) of applied pressure, the settlement of the foundation was the 

same for two different reinforcement lengths of L/B = 3.5 and L/B = 6. 
29

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Huang and Tatsuoka.(60)

Figure 17. Graph. Load-settlement results for different reinforcement lengths (N = 3).

Effect of B on Settlement of Shallow Foundations

Das and Omar conducted an experimental study on surface strip foundations on geogridreinforced sand.

(67) As shown in figure 18, they concluded that the settlement at the ultimate 

bearing capacity increased with a decrease in B. The figure also revealed insignificant effects of 

footing size on settlement under bearing pressures less than approximately 6,266 psf (300 kPa). 

It is noted that these observations were obtained in small-scale experiments.

0

2

4

6

8

10

12

14

16

0 100 200 300 400

Settlement (mm)

Applied Pressure (kPa)

L/B=1

L/B=2

L/B=3.5

L/B=6
30

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Das and Omar.(67)

Figure 18. Graph. Load-settlement results in reinforced sand (DR = 75 percent).

Effect of Embedment Depth of Top Reinforcement Layer on Settlement of Shallow 

Foundations

Mandal and Sah conducted bearing capacity tests on model footings on clay subgrades 

reinforced with geogrids.

(68) Their results, plotted in figure 19, show that the maximum 

percentage reduction in settlement with the use of geogrid reinforcement within the compacted 

and saturated clay was about 45 percent, and it occurred at a depth of 0 to 0.25B below the base 

of the square foundation.

0

5

10

15

20

25

30

35

0 100 200 300 400 500

Footing Settlement (mm)

Bearing Pressure at the Footing Base (kPa)

B=50.8 mm

B=76.2mm

B=101.6

mm
31

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Mandal and Sah.(68)

Figure 19. Graph. Load-settlement results of model footings on clay subgrade reinforced 

with geogrid.

Binquet and Lee conducted a series of experiments on strip footing 2.99 inches (76 mm) wide 

placed on sandy soil reinforced with metal strips.

(69) Figure 20 shows the results of the studies on 

the effect of u of the top reinforcement layer on the settlement of a foundation. They concluded 

that the optimum location of the top layer was at u/B = 1.3. Furthermore, based on experimental 

results obtained from foundations placed on reinforced soil with geogrid, it was concluded that 

the optimum depth for placing the top layer of reinforcement was within 0.25B below the base of 

the foundation. Therefore, the top layer of the metal strip could be located at a lower depth 

compared to geogrid reinforcement in order to have the minimum amount of settlement under 

each applied load.

0

5

10

15

20

25

30

0 50 100 150 200 250

Normalized Settlement s/B (Percent) 

Bearing Pressure at the Footing Base (kPa)

Unreinforced

u/B=1

u/B=0.75

u/B=0.5

u/B=0.25

u/B=0.0
32

1 inch = 25.4 mm = 2.54 cm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Binquet and Lee.(69)

Figure 20. Graph. Load-settlement results for different depth of top layer of metallic 

reinforcement (N = 3).

Effect of Vertical Spacing of Reinforcement (Sv) Layers on Settlement of Shallow 

Foundations

Chen et al. investigated the behavior of square foundations on geosynthetic reinforced clayey soil 

of low to medium plasticity using laboratory model footing tests.

(56) As figure 21 shows, by 

decreasing h between the three reinforcement layers (placed within the zone of influence below 

the footing), the amount of settlement at each applied load pressure decreased.

0

1

2

3

4

5

6

7

8

0 50 100 150

Settlement (mm)

Applied Pressure (kPa)

Unreinforced

u=2.5 cm

u=5.1 cm

u=7.6 cm

u=10.2 cm

u=12.7 cm
33

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Chen et al.(56)

Figure 21. Graph. Load-settlement results for square footing tests with three layers of 

geogrids placed at different vertical spacing.

Effect of Covering Ratio (CR) of Metallic Strip Reinforcement on Settlement of Shallow 

Foundations

An effective parameter for the load-settlement behavior of foundation on soil reinforced with 

metallic strips is the CR of reinforcement in each layer. Figure 22 shows the experimental results 

of the settlement of a foundation placed on reinforced soil with phosphor-bronze strip layers.

(60)

The figure shows by increasing CR, the settlement at each applied pressure decreases. From the 

results, it can be concluded that the decrease in settlement was not proportional to CR. This 

suggests that there is an upper bound in CR, above which a decrease in settlement with the 

increase in CR may not be expected. 

0

5

10

15

20

25

30

35

40

45

0 500 1000 1500 2000

Footing Settlement (mm)

Bearing Pressure at the Footing Base (kPa)

Unreinforced

h=102mm, N=3

h=76mm, N=3

h=51mm, N=3

h=25mm, N=3
34

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Huang and Tatsuoka.(60)

Figure 22. Graph. Load-settlement results for different CRs of reinforcement 

(L = 2B, N = 3).

3.3 SYNTHESIS OF LOAD DEFORMATION RELATIONSHIPS OF BRIDGE 

ABUTMENTS AND PIERS

Effect of Soil Parameters on Load Deformation Relationships

Adams and Nicks conducted an experimental study to investigate secondary deformation 

characteristics of GRS as bridge piers under service load conditions.

(27) Load-settlement 

behaviors of four GRS piers built using two types of soils and woven geotextiles were monitored 

under 30.45 psi (210 kPa) of pressure. The characteristics of the materials used and results 

presented by Adams and Nicks are shown in table 9.

(27) The results show that under service load

conditions, there was no significant increase in settlement for the pier with the weak geotextile

(pier A). Also, the piers with open-graded #8 aggregates experienced slightly more compression

(about 5 percent higher) compared to well-graded A-1-a backfill soil. The results from the pier 

deformation survey over 4 mo indicated that secondary settlement occurred in granular material, 

but it was still within typical tolerable limits for bridges of up to 2 percent vertical strain over the 

life of the bridge.

(32)

0

2

4

6

8

10

12

14

16

0 50 100 150 200 250

Settlement (mm)

Applied Pressure (kPa)

Unreinforced

CR=4.5%

CR=9%

CR=18%
35

Table 9. GRS pier materials and results recorded from vertical deformation survey.

Measurement

Categories

Material Properties and 

Specific Field Surveys Pier A Pier B Pier C Pier D

Backfill material 

properties 

AASHTO soil type #8 A-1-a A-1-a #8

(degrees) 55 54 54 55

c (kPa) 0 5.5 5.5 0

Reinforcement 

properties 

Tf (kN/m) 35 70 70 70

Minimum average roll 

value strength at 2 percent 

strain (kN/m)

3.5 19.3 19.3 19.3

Survey results 

GRS composite settlement 

105 days after load 

placement (mm)

24 23.6 22.5 24.8

Vertical strain in GRS 

composite (percent)

1.03 1.01 0.97 1.07

1 psi = 6.89 kPa

1kN/m = 68.5 lbf/ft

1 inch = 25.4 mm

Note: This table was created by FHWA after Adams and Nicks.(27)

Nicks et al. conducted 19 GRS PTs as a part of FHWA research that investigated axial load 

versus vertical deformation characteristics of GRS piers.

(42) A total of 5 tests were conducted at 

the Defiance County (DC), OH, highway maintenance facility, and 14 were conducted at the 

Turner-Fairbank Highway Research Center (TFHRC). The parameters that varied among tests 

were reinforcement spacing, geotextile strength, soil type, and frictionally connected facing 

element. The parameters of piers tested to investigate the effect of aggregate type on loaddeformation characteristics of the piers and the test results are shown in table 10 and figure 23. 

The applied pressure was calculated as the average of the measured values over the period of 

loading, and the vertical strain was calculated as the averages of the four linear voltage 

displacement transducers (LVDTs) and potentiometers (POTs) located on the footing at the end 

of each load increment. Based on the results, the pier built with the largest aggregate tested 

(#57 stone) had the lowest service limit of all the tests, indicating more deformation under an 

applied load. In addition, the pier built with rounded pea gravel had a lower strength and service 

limit than the more angular aggregate meeting the same gradation specifications for an 

AASHTO #8 material.
36

Table 10. Parametric study on aggregate size.

Test 

No.

Backfill Reinforcement

Type (degree) Facing

cc

(kPa)

Aggregate 

Size

(mm)

Tf

(kN/m)

Sv

(mm)

DC-1 8 54 0 12.7 70 194 CMU

DC-2 8P 46 0 19.05 70 194 CMU

DC-3 57 52 0 25.4 70 194 CMU

DC-4 9 49 0 9.525 70 194 CMU

1 psi = 6.89 kPa

1kN/m = 68.5 lbf/ft

1 inch = 25.4 mm

CMU = Concrete Masonry Unit.

Note: This table was created by FHWA after Nicks et al.

(42)

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Nicks et al.(42)

Figure 23. Graph. Load-deformation behavior from PTs on GRS piers using five types of 

DC backfills.

By comparing identical piers that were similar in all of their characteristics except their 

gradation, Nicks et al. concluded that the use of well-graded material resulted in a considerably 

stiffer load-deformation response than that observed when open-graded material was used.(42)

Helwany et al. conducted finite element analyses (FEAs) of two full-scale loading tests on GRS 

bridge abutments and performed a parametric study to investigate the performance of the 

modular block facing of GRS bridge abutments subjected to live and dead loads from the bridge 

superstructure.

(70) They concluded that more favorable deformation response was attained when 

using soil types that have higher internal and corresponding higher bulk and shear moduli. 

figure 24 shows that when increased from 34 to 40 degrees, the vertical displacement at the 

abutment seat decreased from 1.89 to 1.18 inches (48 to 30 mm) at applied pressure of 4,177 psf 

f

0

1

2

3

4

5

6

7

8

9

0 200 400 600 800 1000 1200 1400

Vertical Strain (Percent)

Applied Pressure (kPa)

DC-1

DC-2

DC-3

DC-4
37

(200 kPa), while vertical displacement showed little variation at a lower applied pressure of

2,088 psf (100 kPa).

1 inch = 2.54 cm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Helwany et al.(70)

Figure 24. Graph. Effects of backfill internal on vertical displacement at abutment seat 

(reinforcement spacing = 7.87 inches (20 cm)).

Helwany et al. also concluded that by using soil types that had higher internal and higher bulk 

and shear moduli, a more favorable deformation response was attained for horizontal 

displacement at the abutment seat and for maximum lateral displacement of the segmental facing 

(see figure 26).(70) At applied pressure of 4,177 psf (200 kPa), by increasing the internal from 

34 to 40 degrees, the horizontal displacement at seat decreased by about 14 percent. As figure 26

shows, at different applied pressures, the maximum lateral displacement of the segmental facing 

decreased in a linear manner with increasing .

0

5

10

15

34 37 40

Vertical Displacement at Seat 

(cm)

Backfill Internal (degrees)

100 kPa

200 kPa

400 kPa

f

f
38

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Helwany et al.(70)

Figure 25. Graph. Effects of backfill internal (reinforcement spacing = 7.87 inches 

(20 cm)) on horizontal displacement at abutment seat.

1 inch = 2.54 cm

Note: This figure was created by FHWA after Helwany et al.(70)

Figure 26. Graph. Effects of backfill internal (reinforcement spacing = 7.87 inches 

(20 cm)) on the maximum lateral displacement of the facing.

Hatami and Bathurst investigated the influence of backfill type on the performance of reinforced 

soil segmental retaining walls (SRWs) under working stress conditions at the end of construction 

(EOC) using a finite difference numerical modeling.

(71) As figure 27 shows, facing deflections 

diminished in magnitude as soil shear strength increased due to an increase in , an increase in 

apparent c, or both. The pattern of deflected shape was also influenced by the increase of

0

10

20

30

40

50

60

34 37 40

Horizontal Displacement at Seat 

(mm)

Backfill Internal (degrees)

100 kPa

200 kPa

400 kPa

f

f

0

5

10

15

34 37 40

Maximum Facing 

Displacement (cm)

Backfill Internal (degrees)

self weight

100 kPa

200 kPa

400 kPa

f

f
39

apparent c. An increase of apparent c moved the location of maximum wall deflection lower 

down the wall and was particularly effective in reducing deflections at the wall crest. The results 

also show the different influences of and c. 

1 ft = 0.305 m

1 inch = 2.54 cm

Note: This figure was created by FHWA after Hatami and Bathurst.(71)

Figure 27. Graph. Influence of apparent c and on lateral displacement of the wall.

Results plotted in figure 28 show that reinforcement loads were greater for the walls with weaker 

backfills, and the distribution of maximum load along the wall height varied between a parabolic 

shape for granular backfill and a linear shape when the backfill had higher value of apparent c 

and was more cohesive.(71)

0

1

2

3

4

5

6

7

0 2 4 6 8 10 12

Elevation (m)

Lateral Displacement (cm)

φ=30°, c=10 kPa

φ=20°, c=10 kPa

φ=40°, c=1 kPa

φ=30°, c=1 kPa

f
40

1 ft = 0.305 m

1kN/m = 68.5 lbf/ft

Note: This figure was created by FHWA after Hatami and Bathurst.(71)

Figure 28. Graph. Influence of backfill apparent c and values on maximum 

reinforcement loads in wall models at EOC.

Skinner and Rowe numerically investigated the short- and long-term behaviors of a 19.68-ft 

(6-m)-high segmental block-faced geosynthetic reinforced retaining wall constructed on a rigid 

base; they also studied two 32.8-ft (10-m)-thick clayey foundations to investigate the effect of 

yielding in the foundation on the stability of the wall.

(72) The horizontal displacements of the wall 

face calculated for the rigid foundation and the two clayey foundations are plotted in figure 29. 

Clayey foundations are significantly more compressible than the rigid foundation. The figure

shows that the deformations at the face and base of the wall were considerably higher for 

soils 1 and 2 than for the rigid foundation. The increased foundation deformation contributed 

significantly to the facing displacement. For the lower viscosity soil 1, there was no significant 

change in behavior between the time of 95 percent consolidation (reached 1 year after EOC) and 

subsequent time (e.g., 7 years). The more viscous soil 2 reached approximately 20 percent

consolidation 1 year after EOC and approximately 95 percent consolidation 7 years after EOC. 

The slight backward rotation of the wall face from EOC to 7 years (95 percent consolidation) for 

soil 1 was caused by local displacements at the face and especially at the toe of the wall.

0

1

2

3

4

5

6

7

0 2 4 6 8 10

Elevation (m)

Load Within Reinforced Soil Zone (kN/m)

φ=30°, c=10 kPa

φ=20°, c=10 kPa

φ=40°, c=1 kPa

φ=30°, c=1 kPa

f
41

1 ft = 0.305 m

1 inch = 25.4 mm

Note: This figure was created by FHWA after Skinner and Rowe.(72)

Figure 29. Graph. Horizontal displacements at wall face.

Helwany et al. conducted FEAs to investigate the effect of backfill type and reinforcement 

strength on the behavior of GRS retaining walls.

(73) A total of 3 different reinforcement stiffness 

values and 16 different backfill materials were implemented in the analyses of 3 walls with 

different heights to produce 144 analysis combinations. The GRS retaining walls were under 

15.23-psi (105-kPa) surcharge pressure. The dimensions and the properties of the different soils

are presented in table 11 and table 12, and the results are plotted in figure 30 through figure 33.

Table 11. GRS retaining wall dimensions.

Wall Height 

(m)

Depth of 

Backfill (m)

Length of 

Geotextile (m) N

3 3.7 1.8 10

4.5 5.5 2.7 15

6 7.3 3.7 20

1 ft = 0.305 m

Note: This figure was created by FHWA after Helwany et al.(73)

10

11

12

13

14

15

16

0 50 100 150 200

Hight Above Top of Foundation (m)

Horizontal Displacement (mm)

Rigid foundation

soil1 at End of Construction

soil 2 at End of Construction

Soil 1 after 1 year and 7 years

Soil 2 after 1 year

Soil 2 after 7 years
42

Table 12. Representative soil parameters.

Soil Type 

Based on 

Unified Soil 

Classification

Backfill 

Designation 

Number

RC Based 

on Percent 

of 

Standard 

Proctor

Moist 

Unit 

Weight

(kN/m3)

for 

Confining 

Pressure = 

1 Atmosphere 

Pressure

(degrees)

Reduction in 

for a 10-Fold 

Increase in 

Confining 

Pressure

(degrees)

c

(kN/m2)

Well-graded 

gravel, poorly 

graded gravel,

well-graded 

sand, poorly 

graded sand

1 105 23.6 42 9 0

2 100 22.8 39 7 0

3 95 22.1 36 5 0

4 90 21.3 33 3 0

Silty sand

5 100 21.3 36 8 0

6 95 20.5 34 6 0

7 90 19.7 32 4 0

8 85 18.9 30 2 0

Silty clayey 

sand

9 100 21.3 33 0 24

10 95 20.5 33 0 19

11 90 19.7 33 0 14

12 85 18.9 33 0 10

Low plasticity 

clay

13 100 21.3 30 0 19

14 95 20.5 30 0 14

15 90 19.7 30 0 10

16 85 18.9 30 0 5

1 kN/m3 = 6.37 lbf/ft3

1kN/m2 = 20.89 lb/ft2

Note: This table was created by FHWA after Helwany et al.(73)

Figure 30 through figure 33 all show that the type of backfill had the most effect on the behavior 

of the GRS retaining wall. They concluded that the stiffness of the geosynthetic reinforcement 

had a considerable effect on the behavior of the GRS retaining wall when the backfill was of 

lower stiffness and shear strength. For example, the 9.84-ft (3-m)-high GRS retaining walls 

made of soils #15 and #16 (lower stiffness and shear strength) exhibited significant improvement 

when a stiffer geosynthetic was utilized. When the 9.84-ft (3-m)-high GRS retaining wall was 

made of soils #13 and #14 (higher stiffness and shear strength), it exhibited relatively small 

improvements when the geosynthetic stiffness was increased. 

f f
43

1 inch = 2.54 cm

1 ft = 0.305 m

1kN/m = 68.5 lbf/ft

Note: This figure was created by FHWA after Helwany et al.(73)

Figure 30. Graph. Maximum lateral displacement versus geosynthetic stiffness for 

soils 1–4.

0

1

2

3

4

5

6

50 100 150 200 250 300 350 400

Maximum Lateral Displacement of Facing 

(cm)

Reinforcement Stiffness (kN/m)

Soil 1, 3m wall

Soil 2, 3m wall

Soil 3, 3m wall

Soil 4, 3m wall

Soil 1, 4.5m wall

Soil 2, 4.5m wall

Soil 3, 4.5m wall

Soil 4, 4.5m wall

Soil 1, 6m wall

Soil 2, 6m wall

Soil 3, 6m wall

soil 4, 6m wall
44

1 inch = 2.54 cm

1 ft = 0.305 m

1kN/m = 68.5 lbf/ft

Note: This figure was created by FHWA after Helwany et al.(73)

Figure 31. Graph. Maximum lateral displacement versus geosynthetic stiffness for 

soils 5–8.

0

5

10

15

20

25

50 100 150 200 250 300 350 400

Maximum Lateral Displacement of Facing 

(cm)

Reinforcement Stiffness (kN/m)

Soil 5, 3m wall

Soil 6, 3m wall

Soil 7, 3m wall

Soil 8, 3m wall

Soil 5, 4.5m wall

Soil 6, 4.5m wall

Soil 7, 4.5m wall

Soil 8, 4.5m wall

Soil 5, 6m wall

Soil 6, 6m wall

Soil 7, 6m wall

Soil 8, 6m wall
45

1 inch = 2.54 cm

1 ft = 0.305 m

1kN/m = 68.5 lbf/ft

Note: This figure was created by FHWA after Helwany et al.(73)

Figure 32. Graph. Maximum lateral displacement versus geosynthetic stiffness for

soils 9–12.

0

0.5

1

1.5

2

2.5

3

3.5

4

50 100 150 200 250 300 350 400

Maximum Lateral Displacement of Facing 

(cm)

Reinforcement Stiffness (kN/m)

Soil 9, 3m wall

Soil 10, 3m wall

Soil 11, 3m wall

Soil 12, 3m wall

Soil 9, 4.5m wall

Soil 10, 4.5m wall

Soil 11, 4.5m wall

Soil 12, 4.5m wall

Soil 9, 6m wall

Soil 10, 6m wall

Soil 11, 6m wall

Soil 12, 6m wall
46

1 inch = 2.54 cm

1 ft = 0.305 m

1kN/m = 68.5 lbf/ft

Note: This figure was created by FHWA after Helwany et al.(73)

Figure 33. Graph. Maximum lateral displacement versus geosynthetic stiffness for

soils 13–16.

Effect of Reinforcement Characteristics on Load Deformation Relationships

Figure 34 and figure 35 show the results from two PTs conducted by Nicks et al. to investigate 

the effect of bearing bed reinforcement on load deformation characteristics of bridge piers.

(42)

Bearing bed reinforcement placed directly underneath the beam seat was recommended in at 

least the top five courses of CMU facing elements for GRS abutments to support the increased 

loads due to the bridge and should be, at a minimum, half the primary spacing.

(32) The two piers 

were identical except one pier (Turner-Fairbank (TF)-8) had two courses of bearing bed 

reinforcement in addition to the primary reinforcement of 7.87-inch (20-cm) spacing, and the 

other pier (TF-7) had no bearing bed reinforcement with only primary reinforcement. The 

applied pressure was calculated as the average of the measured values over the period of loading, 

and the vertical strain was calculated as the averages of the four LVDTs and POTs located on the 

footing at the end of each load increment. The axial deformations plotted in figure 34 indicate 

that the bearing bed provided marginally higher vertical capacity; however, vertical deformation 

was not improved at low strain levels. Figure 35 shows that at service loads (3,550-psf (170-kPa)

applied vertical pressure), the lateral deformation of the top 1.31-ft (0.4-m)-thick bearing bed 

reduced by more than 50 percent due to inclusion of two courses of reinforcement.

0

1

2

3

4

5

6

7

8

9

50 100 150 200 250 300 350 400

Maximum Lateral Displacement of 

Facing (cm)

Reinforcement Stiffness (kN/m)

Soil 13, 3m wall

Soil 14, 3m wall

Soil 15, 3m wall

Soil 16, 3m wall

soil 13, 4.5m wall

Soil 14, 4.5m wall

Soil 15, 4.5m wall

Soil 16, 4.5m wall

Soil 13, 6m wall

Soil 14, 6m wall

Soil 15, 6m wall

Soil 16, 6m wall
47

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Nicks et al.(42)

Figure 34. Graph. Effect of bearing bed reinforcement for TF-7 and TF-8.

1 ft = 0.305 m

1 inch = 25.4 mm

Note: This figure was created by FHWA after Nicks et al.(42)

Figure 35. Graph. Measured lateral deformation at 3,600 psf (172.5 kPa) applied pressure 

for TF-7 (no bearing bed reinforcement) and TF-8 (two courses of bearing bed 

reinforcement).

Wu et al. conducted a series of generic soil geosynthetic composite (GSGC) laboratory 

tests to investigate the composite behavior of GRS mass with varying spacing and Tf of 

reinforcement.

(74) The test program comprised five GSGC tests. The specimen height was 6.56 ft 

(2 m) with a square cross section of 4.59 ft (1.4 m). The test conditions and a summary of the 

0

200

400

600

800

1000

1200

1400

1600

0 5 10 15 20

Applied Pressure (kPa)

Vertical Strain (Percent)

TF-7 (No Bearing Bed)

TF-8 (Bearing Bed)

0

0.4

0.8

1.2

1.6

2

0 1 2 3 4 5

Distance from Top of Wall (m)

Horizontal Displacement (mm)

Tf-7

TF-8

 Bearing bed reinforcements
48

results are presented in table 13. The vertical movement was measured along the top surface of 

the concrete pad placed on top of the specimen before loading. Test 1 was conducted as a 

baseline for the other four tests. The specimen was loaded to 36.26 psi (250 kPa) (nearly up to 

1 percent vertical strain), then unloaded to 0 psi (0 kPa) load and reloaded until failure. Other 

tests were loaded to the failure directly. A prescribed confining pressure of 4.93 psi (34 kPa) was 

applied on the entire surface area of the test specimens for tests 1 through 4. Figure 36 shows the 

load deformation behavior of the five GSGC tests. By comparing the results from tests 2 and 3, it 

can be concluded that the ultimate applied pressure increased by about 35 percent by doubling 

the reinforcement strength. By comparing tests 2 and 4, it can be concluded that by changing the 

reinforcement spacing from 1.31 to 0.66 ft (0.4 m to 0.2 m), the ultimate applied pressure 

increased by more than 50 percent. Therefore, compared to the Tf of reinforcement, the spacing 

of the reinforcement layers plays a more significant role in improving load-settlement behavior 

of a reinforced soil mass. Figure 37 shows lateral displacement of the test specimens at failure

and at applied pressure of 87.02 psi (600 kPa). Test 2, which was a confined specimen with 

0.66-ft (0.2-m) reinforcement spacing, demonstrated the highest ultimate capacity and least 

lateral deformation.

Table 13. Test conditions and results summary of GSGC tests.

