Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

Composite Behavior of Geosynthetic

Reinforced Soil Mass

Publication No. FHWA-HRT-10-077 july 2013
FOREWORD

Through the Federal Highway Administration’s (FHWA) Every Day Counts initiative, 

geosynthetic reinforced soil (GRS) was distinguished apart from traditional mechanically 

stabilized Earth technology. The separation is based on the reinforcement spacing, with GRS 

referred to as alternating layers of closely spaced (≤ 12 inches (300 mm)) geosynthetic 

reinforcement and a compacted granular fill material. The close reinforcement spacing increases 

the soil-geosynthetic interaction, leading to full composite behavior. This study investigated the 

composite behavior of GRS.

A major finding of this study was a new method to evaluate the required reinforcement strength 

based on the results of full-scale plane strain testing conducted at FHWA’s Turner-Fairbank 

Highway Research Center. This semi-empirical equation was subsequently selected by FHWA 

for inclusion in the new internal stability design method presented in the Geosynthetic 

Reinforced Soil Integrated Bridge System Interim Implementation Guide.

(1) The methodology 

and testing that led to this new design equation are presented in this report, along with further 

documentation regarding the composite behavior of GRS and the new FHWA GRS 

design method. 

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-10-077

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

4. Title and Subtitle

Composite Behavior of Geosynthetic Reinforced Soil Mass

5. Report Date

July 2013

6. Performing Organization Code: 

7. Author(s)

Jonathan T.H. Wu, Thang Q. Pham, and Michael T. Adams

8. Performing Organization Report No. 

9. Performing Organization Name and Address

Department of Civil Engineering 

University of Colorado Denver

1200 Larimer Street

Denver, CO 80217-3364

10. Work Unit No.

11. Contract or Grant No.

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

14. Sponsoring Agency Code

15. Supplementary Notes

The FHWA Contracting Officer’s Technical Representative (COTR) was Mike Adams, HRDI-40.

16. Abstract

This study investigated the composite behavior of a geosynthetic reinforced soil (GRS) mass. Many studies have been 

conducted on the behavior of GRS structures; however, the interactive behavior between the soil and geosynthetic 

reinforcement in a GRS mass has not been fully elucidated. Current design methods consider the reinforcement in a 

GRS structure as tiebacks and adopt a design concept that the reinforcement strength and reinforcement spacing 

produce the same effects on the performance of a GRS structure. This has encouraged designers to use stronger 

reinforcement at a larger spacing to reduce time and effort in construction. 

A series of large-size generic soil geosynthetic composite (GSGC) tests were designed and conducted to examine the 

behavior of a GRS mass under well-controlled conditions. The tests clearly demonstrated that reinforcement spacing 

has a much stronger impact than reinforcement strength on the performance of the GRS mass. An analytical model 

was established to describe the relative contribution of reinforcement strength and reinforcement spacing. Based on 

the analytical model, equations were developed to calculate the apparent cohesion of a GRS composite, the ultimate 

load-carrying capacity of a GRS mass, and the required tensile strength of reinforcement for a prescribed value of 

spacing. The equations were verified using measured data from the GSGC tests and measured data from large-size 

experiments by other researchers, as well as by results of the finite element (FE) method of analysis. 

Due to the popularity of GRS walls with modular block facing, an analytical procedure was developed for predicting 

the walls’ lateral movement. This procedure also allows the required tensile strength of the reinforcement to be 

determined by simple calculations. In addition, compaction-induced stresses, which have usually been ignored in 

design and analysis of GRS structures, were investigated. An analytical model for estimating compaction-induced 

stresses in a GRS mass was proposed. Preliminary verification of the model was made by using results from the 

GSGC tests and FE analysis. The dilative behavior of a GRS composite was also examined. The presence of

geosynthetic reinforcement has a tendency to suppress dilation of the surrounding soil and reduce the angle of dilation 

of the soil mass. The dilative behavior offers a new explanation of the reinforcing mechanism, and the angle of 

dilation may be used to reflect the degree of reinforcing of a GRS mass.

17. Key Words

Geosynthetic reinforced soil, GRS, Retaining walls, 

Analysis, Design, Composite, Compaction

18. Distribution Statement

No restrictions. This document is available to the public 

through the National Technical Information Service, 

Springfield, VA 22161.

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

211

22. Price

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 o

F 

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. INTRODUCTION.................................................................................................1

1.1 PROBLEM STATEMENT...............................................................................................1

1.2 RESEARCH OBJECTIVES.............................................................................................3

1.3 RESEARCH TASKS .........................................................................................................3

CHAPTER 2. LITERATURE REVIEW.....................................................................................5

2.1 MECHANICS OF REINFORCED SOIL........................................................................5

2.1.1 Concept of Apparent Cohesion...................................................................................5

2.1.2 Concept of Apparent Confining Pressure ...................................................................6

2.2 COMPOSITE BEHAVIOR OF GRS MASS ..................................................................8

2.3 CIS IN AN UNREINFORCED SOIL MASS ................................................................16

2.3.1 Lateral Earth Pressure Estimation.............................................................................17

2.3.2 Stress Path Theory by Broms and Extension of Broms’ Work by Ingold................18

2.3.3 FE Analysis by Aggour and Brown..........................................................................19

2.3.4 CIS Models by Seed..................................................................................................20

2.4 CIS IN A REINFORCED SOIL MASS.........................................................................22

2.4.1 Ehrlich and Mitchell .................................................................................................22

2.4.2 Hatami and Bathurst .................................................................................................24

2.4.3 Morrison et al............................................................................................................25

2.5 HIGHLIGHTS OF COMPACTION-INDUCED EARTH PRESSURES 

IN THE LITERATURE........................................................................................................26

CHAPTER 3. ANALYTICAL MODEL FOR CALCULATING LATERAL 

DISPLACEMENT OF A GRS WALL WITH MODULAR BLOCK FACING....................29

3.1 EXISTING METHODS FOR ESTIMATING MAXIMUM WALL 

MOVEMENT.........................................................................................................................30

3.1.1 The FHWA Method ..................................................................................................30

3.1.2 The Geoservices Method ..........................................................................................31

3.1.3 The CTI Method .......................................................................................................32

3.1.4 The Jewell-Milligan Method.....................................................................................33

3.2 DEVELOPING AN ANALYTICAL MODEL FOR CALCULATING 

LATERAL MOVEMENT AND CONNECTION FORCES OF A GRS WALL ............37

3.2.1 Lateral Movement of GRS Walls with Negligible Facing Rigidity .........................37

3.2.2. Connection Forces for GRS Walls with Modular Block Facing .............................40

3.2.3 Lateral Movement of GRS Walls with Modular Block Facing ................................43

3.2.4 Required Tensile Strength of Reinforcement of GRS Walls....................................44

3.3 VERIFICATION OF THE ANALYTICAL METHOD ..............................................44

3.3.1 Comparison to the Jewell-Milligan Method for Lateral Wall Movement ................44

3.3.2 Comparison to Measured Data of Full-Scale Experiment by Hatami and 

Bathurst..............................................................................................................................49

3.4 SUMMARY ......................................................................................................................52
iv

CHAPTER 4. GSGC TESTS ......................................................................................................53

4.1 DIMENSIONS OF THE PLANE-STRAIN GSGC TEST SPECIMEN.....................53

4.2 APPARATUS FOR PLANE-STRAIN TEST................................................................61

4.2.1 Lateral Deformation..................................................................................................61

4.2.2 Friction......................................................................................................................62

4.3 TEST MATERIAL ..........................................................................................................63

4.3.1 Backfill......................................................................................................................63

4.3.2 Geosynthetics............................................................................................................66

4.3.3. Facing Block ............................................................................................................69

4.4 TEST PROGRAM ...........................................................................................................69

4.5 TEST CONDITIONS AND INSTRUMENTATION....................................................70

4.5.1 Vertical Loading System...........................................................................................70

4.5.2 Confining Pressure....................................................................................................70

4.5.3 Instrumentation .........................................................................................................70

4.5.4 Preparation of Test Specimen for GSGC Tests ........................................................75

4.6 TEST RESULTS..............................................................................................................85

4.6.1 Test 1—Unreinforced Soil........................................................................................85

4.6.2 Test 2—GSGC Test (T, Sv).......................................................................................89

4.6.3 Test 3—GSGC Test (2T, 2Sv).................................................................................104

4.6.4 Test 4—GSGC Test (T, 2Sv)...................................................................................113

4.6.5 Test 5—GSGC Test (Unconfined with T, Sv).........................................................121

4.7 DISCUSSION OF THE RESULTS..............................................................................129

4.7.1 Effects of Geosynthetic Inclusion (Comparison Between Tests 1 and 2) ..............129

4.7.2 Relationship Between Reinforcement Spacing and Reinforcement Strength 

(Comparison Between Tests 2 and 3)..............................................................................130

4.7.3 Effects of Reinforcement Spacing (Comparison Between Tests 2 and 4)..............131

4.7.4 Effects of Reinforcement Strength (Comparison Between Tests 3 and 4).............131

4.7.5 Effects of Confining Pressure (Comparison Between Tests 2 and 5).....................132

4.7.6 Composite Strength Properties ...............................................................................133

CHAPTER 5. ANALYTICAL MODELS FOR EVALUATING CIS, COMPOSITE 

STRENGTH PROPERTIES, AND REQUIRED REINFORCEMENT STRENGTH .......135

5.1 EVALUATING CIS IN A GRS MASS........................................................................135

5.1.1 Conceptual Model for Simulation of Fill Compaction of a GRS Mass..................135

5.1.2 Simplified Model to Simulate Fill Compaction of a GRS Mass ............................136

5.1.3 Model Parameters of the Proposed Compaction Simulation Model.......................137

5.1.4 Simulation of Fill Compaction Operation...............................................................138

5.1.5 Estimation of K2,c ....................................................................................................141

5.2 STRENGTH PROPERTIES OF GRS COMPOSITE................................................144

5.2.1 Increased Confining Pressure .................................................................................146

5.2.2 Apparent Cohesion and Ultimate Pressure Carrying Capacity of a GRS Mass .....150

5.3 VERIFICATION OF THE ANALYTICAL MODEL WITH 

MEASUREMENT DATA ...................................................................................................151

5.3.1 Comparison Between the Analytical Model and GSGC Test Results....................151

5.3.2 Comparison Between the Analytical Model and Elton and Patawaran’s 

Test Results......................................................................................................................152

5.3.3 Comparison Between the Analytical Model and FE Results..................................154
v

5.4 REQUIRED REINFORCEMENT STRENGTH IN DESIGN..................................155

5.4.1 Proposed Model for Determining Reinforcement Force ........................................155

5.4.2 Comparison of Reinforcement Strength Between the Analytical Model 

and Current Design Equation...........................................................................................157

5.4.3 Verification of the Analytical Model for Determining Reinforcement Strength....158

CHAPTER 6. FE ANALYSES..................................................................................................161

6.1 PLAXIS 8.2.....................................................................................................................161

6.2 CIS IN A GRS MASS ....................................................................................................162

6.3 FE SIMULATION OF THE GSGC TESTS ...............................................................164

6.3.1 Simulation of GSGC Test 1 ....................................................................................169

6.3.2 Simulation of GSGC Test 2 ....................................................................................171

6.3.3 Simulation of GSGC Test 3 ....................................................................................175

6.4 FE ANALYSIS OF GSGC TEST 2 UNDER DIFFERENT CONFINING 

PRESSURES AND DILATION ANGLE OF SOIL-GEOSYNTHETIC 

COMPOSITES.....................................................................................................................179

6.5 VERIFICATION OF CIS MODEL .............................................................................181

CHAPTER 7. SUMMARY AND CONCLUSIONS................................................................187

7.1 SUMMARY ....................................................................................................................187

7.2 FINDINGS AND CONCLUSIONS..............................................................................187

REFERENCES...........................................................................................................................189
vi

LIST OF FIGURES

Figure 1. Illustration. Typical cross section of a GRS wall with modular block facing..................1

Figure 2. Equation. Design strength ................................................................................................2

Figure 3. Illustration. Concept of apparent cohesion due to the presence of reinforcement ...........5

Figure 4. Illustration. Concept of apparent confining pressure due to the presence of 

reinforcement ...................................................................................................................................6

Figure 5. Equation. Increase in confining pressure as a function of reinforcement strength 

and spacing.......................................................................................................................................6

Figure 6. Equation. Principle stress at failure for reinforced soil ....................................................6

Figure 7. Equation. Principle stress at failure for reinforced soil with zero cohesion.....................7

Figure 8. Equation. Total confining stress of reinforced soil ..........................................................7

Figure 9. Equation. Principle stress at failure for reinforced soil substituting the components 

derived in figure 8............................................................................................................................7

Figure 10. Equation. Apparent cohesion for reinforced soil in terms of increase in confining 

stress.................................................................................................................................................7

Figure 11. Equation. Apparent cohesion in terms of reinforcement strength and spacing..............7

Figure 12. Equation. Increase of confining pressure due to reinforcement.....................................7

Figure 13. Equation. Increase of confining pressure by Hausmann ................................................7

Figure 14. Photo. Unconfined test specimen before testing ............................................................8

Figure 15. Photo. Unconfined test specimen after testing ...............................................................9

Figure 16. Graph. Stress-strain curves of specimens reinforced at spacings of 6 and 

12 inches (150 and 300 mm) in large, unconfined compression test...............................................9

Figure 17. Photo. Mini-pier experiments.......................................................................................10

Figure 18. Graph. Stress-strain curves of mini-pier experiments..................................................11

Figure 19. Illustration. Schematic of large-size triaxial tests with specimens 3.6 ft

(1.1 m) high and 1.6 ft (0.5 m) in diameter....................................................................................12

Figure 20. Photo. Setup of large-size triaxial tests with specimens 3.6 ft (1.1 m) high and

1.6 ft (0.5 m) in diameter ...............................................................................................................12

Figure 21. Graph. Large-size triaxial test results...........................................................................13

Figure 22. Graph. Vertical stress distributions at 1.3-kip (6-kN) vertical load of the GRS 

masses without and with reinforcement.........................................................................................14

Figure 23. Graph. Horizontal stress distribution at 1.3-kip (6-kN) vertical load of the GRS 

masses without and with reinforcement.........................................................................................15

Figure 24. Graph. Shear stress distribution at 1.3-kip (6-kN) vertical load of the GRS 

masses without and with reinforcement.........................................................................................16

Figure 25. Equation. At-rest Earth pressure coefficient ................................................................17

Figure 26. Equation. Schmidt’s equation for residual lateral Earth pressures...............................18

Figure 27. Illustration. Hypothetical stress path during compaction.............................................18

Figure 28. Equation. Lateral Earth pressure at rest........................................................................18

Figure 29. Equation. Lateral Earth pressure at K1 .........................................................................19

Figure 30. Equation. Horizontal residual stress after compaction.................................................21

Figure 31. Equation. Vertical residual stress after compaction .....................................................21

Figure 32. Equation. Lateral residual stress...................................................................................22

Figure 33. Illustration. Assumed stress path due to compaction-induced stress ...........................23

Figure 34. Equation. Maximum vertical stress at a given depth during construction ...................23
vii

Figure 35. Equation. Coefficient of Earth pressure at rest.............................................................23

Figure 36. Equation. Maximum lateral stress in terms of compaction and effective soil 

unit weight .....................................................................................................................................23

Figure 37. Equation. Poisson’s ratio under Ko condition...............................................................24

Figure 38. Equation. Bearing capacity factor ................................................................................24

Figure 39. Illustration. FE model for FE analysis..........................................................................26

Figure 40. Illustration. Basic components of a GRS wall with a modular block facing ...............29

Figure 41. Graph. Empirical curve for estimating maximum wall movement during 

construction in the FHWA method................................................................................................31

Figure 42. Equation. Relative displacement coefficient ................................................................31

Figure 43. Equation. Maximum lateral wall displacement during construction for 

extensible reinforcement................................................................................................................31

Figure 44. Illustration. Assumed strain distribution in the Geoservices method...........................32

Figure 45. Equation. Horizontal displacement ..............................................................................32

Figure 46. Equation. Maximum lateral wall displacement according to CTI method...................33

Figure 47. Illustration. Stress and velocity characteristics behind a smooth retaining wall 

rotating about the toe .....................................................................................................................33

Figure 48. Illustration. Major zones of reinforcement forces in a GRS wall and the force 

distribution along reinforcement with ideal length........................................................................34

Figure 49. Equation. Maximum horizontal resultant force required for equilibrium....................35

Figure 50. Equation. Active Earth pressure coefficient.................................................................35

Figure 51. Equation. Ratio of the required reinforcement force and the estimated maximum 

reinforcement force........................................................................................................................35

Figure 52. Illustration. Charts for estimating lateral displacement of GRS walls with the 

ideal length layout..........................................................................................................................36

Figure 53. Equation. Reinforcement force at the base of the wall.................................................37

Figure 54. Illustration. Major zones of the reinforcement force in a GRS wall ............................38

Figure 55. Equation. Horizontal movement...................................................................................38

Figure 56. Equation. Lateral deformation in zone 1 ......................................................................38

Figure 57. Equation. Lateral deformation in zone 2 ......................................................................38

Figure 58. Equation. Total horizontal movement of the wall face ................................................38

Figure 59. Equation. Reinforcement length in zone 1 ...................................................................39

Figure 60. Equation. Reinforcement length in zone 2 ...................................................................39

Figure 61. Equation. Total horizontal movement of the wall face substituting the 

components derived in figure 59 and figure 60 .............................................................................39

Figure 62. Equation. Rearrangement of total horizontal movement of the wall face....................39

Figure 63. Equation. Factored down total horizontal movement of the wall face.........................39

Figure 64. Equation. Simplified horizontal movement of the wall face........................................39

Figure 65. Illustration. Forces acting on two facing blocks at depth zi..........................................40

Figure 66. Equation. Tensile connection force ..............................................................................40

Figure 67. Equation. Horizontal resultant force of lateral Earth pressure acting on the 

two facing blocks...........................................................................................................................41

Figure 68. Equation. Tensile connection force substituting the components derived 

in figure 67.....................................................................................................................................41

Figure 69. Equation. Tensile connection force solved in terms of the weight of the facing 

block and friction between the soil and wall facing ......................................................................41
viii

Figure 70. Equation. Simplified tensile connection force..............................................................41

Figure 71. Equation. Average net Earth pressure on the facing ....................................................41

Figure 72. Equation. Tensile connection force at a given depth....................................................42

Figure 73. Equation. Tensile connection force substituting figure 67...........................................42

Figure 74. Equation. Tensile connection force as a simplification of figure 73............................42

Figure 75. Equation. Tensile connection force ignoring the effect of fiction between the 

back of the block and soil ..............................................................................................................42

Figure 76. Equation. Connection force for a typical GRS wall with modular block facing..........42

Figure 77. Equation. Resistant connection force ...........................................................................42

Figure 78. Graph. Connection forces in reinforcement (q = 0 kip/ft (0 kN/m)) (wall data 

from section 3.3.1 with = 15 degrees). .......................................................................................43

Figure 79. Graph. Connection forces in reinforcement (q = 3.4 kip/ft (50 kN/m)) (wall data 

from section 3.3.1 with = 15 degrees) ........................................................................................43

Figure 80. Equation. Lateral displacement of a GRS wall with modular block facing .................44

Figure 81. Equation. Lateral displacement of a GRS wall with modular block facing 

ignoring the effect of fiction between the back of the block and soil............................................44

Figure 82. Equation. Required tensile reinforcement strength at a given allowable lateral 

movement of the wall face.............................................................................................................44

Figure 83. Graph. Lateral displacement calculated by the Jewell-Milligan method and the 

analytical model, b = 0 kip/ft3 (0 kN/m3), q = 0 kip/ft (0 kN/m) ..................................................45

Figure 84. Graph. Lateral displacement calculated by the Jewell-Milligan method and the 

analytical model, b = 0 kip/ft3 (0 kN/m3

), q = 0.7 kip/ft (10 kN/m) .............................................46

Figure 85. Graph. Lateral displacement calculated by the Jewell-Milligan method and the 

analytical model, b = 0 kip/ft3 (0 kN/m3), q = 3.4 kip/ft (50 kN/m) .............................................46

Figure 86. Graph. Lateral displacement calculated by the Jewell-Milligan method and the 

analytical model, b = 0.06 kip/ft3 (10 kN/m3

), q = 0 kip/ft (0 kN/m)...........................................46

Figure 87. Graph. Lateral displacement calculated by the Jewell-Milligan method and the 

analytical model, b = 0.06 kip/ft3 (10 kN/m3), q = 0.7 kip/ft (10 kN/m)......................................47

Figure 88. Graph. Lateral displacement calculated by the Jewell-Milligan method and the 

analytical model, b = 0.06 kip/ft3 (10 kN/m3), q = 3.4 kip/ft (50 kN/m)......................................47

Figure 89. Graph. Lateral displacement calculated by the Jewell-Milligan method and the 

analytical model, b = 0.13 kip/ft3 (20 kN/m3), q = 0 kip/ft (0 kN/m)...........................................47

Figure 90. Graph. Lateral displacement calculated by the Jewell-Milligan method and the 

analytical model, b = 0.13 kip/ft3 (20 kN/m3

), q = 0.7 kip/ft (10 kN/m)......................................48

Figure 91. Graph. Lateral displacement calculated by the Jewell-Milligan method and the 

analytical model, b = 0.13 kip/ft3 (20 kN/m3), q = 3.4 kip/ft (50 kN/m)......................................48

Figure 92. Graph. Lateral displacement calculated by the Jewell-Milligan method and the 

analytical model, b = 0.19 kip/ft3 (30 kN/m3), q = 0 kip/ft (0 kN/m)...........................................48

Figure 93. Graph. Lateral displacement calculated by the Jewell-Milligan method and the 

analytical model, b = 0.19 kip/ft3 (30 kN/m3

), q = 0.7 kip/ft (10 kN/m)......................................49

Figure 94. Graph. Lateral displacement calculated by the Jewell-Milligan method and the 

analytical model, b = 0.19 kip/ft3 (30 kN/m3), q = 3.4 kip/ft (50 kN/m)......................................49

Figure 95. Equation. Direct shear friction angle............................................................................50

Figure 96. Equation. Empirical facing batter factor ......................................................................50

Figure 97. Graph. Measured lateral displacements with Jewell-Milligan method and 

analytical model, q = 3.4 kip/ft (50 kN/m) ....................................................................................51

ψ

ψ

γ

γ

γ

γ

γ

γ

γ

γ

γ

γ

γ

γ
ix

Figure 98. Graph. Measured lateral displacements with Jewell-Milligan method and 

analytical model, q = 4.8 kip/ft (70 kN/m) ....................................................................................51

Figure 99. Illustration. Typical geometric and loading conditions of a GSGC.............................54

Figure 100. Graph. Global stress-strain curves for GSGCs of different dimensions 

under a confining pressure of 0 psi (0 kPa) ...................................................................................55

Figure 101. Graph. Global stress-strain curves for GSGCs of different dimensions 

under a confining pressure of 4.4 psi (30 kPa) ..............................................................................56

Figure 102. Graph. Global volume change curves for GSGCs of different dimensions 

under a confining pressure of 0 psi (0 kPa) ...................................................................................57

Figure 103. Graph. Global volume change curves for GSGCs of different dimensions 

under a confining pressure of 4.4 psi (30 kPa) ..............................................................................57

Figure 104. Equation. Global vertical strain..................................................................................57

Figure 105. Graph. Global stress-strain curves of unreinforced soil under a confining 

pressure of 4.4 psi (30 kPa)............................................................................................................58

Figure 106. Graph. Global volume change curves of unreinforced soil under a confining 

pressure of 4.4 psi (30 kPa)............................................................................................................58

Figure 107. Illustration. Specimen dimensions for the GSGC tests..............................................59

Figure 108. Illustration. Front view of the test setup.....................................................................60

Figure 109. Illustration. Plan view of the test setup ......................................................................61

Figure 110. Photo. Test bin............................................................................................................62

Figure 111. Graph. Grain size distribution of backfill...................................................................64

Figure 112. Photo. Typical triaxial test specimen before test........................................................64

Figure 113. Photo. Typical triaxial test specimen after test...........................................................65

Figure 114. Graph. Triaxial test results: stress-strain curves of backfill at 0.15 kip/ft3

(24.1 kN/m3) dry density and 5.2 percent moisture .......................................................................65

Figure 115. Graph. Triaxial test results: volume change curves of backfill at confining 

pressures of 5 and 30 psi (34.45 and 103.35 kPa) .........................................................................66

Figure 116. Graph. Mohr-Coulomb failure envelopes of backfill.................................................66

Figure 117. Photo. Uniaxial tension test of Geotex® 4×4..............................................................68

Figure 118. Graph. Load deformation curves of the geosynthetics...............................................69

Figure 119. Illustration. Locations of LVDTs and digital dial indicators .....................................72

Figure 120. Photo. Strain gauge on Geotex® 4×4 geotextile before applying protection tape......72

Figure 121. Photo. Strain gauge on Geotex® 4×4 geotextile after applying protection tape.........73

Figure 122. Photo. Strain gauges mounted on Geotex® 4×4 geotextile ........................................73

Figure 123. Graph. Calibration curve for single-sheet Geotex® 4×4.............................................74

Figure 124. Graph. Calibration curve for double-sheet Geotex® 4×4 ...........................................74

Figure 125. Photo. Applying grease on Plexiglas® surfaces..........................................................75

Figure 126. Photo. Attaching membrane .......................................................................................76

Figure 127. Photo. Placement of the first course of facing block..................................................76

Figure 128. Photo. Compacting the first lift of backfill.................................................................77

Figure 129. Photo. Placing backfill for the second lift ..................................................................78

Figure 130. Photo. Placing a reinforcement sheet .........................................................................78

Figure 131. Photo. Completion of compaction of the composite mass and leveling the 

top surface with 0.2-inch (5-mm)-thick sand layer........................................................................79

Figure 132. Photo. Completed composite mass with a geotextile sheet on the top surface ..........79

Figure 133. Photo. Top surface of the composite mass covered with a sheet of membrane .........80
x

Figure 134. Photo. Removing facing blocks and trimming off excess geosynthetic 

reinforcement .................................................................................................................................80

Figure 135. Photo. Inserting strain gauge cables through the membrane sheet.............................81

Figure 136. Photo. Vacuuming the composite mass with a low pressure......................................81

Figure 137. Photo. Sealing the connection between cable and membrane with epoxy to 

prevent air leaks.............................................................................................................................82

Figure 138. Photo. Checking air leaks under vacuuming ..............................................................82

Figure 139. Photo. LVDTs on an open side of test specimen........................................................83

Figure 140. Illustration. Locations of selected points to trace internal movement of tests 1–5 ....84

Figure 141. Graph. Soil dry unit weight results during specimen preparation ..............................85

Figure 142. Photo. Soil mass at failure of test 1 ............................................................................86

Figure 143. Graph. Test 1 unreinforced soil mass global vertical stress/vertical strain 

relationship.....................................................................................................................................86

Figure 144. Graph. Test 1 unreinforced soil mass global volume change strain relationship.......87

Figure 145. Graph. Lateral displacements on the open face of test 1............................................87

Figure 146. Illustration. Internal displacements of test 1...............................................................88

Figure 147. Photo. Composite mass at failure of test 2 .................................................................90

Figure 148. Photo. Close-up of shear bands at failure of area A in figure 147 .............................91

Figure 149. Photo. Failure planes of the composite mass after testing in test 2............................92

Figure 150. Graph. Test 2 reinforced soil mass global vertical stress-vertical strain 

relationship.....................................................................................................................................94

Figure 151. Graph. Test 2 reinforced soil mass global volume change strain relationship...........94

Figure 152. Graph. Lateral displacements on the open face of test 2............................................95

Figure 153. Illustration. Internal displacements of test 2...............................................................96

Figure 154. Illustration. Locations of strain gauges on geosynthetic sheets in test 2....................97

Figure 155. Graph. Reinforcement strain distribution of the composite mass in layer 1 

of test 2 0.7 ft (0.2 m) from the base..............................................................................................97

Figure 156. Graph. Reinforcement strain distribution of the composite mass in layer 2 

of test 2 1.3 ft (0.4 m) from the base..............................................................................................98

Figure 157. Graph. Reinforcement strain distribution of the composite mass in layer 3 

of test 2 2 ft (0.6 m) from the base.................................................................................................98

Figure 158. Graph. Reinforcement strain distribution of the composite mass in layer 4 

of test 2 2.6 ft (0.8 m) from the base..............................................................................................99

Figure 159. Graph. Reinforcement strain distribution of the composite mass in layer 5 

of test 2 3.3 ft (1.0 m) from the base..............................................................................................99

Figure 160. Graph. Reinforcement strain distribution of the composite mass in layer 6 

of test 2 3.9 ft (1.2 m) from the base............................................................................................100

Figure 161. Graph. Reinforcement strain distribution of the composite mass in layer 7 

of test 2 4.6 ft (1.4 m) from the base............................................................................................100

Figure 162. Graph. Reinforcement strain distribution of the composite mass in layer 8 

of test 2 5.2 ft (1.6 m) from the base............................................................................................101

Figure 163. Graph. Reinforcement strain distribution of the composite mass in layer 9

of test 2 5.9 ft (1.8 m) from the base............................................................................................101

Figure 164. Photo. Aerial view of the reinforcement sheets exhumed from the composite 

mass after test 2 (numbers indicate sheet number)......................................................................102
xi

Figure 165. Illustration. Locations of rupture lines of reinforcement in test 2 based 

on figure 164................................................................................................................................103

Figure 166. Photo. Composite mass after testing of test 3...........................................................104

Figure 167. Graph. Global stress-strain relationship of test 3 .....................................................105

Figure 168. Graph. Lateral displacements on the open face of test 3..........................................106

Figure 169. Illustration. Internal displacements of test 3.............................................................107

Figure 170. Illustration. Location of strain gauges on geosynthetic sheets in test 3 ...................108

Figure 171. Graph. Reinforcement strain distribution of the composite mass in layer 1 

of test 3 1.3 ft (0.4 m) from the base............................................................................................108

Figure 172. Graph. Reinforcement strain distribution of the composite mass in layer 2 

of test 3 2.6 ft (0.8 m) from the base............................................................................................109

Figure 173. Graph. Reinforcement strain distribution of the composite mass in layer 3 

of test 3 3.9 ft (1.2 m) from the base............................................................................................109

Figure 174. Graph. Reinforcement strain distribution of the composite mass in layer 4 

of test 3 5.2 ft (1.6 m) from the base............................................................................................110

Figure 175. Photo. Aerial view of the reinforcement sheets exhumed from the composite 

mass after test 3 (numbers indicate sheet number)......................................................................111

Figure 176. Illustration. Locations of rupture lines of reinforcement in test 3 based 

on figure 175................................................................................................................................112

Figure 177. Photo. Front view of failure planes of the composite mass after test 4....................113

Figure 178. Photo. Back view of failure planes of the composite mass after test 4 ....................113

Figure 179. Graph. Global stress-strain relationship of test 4 .....................................................114

Figure 180. Graph. Lateral displacements on the open face of test 4..........................................115

Figure 181. Illustration. Internal displacements of test 4.............................................................116

Figure 182. Illustration. Locations of strain gauges on geosynthetic sheets in test 4..................117

Figure 183. Graph. Reinforcement strain distribution of the composite mass in layer 1 

of test 4 1.3 ft (0.4 m) from the base............................................................................................117

Figure 184. Graph. Reinforcement strain distribution of the composite mass in layer 2 

of test 4 2.6 ft (0.8 m) from the base............................................................................................118

Figure 185. Graph. Reinforcement strain distribution of the composite mass in layer 3 

of test 4 3.9 ft (1.2 m) from the base............................................................................................118

Figure 186. Graph. Reinforcement strain distribution of the composite mass in layer 4 

of test 4 5.2 ft (1.6 m) from the base............................................................................................119

Figure 187. Photo. Aerial view of the reinforcement sheets exhumed from the composite 

mass after test 4 (numbers indicate sheet number)......................................................................119

