Performance Test for Geosynthetic

Reinforced Soil Including Effects 

of Preloading

FHWA-RD-01-118 JUNE 2001

Research, Development, and Technology

Turner-Fairbank Highway Research Center

6300 Georgetown Pike

McLean, VA 22101-2296
FOREWORD

Geosynthetic reinforced soil (GRS) systems were tested under different loading 

conditions in order to develop a simplified model for predicting the deformation 

characteristics of a GRS mass. A simplified preloading-reloading (SPR) analytical model 

was developed to predict the deformation characteristics of GRS masses subject to 

monotonic loading and preloading/loading. The SPR model was shown to be able to 

accurately predict the results obtained from a revised laboratory performance test. The 

results of this study will be of interest and utility to geotechnologists working with GRS 

systems.

T. Paul Teng, P. E.

Director, Office of Infrastructure,

 Research and Development

NOTICE

This document is disseminated under the sponsorship of the Department of 

Transportation in the interest of information exchange. The United States Government 

assumes no liability for its contents thereof. This report does not constitute a standard, 

specification, or regulation.

The United States Government does not endorse products or manufacturers. Trademarks 

or manufacturer’s names appear herein only because they are considered essential to the 

object of this document.
Technical Report Documentation Page

1. Report No.

FHWA-RD-01-018

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

5. Report Date

June 2001

4. Title and Subtitle

PERFORMANCE TEST FOR GEOSYNTHETIC-REINFORCED SOIL 

INCLUDING EFFECTS OF PRELOADING

6. Performing Organization Code

7. Author(s)

Kanop Ketchart and Jonathan T.H. Wu

8. Performing Organization Report No.

9. Performing Organization Name and Address 10. Work Unit No. (TRAIS)

Reinforced Soil Research Center

University of Colorado at Denver

1200 Larimer Street

Denver, CO 80217-3364

11. Contract or Grant No.

DTFH61-98-P-00402

12. Sponsoring Agency Name and Address 13. Type of Report and Period Covered

Office of Infrastructure R&D

Federal Highway Administration

6300 Georgetown Pike

McLean, VA 22101-2296

14. Sponsoring Agency Code

15. Supplementary Notes

Contracting Officer's Technical Representative (COTR): M.T. Adams

16. Abstract

A study was undertaken to investigate the behavior of Geosynthetic Reinforced Soil (GRS) masses under various loading 

conditions and to develop a simplified analytical model for predicting deformation characteristics of a generic GRS mass. 

Significant emphasis was placed on the effect of preloading. To conduct the study, a revised laboratory test, known as the 

Soil-Geosynthetic Performance (SGP) test, was first developed. The test is capable of investigating the behavior of a 

generic GRS mass in a manner mimicking the field placement condition, and the soil and geosynthetic reinforcement are 

allowed to deform in an interactive manner. A series of SGP tests was performed. Different soils and reinforcements were 

employed, and the soil-geosynthetic composites were subject to various loading sequences. The tests showed that 

preloading typically reduces vertical and lateral deformations of a generic soil mass by a factor 2 to 7, and that prestressing 

(preloading followed by reloading from a non-zero stress level) can further increase the vertical stiffness by a factor of 2 to 

2.5. Correlations between the results of SGP tests and full-scale GRS structures were evaluated. It was found that the 

degree of reduction in settlement due to preloading could be assessed by the SGP test with very good accuracy. Finite 

element analyses were performed to examine the stress distribution in the SGP test. The importance of using small 

reinforcement spacing was evidenced by the stress distribution. A Simplified Preloading-Reloading (SPR) analytical model 

was developed to predict the deformation characteristics of a GRS mass subject to monotonic loading and 

preloading/reloading. The SPR model was shown to be able to accurately predict the results obtained from the SPG tests 

and numerical analysis of automated plane strain reinforcement (APSR) tests.

17. Key Word

Geosynthetic-reinforced soil, deformation, 

soil-geosynthetic performance test, preloading, 

vertical stiffness, settlement, analytical model.

18. Distribution Statement

No restrictions. This document is available 

to the public through the National 

Technical Information Service, Springfield, 

Virginia 22161

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

282

22. Price

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

TABLE OF CONTENTS

Chapter Page

1. Introduction.......................................................................................................... 1

1.1 Problem Statement ............................................................................................... 1

1.2 Research Objectives............................................................................................. 2

1.3 Method of Research............................................................................................. 2

2. Literature Review................................................................................................. 3

2.1 Behavior of Sand Subject to Unloading-Reloading Cycles................................. 3

2.2 Behavior of Geosynthetic Subject to Unloading-Reloading Cycles.................. 10

2.3 Behavior of Soil-Geosynthetic Interface Subject to

 Unloading-Reloading Cycles............................................................................. 15

2.4 Behavior of GRS Mass Subject to Unloading-Reloading Cycles...................... 15

2.4.1 General Behavior ............................................................................................... 15

2.4.2 Preloaded GRS Structures.................................................................................. 21

2.5 Plane Strain Tests for Reinforced-Soil Mass..................................................... 32

3. Laboratory Tests on Soils, Geosynthetics, and Soil-Geosynthetic Interfaces .. 43

3.1 Test Materials..................................................................................................... 43

3.1.1 Soils.................................................................................................................... 43

3.1.2 Geosynthetics..................................................................................................... 47

3.2 Loading System ................................................................................................. 49

3.3 Loading Sequences ............................................................................................ 49

3.4 Conventional Triaxial Compression Tests for Soils.......................................... 53

3.4.1 Test Description................................................................................................. 53

3.4.2 Specimen Preparation and Test Procedure ........................................................ 53

3.4.3 Measurement and Test Data Reduction............................................................. 56

3.4.4 Test Programs .................................................................................................... 57