Parameters Test 1 Test 2 Test 3 Test 4 Test 5

Wide-width tensile ultimate 

strength (kN/m)

No

reinforcement

70 140 70 70

Reinforcement spacing (m) No 

reinforcement

0.2 0.4 0.4 0.2

Confining pressure (kPa) 34 34 34 34 0

Ultimate applied pressure (kPa) 770 2,700 1,750 1,300 1,900

Vertical strain at failure 

(percent)

3 6.5 6.1 4 6

Maximum lateral displacement 

at failure (mm)

47 60 54 53 Not 

measured

1 kN/m = 68.5 lbf/ft

1 ft = 0.305 m

1 psi = 6.89 kPa

1 inch = 25.4 mm

Note: This table was created by FHWA adopted from Wu et al.(74)
49

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Wu et al.(74)

Figure 36. Graph. Load-deformation behaviors for GSGC tests.

1 ft = 0.305 m

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Wu et al.(74)

Figure 37. Graph. Lateral deformation of test specimens at 12,531 psf (600 kPa) and the 

ultimate applied pressure.

Helwany et al. conducted FEAs to investigate the effects of geosynthetic stiffness on the 

performance of GRS abutment.

(70) The stiffness of the base case was assumed to be 36,305 lbf/ft 

(530 kN/m). Results plotted in figure 38 show that the vertical displacement of the abutment seat 

for the base case (for an applied pressure of 4,177 psf (200 kPa)) was reduced by 43 percent

when the geosynthetic stiffness increased by 10 times to 363,050 lbf/ft (5,300 kN/m). 

0

500

1000

1500

2000

2500

3000

0 2 4 6 8 10

Applied Pressure (kPa) 

Vertical Strain (Percent)

Test 1

Test 2

Test 3

Test 4

Test 5

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 20 40 60 80 100

Height (m)

Lateral Displacement (mm)

Test 1 (at 770 kPa)

Test 2 (at 2700 kPa)

Test 3 (at 1750 kPa)

Test 4 (at 1300 kPa)

Test 5 (at 1500 kPa)

Test 1 (at 600 kPa)

Test 2 (at 600 kPa)

Test 3 (at 600 kPa)

Test 4 (at 600 kPa)

Test 5 (at 600 kPa)
50

Conversely, a drastic increase of 250 percent in displacement was noted when the geosynthetic 

stiffness was reduced to 3,603.5 lbf/ft (53 kN/m). Vertical displacement at the abutment seat 

increased drastically when axial stiffness of the geosynthetic dropped below a critical value, and 

the trend became more pronounced with an increase in applied pressure.

1 inch = 2.54 cm

1 psi = 6.89 kPa

1 kN/m = 68.5 lbf/ft

Note: This figure was created by FHWA after Helwany et al.(70)

Figure 38. Graph. Effect of geosynthetic stiffness (reinforcement spacing = 7.87 inches 

(20 cm)) on vertical displacement at abutment seat.

Helwany et al. concluded that the vertical displacement at the abutment seat increased when the 

vertical spacing between reinforcements increased at a high pressure of 58 psi (400 kPa).(70)

Figure 39 shows that the increase in vertical displacement became more significant as the applied 

pressure increased. At an applied pressure of 4,177 psf (200 kPa), an increase of 40 percent in 

the vertical displacement was observed when the reinforcement vertical spacing increased from 

7.87 to 23.62 inches (20 to 60 cm).

0

10

20

30

0 2000 4000 6000

Vertical Displacement at Seat 

(cm)

Geosynthetic Stiffness at 2 Percent Strain 

(kN/m)

100 kPa

200 kPa

400 kPa
51

1 inch = 2.54 cm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Helwany et al.(70)

Figure 39. Graph. Effect of geosynthetic spacing on vertical displacement at abutment seat.

Figure 40 and figure 41 show that the horizontal displacements of the abutment seat and the 

maximum lateral displacement of the segmental wall decreased when the geosynthetic stiffness 

increased to 363,050 lbf/ft (5,300 kN/m) from the base case. Conversely, a drastic increase in 

displacements occurred when the geosynthetic stiffness was reduced to 3,630.5 lbf/ft (53 kN/m).

1 inch = 2.54 cm

1 psi = 6.89 kPa

1 kN/m = 68.5 lbf/ft

Note: This figure was created by FHWA after Helwany et al.(70)

Figure 40. Graph. Effect of geosynthetic stiffness (reinforcement spacing = 7.87 inches 

(20 cm)) on horizontal displacement at abutment seat.

0

5

10

15

20

20 40 60

Vertical Displacement at Seat 

(cm)

Reinforcement Vertical Spacing (cm)

100 kPa

200 kPa

400 kPa

0

2

4

6

8

10

12

14

16

0 1000 2000 3000 4000 5000 6000

Horizontal Displacement at 

Seat (cm)

Geosynthetic Stiffness at 2% Strain (kN/m)

100 kPa

200 kPa

400 kPa
52

1 inch = 2.54 cm

1 psi = 6.89 kPa

1 kN/m = 68.5 lbf/ft

Note: This figure was created by FHWA after Helwany et al.(70)

Figure 41. Graph. Effect of geosynthetic stiffness (reinforcement spacing = 7.87 inches 

(20 cm)) on the maximum lateral displacement of the facing.

Based on the FEA of two full-scale loading tests of GRS bridge abutments as well as a 

parametric study to investigate the performance of GRS bridge abutments, Helwany et al. 

concluded that the horizontal displacement at the abutment seat and the maximum lateral 

displacement of the segmental facing increased with an increase in reinforcement spacing 

(see figure 42 and figure 43).

(70) As figure 42 shows, at applied pressure of 29 psi (200 kPa), an 

increase of 52 percent in the horizontal displacement was observed when reinforcement vertical 

spacing increased from 7.87 to 23.62 inches (20 to 60 cm). At a lower applied pressure of 

14.50 psi (100 kPa), the vertical spacing had a minimum effect on horizontal displacement. As 

shown in figure 43, at an applied pressure of 29 psi (200 kPa), by increasing the reinforcement 

spacing from 7.87 to 23.62 inches (20 to 60 cm), the maximum facing displacement increased by 

about 50 percent.

0

10

20

30

0 2000 4000 6000 8000

Maximum Facing 

Displacement (cm)

Geosynthetic Stiffness at 2 Percent Strain (kN/m)

self weight

100 kPa

200 kPa

400 kPa
53

1 inch = 2.54 cm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Helwany et al.(70)

Figure 42. Graph. Effect of geosynthetic spacing on horizontal displacement at 

abutment seat.

1 inch = 2.54 cm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Helwany et al.(70)

Figure 43. Graph. Effect of geosynthetic spacing on the maximum lateral displacement of 

the facing.

Gotteland et al. performed experimental and numerical studies on two reinforced walls: one was 

reinforced with a non-woven geotextile (represented by NW) and the other with a woven 

geotextile (represented by W) (see figure 44 and figure 45).

(75) The non-woven geotextile was 

3.5 times more extensible than the woven one and approximately half as strong in terms of Tf. 

After construction, the reinforced walls were loaded in the same way as a bridge deck through a 

foundation slab until failure occurred. The 3.28-ft (1-m)-wide foundation was located 4.92 ft 

0

1

2

3

4

5

6

7

8

9

10

20 40 60

Horizontal Displacement at Seat 

(cm)

Reinforcement Vertical Spacing (cm)

100 kPa

200 kPa

400 kPa

0

5

10

15

20

20 40 60

Maximum Facing 

Displacement (cm)

Reinforcement Vertical Spacing (cm)

self weight

100 kPa

200 kPa

400 kPa
54

(1.50 m) from the edge of the facing. As figure 44 shows, the abutment with woven geotextile 

had a higher ultimate bearing capacity, and its settlement was less compared to the non-woven 

one. The results in figure 45 show that lateral deformation of the wall face with woven geotextile

was less than that with non-woven geotextile.

1 inch = 2.54 cm

1 kN/m = 68.5 lbf/ft

FEM = Finite element method.

Note: This figure was created by FHWA after Gotteland et al.(75)

Figure 44. Graph. Central settlement of the foundation versus applied load.

1 ft = 0.305 m

1 inch = 2.54 cm

Note: This figure was created by FHWA after Gotteland et al.(75)

Figure 45. Graph. Wall face displacement at applied pressure of 3,969.1 lb/ft2 (190 kN/m2)

for non-woven and woven reinforcement.

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300

Settlement (cm)

Applied Load (kN/m)

NW (Test)

NW (FEM)

W (Test)

W (FEM)

0

1

2

3

4

5

0 5 10 15 20

Height of the Wall (m)

Wall Face Displacement (cm)

NW (Test)

NW (FEM)

W (Test)

W (FEM)
55

Bathurst et al. conducted experiments on four full-scale modular block walls that were 

constructed with reinforcement layers with different tensile stiffnesses.

(76) The walls were 

11.81 ft (3.6 m) high. Two of the walls (walls 1 and 2) were reinforced with two different PP 

geogrid reinforcements, wall 3 was reinforced with a polyester (PET) geogrid, and wall 4 was 

reinforced with a welded wire mesh (WWM). Walls 1 and 2 were compacted using vibrating 

plate equipment, and walls 3 and 4 were compacted by a vibrating rammer. Figure 46 shows

measured relative horizontal displacements recorded at monitored points on the wall facing 

column shortly after EOC. Each elevation point has a local datum corresponding to the time 

when each row of displacement POTs were installed.

1 ft = 0.305 m

1 inch = 25.4 mm

Note: This figure was created by FHWA after Bathurst et al.(76)

Figure 46. Graph. Relative horizontal displacement of wall facing recorded at EOC.

Hatami and Bathurst investigated the influence of reinforcement properties on the performance 

of reinforced soil SRWs using a finite difference numerical model.

(71) They concluded that 

the deformation response of the model wall with a pinned (fully fixed) reinforcement 

condition was very close to that of the model with interface stiffness between backfill soil and 

reinforcement layers (kb) ≥ 145 lbf/inch/inch (1,000 kN/m/m). As figure 47 shows, for values of 

kb ≤ 145 lbf/inch/inch (1,000 kN/m/m), the lower kb, the greater the wall deformation. The wall 

deformation magnitude increased by a factor of two when the value of kb was reduced by 

two orders of magnitude from kb = 145 lbf/inch/inch (103 kN/m/m) to kb = 1.45 lbf/inch/inch

(10 kN/m/m).

0

0.5

1

1.5

2

2.5

3

3.5

4

0 3 6 9 12 15 18

Height (m)

Horizontal Displacement (mm)

Wall 1 (PP)

Wall 2 (modified PP)

Wall 3 (PET)

Wall 4 (WWM)
56

1 ft = 0.305 m

1 inch = 2.54 cm

1 kN/m/m = 0.145 lbf/inch/inch

Note: This figure was created by FHWA after Hatami and Bathurst.(71)

Figure 47. Graph. Influence of soil-reinforcement interface stiffness value on lateral 

displacement of the wall.

Zevgolis and Bourdeau simulated the performance of MSE abutments with metal strips to 

investigate the effects of different parameters such as the elastic modulus of reinforcement (ER), 

H, magnitude of the applied load, and foundation soil type on the behaviors of the abutments.(4)

They defined five case studies; H1-L3-S2, H1-L3-S3, H2-L1-S3, H2-L2-S2, and H3-L1-S2, 

where H1, H2, and H3 stand for the abutments that were 19.66, 22.97, and 26.24 ft (6, 7, and 

8 m) tall, respectively; L1, L2, and L3 stand for supported spans that were 59.06, 78.74, and 

9,843 ft (18, 24, and 30 m) long with total applied load of 18,152, 22,262, and 26,372 lbf/ft 

(265, 325, and 385 kN/m), respectively; and S2 and S3 represent different foundation soil types. 

For S2, was 30 degrees, c was 104 lb/ft2 (5 kPa), and the unit weight was 121 lb/ft3

(19 kN/m3

). For S3, was 20 degrees, c was 835 lb/ft2 (40 kPa), and the unit weight was 

108 lb/ft3 (17 kN/m3). As figure 48 shows, by increasing Young’s modulus of reinforcement 

from 3.63 to 7.25 ksi (25 to 50 MPa), the maximum vertical deformation of the abutment 

decreased at least 42 percent, and by increasing Young’s modulus of reinforcement from 7.25 to 

14.50 ksi (50 to 100 MPa), the maximum vertical deformation decreased at least 36 percent. 

Moreover, the results indicate that higher MSE abutment had more vertical displacement that 

that of a lower one. 

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6

Elevation (m) 

Lateral Displacement (cm)

pinned (kb=infinity)

kb=10^4 kN/m/m

kb=10^3 kN/m/m

kb=10^2 kN/m/m

kb=10 kN/m/m
57

1 inch = 2.54 cm

1 psi = 6.89 kPa

Figure 48. Graph. Effect of ER on the maximum vertical displacement of MSE abutments 

with metal strips.

(4)

Tatsuoka et al. and Tateyama performed a series of plane strain model tests of metal stripreinforced sand retaining walls with three different numbers of reinforcement layers (N = 2, 5,

and 10).

(77,78) The reinforcement layers were made of phosphor-bronze strips. The model wall 

was 33.07 inches (84 cm) wide, 15.55 inches (39.5 cm) long, and 20.47 inches (52 cm) tall. As 

the results plotted in figure 49 show, by increasing N, the vertical displacement of the foundation 

placed on top of abutment under each applied load decreased. For instance, by increasing N from 

2 to 5, the settlement under applied pressure of 1.02 psi (7 kPa) decreased about 70 percent, and 

by increasing N from 5 to 10, the settlement decreased 53 percent under applied pressure of 

2.03 psi (14 kPa). Cao and Peng simulated these experiments through a nonlinear FEM analysis 

and obtained similar results.

(79) The results showed that the peak footing load of reinforced 

retaining walls increased significantly with an increase in the number of reinforced layers.

The experimental results were obtained by Tateyama, and the FEM results were obtained by 

Cao and Peng.(78,79)

0

4

8

12

16

20

Maximum Vertical Displacement 

0 25000 50000 75000 100000 125000

(cm)

Elastic Modulus (kPa)

H1, L3, S2

H1, L3, S3

H2, L1, S3

H2, L2, S2

H3, L1, S2
58

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Zevgolis and Bourdeau.(4)

Figure 49. Graph. Load-settlement results for the foundation on top of MSE abutment.

Effect of Facing Blocks on Load Deformation Relationships

Nicks et al. conducted five pairs of tests as a part of an FHWA research study to investigate the 

effects of facing elements on load deformation behavior of bridge piers (see figure 50).

(42) They 

concluded that the ultimate capacity of pier increased when a facing element was present; 

however, the magnitude of strain at failure, which was measured through LVDTs and POTs on 

the footing, was similar for a given GRS composite with or without a facing. 

For figure 50, the following parameters were used:

TF-2 and TF-3 with Sv = 7.64 inches (19.4 cm) and Tf = 2,398 lb/ft (35 kN/m).

TF-6 and TF-7 with Sv = 7.64 inches (19.4 cm) and Tf = 4,795 lb/ft (70 kN/m).

TF-9 and TF-10 with Sv = 15.24 inches (38.7 cm) and Tf = 4,795 lb/ft (70 kN/m).

TF-12 and TF-11 with Sv = 3.82 inches (9.7 cm) and Tf = 1,404 lb/ft (20.5 kN/m).

TF-14 and TF-13 with Sv = 11.26 inches (28.6 cm) and Tf = 3,596 lb/ft (52.5 kN/m).

0

2

4

6

8

10

12

0 10 20 30 40 50

Footing Settlement (mm)

Average Footing Pressure (kPa)

N=2 (Experimantal result)

N=5 (Experimantal result)

N=10 (Experimantal result)

N=2 (FEM result)

N=5 (FEM result)

N=10 (FEM result)
59

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Nicks et al.(42)

Figure 50. Graph. Stress-strain response for different piers.

Effect of Prestraining on Load Deformation Relationships

A full-scale GRS bridge pier load test was conducted at FHWA’s TFHRC in 1996.(22,23) The 

GRS pier was prestrained (preloaded) using hydraulic jacks and a specially designed reaction 

system. Results obtained from this instrumented bridge pier show that the prestraining reduced 

vertical settlement of the pier by approximately 50 percent (see figure 51). Figure 52 shows that 

prestraining did not reduce lateral deformation except for near the top of the pier where the 

lateral movement reduced significantly.

0

500

1000

1500

2000

2500

0 5 10 15 20 25

Applied Pressure (kPa)

Vertical Strain (Percent)

CMU (TF-2)

No CMU (TF-3)

CMU (TF-6)

No CMU (TF-7)

CMU (TF-9)

No CMU (TF-10)

CMU (TF-12)

No CMU (TF-11)

CMU (TF-14)

No CMU (TF-13)
60

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Adams and Wu et al.(22,23)

Figure 51. Graph. Load-settlement curves for the pier.

1 ft = 0.305 m

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Adams and Wu et al.(22,23)

Figure 52. Graph. Lateral displacement measured by LVDT.

Two GRS bridge abutments were built in Black Hawk, CO, in 1997 to support a steel bridge.

(23)

Because the thickness of the reinforced soil abutment were different beneath the four footings 

directly supporting the weight of the bridge, the GRS abutment was preloaded to reduce the 

differential settlement between adjacent footings. The abutment was preloaded up to 35.53 psi 

(245 kPa) (1.6 times the design load of 21.76 psi (150 kPa)) for the square footing and 

0

20

40

60

80

0 200 400 600 800 1000

Settlement (mm)

Applied Pressure (kPa)

Initial Loading

 Reloading

0

1

2

3

4

5

6

0 10 20 30 40

Pier Hieght (m)

Lateral Displacement (mm)

415 kPa

900 kPa

415 kPa reload
61

11.60 psi (80 kPa) (2 times the design load of 5.80 psi (40 kPa)) for the rectangular footing. It 

was found that preloading substantially reduced the differential settlement. The differential 

settlements at 21.76 psi (150 kPa) of the preloading cycle for the two abutments were 0.33 and

0.85 inch (8.4 and 21.6 mm). At 21.76 psi (150 kPa) in the reloading cycle, the differential 

settlement of both abutments was less than 0.039 inch (1 mm).(23) Measured results by Wu et al. 

also show that preloading reduced the lateral movement of GRS abutments (see figure 53 and 

figure 54).

(23) At 21.76 psi (150 kPa) in the preloading cycle, the maximum lateral displacements 

in the west abutment (8.86 ft (2.7 m) tall) and the east abutment (17.72 ft (5.4 m) tall) were 0.06 

and 0.52 inch (1.5 and 13.2 mm), respectively. These displacement values were reduced to 0.02 

and 0.18 inch (0.6 and 4.5 mm), respectively, at 21.76 psi (150 kPa) in the reloading cycle. After 

the first reloading cycle, there was no significant reduction in the magnitude of the lateral and 

vertical deformations of the GRS abutments in the subsequent reloading cycles.

(23)

1 ft = 0.305 m

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Wu et al.(23)

Figure 53. Graph. Lateral deformation profiles of the west abutment.

0

0.5

1

1.5

2

2.5

3

-8 -6 -4 -2 0 2 4

Wall Hight (m)

Lateral Deformation (mm)

Preloading at 150 kPa

Preloading at 250 kPa

Reloading at 150 kPa
62

1 ft = 0.305 m

1 inch = 25.4 mm

1 psi = 6.89 kPa

Note: This figure was created by FHWA after Wu et al.(23)

Figure 54. Graph. Lateral deformation profiles of the east abutment.

3.4 EFFECTS OF TRANSIENT LOADS ON DEFORMATIONS OF BRIDGE 

SUPPORTS ON GRANULAR SOILS

Live loads may include traffic load and compaction-induced load. Few research studies have 

investigated the effect of live loads on bridge supports using engineered fills. Based on a

three-dimensional (3D) numerical study on an integral abutment bridge, Olson et al. concluded 

that superstructure deflections related to live load had a secondary effect on the abutment 

displacement but substantially changed their rotation.

(80) As a result, the critical moments at the 

connection between superstructure and foundation were exacerbated by live load in thermal 

expansion and improved in thermal contraction conditions. Chapter 10 of AASHTO LRFD 

Bridge Design Specifications specification states, “Transient load may be omitted for settlement 

analysis for cohesive soils subjected to time-dependent consolidation settlement.”(8) However, 

for cohesionless soils (including engineered fills), transient load may be considered in the 

deformations of shallow foundations and abutments and piers of bridges. For retaining walls and 

bridge abutments, the traditional approach is to add the live load to the dead load and consider 

the combined loads as a permanent dead load. For example, through analytical studies, Kim and 

Barker and Esmaeili and Fatollahzadeh investigated the equivalent surcharge for truck load and 

train load, respectively, on retaining walls and bridge abutments.

(81,82) Presently, the dynamic 

effect of transient load on bridge supports using engineered fills has not been investigated. 

Moreover, there is a lack of literature on the time-dependent and live (transient) load on the 

stress-deformation behaviors of bridge supports in engineered fills. 

0

0.5

1

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30 35

Wall Height (m)

Lateral Deformation (mm)

Preloading at 150 kPa

Preloading at 250 kPa

Reloading at 150 Kpa
63

3.5 DETERMINATION OF STRESS DISTRIBUTIONS IN GRANULAR SOILS UNDER

SHALLOW FOUNDATIONS

Equations to compute vertical stresses at any point in a soil mass due to external vertical loadings 

have been developed based on the theory of elasticity. The formulas that are most widely used 

are the Boussinesq and Westergaard formulas.

(83,84) They were first developed for point loads 

acting at the surface. These formulas have been integrated to obtain stresses below uniform strip 

loads and rectangular loads. In the practice, Boussinesq’s formulas are often preferred, as they 

give conservative results.

The Boussinesq formulas are based on the following assumptions:

(83)

The soil mass is elastic, isotropic, and homogeneous.

The soil is semi-infinite.

The soil is weightless.

In the Westergaard formulas, the material is isotropic with finite and equal horizontal and 

vertical normal moduli and Poison’s ratios but with infinite horizontal shear modulus.

(84) The 

assumptions for Westergaard’s formulas are as follows:

The soil is elastic and semi-infinite.

The soil is composed of numerous closely spaced horizontal layers of negligible 

thickness of an infinite rigid material.

The rigid material permits only the downward deformation of mass in which horizontal 

deformation is zero.

For engineered fills without reinforcement, the Boussinesq and Westergaard formulas can be 

used to determine the stress distributions inside the soil mass. In reinforced engineered fills that 

are used as bridge supports, the reinforced soils are no longer isotropic or homogeneous. 

Therefore, the Boussinesq and Westergaard formulas may not be applicable. In such a case, 

numerical simulations (such as FEM or finite difference method) may be used. Many past 

researches have studied the strain and stress distributions of the reinforcements within 

geosynthetic-reinforced walls. (See references 85–88.) For metallic-reinforced soils, there are 

three common methods used in North American practice for estimating reinforcement loads: the 

AASHTO coherent gravity method, the FHWA structure stiffness method, and the AASHTO 

simplified method. (See references 52, 89, and 36.) Limited studies have been conducted on 

stress distributions in reinforced soils as bridge supports, particularly in SLS. Rowe and Ho 

studied a continuous full-facing panel wall with a hinged toe and reinforced with extensible 

reinforcement in a granular backfill resting on a rigid foundation.

(90) This numerical study 

concluded that among the parameters examined, the distribution of force was most affected by 

the reinforcement stiffness, density, the external between facing and soil, the backfill soil 

internal , and the rigidity of the facing.
64

The stress distribution can be influenced by various soil conditions (i.e., grain size distribution, 

strength parameters, relative density, and fine content), reinforcement characteristics (i.e., Tf, 

stiffness, N, and Sv), and loading conditions, some of which were investigated by Rowe and 

Ho.

(90) However, the literature search conducted by the authors of this report suggests there is a 

lack of documentation and understanding of the effects of various parameters on the stress 

distribution in reinforced engineered fills as bridge supports in SLS.
65

CHAPTER 4. EVALUATION OF PREDICTION METHODS FOR DEFORMATIONS 

OF BRIDGE SUPPORTS ON GRANULAR SOILS

In this chapter, methods that are widely accepted and routinely used to calculate immediate and 

long-term settlement of shallow foundations of bridges, vertical deformation of GRS abutments, 

and lateral displacement of GRS abutments are evaluated. Available methods for long-term 

deformations of shallow foundations on granular soils are also presented.

4.1 METHODS FOR IMMEDIATE SETTLEMENT OF SHALLOW FOUNDATIONS OF 

BRIDGES ON GRANULAR SOILS

Various methods are available to calculate the immediate (elastic) settlement of shallow 

foundations. Das provided a critical review of 12 common methods on elastic settlement of 

shallow foundations on granular soil.

(91) He grouped the methods into three categories: methods 

based on observed settlement of structures and full scale prototypes, semi-empirical methods 

based on a combination of field observations and theoretical studies, and methods based on 

theoretical relationships derived from the theory of elasticity. In this section, the following 

five methods are presented and evaluated:

Modified Schmertmann method.

(92,93)

Hough method.

(94)

Peck and Bazaraa method.

(95)

Burland and Burbidge method.

(96)

D’Appolonia method.

(97,98)

These five methods were evaluated in previous FHWA studies and a SHRP2 study.

(3,12,10) The 

AASHTO LRFD Bridge Design Specifications recommends the use of the Hough method, which 

has the smallest coefficient of variance.

(8,94) However, the Hough method is conservative by a 

factor of approximately two, which often leads to unnecessary use of deep foundations instead of 

spread footings to meet tolerable deformation criteria. FHWA recommends the use of the method 

proposed by Schmertmann because it is a rational method that considers not only the applied 

stress and its associated strain influence distribution with depth for various footing shapes but 

also the elastic properties of the foundation soils, even if they are layered. (See references 6, 7, 

92, 93, and 10.)