Figure 188. Illustration. Locations of rupture lines of reinforcement in test 4 based on 

figure 187.....................................................................................................................................120

Figure 189. Photo. Composite mass at failure of test 5 ...............................................................121

Figure 190. Photo. Front view of failure planes of the composite mass after test 5....................122

Figure 191. Photo. Back view of failure planes of the composite mass after test 5 ....................122

Figure 192. Graph. Global stress-strain relationship of test 5 .....................................................123

Figure 193. Graph. Lateral displacements on the open face of test 5..........................................124

Figure 194. Illustration. Internal displacements of test 5.............................................................125

Figure 195. Illustration. Locations of strain gauges on geosynthetic sheets in test 5..................126

Figure 196. Graph. Reinforcement strain distribution of the composite mass in layer 1 

of test 5 1.3 ft (0.4 m) from the base............................................................................................126
xii

Figure 197. Graph. Reinforcement strain distribution of the composite mass in layer 2 

of test 5 2.6 ft (0.8 m) from the base............................................................................................127

Figure 198. Graph. Reinforcement strain distribution of the composite mass in layer 3 

of test 5 3.9 ft (1.2 m) from the base............................................................................................127

Figure 199. Photo. Aerial view of the reinforcement sheets exhumed from the composite 

mass after test 5 (numbers indicate sheet number)......................................................................128

Figure 200. Illustration. Locations of rupture lines of reinforcement in test 5 based on 

figure 199.....................................................................................................................................128

Figure 201. Equation. Apparent cohesion from Schlosser and Long ..........................................134

Figure 202. Illustration. Conceptual stress path for compaction of a GRS mass ........................135

Figure 203. Illustration. Stress path of the proposed simplified model for fill compaction

of a GRS mass..............................................................................................................................137

Figure 204. Illustration. Locations of compaction loads moving toward section I-I...................139

Figure 205. Illustration. Stress paths during compaction at depth z as compaction loads 

move toward section I-I ...............................................................................................................139

Figure 206. Illustration. Locations of compaction loads moving away from section I-I.............139

Figure 207. Illustration. Stress paths during compaction at depth z as compaction loads 

move away from section I-I.........................................................................................................140

Figure 208. Illustration. Stress path at depth z when subject to multiple compaction passes .....141

Figure 209. Illustration. Stress path of the proposed model for fill compaction of a GRS 

mass..............................................................................................................................................142

Figure 210. Equation. Coefficient of lateral Earth pressure ........................................................142

Figure 211. Equation. Total residual strain..................................................................................142

Figure 212. Equation. Reinforcement force.................................................................................143

Figure 213. Equation. Average residual stress in the soil due to compaction .............................143

Figure 214. Equation. Second equation for average residual stress in the soil due to 

compaction...................................................................................................................................143

Figure 215. Equation. Result of figure 213 and figure 214 .........................................................143

Figure 216. Equation. First equation for estimation of K2,c .........................................................143

Figure 217. Equation. Second equation for estimation of K2,c.....................................................143

Figure 218. Equation. Increased horizontal stress in a GRS mass due to compaction ................143

Figure 219. Equation. Second equation of increased horizontal stress in a GRS mass due 

to compaction...............................................................................................................................144

Figure 220. Equation. Residual lateral stress in a GRS mass due to compaction and the 

effect of CIS in a GRS mass........................................................................................................144

Figure 221. Equation. Stiffness of a soil......................................................................................144

Figure 222. Illustration. Concept of apparent confining pressure and apparent cohesion 

of a GRS composite .....................................................................................................................145

Figure 223. Equation. Apparent cohesion of a GRS composite ..................................................145

Figure 224. Equation. Increased confining pressure....................................................................145

Figure 225. Equation. New method to estimate the increased confining pressure in soil 

due to the presence of reinforcement...........................................................................................146

Figure 226. Equation. Estimation of the factor W .......................................................................146

Figure 227. Illustration. Idealized plane-strain GRS mass for the SPR model............................147

Figure 228. Equation. Force in the reinforcement .......................................................................147

Figure 229. Equation. Horizontal stress in the soil......................................................................147
xiii

Figure 230. Equation. Average vertical stress.............................................................................147

Figure 231. Equation. First equation of average horizontal stress...............................................148

Figure 232. Equation. Second equation of average horizontal stress..........................................148

Figure 233. Equation. Forces in the reinforcement......................................................................148

Figure 234. Equation. Maximum force in the reinforcement ......................................................148

Figure 235. Equation. Average force in the reinforcement .........................................................148

Figure 236. Equation. Second equation of average force in the reinforcement...........................148

Figure 237. Equation. Third equation of average force in the reinforcement..............................148

Figure 238. Equation. Fourth equation of average force in the reinforcement............................149

Figure 239. Equation. Estimation of factor r...............................................................................149

Figure 240. Equation. Maximum reinforcement force ................................................................149

Figure 241. Equation. Average reinforcement force ...................................................................149

Figure 242. Equation. Second estimation of the factor W ...........................................................149

Figure 243. Equation. Increased confining pressure in a GRS mass...........................................150

Figure 244. Equation. Apparent cohesion....................................................................................150

Figure 245. Equation. Reference spacing ....................................................................................150

Figure 246. Equation. Pressure carrying capacity .......................................................................150

Figure 247. Graph. Backfill grain size distribution before and after large-size triaxial tests......153

Figure 248. Graph. Large-size triaxial test results.......................................................................153

Figure 249. Equation. Required strength for reinforcement........................................................155

Figure 250. Equation. Tf divided by Sv ........................................................................................155

Figure 251. Equation. First equation for horizontal stress in a GRS structure ............................156

Figure 252. Equation. Second equation for horizontal stress in a GRS structure........................156

Figure 253. Equation. Third equation for horizontal stress in a GRS structure...........................156

Figure 254. Equation. Second equation for Tf divided by Sv .......................................................156

Figure 255. Equation. Third equation for Tf divided by Sv ..........................................................156

Figure 256. Equation. Lateral constraint pressure .......................................................................156

Figure 257. Equation. Required tensile strength of the reinforcement in design ........................157

Figure 258. Equation. Second equation for required tensile strength of the reinforcement 

in design.......................................................................................................................................157

Figure 259. Equation. Residual lateral stresses in a GRS mass due to compaction ....................162

Figure 260. Graph. Distribution of residual lateral stresses of a GRS mass with depth 

due to fill compaction ..................................................................................................................164

Figure 261. Equation. Poisson’s ratio of the backfill for uniaxial tests.......................................164

Figure 262. Equation. Poisson’s ratio of the backfill for triaxial tests ........................................164

Figure 263. Illustration. Step 1 of analysis for the GSGC tests—placement of first layer..........167

Figure 264. Illustration. Step 2 of analysis for the GSGC tests—compaction of first layer .......167

Figure 265. Illustration. Step 3 of analysis for the GSGC tests—placement of second layer.....167

Figure 266. Illustration. Step 4 of analysis for the GSGC tests—compaction of second layer...167

Figure 267. Illustration. Step 20 of analysis for the GSGC tests—placement of surcharge........168

Figure 268. Illustration. Step 21 of analysis for the GSGC tests—placement of surcharge 

and confining stress......................................................................................................................169

Figure 269. Graph. Comparison of results for GSGC test 1, global vertical stress-strain 

relationship...................................................................................................................................170

Figure 270. Graph. Comparison of results for GSGC test 1, volume change relationship..........170

Figure 271. Graph. Comparison of lateral displacements on open face of GSGC test 1.............171
xiv

Figure 272. Graph. Comparison of global stress-strain relationship of GSGC test 2..................172

Figure 273. Graph. Comparison of lateral displacement at open face of GSGC test 2 ...............173

Figure 274. Graph. Comparison of internal displacements of GSGC test 2................................174

Figure 275. Graph. Comparison of results for GSGC test 2 at reinforcement layer 5.25 ft 

(1.6 m) from the base ...................................................................................................................174

Figure 276. Graph. Comparison of results for GSGC test 2 at reinforcement layer 2.62 ft 

(0.8 m) from the base ...................................................................................................................175

Figure 277. Graph. Comparison of global stress-strain relationship of GSGC test 3..................176

Figure 278. Graph. Comparison of lateral displacement at open face of GSGC test 3 ...............177

Figure 279. Graph. Comparison of internal displacements of GSGC test 3................................178

Figure 280. Graph. Comparison of results for GSGC test 3 at reinforcement layer 3.94 ft 

(1.2 m) from the base ...................................................................................................................178

Figure 281. Graph. Comparison of results for GSGC test 3 at reinforcement layer 1.3 ft 

(0.4 m) from the base ...................................................................................................................179

Figure 282. Graph. FE analyses of GSGC test 2 under different confining pressures—

global stress-strain relationship....................................................................................................180

Figure 283. Graph. FE analyses of GSGC test 2 under different confining pressures—

volume change curves..................................................................................................................180

Figure 284. Illustration. FE mesh to simulate CIS in a reinforced soil mass ..............................181

Figure 285. Graph. Lateral stress distribution of a GRS mass from FE analyses with 

maximum vertical compaction pressures of 29 psi (200 kPa).....................................................182

Figure 286. Graph. Lateral stress distribution of a GRS mass from FE analyses with 

maximum vertical compaction pressures of 72.5 psi (500 kPa)..................................................183

Figure 287. Graph. Comparison of residual lateral stresses of a GRS mass due to fill 

compaction between FE analysis with very fine mesh and the analytical model........................184

Figure 288. Graph. Comparison of residual lateral stresses of a GRS mass due to fill 

compaction between FE analysis with coarse mesh and the analytical model............................185
xv

LIST OF TABLES

Table 1. Properties of materials for the mini-pier experiments.....................................................10

Table 2. Conditions and properties of the backfill and reinforcement used in FE analyses..........54

Table 3. Summary of index properties of backfill .........................................................................63

Table 4. Summary of Geotex® 4×4 properties...............................................................................67

Table 5. Properties of Geotex® 4×4 in fill direction ......................................................................68

Table 6. Test program for GSGC tests...........................................................................................70

Table 7. Dimensions of the GSGC specimens before loading.......................................................83

Table 8. GSGC test 1 result summary ...........................................................................................89

Table 9. GSGC test 2 results summary........................................................................................103

Table 10. Test 3 result summary..................................................................................................112

Table 11. GSGC test 4 result summary .......................................................................................120

Table 12. GSGC test 5 result summary .......................................................................................129

Table 13. Comparison between test 1 and test 2..........................................................................130

Table 14. Comparison between test 2 and test 3 with the same Tf /Sv ratio .................................131

Table 15. Comparison between test 2 and test 4..........................................................................131

Table 16. Comparison between test 3 and test 4..........................................................................132

Table 17. Comparison between test 2 and test 5..........................................................................133

Table 18. Comparison of strength properties of five GSGC tests ...............................................134

Table 19. Model parameters for the proposed compaction simulation model.............................138

Table 20. Values of factor r under different applied pressure and reinforcement lengths ..........149

Table 21. Comparison of the results of the analytical model and the GSGC tests......................151

Table 22. Comparison of the results of Schlosser and Long’s method and the GSGC tests.......152

Table 23. Comparison of the results of the analytical model and Elton and Patawaran’s 

tests ..............................................................................................................................................154

Table 24. Comparison of the results of Schlosser and Long’s method and Elton and 

Patawaran’s tests..........................................................................................................................154

Table 25. Comparison of the results of analytical model and GSGC test 2 with different 

confining pressures from FE analyses .........................................................................................155

Table 26. Comparison of reinforcement forces in proposed model and current design 

equation for a GRS wall...............................................................................................................158

Table 27. Comparison of reinforcement forces in the proposed model and the GSGC tests......159

Table 28. Comparison of reinforcement forces between proposed model and test data 

from Elton and Patawaran............................................................................................................160

Table 29. Parameters and properties of the GSGC tests used in FE analyses.............................166

1

CHAPTER 1. INTRODUCTION

1.1 PROBLEM STATEMENT

Over the past two decades, geosynthetic reinforced soil (GRS) structures, including retaining 

walls, slopes, embankments, roadways, and load-bearing foundations, have gained increasing 

popularity in the United States and abroad. In construction, GRS structures have demonstrated 

several distinct advantages over their conventional counterparts. Generally, GRS structures 

require less over-excavation and are more ductile, more flexible (hence more tolerant to 

differential settlement and to seismic loading), more adaptable to low-permeability backfill, 

easier to construct, and more economical than conventional Earth structures.(2–4)

Among the various types of GRS structures, GRS walls have seen far more applications than 

other types of reinforced soil structures. A GRS wall comprises two major components: a facing 

element and a GRS mass. Figure 1 shows a schematic diagram of a typical GRS wall with a 

modular block facing. 

Figure 1. Illustration. Typical cross section of a GRS wall with modular block facing.

The GRS wall facing may be of various shapes and sizes. It may also be made of different 

materials. However, the other component of a GRS wall, the GRS mass, is always a compacted 

soil mass reinforced by layers of geosynthetic reinforcement. 

Soil is weak in tension and relatively strong in compression and shear. In a reinforced soil, the 

soil mass is reinforced by incorporating an inclusion (or reinforcement) that is strong in tensile 

resistance. Through soil reinforcement interface bonding, the reinforcement restrains lateral 

deformation of the surrounding soil, increases its confinement, reduces its tendency for dilation, 

and, consequently increases the stiffness and strength of the soil mass.
2

Many studies have been conducted on the behavior of GRS structures; however, the interactive 

behavior between soil and reinforcement in a GRS mass has not been fully elucidated. This 

has resulted in design methods that are fundamentally deficient.(5) Perhaps the most serious 

deficiency is that the current methods ignore the composite nature of the GRS mass and consider 

the reinforcement as tiebacks added to the soil mass. The reinforcement strength is determined 

by requiring that the reinforcement be sufficiently strong to resist Rankine, Coulomb, or 

at-rest pressure that is assumed not to be affected by the configuration of the reinforcement. 

Specifically, the design strength of the reinforcement, Trequired, has been determined by 

multiplying an assumed lateral Earth pressure at a given depth, h, by the value of 

reinforcement spacing, Sv, and a safety factor, Fs, as shown by the equation in figure 2.

Trequired = σ h ∗ Sv ∗ Fs

Figure 2. Equation. Design strength.

Figure 2 implies that as long as the reinforcement strength is kept linearly proportional to the 

reinforcement spacing, all walls with the same h (walls of a given height with the same 

backfill compacted to the same density) will behave the same. In other words, a GRS wall with 

reinforcement strength T at spacing Sv will behave the same as one with twice the reinforcement 

strength (2 × T) at twice the spacing (2 × Sv). Figure 2 has important practical significance in 

that it has encouraged designers to use stronger reinforcement at larger spacing because the use 

of larger spacing will generally reduce construction time and effort.

Some engineers, however, have learned that figure 2 cannot be true. In actual construction, 

reinforcement spacing appears to play a much greater role than reinforcement strength in the 

performance of a GRS wall. Researchers at the Turner-Fairbank Highway Research Center 

(TFHRC) conducted a series of full-scale experiments in which a weak reinforcement at a small 

spacing and a strong reinforcement (with several times the strength of the weak reinforcement) at 

twice the spacing were load-tested.(6,7) The former was found to be much stronger than the latter. 

An indepth study on the relationship between reinforcement spacing and reinforcement stiffness/

strength in regards to their effects on the behavior of a GRS mass is of critical importance to the 

design of GRS structures.

The effects of compaction-induced stress (CIS) in unreinforced soil masses and Earth structures 

have been the subject of many studies. (See references 8–14.) These studies indicated that CIS 

would significantly increase the lateral stresses in soil (also known as the locked-in lateral 

stresses or residual lateral stresses) provided that there is sufficient constraint to lateral 

movement of the soil during compaction. The increase in lateral stresses will increase the 

stiffness and strength of the compacted soil mass.

The effect of CIS is likely to be more significant in a soil mass reinforced with layers of 

geosynthetics than in an unreinforced soil mass. This is because the interface bonding between 

the soil and reinforcement will increase the degree of restraint to lateral movement of the soil 

mass during fill compaction. With greater restraint to lateral movement, the resulting locked-in 

lateral stresses are likely to become larger.

In most studies, the effects of CIS in numerical analysis of Earth structures have been either 

overly simplified or ignored. (See references 15–18.) In the case of GRS walls, failure to account 

σ

σ
3

for CIS may have led to the erroneous conclusion by many numerical studies that the equation 

in figure 2 is completely or approximately valid. Evaluation of CIS is an important issue in the 

study of GRS structures.

In addition, GRS walls with modular block facing are rather flexible. Thus, the design of these 

structures should consider not only the stresses in the GRS mass but also the deformation. The 

Jewell-Milligan method is recognized as the best available method for estimating lateral 

movement of GRS walls.(19) However, it only applies to walls with little or no facing rigidity. 

With the increasing popularity of GRS walls with modular block facing where facing rigidity 

should not be ignored, an improvement over the Jewell-Milligan method for calculating lateral 

wall movement is needed.

1.2 RESEARCH OBJECTIVES 

The objectives of this study were fourfold. The first objective was to investigate the composite 

behavior of GRS masses with different reinforcing configurations. The second objective was to 

examine the relationship between reinforcement strength and reinforcement spacing with regard 

to their effects on the behavior of a GRS mass. The third objective was to develop an analytical 

model for evaluating CIS in a GRS mass. The fourth objective was to develop an analytical 

model for predicting lateral movement of a GRS wall with a modular block facing.

1.3 RESEARCH TASKS

To achieve the research objectives, the following tasks were carried out in this study:

1. Reviewed previous studies on the composite behavior of a GRS mass, CIS in a soil 

mass, and the reinforcing mechanism of GRS structures. Previous studies on composite 

behavior of a GRS mass were reviewed. The review included theoretical analyses as 

well as experimental tests. Studies on CIS in an unreinforced soil mass were also reviewed, 

including simulation models for fill compaction. In addition, a literature study on reinforcing 

mechanisms of GRS structures was conducted. 

2. Developed a hand computation analytical model for estimation of CIS in a GRS 

mass. An analytical model for simulation of CIS in a GRS mass was developed. The 

compaction model was developed by modifying an existing fill compaction simulation 

model for unreinforced soil. The model allows CIS in a GRS mass to be estimated by 

hand computations.

3. Developed an analytical model for the relationship between reinforcement strength 

and reinforcement spacing and derived an equation for calculating composite strength 

properties. An analytical model for describing the relationship between reinforcement 

strength and reinforcement spacing was developed. Based on the model and the average 

stress concept for a GRS mass, an equation for calculating the composite strength properties 

of a GRS mass was derived.(20) The model represents a major improvement over the existing 

current design methods used and more precisely reflects the role of reinforcement spacing 

versus reinforcement strength on the performance of a GRS mass. The equation allows the 

strength properties of a GRS mass to be evaluated by a simple hand computation method. 
4

4. Designed and conducted laboratory experiments on a generic soil geosynthetic 

composite (GSGC) to investigate the performance of GRS masses with different 

reinforcing conditions. A GSGC plane-strain test was designed by considering several 

factors culled from previous studies. A series of finite element (FE) analyses were performed 

to determine the dimensions of the test specimen that would yield stress-strain and volume 

change behavior representative of a very large GSGC mass. Five GSGC tests with different 

reinforcement strengths, reinforcement spacing, and confining pressures were conducted. 

These tests allowed direct observation of the composite behavior of a GRS mass in various 

reinforcing conditions. They also provided measured data for verification of analytical and 

numerical models for investigating the behavior of a GRS mass (including the models 

developed in tasks 2 and 3).

5. Performed FE analyses to simulate the GSGC tests and analyze the behavior of the 

GRS mass. FE analyses were performed to simulate the GSGC tests conducted in task 4. The 

analyses allowed the stresses in the soil and forces in the reinforcement to be determined. 

They also allowed an investigation of the behavior of GRS composites under conditions 

different from those employed in the GSGC tests of task 4.

6. Verified the analytical models developed in tasks 2 and 3 by using the measured data 

from the GSGC tests and relevant test data in the literature. The compaction model 

developed in task 2 was employed to determine the CIS for the GSGC tests. The results were 

incorporated into an FE analysis to calculate the global stress-strain relationship and then 

compared to the measured results. The measured data from the GSGC tests, relevant test data 

available in the literature, and results from FE analyses were also used to verify the analytical 

models developed in task 3 for calculating composite strength properties of a GRS mass 

and for calculating required tensile strength of reinforcement based on the forces induced 

in the reinforcement.

7. Developed an analytical model for predicting lateral movement of GRS walls with 

modular block facing. An analytical model was developed for predicting the lateral 

movement of GRS walls with a modular block facing. The model was based on an existing 

model for reinforced soil walls without a modular block facing.(19) The results obtained from 

the model were compared with measured data from a full-scale experiment of a GRS wall 

with modular block facing. The analytical model can also be used in design for determining 

the required design strength of reinforcement under a prescribed value of maximum 

allowable lateral wall movement.
5

CHAPTER 2. LITERATURE REVIEW

A GRS mass is a soil mass that is embedded with layers of geosynthetic reinforcement. These 

layers are typically placed horizontally with a vertical spacing of 8 to 12 inches (200 to 300 mm). 

Under vertical loads, a GRS mass exhibits significantly higher stiffness and strength than an 

unreinforced soil mass. This chapter presents a review of previous studies on the mechanics 

of reinforced soil, the composite behavior of a GRS mass, and CIS in a reinforced soil mass.

2.1 MECHANICS OF REINFORCED SOIL

In literature, three concepts have been proposed to explain the mechanical behavior of a 

GRS mass: (1) the concept of enhanced confining pressure, (2) the concept of enhanced material 

properties, and (3) the concept of reduced normal strains. (See references 21–32.)

The mechanics of a GRS mass have been explained by Schlosser and Long and Yang 

using two concepts: the concept of apparent cohesion and the concept of apparent 

confining pressure.(25,21)

2.1.1 Concept of Apparent Cohesion

In this concept, a reinforced soil is said to increase the major principle stress at failure from 1 to 

1R (with an apparent cohesion C'R) due to the presence of the reinforcement, as shown by the 

Mohr stress diagram in figure 3. If a series of triaxial tests on unreinforced and reinforced soil 

elements were conducted, the failure envelopes of the unreinforced and reinforced soils 

would allow the apparent cohesion C'R to be determined. Yang indicated that the value for 

unreinforced sand and reinforced sand were about the same as long as slippage at the soilreinforcement interface did not occur.(21)

Figure 3. Illustration. Concept of apparent cohesion due to the presence of reinforcement.

σ

σ

φ
6

2.1.2 Concept of Apparent Confining Pressure

In this concept, a reinforced soil is said to increase its axial strength from 1 to 1R (with an 

increase of confining pressure, 3R), as shown in figure 4, due to the tensile inclusion. The 

value of 3R can also be determined from a series of triaxial tests by assuming that will 

remain the same. 

Figure 4. Illustration. Concept of apparent confining pressure due to the presence of 

reinforcement.

Note that the concept of apparent confining pressure allows the apparent cohesion to be 

determined with only the strength data for the unreinforced soil, as shown in figure 5

through figure 13.

(25)

Consider a GRS mass with equally spaced reinforcement of strength Tf and vertical spacing Sv. It 

is assumed that the increase in confining pressure due to the tensile inclusion, 3R, can be 

calculated using the equation in figure 5.

3

f

R

v

T

S

∆ = σ

Figure 5. Equation. Increase in confining pressure as a function of reinforcement strength 

and spacing.

From figure 3 and figure 4 and using Rankine’s Earth pressure theory to equate the principal 

stress at failure, 1R can be calculated using figure 6. 

'

1 3 2 σ σ R CP R P = + K cK

Figure 6. Equation. Principle stress at failure for reinforced soil.

σ σ

∆σ

∆σ φ

∆σ

σ
7

σ 1R = σ 3RKP

Figure 7. Equation. Principle stress at failure for reinforced soil with zero cohesion.

σ 3R = σ 3C + ∆σ 3R

Figure 8. Equation. Total confining stress of reinforced soil.

Using figure 8, figure 7 can be written as figure 9.

Figure 9. Equation. Principle stress at failure for reinforced soil substituting the 

components derived in figure 8.

Equating figure 6 to figure 9, figure 10 is obtained.

2 ' 3R P

R

K

c

∆σ =

Figure 10. Equation. Apparent cohesion for reinforced soil in terms of increase in confining 

stress.

Substituting figure 5 into figure 10 results in figure 11. 

v

f P

R S

T K

c

2 ' =

Figure 11. Equation. Apparent cohesion in terms of reinforcement strength and spacing.

Figure 11 may be useful for evaluating the stability of a reinforced soil mass. Given a granular 

soil with strength parameters c (c = 0) and , figure 11 allows the strength parameters of a 

reinforced soil mass (c'R and R) to be determined as a function of T and Sv.

It should be noted that the validity of figure 11 is questionable. There is a key assumption 

involved in the derivation—the assumption of figure 5, which implies that an increase in Tf has 

the same effect as a proportional decrease in Sv. 

Note that figure 12 represents the increase in confining pressure based on the explanation given 

by Schlosser and Long and Yang (see figure 4), while figure 13 represents the same increase in 

Hausmann’s study, where R T T f ≡ .

(22,25,26)

3

T

v

R

S

∆ = σ

Figure 12. Equation. Increase of confining pressure due to reinforcement.

3

T

v

R

S

∆ ≤ σ

Figure 13. Equation. Increase of confining pressure by Hausmann.(26)

( ) σ 1R = σ 3RKP = σ 3C + ∆σ 3R KP

φ

φ
8

2.2 COMPOSITE BEHAVIOR OF GRS MASS

The behavior of GSGC has been investigated through different types of laboratory experiments 

including small-size (1.9-inch (50-mm)-diameter) triaxial compression tests with a specimen 

diameter no greater than 6 inches (150 mm), large-size (19-inch (500-mm)-diameter) triaxial 

compression tests, large-size (30-inch (760-mm)-diameter) unconfined compression tests, 

unconfined compression tests with cubical specimens, and plane-strain tests. (See references 6, 7, 

20, 31, and 33–35.)

The effects of reinforcement layers on the stiffness and strength of GSGCs has been investigated, 

and the results suggest that unless the reinforcement is placed at locations where lateral 

deformation of the soil occurs, there will not be any reinforcing effect.(33)

There are questions concerning the applicability of these small-size triaxial tests because 

the reinforcement in these tests is very small compared to the typical field installation, 

and factors such as gravity, soil arching, and CIS are not simulated properly. For these 

reasons, several larger triaxial tests and plane-strain tests have been conducted. Elton and 

Patawaran conducted seven unconfined compression tests on 2.5-ft (0.76-m)-diameter and 

5-ft (1.53-m)-high specimens with different types of reinforcement and spacing (see figure 14

and figure 15).(31) Six types of reinforcement were used in the tests with spacing of 6 and 

12 inches (150 and 300 mm). Figure 16 shows the stress-strain curves of the specimens 

reinforced by Tensar® TG500 at spacings of 6 and 12 inches (150 and 300 mm). As shown 

in the figure, the strength of the GSGC was much higher at the 6-inch (150-mm) spacing 

than at the 12-inch (300-mm) spacing.

Figure 14. Photo. Unconfined test specimen before testing.(31)
9

Figure 15. Photo. Unconfined test specimen after testing.(31)

1 kPa = 0.145 psi

1 mm = 0.039 inches

Figure 16. Graph. Stress-strain curves of specimens reinforced at spacings of 6 and 

12 inches (150 and 300 mm) in large, unconfined compression test.(31)

Five unconfined mini-pier experiments were conducted by Adams and his associates.(6,7) The 

dimensions of the specimen were 6.6 ft (2.0 m) high, 3.3 ft (1.0 m) wide, and 3.3 ft (1.0 m) deep. 

The test results showed that the load-carrying capacity was strongly affected by the spacing 

of the reinforcement and was not significantly affected by the strength of the reinforcement. 

Figure 17 shows a photo of the mini-pier experiment, and table 1 shows the material properties 

and conditions for the tests. The stress-strain curves from the tests are presented in figure 18. 

The effect of reinforcement spacing and reinforcement strength on the behavior of the mini-piers 

can be seen in the figure by comparing the difference between curve B (at 1.3-ft (0.4-m) spacing) 

and curve D (at 0.7-ft (0.2-m) spacing) and the difference between curve C (reinforcement 

Stress - Strain curves

0

50

100

150

200

250

300

0 5 10 15 20 25 30

Vertical Strain εv (%)

Stress (kPa)

TG500-12 (Spacing = 12 in.)

TG500 (Spacing = 6 in.)
10

strength = 1.4 kip/ft (21 kN/m)) and curve D (reinforcement strength = 4.8 kip/ft (70 kN/m)). 

The effect of reinforcement spacing is much more pronounced than the effect of 

reinforcement strength.

Figure 17. Photo. Mini-pier experiments.(6)

Table 1. Properties of materials for the mini-pier experiments.(7)

Experiment

Fill Average 

Density 

(kN/m3)

Geotextile Reinforcement Schedule

Polypropylene 

Type

Strength 

(kN/m)

Spacing 

(m)

MP NR 22.4 None None None

MP A 23.0 A2044 70.0 0.4–0.6

MP B 22.7 A2044 70.0 0.4

MP C N/A A2000 21.0 0.2

MP D 22.8 A2044 70.0 0.2

MP NR 22.4 None None None

MP = Mini-pier and NR = Not reinforced.

1 kN/m3 = 0.0064 kip/ft3

1 m = 3.28 ft 

N/A = Not available.
11

1 kPa = 0.145 psi

Figure 18. Graph. Stress-strain curves of mini-pier experiments.(7)

Figure 19 and figure 20 show the setup of the large-size triaxial tests conducted by Ziegler et 

al.(35) The specimens were 1.6 ft (0.5 m) in diameter and 3.6 ft (1.1 m) high. The results also 

show the behavior of the GRS specimens was strongly affected by reinforcement spacing. 

Figure 21 shows the relationship between the applied loads and vertical strains of the test 

specimens. The strength of the specimen increased with an increasing number of reinforcement 

layers. The stiffness of the specimen also increased with an increasing number of reinforcement 

layers for strains of more than about 1 percent. Below 1 percent, the stiffness was not affected 

by the reinforcement layers.
12

1 m = 3.28 ft

Figure 19. Illustration. Schematic of large-size triaxial tests with specimens 3.6 ft

(1.1 m) high and 1.6 ft (0.5 m) in diameter.(35)

Figure 20. Photo. Setup of large-size triaxial tests with specimens 3.6 ft (1.1 m) high and 

1.6 ft (0.5 m) in diameter.(35)
13

1 kN/m2 = 0.021 kip/ft2

Figure 21. Graph. Large-size triaxial test results.

(35)

The behavior of GSGCs has also been investigated through numerical analysis. 

(See references 20 and 36–40.)

Vulova and Leshchinsky conducted a series of analyses using the two-dimensional (2D) finite 

difference program Fast Lagrangian Analysis of Continua (FLAC) Version 3.40.(40,41) From 

the analyses, it was concluded that reinforcement spacing was a major factor controlling the 

behavior of GRS walls. The analysis of GRS walls with reinforcement spacing from 0.7 to 3.3 ft 

(0.2 to 1.0 m) showed that the critical wall height (defined as a general characteristic of wall 

stability) always increased when reinforcement spacing decreased. Reinforcement spacing also 

controlled the mode of failure of GRS walls. In these analyses, CIS in soil was not included.