3.4.5 Test Results and Discussions ............................................................................. 60

3.5 In-Isolation Load-Extension Tests for Geosynthetics........................................ 80

3.5.1 Test Description................................................................................................. 80

3.5.2 Specimen Preparation and Test Procedure ........................................................ 80

3.5.3 Measurement and Test Data Reduction............................................................. 81

3.5.4 Test Programs .................................................................................................... 86

3.5.5 Test Re sults and Discussions ............................................................................. 89

3.6 Interface Direct Shear Tests for Soil-Geosynthetic Interfaces........................... 98

3.6.1 Test Description................................................................................................. 98

3.6.2 Specimen Preparation and Test Procedure ........................................................ 99

3.6.3 Measurement and Test Data Reduction............................................................. 99

3.6.4 Test Programs .................................................................................................. 100

3.6.5 Test Results and Discussions ........................................................................... 103

3.7 Summary and Concluding Remarks ................................................................ 111
iv

TABLE OF CONTENTS (Continued)

Chapter Page

4. SGP Test Apparatus......................................................................................... 112

4.1 First and Second Generations of SGP Test Apparatus .................................... 112

4.1.1 First-Generation SGP Test Apparatus ............................................................. 112

4.1.2 Second-Generation SGP Test Apparatus ......................................................... 113

4.2 Modified SGP Test Apparatus ......................................................................... 113

4.2.1 Apparatus Configurations ................................................................................ 113

4.2.2 Boundary Conditions ....................................................................................... 115

4.2.3 Specimen Preparation and Test Procedure ...................................................... 124

4.2.4 Instrumentation ................................................................................................ 126

4.3 Test Programs .................................................................................................. 133

5. Behavior of GRS Mass Subject to Monotonic Loading and 

 Unloading-Reloading Cycles and Finite Element Analysis............................. 137

5.1 Monotonic-Loading SGP Test Results and Discussions ................................. 137

5.2 Unloading-Reloading SGP Test Results and Discussions ............................... 146

5.3 Effects of Preloading on Deformation and Strength of GRS Mass ................. 160

5.3.1 Effects of Preloading on Deformation............................................................. 160

5.3.2 Effects of Preloading on Strength.................................................................... 162

5.4 Finite Element Analysis of the SGP Test ........................................................ 169

5.4.1 Program Description........................................................................................ 169

5.4.2 Material and Interface Behavior Models ......................................................... 169

5.4.3 Determination of Model Parameters................................................................ 175

5.4.4 Finite Element Modeling ................................................................................. 176

5.4.5 Comparison of Finite Element Analysis with SGP Test Results..................... 177

5.4.6 Stresses in GRS Mass in the SGP Test............................................................ 188

5.5 Summary and Concluding Remarks ................................................................ 194

6. Simplified Preloading-Reloading Model for GRS Mass ................................. 196

6.1 Load-Transfer Module ..................................................................................... 196

6.1.1 Load-Transfer Analysis.................................................................................... 196

6.1.2 Comparison of Load-Transfer Analysis with 

 Experimental and Numerical Analysis Results of the APSR Test .................. 204

6.1.3 Average Stresses in GRS Mass........................................................................ 212

6.2 Deformation Module........................................................................................ 212

6.2.1 Average Stress-Displacement Diagram........................................................... 212

6.2.2 Vertical and Horizontal Displacements ........................................................... 213

6.3 Comparison of SPR Model Prediction with SGP Test Results........................ 217

6.3.1 Application of SPR Model to SGP Test .......................................................... 219

6.3.2 Determination of Material and Interface Properties ........................................ 276
v

TABLE OF CONTENTS (Continued)

Chapter Page

6.3.3 Calculation Example ........................................................................................ 227

6.3.4 Comparison of SPR Model Prediction with SGP Test Results........................ 232

6.4 Parametric Study on Deformation of GRS Mass............................................. 241

6.5 Summary and Concluding Remarks ................................................................ 245

7. Correlation Between SGP Tests and Preloaded GRS Structure ...................... 246

7.1 FHWA Pier ...................................................................................................... 246

7.1.1 Load Test Results............................................................................................. 246

7.1.2 SGP Test Results.............................................................................................. 247

7.1.3 Correlation Between SGP Test and FHWA Pier ............................................. 247

7.2 Black Hawk Abutments................................................................................... 253

7.2.1 Full-Scale Preloading Results.......................................................................... 253

7.2.2 SGP Test Results.............................................................................................. 253

7.2.3 Correlation Between the Modified SGP Test and Black Hawk Abutments.... 253

7.3 Summary and Concluding Remarks ................................................................ 259

8. Summary, Conclusions, and Recommendations.............................................. 260

8.1 Summary.......................................................................................................... 260

8.2 Findings and Conclusions ................................................................................ 261

8.3 Recommendations............................................................................................ 263

References................................................................................................................. 264
vi

FIGURES

Figure Page

2.1 Possible Stress Paths in Triaxial Compression..................................................... 5

2.2 Stress Paths of Conventional Triaxial Compression ............................................ 6

2.3 Stress-Strain Curve from Cyclic Triaxial Compression Tests ............................. 7

2.4 Unloading-Reloading Modulus of Soil in Triaxial Compression ........................ 8

2.5 Response of HPDE Geogrid Specimens to Multi-Increment and 

 Single-Increment Cyclic Loading....................................................................... 11

2.6 Characteristics of Cyclic Response of Geosynthetic Specimen ........................ 12

2.7 Area of Hysteresis Loops for HPDE and PET Specimens ................................ 13

2.8 Unloading-Reloading Modulus for HPDE and PET Specimens ....................... 14

2.9 Interface Friction Angle as Function of Number of Repeated Loadings for 

 Ottawa Sand on HPDE........................................................................................ 17

2.10 Increased Confinement Concept of Soil Reinforcement .................................... 18

2.11 Stress-Strain Relationships from Triaxial Compression Tests on 

 Reinforced Sand .................................................................................................. 19