Modified Schmertmann Method

To estimate settlements of footings in structural fills by the Schmertmann method, an assumption 

must be made about the standard penetration test (SPT) blow count for an SPT sampler to 

penetrate the second and third 6 inches into the subsoil (N-value) that is representative of the 

engineered fill.

(92,93) The FHWA report, Spread Footings for Highway Bridges used an SPT 

N-value of 32 blows/ft (32 blows/0.305 m) corrected for overburden pressure as a representative 

value for estimating settlement in structural fills.

(3) This SPT N-value corresponds to a relative 
66

density of approximately 85 percent at an overburden stress of about 2,000 psf (95.8 kPa) and 

approximately 97 percent RC based on the modified Proctor compaction energy.

(3,18) 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 blow 

count ((N1)60) of 32. However, engineered fills are often compacted to a RC of 95 percent based 

on the modified Proctor compaction energy. For this case, (N1)60 of 23 is more appropriate.

(18)

Based on the modified Schmertmann method, the immediate settlement of spread footing can be 

estimated by the equations found in figure 55 through figure 57.

(93)

Figure 55. Equation. Immediate settlement of spread footing based on modified 

Schmertmann method.

Where:

Si = Immediate settlement.

C1 = Correction factor for strain relief due to soil excavation for foundation embedment, which is 

defined in figure 56.

C2 = Correction factor to consider creep as the time-dependent increase in settlement for t time 

(i.e., number of years) after construction, which is defined in figure 57.

p = Net uniform pressure applied at the foundation depth.

Hi = Thickness of each soil layer.

Iz = Strain influence factor.

X = Factor used to determine the value of elastic modulus. 

Ei = Elastic modulus of layer i in the vertical direction.

Figure 56. Equation. Correction factor to consider foundation embedment depth.

Where p0 = Initial effective stress at the foundation depth.

Figure 57. Equation. Correction factor to consider creep.

Hough Method

The original Hough method was used to estimate immediate settlement of embankments.

(84) It 

was based on uncorrected SPT N-values and included recommendations for cohesionless as well 

as cohesive soils such as sandy clay and remolded clay, respectively. AASHTO modified the 

Hough method and used (N1)60 to eliminate the recommendations for sandy clay and remolded 

clay.

(9,84) However, the settlements estimated by the modified Hough method are usually 

overestimated by a factor of 2 or more based on the data in the FHWA report, Spread Footings 

for Highway Bridges.

(3) Such conservative estimates may be excessive with respect to the 

Si = C1C2∆p��Hi � Iz

XEi

��

n

i = 1

∆

C1 = 1 0.5 �

p0

∆p

� ≥ 0.5

C2 = 1 + 0.2 log10 �

t(years)

0.1 �
67

behavior of the structures founded within, under, or near the embankment. In cases where 

structures are affected by embankment settlement, more refined estimates of the immediate 

settlements are warranted.

In the Hough method, the immediate settlement of sand under a shallow foundation is calculated 

by taking the summation of settlement of subdivided layers of 10 ft (3.05 m) that are influenced 

by the foundation load. The settlement ( H) of each soil layer is calculated using the following:

Figure 58. Equation. Immediate settlement of each soil layer based on the Hough method.

Where:

C = Bearing Capacity Index.

= Initial average effective stress of the subdivided soil layer.

= Vertical stress increase in the subdivided soil layer due to applied foundation load.

Peck and Bazaraa method

The Peck and Bazaraa method is based on the original Terzaghi and Peck empirical 

equation.

(95,99) The SPT blow count is corrected for overburden pressure to reflect the relative 

density of the soil. The immediate settlement of a footing on sand is calculated as follows:

Figure 59. Equation. Immediate settlement of footing based on Peck and Bazaraa method.

Where:

S = Settlement of footing.

Cw = Water table correction factor at depth of B/2 below footing bearing level.

CD = Embedment correction factor.

p = Footing bearing pressure.

(N1)60 can be estimated using the equations in figure 60 and figure 61 as follows:

(for 1,566 lb/ft2 (75 kN/m2))

Figure 60. Equation. SPT blow count corrected for overburden pressure less than or equal 

to 1,566 lb/ft2 (75 kPa).

Where N60 = Standard penetration number that is corrected based on the field conditions.

∆

∆H = Hi �

1

C� log10 �

σ'0 + ∆σ'v

σ'0

�

σ'0

∆σv

′

S = CwCD

2p

(N1)60

� B

B + 0.3�

2

(N1)60 = 

4N60

1 + 0.04σ'

0

σ'0
68

(for > 1,566 lb/ft2 (75 kN/m2))

Figure 61. Equation. SPT blow count corrected for overburden pressure greater than 

1,566 lb/ft2 (75 kPa).

Burland and Burbidge Method

The Burland and Burbidge method is an empirical relationship between average SPT blow count,

foundation width, and foundation subgrade compressibility.(96) It is based on regression analysis

of case studies. The immediate settlement of a footing on granular soil is given by the following:

Figure 62. Equation. Immediate settlement of a footing based on Burland and Burbidge 

method.

Where:

fs = Shape correction factor.

fl = Correction factor for thickness of sand or gravel layer.

ft = Time factor, used if t 3 years.

q = Average gross applied pressure.

Ic = Compressibility Index.

D’Appolonia Method

The D’Appolonia method is based on the elastic theory.

(97,98) The immediate settlement of a 

footing on sand is given by the following:

Figure 63. Equation. Immediate settlement of a footing based on D’Appolonia method.

Where:

M = Modulus of compressibility of sand; it is determined using the empirical chart based on SPT 

results for both normally consolidated and over-consolidated sand; the SPT blow count in the 

chart is the average blow count in the depth B below the footing bearing level.

(97)

= Embedment correction factor, using the chart by Christian and Carrier.

(100)

= Correction factor for thickness of sand layer, using the chart by Christian and Carrier.

(100)

4.2 LONG-TERM SETTLEMENT OF SHALLOW FOUNDATIONS ON GRANULAR 

SOILS

Long-term, or time-dependent, settlement of shallow foundations on granular soils is also known 

as “creep” or “secondary settlement.” Crouse and Wu conducted a study to examine the longterm (greater than 6 mo) performance of seven full-scale GRS walls in the United States and 

Canada.

(101) The walls ranged from 15 to over 40 ft (4.6 to over 12.2 m) in height and typically 

(N1)60 = 

4N60

3.25 + 0.01σ'

0

σ'0

S = f

s fl ft ��q' 2

3

σ'

0� B0.7Ic�

S = 

pB

M μ0μ1

μ0

μ1
69

included surcharge loads from earth fills or highway loads. The geosynthetics were geogrid or 

geotextiles, and the facing consisted of concrete modular blocks, panels, or exposed surface. The 

creep rate of reinforcement ranged from 0.4 to 0.7 percent, with one GRS wall at 1.5 percent. 

Although quantitative creep rate of the GRS walls was not reported, it was found that creep rate 

decreased with time at a decreasing rate.

(102) Adams and Nicks conducted a full-scale study on 

the secondary settlement of four GRS piers.

(27) The results indicate that secondary settlement 

does occur in granular material, but the amount with GRS is still within typical tolerable limits 

for bridges. 

Empirical equations have been proposed by previous researchers to evaluate long-term 

settlement of granular soils due to creep. This section presents four methods. Due to the limited 

data on long-term settlement of shallow foundations on granular soils, evaluation of these 

methods was not conducted.

The modified Schmertmann method considered creep as the time-dependent increase in 

settlement after construction, as shown in figure 57.

(92,93)

Terzaghi, Peck, and Mesri presented the following equation for settlement due to creep

(Screep):

(103)

Figure 64. Equation. Settlement due to creep.

Where: 

= Weighted mean value of measured static cone resistance of cone penetration test (qc) 

between z = 0 to z0, where z is depth from the ground surface, and z0 is the depth under 

consideration.

Wu reported the following creep rate equation by assuming a linear relationship between the log 

scale of creep rate and log scale of time:(102)

Figure 65. Equation. Creep rate of shallow foundations.

Where: 

c = Creep strain (percent).

A = Reference creep rate; (d c/dt) at t = 1 day (percent/day).

m = Creep modulus (equal to slope of log(d c/dt) versus log(t) line; it may be obtained from PTs.

Briaud and Garland and Briaud proposed an expression of time-dependent settlement of footings 

in sand as follows:

(104,105)

Screep = �

0.1

q�c

� z0log �

tdays

1 day�

q�c

dεc

dt = A(t)m
70

Figure 66. Equation. Time-dependent settlement of footings in sand.

Where:

s(t) = Settlement at time t.

s(t1) = Settlement at time t1, where t1 is the reference time (1 min).

n = Time dependency exponent.

Briaud reported that the model identified in figure 66 fit well with a large-scale footing test and 

the n value typically varied from 0.005 to 0.03 for sands.

(105,106) Briaud recommended obtaining 

site-specific n values by creep pressure meter testing.

(105) If this is not available, a value of 0.03 

seems conservative for sand in most cases.

4.3 VERTICAL DEFORMATION OF GRS ABUTMENTS

The approach for determining vertical deformation of a GRS abutment involves empirically 

finding the strain from an applicable PT curve.

(32) The vertical strain of a GRS abutment is found 

from the intersection of the applied vertical stress due to the dead load and the PT design 

envelope for vertical strain. The vertical strain should be limited to 0.5 percent unless additional 

deformation is permitted.

(32) The lateral strain can be then determined analytically assuming no 

volume change in the abutment. 

The vertical displacement ( ) of a GRS abutment with a strip footing is given by the equation in 

figure 67.

(42) This equation is based on a solution for a relative displacement between the center 

of the strip footing and any arbitrary point assuming a constant stiffness with depth and a 

Poisson’s ratio of 0.5 for the GRS material.

(107)

Figure 67. Equation. Vertical displacement of a GRS abutment with a strip footing.

Where:

3.1415926.

EGRS = Young’s elastic modulus of the GRS composite.

q = Applied pressure.

a = Setback distance between the face of the wall and the applied load.

b' = Width of facing block.

4.4 LATERAL DISPLACEMENT OF GRS WALLS AND ABUTMENTS

This section presents six methods for calculating lateral displacement of GRS walls and 

abutments. It is noted that these methods apply to GRS walls and abutments only. Their 

applicability to MSE walls or abutments remains to be verified. 

s(t)

s(tt

) = �

t

t1

�

n

ρρ

ρ = 3qb'

4πEGRS �

1

2�1 +

a +

b'

2

b'

2

�ln �

H2+ �a +

b'

2�

2

�

b'

2�

2 � +

1

2�1

a +

b'

2

b'

2

�ln �

H2 + a2

�

b'

2�

2 � +

H

a

tan-1 �

a + b'

H � +

H

a

tan-1 �

-b'

H ��
71

For the lateral deformations of MSE walls and abutments, the FHWA specification, Design and 

Construction of Mechanically Stabilized Earth Walls and Reinforced Soil Slopes states the 

following:(37)

“With respect to lateral wall displacements, no method is presently available to 

definitively predict lateral displacements, most of which occur during 

construction. The horizontal movements depend on compaction effects, 

reinforcement extensibility, reinforcement length, reinforcement-to-panel 

connection details, and details of the facing system. A rough estimate of probable 

lateral displacements of simple structures that may occur during construction can 

be made based on the reinforcement length to wall-height ratio and reinforcement 

extensibility as shown in Figure ‘2-15’, for the serviceability limit check.”

(Chapter 2, pp. 40)(37)

FHWA Method

Christopher et al. correlated the ratio of reinforcement length and wall height (L/H) with the 

lateral displacement of a reinforced soil wall during construction.

(89) This method is referred to as 

the “FHWA method.” The FHWA method was developed empirically by determining a 

displacement trend from numerical analysis and adjusting the curve to fit with field-measured 

data. The method provides an estimate of the maximum lateral displacement. In this method, 

an empirically derived relative displacement coefficient ( R) was related graphically to L/H.

Based on the graphical relationship, a fourth-order polynomial equation was derived for 

0.3 < L/H < 1.175 shown in figure 68.

(74)

Figure 68. Equation. Displacement coefficient of a reinforced soil wall.

The maximum lateral deformation ( max) of a GRS wall is as follows:

Figure 69. Equation. Maximum lateral deformation of a GRS wall with inextensible 

reinforcement (i.e., metallic reinforcement).

Figure 70. Equation. Maximum lateral deformation of a GRS wall with extensible 

reinforcement (i.e., geosynthetic reinforcement).

Wu et al. stated that figure 70 has been corrected for a wall with a different height and 

surcharge.

(74)

δR = 11.81 �

L

H�

4

42.25 �

L

H�

3

+ 57.16 �

L

H�

2

35.45 �

L

H� + 9.471

δmax = 

δRH

250

δmax = 

δRH

75
72

Geoservices Method

The Geoservices method relies on limit equilibrium analyses to calculate the length of the 

required reinforcement to satisfy a suggested factor of safety with regard to three presumed 

external failure modes (e.g., bearing capacity failure, sliding, and overturning).

(108) The method 

provides a procedure for calculating the lateral wall displacement. The lateral displacement is 

calculated by first choosing a strain limit for the reinforcement. This strain limit is usually less 

than 10 percent and depends on a number of factors, such as the type of wall facing, the 

displacement tolerances, and the type of geosynthetic to be used as reinforcement. Concrete 

facing panels, for example, would not allow much lateral displacement without showing signs of 

distress. Therefore, a low strain limit (1 to 3 percent) should be selected.

(74) Once the strain limit 

has been selected, the method assumes a distribution of strain in the reinforcement for 

calculating wall movement. The maximum horizontal displacement of a GRS wall or abutment,

, can be calculated as follows:

Figure 71. Equation. Maximum horizontal displacement of a GRS wall or abutment based 

on Geoservices method.

Where = Strain limit.

Colorado Transportation Institute (CTI) Method 

In a study for CTI, Wu proposed a service load-based design method, referred to as the CTI 

method, to determine the maximum lateral displacement of a GRS wall or abutment.

(109) In most 

cases, the designer may select a design limit strain ( d) of 1 to 3 percent for the reinforcement for 

H less than or equal to 29.52 ft (9 m). max can be estimated by the following empirical equation

in figure 72:

Figure 72. Equation. Maximum lateral displacement of a GRS wall or abutment based on 

CTI method.

If max exceeds a prescribed tolerance for the wall, a smaller d should be selected so that max of 

the wall will satisfy the performance requirement. Figure 72 applies only to walls with very 

small facing rigidity, such as wrapped-faced walls. Walls with significant facing rigidity have 

smaller maximum lateral displacement. For example, a modular block GRS wall has a max about 

15 percent smaller than that calculated in figure 72.

(74)

Jewell-Milligan Method

Jewell and Jewell and Milligan proposed a method for calculating wall displacement based on 

analysis of stresses and displacements in a reinforced soil mass.

(110,111) This method only applies 

to a GRS wall with flexible facing (i.e., the rigidity of wall facing is ignored). Jewell and 

max

δmax = 

εdL

2

εd

δmax = εd � H

1.25�
73

Milligan provided graphical relationships between a dimensionless displacement factor,

and depth below crest of wall at various soils and dilation angles. Where:(111)

h = Lateral displacement of a GRS wall or abutment with flexible facing. 

Kreinf = Stiffness of reinforcement. 

Pbase = Reinforcement force at the base of the wall.

Z = Depth from the crest of the wall. 

h varies with wall depth, and max occurs in the middle of H. Based on the Jewell and Milligan 

method, Wu et al. derived the following analytical expression of the lateral displacement of a 

GRS wall:(74)

Figure 73. Equation. Lateral displacement of a GRS wall or abutment with flexible facing.

Where:

Prm = Maximum reinforcement force at depth of influence zone (zi).

Kreinf = Stiffness of the reinforcement.

ds = Friction angle of soil based on direct shear test.

= Dilation angle of soil.

Wu Method

Following the theory for the Jewell and Milligan method, Wu et al. proposed an analytical model 

for calculating the lateral movement of a GRS wall with modular block facing.

(74) This method, 

referred to as the “Wu method,” considers the rigidity of wall facing. Figure 74 shows the lateral 

displacement of a GRS wall with modular block facing, and figure 75 shows the lateral 

displacement of a GRS wall with modular block facing while ignoring the effect of fiction 

between the back of the modular block and soil.

Figure 74. Equation. Lateral movement of a GRS wall with modular block facing.

Where:

i = Lateral movement of a GRS wall with modular block facing.

Kh = Horizontal earth pressure coefficient.

s = Unit weight of soil.

Z = Depth from the wall crest.

b = Unit weight of modular block facing.

= Friction angle between modular block facing elements.

= Friction angle between back face of wall and soil.

�

δhKreinf

HPbase � �

Z

H�

δh = �

1

2

� � Prm

Kreinf� (H zi) �tan �45o ψ2

� + tan�90o φds��

∆i = 0.5 �

Kh�γsZ + q�Sv γsb'Svtanδ(1 + tanδtanβ)

Kreinf � (H Z) �tan �45o ψ2

� + tan�90o φds��
74

Figure 75. Equation. Lateral movement of a GRS wall with modular block facing (no 

friction between wall and soil).

Adams Method 

Adams et al. presented a method for calculating lateral displacement of GRS abutments in 

response to a vertical load.

(32) The method, referred to as the “Adams method,” conservatively 

assumes no volume change in a GRS abutment, which represents a worst-case scenario. The 

composite behavior of a properly constructed GRS mass is such that both the reinforcement and 

soil deform laterally together at the same strain. This composite behavior can be used to predict 

both the maximum lateral reinforcement strain and the maximum face deformation at a given 

load. The maximum lateral displacement of an abutment face can be estimated using figure 76. 

The lateral strain is then found using figure 77 and should be limited to 1 percent.

(32)

Figure 76. Equation. Lateral displacement of GRS abutments in response to a vertical load.

Where:

DL = Lateral displacement of GRS abutments in response to a vertical load.

bq,vol = Width of the load along the top of the wall (including the setback).

Dv = Vertical settlement in the GRS abutment. 

Figure 77. Equation. Lateral strain of GRS abutments in response to a vertical load.

Where:

L = Lateral strain.

v = Vertical strain at the top of the wall. 

Note that figure 76 and figure 77 are based on the assumption of a triangular lateral deformation 

and a uniform vertical deformation; this assumption is based on observed deformation behavior 

of GRS.

(32)

4.5 EVALUATION OF THE DEFORMATION PREDICTION METHODS

In this section, experimental data in the literature are applied to the deformation prediction 

methods presented in this chapter for evaluation purposes. In the evaluation, bias (denoted as ), 

which is defined as the ratio of the measured value to the predicted value, is analyzed as a 

statistical variable. A value of 1.0 represents the prediction is the same as the measured 

(observed) deformation.

∆i = 0.5 �

�Kh�γsZ + q�Sv �γbb'Sv�tanδ�

Kreinf � (H Z) �tan �45o ψ

2

� + tan�90o φds��

DL = 2bq,volDv

H

εL = DL

bq,vol

= 2Dv

H = 2εv

λλ

λλ
75

The arithmetic mean of ( ) can be calculated as follows:

Figure 78. Equation. Arithmetic mean value.

Where:

= Arithmetic mean of .

= Sampled value.

N0 = Total number (population) of values.

The standard deviation of ( ) can be calculated as follows:

Figure 79. Equation. Standard deviation.

The coefficient of variation (COV) of can be calculated as follows:

Figure 80. Equation. COV.

Where:

= Standard deviation.

= Mean value.

Each prediction method is evaluated using the following three criteria:

Conservativeness: A prediction method with less than 1.0 represents a conservative 

prediction method, while a prediction method with greater than 1.0 represents an 

unconservative prediction method.

Accuracy: Accuracy of a prediction method is represented by the deviation of mean 

from unity; a mean that is much larger or smaller than unity represents a less accurate 

prediction method.

Reliability: The reliability of a prediction method is indicated by COV; a large COV 

value represents a prediction method that is unreliable.

Immediate Settlement

Laboratory and field observations of immediate settlements are used to evaluate the 

five immediate settlement methods presented in this chapter. Table 14 shows the soil and 

foundation parameters of the case histories used in the evaluation.

λλ

μλ= 

∑ λi

N0

λλ

λλii λλ

λλ

σλ = �∑�λi μλ

�

2

N0 1

λλ

COV = σ

μ

λλ

λλ

λλ

λλ
76

Table 14. Soil and foundation parameters for the case histories.

Case 

History 

No.

B

(m)

L

(m)

Total 

Unit 

Weight 

of Soil

(kN/m3)

Depth from 

Ground 

Surface to 

Groundwater 

Table (m)

Df

(m)

Hinc

(m)

qc

(kN/m2) N

Reference 

Number

Abutment/

Pier Designation in 

the Reference

1 1.0 1.0 15.65 4.9 0.71 11.0 2,500–18,800 16–24 106 None

2 1.5 1.5 15.65 4.9 0.76 11.0 2,500–18,800 16–24 106 None

3 2.5 2.5 15.65 4.9 0.76 11.0 2,500–18,800 16–24 106 None

4 3.0 3.0 15.65 4.9 0.76 11.0 2,500–18,800 16–24 106 None

5 3.0 3.0 15.65 4.9 0.89 11.0 2,500–18,800 16–24 106 None

6 5.2 28.0 18.85 1.2 2.3 14.2 11,768 42* 112 Gentbrugge Ghent 

abutment

7 7.0 36.0 18.85 1.2 2.3 14.2 11,768 42* 112 Gentbrugge Brussels 

abutment

8 6.0 52.5 18.85 1.2 2.8 > zi 11,768 42* 112 Gentbrugge pier A

9 6.0 52.5 18.85 2.5 3.6 > zi 11,768 42* 112 Gentbrugge pier B

10 5.0 8.5 18.85 5.0 2.5 > zi 8,336 24* 113

11 3.0 10.0 18.85 4.6 3.0 > zi 12,749 50* 114 Loopem pier

12 5.8 24 18.85 2.0 2.5 > zi 6,865 17* 112 Denys-Westrem 

abutment

13 2.6 21.0 18.85 2.0 2.0 > zi 6,276 9* 114 Denys-Westrem pier

1 ft = 0.305 m

1 kN/m3 = 6.37 lbf/ft3

1 kN/m2 = 20.89 lbf/ft2

* Indicates that the SPT blow count (N-value) corrected for overburden per Peck and Bazaraa.(94)

Hinc = Depth below footing to (relatively) incompressible stratum (Hinc > zi indicates that the incompressible layer is located below zi).
77

Modified Schmertmann Method

Table 15 lists the predicted and measured values of immediate settlements of shallow 

foundations and and standard normal variable (z) for each measured data point. Based on the 

results, the mean is 0.49, is 0.54, and COV is 1.10.

Table 15. Predicted and measured immediate settlements of shallow foundations using the 

modified Schmertmann method.

Case 

History 

No.

Applied 

Pressure 

(kPa)

Measured 

Immediate 

Settlement 

(mm)

Predicted 

Immediate 

Settlement

(mm)

(Measured/

Predicted) z

1 315.2 4.3 19.0 0.23 0

496.4 7.4 34.0 0.22 -0.19

2

235.6 3.1 18.6 0.17 -0.73

348.0 5.9 30.5 0.19 -0.61

444.9 10.6 41.7 0.25 0.29

3

188.2 2.4 20.0 0.12 -1.41

292.0 5.5 34.9 0.16 -0.87

395.8 10.2 51.1 0.20 -0.5

488.3 16.9 66.5 0.25 0.19

4

130.7 1.6 14.3 0.11 -1.75

390.7 11.4 56.6 0.20 -0.39

490.9 18.1 75.3 0.24 0.1

5

90.7 1.2 8.3 0.14 -1.2

194.7 3.6 22.9 0.16 -1.02

290.7 7.9 38.0 0.21 -0.29

390.9 14.9 55.1 0.27 0.39

487.3 25.9 72.6 0.36 0.5

6 95.8 9.9 6.1 1.62 1.41

7 131.7 11.9 12.1 0.98 0.87

8 158.0 7.9 14.4 0.55 0.61

9 214.5 4.1 18.8 0.22 -0.1

10 181.9 11.9 17.9 0.66 0.73

11 230.8 21.1 10.6 1.99 1.75

12 72.8 11.9 9.3 1.28 1.02

13 196.3 33.0 22.1 1.49 1.2

1 psi = 6.89 kPa

1 inch = 25.4 mm

Figure 81 shows the frequency of occurrence histogram of . The probability plot for is 

depicted in figure 82. The curve follows a lognormal distribution.

λλ

λλ

l

λλ λλ
78

Figure 81. Graph. Frequency of occurrence histogram of for immediate settlements of 

shallow foundations using the modified Schmertmann method.

Figure 82. Graph. Probability plot for measured and predicted settlements using the 

modified Schmertmann method.

Conclusion: 

Any interpretations of the results in this study should consider that the number of measured data 

points is statistically small. With this limitation, it was observed that the low mean (0.49) of 

the modified Schmertmann method indicates this method is highly conservative, and the 

prediction method overestimates immediate settlement of a shallow foundation by a factor of 

2.04. The relatively high COV value (1.10) indicates the method has relatively low reliability.

0

2

4

6

8

10

12

14

16

18

20

Frequency of Occurrence 

λ

l

y = 0.9659ln(x) + 1.0974

R2 = 0.8637

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0.00 0.50 1.00 1.50 2.00 2.50

z

λ

λλ
79

Hough Method

Table 16 lists the predicted and measured values of immediate settlement of shallow foundations 

as well as and z for each measured data point. Based on the results, the mean is 0.49, is 

0.31, and COV is 0.63.