Comparisons of the stress distribution in a soil mass with and without reinforcement were made 

by Ketchart and Wu.(20) The reinforcement was a medium-strength woven geotextile with widewidth strength of 4.8 kip/ft (70 kN/m). The backfill was a compacted road base material, and the 

reinforcement spacing was 1 ft (0.3 m). Figure 22, figure 23, and figure 24 show the vertical, 

horizontal, and shear stress distributions, respectively, at a vertical load of 1.3 kip (6 kN). The 

presence of the reinforcement layers in the soil mass altered the horizontal and shear stress 

distributions but not the vertical stress distribution. The horizontal and shear stresses increased 

significantly near the reinforcement. The largest stresses occurred near the reinforcement and 

reduced with increasing distance from the reinforcement. The extent of appreciable influence 

was only about 0.33–0.49 ft (0.1–0.15 m) from the reinforcement. With the increased lateral 

stress, the stiffness and strength of the soil became larger. Ketchart and Wu emphasized the 

importance of keeping reinforcement spacing less than 1 ft (0.3 m) for GRS walls.
14

1 kPa = 0.145 psi

1 mm = 0.039 inches

Figure 22. Graph. Vertical stress distributions at 1.3-kip (6-kN) vertical load of the GRS 

masses without and with reinforcement.(20)
15

1 kPa = 0.145 psi

1 mm = 0.039 inches

Figure 23. Graph. Horizontal stress distribution at 1.3-kip (6-kN) vertical load of the GRS 

masses without and with reinforcement.(20)
16

1 kPa = 0.145 psi

1 mm = 0.039 inches

Figure 24. Graph. Shear stress distribution at 1.3-kip (6-kN) vertical load of the GRS 

masses without and with reinforcement.(20)

2.3 CIS IN AN UNREINFORCED SOIL MASS

Many studies have been conducted to address CIS in a soil mass. As early as 1943, Terzaghi 

noted that compaction significantly affected lateral Earth pressures.(42) In 1954, Rowe calculated 

lateral Earth pressures for conditions of wall deflection intermediate between the at-rest, fully 

active, and fully passive states.(8) Rowe’s work did not directly address CIS, but it contributed to 

a later study by Broms on compaction-induced Earth pressures.(9) Seed and Seed and Duncan 

developed a simulation model called the “bi-linear hysteretic loading/unloading model” to 

simulate the compaction effect on vertical, non-deflecting structures.(11,43)

Duncan and 

Seed and Duncan et al. also developed a procedure to determine lateral Earth pressure due to 

compaction.(12,13) These studies were considered to have a strong impact on the determination 

of CIS.
17

2.3.1 Lateral Earth Pressure Estimation

The lateral Earth pressure estimation study by Rowe was not directly related to CIS, but it 

addressed lateral Earth pressures for conditions of wall deflection between the at-rest, fully 

active, and fully passive states.(8) Rowe’s stress-strain theory for calculations of lateral pressures 

exerted on structures by cohesionless soils was based on the following hypotheses:

• The degrees of mobilization of the soil friction angle and the soil-wall friction angle

depend on the degrees of interlocking of the soil grains, which in turn depend on the 

fractional movement of the shear planes or slip strain (defined as the ratio of relative 

shear displacement to total slip plane length). The friction angle increases from a 

relatively low value to a higher limiting or ultimate value as slip strain increases.

• Earth pressures acting on a retaining wall or structure may be calculated by conventional 

limiting equilibrium methods (i.e., gravity analyses of sliding wedges) using the 

developed fractional and values.

The basic mechanics of Rowe’s theory are essentially a simple Coulomb analysis of sliding 

wedges. A sample wedge adjacent to a wall or structure is considered. When the structure 

deflects, slip strain occurs along planes AB and AC. Assuming no soil compression, slip strain 

along each plane is calculated as the ratio of shear displacement along the plane to the length of 

the plane. The forces acting on the typical sliding wedge are the weight of the soil, the force 

exerted on a sliding wedge by the underlying soil, and the force exerted on the sliding wedge by 

the wall. 

Rowe substantiated his theory by performing a series of direct shear tests on different sands, 

recording the friction angle developed at various levels of slip strain, and using these values to 

calculate lateral Earth pressures for sample problems. By considering tamping or compaction as 

application and removal of surcharge pressure ho ( = unit weight of soil and ho = surcharge 

head), Rowe postulated that slip strains would be induced by the load application. He suggested 

that in the compression and shear tests, unloading causes relatively small strain reversals. Thus, 

after tamping a fill behind a wall, the lateral pressure will be almost as great as the value, which 

acted under the preconsolidation pressure. From that, the pressure coefficient (K'o) could be 

expressed as shown in the equation in figure 25.

' 1 o

o o

h K K

h

  = +    

Figure 25. Equation. At-rest Earth pressure coefficient.

Where ho is the surcharge head removed and h is the overburden head ( σ / γ h = v ). In any case,

K K o P ≤ , where Kp is the coefficient of passive Earth pressure at limiting condition.

It is interesting to note the similarity between Rowe’s early equation for residual compactioninduced lateral Earth pressures and an equation proposed later by Schmidt to explain residual

lateral Earth pressures resulting from over-consolidation of soils under conditions of no lateral 

strain (i.e., the Ko condition).(44) Schmidt’s equation, which empirically allows for some degree 

of relaxation of lateral stresses following surcharge removal, can be expressed in figure 26.

φ δ

φ δ

γ γ
18

' 1 o

o o

h K K

h

α

  = +    

Figure 26. Equation. Schmidt’s equation for residual lateral Earth pressures.(44)

Where:

= 0.3 to 0.5 for most sands.

= 1.2 sin ' for initially normally consolidated clays.

2.3.2 Stress Path Theory by Broms and Extension of Broms’ Work by Ingold(9,45)

Broms developed a stress path theory to explain residual lateral Earth pressure on rigid, 

vertical, non-yielding structures resulting either from compaction or surcharge loading that is 

subsequently removed.(9) The theoretical basis for Broms’ theory is illustrated in figure 27. An 

element of soil at some depth is considered to exist at some initial stress state represented by 

point A with horizontal and vertical effective stresses of σ ho′ and σ vo

′ . Compaction of the soil is 

considered a process of loading followed by unloading. When the overburden pressure is 

increased (i.e., loading), there is little change in lateral pressure until the ratio of lateral to 

vertical effective stresses is equal to Ko (denoted by point B in figure 27), where Ko is the 

coefficient of Earth pressure at rest. Thereafter, increased vertical stress is accompanied by an 

increased lateral stress according to figure 28, corresponding to primary (or virgin) loading. 

Figure 27. Illustration. Hypothetical stress path during compaction.

σ σ h ov ′ ′ = K

Figure 28. Equation. Lateral Earth pressure at rest.

When the overburden pressure is subsequently decreased (e.g., from point C), the corresponding 

decrease in lateral pressure is small until the ratio of lateral to vertical effective stresses is equal 

α

α φ
19

to some limiting constant K1 (denoted by point D in figure 27). Thereafter, a continued decrease 

in vertical pressure is accompanied by a decrease in lateral stress according to figure 29.

σ σ h v K1 ′ ′ =

Figure 29. Equation. Lateral Earth pressure at K1.

This idealized stress path is in agreement with Rowe’s earlier hypothesis that stress relaxation 

with unloading is negligible until some limiting condition, defined by the K1 line, is reached.(8)

By following this type of stress path, an element of soil can be brought to a final state, which is 

represented by an effective coefficient Keffective, varying KK K o effective ≤ ≤ 1 . Having made this 

idealized assumption of the stress path, Broms then postulated the actual stress path followed by 

a real soil element.(9) Rowe and Ingold both suggested that K1 = KP (the coefficient of passive 

Earth pressure), reasoning that the limiting condition reached is essentially a form of 

passive failure.(8,45)

By employing this theory to estimate the lateral pressure exerted on a vertical, rigid, non-yielding 

structure with a compacted fill, Broms considered the compaction plant to present a load applied 

to the fill surface, inducing vertical stresses that may be approximated as twice as those 

calculated by the Boussinesq stress equation for an infinite half space.(9) Lateral Earth pressures 

acting against the wall were then calculated using figure 28. The resulting horizontal stress 

distribution calculated for a 11.25-T (10.2-t) smooth wheel roller is presented by Broms.

(9)

By considering the backfill process as the placement of a series of soil layers each deposited and 

then compacted one after the other, the compaction-induced lateral pressure for each new layer 

will be surpassed in magnitude by the at-rest Earth pressures due to the static overburden. 

Ingold applied the extension of Broms’ theory in cases where wall deflection during backfilling 

was sufficient to induce an active condition in the lower layers of a backfill that is deposited 

and compacted in lifts by assuming the virgin loading path to be σ σ h Av ′ ′ = K instead of Broms’ 

σ σ h ov ′ ′ = K .

(45) Ingold postulated that passive failure controlled the other limiting condition and 

therefore, K1 = Kp.

(45)

2.3.3 FE Analysis by Aggour and Brown(10)

Aggour and Brown were the first to model compaction-induced lateral Earth pressure by 2D 

FE analysis.(10) Aggour and Brown’s analysis involved the following steps for simulation of 

compaction operation:

1. A layer of soil elements adjacent to a wall was modeled with some initial modulus, E1.

2. Compaction was modeled as some increased vertical load acting uniformly over the entire 

surface of the soil. Simultaneously, the soil modulus was increased to some new and stiffer 

value, E2, to reflect the increase in density during compaction. 

3. The compaction load was then removed. The resulting strains, deflections, and stress 

redistributions were modeled using a stiffer unloading modulus, Eu

2. 
20

4. A new layer of fill with modulus E1 was added to the top of the preceding layer. This 

increased the vertical stresses in the underlying layer. These increased stresses in the 

underlying layer were modeled using the soil modulus E2. 

5. A surface load to model compaction of the new layer was applied, increasing the stresses in 

both these soil layers, and the modulus was increased to E2. 

6. The compacting load was removed and the resulting wall deflections, strains, and stress 

redistributions were modeled using the modulus Eu

2 for both soil layers. 

7. The entire process was then incrementally repeated for subsequent soil layers.

Aggour and Brown used the procedure to model the soil moduli. The effects of increased number 

of compaction passes were modeled by increasing the soil modulus E2. The soil modulus was 

greater for unloading than for reloading. Compaction loading was modeled as a uniform unit 

surface pressure of unit width acting at all points along the full length of the fill, from the wall to 

the right boundary of the FE mesh. The fill materials were placed in five 4-ft (1.22-m) lifts. The 

interface between the soil and the wall was assumed to remain bonded at all times.

The results of this analysis indicate the following:

• Increased wall deflections occurred with increased compactive effort (increased number 

of passes were modeled by increasing E2 values).

• Increased residual lateral pressures near the top of the wall occurred with increased 

compactive effort.

The second sample problem analyzed by Aggour and Brown used the same soil and wall 

geometry, but only the last soil lift placed was compacted.(10) The effects of the compaction of 

the last soil layer were increased wall deflections and increased residual lateral Earth pressures 

near the top of the wall. These results were in agreement on a qualitative basis with field- and 

scale-model observations of the effects of compaction on structural deflections and residual 

lateral Earth pressures. The analyses suggest the potential value of FE analysis for determining

compaction-induced Earth pressures on yielding structures.

2.3.4 CIS Models by Seed(11)

Seed proposed a method to estimate the effects of CIS and associated deflections.(11) The study 

represents the most indepth study on the subject of CIS and involved the following three areas:

• CIS due to different stress paths, including the first cycle Ko reloading stress path, typical 

Ko reloading stress path, multicycle Ko unloading/reloading stress path, and Ko unloading 

following reloading stress path.

• The nonlinear and bilinear hysteretic loading/unloading compaction models for 

simulation of fill compaction behind vertical, non-deflecting structures. 

• FE analysis of fill compaction using the nonlinear and bilinear models.
21

2.3.4.1 First Cycle Ko Reloading Stress Path and Typical Ko Unloading/Reloading Stress Path

Seed proposed the first cycle Ko reloading model.(11) The model was derived from fitting 

available data. Upon loading, the stress path is assumed to follow the Ko line to point A, after 

which, the unloading stress path is followed by K K OCR o o ( )

α ′ = to an arbitrary point B prior to 

reloading where OCR is the overconsolidation ratio, Ko is the at-rest coefficient of Earth 

pressure, is an exponent determined from laboratory or in situ testing, and Ko' is the at-rest 

coefficient of Earth pressure accounting for stress history. Reloading is then assumed to follow a 

linear path to point R, the intersection of the reloading path with the Ko line and to follow the Ko

line thereafter. Point R, the intersecting point of the reloading path with the virgin loading path, 

is determined as shown in figure 30 and figure 31.

*

, ,min ' σσ β hr h = + ∗∆

Figure 30. Equation. Horizontal residual stress after compaction.

* *

, ,

1 v r h r Ko

σ σ =

Figure 31. Equation. Vertical residual stress after compaction.

Where:

= The decrease in horizontal effective stress from the maximum loading at point A to the 

minimum unloading at point B.

= Assumed constant regardless of the degree of unloading that precedes reloading. 

'h,min = Minimum horizontal stress. *

v,r and *h,r = Vertical and horizontal residual stress after compaction, respectively.

2.3.4.2 Multicycle Ko Unloading/Reloading Stress Path and Ko Unloading Following 

Reloading Stress Path

Seed proposed another model for multicycle Ko unloading/reloading conditions.(11) The values 

and are assumed to remain constant regardless of the number of loading-reloading cycles. 

Three situations of unloading were considered. The first situation is for unloading after 

significant loading, the second situation is for unloading after intermediate reloading, and 

the third situation is for unloading after moderate reloading. Note that Seed also developed a 

nonlinear multicycle Ko unloading/reloading compaction model.

2.3.4.4 Simplified Bilinear Approximation to the Nonlinear Model

In this model, the -type nonlinear unloading model for the first cycle unloading is 

approximated by a bilinear unloading path. The relationship between K2 and F in the bilinear 

unloading model shows the relationship between K3 (slope of reloading path) and 3 of 

the model. 

α

∆

β

σ

σ σ

α β

α

β
22

Seed also developed the following simplified hand-calculation procedure for computing CIS:(11)

1. Calculate the peak lateral compaction pressure profile (i.e., 'h,vc,p versus depth 

relationship). 

2. Multiply the 'h,vc,p values with the bilinear model parameter, F.

3. Calculate the lateral residual stress as shown in figure 32.

'

, 0 , , ' ' σ h r = K σ v + F∆σ h vc p

Figure 32. Equation. Lateral residual stress.

4. Reduce the near-the-surface portion of the 'h,r distribution with ' ' σ h,r ≤ K1,φ ',Bσ v at 

all depths.

5. Increase the residual effective stress distribution such that ' ' σ h,r ≥ K0σ v at all depths.

The compaction models developed by Seed were used to determine CIS for full-scale 

experiments and were reported by Duncan and Seed and Duncan et al.(11–13) The publications 

show that CIS could be calculated based on either the simplified method (i.e., the bilinear model) 

or the nonlinear model with the aid of FE analysis. The studies showed that the resulting lateral 

Earth pressures determined by the models are in good agreement with measured data.

2.4 CIS IN A REINFORCED SOIL MASS

Many researchers and engineers have suggested that if a granular backfill is well compacted, a 

GRS mass can usually carry many loads while experiencing little movement. Several studies 

on performance of GRS structures have used simplified and somewhat arbitrary procedures to 

simulate the effects of fill compaction. In past studies, CIS in the fills were ignored completely. 

CIS in a GRS mass is likely to be more pronounced than CIS induced in an unreinforced soil 

mass because soil reinforcement interface friction tends to restrain lateral deformation of the soil 

mass and result in greater values of CIS. A review of previous studies on GRS masses, including 

the effects of CIS, is presented in this section.

2.4.1 Ehrlich and Mitchell(46)

Ehrlich and Mitchell presented a procedure to include CIS in the analysis of reinforced soil walls 

and noted that CIS was a major factor affecting the reinforcement tensions.(46) The assumptions 

involved in the procedure were as follows: 

• The stress path was as shown in figure 33.

• With the multicycle operations of soil placement and compaction during construction, the 

soil surrounding the reinforcement maximum tension point in each compaction lift was 

subjected to only one cycle of loading, as shown in figure 33. 

∆σ

∆σ

σ
23

Figure 33. Illustration. Assumed stress path due to compaction-induced stress.

Loading due to the weight of overlying soil layers plus some equivalent increase in the stress 

state induced by the compaction operations is shown as paths 1–3 in figure 33. This is followed 

by unloading along paths 3–5 to the final residual stress-state condition at the end of 

construction. Ehrlich and Mitchell noted that by following this procedure, the stresses in each 

layer were calculated only once and that each layer calculation was independent of the others.(46)

The specific values of 'z and 'zc at point 3 in figure 33 represent the maximum stress 

applied to the soil at a given depth during the construction process. The maximum past 

equivalent vertical stress, including compaction at the end of construction ( 'zc), can be 

estimated using a new procedure based on the method given by Duncan and Seed for 

conventional retaining walls.(12)

In figure 33, the value of 'zc can be estimated using figure 34 through figure 38. 

' ' xp

zc Ko

σ

σ =

Figure 34. Equation. Maximum vertical stress at a given depth during construction.

1 sin ' Ko = − φ

Figure 35. Equation. Coefficient of Earth pressure at rest.(47)

( ) 0.5 '

' 1 xp o A

QN K

L

γ γ

σ ν= +

Figure 36. Equation. Maximum lateral stress in terms of compaction and effective soil unit 

weight.

σ σ

σ

σ
24

Where:

Q = Maximum vertical operating force of the roller drum.

L = Length of the roller drum.

= Effective soil unit weight.

1

o

o

o

K

K

υ = −

Figure 37. Equation. Poisson’s ratio under Ko condition.





 



  −



 



  +  



 = + 1

2

' tan 45

2

' tan 45 φ 4 φ

γ

o o N

Figure 38. Equation. Bearing capacity factor.

The effects of CIS on compaction and reinforcement stiffness in GRS walls were investigated by 

Ehrlich and Mitchell.(46) Their conclusions were as follows: 

• The soil shearing resistance parameters, the soil unit weight, the depth, the relative soil 

reinforcement stiffness index Si, and the compaction, were the major factors determining 

reinforcement tensions (typical Si for metallic reinforcement = 0.500 to 3.200, plastic 

reinforcement = 0.030 to 0.120, and geotextile reinforcement = 0.003 to 0.012).

• Increasing Si usually means increased lateral Earth pressure and reinforcement tension, 

but at shallow depths, the opposite effect can occur depending on compaction conditions.

• The coefficient of horizontal Earth pressure, K, can be greater than Ko at the top of the 

wall and can be greater than KA to depths of more than 20 ft (6.1 m) depending on the 

relative soil reinforcement stiffness index and the compaction load. 

• Ko is the upper limit for the coefficient of horizontal Earth pressure, K, if there is no 

compaction of the backfill.(46)

2.4.2 Hatami and Bathurst(17)

Hatami and Bathurst noted that fill compaction has two effects on the soil: it increases the lateral 

Earth pressure and it reduces the effective Poisson’s ratio.(17) They suggested that the first 

effect can be modeled in a numerical analysis by applying a uniform vertical stress (1.2 and 

2.3 psi (8 and 16 kPa) depending on compaction load) to the entire surface of each newly 

placed soil layer before analysis and removing it afterwards. This procedure was based on a 

recommendation by Gotteland et al., who simulated the compacting effect by loading and 

unloading a uniform surcharge of 7.3 and 14.5 psi (50 kPa and 100 kPa) on the top of 

the wall.(48)

For the second effect of compaction on the reduction of Poisson’s ratio, Hatami and Bathurst 

used the numerical simulation to find the minimum Poisson’s ratio, min, from matching 

measured and analysis data.(17) The results (wall lateral movement and reinforcement forces) 

γ

ν
25

obtained from the numerical analysis, including compaction effects, were in good agreement 

with the measured data. 

In the numerical analyses, the compaction effects were also accounted for by increasing the 

elastic modulus number, Ke, from triaxial test results by a factor of 2.25 for walls 1 and 2. 

2.4.3 Morrison et al.

(18)

Morrison et al. simulated the effects of fill compaction of shored mechanically stability Earth 

walls.(18) A 7.3-psi (50-kPa) inward pressure was applied to the top, bottom, and exposed faces 

of each lift to simulate the effects of fill compaction. The inward pressure was then reduced to 

1.5 psi (10 kPa) on the top and bottom of a soil lift prior to placement of the next lift to simulate 

vertical relaxation or unloading following compaction. The inward pressure acting on the 

exposed face was maintained at 7.3 psi (50 kPa) because this produced the most reasonable 

model deformation behavior compared with that observed in the field-scale test. It was 

considered that the inward maintained pressures were “locking-in” stresses in soil due 

to compaction. 

The stiffness of soil was increased by a factor of 10 to consider CIS in the GRS mass. This factor 

was about 2.25 in Hatami and Bathurst.(17)

Figure 39 shows the model for FE analysis by Morrison et al.(18) The figure shows the simulation 

of fill compaction of lift 5 by the applying uniform pressures. 
26

1 m = 3.28 ft

Figure 39. Illustration. FE model for FE analysis.(18)

The results of the lateral movement and reinforcement forces showed a good qualitative 

agreement with the measured data. However, general application of the procedure may be 

questionable because neither the method of analysis nor the magnitude of the applied inward 

pressure was properly justified.

2.5 HIGHLIGHTS OF COMPACTION-INDUCED EARTH PRESSURES IN THE 

LITERATURE 

Several important highlights regarding compaction-induced lateral Earth pressures in the 

literature include the following:

• Compaction of soil against a rigid, vertical, non-yielding structure appears to result in the 

following residual lateral pressure distribution: 
27

o The lateral pressure near the surface increases rapidly with depth, exceeding the 

at-rest value, but limited to passive failure pressures.

(9,11)

o At intermediate depths, the lateral pressures exceed the at-rest value and increase less 

rapidly with depth or remain fairly constant with depth.(9,11)

o At greater depths, the lateral pressures appear to be the simple at-rest pressures, 

showing no affects of compaction.(9,11)

• Compaction of soil against deflecting structures appears to increase near the surface.

• The compaction-induced residual Earth pressures are significantly affected by the 

compaction equipment. For compaction by small hand-operated rollers, the increase in 

the lateral pressure occurs within a depth of about 10 to 13 ft (3 to 4 m), but for very 

large rollers, the effect of compaction can be up to 49 to 82 ft (15 to 25 m).(12)

• Structural deflections away from the soil, which occur during fill placement and 

compaction, will reduce the residual lateral Earth pressures. Reduction in pressures 

appears to occur more rapidly in heavily compacted cohesionless soil.(11)

• Compaction-induced residual lateral Earth pressures in cohesive soils appear to dissipate 

with time, even against non-deflecting structures, and eventually approach at-rest values.

• There is some evidence suggesting that the direction of rolling with the compactor can 

have a significant effect on compaction-induced Earth pressures.(46)

• Field observations indicate that available overburden pressures are sufficient that possible 

passive failure does not limit residual lateral Earth pressure and a high percentage of the 

peak lateral Earth pressures induced during compaction may be retained as residual 

pressures. In previously compacted soil, however, additional compaction can result in 

only small increases in peak pressures and at negligible fractions.(10)

• A number of simulation models have been proposed to explain and evaluate the residual 

lateral Earth pressures induced by compaction. Common to all of these theories is the 

idea that compaction represents a form of over-consolidation wherein stresses resulting 

from a temporary or transient loading condition are retained to some extent following 

removal of this peak load.

• Many researchers have simulated fill compaction by application and removal of a surface 

surcharge pressure. (See references 8, 9, 17, and 48.)

• Broms proposed a theory to calculate compaction-induced residual lateral Earth

pressures against a rigid, vertical, frictionless, non-yielding wall.(9) The simulation results 

somewhat agree with available field data for walls sustaining minimal deflections. Broms 

assumed that unloading results in no decrease in lateral stress until a limiting passivefailure-type condition is reached and reloading results in no increase in lateral stress until 

the virgin K0-loading stress path is regained.(9) This type of model does not predict well 
28

the peak lateral stresses induced by fill compaction and is not suited for computing lateral 

stresses induced by a surface compaction plant of finite lateral dimensions (not the entire 

surface). But Broms’ theory is very easy to apply.(9) Some researchers have adopted this 

theory for analysis of GRS structures.(17,18,48)

• Seed developed two models for simulation of fill compaction: a nonlinear model and a 

bilinear model.(11) They are well suited for simulation of compaction operations in GRS 

structures. The simulation results of the two models are rather similar, and both agree 

well with measured data of unreinforced Earth retaining walls. The bilinear model is easy 

to apply using hand calculation. Both models are based on the Ko condition and are very 

useful for estimating CIS for soil only. To use it for GRS structures, indepth studies need 

to be carried out.
29

CHAPTER 3. ANALYTICAL MODEL FOR CALCULATING LATERAL 

DISPLACEMENT OF A GRS WALL WITH MODULAR BLOCK FACING

Over the past two decades, GRS walls have gained increasing popularity in the United States and 

abroad. In actual construction, GRS walls have demonstrated a number of distinct advantages 

over the conventional cantilever and gravity retaining walls. Generally, GRS walls require less 

over-excavation and are more ductile, more flexible (hence more tolerant to differential 

settlement and to seismic loading), more adaptable to low permeability backfill, easier to 

construct, and significantly more economical than conventional Earth structures.(2–4)

A GRS wall comprises two major components: a facing element and a GRS mass. GRS wall 

facing elements have been constructed with different types of material and in different forms 

including wrapped geotextile facing, timber facing, modular concrete block facing, precast 

concrete panel facing, and cast-in-place rigid facing. Among the various facing types, modular 

concrete block facing has been the most popular in North America, mainly because of its ease of 

construction, availability, and low cost. The other component of a GRS wall, the GRS mass, is a 

compacted soil mass reinforced with layers of geosynthetic reinforcement. Figure 40 shows the 

schematic diagram of a typical GRS wall with a modular block facing.

Soil

Reinforcement

H

q

. L

Facing block

Sv

Figure 40. Illustration. Basic components of a GRS wall with a modular block facing.

Current design methods for GRS walls consider only the stresses and forces in the wall system. 

Even though a GRS wall with a modular block facing is a fairly flexible wall system, movement 

of the wall is not accounted for in current designs. A number of empirical and analytical methods 

have been proposed for estimating lateral movement of GRS walls. Although many full-scale 

experiments, numerical analyses, and field experience have clearly indicated the importance 

of facing rigidity on wall movement, most methods do not address the rigidity of the facing.

(See references 49–52.)

The prevailing methods for estimating the maximum lateral displacement of GRS walls include 

the Federal Highway Administration (FHWA) method, the Geoservices method, the Colorado 
30

Transportation Institute (CTI) method, and the Jewell-Milligan method. (See references 2, 19, 

53, and 54.) Among these methods, the Jewell-Milligan method has been found to give the 

closest agreement with FE analysis.(55) However, the method ignores the effect of facing rigidity. 

Strictly speaking, the method is only applicable to reinforced soil walls where there is little 

facing rigidity, such as a wrapped-faced GRS wall. 

A study aimed at developing an analytical model for calculating lateral movement of a GRS wall 

with modular block facing was undertaken.(19) The analytical model is a modification to the 

Jewell-Milligan method by including the rigidity of facing element. This analytical model can be 

used in routine design by determining the required reinforcement strength for a limiting value of 

maximum allowable wall movement. 

To verify the analytical model, the lateral wall displacements calculated by the analytical model 

were compared with the results of the Jewell-Milligan method for GRS walls with negligible 

facing rigidity.(19) In addition, the lateral wall displacements obtained from the analytical model 

were compared with the measured data of a full-scale experiment using a GRS wall with 

modular block facing.(16,17)

In addition to lateral displacement profiles, an equation for determining facing connection forces 

(i.e., the forces in reinforcement immediately behind the facing) is introduced.(19)

3.1 EXISTING METHODS FOR ESTIMATING MAXIMUM WALL MOVEMENT 

The most prevalent methods for estimating the maximum lateral displacement of GRS walls are 

the FHWA method, the Geoservices method, the CTI method, and the Jewell-Milligan method. 

(See references 2, 19, 53, and 54.) A summary of each method is presented in this section.

3.1.1 The FHWA Method(53)

The FHWA method correlates the reinforcement length/wall height (L/H) ratio with the lateral 

displacement of a reinforced soil wall during construction. Figure 41 shows the relationship 

between L/H and R, the empirically derived relative displacement coefficient. Based on 20-ft 

(6-m)-high walls, the R value increases by 25 percent for every 3 psi (20 kPa) of surcharge. For 

higher walls, the surcharge effect may be greater. The curve in figure 41 has been approximated 

by a fourth-order polynomial for 0.3 1.175 L

H

≤ ≤ , as shown in figure 42.

δ

δ
31

1 m = 3.28 ft

Figure 41. Graph. Empirical curve for estimating maximum wall movement during 

construction in the FHWA method.(53)

11.81 42.25 57.16 35.45 9.471

4 3 2

 +



 



  −  



  +  



  −  



 = H

L

H

L

H

L

H

L

R δ

Figure 42. Equation. Relative displacement coefficient.

For extensible reinforcement, the maximum lateral wall displacement, max, can be calculated 

using figure 43 ( max is in units of wall height (H)).





 



 = 75 max

H δ δ R

Figure 43. Equation. Maximum lateral wall displacement during construction for 

extensible reinforcement.

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 a quick estimate of the maximum lateral displacement. Note that the maximum lateral 

displacement, max, as obtained from figure 43, has been corrected for a wall with a different 

height and surcharge.

3.1.2 The Geoservices Method(54)

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). The method 

provides a procedure for calculating the lateral wall displacement.

δ

δ

δ
32

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 (1–3 percent) should be selected.

Geosynthetics have a wide range of material properties depending on, among other factors, the 

way they are manufactured. Non-woven geotextile exhibits low modulus characteristics. If such 

a geosynthetic was chosen as a reinforcement for a wall, design would necessarily imply that a 

large design strain is to be considered.

Once the strain limit has been selected, the method assumes a distribution of strain in the 

reinforcement, as shown in figure 44, for calculating wall movement.

Φ/2

Rankine Surface

Strain Distribution

Reinforcement

εmax

Figure 44. Illustration. Assumed strain distribution in the Geoservices method.(54)

The horizontal displacement, h, is calculated as shown in figure 45.

2

d L

h

ε δ =

Figure 45. Equation. Horizontal displacement.

Where:

d = Strain limit ( max).

L = Reinforcement length.

3.1.3 The CTI Method(2)

Differing from all other design methods based on ultimate strength of the geosynthetic 

reinforcement, the CTI method is a service-load-based design method. The reinforcement

requirements are made in terms of stiffness at a design limit strain as well as the 

ultimate strength. 

δ

ε ε
33

In most cases, the designer will select a design limit strain of 1–3 percent for the reinforcement. 

The maximum lateral displacement of a wall, max, can be estimated by the empirical equation 

in figure 46.





 



 = 1.25 max

H

d δ ε

Figure 46. Equation. Maximum lateral wall displacement according to CTI method.

Where:

d = Design limit strain (typically 1–3 percent for H less than or equal to 30 ft (0.9 m)).

H = Wall height.

If the maximum wall displacement exceeds a prescribed tolerance for the wall, a smaller design 

limit strain should be selected so that the maximum lateral displacement of the wall will satisfy 

the performance requirement. Figure 46 applies only to walls with very small facing rigidity, 

such as wrapped-faced walls. Walls with significant facing rigidity will have smaller maximum 

lateral displacement. For example, a modular block GRS wall will have max about 15 percent 

smaller than that calculated in figure 46.

3.1.4 The Jewell-Milligan Method

Jewell and Jewell and Milligan proposed a procedure for calculating wall displacement 

based on analysis of stresses and displacements in a reinforced soil mass.(56,19) The method 

describes a link between soil stresses (stress fields) in a reinforced soil mass in which a constant 

mobilized angle of friction is assumed with the resulting displacements (velocity fields). There 

are two parameters for plane-strain plastic deformation of soil: the plane-strain angle of friction, 

ps, and the angle of dilation, . The planes on which the maximum shearing resistance ps is 

mobilized are called the “stress characteristics” and are inclined at (45 / 2 +φ ps )  to the direction 

of major principal stress, as shown in figure 47. The directions along which there is no linear 

extension strain in the soil are called the “velocity characteristics” and are inclined at 

(45 / 2 +ψ )  to the direction of major principal stress, as shown in figure 47. 

©Taylor & Francis

Figure 47. Illustration. Stress and velocity characteristics behind a smooth retaining wall 

rotating about the toe.(19)

δ

ε

δ

φ ψ φ
34

Jewell and Milligan noted from limiting equilibrium analyses that there are three important zones 

in a reinforced soil wall, as illustrated in figure 48.