2.12 Ratcheting Mechanism........................................................................................ 20

2.13 Schematic Diagram of Preloaded/Prestressed GRS Structure ........................... 22

2.14 Typical Load Path of Preloaded/Prestressed GRS Structure ............................. 23

2.15 Principal Elements of FHWA Pier...................................................................... 25

2.16 Preloading Assembly of FHWA Pier.................................................................. 26

2.17 Prototype Preloaded/Prestressed GRS Bridge Pier ............................................ 29

2.18 Black Hawk Abutments...................................................................................... 30

2.19 Preloading Assembly of Black Hawk Abutments.............................................. 31

2.20 Behavior of a Unit Cell With and Without Inclusions: 

 (a) Dense Sand and (b) Loose Sand .................................................................... 35

2.21 Schematic Diagram of Plane Strain Compression Test Specimen .................... 36

2.22 Plane Strain Compression Test Results for Unreinforced and 

 Reinforced Sand Specimens ............................................................................... 37

2.23 Cross Section Through the APSR Cell ............................................................... 38

2.24 Stress Distribution in a Steel Inclusion of the APSR Cell ................................. 39

2.25 Schematic Diagram of the Unit Cell Device: 

 (a) Profile and (b) Plan View Section................................................................. 40

2.26 Unit Cell Device Test Results of Unreinforced and Reinforced Soils ............... 41

3.1 Grain Size Distribution of Ottawa Sand ............................................................. 44

3.2 Grain Size Distribution of Road Base Soil ......................................................... 45

3.3 Moisture Content-Dry Unit Weight Relationship of Road Base Soil................. 46

3.4 MTS-810 Loading System.................................................................................. 51

3.5 General Loading Sequences................................................................................ 52

3.6 Conventional Triaxial Compression Test Apparatus.......................................... 55
vii

Figures (Continued)

Figure Page

3.7 Test Results of Monotonic-Loading CTC Tests on Ottawa Sand

 (Tests T-M-S1, 2, and 3).................................................................................... 62

3.8 Test Results of Monotonic-Loading CTC Tests on Road Base Soil

 (Tests T-M-RB1, 2, and 3).................................................................................. 63

3.9 Results of Test T-UR-S1 (Confining Pressure = 69 kPa)................................... 64

3.10 Results of Test T-UR-S2 (Confining Pressure = 207 kPa)................................. 65

3.11 Results of Test T-UR-S3 (Confining Pressure = 345 kPa)................................. 66

3.12 Results of Test T-UR-RB1 (Confining Pressure = 69 kPa)................................ 67

3.13 Results of Test T-UR-RB2 (Confining Pressure = 207 kPa).............................. 68

3.14 Results of Test T-UR-RB3 (Confining Pressure = 345 kPa).............................. 69

3.15 ERL-Z versus 

f

PL

− )

− )

1 3

1 3

(

(

s s

s s

 Relationships of Ottawa Sand ................................... 72

3.16 ERL-PS versus 

f

PL

− )

− )

1 3

1 3

(

(

s s

s s

 Relationships of Ottawa Sand .................................. 73

3.17 ERL-Z versus 

f

PL

− )

− )

1 3

1 3

(

(

s s

s s

 Relationships of Road Base Soil ............................... 74

3.18 ERL-PS versus 

f

PL

− )

− )

1 3

1 3

(

(

s s

s s

 Relationships of Road Base Soil.............................. 75

3.19 Deformation Modulus Versus Confining Pressure Relationships 

 of Ottawa Sand.................................................................................................... 76

3.20 Deformation Modulus Versus Confining Pressure Relationships 

 of Road Base Soil................................................................................................ 77

3.21 p-q Diagram at Failure of Ottawa Sand .............................................................. 78

3.22 p-q Diagram at Failure of Road Base Soil.......................................................... 79

3.23 Typar 3301 Specimen ......................................................................................... 82

3.24 LE Test Setup for Typar 3301 Specimen............................................................ 83

3.25 Amoco 2044 Specimen....................................................................................... 84

3.26 LE Test Setup for Amoco 2044 Specimen......................................................... 85

3.27 Tensile Load Versus Axial Strain Relationship, Test G-M-3301....................... 91

3.28 Tensile Load Versus Axial Strain Relationships, Tests G-M-2044-1, 2............ 91

3.29 Tensile Load Versus Axial Strain Relationships of

 Tests G-UR-3301-1, 2, and 3 (Stress-Controlled Part)....................................... 92

3.30 Tensile Load Versus Axial Strain Relationships of Test G-M-3301 and 

 Tests G-UR-3301-1, 2, 3 (Strain-Controlled Part).............................................. 93

3.31 Tensile Load Versus Axial Strain Relationship 

 of Tests G-UR-2044-1, 2, and 3 (Stress-Controlled Part) ................................. 94
viii

Figures (Continued)

Figure Page

3.32 Tensile Load Versus Axial Strain Relationships of Test G-M-2044-1 and

 Tests G-UR-2044-1, 2 (Strain-Controlled Part).................................................. 95

3.33 Stiffness Ratio Versus

ULT

PL

T

T

 Relationships of Typar 3301 and

 Amoco 2044........................................................................................................ 96

3.34 Failure Load Ratio Versus

ULT

PL

T

T

 Relationships of Typar 3301 and

 Amoco 2044........................................................................................................ 97

3.35 Results of Tests DS-UR-(S+2044)-1, 2, and 3 ................................................. 105

3.36 Results of Tests DS-UR-(RB+2044)-1, 2, and 3 .............................................. 106

3.37 Interface Stiffness Versus Normal Stress Relationships of Ottawa Sand and

 Amoco 2044 Interface....................................................................................... 107