Table 16. Predicted and measured immediate settlements of shallow foundations using the 

Hough method.

Case 

History 

No.

Applied 

Pressure 

(kPa)

Measured

Immediate 

Settlement 

(mm)

Predicted 

Immediate 

Settlement

(mm)

(Measured/

Predicted) z

1 315.2 4.3 29.2 0.15 -1.75

496.4 7.4 38.7 0.19 -1.02

2

235.6 3.1 19.2 0.16 -1.2

348.0 5.9 25.4 0.23 -0.73

444.9 10.6 30.0 0.35 -0.29

3

188.2 2.4 10.4 0.23 -0.87

292.0 5.5 14.9 0.37 -0.19

395.8 10.2 18.9 0.54 0.5

488.3 16.9 22.1 0.76 0.87

4

130.7 1.6 6.2 0.26 -0.61

390.7 11.4 15.8 0.72 0.73

490.9 18.1 18.9 0.96 1.2

5

90.7 1.2 4.6 0.26 -0.5

194.7 3.6 9.2 0.39 -0.1

290.7 7.9 13.0 0.61 0.61

390.9 14.9 16.5 0.90 1.02

487.3 25.9 19.6 1.32 1.75

6 95.8 9.9 19.9 0.50 0.39

7 131.7 11.9 27.2 0.44 0.19

8 158.0 7.9 26.4 0.30 -0.39

9 214.5 4.1 29.5 0.14 -1.41

10 181.9 11.9 27.9 0.43 0.1

11 230.8 21.1 19.2 1.10 1.41

12 72.8 11.9 28.7 0.41 0

13 196.3 33.0 67.0 0.49 0.29

1 psi = 6.89 kPa

1 inch = 25.4 mm

Figure 83 shows the frequency of occurrence histogram of . The probability plot for is 

depicted in figure 84. The curve follows a lognormal distribution.

λλ λλ

l

λλ λλ
80

Figure 83. Graph. Frequency of occurrence histogram of for immediate settlements of 

shallow foundations using the Hough method.

Figure 84. Graph. Probability plot for measured and predicted settlement using the Hough 

method.

Conclusion: 

Any interpretations of the results in this study should consider that the number of measured data 

points is statistically small. With this limitation, it was observed that the low mean (0.49) of 

the Hough method indicates this method is highly conservative, and the prediction method 

overestimates immediate settlement of a shallow foundation by a factor of 2.04. The relatively 

low COV value (0.63) indicates the method has fair reliability. The overestimation of the Hough 

method agrees with the conclusion from the FHWA report, Spread Footings for Highway 

0

2

4

6

8

10

12

14

16

18

Frequency of Occurrence 

λ

l

y = 1.4185ln(x) + 1.284

R2 = 0.988

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1 1.2 1.4

z

λ

λλ
81

Bridges, which concluded that settlements estimated by the modified Hough method are usually 

overestimated by a factor of 2 or more.(3)

Peck and Bazaraa Method

Table 17 lists the predicted and measured values of immediate settlements of shallow 

foundations and and z for each measured data point. Based on the results, the mean is 0.79, 

is 0.77, and COV is 0.97.

Table 17. Predicted and measured immediate settlements of shallow foundations using the 

Peck and Bazaraa method.

Case 

History 

No.

Applied 

Pressure 

(kPa)

Measured 

Immediate 

Settlement 

(mm)

Predicted 

Immediate 

Settlement

(mm)

(Measured/

Predicted) z

1 315.2 4.3 14.1 0.30 -0.87

496.4 7.4 22.6 0.33 -0.39

2

235.6 3.1 12.2 0.25 -1.02

348.0 5.9 18.3 0.32 -0.5

444.9 10.6 23.7 0.45 0

3

188.2 2.4 11.1 0.22 -1.41

292.0 5.5 17.5 0.31 -0.61

395.8 10.2 24.1 0.42 -0.19

488.3 16.9 29.9 0.57 0.19

4

130.7 1.6 7.8 0.21 -1.75

390.7 11.4 24.6 0.46 0.1

490.9 18.1 31.2 0.58 0.29

5

90.7 1.2 5.2 0.23 -1.2

194.7 3.6 11.8 0.31 -0.73

290.7 7.9 18.0 0.44 -0.1

390.9 14.9 24.5 0.61 0.39

487.3 25.9 30.8 0.84 0.5

6 95.8 9.9 4.7 2.11 1.41

7 131.7 11.9 7.1 1.68 1.02

8 158.0 7.9 7.0 1.13 0.87

9 214.5 4.1 10.1 0.41 -0.29

10 181.9 11.9 10.7 1.11 0.73

11 230.8 21.1 6.1 3.46 1.75

12 72.8 11.9 6.3 1.89 1.2

13 196.3 33.0 32.3 1.02 0.61

1 psi = 6.89 kPa

1 inch = 25.4 mm

Figure 85 shows the frequency of occurrence histogram of . The probability plot for is 

depicted in figure 86. The curve follows a lognormal distribution.

λλ λλ

l

λλ λλ
82

Figure 85. Graph. Frequency of occurrence histogram of for immediate settlements of 

shallow foundations using the Peck and Bazaraa method.

Figure 86. Graph. Probability plot for measured and predicted settlement using the Peck 

and Bazaraa method.

Conclusion: 

Any interpretations of the results in this study should consider that the number of measured data 

points is statistically small. With this limitation, it was observed that the less-than-unity mean 

value (0.79) indicates the Peck and Bazaraa method is a conservative prediction method, and the

prediction method overestimates the settlement of a shallow foundation by a factor of 1.26. The 

COV value of 0.97 indicates the method has relatively fair reliability.

0

2

4

6

8

10

12

14

16

Frequency of Occurrence 

λ

l

y = 1.1183ln(x) + 0.6382

R2 = 0.9348

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 1 2 3 4

z

λ

λλ
83

Burland and Burbidge Method

Table 18 lists the predicted and measured values of immediate settlements of shallow 

foundations and and z for each measured data point. Based on the results, the mean is 0.62, 

is 0.49, and COV is 0.79.

Table 18. Predicted and measured immediate settlements of shallow foundations using the 

Burland and Burbidge method.

Case 

History 

No.

Applied 

Pressure 

(kPa)

Measured 

Immediate 

Settlement 

(mm)

Predicted

Immediate 

Settlement

(mm)

(Measured/

Predicted) z

1 315.2 4.3 10.0 0.43 -0.1

496.4 7.4 15.7 0.47 0

2

235.6 3.1 9.9 0.31 -0.73

348.0 5.9 14.6 0.40 -0.39

444.9 10.6 18.7 0.57 0.29

3

188.2 2.4 11.3 0.21 -1.2

292.0 5.5 17.5 0.31 -0.61

395.8 10.2 23.8 0.43 -0.29

488.3 16.9 29.3 0.58 0.39

4

130.7 1.6 8.9 0.18 -1.75

390.7 11.4 26.6 0.43 -0.19

490.9 18.1 33.5 0.54 0.1

5

90.7 1.2 6.2 0.19 -1.41

194.7 3.6 13.3 0.27 -1.02

290.7 7.9 19.8 0.40 -0.5

390.9 14.9 26.6 0.56 0.19

487.3 25.9 33.2 0.78 0.87

6 95.8 9.9 6.6 1.50 1.41

7 131.7 11.9 11.2 1.06 1.2

8 158.0 7.9 11.1 0.71 0.61

9 214.5 4.1 15.0 0.27 -0.87

10 181.9 11.9 17.4 0.68 0.5

11 230.8 21.1 8.6 2.45 1.75

12 72.8 11.9 11.9 1.00 1.02

13 196.3 33.0 43.3 0.76 0.73

1 psi = 6.89 kPa

1 inch = 25.4 mm

Figure 87 shows the frequency of occurrence histogram of . The probability plot for is 

depicted in figure 88. The curve follows a lognormal distribution.

λλ λλ

l

λλ λλ
84

Figure 87. Graph. Frequency of occurrence histogram of for immediate settlements of 

shallow foundations using the Burland and Burbidge method.

Figure 88. Graph. Probability plot for measured and predicted settlement using the 

Burland and Burbidge method.

Conclusion: 

Any interpretations of the results in this study should consider that the number of measured data 

points is statistically small. With this limitation, it was observed that the less-than-unity mean 

value (0.62) indicates that the Burland and Burbidge method is a conservative prediction method, 

and the prediction method overestimates the settlement of a shallow foundation by a factor of 

1.64. The relatively low COV value (0.79) indicates the method has fair reliability.

0

2

4

6

8

10

12

14

Frequency of Occurrence 

λ

l

y = 1.4046ln(x) + 0.967

R2 = 0.9683

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5 3

z

λ

λλ
85

D’Appolonia Method

Table 19 lists the predicted and measured values of immediate settlement of shallow foundations 

and and z for each measured data point. Based on the results, the mean is 1.11, is 0.85, 

and COV is 0.77.

Table 19. Predicted and measured immediate settlements of shallow foundations using the 

D’Appolonia method.

Case 

History 

No.

Applied 

Pressure 

(kPa)

Measured

Immediate 

Settlement

(mm)

Predicted 

Immediate 

Settlement

(mm)

(Measured/

Predicted) z

1 315.2 4.3 4.4 0.98 0.29

496.4 7.4 6.9 1.07 0.5

2

235.6 3.1 5.0 0.62 -0.61

348.0 5.9 7.4 0.80 -0.19

444.9 10.6 9.5 1.12 0.61

3

188.2 2.4 6.8 0.35 -1.02

292.0 5.5 10.5 0.52 -0.73

395.8 10.2 14.3 0.71 -0.29

488.3 16.9 17.6 0.96 0.19

4

130.7 1.6 5.6 0.29 -1.75

390.7 11.4 16.6 0.69 -0.39

490.9 18.1 20.9 0.87 0

5

90.7 1.2 3.8 0.32 -1.41

194.7 3.6 8.1 0.44 -0.87

290.7 7.9 12.0 0.66 -0.5

390.9 14.9 16.2 0.92 0.1

487.3 25.9 20.2 1.28 0.73

6 95.8 9.9 5.4 1.83 0.87

7 131.7 11.9 5.8 2.05 1.02

8 158.0 7.9 9.4 0.84 -0.1

9 214.5 4.1 12.0 0.34 -1.2

10 181.9 11.9 11.3 1.05 0.39

11 230.8 21.1 6.2 3.40 1.75

12 72.8 11.9 3.6 3.31 1.41

13 196.3 33.0 14.1 2.34 1.2

1 psi = 6.89 kPa

1 inch = 25.4 mm

Figure 89 shows the frequency of occurrence histogram of . The probability plot for is 

depicted in figure 90. The curve follows a lognormal distribution.

λλ λλ

l

λλ λλ
86

Figure 89. Graph. Frequency of occurrence histogram of for immediate settlements of 

shallow foundations using the D’Appolonia method.

Figure 90. Graph. Probability plot for measured and predicted settlement using the 

D’Appolonia method.

Conclusion: 

Any interpretations of the results in this study should consider that the number of measured data 

points is statistically small. With this limitation, it was observed that the slightly higher-thanunity mean value (1.11) indicates the D’Appolonia method is a slightly unconservative 

prediction method, and the predicted immediate settlement is on average 91 percent of the 

actually measured settlement of a shallow foundation. The relatively low COV value (0.77) 

indicates the method has fair reliability.

0

2

4

6

8

10

12

Frequency of Occurrence 

λ

l

y = 1.3002ln(x) + 0.1664

R2 = 0.9707

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 1 2 3 4

z

λ

λλ
87

Comparison of the Five Prediction Methods for Immediate Settlement of Shallow Foundation 

on Granular Soils

Table 20 summarizes the statistical analyses of the five prediction methods for immediate 

settlement of shallow foundation on granular soils. Any interpretations of the results in this study 

should consider that the number of measured data points is statistically small. With this 

limitation, it was observed that four of the five methods (modified Schmertmann, Hough, 

Peck and Bazaraa, and Burland and Burbidge) overestimate immediate settlement, while the 

D’Appolonia method slightly underestimates immediate settlement. In comparison, the 

D’Appolonia method is the most accurate method with the mean the closest to unity and 

relatively small COV, followed by the Peck and Barazaa method and the Burland and Burbidge 

method. Both the modified Schmertmann method and the Hough method overestimate

immediate settlement of shallow foundations on granular soils by a factor of approximately 2. 

Table 20. Summary of the statistical analyses of the five prediction methods for immediate 

settlement of shallow foundations on granular soil, results from this study.

Statistical 

Parameters

Modified 

Schmertmann 

Method

Hough

Method

Peck and 

Barazaa

Method

Burland and 

Burbidge

Method

D’Appolonia

Method

Mean 0.49 0.49 0.79 0.62 1.11

0.54 0.31 0.77 0.49 0.85

COV 1.10 0.63 0.97 0.79 0.77

A similar FHWA study was conducted by Gifford to evaluate the five methods based on the 

observed deformations of 34 bridge foundations, and their statistical results are listed in 

table 21 for comparison.

(3) With the acknowledgement of the statistically small data set, Gifford

concluded the following:(3)

“Three of the five methods (Burland and Burbidge, D’Appolonia, and Peck and 

Bazaraa) typically underpredicted settlement, while the other two (Hough and 

Schmertmann) typically overpredicted. The D’Appolonia method was the most 

accurate, on average, with Burland and Burbidge next. The Hough method 

provided the least accurate predictions.”(pp. 75)(3)

Table 21. Summary of the statistical analyses of the five prediction methods for immediate 

settlement of shallow foundations on granular soil, results from Gifford.

(3)

Statistical 

Parameters

Modified 

Schmertmann

Method*

Hough

Method**

Peck and 

Bazaraa

Method*

Burland and 

Burbidge

Method**

D’Appolonia

Method*

Mean 0.74 0.69 1.21 1.14 1.33

0.28 0.49 0.55 1.69 0.94

COV 0.38 0.70 0.45 0.79 0.7

*Based on 10 bridge foundations.

**Based on 24 bridge foundations.

λλ

λλ

λλ
88

Vertical Deformations of GRS Walls and Abutments

In this section, the empirical equation by Adams et al. for predicting vertical deformation of GRS 

walls and abutments is evaluated using field observation data.

(32) To calculate the vertical 

displacement of a GRS wall, the composite Young’s modulus of the GRS wall (EGRS) is needed. 

The equation by Holtz and Lee is used to calculate the GRS composite Young’s modulus (see 

figure 91).

(115) In deriving this equation for the GRS composite Young’s modulus, it is assumed 

that the stress-strain behavior of the soil and reinforcement follows Hooke’s Law and that the 

deformation of the composite material is uniform. 

Figure 91. Equation. Elastic modulus of GRS composite.

Where:

Es = Elastic modulus of soil.

tR = Thickness of reinforcement.

Since Sv tR Sv and ER = J/tR, where J is the stiffness of the reinforcement, then figure 91 can 

be simplified as follows:

Figure 92. Equation. Elastic modulus of GRS composite (modified equation).

Where Ecomp is the elastic modulus of GRS composite. Given q, b', a, H, and EGRS, the vertical 

displacement can be calculated using figure 67. Table 22 presents the parameters used for the 

evaluation.

Table 22. Abutment and GRS wall parameters in case histories.

No.

H

(m)

a

(m)

b'

(m)

Sv

(m)

EGRS

(kN/m2)

Reference 

Number

Wall 

Designations in 

the References

1 4.65 0.15 0.91 0.2 62,731 70 Wall section A

2 4.65 0.15 0.91 0.2 62,669 70 Wall section B

3 4.35 1.5 1.0 0.3–0.6 20,253 75 Wall section 

nonwoven

4 4.35 1.5 1.0 0.3–0.6 20,653 75 Wall section 

woven

5 7.62 0.2 2.44 0.2 240,147 116

6 5.9 1.35 3.81 0.4 62,700 63 Wall section 800

7 5.9 1.35 3.81 0.4 62,700 63 Wall section 400

8 4.5 1.35 3.81 0.4 62,700 63 Wall section 200

1 ft = 0.305 m

1 kN/m2 = 20.89 lbf/ft2

EGRS = ER ×

tR

Sv

+ Es ×

(Sv tR)

Sv

Ecomp ≈ 

J

tR

×

tR

Sv

+ Es ×

Sv

Sv

= 

J

Sv

+ Es
89

Table 23 lists the predicted and measured values of the vertical deformation predictions of GRS 

walls and abutments and and z for each data point. Based on the results, the mean is 7.31, 

is 5.73, and COV is 0.78.

Table 23. Predicted and measured vertical displacements of abutments and GRS walls.

Case 

History 

No.

Applied 

Pressure 

(kPa)

Measured 

Vertical 

Displacement 

(mm)

Predicted 

Vertical 

Displacement 

(mm)

(Measured/

Predicted) z

1

100 14.4 1.9 7.58 0

200 32.7 3.9 8.38 0.11

300 55.4 5.8 9.55 0.43

400 75.5 7.8 9.68 0.55

2

100 25.6 1.9 13.47 0.97

200 58.9 3.9 15.10 1.15

300 103.1 5.8 17.78 1.38

400 158.9 7.8 20.37 1.73

3

50 3.5 3.2 1.09 -1.38

100 7.7 6.5 1.18 -1.15

150 50.6 9.7 5.22 -0.21

180 115.6 11.7 9.88 0.68

200 161.5 13.0 12.42 0.81

4

50 4.5 3.2 1.41 -0.81

100 18.2 6.3 2.89 -0.32

150 60.4 9.5 6.36 -0.11

180 95.8 11.4 8.40 0.21

200 113.0 12.7 8.90 0.32

5 195 5.1 2.2 2.32 -0.55

260 8.2 2.9 2.83 -0.43

6 115 3.0 5.4 0.56 -1.73

7 115 7.0 5.4 1.30 -0.97

8 115 7.0 4.6 1.52 -0.68

1 psi = 6.89 kPa

1 inch = 25.4 mm

Figure 93 shows the frequency of occurrence histogram of . The probability plot for is 

depicted in figure 94. The curve follows a lognormal distribution.

λλ λλ

l

λλ λλ
90

Figure 93. Graph. Frequency of occurrence histogram of of vertical displacement of 

abutments and GRS walls.

R2 = Coefficient of determination.

Figure 94. Graph. Probability plot for measured and predicted vertical displacement of 

abutments and GRS walls.

Conclusion: 

Any interpretations of the results in this study should consider that the number of measured data 

points is statistically small. With this limitation, it was observed that the high mean value 

(7.31) indicates this prediction method for vertical deformations of GRS walls and abutments is 

unconservative. It should be noted that the accuracy of this method is affected by the accuracy in 

determination of the Young’s modulus of the composite material. Since the proposed equation by 

0

1

2

3

4

5

6

7

8

9

10

Frequency of Occurrence 

λλ

l

y = 0.8291ln(x) - 1.3031

R2 = 0.9337

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 5 10 15 20 25

z

λ

λλ
91

Holtz and Lee (see figure 91) is associated with simplifying assumptions, its accuracy also 

depends on the accurate estimation of Young’s moduli of the reinforcement and soil.

(115) Any 

error in these estimations may lead to error in the prediction results. 

Lateral Displacements of GRS Walls and Abutments

In this section, field observations of lateral displacements of GRS walls and abutments are 

applied to the six methods presented previously to evaluate their conservativeness, accuracy, and 

reliability. Table 24 presents the parameters used for the evaluation. 

Table 24. Abutment and GRS wall parameters in case histories.

Case 

History 

No.

H

(m)

L

(m)

Sv

(m) (Degree) (Degree) Facing Type

Reference 

Number

Wall 

Designations in 

the References

1 3.6 2.5 0.6 41(DS) 11 CMU 71 Wall 1

2 3.6 2.5 0.6 41(DS) 11 CMU 71 Wall 2

3 3.6 2.5 0.9 41(DS) 11 CMU 71 Wall 3

4 4.0 3.0 0.4 32(DS) 14 Wrap around 117 N/A

5 6.0 3.6 0.6 40(PS) 11 CMU 118 Wall 1

6 6.0 3.6 0.6 30(PS) 11 CMU 118 Wall 2

7 6.0 3.6 0.6 30(PS) 11 CMU 118 Wall 3

8 6.0 3.6 0.6 20(PS) 11 CMU 118 Wall 4

9 4.0 3.0 0.4 33(TT) 3 Wrap around 119 N/A

10 3.6 2.5 0.6 41(DS) 11 CMU 76 Wall 5

11 5.3 2.0 0.5 40 10 Wrap around 120 N/A

12 7.62 3.2–4.4 0.2 — — CMU 116 N/A

13 4.35 1.3–3.6 0.3–0.6 — — CMU 75 Woven wall

14 4.35 2.7–3.6 0.3–0.6 — — CMU 75 Nonwoven wall

15 5.9 8–12 0.4 — — CMU 63 Wall section 800

16 5.9 8–12 0.4 — — CMU 63 Wall section 400

17 4.5 8–12 0.4 — — CMU 63 Wall section 200

18 4.65 3.15 0.2 — — CMU 70 Wall section A

19 4.65 3.15 0.2 — — CMU 70 Wall section B

1 ft = 0.305 m

— Indicates the values are not provided.

DS = Direct shear test.

PS = Plain strain test.

TT = Triaxial test.

N/A = No wall designation was provided.

FHWA Method

Table 25 lists the predicted and measured values of the lateral displacements of GRS walls and 

abutments and and z for each data point. Based on the results, the mean is 0.12, is 0.10, 

and COV is 0.83.

λλ λλ
92

Table 25. Predicted and measured maximum lateral displacements of GRS walls at EOC

using the FHWA method.

Case 

History 

No.

Measured

Maximum 

Lateral 

Displacement

(mm)

Predicted 

Maximum 

Lateral 

Displacement 

(mm)

(Measured/

Predicted) z

1 5.2 48.4 0.11 0.11

2 7.9 48.4 0.16 0.6

3 6.0 48.4 0.12 0.35

4 15.7 50.6 0.31 1.34

5 3.2 94.6 0.03 -0.6

6 8.4 94.6 0.09 -0.35

7 1.2 94.6 0.01 -1.34

8 2.6 94.6 0.03 -0.91

9 5.1 50.6 0.10 -0.11

10 12.8 48.4 0.26 0.91

1 inch = 25.4 mm

Figure 95 shows the frequency of occurrence histogram of . The probability plot for values 

using the FHWA method is depicted in figure 96. The curve follows a lognormal distribution.

Figure 95. Graph. Frequency of occurrence histogram of for the lateral displacement of 

GRS walls and abutments using the FHWA method.

l

λλ λλ

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0-0.09 0.10-0.19 0.19-0.29 0.30-0.39 0.40-0.49 0.50-1.00

Frequency of Occurrence 

λ

l
93

Figure 96. Graph. Probability plot for measured and predicted lateral displacement of 

GRS walls using the FHWA method.

Conclusion: 

Any interpretations of the results in this study should consider that the number of measured data 

points is statistically small. With this limitation, it was observed that the lower-than-unity mean 

(0.12) of the FHWA method indicates the method is highly conservative, and the predictions 

significantly overestimate the lateral deformations by a factor of 8.33. The relatively low COV 

value (0.83) indicates a fair reliability of this method.

Geoservices Method

Table 26 lists the predicted and measured values of the lateral displacements of GRS walls and 

abutments and and z for each data point. Based on the results, the mean is 1.38, is 1.59, 

and COV is 1.15.

y = 0.7919ln(x) + 1.9556

R2 = 0.9412

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

z

λ

λλ

λλ λλ
94

Table 26. Predicted and measured lateral displacements of GRS walls and abutments using 

the Geoservices method.

Case 

History 

No.