(19) The boundary between zone 1 and 2 is at 

an angle (45 / 2 +ψ )  to the horizontal, and the boundary between zone 2 and 3 is at an angle ds. 

Large reinforcement forces are required in zone 1 to maintain stability across a series of critically 

inclined planes. In zone 2, the required reinforcement forces reduce progressively.

©Taylor & Francis

Figure 48. Illustration. Major zones of reinforcement forces in a GRS wall and the force 

distribution along reinforcement with ideal length.(19)

The assumptions of the Jewell-Milligan method for ideal length of reinforcement are as follows:

• The reinforcement length at every layer extends to the back of zone 2, the so-called 

ideal length.

• The horizontal movement of the facing can be calculated by assuming horizontal 

deflections starting at the fixed boundary between zones 2 and 3 and working to the face 

of the wall.

• The stability of the stress characteristics and the velocity characteristics is equally critical 

in soil. Hence, reinforcement must provide equilibrium for both. The consequence is that 

behind the Rankine active zone in a reinforced soil wall, the equilibrium is governed by 

ds, mobilized on the velocity characteristics.

In figure 48, the maximum horizontal resultant force required for equilibrium, Prm, is equal to the 

active force Pa, as shown in figure 49.

φ

φ
35















 = = + q H H Prm Pa Ka s 2

2 γ

Figure 49. Equation. Maximum horizontal resultant force required for equilibrium.

Where: 

= Unit weight of the soil.

H = Wall height.

qs = Uniform surcharge.

Ka = The active Earth pressure coefficient, which can be expressed as shown in figure 50.





 



 +





 



 + −

= +

− =

2

tan 45

2

tan 45

(1 sin )

(1 sin )

ψ

φ ψ

φ

φ ds

ps

ps Ka

Figure 50. Equation. Active Earth pressure coefficient.

The required reinforcement force Pr in zone 2 at an angle , as shown in figure 48, can be 

estimated from the maximum reinforcement force, Prm, as shown in figure 51.

θ

θ φ

tan

tan( )

a

ds

rm

r

P K

P − =

Figure 51. Equation. Ratio of the required reinforcement force and the estimated 

maximum reinforcement force.

The results of the displacement analyses have been presented in the form of design charts in

figure 52. The charts can be used to determine the distribution of lateral wall displacement along 

the wall face for different values of mobilized internal friction, ps, and angles of dilation, . 

γ

θ

φ ψ
36

©Taylor & Francis

Figure 52. Illustration. Charts for estimating lateral displacement of GRS walls 

with the ideal length layout.(19)
37

To estimate the horizontal deflection at the GRS wall face for reinforcement with the ideal length 

and uniform spacing, the charts in figure 52 can be used. The horizontal deflection at the wall 

face depends on the wall height, H, the mobilized soil shearing resistance, ds, the reinforcement 

force, Pr, and the reinforcement stiffness, K. Figure 52 can also be used to obtain a dimensionless 

factor, base

h

HP

δ K . The horizontal displacement, h, can be calculated from this factor. The 

reinforcement occurs at the base of the wall, Pbase, in the dimensionless factor above. Pbase is 

calculated using figure 53.

( ) base a v H qs P = K s γ +

Figure 53. Equation. Reinforcement force at the base of the wall.

3.2 DEVELOPING AN ANALYTICAL MODEL FOR CALCULATING LATERAL 

MOVEMENT AND CONNECTION FORCES OF A GRS WALL

Jewell and Milligan presented design charts for estimating the deformation of reinforced soil 

walls where the rigidity of the facing can be ignored.(19) Rowe and Ho and Ho and Rowe pointed 

out that there is little variation in the reinforcement forces and the lateral wall deformation when 

L/H is equal to or greater than 0.7.(50,57,58) Note that L/H = 0.7 is commonly used in practice and 

is suggested by AASHTO.(59) Based on a series of numerical analyses of GRS walls, Rowe and 

Ho also showed that the maximum lateral deformation obtained by the Jewell-Milligan method 

with an ideal reinforcement length, as defined by Jewell and Milligan, is generally in good 

agreement with the numerical results for L/H = 0.7.(19,50) For this reason, the Jewell-Milligan 

method can be used to estimate lateral movement of a reinforced soil wall with L/H greater than 

or equal to 0.7. The analytical model developed in this study for GRS walls with modular block 

facing was based on the Jewell-Milligan method.

The derivation of the analytical model is provided in the following sections. It presents the 

derivation of the equations in the Jewell-Milligan method for predicting deformation of a 

reinforced soil wall with negligible facing rigidity, provides the derivation of the equations for 

determining connection forces in the reinforcement for walls with modular block facing, and 

provides equations for calculating lateral movement of GRS walls with modular block facing.

3.2.1 Lateral Movement of GRS Walls with Negligible Facing Rigidity

Figure 54 shows the three major zones in a GRS wall and the force distribution in the 

reinforcement at depth zi used by Jewell and Milligan to develop an analytical model for 

determination of wall deformation.(19) Jewell and Milligan presented design charts based on the 

analytical model (without giving the derivation).(19) The following derivation is presented for 

completeness and for easier reference when showing the derivation of the analytical model 

developed for this study. 

φ

δ
38

Pr m

H

z

(H - z )

i

i

Reinforcement

Zone 3

Zone 1

Zone 2

x

z

Lzone-1 Lzone-2

L 

45 + ψ/2 φds

i

©Taylor & Francis

Figure 54. Illustration. Major zones of the reinforcement force in a GRS wall.(19)

The horizontal movement, h, of the wall face at depth zi can be evaluated using figure 55

through figure 57.

∆h = ∆zone−1 + ∆zone−2

Figure 55. Equation. Horizontal movement.

1

0 inf inf

1

1

− ∫ −

−

∆ = = zone

re

rm

L

re

rm

zone L

K

P dx

K

P zone

Figure 56. Equation. Lateral deformation in zone 1.

∫

− −

−

+

−  −



 



 ∆ = ≈

1 2

1

2

inf inf

2 2

1 zone zone

zone

L L

L

zone

re

rm

re

r

zone L

K

P dx

K

P

Figure 57. Equation. Lateral deformation in zone 2.

Where:

Kreinf = Stiffness of the reinforcement.

Prm = Maximum reinforcement force at depth zi.

Lzone-1 = Reinforcement length in zone 1 at depth zi.

Lzone-2 = Reinforcement length in zone 2 at depth zi.

Substituting figure 56 and figure 57 into figure 55 results in figure 58.





 



 ∆ = −1 + −2

inf 2

1 zone zone

re

rm

h L L

K

P

Figure 58. Equation. Total horizontal movement of the wall face.

∆
39

Substituting figure 59 and figure 60 into figure 58 results in figure 61.

( ) 



 



 − = − − 2

tan 45 1

o ψ zone i L H z

Figure 59. Equation. Reinforcement length in zone 1.

( ) ( ) 



 



 



 



 − = − − − − 2

tan 90 tan 45 2

ψ φ o

ds

o

zone i L H z

Figure 60. Equation. Reinforcement length in zone 2.

( ) ( ) ( ) 















 



 



 



  + − − − −  



 ∆ = − − 2

tan 90 tan 45

2

1

2

tan 45

inf

ψ φ ψ o

ds

o

i

o

i

re

rm

h H z H z

K

P

Figure 61. Equation. Total horizontal movement of the wall face substituting the 

components derived in figure 59 and figure 60.

Rearranging figure 61 results in figure 62 and figure 63.

( ) ( ) 















 



 



 



  + − − − 

 



 ∆ = − − 2

tan 90 tan 45

2

1

2

tan 45

inf

ψ φ ψ o

ds

o o

i

re

rm

h H z

K

P

Figure 62. Equation. Rearrangement of total horizontal movement of the wall face.

( ) ( ) 















 



  + − 

 



 ∆ = − − ds

o o

i

re

rm

h H z

K

P φ ψ tan 90

2

tan 45

2

1

inf

Figure 63. Equation. Factored down total horizontal movement of the wall face.

The value of h, the lateral displacement of a GRS wall at depth zi, can be calculated directly 

from figure 64.

( ) 



 



  + − 

 



 − − 



















 



 ∆ = tan(90 ) 2

tan 45

2

1 0 0

inf

i ds

re

rm

h H z

K

P φ ψ

Figure 64. Equation. Simplified horizontal movement of the wall face.

Where:

Kreinf = Stiffness of the reinforcement.

Prm = Maximum reinforcement force at depth zi.

H = Wall height.

ds = Effective direct shear friction angle of soil.

= Angle of dilation of soil.

∆

φ

ψ
40

3.2.2. Connection Forces for GRS Walls with Modular Block Facing

The connection forcesin figure 64 are defined as the forces in the reinforcement at the back face 

of the wall facing. The assumptions made for the determination of the connection forces include 

the following: 

• The wall face is vertical or nearly vertical.

• There is only friction connection between adjacent facing blocks (i.e., there is no 

additional mechanical connection elements such as lips, keys, or pins). 

• A uniform surcharge is being applied over the entire horizontal crest of the wall.

• Each facing block is a rigid body (i.e., movement is allowed but not the deformation). As 

a facing block moves, the frictional resistance between two adjacent blocks will reach the 

maximum resistance.

Consider the reinforcement at depth, zi, sandwiched between two adjacent facing blocks, as 

shown in figure 65. The frictional forces, F, above and below these blocks are Fi-1 and Fi+1. The 

horizontal resultant force of lateral Earth pressure acting on the two facing blocks is Pi. The 

tensile connection force in the reinforcement is Ti, Wi is the weight of the facing at location at 

depth Zi, Ni is the normal force, and Sr is the reference spacing.

Sv

± Fi+1

b

± Fi-1

Ti

reinforcement

Ni-1

Wi

Ni+1

Ffi

Pi

Top of the wall

Zi

Figure 65. Illustration. Forces acting on two facing blocks at depth zi.

The tensile connection force, Ti, in the reinforcement is shown in figure 66. Pi is calculated using 

figure 67.

( ) Ti = Pi ± Fi+1 − Fi−1

Figure 66. Equation. Tensile connection force.
41

P K z qS i h si v = + (γ )

Figure 67. Equation. Horizontal resultant force of lateral Earth pressure acting on the two 

facing blocks.

If ( ) 0, Pi ± Fi+1 − Fi−1 < Ti should be set equal to 0, as geosynthetic reinforcement can resist only 

tensile forces (i.e., Ti is always greater than or equal to 0).

From figure 65, figure 68 to figure 70 are derived.

Ti = Pi ± (Ni+1 − Ni−1 )tan δ ; Ti = 0 if Ti ≤ 0

Figure 68. Equation. Tensile connection force substituting the components derived in 

figure 67.

Where Ni+1 and Ni-1 are normal forces on the top and the bottom of the two adjacent blocks.

Ti = Pi ± (Wi + Ffi )tan δ

Figure 69. Equation. Tensile connection force solved in terms of the weight of the facing 

block and friction between the soil and wall facing.

Or

Ti = Pi ± (γ bbS v + pSv tan β )tan δ

Figure 70. Equation. Simplified tensile connection force.

Where:

Ffi = Frictional resultant force between wall facing and soil.

b = Unit weight of facing block.

b = Width of facing block.

Sv = Reinforcement spacing.

= Friction angle between modular block facing elements (δ can be the friction angle between 

facing blocks if there is no reinforcement between the blocks, or it can be the friction angle 

between facing block and geosynthetic if there is reinforcement sandwiched between blocks).

= Friction angle between back face of wall and soil.

p = Average net Earth pressure acting on the facing due to Earth pressure on the facing and the 

pressure caused by the reinforcement force. The value of p can be estimated as shown in 

figure 71.

1 1 tan i i

b

v

F F p b S γ δ + − − = =

Figure 71. Equation. Average net Earth pressure on the facing.

Substituting figure 71 into figure 70, Ti, the connection force at depth zi, can be determined as 

shown in figure 72 and figure 73.

γ

δ

β
42

Ti = Pi ± (γ bbSv + γ bbSv tanδ tan β )tanδ

Figure 72. Equation. Tensile connection force at a given depth.

Ti = Kh (γ s zi + q)Sv ± (γ bbSv + γ bbSv tanδ tan β )tanδ

Figure 73. Equation. Tensile connection force substituting figure 67.

Therefore, the tensile connection force in the reinforcement at depth zi can be expressed as 

shown in figure 74.

= (γ + ) ± γ tan δ (1+ tan δ tan β ) i h s i q Sv bbS v T K z ; T = 0 if T ≤ 0

Figure 74. Equation. Tensile connection force as a simplification of figure 73.

Note that if the friction between the back face of the wall facing and the soil behind the wall is 

ignored, the connection force at depth zi is as shown in figure 75. 

(γ ) (γ )(tan δ ) i h s i q Sv bbS v T = K z + ± ; T = 0 if T ≤ 0

Figure 75. Equation. Tensile connection force ignoring the effect of fiction between the 

back of the block and soil.

Calculating the reinforcement connection forces in a GRS wall with modular block facing by a 

simple equation can eliminate a considerable amount of work designing a GRS wall. In 

designing GRS walls with segmental facing, the connection forces are involved. A series of 

experimental tests to measure the connection forces were conducted by many researchers. 

According to the results, if the blocks are heavy and well connected, the GRS walls with block 

facing would perform very well.(16,17) The values of the connection forces can be estimated by 

using figure 76 for a typical GRS wall with modular block facing.

(γ ) (γ )(tan δ ) i h s i q Sv bbS v T = K z + −

Figure 76. Equation. Connection force for a typical GRS wall with modular block facing.

The resistant connection force at depth zi at facing can be estimated using figure 77.

2γ (tan δ ) Fr = bbzi

Figure 77. Equation. Resistant connection force.

Comparisons of connection forces and maximum friction capacity at facing blocks are shown in 

figure 78 and figure 79.
43

1 kN = 224.81 lbf

1 m = 3.28 ft

Figure 78. Graph. Connection forces in reinforcement (q = 0 kip/ft (0 kN/m)) 

(wall data from section 3.3.1 with = 15 degrees).

1 kN = 224.81 lbf

1 m = 3.28 ft

Figure 79. Graph. Connection forces in reinforcement (q = 3.4 kip/ft (50 kN/m)) 

(wall data from section 3.3.1 with = 15 degrees).

Figure 78 and figure 79 show the values of connection forces with the maximum connection 

friction forces with a surcharge of 0 and 3.4 kip/ft (0 and 50 kN/m). For most of the cases, the 

lightweight blocks (without strong key connections between blocks) can be used for GRS walls. 

With the heavy surcharge, some blocks at the top of the wall may be unstable, as shown in 

figure 79.

3.2.3 Lateral Movement of GRS Walls with Modular Block Facing

From figure 64 and figure 76, the displacement of a GRS wall with modular block facing at 

depth zi can be determined by figure 80.

ψ

ψ
44

( ) ( ) inf

tan (1 tan tan ) 0.5 tan 45 tan (90 ) 2

h si v b v

i i ds

re

K z q S bS H z

K

γ γ δ δβ ψ φ

  +− +     ∆ =   − °− + °−          

Figure 80. Equation. Lateral displacement of a GRS wall with modular block facing.

Figure 80 is the analytical model in this study. When the frictional resistance between the back 

face of the wall facing and the soil can be ignored, the displacement of the wall at depth zi will 

reduce to figure 81.

( ) ( )( ) ( )

inf

tan

0.5 tan 45 tan (90 ) 2

h si v b v

i i ds

re

K z q S bS H z

K

γ γδ ψ φ

  + −     ∆ =   − °− + °−          

Figure 81. Equation. Lateral displacement of a GRS wall with modular block facing 

ignoring the effect of fiction between the back of the block and soil.

Note that the lateral movement calculated by figure 81 will be slightly larger than that calculated 

by figure 80.

3.2.4 Required Tensile Strength of Reinforcement of GRS Walls

The analytical model for estimating wall movement can also be used to determine the required 

reinforcement strength for a limiting value of maximum lateral wall movement (e.g., 2 inches 

(50 mm) or 1 percent of wall height, whichever is smaller) for any given backfill strength 

properties. The required reinforcement strength, Trequired, can be determined from the maximum 

allowable lateral movement at the wall face, max, as shown in figure 82.

( )

max inf 2

tan 45 tan (90 ) 2

re

required

i ds

K T

H z ψ φ

∆ =     − °− + °−        

Figure 82. Equation. Required tensile reinforcement strength at a given allowable lateral 

movement of the wall face.

Figure 82 applies to any facing rigidity because the force T is related only to max and is 

unaffected by the facing rigidity.

3.3 VERIFICATION OF THE ANALYTICAL METHOD

To verify the analytical model developed in this study, the model calculation results were first 

compared to the Jewell-Milligan method for GRS walls with negligible facing rigidity. The 

model calculation results were then compared to measured data from a full-scale experiment. 

3.3.1 Comparison to the Jewell-Milligan Method for Lateral Wall Movement

The model calculation results of wall movement from the analytical model were first compared 

to the results of the Jewell-Milligan method using an example.(19) The conditions of the wall in 

this example are as follows: 

• Wall height: H = 13 ft (4.0 m).

∆

∆
45

• Geosynthetic reinforcement: Vertical spacing (Sv) = 1.3 ft (0.4 m) and stiffness 

(Kreinf) = 13.7 kip/ft (200 kN/m).

• Backfill: Free-draining granular soil unit weight ( s) = 0.11 kip/ft3 (18 kN/m3), 

cohesion (c) = 0, friction angle ( ds) = 35 degrees, and dilation angle ( ) = 5 degrees.

• Facing: Modular concrete blocks width (b) = 1 ft (0.3 m), unit weight ( b) = 0, 0.13, and 

0.19 kip/ft3 (0, 20, and 30 kN/m3).

• Interface between adjacent blocks: Cohesion (c) = 0 and friction angle ( ) = 

25 degrees.

• Interface friction between back face of facing and soil: = 0 degrees.

The results of the comparisons between the analytical model and the Jewell-Milligan method are 

shown in figure 83 through figure 94 for different weights of facing blocks (unit weight of block 

γb = 0, 0.06, 0.13, and 0.19 kip/ft3 (0, 10, 20, and 30 kN/m3)), each with different values of 

surcharge pressure (q = 0, 0.7, and 3.4 kip/ft (0, 10, or 50 kN/m)). The value q = 0.7 kip/ft 

(10 kN/m) represents a typical surcharge for highway design. These figures indicate that for all 

facing conditions (i.e., for different values of b), the effect of surcharge on wall movement is 

significant. The deformed shape of the wall face is different at q = 0 and 3.4 kip/ft (0 and 

50 kN/m). At q = 0 kip/ft (0 kN/m), the wall bulges at mid-height, but as the surcharge increases, 

the top of the wall face begins to move outward. At q = 3.4 kip/ft (50 kN/m), the largest wall 

movement occurs near the top of the wall.

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 83. Graph. Lateral displacement calculated by the Jewell-Milligan method 

and the analytical model, b = 0 kip/ft3 (0 kN/m3), q = 0 kip/ft (0 kN/m).

γ

φ ψ

γ

δ

β

γ

 

0

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4

0 20 40 60

Lateral Displacement 

(mm)

Depth from the Top (m)

Analytical model

Jew ell-Milligan

method

γ
46

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 84. Graph. Lateral displacement calculated by the Jewell-Milligan method 

and the analytical model, b = 0 kip/ft3 (0 kN/m3), q = 0.7 kip/ft (10 kN/m).

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 85. Graph. Lateral displacement calculated by the Jewell-Milligan method 

and the analytical model, b = 0 kip/ft3 (0 kN/m3

), q = 3.4 kip/ft (50 kN/m).

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 86. Graph. Lateral displacement calculated by the Jewell-Milligan method 

and the analytical model, b = 0.06 kip/ft3 (10 kN/m3

), q = 0 kip/ft (0 kN/m).

 

0

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4

0 20 40 60

Lateral Displacement 

(mm)

Depth from the Top (m)

Analytical model

Jew ell-Milligan

method

γ 

0

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4

0 20 40 60

Lateral Displacement 

(mm)

Depth from the Top (m)

Analytical model

Jew ell-Milligan

method

γ

γ
47

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 87. Graph. Lateral displacement calculated by the Jewell-Milligan method 

and the analytical model, b = 0.06 kip/ft3 (10 kN/m3

), q = 0.7 kip/ft (10 kN/m).

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 88. Graph. Lateral displacement calculated by the Jewell-Milligan method 

and the analytical model, b = 0.06 kip/ft3 (10 kN/m3

), q = 3.4 kip/ft (50 kN/m).

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 89. Graph. Lateral displacement calculated by the Jewell-Milligan method 

and the analytical model, b = 0.13 kip/ft3 (20 kN/m3

), q = 0 kip/ft (0 kN/m).

γ

γ

γ
48

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 90. Graph. Lateral displacement calculated by the Jewell-Milligan method 

and the analytical model, b = 0.13 kip/ft3 (20 kN/m3

), q = 0.7 kip/ft (10 kN/m).

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 91. Graph. Lateral displacement calculated by the Jewell-Milligan method 

and the analytical model, b = 0.13 kip/ft3 (20 kN/m3), q = 3.4 kip/ft (50 kN/m).

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 92. Graph. Lateral displacement calculated by the Jewell-Milligan method 

and the analytical model, b = 0.19 kip/ft3 (30 kN/m3

), q = 0 kip/ft (0 kN/m).

γ

γ

γ
49

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 93. Graph. Lateral displacement calculated by the Jewell-Milligan method 

and the analytical model, b = 0.19 kip/ft3 (30 kN/m3

), q = 0.7 kip/ft (10 kN/m).

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 94. Graph. Lateral displacement calculated by the Jewell-Milligan method 

and the analytical model, b = 0.19 kip/ft3 (30 kN/m3), q = 3.4 kip/ft (50 kN/m).

As shown in figure 83 through figure 85, when the facing block is weightless (i.e., unit weight 

b = 0 kip/ft3 (0 kN/m3

)), the analytical model gives nearly identical lateral wall movement 

to the Jewell-Milligan method. This is to be expected because facing rigidity is ignored in 

the Jewell-Milligan method. The figures show that as the facing blocks becomes heavier 

(i.e., unit weight increases), the wall movement becomes smaller. When a heavy facing block 

( b = 0.19 kip/ft3 (30 kN/m3)) is used, the maximum lateral wall movement can be as much as 

35 percent smaller than a wall with negligible facing rigidity.

3.3.2 Comparison to Measured Data of Full-Scale Experiment by Hatami and Bathurst(16,17)

A full-scale experiment of a GRS wall with modular block facing is one of a series of laboratory 

experiments conducted by Hatami and Bathurst and was referred to as “wall 1” by the 

authors.

(16,17) The parameters of the GRS wall are as follows:

• Wall height: H = 12 ft (3.6 m) high with a facing batter of 8 degrees from vertical and 

seated on a rigid foundation.

γ

γ

γ

γ
50

• Soil: A clean uniform beach sand ( s) = 0.107 kip/ft3 (16.8 kN/m3), ps = 44 degrees, 

= 11 degrees, and c = 0.3 psi (2 kPa).

• Geosynthetic reinforcement: A weak biaxial polypropylene geogrid, vertical spacing = 

2 ft (0.6 m), reinforcement stiffness = 7.88 kip/ft (115 kN/m), and ultimate strength = 

0.96 kip/ft (14 kN/m).

• Facing: Solid masonry concrete blocks (12 inches (300 mm) high by 6 inches (150 mm) 

wide by 8 inches (200 mm) deep) with a shear key on the top surface of block and b = 

0.13 kip/ft3 (20 kN/m3).

• Interface between facing blocks: Friction angle between blocks ( b-b) = 57 degrees and

cohesion between blocks (cb-b) = 6.7 psi (46 kPa).

Because the analytical model requires that the direct shear friction angle be used in model 

calculations and assumes a vertical wall face, the direct shear friction angle of the soil and the 

facing batter factor were determined before using the analytical model to evaluate the lateral 

movement of the facing. 

The direct shear friction angle was calculated as shown in figure 95. 

sin cos sin 44 cos11

tan 40

1 sin sin 1 sin 44 sin11

ps

ds

ps

φ ψ

φ

φ ψ

° ° = = = °

− − °°

Figure 95. Equation. Direct shear friction angle.

The empirical facing batter factor, fb, was calculated from Allen and Bathurst, with facing 

batter of 8 degrees, as shown in figure 96.

(60)

= 0.88 













 Φ =

d

avh

abh

fb K

K

Figure 96. Equation. Empirical facing batter factor.

Where:

Kabh = The horizontal component of the active Earth pressure coefficient accounting for 

wall face batter.

Kavh = The horizontal component of the active Earth pressure coefficient for a vertical wall.

d = Constant coefficient. 

Allen and Bathurst found that the value of d = 0.5 would yield the best fit for available Tmax data 

and recommended using d = 0.5 for determining fb.

(60)

Figure 97 and figure 98 show lateral movement of the GRS wall under surcharge pressures of 3.4 

and 4.8 kip/ft (50 and 70 kN/m), respectively, for the mean value of measured displacement, the 

Jewell-Milligan method, and the analytical model.(17) The figures show that the lateral movement 

calculated by the analytical model is in close agreement with the measured values. Lateral wall 

movement given by the analytical model agrees much better with the measured values than that 

γ φ

ψ

γ

δ

Φ

Φ
51

calculated by the Jewell-Milligan method for both surcharge pressures. The lateral movement 

obtained by the Jewell-Milligan method was as much as 3.5 times as large as the measured 

movement. Note that the analytical model, not unlike the Jewell-Milligan method, produced a 

displacement profile that had lower bending stiffness than the measured profile. However, 

considering that the analytical model is a simplified model, the simulation is adequate.

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 97. Graph. Measured lateral displacements with Jewell-Milligan method 

and analytical model, q = 3.4 kip/ft (50 kN/m).

1 m = 3.28 ft

1 mm = 0.039 inches

Figure 98. Graph. Measured lateral displacements with Jewell-Milligan method 

and analytical model, q = 4.8 kip/ft (70 kN/m).
52

3.4 SUMMARY

An analytical model was developed to predict the profile of lateral movement of a GRS wall with 

modular block facing. The connection forces in the reinforcement can also be determined by a 

simple equation. The equation for the lateral movement can also be used in design where the 

required reinforcement strength can be determined for a prescribed value of maximum allowable 

lateral wall movement for a given backfill condition. The analytical model has been verified 

through comparisons with the Jewell-Milligan method. The Jewell-Milligan method is a special 

case of the analytical model for GRS walls with negligible facing rigidity. Comparisons were 

also made with a full-scale experiment of a GRS wall with modular block facing. The analytical 

model offers a simple and improved tool for predicting lateral movement of a GRS wall with 

modular block facing.
53

CHAPTER 4. GSGC TESTS

The understanding of GSGC behavior in reinforced soil structures has been lacking. As a result, 

current design methods have considered the geosynthetic layers simply as added tensile elements 

and have failed to account for the interaction between soil and geosynthetics. A series of GSGC 

laboratory tests were designed and conducted to examine the behavior of a GSGC with varying 

spacing and strength of reinforcement, provide test data for verifying the analytical model for 

calculating strength properties of a GRS composite as described in chapter 5, and provide test 

data for calibration of an FE model for a GRS mass. The GSGC tests were conducted at TFHRC 

in McLean, VA.

4.1 DIMENSIONS OF THE PLANE-STRAIN GSGC TEST SPECIMEN

A soil mass reinforced by layers of geosynthetic reinforcement is not a uniform mass. To 

investigate the behavior of GSGCs by conducting laboratory tests, it is necessary to determine 

the proper dimensions of the test specimen so that the test provides an adequate representation of 

GSGC behavior. 

A number of factors were considered prior to determining the test specimen dimensions of the 

GSGC test, including the following:

• Plane-strain condition: Because most GRS structures resemble a plane-strain condition, 

the test should be conducted in a plane-strain condition. 

• Backfill particle size: To alleviate the effects of particle size on the test specimen, the 

dimensions of a generic GRS mass should be at least 6 times as large as the maximum 

particle size of the soil specimen, as suggested by the U.S. Army Corps of Engineers, 

and 15 times larger than the average particle size (D50).(61) The recommended maximum 

particle size for the backfill of GRS structures is 0.75 inches (19 mm).(62) The specimen 

dimension, therefore, should be at least 4.7 inches (120 mm).

• Reinforcement spacing: The reinforcement spacing plays an important role in the 

deformation behavior of GRS structures and the load-transfer mechanism of reinforced

soil masses.(63) The height of a generic GRS mass should be able to accommodate the 

typical reinforcement spacing of 8 to 12 inches (200 to 300 mm) for GRS walls.

• Size of reinforcement sheet: The specimen dimensions in the plane-strain direction, 

referred to as the width, W, and in the longitudinal direction, referred to as length, L, 

should be sufficiently large to provide adequate representation of the geosynthetic 

reinforcement. For polymer grids, enough grid cells need to be included for a good 

representation of the polymer grid. For nonwoven geotextiles, the aspect ratio of the 

reinforcement specimen (i.e., the ratio of width to length) should be sufficiently large 

(e.g., greater than 4) to alleviate significant necking effect. There will be a little necking 

effect for woven geotextiles regardless of the aspect ratio.

Using Plaxis Version 8.2, a series of FE analyses were conducted to examine the effect of 

specimen dimensions on the resulting global stress-strain and volume change relationships of the 
54

composites. The objective of the FE analyses was to determine proper dimensions of a GSGC 

that will produce load-deformation behavior sufficiently close to that of a large mass of soilgeosynthetic composite, referred to as the reference composite. 

Figure 99 shows the typical geometric and loading conditions of the GSGC tests. The reference 

GSGC is taken as a reinforced soil mass with dimensions of 23 ft (7.0 m) high and 16 ft (4.9 m) 

wide in a plane-strain condition. Four different dimensions of GSSCs were analyzed with 

varying specimen heights (23, 6.6, 3.3, and 1.6 ft (7.0, 2.0, 1.0 and 0.5 m), while the width of the 

test specimen was kept as 0.7 × H. In these analyses, the soil was a dense sand. The sand was 

reinforced by a medium-strength woven geotextile (Geotex® 4×4) at 0.7 ft (0.2 m) vertical 

spacing. Table 2 lists the conditions and properties of the soil and reinforcement used in 

the analyses.

Soil

Reinforcement

Sv = 0.2 m

H

σv

W = 0.7 H

σc σc

1 m =3.28 ft

Figure 99. Illustration. Typical geometric and loading conditions of a GSGC.

Table 2. Conditions and properties of the backfill and reinforcement used in FE analyses.

Element Description

Soil A dense sand where unit weight = 17 kN/m3; cohesion = 5 kPa; angle 

of internal friction ( ) = 38 degrees; angle of dilation ( ) = 8 degrees; 

soil modulus (E50) = 40,000 kPa; and Poisson’s ratio = 0.3

Reinforcement Geotex® 4×4 axial stiffness (EA) = 1,000 kN/m; ultimate strength

(Tult) = 70 kN/m; and reinforcement spacing = 0.2 m

Confining pressure Constant confining pressures of 0 and 30 kPa

1 kN/m3 = 0.006 kip/ft3

1 kPa = 0.145 psi

1 kN/m = 0.068 kip/ft

1 m = 3.28 ft

φ ψ
55

The global stress-strain curves obtained from the analyses are shown in figure 100 and

figure 101 for confining pressures ( c) of 0 and 4.4 psi (0 and 30 kPa), respectively 

(a confining pressure of 4.4 psi (30 kPa) is representative of the lateral stress at the 

mid-height of a 23-ft (7.0-m)-high wall). The corresponding global volume change curves are 

shown in figure 102 and figure 103. The global vertical strain ( v) was calculated by figure 104.

1 kPa = 0.145 psi

1 m = 3.28 ft

Figure 100. Graph. Global stress-strain curves for GSGCs of different dimensions under a 

confining pressure of 0 psi (0 kPa).