3.38 Interface Stiffness Versus Normal Stress Relationships of Road Base Soil

 and Amoco 2044 Interface ................................................................................ 108

3.39 Peak Shear Stress Versus Normal Stress Relationships of Ottawa sand

 and Amoco 2044 Interface ................................................................................ 109

3.40 Peak Shear Stress Versus Normal Stress Relationships of Road Base Soil

 and Amoco 2044 Interface ................................................................................ 110

4.1 First-Generation SGP Test................................................................................ 117

4.2 Second-Generation SGP Test ........................................................................... 117

4.3 Schematic Diagram of the Modified SGP Test................................................. 118

4.4 Modified SGP Test Apparatus on MTS-810 Loading System Before Testing 119

4.5 Specimen Dimensions of Modified SGP Test .................................................. 120

4.6 Rigid Container of Modified SGP Test Apparatus ........................................... 121

4.7 Top View of Modified SGP Test Apparatus..................................................... 122

4.8 Cross Section of Modified SGP Test Apparatus (Section A-A)....................... 123

4.9 Specimen Preparation for Ottawa Sand Specimen ........................................... 128

4.10 Specimen Preparation for Road Base Soil Specimen....................................... 129

4.11 Strain Gauge Layout ......................................................................................... 130

4.12 Strain Gauge Calibration with LE Test............................................................. 131

4.13 Calibration Curve for Strain Gauges................................................................. 132

5.1 Vertical Load Versus Displacement Relationships of Tests

 P-M-RB and P-M-(RB+2044) .......................................................................... 140

5.2 Vertical Load Versus Displacement Relationships of Tests

 P-M-S, P-M-(S+3301), and P-M-(S+2044)...................................................... 141

5.3 Horizontal Displacements of Points T, M, and B at 4-kN, 8-kN, and 11-kN

 Vertical Loads................................................................................................... 142
ix

Figures (Continued)

Figure Page

5.4 Two Failure Modes in SGP Tests..................................................................... 143

5.5 Diagonal Shear Failure...................................................................................... 144

5.6 Wedge-Type Shear Failure ............................................................................... 145

5.7 Vertical Load Versus Displacement Relationships of Test P-UR-S................. 151

5.8 Vertical Load Versus Displacement Relationships of Test P-UR-(S+2044)-1 152

5.9 Vertical Load Versus Displacement Relationships of Test P-UR-(S+2044)-2 153

5.10 Vertical Load Versus Displacement Relationships of Test P-UR-(S+2044)-3 154

5.11 Vertical Load Versus Displacement Relationships of Test P-UR-RB.............. 155

5.12 Vertical Load Versus Displacement Relationships of Test P-UR-(RB+2044). 156

5.13 Vertical Applied Pressure Versus Displacement Relationships of 

 the FHWA Pier.................................................................................................. 157

5.14 Conceptual Stress Diagrams for the RL-Z and RL-PS Paths ........................... 158

5.15 Vertical Load Versus Reinforcement Strain Relationship of 

 Test P-UR-(RB+2044), Gage R-3..................................................................... 159

5.16 Vertical Load Versus Displacements of Virgin Specimen from

 Test P-M-(S+2044) and Preloaded Specimens from 

 Tests P-UR-(S+2044)-1,2,3 .............................................................................. 163

5.17 Vertical Load Versus Displacements of Virgin Specimen from

 Test P-M-(RB+2044) and Preloaded Specimens from 

 Tests P-UR-(RB+2044) .................................................................................... 164

5.18 Vertical Load Versus Reloading Displacement Relationships (RL-Z path)

 of Tests P-UR-S and P-UR-(S+2044)-1 ........................................................... 165

5.19 Vertical Load Versus Reloading Displacement Relationships (RL-Z path)

 of Tests P-UR-RB and P-UR-(RB+2044)......................................................... 166

5.20 Vertical Load Versus Reloading Displacement Relationships (RL-PS path)

 of Tests P-UR-RB and P-UR-(RB+2044)......................................................... 167

5.21 Hyperbolic Model of Stress-Strain Behavior.................................................... 179

5.22 Component of Interface Elements and Hyperbolic

 Shear Stress-Relative Shear Displacement ....................................................... 180

5.23 Calculated Versus Measured CTC Test Results of Road Base Soil ................. 182

5.24 Calculated Versus Measured DS Test Results of Road Base Soil and 

 Amoco 2044 Interface....................................................................................... 183

5.25 Finite Element Discretizations of SGP Test Specimens ................................... 184

5.26 Measured and Calculated Vertical and Average Horizontal Displacements

 of Test P-M-RB................................................................................................. 185

5.27 Measured and Calculated Vertical and Average Horizontal Displacements

 of Test P-M-(RB+2044).................................................................................... 186

5.28 Calculated Strain Distributions in the Middle Reinforcement Layer ............... 187
x

Figures (Continued)

Figure Page

5.29 Vertical Stress Distributions at 6-kN Vertical Load of

 Tests P-M-RB and P-M-(RB+2044)................................................................. 190

5.30 Horizontal Stress Distributions at 6-kN Vertical Load of

 Tests P-M-RB and P-M-(RB+2044)................................................................. 191

5.31 Shear Stress Distributions at 6-kN Vertical Load of 

 Tests P-M-RB and P-M-(RB+2044)................................................................. 192

5.32 Distribution of Minor Principal Stress Ratio at 6-kN Vertical Load of 

 Test P-M-(RB+2044) ........................................................................................ 193

6.1 An Idealized Plane-Strain GRS Mass for the SPR Model................................ 197

6.2 Equilibrium of Differential Soil and Reinforcement Elements ....................... 198

6.3 Schematic Diagrams of the APSR Cell ............................................................ 207

6.4 Predicted and Measured Normalized Reinforcement Stress Distributions

 in the APSR Cell............................................................................................... 209