Elevation 

(m)

Measured

Lateral 

Displacement

(mm)

Predicted 

Lateral 

Displacement 

(mm)

(Measured/

Predicted) z Notes

1

3.3 1.5 0.7 2.11 0.84

Results are 

obtained at EOC

2.7 5.1 2.4 2.12 0.98

2.1 5.2 3.0 1.74 0.55

1.5 5.0 8.9 0.56 -0.35

0.9 3.7 7.4 0.51 -0.5

0.3 2.4 6.9 0.34 -1.06

2

3.3 6.3 4.5 1.39 0.40

Results are 

obtained at EOC

2.7 8.0 5.9 1.35 0.30

2.1 6.4 6.9 0.93 0.11

1.5 4.7 12.3 0.38 -0.98

0.9 3.8 9.9 0.39 -0.91

0.3 1.2 7.2 0.17 -1.46

3

3.1 2.1 9.4 0.22 -1.33

Results are 

obtained at EOC

2.2 6.0 8.7 0.69 -0.25

1.3 5.2 8.4 0.62 -0.3

0.5 2.1 6.6 0.32 -1.14

4

3.6 0.8 0.0 N/A N/A

Results are 

obtained at EOC

2.8 9.8 7.2 1.36 0.35

2 15.7 9.6 1.64 0.45

1.2 8.6 0.9 9.56 2.09

0.4 13.1 6.0 2.18 1.14

9

3.6 0.2 0.2 1.33 0.25

Results are 

obtained at EOC

2.8 5.1 7.3 0.67 -0.21

2 4.2 9.6 0.44 -0.78

1.2 2.3 3.0 0.76 0.02

0.4 2.8 6.0 0.47 -0.60

10

3.3 3.9 5.0 0.78 0.07

Results are 

obtained at EOC

2.7 9.9 13.4 0.74 -0.07

2.1 11.4 15.9 0.72 -0.11

1.5 12.6 13.4 0.94 0.16

0.9 8.1 16.4 0.49 -0.55

0.3 1.9 6.3 0.30 -1.23

11

4.5 81.5 47.5 1.72 0.5

Results are 

obtained under 

84 kPa of applied 

pressure

4 82.1 44.0 1.87 0.66

3.5 82.7 42.5 1.95 0.72

3 78.2 44.0 1.78 0.60

2.5 71.1 33.5 2.12 1.06

2 60.3 28.5 2.12 0.91

1.5 45.1 21.5 2.10 0.78

l
95

1 31.5 11.0 2.86 1.23

0.5 18.9 6.5 2.91 1.33

12

6.5 8.0 2.1 3.81 1.60 Results are 

obtained under 

131 kPa of applied 

pressure

5.9 8.0 2.6 3.08 1.46

5.1 14.0 2.2 6.36 1.79

13

3.8 83.3 111.3 0.75 -0.02 Results are 

obtained under 

190 kPa of applied 

pressure

2.6 57.7 46.6 1.24 0.21

1.5 21.6 30.2 0.71 -0.16

0.6 7.2 15.7 0.46 -0.66

14

3.8 106.7 244.2 0.44 -0.72 Results are 

obtained under 

190 kPa of applied 

pressure

2.6 96.9 182.2 0.53 -0.45

1.5 21.8 53.6 0.41 -0.84

0.6 0.9 8.8 0.10 -1.79

15

2.4 1.1 19.8 0.06 -2.09 Results are 

obtained under 

115 kPa of applied 

pressure

4 4.0 23.8 0.17 -1.60

4.8 4.0 7.4 0.54 -0.40

1 ft = 0.305 m

1 inch = 25.4 mm

1 psi = 6.89 kPa

N/A = not applicable since the predicted value is zero.

Figure 97 shows the frequency of occurrence histogram of . The probability plot for value 

obtained based on the result of the Geoservices method is depicted in figure 98. The curve 

follows a lognormal distribution.

Figure 97. Graph. Frequency of occurrence histogram of for the lateral displacement of 

GRS walls and abutments using the Geoservices method.

λλ λλ

0

5

10

15

20

25

30

35

Frequency of Occurrence 

λ

l
96

Figure 98. Graph. Probability plot for measured and predicted lateral displacement of 

GRS walls using the Geoservices method.

Conclusion: 

Any interpretations of the results in this study should consider that the number of measured data 

points is statistically small. With this limitation, it was observed that the greater-than-unity value 

of the mean (1.38) indicates the Geoservices method is an unconservative prediction method, 

and the predicted lateral displacement is on average 72 percent of the actually measured lateral 

displacements. The relatively high COV value (1.15) indicates a relatively low reliability of 

this method.

CTI Method

Table 27 lists the predicted and measured values of the lateral displacements of GRS walls and 

abutments and and z for each data point. Based on the results, the mean is 0.59, is 0.64, 

and COV is 1.08.

y = 0.9332ln(x) + 0.1368

R2 = 0.9761

-3

-2

-1

0

1

2

3

0.00 2.00 4.00 6.00 8.00 10.00 12.00

z

λ

λλ

λλ λλ
97

Table 27. Predicted and measured maximum lateral displacements of GRS walls using the 

CTI method.

Case 

History 

No.

Elevation 

(m)

Measured

Maximum 

Lateral 

Displacement

(mm)

Predicted

Maximum 

Lateral 

Displacement 

(mm)

(Measured/

Predicted) z Notes

1

3.3 1.5 1.4 1.07 1.33

Results are 

obtained at EOC

2.7 5.1 4.7 1.09 1.46

2.1 5.2 5.9 0.88 1.06

1.5 5.0 17.3 0.29 -0.4

0.9 3.7 14.4 0.26 -0.72

0.3 2.4 13.5 0.18 -1.33

2

3.3 6.3 8.7 0.72 0.78

Results are 

obtained at EOC

2.7 8.0 11.5 0.70 0.60

2.1 6.4 13.4 0.48 0.11

1.5 4.7 23.8 0.20 -1.14

0.9 3.8 19.3 0.20 -1.06

0.3 1.2 13.9 0.09 -1.79

3

3.1 2.1 18.3 0.11 -1.6

Results are 

obtained at EOC

2.2 6.0 16.8 0.36 -0.21

1.3 5.2 16.3 0.32 -0.35

0.5 2.1 12.8 0.16 -1.46

4

3.6 0.8 0 N/A N/A

Results are 

obtained at EOC

2.8 9.8 15.4 0.64 0.4

2 15.7 20.5 0.77 0.91

1.2 8.6 1.9 4.53 2.09

0.4 13.1 12.8 1.02 1.23

9

3.6 0.2 0.3 0.67 0.5

Results are 

obtained at EOC

2.8 5.1 15.6 0.33 -0.3

2 4.2 20.5 0.20 -0.91

1.2 2.3 6.4 0.36 -0.16

0.4 2.8 12.8 0.22 -0.84

10

3.3 3.9 5.4 0.72 0.72

Results are 

obtained at EOC

2.7 9.9 14.5 0.68 0.55

2.1 11.4 17.2 0.66 0.45

1.5 12.6 14.5 0.87 0.98

0.9 8.1 17.7 0.46 -0.02

0.3 1.9 6.8 0.28 -0.50

11

4.5 81.5 190.0 0.43 -0.11

Results are 

obtained under 84 

kPa of applied 

pressure

4 82.1 176.0 0.47 0.07

3.5 82.7 170.0 0.49 0.16

3 78.2 176.0 0.44 -0.07

2.5 71.1 134.0 0.53 0.30

2 60.3 114.0 0.53 0.25

l
98

1.5 45.1 86.0 0.52 0.21

1 31.5 44.0 0.72 0.66

0.5 18.9 26.0 0.73 0.84

12

6.5 8.0 7.3 1.10 1.10 Results are 

obtained under 

131 kPa of applied 

pressure

5.9 8.0 8.8 0.91 1.14

5.1 14.0 7.6 1.84 1.79

13

3.8 83.3 180.4 0.46 0.02 Results are 

obtained under 

190 kPa of applied 

pressure

2.6 57.7 104.2 0.55 0.35

1.5 21.6 77.7 0.28 -0.55

0.6 7.2 36.6 0.20 -1.06

14

3.8 106.7 398.2 0.27 -0.6 Results are 

obtained under 

190 kPa of applied 

pressure

2.6 96.9 338.5 0.29 -0.45

1.5 21.8 121.0 0.18 -1.23

0.6 0.9 22.6 0.04 -2.09

15

2.4 1.1 3.2 0.34 -0.25 Results are 

obtained under 

115 kPa of applied 

pressure

4 4.0 15.2 0.26 -0.66

4.8 4.0 16.4 0.24 -0.78

1 ft = 0.305 m

1 inch = 25.4 mm

1 psi = 6.89 kPa

N/A = The value could not be calculated.

Figure 99 shows the frequency of occurrence histogram of . The probability plot for value 

obtained based on the result of the CTI method is depicted in figure 100. The curve follows a 

lognormal distribution.

Figure 99. Graph. Frequency of occurrence histogram of for the lateral displacement of 

GRS walls and abutments using the CTI method.

λλ λλ

0

5

10

15

20

25

30

35

Frequency of Occurrence 

λ

l
99

Figure 100. Graph. Probability plot for measured and predicted lateral displacement of 

GRS walls using the CTI method.

Conclusion: 

Any interpretations of the results in this study should consider that the number of measured data 

points is statistically small. With this limitation, it was observed that the lower-than-unity mean 

(0.59) indicates the CTI method is a conservative prediction method, and it overestimates the 

lateral deformation by a factor of 1.69. The relative high COV value (1.08) indicates a relatively 

low reliability of this method.

Jewell-Milligan Method

Table 28 lists the predicted and measured values of the lateral displacements of GRS walls and 

abutments and and z for each data point. Based on the results, the mean is 0.74, is 0.59, 

and COV is 0.80.

y = 1.1667ln(x) + 0.9919

R2 = 0.9581

-4

-3

-2

-1

0

1

2

3

4

0.00 1.00 2.00 3.00 4.00 5.00

z

λ

λλ

λλ λλ
100

Table 28. Predicted and measured lateral displacements of GRS walls and abutments using 

the Jewell-Milligan method.

Case 

History 

No.

Elevation 

(m)

Measured

Lateral 

Displacement

(mm)

Predicted 

Lateral 

Displacement 

(mm)

(Measured/

Predicted) z Notes

4

3.6 0.79 6.0 0.13 -1.28

Results are 

obtained at 

EOC

2.8 9.8 14.0 0.70 0.25

2.0 15.7 16.7 0.94 0.67

1.2 8.6 14.2 0.61 0

0.4 13.1 6.4 2.05 1.28

9

3.6 0.2 5.9 0.03 -1.65

Results are 

obtained at

EOC

2.8 5.1 13.8 0.37 -0.67

2.0 4.2 16.4 0.26 -0.84

1.2 2.3 14.0 0.16 -1.04

0.4 2.8 6.3 0.44 -0.52

11

4.5 81.5 36.1 2.26 1.65

Results are 

obtained 

under 84 kPa 

of applied 

pressure

4 82.1 62.6 1.31 1.04

3.5 82.7 82.1 1.01 0.84

3 78.2 94.8 0.82 0.52

2.5 71.1 98.0 0.73 0.39

2 60.3 94.2 0.64 0.13

1.5 45.1 83.2 0.54 -0.13

1 31.5 62.3 0.51 -0.25

0.5 18.9 39.1 0.48 -0.39

1 ft = 0.305 m

1 inch = 25.4 mm

1 psi = 6.89 kPa

Figure 101 shows the frequency of occurrence histogram of . The probability plot for value 

obtained based on the results of the Jewell-Milligan method is depicted in figure 102. The curve 

follows a lognormal distribution.

l

λλ λλ
101

Figure 101. Graph. Frequency of occurrence histogram of for the lateral displacement of 

GRS walls and abutments using the Jewell-Milligan method.

Figure 102. Graph. Probability plot for measured and predicted lateral displacement of 

GRS walls using the Jewell-Milligan method.

Conclusion: 

Any interpretations of the results in this study should consider that the number of measured data 

points is statistically small. With this limitation, it was observed that the lower-than-unity mean 

(0.74) indicates the Jewell-Milligan method is a conservative prediction method, and it 

overestimates lateral deformation by a factor of 1.35. The relative low COV value (0.80) 

indicates the method has fair reliability.

0

1

2

3

4

5

6

7

8

9

0-0.49 0.50-0.99 1.00-1.49 1.50-1.99 2.00-2.49 2.50-3.00

Frequency of Occurrence 

λ

l

y = 0.856ln(x) + 0.5622

R2 = 0.9019

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0.00 0.50 1.00 1.50 2.00 2.50

z

λ

λλ
102

Wu Method

Table 29 lists the predicted and measured values of the lateral displacements of GRS walls and 

abutments and and z for each data point. Based on the results, the mean is 0.24, is 0.12, 

and COV is 0.50.

Table 29. Predicted and measured lateral displacements of GRS walls and abutments with 

modular block facing using the Wu method.

Case 

History 

No.

Elevation 

(m)

Measured

Lateral 

Displacement

(mm)

Predicted 

Lateral 

Displacement 

(mm)

(Measured/

Predicted) z Notes

1

3.3 1.5 4.7 0.3191 0.56

Results are 

obtained at EOC

2.7 5.1 13.8 0.3696 1.18

2.1 5.2 18.4 0.2826 0.42

1.5 5.0 18.7 0.2674 0.32

0.9 3.7 14.5 0.2552 0.19

0.3 2.4 5.9 0.4068 1.49

1

3.3 9.3 40.7 0.2285 0.11

Results are 

obtained at 30 kPa 

of applied pressure

2.7 7.2 43.3 0.1663 -0.37

2.1 6.5 41.5 0.1566 -0.42

1.5 5.2 35.3 0.1473 -0.61

0.9 3.3 24.5 0.1347 -0.83

0.3 1.4 9.1 0.1538 -0.46

1

3.3 31.6 88.9 0.3555 0.89

Results are 

obtained at 70 kPa 

of applied pressure

2.7 31.3 82.0 0.3817 1.27

2.0 25.6 70.8 0.3616 1.1

1.5 15.5 56.1 0.2763 0.37

1.1 11.1 45.9 0.2418 0.15

0.5 4.7 23.5 0.2000 -0.11

2

3.3 6.27 9.4 0.6670 2.12

Results are 

obtained at EOC

2.7 7.98 27.5 0.2902 0.46

2.1 6.41 36.8 0.1742 -0.32

1.5 4.68 37.3 0.1255 -1.1

0.9 3.83 29.0 0.1321 -0.96

0.3 1.22 11.9 0.1025 -1.49

2

3.3 11.4 81.8 0.1394 -0.71

Results are 

obtained at 30 kPa 

of applied pressure

2.7 11.5 86.6 0.1328 -0.89

2.0 10.5 81.9 0.1282 -1.03

1.5 7.1 69.1 0.1027 -1.37

1.1 8.0 58.6 0.1365 -0.77

0.5 3.9 32.0 0.1219 -1.18

2

3.3 46.5 177.3 0.2623 0.28 Results are 

obtained at 70 kPa 

of applied pressure

2.7 57.9 164.3 0.3524 0.77

2.0 50.6 140.7 0.3596 1.03

λλ λλ

l
103

1.4 37.0 110.9 0.3336 0.66

1.1 32.6 91.8 0.3551 0.83

0.5 15.8 46.1 0.3427 0.71

3

3.1 2.07 9.2 0.2250 0.06

Results are 

obtained at EOC

2.2 6.00 20.2 0.2970 0.51

1.3 5.24 20.0 0.2620 0.24

0.5 2.14 10.4 0.2058 -0.02

10

3.3 3.9 8.2 0.4756 1.83

Results are 

obtained at EOC

2.7 9.9 24.0 0.4125 1.64

2.1 11.4 32.0 0.3563 0.96

1.5 12.6 32.5 0.3877 1.37

0.9 8.1 25.2 0.3214 0.61

0.3 1.9 10.3 0.1845 -0.19

10

3.3 10.4 69.5 0.1496 -0.51

Results are 

obtained at 30 kPa 

of applied pressure

2.7 10.6 74.1 0.1430 -0.66

2.1 7.8 71.1 0.1097 -1.27

1.5 6.1 59.9 0.1018 -1.64

0.8 3.5 37.7 0.0928 -1.83

0.5 1.7 25.7 0.0661 -2.12

10

3.3 27.5 151.0 0.1821 -0.24

Results are 

obtained at 70 kPa 

of applied pressure

2.7 29.7 140.9 0.2108 0.02

2.1 25.0 122.6 0.2039 -0.06

1.5 18.3 96.5 0.1896 -0.15

0.8 10.1 57.1 0.1769 -0.28

0.5 5.4 36.6 0.1475 -0.56

1 ft = 0.305 m

1 inch = 25.4 mm

1 psi = 6.89 kPa

Figure 103 shows the frequency of occurrence histogram of . The probability plot for the 

value obtained based on the result of the analytical model is depicted in figure 104. The curve 

follows a lognormal distribution.

λλ λλ
104

Figure 103. Graph. Frequency of occurrence histogram of for the lateral displacement of 

GRS walls and abutments using the Wu method.

Figure 104. Graph. Probability plot for measured and predicted lateral displacement of 

GRS walls using the Wu method.

Conclusion: 

Any interpretations of the results of this study should consider that the number of measured data 

points is statistically small. With this limitation, it was observed that the lower-than-unity mean 

(0.24) indicates the Wu method is a conservative prediction method, and it overestimates 

lateral deformation by a factor of 4.17. The low COV value (0.50) indicates the method has 

good reliability.

0

2

4

6

8

10

12

14

0-0.19 0.20-0.39 0.40-0.59 0.60-0.79 0.80-1.00

Frequency of Occurrence 

λ

l

y = 1.9418ln(x) + 2.5393

R2 = 0.9648

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0.00 0.20 0.40 0.60 0.80

z

λ

λλ
105

Adams Method

Table 30 lists the predicted and measured values of the lateral displacements of GRS walls and 

abutments and and z for each data point. Based on the results, the mean is 1.13, is 0.41, 

and COV is 0.36.

Table 30. Predicted and measured lateral displacements of GRS walls and abutments using 

the Adams method.

Case 

History 

No.

Applied 

Pressure

(kPa)

Measured 

Lateral 

Displacement 

(mm)

Predicted

Lateral 

Displacement

(mm)

(Measured/

Predicted) z Notes

11 84 82.7 73.4 1.13 -0.10 None

12 131 14.3 15.2 0.94 -0.29 None

13 0 8.6 11.4 0.75 -0.50 Results are 

obtained at EOC

14 0 11.1 15.3 0.73 -0.74 Results are 

obtained at EOC

15 115 10 5.6 1.79 1.43 None

16 115 9 12.7 0.71 -1.02 None

17 115 7 16.0 0.44 -1.43 None

18 207 23.4 16.3 1.44 0.74 None 475 57.3 41.8 1.37 0.50

19

214 36.4 27.5 1.32 0.29

317 57.8 45.4 1.27 0.10 None

414 113.4 69.2 1.64 1.02

1 psi = 6.89 kPa

1 inch = 25.4 mm

Figure 105 shows the frequency of occurrence histogram of . The normal probability plot for 

value obtained based on the results of the Adams method is depicted in figure 106. The curve 

follows a normal distribution.

λλ λλ

l

λλ λλ
106

Figure 105. Graph. Frequency of occurrence histogram of for the lateral displacement of 

GRS walls and abutments using the Adams method.

Figure 106. Graph. Probability plot for measured and predicted lateral displacement of 

GRS walls using the Adams method.

Conclusion:

Any interpretations of the results of this study should consider that the number of measured data 

points is statistically small. With this limitation, it was observed that the slightly higher-thanunity mean (1.13) indicates the Adams method is a slightly unconservative prediction method,

and the predicted lateral displacement is on average 88 percent of the actually measured lateral 

deformation. The low COV value (0.36) indicates the method has good reliability.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0-0.39 0.40-0.79 0.80-1.19 1.20-1.59 1.60-1.99 2.00-2.40

Frequency of Occurrence 

λ

l

y = 2.0236x - 2.2801

R2 = 0.9759

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0.00 0.50 1.00 1.50 2.00

z

λ

λλ
107

Comparison of the Six Prediction Methods for Lateral Displacement of GRS Abutments and 

Walls 

Table 31 summarizes the statistical analyses of the six prediction methods for lateral 

displacement of GRS abutments and walls. The Adams method is the most accurate method for 

predicting the maximum lateral displacement of GRS walls and abutments with the mean the 

closest to unity and small COV. The Jewell-Milligan method is a conservative and relatively 

accurate method for predicting the lateral displacement of GRS walls and abutments with 

negligible facing rigidity. For predicting the displacement of GRS walls and abutments with 

CMU facing block, the CTI method may also be used, although it may overestimate lateral 

deformations by a factor of 1.69 with relatively low reliability.

Table 31. Summary of the statistical analyses of the six prediction methods for lateral 

displacements of GRS abutments and walls.

Statistical 

Parameters

FHWA

Method

Geoservices

Method

CTI

Method

JewellMilligan

Method

Wu

Method

Adams

Method

Mean 0.12 1.38 0.59 0.74 0.24 1.13

0.10 1.59 0.64 0.59 0.12 0.41

COV 0.38 1.15 1.08 0.80 0.50 0.36

λλ

λλ

109

CHAPTER 5. NUMERICAL AND CONSTITUTIVE MODELS FOR COMPACTED 

FILL AND REINFORCED SOIL FOR BRIDGE SUPPORTS

5.1 MODELING OF COMPACTED SOILS

Various constitutive models have been utilized to model compacted soils, such as the linear 

elastic model, elastic-plastic Mohr-Coulomb model, hyperbolic stress-strain models, modified 

Cam Clay model, elastic-plastic viscoplastic models, extended two-invariant geologic cap model, 

and generalized plasticity models. (See references 121, 72, 122–128, 74, 129–135, 70, and 136.)

An excellent review of the capabilities and shortcomings of different soil constitutive models can 

be found in Lade’s publication, “Overview of Constitutive Models for Soils.”(137) The soils can 

be any type: plastic or non-plastic, open-graded or well-graded, and coarse-grained or finegrained, if appropriate models with appropriate input parameters are used.

Assignment of reasonable values for parameters used in soil constitutive models greatly 

influences the success and accuracy of any numerical analysis. For simple soil constitutive 

models, material parameters are often readily available from routine laboratory tests; however, 

that is not always the case for advanced constitutive models and precise identification of 

parameter values imposes a significant challenge. The effect of constitutive models on simulated 

responses of GRS structures has been investigated. Hatami and Bathurst compared the results of 

finite difference analyses (using FLAC2D ) for GRS SRWs with measured results from 

physical tests.

(71) They modeled compacted fill soil using the hyperbolic stress-strain model 

proposed by Duncan et al. combined with a Mohr-Coulomb failure criterion and the simple 

linear elastic-plastic Mohr-Coulomb model.

(138) The simple elastic-plastic soil model was shown 

to be sufficient for predicting wall deformation, footing reaction response, and peak strain values 

in reinforcement layers for strains of less than 1.5 percent if appropriate values for the constant 

elastic modulus and Poisson’s ratio for the sand backfill soil are used. However, it is problematic 

to select a suitable single-value elastic modulus given the stress level dependency of granular 

soils. Different trends in the distribution of strains were observed when the nonlinear and linear 

elastic–plastic soil models were used, with the former giving a better fit to the measured data.

Huang et al. employed three well-known constitutive soil models in finite difference analyses 

(using FLAC2D ) of two instrumented reinforced soil segmental walls reported by Hatami and 

Bathurst.

(139,71,118) These models (in order of increasing complexity) are the linear elastic-plastic 

Mohr-Coulomb model, the Duncan-Chang hyperbolic model with a modification by 

Boscardin et al., and Lade’s single hardening constitutive model for frictional soils. (See 

references 138 and 140–143.) The modified Duncan-Chang model accounts for plane strain 

condition in addition to the triaxial condition considered in the original version of the 

model.

(138,71) Lade’s model considers a single yield surface and can capture both work-hardening 

and softening for frictional geomaterials.

(141–143) Major advantages of such a model lies in the 

fact that the effects of stress-dependent stiffness, shear dilatancy, and strain softening on soil 

mechanical behavior are accounted for. Moreover, the effects of plane strain conditions are 

explicitly accounted for within this model, and no empirical adjustment, as done for the modified 

Duncan-Chang model, is required to increase elastic modulus values from triaxial test results. On 

the downside, several model parameters lack physical meaning, and thus application of this 

model demands significant expertise in interpreting available test results, calibration of model 
110

parameters using element test results, and assignment of correct values for the model parameters. 

Predictions from analyses using the considered soil constitutive models were within 

measurement accuracy for the end-of-construction and surcharge load levels corresponding to 

working stress conditions. The elastic-plastic Mohr-Coulomb model was reported to be best

suited for the analysis of reinforced soil walls that are at incipient collapse than for the working 

stress conditions. The modified Duncan-Chang model with plane strain boundary condition was 

reported to be a better candidate considering an optimal balance between prediction accuracy and 

availability of parameters from conventional triaxial compression tests.

Helwany et al. used a cap plasticity model to represent soil constitutive behavior in plane strain 

FEAs (using finite element (FE) code DYNA3D, an older version of LS-DYNA) of full-scale 

GRS bridge abutment testing.

(70,144) Drucker and Prager yield criterion is used in association with 

a strain hardening elliptic cap model.

(145,146) Such a model is capable of accounting for the effects 

of stress history, loading path, and intermediate principal stress on mechanical behavior of 

soil.

(147) However, a two-invariant based model, such as the one used by Helwany et al. cannot 

capture dilatancy and anisotropy (stress-induced and fabric).

(70) Recently, Wu et al. conducted 

two-dimensional numerical analyses using PLAXIS to simulate laboratory-scale GSGC tests that 

aimed to investigate the performance of GRS masses with different reinforcing conditions.

(74) In 

the numerical analyses, the compacted soil was modeled using a hardening soil model, the 

reinforcement was modeled as a linear elastic material with an ultimate Tf, and sequential 

placement of reinforcements and compaction-induced stresses were considered. The FE results 

were in good agreement with laboratory test results. The FEAs demonstrated that the presence of 

geosynthetic reinforcement had a tendency to suppress dilation of the surrounding soil, which 

was potentially due to increased confinement provided by the embedded reinforcement layers 

and, thus, reduced the angle of dilation of the soil mass. Soil dilation is an important mechanism 

that controls the efficiency of load transfer from the reinforcement to the soil during shear 

deformations in reinforced soil structures.

(148) The dilation behavior offers a new explanation of 

the reinforcing mechanism, and the angle of dilation provides a quantitative measure of the 

degree of reinforcing effect of a GRS mass.