σ

ε
56

1 kPa = 0.145 psi

1 m = 3.28 ft

Figure 101. Graph. Global stress-strain curves for GSGCs of different dimensions under a 

confining pressure of 4.4 psi (30 kPa).
57

1 m = 3.28 ft

Figure 102. Graph. Global volume change curves for GSGCs of different dimensions under 

a confining pressure of 0 psi (0 kPa).

1 m = 3.28 ft

Figure 103. Graph. Global volume change curves for GSGCs of different dimensions under 

a confining pressure of 4.4 psi (30 kPa).

 100% 

 



 ∆ = H

H v ε

Figure 104. Equation. Global vertical strain.

Where:

∆H = Total vertical displacement of the specimen.

H = Initial height of the specimen.

Figure 100 and figure 101 indicate that a composite with a height of 6.6 ft (2.0 m), width of 4.6 ft 

(1.4 m), and confining pressure of 4.4 psi (30 kPa) yielded stress-strain and volume change 

relationships that were sufficiently close to those of the reference composite. Specimen sizes 

with heights of 3.3 and 1.6 ft (1.0 and 0.5 m) appeared too small to provide an adequate 

representation of the reference composite.

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10 12 14 16

Global Vertical Strain εv (%)

Global Volumetric Strain 

∆V/V (%)

7.0 m x 4.9 m

2.0 m x 1.4 m

1.0 m x 0.7 m

0.5 m x 0.35 m

Specimen Dimensions:
58

For comparison, additional analyses were conducted on unreinforced soil. Figure 105 and 

figure 106 show the global stress-strain curves and global volume change curves of the soil 

masses without any reinforcement for the different specimen dimensions. The results indicate 

that a specimen height as small as 1.6 ft (0.5 m) will yield nearly the same stress-strain and 

volume change relationships as the reference soil mass of height 23 ft (7.0 m) when 

reinforcement is not present.

1 kPa = 0.145 psi

1 m = 3.28 ft

Figure 105. Graph. Global stress-strain curves of unreinforced soil under a confining 

pressure of 4.4 psi (30 kPa).

1 m = 3.28 ft

Figure 106. Graph. Global volume change curves of unreinforced soil under a confining 

pressure of 4.4 psi (30 kPa).
59

Based on the results of the FE analyses, a specimen height of 6.6 ft (2.0 m) and depth of 4.6 ft 

(1.4 m) with 0.7-ft (0.2-m) reinforcement spacing was selected for the GSGC tests. The actual 

specimen dimensions for the GSGC tests are shown in figure 107. Figure 108 and figure 109

show the front and plan views of the GSGC test setup.

1 m = 3.28 ft

Figure 107. Illustration. Specimen dimensions for the GSGC tests.
60

160.00

81.65

Load cell LC1

(1000 kip)

11.38

108.00

2.625'' steel plate

70.00

36.00

1

3.00

1.50

6.00

6.00

5.0

2.6 6.0

76.25

134.63

33.00

30.00

2.87

70.00

74.25

53.375

74.00

A 2

7.63

36.00

3

11.38

30.75

51.98

(Note: All Dimensions in Inches)

49.00

jack

12.25

Load cell LC2

(300 kip)

2'' steel plate

12.00

25.19

1.94 4.00 12.00 1.12

5.62

2.63

16.93

12.25

16.93

34.00

26.00

2.00

A

2.00

steel plate 

(26''x32.5''x2'')

concrete pad 

(49''x41 3/8''x12'')

concrete block 

(7.625''x7.625''x15.625'')

9.63

steel plate 

(43''x34''x2'')

steel plate 

(43''x34''x2'')

D=1.125''

FRONT VIEW

1 mm = 0.039 inches

Figure 108. Illustration. Front view of the test setup.
61

36.00 108.00 36.00

PLAN

75.87

36.94 36.94

17.00 74.00 17.00

36.00

Open Face: Concrete blocks 

(7.625''x7.625''x15.625'') would 

be removed before testing

26.63

1 3

A

2

23.25

21.50

19.50

47.00

47.00

47.00

53.375 26.63 47.00

7.63

1.25

Rigid frame

Anchor

Specimen

(Note: All Dimensions in Inches)

1 mm = 0.039 inches

Figure 109. Illustration. Plan view of the test setup.

4.2 APPARATUS FOR PLANE-STRAIN TEST

To maintain a plane-strain condition for the GSGC specimens throughout the tests, two major 

factors were considered: (1) the test bin needed to be sufficiently rigid to have negligible lateral 

deformation in the longitudinal direction (i.e., the length direction) and (2) the friction between 

the backfill and the side panels of the test bin needed to be minimized to nearly zero.

4.2.1 Lateral Deformation

Five GSGC masses were tested inside a test bin. The test bin was designed to experience little 

deformation for a surcharge pressure up to 410 psi (2,800 kPa). The test bin is shown in 

figure 110.
62

Figure 110. Photo. Test bin.

4.2.2 Friction

Two transparent Plexiglas® panels were attached inside the steel tubing frame to form the side 

surfaces of the test bin. To minimize the friction between the Plexiglas® and the backfill in these 

surfaces, a lubrication layer was created on the inside surfaces of the Plexiglas® panels. The 

lubrication layer consisted of a 0.02-inch (0.5-mm)-thick latex membrane and an approximately 

0.04-inch (1 mm)-thick lubrication agent (Dow Corning® 4 Electrical Insulating Compound 

NSF 6). This procedure has been used successfully in many plane-strain tests conducted by 

Tatsuoka and his associates at University of Tokyo and by the lead author of this paper in many 

large-scale experiments. (See references 64–68.) The friction angle between the lubricant layer 

and the Plexiglas®, as determined by direct shear test, was less than 1 degree.
63

4.3 TEST MATERIAL

The backfill and geotextile reinforcement employed in the tests are described in the 

following sections.

4.3.1 Backfill

The backfill was a crushed diabase from a source near Washington, DC. Before conducting the 

GSGC tests, a series of laboratory tests was performed to determine the properties of the backfill, 

including the following:

• Gradation test.

• Specific gravity and absorption test of the coarse aggregates.

• Moisture-density tests (Proctor compaction) with rock correction.

• Large-sized triaxial tests with specimen diameter of 6 inches (152 mm).

A summary of some index properties is given in table 3. The grain size distribution of the soil 

is shown in figure 111. Two gradation tests were performed, and the results agreed well with 

each other.

Table 3. Summary of index properties of backfill.

Classification

Well-Graded Gravel: 

Soil Classification A-1a per 

AASHTO M-15 and Soil 

Classification GW-GM per 

ASTM D 2487(69,70)

Maximum dry unit weight 0.15 kip/ft3 (24.1 kN/m3)

Optimum moisture content 5.2 percent

Specific gravity of soil solids 3.03
64

1 mm = 0.039 inches

Figure 111. Graph. Grain size distribution of backfill.

Four triaxial tests were conducted at confining pressures of 5, 15, 30, and 70 psi (34, 103, 207, 

and 482 kPa), and the results were compared with those performed at the University of Colorado 

Denver on the same soil. The soil specimen was approximately 6 inches (152 mm) in diameter 

and 12 inches (305 mm) in height. The shapes of a typical specimen before and after failure are 

shown in figure 112 and figure 113, respectively. Figure 114 and figure 115 present the stressstrain and volume change curves of the tests. The stress-strain curves obtained by Ketchart and 

Wu are included for comparison and to furnish a more complete set of data.(68) The stress-strain 

relationships agree well in trend with those by Ketchart and Wu.(68) The Mohr-Coulomb failure 

envelopes of the backfill are shown in figure 116. For confining pressures between 0 and 30 psi

(0 and 103 kPa), the strength parameters are c = 10.3 psi (71.0 kPa) and = 50 degrees. For 

confining pressures between 30 and 110 psi (103 and 758 kPa), the strength parameters are 

c = 35.1 psi (242 kPa) and = 38 degrees.

Figure 112. Photo. Typical triaxial test specimen before test.

φ

φ
65

Figure 113. Photo. Typical triaxial test specimen after test.

1 kPa = 0.145 psi

Figure 114. Graph. Triaxial test results: stress-strain curves of backfill at 0.15 kip/ft3

(24.1 kN/m3

) dry density and 5.2 percent moisture.
66

1 kPa = 0.145 psi

Figure 115. Graph. Triaxial test results: volume change curves of backfill at confining 

pressures of 5 and 30 psi (34.45 and 103.35 kPa).

σ3 = 15 psi

σ3 = 30 psi

Shear Streess (psi)

Normal Stress (psi)

σ3 = 5 psi

σ3 = 70 psi

σ3 = 110 psi

0 30 98 172 265 433 616

C2 = 35.1 psi

C1 = 10.3 psi

1 kPa = 0.145 psi

Figure 116. Graph. Mohr-Coulomb failure envelopes of backfill.

4.3.2 Geosynthetics

The geosynthetic used in the experiments was Geotex® 4×4 manufactured by Propex® (formally 

known as Amoco 2044). This geosynthetic is a woven polypropylene geotextile. Table 4 shows 

its strength properties as provided by the manufacturer.
67

Table 4. Summary of Geotex® 4×4 properties.

Property Test Method

Machine 

Direction (i.e., 

Wrap Direction)

Cross Direction 

(i.e., Fill 

Direction)

Tensile strength 

(grab) ASTM D4632(71)

0.6 kip

(2.67 kN)

0.5 kip 

(2.22 kN)

Wide-width tensile 

ultimate strength ASTM D4595(72)

400 lb/inch 

(70 kN/m)

400 lb/inch 

(70 kN/m)

Wide-width strength 

at 5 percent strain ASTM D4595(72)

121 lb/inch 

(21 kN/m)

217 lb/inch 

(38 kN/m)

Wide-width 

ultimate elongation ASTM D4595(72) 10 percent 10 percent

Puncture ASTM D4833(73) 170 lb (0.8 kN)

Trapezoid tearing 

strength ASTM D4533(74) 250 lb (1.11 kN)

Two types of geosynthetics were used for the experiments: a single sheet of Geotex® 4×4 and a 

double sheet Geotex® 4×4 (by gluing two sheets together using 3M® Super 77 spray adhesive). 

The double sheet was used to create a geosynthetic that was approximately twice as stiff (and as 

strong) while maintaining the same interface condition as that of the single-sheet geosynthetic. 

Geotex® 4×4 geotextile has been used in the construction of hundreds of GRS walls and in many 

full-scale experiments, including the FHWA GRS pier, Havana Yard Test abutment and pier, 

Blackhawk preloaded GRS bridge abutment, and National Cooperative Highway Research 

Program test abutments. (See references 6 and 75–77.)

Uniaxial tension tests were performed on both types of geosynthetic to determine the loaddeformation behavior using a specimen 12 inches (305 mm) wide and 6 inches (152 mm) long 

(see figure 117). The stiffness and strength of the two geosynthetics are shown in table 5, and 

load-deformation curves are shown in figure 118. The stiffness and strength of the double-sheet 

Geotex® 4×4 were approximately twice as much as those of the single-sheet Geotex® 4×4 with 

the breakage strain almost the same.
68

Figure 117. Photo. Uniaxial tension test of Geotex® 4×4.

Table 5. Properties of Geotex® 4×4 in fill direction.

Geosynthetic

Wide-Width Tensile Strength per ASTM D4595(72)

Stiffness (kN/m) at 

1 Percent Strain

Ultimate Strength (kN/m) 

(Percent at Break)

Single-sheet Geotex® 4×4 1,000 70 (12 percent)

Double-sheet Geotex® 4×4 1,960 138 (12 percent)

1 kN/m = 0.069 kip/ft
69

1 kN/m = 68.52 lbf/ft

Figure 118. Graph. Load deformation curves of the geosynthetics.

4.3.3. Facing Block

Blocks used for the facing of the GSGC mass during specimen preparation were hollow concrete 

blocks with dimensions of 15.625 by 7.625 by 7.625 inches (397 by 194 by 194 mm) and an 

average weight of 40 lb/block (18.1 kg/block).

4.4 TEST PROGRAM

The test program comprised five GSGC tests. Their test conditions are shown in table 6. The 

plate compactor used for the tests (MBW GP1200) had a weight of 120 lb (54 kg), plate 

dimensions of 12 by 21 inches (305 by 533 mm), centrifugal force of 1,500 lbf (6,700 N), 

rotation speed of 5,000 vibrations/min, and moving speed of 70 ft/min (21 m/min).
70

Table 6. Test program for GSGC tests.

Test 

Designation

Geosynthetic 

Reinforcement

Confining 

Pressure

(kPa)

Wide-Width 

Strength of 

Reinforcement

(kN/m)

Reinforcement 

Spacing, Sv 

(m)

Test 1 None 34 None No reinforcement

Test 2 Geotex® 4×4 34 70 0.2

Test 3

Double-sheet 

Geotex® 4×4 34 140 0.4

Test 4 Geotex® 4×4 34 70 0.4

Test 5 Geotex® 4×4 0 (unconfined) 70 0.2

1 kPa = 0.145 psi

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

4.5 TEST CONDITIONS AND INSTRUMENTATION

4.5.1 Vertical Loading System

The vertical loads were applied to the test specimens by using a 1,000,000-lb- (454,000-kg)-

capacity loading frame with a 1,000,000-lb (454,000-kg) hydraulic jack. Loads were measured 

by load cells and by hydraulic jack pressure gauges. For test 1, two load cells of 100,000 and 

300,000 lb (45,400 and 136,200 kg) were used to measure the loads. For tests 2 through 5, a 

1,000,000-lb (454,000-kg) load cell was used to measure the loads. A 12-inch (305-mm)-thick 

concrete pad was placed on top of the specimen before loading. Vertical loads were applied in 

equal increments with 10 min of elapsed time between increments to allow for equilibrium. The 

elapsed time also allowed manual recording of displacements of the test specimen. The vertical 

loads were applied until a failure condition was reached to determine the strength of the 

composite specimen. The applied pressures on the composite specimens were determined 

from the applied vertical loads divided by the surface areas of the composite specimens.

4.5.2 Confining Pressure

The confining pressure on the test specimens was applied by vacuuming. The entire surface area 

of the test specimen was vacuum-sealed with a 0.02-inch (0.5-mm)-thick latex membrane. A 

prescribed confining pressure of 5 psi (34 kPa) was applied for tests 1 through 4 by connecting 

the latex membrane to a suction device through two 0.234-inch (6-mm)-diameter flexible plastic 

tubes. Only test 5 was conducted without confining pressure. 

4.5.3 Instrumentation

The specimens were instrumented to monitor their performance during tests. The instruments 

used include the following:

• Vertical movement: Three linear variable displacement transducers (LVDT) and 

two digital dial indicators were installed on the top of the concrete pad to measure the 
71

vertical movement of the specimen during loading. The vertical movement was measured 

along the top surface of the concrete pad.

• Lateral movement: Ten LVDTs and two digital dial indicators were installed along the 

height of the specimen (two open sides of the specimen) to measure the lateral movement 

of the specimen. The location of the LVDTs and digital dial indicators are shown in 

figure 119.

• Internal movement: The internal movement of the soil at selected points in the soil 

mass was traced by marking the locations of preselected points on a 2-by-2-inch 

(51-by-51-mm) grid system drawn on the membrane.

• Reinforcement strain: To measure the strains in the geotextile, a number of high 

elongation strain gauges manufactured by Measurements Group, Inc. (type EP-08-

250BG-120) were used. Each strain gauge was glued to the geotextile at only two ends 

to avoid inconsistent local stiffening of geotextile due to the adhesive. The strain gauge 

attachment technique was developed at the University of Colorado Denver. The gauge 

was first mounted on a 0.97-by-3.0-inch (25-by-76-mm) patch of a lightweight nonwoven 

geotextile (see figure 120 and figure 121). A microcrystalline wax and rubber coating 

(M-Coat B Nitrile Rubber) were used to protect the gauges from moisture. To check the 

effectiveness of the moisture protection technique, the geotextile specimens with the 

strain gauges were tested after immersion in water for 24 h. Before placing the 

reinforcement sheet in the test specimen, an M-Coat FB-2 butyl rubber tape was used to 

protect the gauges during compaction (see figure 121). To measure the strain distribution 

of the reinforcement, six strain gauges were mounted on each Geotex® 4×4 sheet 

(see figure 122).
72

FRONT VIEW

SIDE VIEW

Cross Section A-A

TOP VIEW

72.25'' (1835.15) 47.37'' (1203.32)

1-1/4''

73.72 (1872.49)

55.12'' (1400)

5.35''

11.37

(288.92)

10.4

(264.16)

11.37

(288.92)

11.37

(288.92)

11.37

(288.92)

11.37

(288.92)

11.37

(288.92)

76.3'' (1938)

81.65'' (2073.91)

304.8

13.0

(332.1)

13.0

(332.1)

11.0

(297.4)

13.0

(332.1)

2.34

(59.49)

LVDT

Dial Indicator

13.0

(332.1) 304.8

2.34

(59.49)

11.0

(297.4)

13.0

(332.1)

13.0

(332.1)

Dial Indicator

LVDT

13.0

(332.1)

76.3'' (1938)

81.65'' (2073.91)

13.0

(332.1) 304.8

304.8

Dial Indicator

13.0

(332.1)

13.0

(332.1)

11.0

(297.4)

2.34

(59.49)

5.35''

55.12'' (1400)

72.25'' (1835.15)

2.34

(59.49)

11.0

(297.4)

13.0

(332.1)

13.0

(332.1)

LVDT LVDT

Dial Indicator

GSGC MASS

13.0

(332.1)

11.37

(288.92)

76.3'' (1938)

81.65'' (2073.91)

304.8

10.4

(264.16)

13.0

(332.1)

13.0

(332.1)

11.0

(297.4)

2.34

(59.49)

11.37

(288.92)

11.37

(288.92)

11.37

(288.92)

11.37

(288.92)

11.37

(288.92)

Dial Indicator

2''

LVDT

LVDTs on the 

open side

Dial Indicator on 

the open side6''

Dial Indicator on 

the top surface

LVDT on the top 

surface 

LVDT on the top surface (the 

location can be adjusted 

dependent on the size of the 

loading system)

Footing on the top 

of GRS specimen

A

Jack

Center line

6''

Dial Indicator

4''

4''

Dial Indicator on 

the top surface

Location of LVDTs and Dial Indicators

Figure 119. Illustration. Locations of LVDTs and digital dial indicators.

Figure 120. Photo. Strain gauge on Geotex® 4×4 geotextile before applying protection tape.
73

Figure 121. Photo. Strain gauge on Geotex® 4×4 geotextile after applying protection tape.

Figure 122. Photo. Strain gauges mounted on Geotex® 4×4 geotextile.

Due to the presence of the lightweight geotextile patch, calibration of the strain gauge was 

needed. The calibration tests were performed to relate the strain obtained from the strain gauge to 

the actual strain of the reinforcement. Figure 123 and figure 124 show the calibration curves 

along the fill direction of Geotex® 4×4 geotextile for the single-sheet and double-sheet 

specimens, respectively.
74

Figure 123. Graph. Calibration curve for single-sheet Geotex® 4×4.

Figure 124. Graph. Calibration curve for double-sheet Geotex® 4×4.

y = 1.172x

R2

 = 0.9913

0

1

2

3

4

5

6

0 1 2 3 4 5

Strain from Strain Gage (%)

Strain from Instron Machine (%)

y = 1.078x

R2 = 0.9986

0

1

2

3

4

5

6

0 1 2 3 4 5

Strain from Strain Gauge (%)

Strain from Instron Machine (%)
75

4.5.4 Preparation of Test Specimen for GSGC Tests

The preparation procedure of a typical composite mass with the dimensions of 6.6 by 4.6 by 

3.9 ft (2.0 by 1.4 by 1.2 m) is as follows:

1. Mark the anticipated location of the GSGC mass on the Plexiglas®.

2. Apply approximately 0.04-inch (1-mm)-thick lubricating agent (Dow Corning® 4 

Electrical Insulating Compound NSF 61) evenly on the inside surfaces of the Plexiglas®

(see figure 125).

Figure 125. Photo. Applying grease on Plexiglas® surfaces.

3. Attach a sheet of membrane (with 2.0-by-2.0-inch (51-by-51-mm) grid system predrawn on 

membrane) over each Plexiglas® and at the bottom of the specimen (see figure 126).
76

Figure 126. Photo. Attaching membrane.

4. Lay a course of the facing blocks on the open sides of the specimen (see figure 127).

Figure 127. Photo. Placement of the first course of facing block.
77

5. Place the backfill in the test bin and compact in 0.7-ft (0.2-m) lifts (see figure 128 and 

figure 129). If needed, check and adjust the backfill moisture before compaction to achieve 

the target moisture of 5.2 percent.

Figure 128. Photo. Compacting the first lift of backfill.
78

Figure 129. Photo. Placing backfill for the second lift.

6. Check the water content and dry unit weight of each lift by using a nuclear density gauge 

(Troxler 3440) by the direct transmission method.

7. Place the next layer of geosynthetic reinforcement (with strain gauges already mounted), 

covering the entire top surface area of compacted fill and the facing blocks (see figure 130).

Figure 130. Photo. Placing a reinforcement sheet.
79

8. Repeat steps 4 to 8 until the full height of the composite mass is reached.

9. Sprinkle a 0.2-inch (5-mm)-thick fine sand layer over the top surface of the completed 

composite mass to level the surface and protect the membrane from being punctured by 

gravel in the backfill (see figure 131).

Figure 131. Photo. Completion of compaction of the composite mass and leveling the top 

surface with 0.2-inch (5-mm)-thick sand layer.

10. Place a geosynthetic sheet on top of the composite mass (see figure 132).

Figure 132. Photo. Completed composite mass with a geotextile sheet on the top surface.
80

11. Glue a sheet of membrane to the top edge of the side membrane sheets (see figure 133).

Figure 133. Photo. Top surface of the composite mass covered with a sheet of membrane.

12. Remove all facing blocks and trim off the excess geotextile (see figure 134).

Figure 134. Photo. Removing facing blocks and trimming off excess 

geosynthetic reinforcement.

13. Insert strain gauge cables through the plastic openings that were already attached on the 

membrane sheets at prescribed locations (see figure 135).
81

Figure 135. Photo. Inserting strain gauge cables through the membrane sheet.

14. Glue membrane sheets to enclose entire composite mass.

15. Apply vacuum to the composite mass at a low pressure of 2.0 psi (14 kPa) (see figure 136).

Figure 136. Photo. Vacuuming the composite mass with a low pressure.

16. Seal the connection between cables and membrane with epoxy to prevent air leaks 

(see figure 137). The low vacuum pressure allows the epoxy to seal the connection well.
82

Figure 137. Photo. Sealing the connection between cable and membrane 

with epoxy to prevent air leaks.

17. Raise the vacuum pressure to 4.9 psi (34 kPa) and check air leaks under vacuuming 

(see figure 138). Measure the specimen dimensions (see table 7 for specimen dimensions 

of five tests).

Figure 138. Photo. Checking air leaks under vacuuming.
83

Table 7. Dimensions of the GSGC specimens before loading.

Test

Height,

inches (m)

Width,

inches (m)

Length,

inches (m)

Test 1 76.25 (1.937) 57.00 (1.448) 47.00 (1.194) 

Test 2 76.35 (1.939) 54.00 (1.372) 46.75 (1.187) 

Test 3 76.35 (1.939) 53.00 (1.346) 46.75 (1.187) 

Test 4 76.30 (1.938) 58.75 (1.492) 46.75 (1.187) 

Test 5 76.35 (1.939) 49.00 (1.245) 46.75 (1.187) 

Figure 139 shows the LVDTs to monitor the lateral movement of a test specimen. The locations 

of the selected points for the tests are depicted in figure 140. The measured dry unit weights of 

five tests are shown in figure 141.

Figure 139. Photo. LVDTs on an open side of test specimen.
84

2.50

2.50 24.50

42.00

66.00

16.00

1 2 3

4 5 6

7 8 9

2x2'' Grid System

10.25

60.25

34.25

32.50

54.00

16.00

42.00

31.38

3.38

3.38

4

7

10.35

10

1

5 6

34.35

8 9

2x2'' Grid System

11

2 3

(b): Tests 3,4 and 5

Width

Width

Heigth = 76.25 in. (Test 1), 76.35 in. (Test 2) Height = 76.30 in.

15.38

(a): Tests 1 and 2

1 mm = 0.039 inches

Figure 140. Illustration. Locations of selected points to trace internal movement of 

tests 1–5.
85

1 m = 3.28 ft

1 kN/m3 = 0.006 kip/ft3

Figure 141. Graph. Soil dry unit weight results during specimen preparation.

4.6 TEST RESULTS 

4.6.1 Test 1—Unreinforced Soil

Test 1 is perhaps the largest plane-strain test for soil with a confining pressure. It was conducted 

as the baseline for the other four GSGC tests.

The loading sequence of the soil mass was as follows:

• Loading up to a vertical pressure of 36 psi (250 kPa) (nearly 1 percent vertical strain).

• Unloading to zero.

• Reloading until a failure pressure of 110 psi (770 kPa) was reached.

The soil mass at failure is shown in figure 142. Figure 143 shows the global vertical stress-strain 

relationship, and figure 144 shows the volume change relationships of the soil mass. The average 

lateral displacements on the open faces of the soil mass under different vertical stresses, 

measured by LVDTs, are presented in figure 145. The internal displacements of the soil at 

selected points under vertical applied pressures of 28, 45, 90, and 110 psi (190, 310, 620, 

and 770 kPa) are shown in figure 146. The test 1 results for unreinforced soil are summarized 

in table 8.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

15 18 21 24 27 30

Dry Unit Weight (kN/m3)

Specimen Height (m)

Test 1

Test 2

Test 3

Test 4

Test 5
86

Figure 142. Photo. Soil mass at failure of test 1.

1 kPa = 0.145 psi

Figure 143. Graph. Test 1 unreinforced soil mass global vertical stress/vertical strain 

relationship.

0

100

200

300

400

500

600

700

800

900

0 1 2 3 4 5 6

Global Vertical Strain (%)

Applied Vertical Stress (kPa)
87

Figure 144. Graph. Test 1 unreinforced soil mass global volume change strain relationship.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 145. Graph. Lateral displacements on the open face of test 1. 

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3 3.5

Global Vertical Strain (%)

Volumetric Strain (%)

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0 10 20 30 40 50

Lateral Displacement (mm)

Specimen Height (m)

200 kPa

400 kPa

600 kPa

770 kPa

700 kPa

Applied Pressure:
88

76.25

Test 1

57.00

2.50

2.50

42.00

66.00

16.00

1

2'' x 2'' Grid System

10.25

34.25

32.50

4 5 6

2 3

7 8 9

Before Loading

190 kPa (75 kips)

310 kPa (120 kips)

620 kPa (240 kips)

770 kPa (300 kips)

Legend:

(All Displacements in inches, Drawn to Scale of the Soil Mass)

Note:

1 N = 0.00022 kip

1 mm = 0.039 inches

Figure 146. Illustration. Internal displacements of test 1.
89

Table 8. GSGC test 1 result summary. 

Parameter Measurement

Test 

condition

Geosynthetic reinforcement None

Wide-width strength of reinforcement None

Reinforcement spacing No reinforcement

Confining pressure 34 kPa

Test results

Applied stress at vertical strain of 1 percent 335 kPa 

Ultimate applied pressure 770 kPa

Vertical strain at failure 3 percent

Maximum lateral displacement of the open 

face at failure 47 mm

Stiffness at 1 percent vertical strain (Eat 1%) 33,500 kPa

Stiffness for unloading-reloading (Eur) 87,100 kPa

1 mm = 0.039 inches

1 kPa = 0.145 psi

4.6.2 Test 2—GSGC Test (T, Sv)

In the second test, the GSGC mass was reinforced by nine sheets of single-sheet Geotex® 4×4 

with spacing of 0.7 ft (0.2 m). The soil layer was compacted at 0.7-ft (0.2-m)-thick lifts. Each 

reinforcement sheet was mounted with 54 strain gauges.

The failure load in this test was 1,000,000 lb (454,000 kg). All nine reinforcement sheets were 

ruptured after testing. The composite mass after testing is shown in figure 147. The shear bands 

of the composite mass after testing are visible through the diagonal lines of the mass (see 

figure 147 and figure 148). Along the shear bands, the square grids of 2 by 2 inches (51 by 

51 mm) were severely distorted after testing (see figure 148). These shear bands correspond 

exactly with the failure surfaces shown in figure 149.
90

Figure 147. Photo. Composite mass at failure of test 2.
91

Figure 148. Photo. Close-up of shear bands at failure of area A in figure 147.
92

Figure 149. Photo. Failure planes of the composite mass after testing in test 2.

The measured data from test 2 were as follows:

• Global stress-strain relationship: Figure 150 and figure 151 show the global stressstrain relationship of the composite up to and after failure. The maximum applied vertical 

pressure was about 390 psi (2,700 kPa), and the corresponding vertical displacement was 

4.88 inches (125 mm) (6.5 percent vertical strain).

• Lateral displacement: The average lateral displacement profiles are on the open faces 

of the composite under different vertical pressures, as shown in figure 152. The lateral 
93

displacements were nearly uniform along the height of the composite up to a pressure 

of about 87 psi (600 kPa). At vertical pressures between 110 and 220 psi (770 and 

1,500 kPa), the maximum lateral displacement occurred at about 3

/8 H from the 

base, where H is the height of the composite mass. The locations of the maximum 

displacements were about the same as those of test 1 (unreinforced). The maximum 

lateral displacement at the mid-height of the composite under the applied pressure of

390 psi (2,700 kPa) was 2.3 inches (60 mm).

• Internal displacement: The internal displacements of the composite mass at selected 

points under vertical applied pressures of 39 to 390 psi (270 to 2,700 kPa) at increments 

of 39 psi (270 kPa) are shown in figure 153. At points near the open faces—1 and 3, 

4 and 6, and 7 and 9—the displacements moved downward and outward with angles that 

were measured after testing of about 67, 47, and 31 degrees, respectively, to the 

horizontal. The vertical displacements of the points at the upper part of the soil mass were 

greater than those at the lower part. Along the center line, there were only vertical 

displacements for points 2, 5, and 8. There was almost no displacement at point 8 near 

the bottom and at the center line. The maximum lateral displacement in the soil body was 

3.3 inches (60 mm) at mid-height on the open sides, and the maximum vertical 

displacement was 4.87 inches (125 mm) at the top of the specimen.

• Reinforcement strain: Figure 154 shows the locations of the strain gauges on the 

geosynthetic sheets. The strain in the reinforcement of the GSGC mass is shown in 

figure 155 through figure 163. Most of the strain gauges performed well at strains less 

than 4 percent. All reinforcement layers were found ruptured after the test was 

completed. The locations of the rupture lines can be seen from the aerial view of the 

reinforcement sheets exhumed from the composite after testing (see figure 164). Based 

on the locations of the rupture lines, the rupture planes can be constructed as shown in 

figure 165. This figure agrees perfectly with the shear bands shown in figure 149. The 

maximum strain in reinforcement at rupture was about 12 percent, while the measured 

data from the strain gauges were less than 4 percent. The strain distributions in figure 155

through figure 163 show that the locations of the maximum strain in reinforcement were 

different between layers. In reinforcement layers near at the mid-height of the GSGC 

mass (2.6 and 3.3 ft (0.8 and 1.0 m) from the base), the maximum reinforcement strains 

were close to the centerline. In the reinforcement layers near the top and the base of the 

GSGC mass (0.7 and 5.9 ft (0.2 and 1.8 m) from the base), the maximum reinforcement 

strains were at about 1 ft (0.3 m) from the edge of the composite mass. The maximum 

strain locations in all reinforcement layers were at the ruptured lines of reinforcement, 

as shown in figure 164 and figure 165.
94

1 kPa = 0.145 psi

Figure 150. Graph. Test 2 reinforced soil mass global vertical stress-vertical strain 

relationship.

Figure 151. Graph. Test 2 reinforced soil mass global volume change strain relationship.