6.5 Average Stress-Displacement Diagram for Monotonic Loading...................... 215

6.6 Average Stress-Displacement Diagram for Unloading and Reloading ............ 216

6.7 SGP-GRS Mass................................................................................................. 218

6.8 Tensile Load Versus Axial Strain Relationship of Amoco 2044

 at Small Strain................................................................................................... 225

6.9 Predicted Versus Measured Vertical and Average Horizontal

 Displacements of Test P-M-(S+2044) .............................................................. 234

6.10 Predicted Versus Measured Vertical and Average Horizontal

 Displacements of Test P-M-(RB+2044) ........................................................... 235

6.11 Predicted Versus Measured Reloading Vertical and Horizontal 

 Displacements of Test P-UR-(S+2044), RL-Z Path......................................... 236

6.12 Predicted Versus Measured Reloading Vertical and Horizontal 

 Displacements of Test P-UR-(S+2044), RL-PS Path....................................... 237

6.13 Predicted Versus Measured Reloading Vertical and Horizontal 

 Displacements of Test P-UR-(RB+2044), RL-Z Path...................................... 238

6.14 Predicted Versus Measured Reloading Vertical and Horizontal 

 Displacements of Test P-UR-(RB+2044), RL-PS1 Path.................................. 239

6.15 Predicted Versus Measured Reloading Vertical and Horizontal 

 Displacements of Test P-UR-(RB+2044), RL-PS2 Path.................................. 240

6.16 Vertical Displacement Ratio Versus Stiffness Ratio Relationships................. 243

6.17 Horizontal Displacement Ratio Versus Stiffness Ratio Relationships ............. 244

7.1 Vertical Applied Pressure Versus Displacement relationships of

 the FHWA Pier.................................................................................................. 249

7.2 Vertical Load versus Vertical Displacement Relationships of the SGP Test... 250
xi

Figures (Continued)

Figure Page

7.3 Vertical Improvement Ratio Versus Applied Load Level Relationships of

 the FHWA Pier and SGP Test ......................................................................... 251

7.4 Horizontal Improvement Ratio Versus Applied Load Level Relationships of

 the FHWA Pier and SGP Test .......................................................................... 252

7.5 Vertical Applied Pressure Versus Average Settlement Relationships

 of Footing #1 of the Black Hawk Abutments................................................... 255

7.6 Vertical Applied Pressure Versus Average Settlement Relationships

 of Footing #3 of the Black Hawk Abutments................................................... 256

7.7 Predicted and Measured Vertical Load Versus Vertical Displacement of

 the Modified SGP Tests.................................................................................... 257

7.8 Vertical Improvement Ratio Versus Applied Load Level Relationships of 

 the Black Hawk Abutments and SGP Tests...................................................... 258
xii

TABLES

Table Page

2.1 Summary of Four Plane Strain Compression Tests for Reinforced-Soil Mass.... 42

3.1 Some Index Properties of Geosynthetics.............................................................. 48

3.2 CTC Test Program for the Ottawa Sand ............................................................... 58

3.3 CTC Test Program for the Road Base Soil........................................................... 59

3.4 LE Test Program for Typar 3301.......................................................................... 87

3.5 LE Test Program for Amoco 2044........................................................................ 88

3.6 DS Test Program for the Ottawa Sand and Amoco 2044 Interface .................... 101

3.7 DS Test Program for the Road Base Soil and Amoco 2044 Interface ................ 102

4.1 SGP Test Program for the Ottawa Sand Specimen............................................. 134

4.2 SGP Test Program for the Road Base Soil Specimen......................................... 136

5.1 Summary of Failure Loads of the SGP Tests...................................................... 168

5.2 Summary of Hyperbolic Soil Parameters for Finite Element Analysis.............. 181

5.3 Summary of Interface Properties for Finite Element Analysis........................... 181

6.1 Input Parameters for Load-Transfer Analysis of the APSR Test Specimen....... 208

6.2 Reference Properties for Comparison of Maximum Normalized

 Reinforcement Stress for Table 6.3 .................................................................... 210

6.3 Comparison of Maximum Normalized Reinforcement Stress from

 Finite Element Analysis and Load-Transfer Analysis ........................................ 211

6.4 Summary of Soil Properties for the SPR Model................................................. 222

6.5 Summary of Interface Properties for the SPR Model......................................... 226

6.6 Calculation Example of the SPR Model for SGP-GRS Mass............................. 228

6.7 Properties for the Baseline GRS Mass................................................................ 242
1

1. Introduction 

1.1 Problem Statement 

A geosynthetic-reinforced soil (GRS) mass is a soil mass containing 

horizontally placed layers of geosynthetic reinforcement. When subject to a vertical 

load, a GRS mass typically exhibits higher stiffness and higher load carrying 

capacity than a soil mass without the reinforcement. The increase in stiffness and 

strength is a result of an internal restraining effect imposed by the geosynthetic 

reinforcement on the GRS mass. The geosynthetic reinforcement restrains 

deformation of the GRS mass along the axial direction of the reinforcement because 

of soil-geosynthetic interaction.

The behavior of GRS masses has been studied by using laboratory tests such 

as triaxial compression tests (e.g., Yang, 1974; Broms, 1978) and plane strain 

compression tests (e.g., McGown et al., 1978; Tatsuoka and Yamauchi, 1986; 

Whittle et al., 1992; Boyle, 1995). Most of these tests, however, are of relatively 

small dimensions and can lead to misleading results. 

In recent years, a number of full-scale tests have been conducted to investigate 

the behavior of GRS masses (e.g., Tatsuoka et al., 1997; Adams, 1997; Uchimura et 

al., 1998). Although these full-scale tests provided valuable information, it is cost 

prohibitive and very time consuming to investigate the behavior of GRS masses 

with different types of soils and reinforcements under various loading conditions by 

using only full-scale tests. 