In summary, past research studies have shown that various constitutive behaviors of compacted 

fill play an important role in the response of structures founded on engineered fills, which may 

manifest at different strain levels. For example, the strain-softening behavior may be important 

for pullout conditions but negligible for working conditions and SLS conditions with small 

allowable strains. The effect of strain hardening and dilation at SLS conditions may or may not 

be significant and warrants additional investigation. Although constitutive models that are 

capable of producing nonlinear stress-strain behaviors have shown to be more advantageous, 

simple linear elastic-plastic models may be sufficient for predicting the deformation of

engineered fills and strains in reinforcement layers for working conditions and SLS conditions if 

appropriate model parameters are used. 

5.2 MODELING REINFORCED SOIL AS A SINGLE COMPOSITE MATERIAL

In early numerical analyses of reinforced soils, the reinforcement and its surrounding soil are 

modeled as a single composite material.

(149–151) In this approach, it is assumed that: (1) the 

friction between reinforcements and compacted soil is large enough so that there is no relative 

displacement between the two materials, and (2) the strain of compacted soil in the horizontal 
111

direction is equal to that of the reinforcements. The assumptions behind this approach, 

however, may not be valid for SLS, where slippage between reinforcement and soil may not be 

negligible.

(118) In recent numerical analyses, the reinforcement and surrounding compacted soil 

are hence modeled separately.

5.3 MODELING OF REINFORCEMENTS

Geosynthetic or metallic reinforcements are often modeled as a linear elastic material. (See 

references 72, 74, 121, 123, 124, 127, 128, 131, 132, and 152–155.) This treatment is considered 

sufficient as the stress and strain levels in working condition are generally low. In FE models, 

reinforcements are often modeled as slender objects (e.g., cable element) with a normal stiffness 

but with no bending stiffness.

(124) This simplification is generally valid.(156)

The nonlinear stress-strain behavior of geosynthetic reinforcement has been considered. 

Ling et al. modeled the geosynthetic reinforcement as a nonlinear material, having developed a 

hyperbolic load-strain relationship.

(157,158) Using their FEM model, Ling et al. simulated the 

construction response of a GRS retaining wall with a concrete-block facing.

(157) Comparisons 

between measured and predicted behavior were presented for the wall deformation, vertical and 

lateral stresses, and strains in the geogrid layers. Satisfactory agreement between the measured 

and predicted results was observed. Under the working condition, however, the strains in the 

geogrid layers were small (less than 1 percent); hence, the geogrid essentially behaved as a linear 

elastic material. Fakharian and Attar simulated the well-instrumented Founders/Meadows

segmental GRS bridge abutment near Denver, CO, where the geosynthetic reinforcement was 

modeled using elastic-plastic cable elements in FLAC 2D.

(134) Satisfactory agreement was 

observed between the simulated and recorded facing displacement, vertical earth pressures, and 

geogrid strains. They observed that the maximum horizontal displacement of the facing due to 

deck load for the bridge abutment occurred at an elevation equivalent to 60 percent of the height 

of the front face of the abutment. They also observed that the geogrid experienced small strains 

(less than 1 percent) under the working condition. 

For some cases, time-dependent behaviors of reinforcements could be important. For example, 

secondary settlement behavior has recently been observed in experimental studies on foundations 

supported by GRS.

(21,27) Hence, it is important that time-dependent behaviors (e.g., creep) of 

geosynthetic reinforcements are accounted for in the modeling of GRS. For example, 

Sharma et al. modeled the reduction of linear elastic stiffness values with time based on the 

results of creep tests.

(159) Lopes et al. simulated the load-strain-time response of an instrumented 

sloped reinforced wall by using a viscoelastic creep model.

(160) Karpurapu and Bathurst modeled 

both the nonlinear load–strain and time-dependent responses of a polymeric geogrid using a 

parabolic load–strain model fitted to the results of creep tests.

(129) The geosynthetic 

reinforcements were recently modeled using an elastic-viscoplastic bounding surface model to 

investigate the long-term performance of GRS structures.

(135,161) Kongkitkul et al. presented an 

elastic-viscoplastic model that describes rate-dependent load-strain behavior of polymer 

geosynthetic materials.

(162) The constitutive model is comprised of three components: a hypoelastic component, a nonlinear inviscid component, and a nonlinear viscous component. 

Omission of one or more nonlinear components in this model yields the nonlinear elastic-plastic 

or hypo-elastic models, which are rather common in literature.
112

In summary, past research has shown that for reinforced soils, it is reasonable to model the 

reinforcements as linear elastic materials under working conditions because the strains developed 

in the reinforcements are generally small. The effect of nonlinear and time-dependent stressstrain behaviors of reinforcements, particularly geosynthetic reinforcements, on engineered fills 

at SLS and long term conditions is relatively unknown and warrants additional research.

5.4 MODELING OF SOIL-REINFORCEMENT INTERACTIONS

Several research studies have investigated soil-reinforcement interactions using analytical and 

numerical methods. (See references 153 and 163–170.) Palmeira provides a comprehensive 

summary of different experiments and theoretical models used to evaluate soil-geosynthetics 

interactions under different loading and boundary conditions.

(171) Common numerical analyses 

(mostly using FE or finite difference scheme) of GRS structures and foundations on reinforced 

soil usually idealize geogrid layers as equivalent planar reinforcement layers with frictional 

characteristics. The geometric shape of the geogrid layer, particularly the presence or absence of 

transverse reinforcement, and bending stiffness are often ignored. Although these simplifications 

may not be valid under pullout loading conditions, they are generally valid under working 

conditions and, likely, SLS conditions.(172,173)

The basic differences between metal and geosynthetic reinforcement are their stiffness, 

structures, and the interactions occurring at the reinforcement-soil interfaces.

(115) Metal 

reinforcement is usually in the form of straps or mats, whereas geosynthetic reinforcement is 

usually in the form of grids or planar sheets. The planar structure and flexibility of geosynthetics 

enable the shear forces inside the soil mass to be transferred to geosynthetic reinforcement more 

uniformly and without interruptions. Metal reinforcements usually have smooth surfaces; 

whereas most geosynthetics have fabric-like surfaces (geotextiles) or grid structures (geogrids), 

which produce better soil-reinforcement bonding. Consequently, slippage occurs at the interface 

between soil and metal reinforcement, but in GRSs, the slippage surfaces were observed to occur 

inside the soil mass next to the reinforcement.

(174) Many of the modeling techniques for soilgeosynthetic interactions are also applicable to the interaction between soil and metallic 

reinforcements after adjustments to model parameters accounting for the aforementioned 

differences.

In most of the earlier FEM simulations of GRS, the soil-reinforcement interface behavior was 

modeled by using interface elements, such as joint elements of zero or non-zero thickness and 

node compatibility spring elements. (See references 129, 131, 133, and 175–186.) In this 

approach, the interface elements were formulated as a stiff spring in each of the shear and normal 

directions until slip occurred, at which point deformation could occur along the interface 

according to a Mohr-Coulomb failure criterion. (See references 72, 122, 128, and 135.) This 

approach also enables the specification of a decreased interface friction compared to the friction 

of the soil to model residual friction at the soil-reinforcement interface.

(127,130) However, this 

approach involves assumption of horizontal and vertical stiffness values for the interface 

elements that are difficult to determine experimentally.

(121) In 3D FEAs of a square footing 

bearing on reinforced sand, Kurian et al. employed 3D interface elements with zero thickness 

and with shear stiffness following a hyperbolic relation.

(152,187) Penalty-type interface elements 

that allow sliding, friction, and separation facilitate modeling of interfaces between any two 

dissimilar materials have also been used in FE modeling of GRS structures and foundations 
113

bearing on reinforced soil.

(70,134) More recently, the soil-reinforcement interface behavior has 

been modeled using contact algorisms without assuming the contact stiffness values.(121)

5.5 NUMERICAL MODELING OF STRUCTURES SUPPORTED BY ENGINEERED 

SOILS

Most numerical models discussed previously were utilized to conduct parametric studies to 

investigate the effect of various parameters such as geometry and arrangement of reinforcement 

and soil properties on the response of structures supported by engineered soils. Few of these 

models have been validated against large-scale physical tests, and they are discussed in 

this section.

Karpurapu and Bathurst modeled the behavior of two carefully constructed and monitored largescale GRS retaining walls (9.84 ft (3 m) high).

(129) The walls were constructed using a dense sand 

fill and layers of geosynthetic reinforcement attached to two different facing treatments: an 

incremental panel wall versus a full height panel wall. The model walls were taken to collapse 

using a series of uniform surcharge loads applied at the sand fill surface. To model the GRS 

retaining wall, a modified form of hyperbolic stress-strain model was used to model the backfill 

soil. A nonlinear equation developed from isochronous load-strain-time test data was used to 

model the reinforcement, and the soil-reinforcement interface was modeled using joint elements 

of zero thickness.

(138) To investigate the effect of soil dilation on GRS wall performance, two sets

of numerical analyses were performed: one set with a soil dilation angle of 0 degrees and the 

other using a value of 15 degrees based on laboratory direct shear test results. The numerical 

analyses with no dilation were shown to have predicted much greater panel displacements and 

larger reinforcement strains. In some cases, the over-prediction was greater than measured values 

even at working load conditions by a factor of 2; whereas the numerical analyses with 15-degree 

soil dilation accurately predicted panel displacements and reinforcement strains. The results of 

their numerical study indicate that it is possible to accurately simulate all significant performance 

features of GRS walls at both working load and collapse conditions, and it is important to 

properly model facing treatment and consider soil dilation in the behaviors of GRS walls even at 

working load conditions.

Holtz and Lee developed FLAC2D models to simulate six case histories, including the 

WSDOT geotextile wall (41.34 ft (12.6 m) high) in Seattle, WA, and five of the test walls 

(20.01 ft (6.1 m) high) constructed at the FHWA reinforced soil project site in Algonquin, 

IL.(120,188) The reinforcements for these walls included woven and nonwoven geotextiles, 

geogrids, steel strips, and steel bar mats. In these models, the compacted soil was modeled using 

a nonlinear elastic-plastic Mohr-Coulomb model with a hyperbolic stress-strain relationship, and 

the reinforcements were modeled as linear elastic materials with tensile and compressive 

strength. It was assumed that no slippage occurred between the soil and geosynthetic 

reinforcements, and interface elements were used to model the interaction between different 

materials or the discontinuities between the same materials, such as interfaces between backfill 

soil and structural facing and interfaces between structural facing units. Construction 

consequence of the walls was modeled by applying a uniform vertical stress equivalent to the 

overburden stress from each lift to the entire surface of each new soil layer before solving the 

model to equilibrium. Results of this study confirmed that the developed models were able to 
114

provide reasonable working strain information of GRS walls. (120) However, accurate material 

properties were the key to a successful performance modeling of GRS walls.

Hatami and Bathurst conducted numerical modeling of four full-scale reinforced-soil SRWs 

(11.81 ft (3.6 m) high) using FLAC2D .

(118) The reinforcements for these walls included PP 

geogrid, PET geogrid, and WWM. In their model, the compacted soil was modeled using a 

nonlinear elastic-plastic model with a Mohr-Coulomb failure criterion and a dilation angle.

(189)

Compaction-induced stresses in the segmental walls were modeled by applying a transient 

uniform vertical pressure to the backfill surface at each stage during the simulation of wall 

construction. The effect of compaction on the reduction of fill Poisson’s ratio was modeled by 

adjusting soil model parameters from triaxial and plane strain tests to ensure reasonably low 

values of Poisson’s ratio. These modeling techniques were shown to have greatly improved the 

match between measured and predicted features. Results of this study showed that it is important 

to include compaction effects in the simulations in order to accurately model the construction 

and surcharge loading response of the reinforced soil walls. Comparison of predicted and 

measured results also suggested that the assumption of a perfect bond between the reinforcement 

and the soil may not be valid. In a follow up study, Hatami and Bathurst investigated the 

influence of backfill material type on the performance of soil-reinforced walls under working

stress condition.

(190) It was concluded that the addition of a small amount of cohesive strength 

can significantly reduce wall lateral displacements in case of negligible relative displacement 

between reinforcement and backfill soil.

Helwany et al. conducted a numerical study on the effects of backfill on the performance of GRS 

retaining walls.

(73) In their numerical model, the backfill soil was modeled using the modified 

hyperbolic model, and the reinforcement was modeled as linear elastic.

(138) Their numerical 

model was validated by comparing the results with the measurements from a well-instrumented 

large-scale laboratory test conducted on a GRS retaining wall (9.84 ft (3 m) high) under wellcontrolled test conditions.

(191) The validated model was then utilized to conduct a parametric 

study on the effects of backfill on the performance of GRS retaining walls. It was shown that the 

stiffness of the geosynthetic reinforcement had a considerable effect of the behavior of the GRS 

retaining wall when the stiffness and shear strength of the backfill were relatively low. 

Ling et al. simulated the performance of a full-scale instrumented GRS retaining wall (16.40 ft 

(5 m) high) using an FEM model.

(158) The retaining wall was backfilled with a volcanic ash clay 

reinforced with a woven-nonwoven geotextile, and details of the test conditions were provided 

by Murata et al.

(192) In the FEM model, the backfill soil was modeled as a Hookean material, the 

geotextile was modeled as having a hyperbolic stress-strain relationship, and no slippage was 

allowed at the soil-reinforcement interface. Compaction stresses induced during construction 

were not accounted for in the model. Results of their study indicated that the FEM model was 

able to capture the overall behavior of the retaining wall. The results showed that the GRS 

retaining wall performed as an integrated system, with the facing, geosynthetic and backfill soil 

interacting with each other to facilitate stress transfer and thus minimized deformation. It was 

also shown that stiffness values of the facing and reinforcements played equally important roles 

in the performance of GRS walls. 

In a follow-up study, Ling et al. simulated another full-scale instrumented GRS retaining wall 

(19.68 ft (6 m) high) using an improved FEM model.

(157) The retaining wall was backfilled
115

with a silty sand reinforced with a UX geogrid. Details of the test conditions were 

provided.

(193,194) In the improved FEM model, the backfilled soil was modeled using a nonlinear 

hyperbolic model, the geogrid was modeled as a having a hyperbolic stress-strain relationship, 

and the interface behaviors were modeled using interface elements allowing slippage.

(138) The 

results indicate that the FEM model predictions matched the measured results in terms of wall 

deformation, vertical and lateral stress, and strains in the geogrid layers.

Rowe and Skinner modeled the performance of a full-scale GRS retaining wall (26.25 ft (8 m)

high) constructed on a layered soil foundation.

(122) The foundation consisted of a 2.62-ft (0.8-m)

hard crust underlain by 9.68 ft (2.95 m) of soft loam (sandy/silty) and then 4.26 ft (1.3 m) of stiff 

clay. Below the clay was 5.74 ft (1.75 m) of fine sand underlain by a layer of clayey/fine sand 

extending to a depth below 32.80 ft (10 m). The wall was constructed with 16 segmented 

concrete facing blocks, a sandy backfill material with 30 percent fines, and 11 layers of geogrid 

reinforcement 19.68 ft (6 m) long. In the FEM model, the backfill and foundation soils were 

modeled using an elastic-plastic model with a Mohr-Coulomb failure criterion, the geogrid was 

modeled as linear elastic, and the soil-reinforcement interface was modeled using interface 

elements. Compaction stresses induced during construction were not accounted for in the model. 

It was observed that the predicted behavior compared reasonably well with the observed 

behavior of the full-scale wall. The numerical results indicate that for the case of a GRS wall 

constructed on a yielding foundation, the stiffness and strength of the foundation can have a 

significant effect on the wall’s behavior. A highly compressible and weak foundation layer can 

significantly increase the deformations at the wall’s face and base and the strains in the 

reinforcement layers. It is interesting to note that trial analyses (with and without considering 

dilation) performed during this study did not exhibit any significant effects of dilation on 

analyses results except for a small difference in the vertical stress at the toe of the wall.

Helwany et al. simulated the behavior of full-scale GRS bridge abutment (15.25 ft (4.65 m) high) 

using LS-DYNA (formerly known as DYNA3D).

(70) The backfill soil was simulated utilizing an 

extended two-invariant geologic cap model, and the geosynthetic reinforcement was modeled as 

an isotropic elastic-plastic material. The FEAs show that the performance of a GRS abutment, 

resulting from complex interaction among the various components, subjected to a service load or 

a limiting failure load can be simulated in a reasonably accurate manner. This numerical 

investigation also showed that the performance of GRS bridge abutments is greatly affected by 

the soil placement conditions (signified by the friction angle of the compacted soil), 

reinforcement stiffness, and reinforcement spacing.

The numerical studies presented show that numerical models can realistically model the 

mechanical behavior of soil-geosynthetic composite and capture the performance features of 

GRS walls, such as the wall deformation, vertical and lateral stress, and strains in the geogrid 

layers, at both working load and collapse conditions. These studies have highlighted the 

importance of properly modeling complex constitutive behaviors of compacted fill and 

foundation soil (e.g., soil dilatancy and softening at large displacement), stress-strain relationship 

of reinforcements, and sequential construction and compaction-induced stresses. However, no 

numerical studies have been conducted to investigate the SLS of structures supported by 

engineered soil.
116

5.6 NUMERICAL MODELING OF LONG-TERM BEHAVIOR OF GRS STRUCTURES

Although past studies have produced reasonable solutions, particularly when the material model 

parameters were calibrated to fit model-scale test results, to understand short-term (immediately 

after load placement) load-settlement behavior of shallow foundations bearing on GRS, few of 

these studies could account for time-dependent secondary deformation (settlement) behavior of 

foundations under service load. Such secondary settlement behavior has recently been observed 

in experimental studies, and it is important that such deformation is accounted for in calculation 

of total foundation settlement.

(21,27) Moreover, it is also important to understand the stress 

distribution profile below the footing on reinforced ground. Such understanding will further 

facilitate economic design by restricting fill placement only down to the zone of influence below 

the foundation. Several numerical studies on long-term behavior of GRS structures are 

summarized in this section.

Helwany and Wu developed a numerical model for analyzing long-term performance of GRS 

structures.

(195) In their model, compacted soil was modeled using an anisotropic extension of the 

Cam-clay model, which is capable of describing the effects of stress anisotropy, stress 

reorientation, and creep of normally consolidated and lightly overconsolidated clays. A

generalized geosynthetic creep model developed by Helwany and Wu was used to simulate timedependent behavior of the geosynthetic reinforcement.

(195) It was assumed that slippage did not 

occur at the soil-geosynthetic interface under service loads, which was generally valid for 

extensible geosynthetic reinforcement. This investigation clearly demonstrates that the timedependent deformation behavior of the confining soil played an important role in the long-term 

creep behavior of GRS structures. Hence, a rational design of GRS structures must account for 

the long-term soil-geosynthetic interaction.

Liu and Won and Liu et al. modeled the long-term behavior of GRS retaining walls with

different backfill soils.

(186,135) According to Liu and Won, the backfill soil was assumed to be 

time independent and modeled using a generalized plasticity model for sand, the reinforcement 

was modeled using the elastic-plastic viscoplastic bounding surface model for geosynthetics, and 

the soil-reinforcement interface was modeled using interface elements. (See references 186, 136, 

161, and 196.) According to Liu et al., the backfill soil was modeled as time dependent using an 

elastic-plastic viscoplastic model obeying Drucker-Prager yield criterion and Singh-Mitchell 

creep model but with nonlinear elastic properties.

(135) The reinforcement and soil-reinforcement 

interface were modeled in the same way as Liu and Won.

(186) In both studies, the numerical 

models were validated using the experimental results of a long-term PT on sand-geosynthetic 

composite reported in Helwany and Wu and Helwany.

(197,198)

Liu and Won and Liu et al. demonstrated that the load distribution in backfill soil and 

reinforcement depended on their time-dependent properties, which determine the long-term 

performance of GRS walls.

(186,135) It was shown that large soil creep can lead to a significant 

increase in both wall displacement and reinforcement load. Conversely, if soil creep is smaller 

than reinforcement creep, reinforcement load would decrease due to load relaxation, but the soil 

stress could increase significantly. This indicates that backfill soil must have adequate strength to 

compensate the long-term reduction of load carried by reinforcement due to load relaxation. The 

results of these studies indicate that in the design of GRS structures, it is necessary to take into 
117

account the relative creep rate of reinforcement and backfill soil, especially if backfill soil with 

high cohesive fines contents is used.

Past numerical studies have shown that the creep deformation of a GRS wall is a result of soilgeosynthetic interaction. The creep rate of the geosynthetic reinforcement may accelerate or 

decrease depending on the relative creep rate between the backfill and geosynthetic 

reinforcement.

(199) For a GRS structure with a well-compacted granular backfill, the timedependent deformation is small and the rate of deformation of the soil-geosynthetic composite 

typically decreases rapidly with time.

(199) Hence, creep deformation of geosynthetic 

reinforcement in a GRS structure may or may not be a design issue, depending on the soilgeosynthetic interaction. It should be noted that no numerical studies have been conducted to 

investigate the long-term deformation of GRS walls supported by reinforced soil.

5.7 SIMILARITIES AND DIFFERENCES BETWEEN PIER AND ABUTMENT 

FOUNDATION DEFORMATION MODELS

In common transportation engineering practice, deep foundations are frequently used to support 

lateral and vertical loads at pier and abutment locations for bridges. However, recent research 

shows that spread footings, if analyzed and designed adequately, can be an economic option for 

bridge support.

(200) Although shallow foundations may provide a viable alternative in terms of 

their capacity to support structural load, their use is often restricted to avoid excessive settlement 

at bridge foundation locations. Nonetheless, settlement calculations and the serviceability limit 

state criteria set to check the calculated settlement are often overly conservative in terms of 

actual load-settlement response of shallow spread footings bearing on compacted, reinforced or 

unreinforced engineered fills and the tolerable movement criteria used to design them. While 

similar foundation-soil load transfer mechanisms can be expected, for a given bearing stratum 

(i.e., engineered fills with or without embedded reinforcement layers) at both pier and abutment 

locations, the load-deformation behavior is expected to vary at these locations. The major 

difference would arise from the 3D (close or similar to a triaxial condition) stress state existing 

below square, rectangular, and circular spread footings when compared to a confined plane 

strain condition (i.e., strain in the out-of-the plane direction is zero) strain existing at the 

abutment locations.

Dimensions of shallow foundation affect bearing capacity and load-displacement behavior on 

granular soil.

(201) Fakher and Jones point out that the foundation dimension effects should be 

studied in order to critically judge the behavior of foundations on reinforced soil and that the role 

of reinforcement in enhancing foundation performance might be misjudged without the 

consideration of such effect.

(202) Based on results of FE simulations, Chen and Abu-Farsakh 

show that foundation dimension effects became negligible when reinforcement depth ratio (i.e., 

ratio of total reinforcement depth to foundation width) and reinforcement ratio (ERAr/EsAs; where 

Ar and As are area of reinforcement and reinforced soil per unit width, respectively) remains 

constant.

(154) Such a conclusion is valid for design for ULS (e.g., bearing capacity of foundation) 

with a specified relative settlement (i.e., ratio of settlement and characteristic width of a 

foundation) criterion. However, for serviceability limit state design based on absolute values 

of foundation settlement, dimensions of shallow foundations are expected to play a major 

role in SLS.
118

Apart from the difference in bearing capacity failure mechanism under the above stated 

conditions, an additional difference is expected to arise from state-dependent strength behavior 

of compacted granular fill material and placement conditions; a reflection of this would be 

through different degrees of dilation for the same compacted density.

(70,203) Such differences in 

strength-deformation behavior are likely to change the load-deformation behavior of shallow 

foundations at pier bents and the compacted fill at abutment locations. Another key difference 

might arise from the load eccentricity caused by the combined loading and the ratio of lateral to 

vertical loading. Load eccentricity may have a larger impact on lateral and vertical movements of 

spread footings below bridge piers when compared to its effect in controlling movements at 

abutment support locations.
119

CHAPTER 6. CONCLUSIONS

6.1 CONCLUSIONS

In the evaluation of five widely used methods of estimating immediate settlement of shallow 

foundations on granular soils, it was observed that four of the five methods (modified 

Schmertmann, Hough, Peck and Bazaraa, and Burland and Burbidge) overestimate immediate 

settlement, and the D’Appolonia method slightly underestimates immediate settlement. In 

comparison, the D’Appolonia method is the most accurate method with the mean the closest to 

unity and relatively small COV, followed by the Peck and Barazaa method and the Burland and 

Burbidge method. Both the modified Schmertmann method and the Hough method overestimate 

immediate settlement of shallow foundations on granular soils by a factor of approximately 2. 

It is noted that this conclusion is based on measured data whose population may be 

statistically small.

In the evaluation of six prediction methods for lateral displacements of GRS abutments and 

walls, it was concluded that the Adams method is the most accurate method for predicting the 

maximum lateral displacement of GRS walls and abutments with the mean the closest to unity 

and small COV. The Jewell-Milligan method is a conservative and relatively accurate method for 

predicting the lateral displacement of GRS walls and abutments with negligible facing rigidity. 

For predicting the displacement of GRS walls and abutments with CMU facing block, the CTI 

method may also be used, although it may overestimate lateral deformations by a factor of 1.69 

with a relatively high COV. It is noted that this conclusion is based on measured data whose 

population may be statistically small.

Currently, there is only one method available in estimating elastic vertical deformation of GRS 

abutments and walls; it is an empirical equation proposed by Adams et al.

(32) This method uses 

the composite Young’s modulus of the GRS composite. Although the field observation data 

that are used to evaluate this empirical method show that this method is highly unconservative, 

it should be noted that the accuracy of the prediction method depends on the accurate 

determination of the composite Young’s modulus, which lacks in the literature. It should also be 

noted that this conclusion is based on measured data whose population may be statistically small.