0

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5 6 7 8 9

Global Vertical Strain (%)

Applied Vertical Stress (kPa)

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 1 2 3 4 5 6 7

Global Vertical Strain (%)

Volumetric Strain (%)
95

1 m = 3.28 ft

1 mm = 0.039 inches

1 kPa = 0.145 psi

Figure 152. Graph. Lateral displacements on the open face of test 2.
96

2'' x 2'' Grid System

76.35

Test 2

54.00

3.00

3.00

38.00

66.00

16.00

1 2 3

4 5 6

7 8 9

10.35

38.35

31.00

Before Loading

270 kPa

540 kPa

2,700 kPa

...

Legend:

(All Displacements in inches, Drawn to Scale of the Composite Mass)

Note:

1 mm = 0.039 inches

1 kPa = 0.145 psi

Figure 153. Illustration. Internal displacements of test 2.
97

Strain Gages

11.00 8.00 8.00 8.00 8.00 11.00

54

7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63

Sheet No 9

Sheet No 8

Sheet No 7

Sheet No 6

Sheet No 5

Sheet No 4

Sheet No 3

Sheet No 2

Sheet No 1

Reinforcement

(Note: All Dimensions in inches)

1 mm = 0.039 inches

Figure 154. Illustration. Locations of strain gauges on geosynthetic sheets in test 2.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 155. Graph. Reinforcement strain distribution of the composite mass in layer 1 of 

test 2 0.7 ft (0.2 m) from the base.
98

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 156. Graph. Reinforcement strain distribution of the composite mass in layer 2 of 

test 2 1.3 ft (0.4 m) from the base.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 157. Graph. Reinforcement strain distribution of the composite mass in layer 3 of 

test 2 2 ft (0.6 m) from the base.
99

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 158. Graph. Reinforcement strain distribution of the composite mass in layer 4 of 

test 2 2.6 ft (0.8 m) from the base.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 159. Graph. Reinforcement strain distribution of the composite mass in layer 5 of 

test 2 3.3 ft (1.0 m) from the base.
100

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 160. Graph. Reinforcement strain distribution of the composite mass in layer 6 of 

test 2 3.9 ft (1.2 m) from the base.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 161. Graph. Reinforcement strain distribution of the composite mass in layer 7 of 

test 2 4.6 ft (1.4 m) from the base.
101

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 162. Graph. Reinforcement strain distribution of the composite mass in layer 8 of 

test 2 5.2 ft (1.6 m) from the base.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 163. Graph. Reinforcement strain distribution of the composite mass in layer 9 

of test 2 5.9 ft (1.8 m) from the base.
102

Figure 164. Photo. Aerial view of the reinforcement sheets exhumed from the composite 

mass after test 2 (numbers indicate sheet number).
103

Rupture Lines

54

7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63

1

2

3

4

5

6

7

8

9

Reinforcement

(Note: All Dimensions in inches, Drawn to Scale)

1 mm = 0.039 inches

Figure 165. Illustration. Locations of rupture lines of reinforcement in test 2 

based on figure 164.

The results of test 2 are summarized in table 9.

Table 9. GSGC test 2 results summary.

Parameter Measurement

Test 

condition

Geosynthetic reinforcement Geotex® 4×4

Wide-width strength of reinforcement 70 kN/m

Reinforcement spacing 0.2 m

Confining pressure 34 kPa

Test results

Ultimate applied pressure 2,700 kPa

Vertical strain at failure 6.5 percent

Maximum lateral displacement of the open 

face at failure 60 mm

Stiffness at 1 percent vertical strain (Eat 1%) 61,600 kPa

Maximum strain in reinforcement at ruptured 12 percent

Maximum measured strain in reinforcement 4.0 percent

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 kPa = 0.145 psi

1 mm = 0.039 inches
104

4.6.3 Test 3—GSGC Test (2T, 2Sv)

In this test, the GSGC mass was reinforced by four double sheets of Geotex® 4×4 at a 1.31-ft

(0.4-m) spacing. The strength and stiffness of the double-sheet reinforcement were nearly 

doubled compared to those of the single-sheet reinforcement used in test 2. The GSGC mass 

after testing is shown in figure 166.

Figure 166. Photo. Composite mass after testing of test 3.

The measured data of test 3 were as follows:

• Global stress-strain relationship: The maximum applied vertical pressure was about 

254 psi (1,750 kPa), as shown in figure 167. The vertical displacement at the failure 

pressure was 4.6 inches (118 mm) (6.1 percent global vertical strain).
105

• Lateral displacement: The average lateral displacement profiles on the open faces of 

the composite under different vertical pressures are shown in figure 168. The maximum 

lateral displacement under the failure pressure of 254 psi (1,750 kPa) was 2.1 inches 

(54 mm). 

• Internal displacement: Internal displacements at selected points are shown in 

figure 169. The trend of the internal movements in test 3 was nearly the same as in test 2. 

For points 1, 3, 4, 5, 6, 7, and 9 near the open faces, the displacements moved downward 

and outward with angles from 49 to 71 degrees to the horizontal. For points 2, 5, and 8 

along the center line, the displacements were almost vertical. The maximum vertical 

displacement at the top of the specimen was 4.6 inches (118 mm).

• Reinforcement strain: Figure 170 shows the locations of the strain gauges on the 

geosynthetic sheets. The strain in the reinforcement of the GSGC mass is shown in 

figure 171 through figure 174. Three reinforcement layers near the top of the composite 

were ruptured after testing. Figure 175 shows an aerial view of the locations of the 

rupture line on the reinforcement sheets exhumed from the composite after testing. Based 

on the locations of the rupture line, the rupture planes can be constructed, as shown in 

figure 176. This rupture line agrees perfectly with the failure line in figure 166. The 

maximum strain in reinforcement was 4 percent and was located near the ruptured line, as 

shown in figure 176. 

1kPa = 0.145 psi

Figure 167. Graph. Global stress-strain relationship of test 3.

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

Global Vertical Strain (%)

Applied Vertical Stress (kPa)
106

1 m = 3.28 ft

1 mm = 0.039 inches

1 kPa = 0.145 psi

Figure 168. Graph. Lateral displacements on the open face of test 3.

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

0.0 10.0 20.0 30.0 40.0 50.0 60.0

Lateral Displacement (mm)

Specimen Height (m)

260 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

1250 kPa

1500 kPa

1750 kPa

Applied Pressure:
107

76.35

Test 3

53.00

2.50

2.50

42.00

66.00

16.00

2x2'' Grid System

10.35

60.36

34.35

54.00

1 2

4

10 11

5 6

7 8 9

2'' x 2'' Grid System

3

30.50

Before Loading

280 kPa

560 kPa

840 kPa

1120 kPa

1400 kPa

1680 kPa

1750 kPa

14.5

Legend:

(All Displacements in inches, Drawn to Scale of the Composite Mass)

Note:

1 mm = 0.039 inches

1 kPa = 0.145 psi

Figure 169. Illustration. Internal displacements of test 3.
108

Strain Gages

10.50 8.00 8.00 8.00 8.00 10.50

53.00

15.25 15.25 15.25 15.25 15.25

Sheet No 4

Sheet No 3

Sheet No 2

Sheet No 1

Reinforcement

(Note: All Dimensions in inches)

1 mm= 0.039 inches

Figure 170. Illustration. Location of strain gauges on geosynthetic sheets in test 3.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 171. Graph. Reinforcement strain distribution of the composite mass in layer 1 of 

test 3 1.3 ft (0.4 m) from the base.
109

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 172. Graph. Reinforcement strain distribution of the composite mass in layer 2 of 

test 3 2.6 ft (0.8 m) from the base.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 173. Graph. Reinforcement strain distribution of the composite mass in layer 3 of 

test 3 3.9 ft (1.2 m) from the base.
110

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 174. Graph. Reinforcement strain distribution of the composite mass in layer 4 of 

test 3 5.2 ft (1.6 m) from the base.
111

Figure 175. Photo. Aerial view of the reinforcement sheets exhumed from the composite 

mass after test 3 (numbers indicate sheet number).
112

53

Test 3

Rupture Lines

15.25 15.25 15.25 15.25 15.25

1

2

3

4

Reinforcement

(Note: All Dimensions in inches, Drawn to Scale)

1 mm = 0.039 inches

Figure 176. Illustration. Locations of rupture lines of reinforcement in test 3 based on 

figure 175.

The results of test 2 are summarized in table 10.

Table 10. Test 3 result summary.

Parameter Measurement

Test 

conditions

Geosynthetic reinforcement Geotex® 4×4

Wide-width strength of reinforcement 140 kN/m

Reinforcement spacing 0.4 m

Confining pressure 34 kPa

Test results

Ultimate applied pressure 1,750 kPa

Vertical strain at failure 6.1 percent

Maximum lateral displacement of the open 

face at failure 54 mm

Stiffness at 1 percent vertical strain (Eat 1%) 48,900 kPa

Maximum strain in reinforcement at rupture 12 percent

Maximum measured strain in reinforcement 4.0 percent

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 mm = 0.039 inches

1 kPa = 0.145 psi
113

4.6.4 Test 4—GSGC Test (T, 2Sv)

The reinforcement used in this test was a single sheet of Geotex® 4×4 at spacing of 1.3 ft 

(0.4 m). The composite mass after testing is shown in figure 177 and figure 178. The failure 

surfaces can be seen clearly in the figures.

Figure 177. Photo. Front view of failure planes of the composite mass after test 4.

Figure 178. Photo. Back view of failure planes of the composite mass after test 4.
114

The measured data for test 4 are as follows:

• Global stress-strain relationship: The maximum applied vertical pressure was about 

190 psi (1,300 kPa), as shown in figure 179. The vertical displacement at the failure 

pressure was 3.0 inches (77 mm) (4.0 percent global vertical strain). 

• Lateral displacement: The average lateral displacements on the open faces of the 

composite mass under different vertical pressures are shown in figure 180. The 

maximum lateral displacement under the failure pressure was 2.0 inches (52 mm).

• Internal displacements: Internal displacements at selected points are shown in 

figure 181. The trends of the internal movements in tests 2, 3, and 4 were identical. For 

points 1, 3, 4, 5, 6, 7, and 9 near the open faces, the displacements moved downward and 

outward with angles from 30 to 63 degrees to the horizontal. For points 2, 5, and 8 along 

the center line, the displacements were almost vertical. The maximum vertical 

displacement at the top of the specimen was 3.0 inches (77 mm).

• Reinforcement strain: Figure 182 shows the locations of the strain gauges on the 

geosynthetic sheets. The strain in the reinforcement of the GSGC mass is shown in 

figure 183 through figure 186. All reinforcement layers near the top of the composite 

were ruptured after the test was completed. The locations of the rupture lines are shown 

in figure 187. Based on the locations of the rupture line, the rupture planes can be 

constructed, as shown in figure 188. This rupture line agrees perfectly with the failure 

line in figure 177 and figure 178. The maximum strain in reinforcement at rupture was 

about 12 percent and located near the rupture line, as shown in figure 188.

1 kPa = 0.145 psi

Figure 179. Graph. Global stress-strain relationship of test 4.

0

200

400

600

800

1,000

1,200

1,400

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Global Vertical Strain (%)

Applied Vertical Stress (kPa)
115

1 m = 3.28 ft

1 mm = 0.029 inches

1 kPa = 0.145 psi

Figure 180. Graph. Lateral displacements on the open face of test 4.
116

76.30

Test 4

58.00

3.00

3.00

42.00

16.00

10.35

34.35

54.00

15.00

31.00

1 2

10

4 5

11

6

7 8 9

2'' x 2'' Grid System

3

Before Loading

250 kPa

500 kPa

750 kPa

1000 kPa

1250 kPa

1300 kPa

Legend:

Note:

(All Displacements in inches, Drawn to Scale of the Composite Mass)

1 mm = 0.039 inches

1 kPa = 0.145 psi

Figure 181. Illustration. Internal displacements of test 4.
117

Strain Gages

13.35 8.00 8.00 8.00 8.00 13.35

58.75

15.25 15.25 15.25 15.25 15.25

Sheet No 4

Sheet No 3

Sheet No 2

Sheet No 1

Reinforcement

(Note: All Dimensions in inches)

1 mm = 0.039 inches

Figure 182. Illustration. Locations of strain gauges on geosynthetic sheets in test 4.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 183. Graph. Reinforcement strain distribution of the composite mass in layer 1 of 

test 4 1.3 ft (0.4 m) from the base.
118

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 184. Graph. Reinforcement strain distribution of the composite mass in layer 2 of 

test 4 2.6 ft (0.8 m) from the base.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 185. Graph. Reinforcement strain distribution of the composite mass in layer 3 of 

test 4 3.9 ft (1.2 m) from the base.
119

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 186. Graph. Reinforcement strain distribution of the composite mass in layer 4 of 

test 4 5.2 ft (1.6 m) from the base.

Figure 187. Photo. Aerial view of the reinforcement sheets exhumed from the composite 

mass after test 4 (numbers indicate sheet number).
120

53

Test 3

Rupture Lines

15.25 15.25 15.25 15.25 15.25

1

2

3

4

Reinforcement

(Note: All Dimensions in inches, Drawn to Scale)

1 mm = 0.039 inches

Figure 188. Illustration. Locations of rupture lines of reinforcement in test 4 

based on figure 187.

The test 4 results are summarized in table 11.

Table 11. GSGC test 4 result summary.

Parameter Measurement

Test 

conditions

Geosynthetic reinforcement Geotex® 4×4

Wide-width strength of reinforcement 70 kN/m

Reinforcement spacing 0.4 m

Confining pressure 34 kPa

Test results

Ultimate applied pressure 1,300 kPa

Vertical strain at failure 4.0 percent

Maximum lateral displacement of the open 

face at failure 53 mm

Stiffness at 1 percent vertical strain (Eat 1%) 46,600 kPa

Maximum strain in reinforcement at rupture 12 percent

Maximum measured strain in reinforcement 2.0 percent

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 mm = 0.039 inches

1 kPa = 0.145 psi
121

4.6.5 Test 5—GSGC Test (Unconfined with T, Sv)

The configuration of this test was the same as test 2. The reinforcement was single-sheet 

Geotex® 4×4 at a spacing of 0.6 ft (0.2 m). Confining pressure was not applied for this test. 

Without applying confining pressure, the soil on the open faces fell off continuously with 

increasing applied pressure. The composite mass and failure surfaces after testing are shown 

in figure 189 through figure 191.

Figure 189. Photo. Composite mass at failure of test 5.
122

Figure 190. Photo. Front view of failure planes of the composite mass after test 5.

Figure 191. Photo. Back view of failure planes of the composite mass after test 5.

The measured data of test 5 are as follows: 

• Global stress-strain relationship: The maximum applied vertical pressure was about 

270 psi (1,900 kPa), as shown in figure 192. The vertical displacement at the failure 

pressure was 4.33 inches (111 mm) (6.0 percent global vertical strain).
123

• Lateral displacement: The average lateral displacements on the open faces of the 

composite mass under different vertical pressures are shown in figure 193. The maximum 

lateral displacement at the open faces under the failure pressure could not be measured 

because the soil at these faces dropped during testing under the high applied pressures.

• Internal displacements: Internal displacements at selected points are shown in 

figure 194. The trend of the internal movements in test 5 was nearly the same as that in 

tests 2, 3, and 4. For points 1, 3, 4, 5, 6, 7, and 9 near the open faces, the displacements 

move downward and outward with angles of 35 to 63 degreesto the horizontal. For points 

2, 5, and 8 along the center line, the displacements were almost vertical. The maximum 

vertical displacement at the top of the specimen was 4.33 inches (111 mm).

• Reinforcement strain: Figure 195 shows the locations of the strain gauges on the 

geosynthetic sheets. The strain in the reinforcement of the GSGC mass is shown in 

Figure 196 through figure 198. Eight reinforcement layers near the top of the composite 

were ruptured after testing. Figure 199 shows the locations of the rupture lines from an 

aerial view of the reinforcement sheets exhumed from the composite after testing. Based 

on the locations of the rupture line, the rupture planes can be constructed (see figure 200). 

This rupture line agrees perfectly with the failure line in figure 189. The maximum strain 

in reinforcement measured was 3.2 percent and located at near the rupture line, as shown 

in figure 200.

1 kPa = 0.145 psi

Figure 192. Graph. Global stress-strain relationship of test 5.

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

2,200

0 1 2 3 4 5 6 7 8

Global Vetical Strain (%)

Applied Vertical Stress (kPa)
124

1 m = 3.28 ft

1 mm = 0.039 inches

1 kPa = 0.145 psi

Figure 193. Graph. Lateral displacements on the open face of test 5.

0.000

0.250

0.500

0.750

1.000

1.250

1.500

1.750

2.000

0.0 10.0 20.0 30.0 40.0

Lateral Displacement (mm)

Specimen Height (m)

200 kPa

400 kPa

600 kPa

1500 kPa

Applied Pressure:
125

76.35

Test 5

49.00

2.50

2.50

42.00

16.00

10.35

60.35

34.35

12.50

28.50

54.00

1

10

2 3

11

4 5 6

7 8 9

2'' x 2'' Grid System

Before Loading

300 kPa

600 kPa

900 kPa

1200 kPa

1500 kPa

1800 kPa

Legend:

(All Displacements in inches, Drawn to Scale of the Composite Mass)

Note:

1 mm = 0.039 inches

1 kPa = 0.145 psi

Figure 194. Illustration. Internal displacements of test 5.
126

Strain Gages

8.50 8.00 8.00 8.00 8.00 8.50

49.00

15.25 15.25 15.25 15.25 15.25

Sheet No 9

Sheet No 8

Sheet No 7

Sheet No 6

Sheet No 5

Sheet No 4

Sheet No 3

Sheet No 2

Sheet No 1

Reinforcement

(Note: All Dimensions in inches)

1 mm = 0.039 inches

Figure 195. Illustration. Locations of strain gauges on geosynthetic sheets in test 5.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 196. Graph. Reinforcement strain distribution of the composite mass in layer 1 of 

test 5 1.3 ft (0.4 m) from the base.

0

0.5

1

1.5

2

2.5

3

3.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Distance from the Edge of the Composite Mass (m)

Strain (%)

100 kPa

200 kPa

300 kPa

400 kPa

500 kPa

600 kPa

750 kPa

Applied Pressure:
127

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 197. Graph. Reinforcement strain distribution of the composite mass in layer 2 of 

test 5 2.6 ft (0.8 m) from the base.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 198. Graph. Reinforcement strain distribution of the composite mass in layer 3 of 

test 5 3.9 ft (1.2 m) from the base.

0

0.5

1

1.5

2

2.5

3

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Distance from the Edge of the Composite Mass (m)

Strain (%)

100 kPa

200 kPa

300 kPa

400 kPa

500 kPa

600 kPa

750 kPa

Applied Pressure:

0

0.2

0.4

0.6

0.8

1

1.2

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Distance from the Edge of the Composite Mass (m)

Strain (%)

100 kPa

200 kPa

300 kPa

400 kPa

525 kPa

Applied Pressure:
128

Figure 199. Photo. Aerial view of the reinforcement sheets exhumed from the composite 

mass after test 5 (numbers indicate sheet number). 

Rupture Lines

49

7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63

1

2

3

4

5

6

7

8

9

Test 5

Reinforcement

(Note: All Dimensions in inches, Drawn to Scale)

1 mm = 0.039 inches

Figure 200. Illustration. Locations of rupture lines of reinforcement in test 5 based on 

figure 199.
129

The test results of test 5 are summarized in table 12.

Table 12. GSGC test 5 result summary.

Parameter Measurement

Test 

condition

Geosynthetic reinforcement Geotex® 4×4

Wide-width strength of reinforcement 70 kN/m

Reinforcement spacing 0.2 m

Confining pressure 0

Test results

Ultimate applied pressure 1,900 kPa

Vertical strain at failure 6.0 percent

Maximum lateral displacement of the open 

face at failure Not measured

Stiffness at 1 percent vertical strain (Eat 1%) 52,900 kPa

Maximum strain in reinforcement at ruptured 12 percent

Maximum measured strain in reinforcement 3.2 percent

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 kPa = 0.145 psi

4.7 DISCUSSION OF THE RESULTS

The results of the GSGC tests are discussed in terms of the following:

• Effects of geosynthetic inclusion (comparison between tests 1 and 2).

• Relationship between reinforcement spacing and reinforcement strength 

(comparison between tests 2 and 3). 

• Effects of reinforcement spacing (comparison between tests 2 and 4).

• Effects of reinforcement stiffness (comparison between tests 3 and 4).

• Effects of confining pressure (comparison between tests 2 and 5).

• Composite strength properties.

4.7.1 Effects of Geosynthetic Inclusion (Comparison Between Tests 1 and 2)

Table 13 shows the result comparisons between an unreinforced soil mass (test 1) and a soil mass 

reinforced by Geotex® 4×4 at a 0.7-ft (0.2-m) spacing (test 2). The reinforced soil was much 

stronger than the unreinforced soil. The ultimate applied pressure for the GSGC mass was about 

3.5 times as large as the strength of the soil mass without reinforcement. The stiffness of the 

unreinforced soil mass was 50 percent of that for the reinforced soil mass. In addition, the 

reinforced soil mass was much more ductile than the unreinforced soil mass. The global vertical 

strain was 6.5 percent at failure for test 2, whereas it was only 3.0 percent for test 1.
130

Table 13. Comparison between test 1 and test 2.

Parameter Test 1 Test 2 (T, Sv)

Geosynthetic reinforcement None Geotex® 4×4

Wide-width strength of reinforcement None Tf = 70 kN/m

Reinforcement spacing No reinforcement Sv = 0.2 m

Confining pressure 34 kPa 34 kPa

Ultimate applied pressure 770 kPa 2,700 kPa

Vertical strain at failure 3 percent 6.5 percent

Maximum lateral displacement of the open 

face at failure 47 mm 60 mm

Stiffness at 1 percent vertical strain (Eat 1%) 33,500 kPa 61,600 kPa

Stiffness for unloading-reloading (Eur) 87,100 kPa Not applied

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft.

1 kPa = 0.145 psi

1 mm = 0.039 inches

4.7.2 Relationship Between Reinforcement Spacing and Reinforcement Strength 

(Comparison Between Tests 2 and 3)

Comparing the results of tests 2 and 3 demonstrates the relationship between reinforcement 

spacing and reinforcement strength (see table 14). As noted in section 2.1, the current design 

methods are based on the concept that reinforcement spacing and reinforcement strength play an 

equal role in the performance of a GRS mass. In other words, a GRS wall with reinforcement 

strength Tf at spacing Sv will behave the same as the one with reinforcement strength of 2 × Tf at 

spacing 2 × Sv. The results of tests 2 and 3 demonstrate that this assumption is incorrect. Even 

with the same Tf /Sv ratio (7.3 kip/ft2 (350 kN/m2

)) in tests 2 and 3, the stiffness and strength of 

test 2 (with Tf and Sv = 0.7 ft (0.2 m)) was much higher than that of test 3 (with 2Tf and Sv = 

1.3 ft (0.4 m)). The strength of the composite mass in test 3 was only 65 percent of the strength 

in test 2. These results suggest that reinforcement spacing plays a more important role than 

strength of reinforcement in a reinforced soil mass.
131

Table 14. Comparison between test 2 and test 3 with the same Tf /Sv ratio.

Parameter Test 2 (T, Sv) Test 3 (2T, 2Sv)

Wide-width strength of reinforcement (Tf) 70 kN/m 140 kN/m

Reinforcement spacing (Sv) 0.2 m 0.4 m

Tf /Sv 350 kPa 350 kPa

Confining pressure 34 kPa 34 kPa

Ultimate applied pressure 2,700 kPa 1,750 kPa

Stiffness at 1 percent vertical strain (Eat 1%) 61,600 kPa 48,900 kPa

Vertical strain at failure 6.5 percent 6.1 percent

Maximum lateral displacement of the open 

face at failure 60 mm 54 mm

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 kPa = 0.145 psi

1 mm = 0.039 inches

4.7.3 Effects of Reinforcement Spacing (Comparison Between Tests 2 and 4)

The effects of reinforcement spacing can be seen by comparing the results of tests 2 and 4 

(see table 15). All test conditions in the two tests were the same except the reinforcement 

spacing. The spacing was 1.3 ft (0.4 m) in test 4 and 0.65 ft (0.2 m) in test 2. The results 

demonstrate the importance of reinforcement spacing on the behavior of a GRS mass. With 

reinforcement spacing of 0.7 ft (0.2 m), the strength of the GRS mass was about twice as high as 

the one with the 1.3-ft (0.4-m) spacing. The corresponding increase in stiffness at 1 percent strain 

was about 30 percent. The GRS mass at the 0.7-ft (0.2-m) spacing also exhibited significantly 

higher ductility than at the 1.3-ft (0.4-m) spacing.

Table 15. Comparison between test 2 and test 4.

Parameter Test 2 (T, Sv) Test 4 (T, 2Sv)

Wide-width strength of reinforcement (Tf) 70 kN/m 70 kN/m

Reinforcement spacing (Sv) 0.2 m 0.4 m

Tf /Sv 350 kPa 175 kPa

Confining pressure 34 kPa 34 kPa

Ultimate applied pressure 2,700 kPa 1,300 kPa

Vertical strain at failure 6.5 percent 4.0 percent

Maximum lateral displacement of the open 

face at failure 60 mm 53 mm

Stiffness at 1 percent vertical strain (Eat 1%) 61,600 kPa 46,600 kPa

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 kPa = 0.145 psi

1 mm = 0.039 inches

4.7.4 Effects of Reinforcement Strength (Comparison Between Tests 3 and 4)

The effects of reinforcement strength can be seen by comparing the results of tests 3 and 4 (see 

table 16). All test conditions in the two tests were identical except that reinforcement strength in 

test 3 was almost twice as high as that in test 4. The results indicate that the increase in strength 
132

of the GRS mass due to doubling the reinforcement strength was about 35 percent. This increase 

was much smaller than doubling the reinforcement spacing, where the increase in strength of the 

GRS mass was over 100 percent. The increase in stiffness at 1 percent strain due to doubling the 

reinforcement strength was only about 5 percent, compared to about a 30 percent increase due to 

doubling the reinforcement spacing.

Table 16. Comparison between test 3 and test 4.

Parameter Test 3 (2T, 2Sv) Test 4 (T, 2Sv)

Wide-width strength of reinforcement (Tf) 140 kN/m 70 kN/m

Reinforcement spacing (Sv) 0.4 m 0.4 m

Tf /Sv 350 kPa 175 kPa

Confining pressure 34 kPa 34 kPa

Ultimate applied pressure 1,750 kPa 1,300 kPa

Vertical strain at failure 6.1 percent 4.0 percent

Maximum lateral displacement of the open 

face at failure 54 mm 53 mm

Stiffness at 1 percent vertical strain (Eat 1%) 48,900 kPa 46,600 kPa

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 kPa = 0.145 psi

1 mm = 0.039 inches

4.7.5 Effects of Confining Pressure (Comparison Between Tests 2 and 5)

The effects of confining pressure can be seen by comparing the test results of tests 2 and 5 (see 

table 17). All test conditions in the two tests were identical except that the confining pressure in 

test 2 was 4.9 psi (34 kPa) and test 5 was conducted without confinement. The results indicate 

that the increase in strength due to the confining pressure was about 40 percent. The increase in 

stiffness at 1 percent strain due to the confining pressure was about 15 percent.
133

Table 17. Comparison between test 2 and test 5.

Parameter Test 2 (T, Sv) Test 5 (T, Sv)

Wide-width strength of reinforcement (Tf) 70 kN/m 70 kN/m

Reinforcement spacing (Sv) 0.2 m 0.2 m

Tf /Sv 350 kPa 350 kPa

Confining pressure 34 kPa 0

Ultimate applied pressure 2,700 kPa 1,900 kPa

Vertical strain at failure 6.5 percent 6.0 percent

Maximum lateral displacement of the open 

face at failure 60 mm Not measured

Stiffness at 1 percent vertical strain (Eat 1%) 61,600 kPa 52,900 kPa

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 kPa = 0.145 psi

1 mm = 0.039 inches

4.7.6 Composite Strength Properties

Table 18 shows a comparison of the composite strength properties of the five GSGC tests as 

obtained from the measured data and calculated from Schlosser and Long’s method by assuming 

the friction angle remains the same as unreinforced soil (i.e., the same value as in test 1).(25)

The apparent cohesion, cR, from Schlosser and Long’s method is calculated as shown in 

figure 201.

(25)

φ
134

Table 18. Comparison of strength properties of five GSGC tests.

Parameter

Test 1

(unreinforced)

Test 2

(T, Sv)

Test 3

(2T, 2Sv)

Test 4

(T, 2Sv)

Test 5

(T, Sv)

Wide-width strength of 

reinforcement, Tf (kN/m) 70 140 70 70

Reinforcement spacing, Sv (m) 0.2 0.4 0.4 0.2

Tf /Sv (kPa) 350 350 175 350

Confining pressure (kPa) 34 34 34 34 0

Apparent cohesion, cR, (kPa) by 

Schlosser and Long’s method 550 550 310 550

Ultimate applied pressure (kPa) 

from measured data 770 2,700 1,750 1,300 1,900

Ultimate applied pressure (kPa) by 

Schlosser and Long’s method 3,250 3,250 1,930 3,030

Difference in ultimate pressure 

between measured data and 

Schlosser and Long’s method 

(percent) 20 86 48 59

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 kPa = 0.145 psi

Note: Blank cells indicate parameters for which there were no measurements.

2

f

R p

v

T

c Kc

S

= +

Figure 201. Equation. Apparent cohesion from Schlosser and Long.(25)

Where:

c = Cohesion of the backfill.

Tf = Strength of reinforcement.

Sv = Reinforcement spacing.

Kp = Coefficient of passive Earth pressure.

The values calculated from Schlosser and Long’s method were higher than the measured values 

by 20 to 86 percent.
135

CHAPTER 5. ANALYTICAL MODELS FOR EVALUATING CIS, COMPOSITE 

STRENGTH PROPERTIES, AND REQUIRED REINFORCEMENT STRENGTH 

This chapter describes analytical models for evaluating CIS in a GRS mass, strength properties 

of a GRS mass, and required tensile strength of reinforcement in the design of GRS structures. 

The first analytical model is a simple compaction model that is capable of estimating CIS, 

or the increase of the horizontal stresses, in a GRS mass due to fill compaction. The model 

was developed by combining a compaction model developed by Seed, the companion handcalculation procedure for an unreinforced soil mass by Duncan and Seed, and the theory of 

GRS composite behavior proposed by Ketchart and Wu.(11,12,20)

The second analytical model is for the determination of the strength properties of a GRS 

composite mass. With the analytical model, a new relationship between reinforcement strength 

and reinforcement spacing is introduced to reflect an observation made in actual construction 

and in controlled experiments regarding the relative effects of reinforcement spacing and 

reinforcement strength on the performance of GRS structures. 

The third analytical model is for the determination of reinforcement strength in design. This 

model was also developed based on the relationship between reinforcement strength and 

reinforcement spacing.

5.1 EVALUATING CIS IN A GRS MASS

5.1.1 Conceptual Model for Simulation of Fill Compaction of a GRS Mass

Based on previous studies regarding CIS for unreinforced soil masses and very limited studies 

for reinforced soil masses, a conceptual stress path for loading-unloading-reloading of a GRS 

mass is shown in figure 202. 

σ'h = Ki,c σ'v

σv

σh

K1,c-line 

K1,c

1

B

σ'v + ∆σ'v,c,max

G

Unloading-curve

E

F

A

D

C

σ'v

Ki,c-line 

K3,c-line 

K3,c-line 

∆σ'h,c,r

Figure 202. Illustration. Conceptual stress path for compaction of a GRS mass.
136

Elements in figure 202 are as follows:

• A GRS mass is loaded (due to application of compaction loads) from an initial state 

(point A) following the Ki,c line (with horizontal stress, h Ki c v ' ' σ = , σ , where Ki,c is the 

coefficient of lateral Earth pressure of the GRS mass for initial loading) up to point B. 

At point B, the GRS mass reaches a maximum stress state with the vertical stress of 

,max , ,max ' ' ' σ v = σ v + ∆σ v c ( 'v is the vertical stress at the initial stress and 'v,c,max is 

the maximum increase in vertical stress due to compaction loading).