Wu and Helwany (1996) developed a large-scale laboratory test, known as the 

Soil-Geosynthetic Performance (SGP) test, to investigate the behavior of soilgeosynthetic interaction on long-term behavior of GRS masses under plane strain 

condition. Ketchart and Wu (1996) subsequently proposed a revised SGP test to 

simplify the sample preparation procedure. 

The main features of these SGP tests are: 

1. The test specimen is in a state of plane strain condition, a prevailing 

condition in typical GRS structures. 

2. The soil in the SGP tests can be prepared in a manner mimicking the 

field conditions. The soil can be compacted to simulate the field 

placement density and moisture of a GRS structure. The effect of 

changing moisture content after construction can also be investigated. 

3. The SGP tests are capable of simulating the typical load transfer 

mechanism in GRS structures. In the SGP tests, the reinforcement and 

the confining soil are allowed to deform in an interactive manner. The 

tensile stresses in the reinforcement are induced by the stresses developed 

in the soil resulting from self-weight of the soil and externally applied 

loads. 

4. The boundary displacements of the GRS mass, in both vertical and 

lateral directions, as well as its internal displacements and reinforcement 

strains can be accurately measured. 

5. The SGP tests can accommodate a generic GRS mass containing a wide 

variety of backfill types. Due to their relatively large dimensions, the 

SGP test apparatuses can accommodate backfill with a maximum 
2

particle size up to about 50 mm (2 in) and D50 up to about 30 mm (1.2 

in). This covers the entire range of allowable particle sizes and 

gradations recommended by Elias and Christopher (1996). 

Preloading is known to be an effective means to reduce post-construction 

settlement of earth structures. A number of full-scale tests have recently been 

conducted to examine the effects of preloading on the performance of GRS bridge 

supporting structures (Tatsuoka et al., 1997; Adams, 1997; Uchimura et al, 1998; 

Ketchart and Wu, 1998). Although these tests showed very promising results, the 

fundamental behavior of preloaded GRS masses has not been fully elucidated. 

Many important questions, such as what is the appropriate preloading magnitude, 

what is an efficient loading sequence, and how much benefits are to be gained for a 

given GRS mass, have remained unanswered. 

1.2 Research Objectives 

The objectives of this study were two-fold. The first objective was to 

investigate the behavior of GRS masses with different soils and reinforcements 

under various loading conditions, including preloading. A revised SGP test capable 

of investigating the behavior of a generic GRS mass with improved precision was to 

be developed for the study. In addition, correlations between the results of the SGP 

test and the full-scale GRS structures were to be evaluated. The second objective 

was to develop a simplified analytical model for predicting deformation 

characteristics of a generic GRS mass. 

1.3 Method of Research

To fulfill the research objectives outlined above, the following six tasks were 

undertaken: 

Task 1: Review previous studies on the behavior of sands, geosynthetics, soil 

geosynthetic interfaces, and GRS masses subject to unloading-reloading cycles, and 

on plane-strain tests of reinforced soil masses (see Chapter 2). 

Task 2: Conduct laboratory tests to examine the behavior of different soils, 

geosynthetics, and soil-geosynthetic interfaces subject to unloading-reloading cycles 

(see Chapter 3). 

Task 3: Develop a revised SGP test apparatus so that the behavior of GRS masses 

can be investigated with improved precision (see Chapter 4). 

Task 4: Conduct a series of SGP tests to investigate the behavior of GRS masses 

subject to different loading sequences. Finite element analysis was also conducted 

to examine the stress distribution in the generic GRS mass of the SGP test (see 

Chapter 5). 

Task 5: Develop a simplified analytical model for predicting deformation 

characteristics of a generic GRS mass (see Chapter 6). 

Task 6: Examine the correlation between the SGP test and preloaded full-scale 

GRS structures (see Chapter 7). 
3

2. Literature Review

 A review of some previous studies on the behavior of soils, geosynthetics, 

soil-geosynthetic interfaces, and GRS masses subject to unloading-reloading cycles is 

presented in this chapter. Such unloading-reloading cycles are categorized as a static 

load on the basis of Ishihara’s (1998) definition, as the load application lasts for more 

than 10 seconds. In addition, the preloaded GRS structures are briefly described. 

This chapter also presents a review of four plane strain tests conducted on reinforced 

soils. 

2.1 Behavior of Sand Subject to Unloading-Reloading Cycles 

When a mass of sand is subjected to a stress variation, its deformation can be 

considered as the sum of a recoverable (elastic) component and an irrecoverable 

(plastic) component. From the standpoint of the deformation of grains and sliding 

between grains, the recoverable part is due to the elastic deformation of individual 

grains, whereas the irrecoverable part is primarily caused by the sliding between 

individual grains. 

Lade and Duncan (1976) proposed criteria to define primary loading, 

unloading, and reloading modes for different stress paths of a triaxial compression 

test. Figure 2.1 shows a diagram representing the stress paths that can be produced in 

a triaxial compression in terms of the deviator stress (σ1-σ3) and the confining stress 

(σ3). A “stress level” is used as the basis in formulating a criterion for the mode of 

deformation. The “stress level” refers to the fraction of the soil strength that is 

mobilized. For a cohesionless soil, a straight line passing through the origin of σ1-σ3

versus σ3 diagram represents a constant stress level. Proportional loading occurs 

when the stresses change in a manner that the stress level remains constant (stress 

paths 5 and 9). Unloading is experienced whenever the stress level decreases (stress 

paths 6, 7, 8, and 11). Reloading is said to occur whenever the stress level increases 

but remains less than the past maximum value experienced by the soil (stress path 

10). Primary loading is experienced only when the stresses change in such a manner 

that the stress level exceeds its past maximum value (stress paths 1, 2, 3, and 4). The 

stress-path for a conventional triaxial compression test in which the confining 

pressure remains constant while the axial stress is increased is represented by a 

vertical line, as shown in Figure 2.2. 