6.2 KNOWLEDGE GAPS AND DATA NEEDS FOR BRIDGE SUPPORTS USING

ENGINEERED FILLS

Based on the synthesis of the literature and current guidelines and methods on bridge supports 

using engineered fills, the following knowledge gaps and data needs for bridge supports using 

engineered fills were identified:

The current analyses primarily predict immediate settlement only. While it is a common 

assumption that granular or engineered fills do not exhibit secondary deformation, it has 

been observed in in-service bridge abutment applications and large-scale piers in 

laboratory tests.

(27,32) Among the limited number of methods for predicting long-term (or 

time-dependent secondary post-construction) deformation of granular soils, long-term 

field observations or long-term PTs are needed to derive coefficients that are used in the 

λλ

λλ
120

prediction methods. Furthermore, long-term deformation data of bridge supports on 

engineered fills are rather limited, so that the evaluation of currently available long-term 

deformation prediction methods cannot be performed. 

There is a particular lack of prediction methods for vertical (for both immediate and longterm) deformations of MSE and GRS bridge abutments and piers.

There is lack of comprehensive knowledge of the effects of soil characteristics and 

compaction efforts on the SLS performances of bridge supports using engineered fills. 

Accordingly, current design guides provide specific requirements on engineered fills for 

bridge support, and design is limited to the conditions and parameters under which testing 

has occurred. In addition, the parameters used (e.g., , c, etc.) may vary depending on the 

measurement technique and the design method selected, which may have an impact on 

the SLS analysis. Other different types of fill materials are not being used due to a lack of 

data on their impact.

Stress distribution in soils can be influenced by various soil conditions (i.e., grain size 

distribution, strength parameters, relative density, and fine content), reinforcement 

characteristics (i.e., Tf, stiffness, N, and Sv), and loading conditions. Some of these 

parameters were investigated previously.

(90) However, the current literature suggests there 

is a lack of documentation and understanding of the effects of various parameters on the 

stress distribution in reinforced engineered fills as bridge supports in SLS.

The dynamic effect of transient load on bridge supports using engineered fills has not 

been investigated. There is a lack of literature on the time-dependent and live (transient) 

load on the stress-deformation behaviors of bridge supports using engineered fills.
121

REFERENCES

1. Mertz, D. (2012). Steel Bridge Design Handbook: Limit States, Report No. FHWA-IF-12-

052-Vol.10, Office of Bridge Technology, Federal Highway Administration, 

Washington, DC.

2. DiMillio, A.F. (1982). Performance of Highway Bridge Abutments on Spread Footings on 

Compacted Fill, Report No. FHWA RD-81-184, Federal Highway Administration, 

Washington, DC.

3. Gifford, D.G., Kraemer, S.R., Wheeler, J.R., and McKown, A.F. (1987). Spread Footings 

for Highway Bridges, Report No. FHWA RD-86-185, Federal Highway Administration, 

Washington, DC.

4. Zevgolis, I. and Bourdeau, P.L. (2007). Mechanically Stabilized Earth Wall Abutments 

for Bridge Support, Report No. FHWA/IN/JTRP-2006/38, Joint Transportation 

Research Program, Indiana Department of Transportation and Purdue University, 

West Lafayette, IN.

5. Abu-Hejleh, N.M., Alzamora, D., Mohamed, K., Saad, T., and Anderson, S. (2014). 

Implementation Guidance for Using Spread Footings on Soils to Support Highway Bridges, 

Report No. FHWA-RC-14-001, Federal Highway Administration Resource Center, 

Matteson, IL.

6. Samtani, N.C. and Nowatzki, E.A. (2006a). Soils and Foundations Reference Manual: 

Volumes I, Report No. FHWA-NHI-06-088, Federal Highway Administration, 

Washington, DC.

7. Samtani, N.C., Nowatzki, E.A., and Mertz, D.R. (2010). Selection of Spreading Footings 

on Soils to Support Highway Bridge Structures, Report No. FHWA-RC/TD-10-001, 

Federal Highway Administration, Washington, DC.

8. AASHTO. (2014). AASHTO LRFD Bridge Design Specifications, 7th Edition, American 

Association of State Highway and Transportation Officials, Washington, DC.

9. AASHTO. (2008). Manual for Bridge Evaluation, American Association of State Highway 

and Transportation Officials, Washington, DC.

10. Modjeski and Masters, Inc., University of Nebraska, Lincoln, University of Delaware, and 

NCS Consultants, LLC. (2015). Bridges for Service Life Beyond 100 Years: Service Limit 

State Design, SHRP2 Report S2-R19B-RW-1, Transportation Research Board of National 

of Academies, Washington, DC.

11. Paikowsky, S.G., Lesny, K., Amatya, S., Kisse, A., Muganga, R., and Canniff, M.Â. 

(2010). LRFD Design and Construction of Shallow Foundations for Highway Bridge 

Structures, NCHRP Report No. 651 for Project NCHRP 24-31, National Cooperative 

Highway Research Program, Washington, DC.
122

12. Kimmerling, R.E. (2002). Geotechnical Engineering Circular No. 6: Shallow Foundations, 

Report No. FHWA-SA-02-054, Federal Highway Administration, Washington, DC.

13. American Association of State and Highway Transportation Officials. (2015). “AASHTO 

T27-14: Sieve Analysis of Fine and Coarse Aggregates,” Standard Specifications for 

Transportation Materials and Methods of Sampling and Testing, 35th Edition and 

AASHTO Provisional Standards, 2015 Edition. Washington, DC.

14. American Association of State and Highway Transportation Officials. (2015). “AASHTO 

T90-15: Determining the Plastic Limit and Plasticity Index of Soils,” Standard 

Specifications for Transportation Materials and Methods of Sampling and Testing, 

35th Edition and AASHTO Provisional Standards, Washington, DC.

15. American Association of State and Highway Transportation Officials. (2015). “AASHTO 

T104-99 (2011): Soundness of Aggregate by Use of Sodium Sulfate or Magnesium 

Sulfate,” Standard Specifications for Transportation Materials and Methods of Sampling 

and Testing, 35th Edition and AASHTO Provisional Standards, Washington, DC.

16. American Association of State and Highway Transportation Officials. (2015). “AASHTO 

T99-15: Moisture-Density Relations of Soils Using a 2.5-kg (5.5-lb) Rammer and a 

305-mm (12-in.) Drop,” Standard Specifications for Transportation Materials and 

Methods of Sampling and Testing, 35th Edition and AASHTO Provisional Standards, 

Washington, DC.

17. American Association of State and Highway Transportation Officials. (2015). “AASHTO 

T180-15: Moisture-Density Relations of Soils Using a 4.54-kg (10-lb) Rammer and a 

457-mm (18-in.) Drop,” Standard Specifications for Transportation Materials and 

Methods of Sampling and Testing, 35th Edition and AASHTO Provisional Standards, 

Washington, DC.

18. Samtani, N.C. and Nowatzki, E.A. (2006b). Soils and Foundations Reference Manual: 

Volume II, Report No. FHWA-NHI-06-089, Federal Highway Administration, 

Washington, DC.

19. Vidal, H. (1969). “The Principle of Reinforced Earth,” Highway Research Record 282, 

1–16, Transportation Research Board, Washington, DC. 

20. Hanna, B.E. (1977). “The Use of Reinforced Earth Walls as Bridge Abutments,”

Proceedings of the 28th Annual Highway Geology Symposium, 57–60, South Dakota 

School of Mines & Technology, Rapid City, SD. 

21. Adams, M., Nicks, J., Stabile, T., Wu, J., Schlatter, W., and Hartmann, J. (2011a). 

Geosynthetic Reinforced Soil Integrated Bridge System Synthesis Report, Report No. 

FHWA-HRT-11-027, Federal Highway Administration, Washington, DC.

22. Adams, M. (1997). “Performance of a Pre-Strained Geosynthetic Reinforced Soil Bridge 

Pier,” International Symposium on Mechanically Stabilized Backfill, 35–53.
123

23. Wu, J.T.H., Ketchart, K., and Adams, M. (2001). GRS Bridge Piers and Abutments, 

Report No. FHWA-RD-00-038, Federal Highway Administration, Washington, DC.

24. Sun, C. and Graves, C. (2013). Evaluation of Mechanically Stabilized Earth (MSE) Walls 

for Bridge Ends in Kentucky: What Next?, KTC-13-11/SPR443-12-1F, Kentucky 

Transportation Center, University of Kentucky, Lexington, KY.

25. Abernathy, C. (2013). Geosynthetic Reinforced Soil—Integrated Bridge System (GRS-IBS),

Experimental Projects Construction Report, Montana Department of Transportation,

Helena, MT.

26. Talebi, M., Meehan, C., Cacciola, D., and Becker, M. (2014). “Design and Construction of 

a Geosynthetic Reinforced Soil Integrated Bridge System,” Proceedings of GeoCongress 

2014, GSP No. 234, American Society of Civil Engineers, Atlanta, GA.

27. Adams, M. and Nicks, J. (2014). “Secondary Settlement of Geosynthetic Reinforced Soil 

Piers: Preliminary Results,” Proceedings of GeoCongress 2014, GSP No. 234, 4,228–

4,237, American Society of Civil Engineers, Atlanta, GA.

28. Warren, K., Whelan, M., Hite, J., and Adams, M. (2014). “Three Year Evaluation of 

Thermally Induced Strain and Corresponding Lateral End Pressures for a GRS IBS in 

Ohio,” Proceedings of GeoCongress 2014, GSP No. 234, American Society of Civil 

Engineers, Atlanta, GA.

29. Budge, A., Dasenbrock, D., Mattison, D., Bryant, G., Grosser, A., Adams, M., and 

Nicks, J. (2014). “Instrumentation and Early Performance of a Large Grade GRS-IBS 

Wall,” Proceedings of GeoCongress 2014, GSP No. 234, American Society of Civil 

Engineers, Atlanta, GA.

30. Tatsuoka, F. (2008) “Recent Practice and Research of Geosynthetic-Reinforced Earth 

Structures in Japan,” Journal of GeoEngineering, 3(3), 77–100.

31. Kempton, G., Özçelik, H., Naughton, P., Mum, N., and Dundar, F. (2008). The Long Term 

Performance of Polymeric Reinforced Walls Under Static and Seismic Conditions, Fourth 

European Geosynthetics Conference, Paper No. 181, Edinburgh, UK.

32. Adams, M., Nicks, J., Stabile, T., Wu, J., Schlatter, W., and Hartmann, J. (2011b). 

Geosynthetic Reinforced Soil Integrated Bridge System Interim Implementation Guide,

Report No. FHWA-HRT-11-026, Federal Highway Administration, Washington, DC.

33. Cheney, R.S. and Chassie, R.G. (2000). Soils and Foundation Workshop Reference 

Manual, Publication No. FHWA NHI-00-045, Federal Highway Administration, 

Washington, DC.

34. Anderson, P.L. and Brabant, K. (2010). Increased Use of MSE Abutments, Association for 

Metallically Stabilized Earth, Reston, VA. Obtained from: http://amsewalls.org/

technical_papers.html. Site last accessed November 11, 2015.
124

35. Elias, V. and Christopher, B.R. (1998). Mechanically Stabilized Earth Walls and 

Reinforced Soil Slopes Design and Construction Guidelines, FHWA Report No. FHWASA-96-071, Federal Highway Administration, Washington, DC.

36. Elias, V., Christopher, B.R., and Berg, R.R. (2001). Mechanically Stabilized Earth Walls 

and Reinforced Soil Slopes Design and Construction Guidelines, FHWA Report No. 

FHWA-NHI-00-043, Federal Highway Administration, Washington, DC.

37. Berg, R.R., Christopher, B.R., and Samtani, N.C. (2009). Design of Mechanically 

Stabilized Earth Walls and Reinforced Soil Slopes—Volume I, Publication No. FHWANHI-10-024, National Highway Institute, Federal Highway Administration, 

Washington, DC.

38. Koerner, R.M. and Soong, T-Y. (2001), “Geosynthetic Reinforced Segmental Retaining 

Walls,” Geotextiles and Geomembranes, 19(6), 359–386. 

39. National Concrete Masonry Association. (1997). Design Manual for Segmental Retaining 

Walls, Collin, J.G. (Ed.), 289, Herndon, VA.

40. Munfakh, G., Arman, A., Collin, J.G., Hung, J.C., and Brouillette, R.P. (2001). Shallow 

Foundations Reference Manual, Report No. FHWA-NHI-01-023, Federal Highway 

Administration, Washington, DC.

41. Adams, M. and Collin, J. (1997). “Large Model Spread Footing Load Tests on 

Geosynthetic Reinforced Soil Foundations,” Journal of Geotechnical and 

Geoenvironmental Engineering, 123(1), 66–72.

42. Nicks, J.E., Adams, M.T., Ooi, P.S.K., and Stabile, T. (2013). Geosynthetic Reinforced Soil 

Performance Testing—Axial Load Deformation Relationships, Report No. FHWA-HRT13-066, Federal Highway Administration, Washington, DC.

43. Moulton, L.K., Ganga Rao, H.V.S., and Halvorsen, G.T. (1982). Tolerable Movement 

Criteria for Highway Bridges, Report No. FHWA/RD-81/162, Federal Highway

Administration, Washington, DC.

44. Moulton, L.K., Ganga Rao, H.V.S., and Halvorsen, G.T. (1985). Tolerable Movement 

Criteria for Highway Bridges, Report No. FHWA/RD-85/107, Federal Highway 

Administration, Washington, DC.

45. Barker, R.M., Duncan, J.M., Rojiani, K.B., Ooi, P.S.K., Tan, C.K., and Kim, S.G. (1991). 

Manuals for the Design of Bridge Foundations, NCHRP Report 343, National Cooperative 

Highway Research Program, Washington, DC.

46. Washington State Department of Transportation. (2014). Geotechnical Design Manual, 

WSDOT, Tumwater, WA.

47. Arizona Department of Transportation. (2009). Bridge Design Guidelines, AZDOT, 

Phoenix, AZ.
125

48. Wahls, H. (1983). NCHRP Synthesis of Highway Practice Report 107: Shallow 

Foundations for Highway Structures, National Cooperative Highway Research Program, 

Washington, DC.

49. Bozozuk, M. (1978). “Bridge Foundations Move,” Transportation Research Record 678, 

17–21, Transportation Research Board, Washington, DC.

50. Walkinshaw, J.L. (1978). “Survey of Bridge Movements in the Western United States,” 

Transportation Research Record 678, 6–11, Transportation Research Board, 

Washington, DC.

51. Wahls, H.E. (1990). Design and Construction of Bridge Approaches, NCHRP Synthesis of 

Highway Practice 159, 45, Transportation Research Board, Washington, DC.

52. AASHTO. (2002). Standard Specifications for Highway Bridges, 17th Ed., American 

Association of State Highway and Transportation Officials, Washington, DC.

53. Fragaszy, R.J. and Lawton, E. (1984). “Bearing Capacity of Reinforced Sand Subgrades,” 

Journal of Geotechnical Engineering, 110(10), 1,500–1,507.

54. Basudhar, P.K., Saha, S., and Deb, K. (2007). “Circular Footings Resting on GeotextileReinforced Sand Bed,” Geotextiles and Geomembranes, 25, 377–384.

55. Omar, M.T., Das, B.M., Puri, V.K., and Yen, S.C. (1993). “Ultimate Bearing Capacity of 

Shallow Foundations on Sand with Geogrid-Reinforcement,” Canadian Geotechnical 

Journal, 30, 545–549.

56. Chen, Q., Abu-Farsakh, M.Y., Sharma, R., and Zhang, X. (2007). “Laboratory 

Investigation of Behavior of Foundations on Geosynthetic-Reinforced Clayey Soil,” 

Transportation Research Record 2004, 28–38, Transportation Research Board,

Washington, DC.

57. ASTM D 1196-93. (2004). “Standard Test Method for Nonrepetitive Static Plate Load 

Tests of Soils and Flexible Pavement Components, for Use in Evaluation and Design of 

Airport and Highway Pavements,” Book of Standards Volume 04.08, ASTM International, 

West Conshohocken, PA.

58. Das, B.M., Shin, E.C., and Omar, M.T. (1994). “The Bearing Capacity of Surface Strip 

Foundations on Ggeogrid-Reinforced Sand and Clay—Comparative Study,” Geotechnical 

and Geological Engineering, 12(1), 1–14.

59. Phanikumar, B.R., Prasad, R., and Singh, A. (2009). “Compressive Load Response of 

Geogrid-Reinforced Fine, Medium and Coarse Sands,” Geotexiles and Geomembranes,

27, 183–186.

60. Huang, C.C. and Tatsuoka, F. (1990). “Bearing Capacity of Reinforced Horizontal Sandy 

Ground,” Geotextiles and Geomembranes, 9(1), 51–82.
126

61. Latha, G.M. and Somwanshi, A. (2009). “Bearing Capacity of Square Footings on 

Geosynthetic Reinforced Sand,” Geotexiles and Geomembranes, 27, 281–294.

62. Elton, D.J. and Patawaran, M.A. (2004). “Mechanically Stabilized Earth Reinforcement 

Tensile Strength from Tests of Geotextile-Reinforced Soil,” Transportation Research 

Record 1868, 81–88, Transportation Research Board, Washington, DC.

63. Abu-Hejleh, N., Wang, T., and Zornberg, J.G. (2000). “Performance of GeosyntheticReinforced Walls Supporting Bridge and Approaching Roadway Structures,” Advances in 

Transportation and Geoenvironmental Systems Using Geosynthetics, ASCE/Geotechnical 

Special Publication No. 103, 218–243.

64. Abu-Hejleh, N., Zornberg, J.G., Wang, T., and Watcharamonthein, J. (2002). “Monitored 

Displacements of Unique Geosynthetic-Reinforced Soil Bridge Abutments,” Geosynthetics 

International, 9(1), 71–95. 

65. ASTM D 2487. (2011). “Standard Practice for Classification of Soils for Engineering 

Purposes (Unified Soil Classification System,” Book of Standards Volume 04.08, ASTM 

International, West Conshohocken, PA.

66. American Association of State and Highway Transportation Officials. (2015). “AASHTO 

M145-91 (2012): Classification of Soils and Soil-Aggregate Mixtures for Highway 

Construction Purposes,” Standard Specifications for Transportation Materials and 

Methods of Sampling and Testing, 35th Edition and AASHTO Provisional Standards, 

Washington, DC.

67. Das, B.M. and Omar, M.T. (1994). “The Effects of Foundation Width on Model Tests for 

the Bearing Capacity of Sand with Geogrid Reinforcement,” Geotechnical and Geological 

Engineering, 12(2), 133–141.

68. Mandal, J.N. and Sah, H.S. (1992). “Bearing Capacity Tests on Geogrid-Reinforced Clay,” 

Geotexiles and Geomembranes, 11, 327–333.

69. Binquet, J. and Lee, K.L. (1975). “Bearing Capacity Tests on Reinforced Earth 

Slabs,” Journal of the Geotechnical Engineering Division, 101(12), 1,241–1,255.

70. Helwany, S.M.B, Wu, J.T.H., and Kitsabunnarat, A. (2007). “Simulating the Behavior of 

GRS Bridge Abutments,” Journal of Geotechnical and Geoenvironmental Engineering,

133(10), 1,229–1,240.

71. Hatami, K. and Bathurst, R.J. (2005). “Development and Verification of a Numerical 

Model for the Analysis of Geosynthetic-Reinforced Soil Segmental Walls Under Working 

Stress Conditions,” Canadian Geotechnical Journal, 42(4), 1,066–1,085.

72. Skinner, G.D. and Rowe, R.K. (2003). “Design and Behavior of Geosynthetic Reinforced 

Soil Walls Constructed on Yielding Foundations,” Geosynthetics International, 10(6),

200–214.
127

73. Helwany, S.M.B., Reardon, G., and Wu, J.T.H. (1999). “Effects of Backfill on the 

Performance of GRS Retaining Walls,” Geotextiles and Geomembranes, 17(1), 1–16.

74. Wu, J.T.H., Pham, T.Q., and Adams, M.T. (2013). Composite Behavior of Geosynthetic 

Reinforced Soil Mass, Report No. FHWA-HRT-10-077, Washington, DC.

75. Gotteland, P., Gourc, J.P., and Villard, P. (1997) “Geosynthetic Reinforced Structures as 

Bridge Abutment: Full Scale Experimentation and Comparison with Modelisations,” 

International Symposium on Mechanically Stabilized Backfill, 25–34.

76. Bathurst, R.J., Nernheim, A., Walters, D.L., Allen, T.M., Burgess, P., and Saunders, D.D. 

(2009). “Influence of Reinforcement Stiffness and Compaction on the Performance of Four 

Geosynthetic Reinforced Soil Walls,” Geosynthetics International, 16(1), 43–59.

77. Tatsuoka, F., Tateyama, M., and Murata, O. (1989). “Earth Retaining Wall with a Short 

Geotextile and a Rigid Facing,” Proceedings of the 12th International Conference on Soil 

Mechanics and Foundation Engineering 2, 1,311–1,314, Rio de Janeiro, Brazil.

78. Tateyama, M. (1996). Reinforced-Soil Retaining Wall Soil with Full-Height Rigid Facing 

and its Appliance, Doctoral Thesis, University of Tokyo, Japan. 

79. Cao, Y.B. and Peng, F.L. (2011). “Numerical Study on Effects of the Number of 

Reinforcement Layers for Reinforced-Sand Retaining Wall,” Geo-Frontiers 2011 

Advances in Geotechnical Engineering, 3,505–3,515, American Society of Civil Engineers, 

Atlanta, GA.

80. Olson, S.M., Holloway, K.P., Buenker, J.M., Long, J.H., and LaFave, J.M. (2013). Thermal 

Behavior of IDOT Integral Abutment Bridges and Proposed Design Modifications, Illinois 

Center for Transportation Research Report, ICT-12-022, University of Illinois at UrbanaChampaign, Champaign, IL.

81. Kim, J.S. and Barker, R.M. (2002). “Effect of Live Load Surcharge on Retaining Walls and 

Abutments,” Journal of Geotechnical and Geoenvironmental Engineering, 128(10),

803–813.

82. Esmaeili, M. and Fatollahzadeh, A. (2013). “Effect of Train Live Load on Railway Bridge 

Abutments,” Journal of Bridge Engineering, 18(6), 576–583.

83. Boussinesq, J.V. (1885). “Sur la résistance qu’oppose un fluide indéfini au repos, sans 

pesanteur, au mouvement varié d’une sphère solide qu’il mouille sur toute sa surface, 

quand les vitesses restent bien continues et assez faibles pour que leurs carrés et produits 

soient négligeables.” Comptes Rendu de l'Academie des Sciences, 100, 935–937.

84. Westergaard, H.M. (1938). “A Problem of Elasticity Suggested by a Problem in Soil 

Mechanics; Soft Material Reinforced by Numerous Strong Horizontal Sheets,” Mechanics 

of Solids, Stephen Timoshenko 60th Anniversary Volume, 268-277, MacMillan Co., 

New York, NY. 
128

85. Allen, T.M., Christopher, B.R., and Holtz, R.D. (1991). “Performance of a 12.6-m-High 

Geotextile Wall in Seattle, Washington,” Proceedings of the International Symposium on 

Geosynthetic-Reinforced Soil Retaining Walls, 81–100, Netherlands.

86. Bathrust, R.J., Karpurapu, R., and Jarrett, P.M. (1992). “Finite Element Analysis of a

Geogrid Reinforced Soil Wall,” Grouting, Soil Improvement and Geosynthetics, 

1,213–1,224, American Society of Civil Engineers, Atlanta, GA.

87. Fishman, K.L., Desai, C.S., and Sogge, R.L. (1993). “Field Behavior of Instrumented 

Geogrid Soil Reinforced Wall,” Journal of Geotechnical Engineering, 119(8),

1,293–1,307.

88. Zornberg, J.G. and Mitchell, J.K. (1994). “Finite Element Prediction of the Performance of 

an Instrumented Geotextile-Reinforced Wall,” Proceedings of the 8th International

Conference of the International Association for Computer Methods and Advances in 

Geomechanics, 1,433–1,438, Morgantown, WV.

89. Christopher, B.R., Gill, S.A., Giroud, J-P., Juran, I., Mitchell, J.K., Schlosser, F., and 

Dunnicliff, J. (1990). Reinforced Soil Structures Volume 1: Design and Construction 

Guidelines, Report No. FHWA-RD- 89-043, Federal Highway Administration, 

Washington, DC.

90. Rowe, R.K. and Ho, S.K. (1993). “Continuous Panel Reinforced Soil Walls on Rigid 

Foundations,” Journal of Geotechnical and Geoenvironmental Engineering, 123(10),

912–920.

91. Das, B. (2013) Elastic Settlement of Shallow Foundations on Granular Soil: A Critical 

Review, California State University, Sacramento, CA. Obtained from: http://gle.wisc.edu/

wp-content/uploads/2013/07/Elastic-Settlement-Shallow-Foundations_A-Critical-Review2.pdf. Site last accessed November 11, 2015.

92. Schmertmann, J.H. (1970). “Static Cone to Compute Static Settlement Over Sand,” Journal 

of Soil Mechanics & Foundations Division, 96(3), 1,011–1,043.