• Upon unloading (i.e., removal of the compaction loads), the stresses in the soil are 

reduced by following a nonlinear path from point B to point C.

• In cases of significant unloading in which the unloading path reaches the limiting line 

(K1,c) at point E, further unloading stress path will follow line EF (with h K c v ' ' σ = 1, σ ).

• Upon reloading due to the next cycle of compaction-load application, the stress follows 

a K3,c line (with h K c v ' ' σ = 3, σ ) from either point C or point F until it meets the initial 

loading path (line AB). 

• The subsequent cycles of unloading and reloading will not deviate much from the K3,c

line, as suggested by Broms, Seed, and Ehrlich and Mitchell.

(9,11,46) Therefore, the same 

K3 line can be used for all subsequent cycles of reloading and unloading.

5.1.2 Simplified Model to Simulate Fill Compaction of a GRS Mass 

A simplified compaction simulation model is proposed for simulation of fill compaction of a 

GRS mass, as depicted in figure 203. By using the proposed model, the increase of the horizontal 

stresses in a GRS mass due to compaction can be estimated. These stresses, namely CIS, are 

represented by the horizontal residual stresses, 'h,c,r, in figure 203. The proposed model is 

based on the bilinear compaction model for an unreinforced soil mass suggested by Seed and the 

companion hand-calculation procedure suggested by Duncan and Seed.(11,12) The proposed model 

considers the presence of geosynthetic inclusions. 

σ ∆σ

∆σ
137

A Unreinforced soil

σ'h = Ki,c σ'v

σ'h,c

σ'h,s

σ'v

Ki,c-line

σv

σh

1

KA

1

KA-line 

K2,c-line 

S

C

∆σ'h,s,r

B

∆σ'h,c,max

∆σ'h,c,r

σ'v + ∆σ'v,c,max

D

σ'h = K3,c σ'v

σ'h = K2,c σ'v

K3,c-line 

1

K1,c

K1,c-line 

E

F

K0

K0-line 

Figure 203. Illustration. Stress path of the proposed simplified model for fill compaction 

of a GRS mass.

The stress path for fill compaction of a GRS mass in the proposed model can be considered as a 

simplified form of the conceptual model described in section 5.1. The differences between the 

simplified model and the conceptual model are as follows:

• Upon removal of the compaction loads, the stresses in the soil are reduced by following 

the K2,c line from point B to point C, of which the vertical stress, ’v, is equal to that of 

point A. The horizontal residual stress due to the compaction loading is 'h,c,r.

• In the case of an unreinforced soil mass (or where the reinforcement stiffness is 

negligible), the stress in the soil in response to the removal of compaction loads will 

reduce to point S (instead of point C). The horizontal residual stress due to compaction 

loading will be 'h,s,r with 'h,s,r ≤ 'h,c,r.

• Upon application of the next cycle of compaction loads or placement of new fill layers, 

the reloading path will follow the K3,c line (with h K c v ' ' σ = 3, σ , and K3, c ≤ K2, c ). The 

stress path follows the K3,c line from point C or point F until it meets the initial loading 

path. It then follows the Ki,c line to a new stress state.

5.1.3 Model Parameters of the Proposed Compaction Simulation Model

Four model parameters are needed for the proposed compaction simulation model: Ki,c, K1,c, K2,c, 

and K3,c. These parameters can be estimated from soil and reinforcement properties using 

correlations shown in table 19. The empirical coefficients (e.g., and F) are calibrated by the 

measured data from the GSGC tests described in chapter 4. Recommended values of the 

empirical coefficients are given for routine applications. Alternatively, the model parameters can 

be obtained directly from the results of GSGC tests. Note that the term 















s v − r

r

E S J

E

0.7

0.7 for the 

estimation of K2, c is to account for the presence of reinforcement. For hand calculations, the 

σ

∆σ

∆σ ∆σ ∆σ

α
138

maximum increase of vertical stress due to compaction, , ,max ' ∆σ v c , can be estimated simply by 

using Westergaard's solution as shown in figure 203.

(78)

Table 19. Model parameters for the proposed compaction simulation model.

Parameter Name

Range of the

Parameter 

Values

Preliminary Estimation Based on 

Soil and Reinforcement 

Properties

Ki,c Coefficient of lateral 

Earth pressure of a 

GRS mass for initial 

loading

KA ≤ Ki,c ≤ K0 Ki,c ≅ β KA

1.0 1.5 ≤ ≤ β





 



 ≅ − 2

' tan 45 2 φ KA

1 sin ' K0 ≅ − φ

K1,c Limiting coefficient of 

lateral Earth pressure 

for unloading

K1,c ≅ KP





 



 ≅ ≅ +

2

' tan 45 2

1,

φ K c KP

K2,c Coefficient of lateral 

Earth pressure for 

unloading

0 ≤ K2,c ≤ K0

i c

s v r

r

c K

E S E

E K2, F , 0.7

1 1 0.7 



 





















− ≅ − +

( )

( 1) 1 −

− = − OCROCR OCR F

α

; α ≅ sin φ'

K3,c Coefficient of lateral 

Earth pressure for 

reloading

0 ≤ K3,c ≤ K0 K3,c ≅ K2,c

Ko = Coefficient of at-rest lateral Earth pressure.

KA = Coefficient of active lateral Earth pressure.

KP = Coefficient of passive lateral Earth pressure.

OCR = Over-consolidation ratio.

Es = Soil stiffness (kPa).

Er = Reinforcement stiffness (kN/m).

Sv = Reinforcement spacing (m).

5.1.4 Simulation of Fill Compaction Operation

Fill compaction is a complex operation in terms of change in stresses. This section describes the 

maximum increase of vertical stress at depth z along a given section in a soil mass due to typical 

compaction operation. Consider the change of vertical stress at depth z in section I-I due to 

moving compaction loads, as shown in figure 204 through figure 207. The directions of the 

moving compaction plant may either be coming toward section I-I or moving away from 

section I-I. The compaction loads are simulated by loading and unloading at different locations 

(locations 1, 2, and i), as shown in figure 204 and figure 206. Figure 205 and figure 207 show the 

stress path of the stresses at depth z along section I-I.
139

compaction load

location i location 2 location 1

I

I

∆σ'v

Ζ

 

 

 

 

Figure 204. Illustration. Locations of compaction loads moving toward section I-I.

A

σ'v

σ

σh

G

F

C

D

B

E

1

2

i

changing K2,c-line due to 

passes of compaction

Ki,c-line

K2,c and K3,c-line

(Assume: K2,c = K3,c)

∆σ'h,c,r

σ'v + ∆σ'v,c,max

Figure 205. Illustration. Stress paths during compaction at depth z as compaction loads 

move toward section I-I.

compaction load

location 1 location 2 location i

I

I

∆σ'v

Ζ

P

 

 

 

 

Figure 206. Illustration. Locations of compaction loads moving away from section I-I.
140

A

σ'v

σh

G

F

B

D

1

2

i

changing K2,c-line due to 

passes of compaction

Ki,c-line

K2,c and K3,c-line

(Assume: K2,c = K3,c)

∆σ'h,c,r

σ'v + ∆σ'v,c,max

Figure 207. Illustration. Stress paths during compaction at depth z as compaction loads 

move away from section I-I.

Elements in figure 205 are as follows:

• The initial stress condition at depth z along section I-I is denoted by point A, with the 

initial vertical stress being v.

• With the compaction loads at location 1, the stresses will increase by following the Ki,c

line to point B.

• As the compaction loads are removed from location 1, the stresses will reduce from 

point B to point C by following the K2,c line.

• When compaction loads move to a new location (location 2), the stresses will increase 

from point C through point B to point D.

• As the compaction loads are removed from location 2, the stresses will reduce from 

point D to point E by again following the K2,c line.

• The previous steps are repeated for all subsequent new locations as the compaction plant 

moves toward section I-I. As the compaction plant moves closer to section I-I, the 

vertical stress at depth z will become larger.

• The maximum vertical stress condition will be reached when the compaction plant is 

directly above section I-I. The corresponding stress condition is represented by point F. 

Upon removal of the compaction loads, the stress path will follow the K2 line to point G.

In figure 206 and figure 207, the compaction plant moves away from section I-I. Initially, the 

compaction is located directly above section I-I, which causes the stresses to increase from 

point A to point F due to the compaction loads. As the compaction loads are removed from 

section I-I, the stresses are reduced from point F to point G, following the K2,c line. As the 

compaction plant moves away from section I-I, the stress conditions will move to points D and B 

along line FG. As the compaction plant is finally removed, the stress condition will be at point G. 

σ
141

As shown in figure 204 through figure 207, the residual stresses, denoted by the vertical distance 

AG, are the same for the two cases. This indicates that to determine the CIS at a certain section 

due to a moving compaction plant, only the residual lateral stresses need to be determined as the 

compaction loads are directly above the section under consideration.

Figure 208 shows the conceptual stress path on the effect of the number of compaction passes. 

For the first pass, the residual stress at point A is represented by point G. With the subsequent 

pass of the compaction plant, the slope of the K2 line increases, and point G becomes point G'. 

As the number of compaction pass increases, the final residual stresses will move from G' to 

G'' to G'''.

A

σ'v

σv

σh

G

F G'''

G'

G''

∆σ'h,c,r

changing K2,c-line due to a 

number of compaction passes 

K2,c and K3,c-line

(Assume: K2,c = K3,c)

Ki,c-line

σ'v + ∆σ'v,c,max

Figure 208. Illustration. Stress path at depth z when subject to multiple compaction passes.

5.1.5 Estimation of K2,c

This section presents the estimation of K2,c in the proposed model for determining CIS in a GRS 

mass. Two stress reduction factors, F and A, are introduced (see figure 209). Factor F represents 

CIS for unreinforced soil in Seed’s model, and factor A is considered the presence of the 

reinforcement in the GRS mass.(11)
142

A

K2, s for soil

σ'v

Ki, c - line

σv

σh

K2, c for composite 

S

C

B

∆σ

σ'v + ∆σ'v, c, max

G*(∆σ)

F∗(∆σ)

Figure 209. Illustration. Stress path of the proposed model for fill compaction of a GRS 

mass.

5.1.5.1 Compacted Soil 

For an unreinforced soil fill, the coefficient of lateral Earth pressure for unloading in figure 203

can be estimated by using the expression in figure 210, as suggested by Seed.(11)

( ) K2,s = 1− F Ki,c

Figure 210. Equation. Coefficient of lateral Earth pressure.

Where:

( )

1

1 −

− = − OCROCR OCR F

α

.

α ≅ sin φ' .

OCR ≅ 5 for typical compacted sand.(11)

5.1.5.2 GRS Composite

For a GRS mass, total residual strain in the soil can be determined as shown in figure 211.

( ) ( )

s

s E

F G σ

ε

+ ∆ =

Figure 211. Equation. Total residual strain.

Where:

F and G = Stress reduction factors shown in figure 209.

∆σ = Increase in horizontal stress due to compaction.

Es = Soil stiffness.
143

From figure 211, the reinforcement force, T, due to residual strain in the soil can be determined 

as shown in figure 212.

( ) r

s

E

E

F G T 













 + ∆ = σ

Figure 212. Equation. Reinforcement force.

Where Er is the reinforcement stiffness.

The average residual stress in the soil due to compaction,G * (∆σ ), is calculated as shown in 

figure 213 and figure 214.

( )

v

r

s S

E

E

F G G 













 + ∆ ∆ = σ * σ 0.7

Figure 213. Equation. Average residual stress in the soil due to compaction.

G Es Sv F Er 7 G Er = 0.7 + 0.

Figure 214. Equation. Second equation for average residual stress in the soil due to 

compaction.

Figure 215 is a result of the previous two equations.

s v r

r

E S E

F E G

0.7

0.7

− =

Figure 215. Equation. Result of figure 213 and figure 214.

Substituting figure 215 into figure 216 results in figure 217.

[ ( ) ] K2,c = 1 − F + G Ki,c

Figure 216. Equation. First equation for estimation of K2,c.

i c

s v r

r

c K

E S E

E K2, F , 0.70.7 1 1 



 





















− ≅ − +

Figure 217. Equation. Second equation for estimation of K2,c.

The factor 0.7 in figure 213 is explained in section 5.2.1. The increased horizontal stress in a 

GRS mass due to compaction can be estimated using figure 218.

( ) ( ) h, c G F v, c, max Ki, c K2, c ∆σ = ∆σ + = ∆σ ' −

Figure 218. Equation. Increased horizontal stress in a GRS mass due to compaction.

Substituting figure 217 into figure 218 results in figure 219 and figure 220.
144





















 





















− ∆ = ∆ − + +

s v r

r

h c v c i c E S E

E K F

0.7

0.7 ' 1 1 1 σ , σ , , max ,

Figure 219. Equation. Second equation of increased horizontal stress in a GRS mass due to 

compaction.

















− ∆ = ∆ +

s v r

r

h c v c i c E S E

E K F

0.7

0.7 ' 1 σ , σ , , max ,

Figure 220. Equation. Residual lateral stress in a GRS mass due to compaction and the 

effect of CIS in a GRS mass.

Figure 220 shows the calculation of the residual lateral stress in a GRS mass due to compaction 

as well as the effect of CIS in a GRS mass.

Using figure 220, the increase in lateral stress in a GRS mass can be estimated, and the increase 

in soil stiffness can be evaluated. For example, the stiffness of a soil can be evaluated using 

figure 221.

( ) ( ( ))

( )

n

a

h c

a

h c

f h c

P

K P

c

R

t

E 













 + ∆

















+ + ∆

− − + ∆ = − 3 ,

2

3 ,

1 3 ,

2 cos 2 sin

1 sin

1

σ σ

φ σ σ φ

φ σ σ σ

Figure 221. Equation. Stiffness of a soil.

Where:

Et = Tangent modulus.

Rf = Ratio of ultimate deviator stress to the failure deviator stress.

c = Cohesive strength.

= Angle of friction.

Pa = Atmospheric pressure.

K and n = Material parameters.

5.2 STRENGTH PROPERTIES OF GRS COMPOSITE

Schlosser and Long proposed the concepts of increase of apparent confining pressure and 

apparent cohesion of a GRS composite.(25) The Mohr circles of an unreinforced cohesive soil and 

a reinforced cohesive soil at failure are shown in figure 222. 

φ
145

Figure 222. Illustration. Concept of apparent confining pressure and apparent cohesion of 

a GRS composite.

The apparent cohesion of a GRS composite can be determined as shown in figure 223.

c

K

c

R P

R +

∆ = 2

σ 3

Figure 223. Equation. Apparent cohesion of a GRS composite.

Where:

R c = Apparent cohesion of a GRS composite.

c = Cohesion of soil.

Kp = Coefficient of passive Earth pressure.

∆σ 3R = Increase of confining pressure due to reinforcement.

Schlosser and Long also proposed figure 224 to calculate increased confining pressure.(25)

v

f

S

T

∆σ 3 =

Figure 224. Equation. Increased confining pressure.

This expression implies that an increase in reinforcement strength, Tf, has the same effect as a 

proportional decrease in reinforcement spacing, Sv. Many experimental test results have shown 

that figure 224 is not correct. Reinforcement spacing plays a more important role than 

reinforcement strength. (See references 6, 7, 30, 31, and 35.) This point is also supported by the 

experiments conducted as a part of this study and presented in chapter 4. 
146

5.2.1 Increased Confining Pressure

A new method to estimate the increased confining pressure in soil due to the presence of 

reinforcement is expressed in figure 225. 















 ∆ =

v

f

S

T

σ 3 W

Figure 225. Equation. New method to estimate the increased confining pressure in soil due 

to the presence of reinforcement.

Where the factor, W, can be estimated as shown in figure 226.

















= ref

v

S

S

W r

Figure 226. Equation. Estimation of the factor W.

Where:

Tf = Extensile strength of reinforcement.

r = Dimensionless factor.

Sv = Vertical spacing of reinforcement.

Sref = Reference spacing.

To estimate the factor r in figure 226, the concept of average stresses proposed by Ketchart and 

Wu was employed.(20) However, instead of using average stresses, average reinforcement forces 

were used.

5.2.1.1 Average Stress in GRS Mass by Ketchart and Wu(20)

Ketchart and Wu developed a concept of average stress to determine the behavior of a GRS 

composite based on a load transfer analysis.(20) From a simplified preloading-reloading (SPR) 

model for GRS mass, the equations to calculate stresses and displacements of a GRS mass were 

developed using the idealized geometry of a plane-strain GRS mass and differential elements of 

soil and reinforcement for equilibrium equations, as shown in figure 227.
147

Figure 227. Illustration. Idealized plane-strain GRS mass for the SPR model.

Based on the equilibrium equations and several assumptions, the stresses in soil and the force in 

the reinforcement can be calculated using the following equations. 

The force in the reinforcement is calculated with figure 228.

( )

( )















 − 

 



 − 













 − 



 



 − 















− = L

x

E

F A E P P

s

s

v h

s

s

x r r α

α

α

υ β

υ

υ

cosh

cosh 1 1 1

1 2

2

Figure 228. Equation. Force in the reinforcement.

The horizontal stress in the soil is calculated with figure 229.

( )

( ) 













 



 



 + − 













 − 















− + 















− = − 2 2 1

cosh

cosh

1 1 α

β

α

α

α

β

υ

υ

υ

υ

σ

L

x P Pv Ph

s

s

v

s

s

x

Figure 229. Equation. Horizontal stress in the soil.

Based on a load-transfer analysis, the average stresses were determined. 

The average vertical stress, , is assumed to be equal to the boundary vertical pressure, as 

shown in figure 230.

σ v = Pv

Figure 230. Equation. Average vertical stress.

σ v
148

The average horizontal stress, σ h , is as shown in figure 231 and figure 232.

L

x dx

L

x

h

∫

= 0

σ ( )

σ

Figure 231. Equation. First equation of average horizontal stress.

( ) 













 



 



 + − 













 − 















− − 















− = 1 .

tanh 1

1 1 2 L

L P Pv Ph

s

s

v

s

s

h

α

α

α

β

υ

υ

υ

υ

σ

Figure 232. Equation. Second equation of average horizontal stress.

5.2.1.2. Average Reinforcement Forces in a GRS Mass

The equations of the forces in the reinforcement and the maximum force in the reinforcement are 

expressed as shown in figure 233 and figure 234.

( )

( )















 − 

 



 − 













 − 



 



 − 















− = L

x

E

F A E P P

s

s

v h

s

s

x r r α

α

α

υ β

υ

υ

cosh

cosh 1 1 1

1 2

2

Figure 233. Equation. Forces in the reinforcement.

( )















 − 

 



 − 













 − 



 



 − 















− = E L

F A E P P

s

s

v h

s

s

r r α α

υ β

υ

υ

cosh

1 1 1 1

1 2

2

max

Figure 234. Equation. Maximum force in the reinforcement.

The average force in the reinforcement is calculated as shown in figure 235.

L

F dx

F

L

∫ x

= 0

Figure 235. Equation. Average force in the reinforcement.

Substituting figure 233 into figure 235 results in figure 236 and figure 237, which is simplified to 

figure 238.

( )

( ) ∫ 















 − 

 



 − 













 − 



 



 − 















− =

L

s

s

v h

s

r r s dx

L

x

E

P P

L

A E F

0

2

2

cosh

cosh 1 1 1

1 α

α

α

υ β

υ

υ

Figure 236. Equation. Second equation of average force in the reinforcement.

( )

( ) ∫ 













  − 

 



 − 













 − 



 



 − 















− =

L

s

s

v h

s

r r s dx

L

x

E

P P

L

A E F

0

2

2

cosh

cosh 1 1 1

1

.

α

α

α

υ β

υ

υ

Figure 237. Equation. Third equation of average force in the reinforcement.
149

( )

( )















 − 

 



 − 













 − 



 



 − 















− = L

x L

E

P P

L

A E F

s

s

v h

s

r r s

α α

α

α

υ β

υ

υ

cosh

sinh 1 1

1

.

2

2

Figure 238. Equation. Fourth equation of average force in the reinforcement.

Introducing a factor Fmax

F

r = and using figure 234 and figure 238, r can be determined using 

figure 239.

( ) ( )

(cosh( ) 1)

cosh sinh

−

− = L LL L L

r

α α

α α α

Figure 239. Equation. Estimation of factor r.

Table 20 shows the values of factor r for different applied pressures and reinforcement lengths 

using the data from the calculation example in the SPR model.(20)

Table 20. Values of factor r under different applied pressure and reinforcement lengths.

Increment of 

Vertical Pressure 

(Pv) (kPa)

Reinforcement 

Length,

L (m)

( Fmax

F

r = )

9.0 0.127 13.875 0.698

18.0 0.127 14.616 0.701

9.0 0.225 6.851 0.691

18.0 0.225 6.966 0.692

1 kPa = 0.145 psi

1 m = 3.28 ft

Table 20 shows that the average reinforcement forces are about 70 percent of the maximum 

reinforcement force. The highest value of the maximum reinforcement force, Fmax, cannot exceed 

the tensile strength of reinforcement, Tf, as shown in figure 240.

Fmax = Tf

Figure 240. Equation. Maximum reinforcement force.

The average reinforcement force is as shown in figure 241.

Tavg 7 Tf = 0.

Figure 241. Equation. Average reinforcement force.

Figure 226 becomes figure 242.

















= ref

v

S

S

W 0.7

Figure 242. Equation. Second estimation of the factor W.

α
150

5.2.2 Apparent Cohesion and Ultimate Pressure Carrying Capacity of a GRS Mass

Substituting figure 242 into figure 225, the increased confining pressure in a GRS mass is 

calculated in figure 243.





































=













 ∆ = 















v

S f

S

v

f

S

T

S

T

W ref

v

σ 3 0.7

Figure 243. Equation. Increased confining pressure in a GRS mass.

Therefore, the apparent cohesion, cR, of a GRS composite can be evaluated using figure 244.

3 0.7

2 2

v

ref

S

S f

R p p

v

T

c Kc K c

S

σ

       

  ∆   = += +    

Figure 244. Equation. Apparent cohesion.

Where:

c = Cohesion of soil.

Kp = Coefficient of passive Earth pressure.

Tf = Extension strength of reinforcement.

Sv = Vertical spacing of reinforcement.

Sref = Reference spacing, which can be calculated using figure 245. 

S d ref = 6 max

Figure 245. Equation. Reference spacing.

Where:

dmax = Maximum particle/grain size of soil.

Therefore, the ultimate pressure carrying capacity, σ 1R , of a soil-geosynthetic composite mass is 

calculated using figure 246.

1 3 2 f

R p p

v

T

W K cK

S

σ σ

 

=+ +    

Figure 246. Equation. Pressure carrying capacity.

Where σ 3 is the confining pressure.
151

5.3 VERIFICATION OF THE ANALYTICAL MODEL WITH MEASUREMENT DATA

Verification of the proposed analytical model for GRS composite strength properties was made 

by comparing the model calculation results with the measured data from GSGC tests presented in 

chapter 4 and with the measured data by Elton and Patawaran.(31)

5.3.1 Comparison Between the Analytical Model and GSGC Test Results

The dimensions of the GSGC tests were 6.6 ft (2 m) high and 4.6 ft (1.4 m) wide in a planestrain condition. The soil mass in the tests was reinforced with Geotex® 4×4 geotextile at 

0.7- and 1.3-ft (0.2- and 0.4-m) spacing. For the diabase soil used in GSGC tests, the maximum 

particle size was about 1.3 inches (66 mm). Therefore, Sref = 6 dmax = 7.8 inches (0.2 m). 

Comparisons of the results between the analytical model and the GSGC tests are presented in 

table 21. The deviatoric stresses at failure calculated from the analytical model are in good 

agreement with those of the GSGC tests, with differences of less than 10 percent.

Table 21. Comparison of the results of the analytical model and the GSGC tests.

Parameter

Test 2 

(T, S)

Test 3 

(2T, 2S)

Test 4 

(T, 2S)

Tf (kN/m) 70 140 70

Sv (m) 0.2 0.4 0.4

∆σ 3 (kN/m2

) by the analytical model 245 172 86

cR (kN/m2) by the analytical model 407 305 188

( ) σ 1R − σ 3 (kN/m2

) from measured data 2,700 1,750 1,300

( ) σ 1R − σ 3 (kN/m2

) by the analytical model 2,460 1,900 1,250

Difference between analytical model and 

measured data -9 percent +8 percent -4 percent

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 kN/m2 = 0.021 kip/ft2

Note: Internal friction angle of soil = 50 degrees and cohesion of soil = 10.15 psi (70 kPa).

For reference purposes, comparisons of the results between Schlosser and Long’s method and the 

GSGC tests are presented in table 22. The deviatoric stresses at failure calculated from Schlosser 

and Long’s method are about 20 to 86 percent larger than the measured values.
152

Table 22. Comparison of the results of Schlosser and Long’s method and the GSGC tests.

Parameter

Test 2 

(T, S)

Test 3 

(2T, 2S)

Test 4 

(T, 2S)

Tf (kN/m) 70 140 70

Sv (m) 0.2 0.4 0.4

∆σ 3 (kN/m2

) by Schlosser and Long’s method 350 350 175

cR (kN/m2) by Schlosser and Long’s method 550 550 310

( ) σ 1R − σ 3 (kN/m2

) from measured data 2,700 1,750 1,300

( ) σ 1R − σ 3 (kN/m2

) by Schlosser and Long’s 

method 3,250 3,250 1,930

Difference between Schlosser and Long’s 

method and measured data +20 percent +86 percent +48 percent

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 kN/m2 = 0.021 kip/ft2

Note: Internal friction angle of soil = 50 degrees and cohesion of soil = 10.15 psi (70 kPa).

5.3.2 Comparison Between the Analytical Model and Elton and Patawaran’s Test Results

Elton and Patawaran conducted seven large-size triaxial tests for reinforced soil 5 ft (1.5 m) in 

height and 2.5 ft (0.76 m) in diameter.(31) All the tests were conducted under an unconfined 

condition. The properties of the tests were as follows:

• Backfill: The soil used in the test was a poorly graded sand with the gradation test results 

shown in figure 247. The maximum dry unit weight, dry, was 121 pcf (1,900 kg/m3), the 

optimum moisture content, wopt, was 9.3 percent, the internal friction, , was 40 percent, 

and the cohesion, c, was 4 psi (27 kPa).

• Reinforcement: Six types of reinforcement (TG500, TG600, TG700, TG800, TG1000, 

and TG028) were used for the tests with reinforcement spacing of 6 and 12 inches 

(150 and 300 mm).

γ

φ
153

1 mm = 0.039 inches

Figure 247. Graph. Backfill grain size distribution before and after large-size triaxial 

tests.(31)

The maximum particle size of the backfill in the large-size triaxial tests was dmax = 0.5 inches 

(12.7 mm). Therefore, Sref = 6 dmax = 3 inches (0.08 m). The measured results are shown in

figure 248. The comparisons of Elton and Patawaran’s tests results with the analytical model 

and with Schlosser and Long’s method are presented in table 23 and table 24, respectively.

1 ksf = 47.88 kPa

Figure 248. Graph. Large-size triaxial test results.(31)
154

Table 23. Comparison of the results of the analytical model and Elton and Patawaran’s 

tests.(31)

Parameter

TG 

500

TG 

500

TG 

600

TG 

700

TG 

800

TG 

1000

TG 

028

Tf (kN/m) 9 9 14 15 19 20 25

Sv (m) 0.15 0.30 0.15 0.15 0.15 0.15 0.15

∆σ 3 (kN/m2

) by the analytical model 30 8 47 48 62 67 83

cR (kN/m2) by the analytical model 60 36 78 79 94 99 116

( ) σ 1R − σ 3 (kN/m2

) from measured data 230 129 306 292 402 397 459

( ) σ 1R − σ 3 (kN/m2

) by the analytical 

model 256 153 333 341 402 426 498

Difference between the analytical model 

and measured data (percent) 11 18 9 17 0 7 8

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 kN/m2 = 0.021 kip/ft2

Note: Internal friction angle of soil = 40 degrees and cohesion of soil = 4.0 psi (27.6 kPa).

Table 24. Comparison of the results of Schlosser and Long’s method and Elton and 

Patawaran’s tests.(31)

Parameter

TG 

500

TG 

500

TG 

600

TG 

700

TG 

800

TG 

1000

TG 

028

Tf (kN/m) 9 9 14 15 19 20 25

Sv (m) 0.15 0.30 0.15 0.15 0.15 0.15 0.15

∆σ 3 (kN/m2

) by Schlosser and Long’s 

method 59 30 92 95 122 132 163

cR (kN/m2) by Schlosser and Long’s 

method 91 59 126 130 158 169 202

( ) σ 1R − σ 3 (kN/m2

) from measured data 230 129 306 292 402 397 459

( ) σ 1R − σ 3 (kN/m2

) by Schlosser and 

Long’s method 390 254 541 557 678 726 868

Difference between Schlosser and 

Long’s method and measured data 

(percent) 70 97 77 91 69 83 89

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 kN/m2 = 0.021 kip/ft2

Note: Internal friction angle of soil = 40 degrees; cohesion of soil = 4.0 psi (27.6 kPa).

The differences in the deviatoric stresses at failure calculated from the analytical model and 

Elton and Patawaran’s measured data are less than 18 percent. The results calculated from 

Schlosser and Long’s method are 69 to 97 percent larger than the measured values.

5.3.3 Comparison Between the Analytical Model and FE Results

FE analyses were conducted to provide additional data for verifying the analytical model. The 

test conditions and material properties used for the FE analyses were the same as those used in 
155

GSGC test 2 but with confining pressures of 4.9, 10, 15, and 29 psi (34, 70, 100, and 200 kPa). 

The confining pressure used in GSGC test 2 was 4.9 psi (34 kPa). The comparison shown in 

table 25 indicates that the results of the analytical model are in good agreement with those 

obtained from the FE analyses at the different confining pressures. The largest difference in 

terms of the deviatoric stress at failure is 9 percent. 

Table 25. Comparison of the results of analytical model and GSGC test 2 

with different confining pressures from FE analyses.

Parameter

= 

34 kPa

= 

70 kPa

= 

100 kPa

= 

200 kPa

∆σ 3 (kN/m2

) by the analytical model 245 245 245 245

cR (kN/m2) by the analytical model 407 407 407 407

( ) σ 1R − σ 3 (kN/m2

) from FE analysis 2,700 2,970 3,190 3,860

( ) σ 1R − σ 3 (kN/m2

) by the analytical model 2,490 2,760 2,990 3,740

Difference between the analytical model and 

FE analyses -8 percent -7 percent -6 percent -3 percent

1 kPa = 0.145 psi

1 kN/m2 = 0.021 kip/ft2

Note: Internal friction angle of soil = 50 degrees, cohesion of soil = 10.15 psi (70 kPa), reinforcement strength = 

4.83 kip/ft (70 kN/m), and reinforcement spacing = 0.65 ft (0.2 m).

5.4 REQUIRED REINFORCEMENT STRENGTH IN DESIGN

In this section, an analytical model for determining required tensile strength in reinforcement is 

developed, the analytical model is compared with the current design equation, and verification of 

the analytical model is presented.

5.4.1 Proposed Model for Determining Reinforcement Force 

In current design methods, figure 249 is used to determine the required reinforcement strength 

for the design of GRS structures.

required h v Fs T = σ ∗ S ∗

Figure 249. Equation. Required strength for reinforcement.

Where:

Trequired = Required strength for reinforcement at depth z.

h = Horizontal stress in a GRS mass at depth z.

Fs = Safety factor.

Assuming Fs = 1, then Trequired = Tf , the ultimate strength of reinforcement, and figure 249

becomes figure 250.

h

v

f

S

T = σ

Figure 250. Equation. Tf divided by Sv.

σ3 σ3 σ3 σ3

σ
156

Note that when the horizontal stress, h, is a constant, the ratio Tf /Sv becomes a constant 

(i.e., Tf is linearly proportional to Sv). Using figure 225, a new expression for the increase of 

confining pressure due to tensile inclusion, a modified equation for determination of required 

reinforcement strength can be obtained. The horizontal stress, h, in a GRS structure at depth z

is calculated using figure 251 or figure 252.