When a soil specimen is unloaded, individual grains do not rebound to their 

original positions but remain approximately in their displaced positions (Makhlouf 

and Stewart, 1965). If a soil specimen is unloaded from a stress state, A (see Figure 

2.3), to another stress state, B, then reloaded again to the original stress condition, A, 

along the same stress-strain curve, the unloading and reloading stress-strain paths 

coincide in a reversible process (Holubec, 1968). In general, the identity of the 

unloading and reloading paths is not perfect, especially in the high-stress range, as 
4

evidenced by a hysteresis loop. A hysteresis loop exists as shown in the third 

unloading-reloading cycle of the stress-strain curve in Figure 2.3. The hysteresis loop 

in the unloading-reloading cycle implies that: (a) there is no longer a one-to-one 

relationship between stress and strain in this unloading-reloading region, and (b) 

energy is dissipated in an unloading-reloading cycle, which also implies inelastic 

response (Wood, 1990). 

Holubec (1968) suggested that the identity of the unloading and reloading 

paths can be assumed if the width of a hysteresis loop is small compared with the 

magnitude of the reversible strains, or when specimens are unloaded to zero-shearing 

stress from a stress less than approximately 80% of the maximum deviator stress. 

Barden et al. (1969) also observed that if the unloading-reloading cycle takes place 

when a principle stress ratio (σ1/σ3) is less than two-third of the peak value, a 

hysteresis loop is small. However, if the unloading-reloading cycle is in a region that 

has peak or post-peak values of principle stress ratios, then the hysteresis loop is 

significant. Note that the width of the hysteresis loop of sand in a conventional 

triaxial compression test was the greatest in the first cycle and decreased in 

subsequent cycles (Makhlouf and Stewart, 1965). 

The deformation of sand in the unloading-reloading range that takes place at 

moderate stress levels (i.e., not close to the failure stress) can be approximately 

characterized as linear elastic (Holubec, 1968; Duncan and Chang, 1970; Coon and 

Evans, 1971; Lade and Duncan, 1975). The average secant modulus of the 

unloading-reloading loop was defined as the unloading-reloading modulus (Eur) by 

Duncan and Chang (1970), as shown in Figure 2.4. The unloading-reloading 

modulus is proportional to the confining stress (Duncan and Chang, 1970). The 

unloading-reloading modulus depends upon the change of the deviator stress in an 

unloading-reloading cycle (Makhlouf and Stewart, 1965). The unloading-reloading 

modulus increases if the change of deviator stress is held constant but the magnitude 

of minimum deviator stress is increased. With a constant magnitude of the maximum 

stress, the unloading-reloading modulus decreases with decreasing minimum deviator 

stress in unloading-reloading cycles. 

The deformations of granular soils in the primary loading are almost 

unaffected by the previous unloading-reloading cycles that occur at lower stress 

levels (Makhlouf and Stewart, 1965; Ko and Scott, 1967). Unlike those in the 

primary loading stress path, the deformation of sand under a reloading stress path is 

very much dependent on the stress histories it has experienced. 
5

Figure 2.1: Possible Stress Paths in Triaxial Compression 

(After Lade and Duncan, 1976) 
6

 Figure 2.2: Stress Paths of Conventional Triaxial Compression 

 (After Lade and Duncan, 1976) 
7

Figure 2.3: Stress Strain Curve from Cyclic Triaxial Compression Tests 

 (After Holubec, 1968) 
8

Figure 2.4: Unloading Reloading Modulus of Soil in Triaxial Compression 

(After Duncan and Chang, 1970) 
9

Yoshimi et al. (1975) used an adaptation of a quicksand tank to reproduce 

uniform void ratios in large samples of sand using a controlled upward flow of water. 

By reversing the direction of water flow, one-dimensional loading was induced over 

the entire sample. They found that a normally consolidated sand sample was about 

six times more compressible than a prestressed sample, even though their initial void 

ratios or densities were equal. 

Lambrechts and Leonards (1978) conducted a series of triaxial compression 

tests under different stress paths to examine effects of stress history on deformation of 

sand. Each set of stress paths used in simulating different stress histories was a 

combination of stress-path segments including proportional loading, unloading, and 

reloading. At the end of each set of such stress paths, the axial stress was increased 

while maintaining a constant confining pressure as in a conventional triaxial test. 

They found that by prestressing the sand under Ko-condition, the modulus of 

deformation under the conventional triaxial compression loading increased by one 

order of magnitude. 

Bishop and Eldin (1953) studied the effect of stress history on the angle of 

internal friction of sand by conducting a number of triaxial compression tests. They 

concluded that the angle of internal friction of sand is independent of the stress 

history. This conclusion was confirmed by Lade and Duncan (1976) and Lambrechts 

and Leonards (1978). 

Based on the literature review outlined above, the behavior of sand subject to 

preloading-reloading loads is summarized as follows: 

1. Elastic behavior can be assumed for sand under unloading-reloading cycles 

that take place at moderate stress levels. 

2. A hysteresis loop exists in unloading-reloading cycles. The hysteresis loop 

indicates inelastic behavior and energy dissipation during unloading and reloading. 

The width or area of the hysteresis loop becomes significant during unloading and 

reloading at high stress levels. 

3. An average secant modulus of the unloading-reloading loop can be 

represented by the unloading-reloading modulus (Eur). The unloading-reloading 

modulus (Eur) is proportional to the confining stress and also depends on maximum 

and minimum values of deviator stress change in the unloading-reloading cycles. 

4. Deformation of sand under a reloading stress path is strongly influenced by 

the stress history. The deformation moduli increase significantly after the sand has 

been prestressed. 