93. Schmertmann, J.H., Hartman, J.P., and Brown, P.R. (1978). “Improved Strain Influence 

Factor Diagrams,” Journal of the Geotechnical Engineering Division, 104(GT8), 

1,131–1,135.

94. Hough, B.K. (1959). “Compressibility as Basis for Soil Bearing Value,” Journal of the Soil 

Mechanics and Foundations Division, 85(SM4, Part 1), 11–39. 

95. Peck, R.B. and Bazaraa, A.R.S.S. (1969). “Discussion of Paper by D’Appolonia et al.,”

Journal of the Soil Mechanics and Foundations Division, 95(3), 305–309.

96. Burland, J.B. and Burbidge, M.C. (1985). “Settlement of Foundations on Sand and 

Gravel,” Proceedings of the Institution of Civil Engineers, 78(1), 1,325–1,381.
129

97. D’Appolonia, D.J., D’Appolonia, E.E., and Brissette, R.F. (1968). “Settlement of Spread

Footings on Sand,” Journal of the Soil Mechanics and Foundations Division, 94(SM3), 

735–760.

98. D’Appolonia, D.J., D’Appolonia, E.E., and Brissette, R.F. (1970). “Closure to Discussions 

on ‘Settlement of Spread Footings on Sand,’” Journal of the Soil Mechanics and 

Foundations Division, 96(SM2), 754–761.

99. Terzaghi, K. and Peck, R.B. (1948). Theoretical Soil Mechanics, 2nd Ed., John Wiley & 

Sons, New York, NY.

100. Christian, J.T. and Carrier, W.D. (1978). “Janbu, Bjerrum and Kjaernsli’s Chart 

Reinterpreted,” Canadian Geotechnical Journal, 15, 123–128.

101. Crouse, P.E. and Wu, J.T.H. (1996). Long-Term Performance of GRS Retaining Walls,

Research Report, Department of Civil Engineering, University of Colorado at Denver,

Denver, CO.

102. Wu, J.T.H. (2001). Revising the AASHTO Guidelines for Design and Construction of GRS 

Walls, Report CDOT-DTD-R-2001-16, University of Colorado at Denver, Denver, CO.

103. Terzaghi, K., Peck, R.B., and Mesri, G. (1996). Soil Mechanics in Engineering Practice,

Third Ed., John Wiley & Sons, New York, NY. 

104. Briaud, J-L. and Garland, E. (1985). “Loading Rate Method for Pile Response in Clay,” 

Journal of Geotechnical Engineering, 111(3), 319–335.

105. Briaud, J-L. (2007). “Spread Footings in Sand: Load Settlement, Curve Approach,”

Journal of Geotechnical and Geoenvironmental Engineering, 133(8), 905–920.

106. Briaud, J-L. and Gibbens, R.M. (1999). “Behavior of Five Large Spread Footings in Sand,” 

Journal of Geotechnical Engineering, 125(9), 787–796.

107. Gibson, R.E. (1967). “Some Results Concerning Displacements and Stresses in a NonHomogeneous Elastic Half Space,” Geotechnique, 17, 58–67.

108. Giroud, J.P. (1989). Geotextile Engineering Workshop-Design Examples, Report No. 

FHWA HI-89-002, Federal Highway Administration, Washington, DC.

109. Wu, J.T.H. (1994). Design and Construction of Low Cost Retaining Walls: The Next 

Generation in Technology, Report No. CTI-UCD-1-94, Colorado Transportation Institute, 

Denver, CO.

110. Jewell, R.A. (1988). “Reinforced Soil Wall Analysis and Behavior,” The Application of 

Polymeric Reinforcement in Soil Retaining Structures, NATO Advanced Research 

Workshop, Kluwer, Netherlands.
130

111. Jewell, R.A. and Milligan, G.W. (1989). “Deformation Calculation for Reinforced Soil 

Walls,” Proceedings of the 12th International Conference on Soil Mechanics and 

Foundation Engineering, 1,259–1,262, Rio de Janeiro, Brazil.

112. DeBeer, E. (1948). “Settlement Records of Bridges Founded on Sand,” Proceedings of the 

Second International Conference on Soil Mechanics and Foundation Engineering, 2, 111.

113. Bergdahl, V. and Ottosson, E. (1982). “Calculation of Settlements on Sands from Field 

Test Results,” Proceedings of the Second European Symposium on Penetration Testing, 1, 

229–234.

114. DeBeer, E.E. and Martens, A. (1956). “Discussion of ‘Penetration Tests and Bearing 

Capacity of Cohesionless Soils by GG Meyerhof,’” Journal of the Soil Mechanics and 

Foundations Division, 1,095–1,097.

115. Holtz, R.D. and Lee, W.F. (2002). Internal Stability Analysis of Geosynthetic Reinforced 

Retaining Walls, Report No. WA-RD 532.1, Washington State Transportation Center,

Seattle, WA.

116. Ketchart, K. and Wu, J.T.H. (1997). “Performance of Geosynthetic-Reinforced Soil Bridge 

Pier and Abutment, Denver, Colorado, USA,” International Symposium on Mechanically 

Stabilized Backfill, 101–116.

117. Bueno, B.S., Benjamim, C.V.S., and Zornberg, J.G. (2005). “Field Performance of a FullScale Retaining Wall Reinforced with Nonwoven Geotextiles,” Proceedings of GeoFrontier 2005, Austin, TX.

118. Hatami, K. and Bathurst, R.J. (2006a). “A Numerical Model for Reinforced Soil Segmental 

Walls Under Surcharge Loading,” Journal of Geotechnical and Geoenvironmental 

Engineering, 132(6), 673–684.

119. Benjamim, C.V.S., Bueno, B.S., and Zornberg, J.G. (2007). “Field Monitoring Evaluation 

of Geotextile-Reinforced Soil-Retaining Walls,” Geosynthetics International, 14(2), 

100–118.

120. Benigni, C., Bosco, G., Cazzuffi, D., and Col, R.D. (1996). “Construction and Performance 

of an Experimental Large Scale Wall Reinforced with Geosynthetics,” Earth 

Reinforcement, 1, 315–320.

121. Basudhar, P.K., Dixit, P.M., Gharpure, A., and Deb, K. (2008). “Finite Element Analysis 

of Geotextile-Reinforced Sand-Bed Subjected to Strip Loading,” Geotextiles and 

Geomembranes, 26, 91–99.

122. Rowe, R.K. and Skinner, G.D. (2001). “Numerical Analysis of Geosynthetic Reinforced 

Retaining Wall Constructed on a Layered Soil Foundation,” Geotextiles and 

Geomembranes, 19, 387–412.
131

123. Leshchinsky, D. and Vulova, C. (2001). “Numerical Investigation of the Effects of 

Geosynthetic Spacing on Failure Mechanisms in MSE Block Walls,” Geosynthetics 

International, 8(4), 343–365.

124. Boushehrian, J.H. and Hataf, N. (2003). “Experimental and Numerical Investigation of the 

Bearing Capacity of Model Circular and Ring Footings on Reinforced Sand,” Geotextiles 

and Geomembranes, 21, 241–256.

125. Skinner, G.D. and Rowe, R.K. (2005). “Design and Behavior of a Geosynthetic Reinforced 

Retaining Wall and Bridge Abutment on a Yielding Foundation,” Geotextiles and 

Geomembranes, 23, 234–260.

126. Ghazavi, M. and Lavasan, A.A. (2008). “Interface Effect of Shallow Foundations 

Constructed on Sand Reinforced with Geosynthetics,” Geotextiles and Geomembranes, 

26, 404–415.

127. Alamshahi, S. and Hataf, N. (2009). “Bearing Capacity of Strip Footings on Sand Slopes 

Reinforced with Geogrid and Grid-Anchor,” Geotextiles and Geomembranes, 27, 217–226.

128. Chen, B., Luo, R., and Sun, J. (2011). “Time-Dependent Behaviors of Working 

Performance of Biaxial Reinforced Composite Foundation,” Institute of Electrical and 

Electronics Engineers Conference 2011, 915–920.

129. Karpurapu, R. and Bathurst, R.J. (1995). “Behavior of Geosynthetic Reinforced Soil 

Retaining Walls Using the Finite Element Method,” Computers and Geotechnics, 17(3),

279–299.

130. El Sawaaf, M. (2007). “Behavior of Strip Footing on Geogrid-Reinforced Sand Over a Soft 

Clay Slope,” Geotextiles and Geomembranes, 25(1), 50–60.

131. Ahmed, A., El-Tohami, A.M.K., and Marei, N.A. (2008). “Two-Dimensional Finite 

Element Analysis of Laboratory Embankment Model,” Geotechnical Engineering for 

Disaster Mitigation and Rehabilitation, 1,003–1,018.

132. Zidan, A.F. (2012). “Numerical Study of Behavior of Circular Footing on GeogridReinforced Sand Under Static and Dynamic Loading,” Geotechnical and Geological 

Engineering, 30, 499–510.

133. Bhattacharjee, A. and Krishna, A.M. (2013). “Strain Behavior of Backfill Soil of Wrap 

Faced Reinforced Soil Walls: A Numerical Study,” Proceedings of the 18th Southeast 

Asian Geotechnical Conference, Advances in Geotechnical Infrastructure, Singapore.

134. Fakharian, K. and Attar, I.H. (2007). “Static and Seismic Numerical Modeling of 

Geosynthetic-Reinforced Soil Segmental Bridge Abutments,” Geosynthetics International, 

14(4), 228–243.

135. Liu, H., Wang, X., and Song, E. (2009). “Long-Term Behavior of GRS Retaining Walls 

with Marginal Backfill Soils,” Geotextiles and Geomembranes, 27, 295–307.
132

136. Ling, H.I. and Liu, H. (2003). “Pressure Dependency and Densification Behavior of Sand 

Through a Generalized Plasticity Model,” Journal of Engineering Mechanics, 129(8),

851–860.

137. Lade, P.V. (2005). “Overview of Constitutive Models for Soils,” Soil Constitutive Models: 

Evaluation, Selection and Calibration, ASCE Geotechnical Special Publication No. 128, 

1–34.

138. Duncan, J.M., Byrne, P.M., Wong, K.S., and Mabry, P. (1980). Strength, Stress-Strain and 

Bulk Modulus Parameters for Finite Element Analyses of Stresses and Movements in Soil 

Masses, Report No. UCB/GT/80-01, University of California, Berkeley, Berkeley, CA.

139. Huang, B., Bathurst, R.J., and Hatami, K. (2009) “Numerical Study of Reinforced Soil 

Segmental Walls Using Three Different Constitutive Soil Models,” Journal of 

Geotechnical and Geoenvironmental Engineering, 135(10), 1,486–1,498.

140. Boscardin, M.D., Selig, E.T., Lin, R.S., and Yang, G.R. (1990). “Hyperbolic Parameters 

for Compacted Soils,” Journal of Geotechnical Engineering, 116(1), 88–104.

141. Kim, M.K. and Lade, P.V. (1988). “Single Hardening Constitutive Model for Frictional 

Materials I: Plastic Potential Function,” Computers and Geotechnics, 5(4), 307–324.

142. Lade, P.V. and Kim, M.K. (1988a). “Single Hardening Constitutive Model for Frictional 

Materials II: Yield Criterion and Plastic Work Contours,” Computers and Geotechnics, 

6(1), 13–29.

143. Lade, P.V. and Kim, M.K. (1988b). “Single Hardening Constitutive Model for Frictional 

Materials III: Comparisons with Experimental Data,” Computers and Geotechnics, 6(1),

31–47.

144. Hallquist, J.O. and Whirley, R.G. (1989). Dyna3D User’s Manual: Nonlinear Dynamic 

Analysis of Structures in Three Dimensions, Rev. 5, Report UCID-19592, Lawrence 

Livermore National Laboratory University of California, Livermore, CA.

145. Drucker, D.C. and Prager, W. (1952). “Soil Mechanics and Plasticity Analysis or Limit 

Design,” Quarterly of Applied Mathematics, 10(2), 157–165.

146. DiMaggio, F.L. and Sandler, I.S. (1971). “Material Model for Granular Soils,” Journal of 

the Engineering Mechanics Division, 97(3), 935–950.

147. Huang, T.K. and Chen, W.F. (1990). “Simple Procedure for Determining Cap-PlasticityModel Parameters,” Journal of Geotechnical Engineering, 116(3), 492–513.

148. Johnston, R.S. and Romstad, K.M. (1989). “Dilation and Boundary Effects in Large Scale 

Pull-Out Tests,” Proceedings of the 12th International Conference on Soil Mechanics and 

Foundation Engineering, 1,263–1,266, Rio de Janeiro, Brazil.
133

149. Otani, J., Ochiai, H., and Miyata, Y. (1994). “Bearing Capacity of Geogrid Reinforced 

Ground,” Fifth International Conference on Geotextiles, Geomembranes and Related 

Products, Singapore.

150. Otani, J., Ochiai, H., and Yamamoto, K. (1998). “Bearing Capacity Analysis of Reinforced 

Foundations on Cohesive Soil,” Geotextiles and Geomembrane, 16, 195–206.

151. Yamamoto, K. and Otani, J. (2002). “Bearing Capacity and Failure Mechanism of 

Reinforced Foundations Based on Rigid-Plastic Finite Element Formulation,” Geotextiles 

and Geomembranes, 20, 367–393.

152. Kurian, N.P., Beena, K.S., and Kumar, R.K. (1997). “Settlement of Reinforced Sand in 

Foundations,” Journal of Geotechnical and Geoenvironmental Engineering, 123(9),

818–827.

153. Dias, A.C. (2003). Numerical Analyses of Soil–Geosynthetic Interaction in Pull-out Tests,

M.Sc. Thesis, University of Brasilia, Brasilia, Brazil.

154. Chen, Q. and Abu-Farsakh, M. (2011). “Numerical Analysis to Study the Scale Effect of 

Shallow Foundation on Reinforced Soils,” Proceedings of GeoFrontiers 2011, 595–604.

155. Raftari, M., Kassim, K.A., Rashid, A.S., and Moayedi, H. (2013). “Settlement of Shallow 

Foundations near Reinforced Slopes,” Electronic Journal of Geotechnical Engineering, 18, 

797–808.

156. Chakraborty, D. and Kumar, J. (2014). “Bearing Capacity of Strip Foundations in 

Reinforced Soils,” International Journal of Geomechanics, 14(1), 45–58.

157. Ling, H.I., Cardany, C.P., Sun, L-X., and Hashimoto, H. (2000). “Finite Element Study of a 

Geosynthetic-Reinforced Soil Retaining Wall with Concrete-Block Facing,” Geosynthetics 

International, 7(3), 163–188.

158. Ling, H.I., Tatsuoka, F., and Tateyama, M. (1995). “Simulating Performance of GRS-RW 

by Finite-Element Procedure,” Journal of Geotechnical Engineering, 121(4), 330–340.

159. Sharma, K.G., Rao, G.V., and Raju, G.V.S.S. (1994). “Elasto-Plastic Analysis of a 

Reinforced Soil Wall by FEM,” Proceedings of the 8th International Conference on 

Computer Methods and Advances in Geomechanics, Morgantown, WV.

160. Lopes, M.L., Cardoso, A.S., and Yeo, K.C. (1994). “Modelling Performance of a Sloped 

Reinforced Soil Wall Using Creep Function,” Geotextiles and Geomembranes, 13, 

181–197.

161. Liu, H. and Ling, H.I. (2007). “A Unified Elastoplastic-Viscoplastic Bounding Surface 

Model of Geosynthetics and its Applications to GRS-RW Analysis,” Journal of 

Engineering Mechanics, 133(7), 801–815.
134

162. Kongkitkul, W., Chantachot, T., and Tatsuoka, F. (2014). “Simulation of Geosynthetic 

Load-Strain-Time Behaviour by the Non-Linear Three-Component Model,” Geosynthetics 

International, 21(4), 244–255.

163. Abramento, M. (1993). Analysis and Measurement of Stresses in Planar Soil 

Reinforcements, Ph.D. Thesis, Massachusetts Institute of Technology, Boston, MA.

164. Bergado, D.T. and Chai, J.C. (1994). “Pullout Force/Displacement Relationship of 

Extensible Grid Reinforcement,” Geotextiles and Geomembranes, 13(5), 295–316.

165. Sobhi, S. and Wu, J.T.H. (1996). “An Interface Pullout Formula for Extensible Sheet 

Reinforcement,” Geosynthetics International, 3(5), 565–582.

166. Madhav, M.R., Gurung, N., and Iwao, Y. (1998). “A Theoretical Model for the Pull-Out 

Response of Geosynthetic Reinforcement,” Geosynthetics International, 5(4), 399–424.

167. Gurung, N. (2001). “1-D Analytical Solution for Extensible and Inextensible Soil/Rock 

Reinforcement in Pull-Out Tests,” Geotextiles and Geomembranes, 19(4), 195–212.

168. Gurung, N. and Iwao, Y. (1999). “Comparative Model Study of Geosynthetic Pull-Out 

Response,” Geosynthetics International, 6(1), 53–68.

169. Perkins, S.W. (2001). Numerical Modelling of Geosynthetic Reinforced Flexible 

Pavements, Report No. FHWA/MT-01-003/99160-2, Federal Highway Administration, 

Washington, DC.

170. Khedkar, M.S. and Mandal, J.N. (2009). “Pullout Behaviour of Cellular Reinforcements,” 

Geotextiles and Geomembranes, 27(4), 262–271.

171. Palmeira, E.M. (2009). “Soil-Geosynthetic Interaction: Modelling and Analysis,” 

Geotextiles and Geomembranes, 27, 368–390.

172. Santos, E.C.G. (2007). The Use of Construction Residues and Recycled Rubble in 

Reinforced Soil Structures. M.Sc. Thesis, University of Sao Paulo, Sao Carlos, Brazil.

173. Brown, S.F., Kwan, J., and Thom, N.H. (2007). “Identifying the Key Parameters that 

Influence Geogrid Reinforcement of Railway Ballast,” Geotextiles and Geomembranes,

25(6), 326–335. 

174. Boyle, S.R. (1995). Deformation Prediction of Geosynthetic Reinforced Soil Retaining 

Walls, Ph.D. Dissertation, University of Washington, Seattle, WA.

175. Brown, B.S. and Poulos, H.G. (1981). “Analysis of Foundations on Reinforced Soil,” 

Proceedings of the 10th International Conference on Reinforced Soil, 3, 595–598, 

Stockholm, Sweden.
135

176. Andrawes, K.Z., Mcgown, A., Wilson-Fahmy, R.F., and Mashhour, M.M. (1982). “The 

Finite Element Method of Analysis Applied to Soil–Geotextile Systems,” Second 

International Conference of Geotextiles, 695–700, Las Vegas, NV.

177. Love, J.P., Burd, H.J., Milligan, G.W.E., and Houlsby, G.T. (1987). “Analytical and Model 

Studies of Reinforcement of a Layer of Granular Fill on a Soft Clay Subgrade,” Canadian 

Geotechnical Journal, 24, 611–622.

178. Rowe, R.K. and Soderman, K.L. (1987). “Stabilization of Very Soft Soils Using High 

Strength Geosynthetics: The Role of Finite Element Analyses,” Geotextiles and 

Geomembranes, 6, 53–80.

179. Matsui, T. and San, K.C. (1988). “Finite Element Stability Analysis Method for Reinforced 

Slopecutting,” International Geotechnical Symposium on Theory and Practice of Earth 

Reinforcement, 317–322, Fukoka, Japan.

180. Gens, A., Carol, I., and Alonso, E.E. (1988). “An Interface Element Formulation for the 

Analysis of Soil-Reinforcement Interaction,” Computer and Geotechnics, 7(1–2), 133–151.

181. Poran, C.J., Herrmann, L.R., and Romstad, K.M. (1989). “Finite Element Analysis of 

Footings on Geogrid-Reinforced Soil,” Proceedings of Geosynthetics, 231–242, 

San Diego, CA.

182. Hird, C.C., Pyrah, I.C., and Russell, D. (1990). “Finite Element Analysis of the Collapse of 

Reinforced Embankments on Soft Ground,” Geotechnique, 40(4), 633–640.

183. Burd, H.J. and Brocklehurst, C.J. (1990). “Finite Element Studies of the Mechanics of 

Reinforced Unpaved Roads,” Proceedings of the Fourth International Conference on 

Geotextiles, Geomembranes and Related Products, 217–221, The Hauge, Netherlands.

184. Wilson-Fahmy, R.F. and Koerner, R.M. (1993). “Finite Element Modeling of Soil Geogrid 

Interface with Application to the Behavior of Geogrids in Pullout Loading Conditions,” 

Geotextiles and Geomembranes, 12, 479–501.

185. Abdel-Baki, M.S. and Raymond, G.P. (1994). “Numerical Analysis of Geotextile 

Reinforced Soil Slabs,” Fifth International Conference on Geotextiles, Geomembranes and 

Related Products, Singapore.

186. Liu, H. and Won, M-S. (2009). “Long-Term Reinforcement Load of GeosyntheticReinforced Soil Retaining Walls,” Journal of Geotechnical and Geoenvironmental 

Engineering, 135(7), 875–889.

187. Duncan J.M. and Chang, C.Y. (1970). “Nonlinear Analysis of Stress and Strain in Soils,”

Journal of Soil Mechanics and Foundations Divisions, 96(SM5), 1,629–1,654.

188. Christopher, B.R. (1993). Deformation Response and Wall Stiffness in Relation to 

Reinforced Soil Wall Design, Ph.D. Dissertation, Purdue University, West Lafayette, IN.
136

189. Itasca Consulting Group, Inc. (2001). Fast Lagrangian Analysis of Continua (FLAC), 

Itasca Consulting Group, Inc., Minneapolis, MN.

190. Hatami, K. and Bathurst, R.J. (2006b). “Parametric Analysis of Reinforced Soil Walls with 

Different Backfill Material Properties,” North American Geosynthetics Society 2006 

Conference, 1–15, Las Vegas, NV. 

191. Wu, J.T.H. (1992). “Geosynthetic-Reinforced Soil Retaining Walls,” International 

Symposium on Geosynthetic-Reinforced Soil Retaining Walls, Wu (Ed.), Denver, CO.

192. Murata, O., Tateyama, M., and Tatsuoka, F. (1991). “A Reinforcing Method for Earth 

Retaining Walls Using Short Reinforcing Members and a Continuous Rigid Facing,”

Proceedings of the ASCE Geotechnical Engineering Congress, 935–946, New York, NY.

193. Miyatake, H., Ochiai, Y., Maruo, S., Nakane, A., Yamamoto, M., Terayama, T., Maejima, 

T., and Tsukada, Y. (1995). “Full-Scale Failure Experiments on Reinforced Earth Wall 

with Geotextiles (Part 2)—Facing with Concrete Blocks,” Proceedings of 30th Annual 

Conference of Geotechnical Engineering, 2,427–2,430, Kanazawa, Japan.

194. Tajiri, N., Sasaki, H., Nishimura, J., Ochiai, Y., and Dobashi, K. (1996). “Full-Scale 

Failure Experiments of Geotextile-Reinforced Soil Walls with Different Facings,

Proceedings of the International Symposium on Earth Reinforcement, 1, 525–530, 

Fukuoka, Kyushu, Japan.

195. Helwany, S.M.B. and Wu, J.T.H. (1992). “A Generalized Creep Model for Geosynthetics,” 

Proceedings of the International Symposium on Earth Reinforcement Practice, 79–84, 

Fukuoka, Kyushu, Japan.

196. Liu, H. and Ling, H.I. (2005). “Constitutive Modeling of the Time Dependent Monotonic 

and Cyclic Behavior of Geosynthetics,” Geosynthetics and Geosynthetic-Engineered Soil 

Structures, 281–302, Columbia University Press, New York, NY.

197. Helwany, S.M.B. (1993). “Long-Term Interaction Between Soil and Geosynthetic in 

Geosynthetic-Reinforced Soil Structures,” Ph.D. Thesis, University of Colorado at Denver, 

Denver, CO.

198. Wu, J.H.T. and Helwany, S.M.B. (1996). “A Performance Test for Assessment of LongTerm Creep Behavior of Soil-Geosynthetic Composites,” Geosynthetics International, 

3(1), 107–124.

199. Wu, J.T.H. and Adams, M.T. (2007). “Myth and Fact on Long-Term Creep of GRS 

Structures,” Geotechnical Special Publication No. 165, Geosynthetics in Reinforcement and 

Hydraulic Applications, Proceedings for Geo-Denver, Denver, CO.

200. Abu-Hejleh, N., Mohammed, K., and Alzamora, D.E. (2013). “Recommendations for the 

Use of Spread Footings on Soils to Support Highway Bridges,” Transportation Research 

Board 2013 Annual Meeting Compendium of Papers, Transportation Research Board, 

Washington, DC.
137

201. Cerato, A.B. and Luteneger, A.J. (2007). “Scale Effects of Shallow Bearing Capacity on 

Granular Material,” Journal of Geotechnical and Geoenvironmental Engineering, 133(10),

1,192–1,202.

202. Fakher, A. and Jones, C.J.F.P. (1996). “Discussion: Bearing Capacity of Rectangular 

Footings on Geogrid-Reinforced Sand,” Journal of Geotechnical Engineering, 122(4),

326–327.

203. Bolton, M.D. (1986). “The Strength and Dilatancy of Sands,” Géotechnique, 36(1), 65–78.
HRDI-40/02-16(WEB)E