σ h = σ 3 + ∆σ 3

Figure 251. Equation. First equation for horizontal stress in a GRS structure.

∆σ 3 = σ h − σ 3

Figure 252. Equation. Second equation for horizontal stress in a GRS structure.

Substituting figure 225 into figure 250 leads to figure 253 and figure 254.

v

f

h S

T

σ − σ 3 = W

Figure 253. Equation. Third equation for horizontal stress in a GRS structure.

( )

S W

T h

v

f σ −σ 3 =

Figure 254. Equation. Second equation for Tf divided by Sv.

Substituting figure 241 into figure 254 results in figure 255.

( )

















− =

6 max

3

0.7 d

S

h

v

f

S v

T σ σ

Figure 255. Equation. Third equation for Tf divided by Sv.

For a GRS wall with modular block facing, the lateral constraint pressure, 3, at depth z, can be 

estimated as shown in figure 256.

σ γ tan δ 3 b = b

Figure 256. Equation. Lateral constraint pressure.

Where:

b = Unit weight of facing block.

b = Width of facing block.

= Friction angle between modular block facing elements ( can be the friction angle between 

facing blocks if there is no reinforcement between the blocks or it can be the friction angle 

between facing block and geosynthetic if there is reinforcement sandwiched between blocks).

dmax = Maximum grain size of the backfill.

The required tensile strength of the reinforcement in design is shown in figure 257. 

σ

σ

σ

γ

δ δ
157

v s

d

S

h Trequired S F v

* *

0.7 6 max

3



















 − =

















σ σ

Figure 257. Equation. Required tensile strength of the reinforcement in design.

Where h is the maximum lateral stress in a GRS mass and can be evaluated as the Rankin 

active Earth pressure. Note that Trequired is always equal or greater than zero. For a GRS mass 

without lateral constraint (e.g., a wrapped wall), 3 equals 0, and figure 257 becomes figure 258.

v s

d

S

h Trequired S F v

* *

0.7 6 max 



















=

















σ

Figure 258. Equation. Second equation for required tensile strength of the reinforcement in 

design.

5.4.2 Comparison of Reinforcement Strength Between the Analytical Model and Current 

Design Equation

A comparison of reinforcement forces was made between the proposed model (figure 257) and 

the current design equation (figure 249). The reinforcement forces in a 20-ft (6.0-m)-high GRS 

wall, as determined by the two equations, are shown in table 26. Note that the facing stiffness is 

ignored in the current design method, while the facing rigidity, as denoted by the lateral 

constraint pressure, 3, can be accounted for in the proposed model.

σ

σ

σ
158

Table 26. Comparison of reinforcement forces in proposed model and current design 

equation for a GRS wall.

z (m)

Trequired (kN/m) for Fs = 1

Current 

Design 

Equation

Proposed Model

No Facing

Modular Block 

Facing with 

b−b δ = 35 degrees

Modular Block 

Facing with 

b−b δ = 54 degrees

0.4 0.3 0.4 0.0 0.0

0.8 0.6 0.9 0.0 0.0

1.2 1.0 1.3 0.0 0.0

1.6 1.3 1.8 0.3 0.0

2.0 1.6 2.2 0.8 0.0

2.4 1.9 2.7 1.2 0.0

2.8 2.3 3.1 1.7 0.3

3.2 2.6 3.5 2.1 0.7

3.6 2.9 4.0 2.5 1.2

4.0 3.2 4.4 3.0 1.6

4.4 3.6 4.9 3.4 2.0

4.8 3.9 5.3 3.9 2.5

5.2 4.2 5.8 4.3 2.9

5.6 4.5 6.2 4.8 3.4

6.0 4.9 6.6 5.2 3.8

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

b–b = Friction angle between facing blocks.

Note: Internal friction angle of soil = 38 degrees, cohesion of soil = 0, reinforcement spacing = 

0.65 ft (0.2 m), maximum grain size of soil = 1.48 inches (38 mm), unit weight of soil = 

0.11 kip/ft3

) (17 kN/m3), unit weight of facing block = 0.16 kip/ft3 (25 kN/m3), and width of 

blocks = 0.98 ft (0.3 m).

5.4.3 Verification of the Analytical Model for Determining Reinforcement Strength

Verification of the analytical model for determination of reinforcement strength was made by 

comparing the forces in reinforcement at failure from the GSGC tests with the data measured by 

Elton and Patawaran and with a typical GRS wall.(31)

Table 27 shows a comparison of the results from the proposed model and measured data from the 

GSGC tests. Note that cohesion, c, was included in model calculations. The largest difference in 

reinforcement forces between the two is 16 percent, whereas there is 47 percent difference 

between the current design methods and the test data. 

δ
159

Table 27. Comparison of reinforcement forces in the proposed model and the GSGC tests.

Parameter

Test 2

(T, S)

Test 3

(2T, 2S)

Test 4

(T, 2S)

Test 5

(T, S)

Reinforcement 

force at failure, Tf

(kN/m) 70 140 70 70

Reinforcement 

spacing, Sv (m) 0.2 0.4 0.4 0.2

Measured failure 

pressure (kPa) 2,700 1,750 1,300 1,900

Lateral constraint 

pressure σ 3 (kPa) 34 34 34 0

Maximum 

reinforcement force 

from current design 

equation (kN/m) 62.4 74.4 50.5 41.2

Difference between 

current design 

equation and Tf 

(percent) -11 -47 -28 -41 

Maximum 

reinforcement force 

from proposed 

model (kN/m) 79.4 124.1 75.4 58.8

Difference between 

proposed model 

and Tf (percent) +13 -11 +8 -16 

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 kPa = 0.145 psi

Note: Internal friction angle of soil = 50 degrees, cohesion of soil = 10.15 psi (70 kPa), unit 

weight of soil = 0.15 kip/ft3 (24 kN/m3

), and maximum grain size of soil = 1.29 inches (33 mm).

A comparison of the reinforcement forces between the proposed model and the measured data 

from Elton and Patawaran’s tests is shown in table 28.

(31) The largest difference in reinforcement 

forces between the two is 13 percent, whereas it was as high as 74 percent between the current 

design method and the test results. The proposed model clearly gives a much improved value for 

estimating reinforcement strength compared to the current design methods.
160

Table 28. Comparison of reinforcement forces between proposed model and test data 

from Elton and Patawaran.

(31)

Parameter

TG 

500

TG 

500

TG 

600

TG 

700

TG 

800

TG 

1000

TG 

028

Reinforcement force at failure, Tf

(kN/m) 9 9 14 15 19 20 25

Reinforcement spacing, Sv (m) 0.15 0.30 0.15 0.15 0.15 0.15 0.15

Measured failure pressure (kPa) 230 129 306 292 402 397 459

Maximum reinforcement force from 

current design equation (kN/m) 4.47 2.35 6.95 6.49 10.08 9.91 11.94

Difference between current design 

equation and Tf (percent) -50 -74 -50 -57 -47 -50 -52

Maximum reinforcement force from 

proposed model (kN/m) 9.02 9.56 14.02 13.10 20.34 20.01 24.09

Difference between proposed model 

and Tf (percent) 0 +6 0 -13 +7 0 -4

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

1 kPa = 0.145 psi

Note: Internal friction angle of soil = 40 degrees, cohesion of soil = 4.0 psi (27.6 kPa), unit weight of soil = 

0.12 kip/ft3 (18.8 kN/m3

), lateral constraint pressure = 0 psi (0 kPa), and maximum grain size of soil = 0.49 inches 

(12.7 mm).
161

CHAPTER 6. FE ANALYSES

The GSGC tests described in chapter 4 were simulated using the FE method of analysis. The 

behavior of the reinforced soil mass in GSGC test 2 under different confining pressures, which 

was not part of the experimental program, was investigated using the FE model. The angle of 

dilatation of a GRS composite was studied. In addition, the analytical model developed for 

evaluation of CIS in a GRS mass was verified by comparing the model results with those 

obtained from the FE analyses.

Many FE codes are available for the analysis of soil-structure interaction problems, including 

Abaqus, FLAC, LS-Dyna®, Plaxis, Sage Crisp®, and Sigma/W® (Geoslope). Plaxis 8.2 code was 

selected for the analysis in this study due primarily to the author’s familiarity with the code. This 

code has been used successfully for the analysis of various Earth structures, including GRS 

structures.(79–81)

6.1 PLAXIS 8.2

Version 8.2 of Plaxis is an FE code intended for 2D analysis of deformation and stability 

problems in geotechnical engineering. The details of Plaxis 8.2 can be found in the software 

manual.(81) Following is a brief description of some key features of the program:

• Graphical input of geometry models: The input of layers, structures, construction 

stages, loads, and boundary conditions is based on computer-aided design drawing 

procedures, which allows for a detailed modeling of the geometry. From the geometry 

model, a 2D FE mesh is easily generated.

• Automatic mesh generation: Plaxis allows for automatic generation of 2D FE meshes 

with options for global and local mesh refinement. 

• High-order elements: Quadratic 6-node and fourth-order 15-node triangle elements are 

available to describe the stress-deformation behavior of the soil.

• Plates/beams: Special beam elements can be used to model the bending of retaining 

walls, tunnel linings, shells, and other slender structures. The behavior of these elements 

is defined using a flexural rigidity, a normal stiffness, and an ultimate bending moment. 

Plates with interfaces can also be used to model the behavior of structures.

• Interfaces: Joint elements are available to model soil-structure interface behavior. For 

example, joint elements can be used to simulate the thin zone of intensely shearing 

material at the contact between a retaining wall and the surrounding soil, a tunnel lining 

and the soil, or reinforcement and surrounding soil. Values of the interface friction angle 

and adhesion are generally not the same as the friction angle and cohesion of the 

surrounding soil.

• Anchors: Elastoplastic spring elements can be used to model anchors and struts. The 

behavior of these elements is defined using a normal stiffness and a maximum force. 
162

A special option exists for the analysis of prestressed ground anchors and 

excavation supports.

• Geogrids/geotextiles: Geogrids or geotextiles in GRS structures can be simulated in 

Plaxis by special tension elements. It is often convenient to combine these elements with 

joint elements to model the interaction between geosynthetic reinforcement and the 

surrounding soil.

• Tunnels: Plaxis offers a convenient option for creating circular and non-circular tunnels 

using arcs and lines. Plates and interfaces may be used to model the tunnel lining and the 

interaction with the surrounding soil. Fully isoparametric elements can be used to model 

the curved boundaries within the mesh. Various methods are available for the analysis of 

the deformation caused by various methods of tunnel construction.

• Mohr-Coulomb model: This non-linear model is based on soil parameters that are wellknown in geotechnical engineering practice. Not all non-linear features of soil behavior 

are included in this model; however, the Mohr-Coulomb model can be used to compute 

realistic support pressures for tunnel faces, ultimate loads for footings, etc. It can also be 

used to calculate safety factors using a phi-c reduction approach.

• Advanced soil models: In addition to the Mohr-Coulomb model, Plaxis offers a variety 

of advanced soil models. A general second-order model called the hardening soil model, 

an elastoplastic type of hyperbolic model, is available. To accurately model the timedependent and logarithmic compression behavior of normally consolidated soft soils, a 

creep model is also available, referred to as the soft soil creep model. In addition, a 

special model is available for the analysis of anisotropic behavior of jointed rock. 

• User-defined soil models: A special feature in Plaxis 8.2 is a user-defined soil 

model option. This feature enables users to include self-programmed soil models 

for the analysis. 

• Staged construction: This feature enables realistic simulation of construction of Earth

structures by activating and deactivating compaction loads and simulation of excavation 

processes by activating and deactivating clusters of elements, application of loads, 

changing of water tables, etc. The procedure allows for a realistic assessment of stresses 

and displacements caused by, for example, compaction loads or soil excavation during 

underground construction.

6.2 CIS IN A GRS MASS

The residual lateral stresses in a GRS mass due to compaction can be evaluated by figure 259. 

(See section 5.15 for details.)

















− ∆ = ∆ +

s v r

r

v c i c E S E

E K F

0.7

0.7

σ 3 σ , , max , 1

Figure 259. Equation. Residual lateral stresses in a GRS mass due to compaction.
163

To illustrate how to compute the residual lateral stresses, or CIS, in a GRS mass, a 19.68-ft 

(6-m)-high GRS mass was used as an example. The parameters for the calculation of CIS 

are as follows:

• Soil: A dense sand with unit weight= 0.11 kip/ft3 (17 kN/m3

), angle of internal 

friction = 45 degrees, soil modulus = 4,400 psi (30,000 kPa), and compaction 

lift = 0.7 ft (0.2 m).

• Geosynthetics: Er = 290 psi (2,000 kPa) and Sv = 0.7 ft (0.2 m).

The vertical maximum pressures of 6.4, 15, 29, 44, and 73 psi (44, 100, 200, 300, and 500 kPa) 

due to compaction were used for the calculation of the residual stresses. Note that the maximum 

vertical compaction stress of 6.4 psi (44 kPa) was the contact pressure used in the GSGC tests 

described in chapter 4.

Figure 260 shows the distribution of the residual lateral stresses with depth due to the different 

maximum compaction pressures. The values of the lateral residual stresses in this figure were 

calculated based on figure 258 with the assumption that the compaction lift of 0.7 ft (0.2 m) is 

small compared to the dimensions of the compaction plant. As a result, the distribution of the 

lateral residual stress within the 0.7-ft (0.2-m)-thick lift due to compaction is constant. Near the 

surface, the lateral residual stresses will follow the limiting lateral Earth pressure for the 

unloading condition (i.e., the K1,c line, as shown in figure 203 and table 19).
164

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 260. Graph. Distribution of residual lateral stresses of a GRS mass with depth due 

to fill compaction.

6.3 FE SIMULATION OF THE GSGC TESTS

Plaxis 8.2 was used for the simulation of GSGC tests 1, 2, and 3, as described in chapter 4. 

The backfill of all GSGC test specimens was compacted at 0.7-ft (0.2-m) lifts using an MBW 

GP1200 plate compactor with a contact pressure of 6.4 psi (44 kPa). The soil stiffness, ref E50 , can 

be estimated from triaxial tests using Janbu’s equation.(82) The Poisson’s ratio of the backfill can 

be estimated as shown in figure 261 for uniaxial tests and figure 262 for triaxial tests.

( ) V E

V z

x y z

σ = ε + ε + ε = 1− 2ν

∆

Figure 261. Equation. Poisson’s ratio of the backfill for uniaxial tests.

( )( )

( ν )

ν ν σ

ε ε ε −

+ − = + + = ∆

1

1 1 2

V E

V z

x y z

Figure 262. Equation. Poisson’s ratio of the backfill for triaxial tests.
165

For GSGC test 1 (unreinforced soil), the soil model and parameters used in the analysis 

are as follows:

• Soil hardening model.

• Dry unit weight, d = 0.15 kip/ft3 (24 kN/m3), wet unit weight, and t = 0.16 kip/ft3

(25 kN/m3).

• Angle of internal friction = 50 degrees, angle of dilation = 17.5 degrees, and cohesion = 

10 psi (70 kPa) (for confining pressure less than 30 psi (206.7 kPa)).

• Soil modulus, ref E50 = 9,000 psi (62,000 kPa), unloaded-reloaded reference modulus, ref Eur = 

18,000 psi (124,000 kPa), and Poisson’s ratio, = 0.37.

• Power, m = 0.5.

For the GSGC tests, the backfill stiffness was increased due to CIS as follows: 

1. Place the first lift of facing blocks and soil. The compaction lift thickness was 0.7 ft (0.2 m).

2. Apply a uniform vertical stress of 6.4 psi (44 kPa) over the entire surface of each newly 

placed soil layer before analysis, and remove it afterwards. This step was employed to 

simulate the compaction operation.

3. Place a sheet of reinforcement at preselected reinforcement spacing to cover the entire 

backfill surface plus the facing blocks.

4. Place another lift of facing blocks and soil.

5. Repeat steps 2 to 4 until the fill reached the total height of the specimen.

6. Remove facing blocks.

7. Apply a prescribed confining pressure.

8. Apply vertical stresses on the top of the specimen at equal increments until failure.

The properties of the backfill were modified due to compaction effects. The Poisson’s ratio 

under plane-strain condition was reduced to min, as suggested by Hatami and Bathurst. (17) Soil 

modulus ref E50 was calculated using the increase in confining pressure due to compaction. The 

value of ref E50 can be estimated by using equation 80 with 3 3 3 σ ' = σ ' S + ∆σ , where ∆σ 3 can be 

estimated by figure 221. Note that the elastic modulus was increased by factor of 2.25 for walls 1 

and 2 in Hatami and Bathurst’s numerical analyses and by a factor of 10 in the FE analyses by 

Morrison, et al.(17,18)

The conditions and properties of the backfill and reinforcement of GSGC tests 2 and 3 used in 

the FE analyses are shown in table 29.

γ γ

ν

ν
166

Table 29. Parameters and properties of the GSGC tests used in FE analyses.

Category Description

Soil Material, diabase; Soil model, hardening soil model; dry unit weight, 

d = 24 kN/m3

; wet unit weight, w = 25 kN/m3; cohesion, c = 70 kPa; 

angle of internal friction, = 50 degrees; angle of dilation, 

ψ = 17 degrees; soil modulus, ref E50 = 63,400 kPa, ref Eur = 126,800 kPa; 

Poisson’s ratio, = 0.2; power, m = 0.5

Reinforcement GSGC test 2: Single-sheet Geotex® 4×4: axial stiffness, EA = 

1,000 kN/m; ultimate strength, Tult = 70 kN/m; reinforcement spacing, 

Sv = 0.2 m

GSGC test 3: Double-sheet Geotex® 4×4: axial stiffness, EA = 

2,000 kN/m; ultimate strength, Tult = 140 kN/m; reinforcement spacing, 

Sv = 0.4 m

Facing block FE model, linear elastic model; modulus, E = 3*107 kPa; unit weight, 

= 12.5 kN/m3 (hollow blocks); Poisson’s ratio, = 0.

Block-block 

interface

FE model, Mohr-Coulomb model; modulus, E = 3*106 kPa; unit 

weight, = 0 kN/m3; cohesion, c = 2 kPa; angle of internal friction,

= 33 degrees; Poisson’s ratio, = 0.45

Confining pressure Constant confining pressures of 34 kPa for the GSGC tests 1–4

1 kN/m3 = 0.006 kip/ft3

1 kPa = 0.145 psi

1 kN/m = 0.069 kip/ft

1 m = 3.28 ft

Note: Soil-reinforcement interface was assumed to be fully bonded in the analyses.

Figure 263 through figure 268 show the steps in the FE analyses. The first 20 steps were used for 

modeling the preparation of the specimen. The loading began from step 21. 

γ γ

φ

ν

γ ν

γ

φ ν
167

Figure 263. Illustration. Step 1 of analysis for the GSGC tests—placement of first layer.

Figure 264. Illustration. Step 2 of analysis for the GSGC tests—compaction of first layer.

Figure 265. Illustration. Step 3 of analysis for the GSGC tests—placement of second layer.

Figure 266. Illustration. Step 4 of analysis for the GSGC tests—compaction of second layer.
168

Note: The full height of the GSGC mass was reached at the last 

step of the specimen preparation.

Figure 267. Illustration. Step 20 of analysis for the GSGC tests—placement of surcharge.
169

Note: The facing blocks were removed and confining pressure and 

vertical pressures were applied (during loading).

Figure 268. Illustration. Step 21 of analysis for the GSGC tests—placement of surcharge 

and confining stress.

6.3.1 Simulation of GSGC Test 1

The global stress-strain relationship and volume change relationship obtained from FE analysis 

and the GSGC tests are shown in figure 269 and figure 270. The analysis results are in good 

agreement with the measured data. The maximum differences of the results between the FE 

analysis and the tests were about 5 percent. Figure 271 shows the lateral movements on the open 

faces of the specimen at 29, 58, 87, and 110 psi (200, 400, 600, and 770 kPa). These results from 

FE analyses and the tests are also in good agreement.
170

1 kPa = 0.145 psi

Figure 269. Graph. Comparison of results for GSGC test 1, global vertical 

stress-strain relationship.

Figure 270. Graph. Comparison of results for GSGC test 1, volume change relationship.

0

100

200

300

400

500

600

700

800

900

0 1 2 3 4 5 6 7

Global Vertical Strain (%)

Applied Vetical Stress (kPa)

FE Analysis

Measured Data
171

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 271. Graph. Comparison of lateral displacements on open face of GSGC test 1.

6.3.2 Simulation of GSGC Test 2

The global stress-strain relationships, as obtained from FE analysis and the GSGC tests, are 

shown in figure 272. The results of the FE analysis with and without consideration of CIS are 

included in the figure. The results with consideration of CIS give a slightly better simulation of 

the stress-strain curve. It should be noted that the compaction energy used in the GSGC tests was 

very low. As a result, the magnitude of CIS was very small and the effect of CIS on the global 

stress-strain relationship was not significant.
172

1 kPa = 0.145 psi

Figure 272. Graph. Comparison of global stress-strain relationship of GSGC test 2.

Figure 273 shows the lateral displacements on the open faces of the specimen at applied 

pressures of 58, 145, 290, and 360 psi (400, 1,000, 2,000, and 2,500 kPa). The simulated 

lateral displacements are no more than 5 percent greater than the measured values.
173

1 m = 3.28 ft

1 mm = 25.4 inches

1 kPa = 0.145 psi

Figure 273. Graph. Comparison of lateral displacement at open face of GSGC test 2.

Figure 274 shows the simulated and measured displacements of the GSGC mass at selected 

points in figure 153. The simulated displacements are in agreement with the measured values.
174

1 mm = 0.039 inches

Figure 274. Graph. Comparison of internal displacements of GSGC test 2.

A comparison of the distribution of strains in the reinforcement in GSGC test 2 between the FE 

analyses and measured data are shown in figure 275 and figure 276. The simulated strains are in 

good agreement with the measured values.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 275. Graph. Comparison of results for GSGC test 2 at reinforcement layer 5.25 ft 

(1.6 m) from the base.
175

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 276. Graph. Comparison of results for GSGC test 2 at reinforcement layer 2.62 ft 

(0.8 m) from the base.

6.3.3 Simulation of GSGC Test 3

A comparison of the global stress-strain relationships obtained from FE analysis and measured 

data of GSGC test 3, are shown in figure 277. The FE results are in agreement with the measured 

data. The lateral displacements on the open faces at applied pressures of 58, 87, 116, 145, and 

180 psi (400, 600, 800, 1,000, and 1,250 kPa) are shown in figure 278. Figure 279 shows a 

comparison of simulated and measured internal displacements of the GSGC test 3 specimen at 

selected points in figure 169. Once again, the results from FE analyses are in good agreement 

with the measured values.
176

1 kPa = 0.145 psi

Figure 277. Graph. Comparison of global stress-strain relationship of GSGC test 3.

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0 1 2 3 4 5 6 7 8

Global Vertical Strain (%)

Deviatoric Stress (kPa)

Measured Data

FE Analyses
177

1 m = 3.28 ft

1 mm = 0.039 inches

1 kPa = 0.145 psi

Figure 278. Graph. Comparison of lateral displacement at open face of GSGC test 3.
178

1 mm = 0.039 inches

Figure 279. Graph. Comparison of internal displacements of GSGC test 3.

The comparisons of the distribution of strains in the reinforcement in GSGC test 3 between FE 

analyses and measured data are shown in figure 280 and figure 281. The simulated strains are in 

agreement with the measured values.

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 280. Graph. Comparison of results for GSGC test 3 at reinforcement layer 3.94 ft 

(1.2 m) from the base.
179

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 281. Graph. Comparison of results for GSGC test 3 at reinforcement layer 1.3 ft 

(0.4 m) from the base.

6.4 FE ANALYSIS OF GSGC TEST 2 UNDER DIFFERENT CONFINING PRESSURES 

AND DILATION ANGLE OF SOIL-GEOSYNTHETIC COMPOSITES

Figure 282 shows a comparison of the global stress-strain relationship obtained from FE analysis 

and the measured data of GSGC test 2. Figure 283 shows a comparison of the volume change 

relationships. GSGC test 2 was conducted under a confining pressure of 4.9 psi (34 kPa). The 

global stress-strain and volume change relationships under the confining pressure of 4.9 psi

(34 kPa) as obtained from FE analysis are in good agreement with the measured data. To provide 

additional data under different confining pressures, the FE model was used to generate data 

under confining pressures of 15 and 29 psi (100 and 200 kPa), as shown in the figures. 
180

1 kPa = 0.145 psi

Figure 282. Graph. FE analyses of GSGC test 2 under different confining pressures—

global stress-strain relationship.

1 kPa = 0.145 psi

Figure 283. Graph. FE analyses of GSGC test 2 under different confining pressures—

volume change curves.

It is interesting to note that the reinforcing mechanism of a GRS mass can be viewed in terms of 

the angle of dilation. The angle of dilation of a GRS mass is smaller than the angle of dilation of 

an unreinforced soil mass. Using the data in figure 282 and figure 283 as an example, the angles 

of dilation of the soil-geosynthetic composites were approximately -8, -11, and -12 degrees 

(a negative dilation angle means no dilation; the greater the absolute value, the less likely 

the material will dilate) under confining pressures of 4.9, 15, and 29 psi (34, 100, and 

200 kPa), respectively. The angle of dilation of the unreinforced soil was +17 degrees under a 

confining pressure up to 29 psi (200 kPa). This suggests that the presence of geosynthetic 

reinforcement has a tendency to suppress dilation of the surrounding soil. A soil having less 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 1 2 3 4 5 6 7 8 9

Global Vertical Strain (%)

Deviatoric Stress (kPa)

34 kPa (Measured)

34 kPa (FE)

100 kPa (FE)

200 kPa (FE)

Confining Pressure:
181

tendency to dilate will become stronger. 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.

6.5 VERIFICATION OF CIS MODEL

The analytical model for evaluating CIS, as described in section 3.2, was verified using the FE 

method of analysis. The FE analysis was carried out by using Plaxis 8.2.(81) To verify the CIS 

model, a 20-ft (6-m)-high GRS mass was chosen as an example. The parameters used for the 

calculation of CIS in the analytical model and the FE analysis are as follows:

• Soil: A dense sand with mass unit weight = 0.12 kip/ft3 (17 kN/m3

), angle of internal 

friction= 45 degrees, loading modulus = 4,400 psi (30,000 kPa), unloading modulus = 

13,000 psi (90,000 kPa), Poisson ratio = 0.2, and compaction lift = 0.7 ft (0.2 m). (The 

behavior of the soil was simulated in FE analysis by using the hardening soil model in 

plane-strain condition.)

• Geosynthetics: Tensile modulus = 290 psi (2,000 kPa) and reinforcement spacing =

0.7 ft (0.2 m).

• Interface: The interface between the soil and geosynthetic reinforcement is fully bonded.

The very fine mesh of an FE analyses to simulate CIS in a GRS mass is shown in figure 284. 

Figure 285 and figure 286 show the lateral stress distributions at the center line of the GRS mass 

without considering CIS and with CIS under the maximum compaction pressures of 29 and 

73 psi (200 and 500 kPa). The compaction operation was simulated by loading and unloading 

at different locations on the surface area of each lift. The residual lateral stresses were the 

differences between the lateral stresses with simulating CIS and those without CIS at the 

same location, as shown in figure 285 and figure 286.

Figure 284. Illustration. FE mesh to simulate CIS in a reinforced soil mass.
182

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 285. Graph. Lateral stress distribution of a GRS mass from FE analyses with 

maximum vertical compaction pressures of 29 psi (200 kPa).
183

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 286. Graph. Lateral stress distribution of a GRS mass from FE analyses with 

maximum vertical compaction pressures of 72.5 psi (500 kPa).

Comparisons of residual lateral stress distribution resulting from compaction pressures of 

29 and 73 psi (200 and 500 kPa) between the CIS model and the FE analysis are shown in 

figure 287. The CIS calculated from the hand computation model are in good agreement with the 

values obtained from the FE analysis. Note that the residual lateral stresses in a GRS mass are 

higher under a higher vertical compaction pressure. In actual construction, the maximum vertical 

pressure of compaction is in the range of 29 to 73 psi (200 to 500 kPa). As shown in figure 287, 

the effects of CIS can be significant in actual construction. The zigzag of the FE analyses lines in 

figure 287 was caused by the thickness of compaction lift of 0.7 ft (0.2 m). A larger compaction 

lift indicates a larger amplitude of the zigzag, and the effect of CIS is smaller.
184

1 m = 3.28 ft

1 kPa = 0.145 psi

Figure 287. Graph. Comparison of residual lateral stresses of a GRS mass due to fill 

compaction between FE analysis with very fine mesh and the analytical model.

The FE analyses are more accurate with finer meshes, but the results for one curve from the FE 

analysis took more than 20 h of inputting data and running the program with a strong computer 

configuration (e.g., dual core 1.86 GHz, 3 GB RAM). Conversely, the analytical model is simple 

and can use hand calculations. To speed up the FE analysis process, a coarse mesh can be used 

with somewhat tolerated error. Figure 288 shows the comparison between FE results with a 

coarse mesh and the analytical model. The FE results were obtained from simulating the 

compaction operation by applying the compaction pressure over the entire surface area of the 

GRS mass at each compaction lift. Figure 287 and figure 288 show that the fine mesh should be 

used when analyzing GRS structures.
185

1 m = 3.28 ft

1 kPa = 0/145 psi

Figure 288. Graph. Comparison of residual lateral stresses of a GRS mass due to fill 

compaction between FE analysis with coarse mesh and the analytical model.

187

CHAPTER 7. SUMMARY AND CONCLUSIONS

7.1 SUMMARY 

This study investigated the composite behavior of a GRS mass. It focused on the strength of a 

GRS mass, CIS in a GRS mass, the lateral deformation of a GRS wall with modular block 

facing, and the development of a rational design procedure for determining the required 

reinforcement strength of a GRS wall by considering both lateral stresses in the fill and lateral 

wall deformation of the wall system. 

The following tasks were carried out:

• Reviewed previous studies on composite behavior of a GRS mass and CIS in an 

unreinforced soil mass and a GRS mass.

• Designed a GSGC test for investigating the composite behavior of a GRS mass and 

conducted five GSGC tests with well-controlled conditions and extensive instrumentation 

to monitor behavior under different reinforcement spacing, reinforcement strength, and 

confining pressure.

• Developed an analytical model for the relationship between reinforcement strength 

and reinforcement spacing and derived an equation for calculating composite 

strength properties. 

• Developed a hand computation analytical model for simulation of CIS in a GRS mass.

• Performed FE analyses to simulate the GSGC tests, generate additional data (with 

different confining pressures) for verifying the analytical models in this study, and 

investigate the behavior of GRS composites.

• Verified the analytical models using measured data from the GSGC tests, relevant test 

data available in the literature, and FE analyses. 

• Developed an analytical model for predicting lateral movement of GRS walls with 

modular block facing.

7.2 FINDINGS AND CONCLUSIONS

The findings and conclusions of this study are as follows:

• The results of the GSGC tests were consistent and appear very reliable. The tests provide 

direct observation of the behavior of a GRS mass as related to reinforcement strength and 

spacing. The tests also provide a better understanding of the composite behavior of a 

GRS mass and can be used for validation of analytical models in this study and other 

models of GRS structures in the future.
188

• An equation describing the relative effects of reinforcement spacing and reinforcement 

strength was developed and verified. Based on the equation, the required reinforcement 

strength in a GRS wall can be determined, as can the composite strength properties and 

ultimate pressure carrying capacity of a GRS mass.

• An analytical model for calculating lateral deformation of a GRS wall with modular 

block facing was developed and verified. The required tensile strength of reinforcement 

in design can be determined for a prescribed value of the maximum allowable lateral 

movement of a wall.

• An analytical model for simulating compaction operation of a GRS mass was developed. 

The model allows CIS in the fill to be determined. 

• The presence of geosynthetic reinforcement has a tendency to suppress dilation of the 

surrounding soil and reduce the angle of dilation of the soil mass. 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.
189

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