5. The angle of internal friction or the shear strength of sand is independent of 

the stress history. 
10

2.2 Behavior of Geosynthetics Subject to Unloading-Reloading Cycles 

Some studies have been conducted by in-isolation cyclic load extension tests 

to examine the cyclic behavior of geosynthetics. Barthurst and Cai (1994) conducted 

a series of in-isolation cyclic load-extension tests on HDPE (high density 

polyethylene) and PET (polyester) geogrid specimens. The specimens were tested at 

different loading frequencies from 0.1 to 3.5 Hz and over a range of load amplitudes. 

Figure 2.5 shows typical load-strain response curves of the HPDE geogrid specimens 

under multi-increment and single-increment cyclic loadings. A hysteresis loop exists 

at all unloading-reloading cycles. Accumulative plastic strains due to multiple cycles 

of cyclic loading are evident. Some qualitative features of a cyclic load-deformation 

response curve are illustrated in Figure 2.6. Figure 2.6 identifies the parameters that 

can be used to characterize the load-deformation response as a function of strain. A 

non-linear hysteresis load-deformation loop for each unloading-reloading cycle (εur, 

Tur) is defined by the average unloading-reloading modulus (Jur) of the unloadingreloading cycle and its contained area (Aur). 

 The area of a hysteresis loop (Aur) of the cyclic load-deformation curves of the 

geogrid specimens was found to be strongly influenced by the strain level and the 

frequency of loading. The area, Aur , increases with the strain level and decreases 

with increasing frequency at a given strain, as shown in Figure 2.7. It should be 

noted that below 0.5% strain of the HDPE geogrid and 0.8% strain of the PET 

geogrid, the specimens behaved in a linear elastic manner with fully recoverable 

strain. Figure 2.8 shows the average unloading-reloading modulus versus strain 

relationships for different load amplitudes and frequencies. The average unloadingreloading modulus, Jur, of the HDPE specimens reduces with the strain level, whereas 

the PET specimens showed a reduction of Jur up to about 3% of strains followed by an 

increase. 

 Similar in-isolation cyclic load-extension tests on HDPE geogrids were 

conducted by Nocola and Montanelli (1997). The specimens were tested at different 

loading frequencies from 0.1 to 1.0 Hz and over different cyclic loading ranges. The 

tests showed that the unloading-reloading modulus, Jur, increases with strains until it 

reaches a yield point after which the unload-reload tensile modulus gradually 

decreases with increasing strains. 

 In summary, the unloading-reloading behavior of geosynthetics can be 

quantified by the unloading-reloading modulus (Jur) and the area of a hysteresis loop 

(Aur). The hysteresis loop occurs when geosynthetics are subjected to unloadingreloading cycles. The area of hysteresis loop increases with strain level. At small 

strains (0.5% to 0.8%), the area of hysteresis loop becomes negligible, and the 

geogrids behave in a linear manner. For HPDE geogrids, the unloading-reloading 

modulus increases slightly with increasing strains until it reaches a “yield” point, after 

which the unloading-reloading modulus reduces with increasing strains. 
11

Figure 2.5: Response of HPDE Geogrid Specimens to Multi-Increment and 

Single-Increment Cyclic Loading (After Bathurst and Cai, 1994) 
12

Figure 2.6: Characteristics of Cyclic Response of Geosynthetic Specimen 

(After Bathurst and Cai, 1994) 
13

Figure 2.7: Area of Hysteresis Loops for HPDE and PET Specimens 

 (After Bathurst and Cai, 1994) 
14

Figure 2.8: Unloading-Reloading Modulus for HPDE and PET Specimens 

(After Bathurst and Cai, 1994) 
15

2.3 Behavior of Soil-Geosynthetic Interfaces Subject to Unloading-Reloading 

Cycles 

A limited number of works on the behavior the soil-geosynthetic interfaces 

subject to unloading-reloading cycles were available in the literature. O’Rourke et al.

(1990) conducted a series of direct shear tests on Ottawa sand and HDPE 

geosynthetic. The tests showed that the shear strength of the interface was not 

affected by the repeated loading, as shown in Figure 2.9. Figure 2.10 shows the shear 

strength of the interface plotted versus number of repeated loadings before shear to 

failure. 

2.4 Behavior of GRS Masses Subject to Unloading-Reloading Cycles 

2.4.1 General Behavior 

A GRS mass is a soil mass embedded with layers of geosynthetic 

reinforcement. In this study, unless otherwise specified, the reinforcement layers are 

horizontally oriented. This section begins with a presentation of the strength and 

deformation behavior of a GRS mass, followed by the effects of preloading on a GRS 

mass. 

Under vertical loading, a GRS mass shows a higher load carrying capacity 

than a soil mass without reinforcement. This reinforcing effect of reinforcement has 

been explained by an increased confinement concept by Yang (1974). The concept is 

illustrated by the Mohr stress diagram shown in Figure 2.10. The vertical and lateral 

stresses are assumed to be major and minor principal stresses, respectively. Circle A 

represents an at-failure stress state of a soil mass without reinforcement. The vertical 

and lateral stresses at failure for the soil mass are σ1 and σ3c, respectively (see Figure 

2.10). With a reinforcement, the lateral stress at failure is increased by ∆σ3R, which is 

equal to the tensile strength of the reinforcement. As a consequence, the vertical 

stress at failure increases to σ1R, i.e., a higher load carrying capacity is obtained. It is 

assumed that there is no slippage at the soil-reinforcement interface and that failure of 

the reinforced soil mass is due to rupture of the reinforcement. 

Under a vertical load, the GRS mass exhibits both lateral and vertical 

deformation responses. The soil expands laterally with the geosynthetic and 

mobilizes tensile forces in the geosynthetic through the friction between the soil and 

the geosynthetic. The tensile force in the geosynthetic restrains the lateral movement 

of the soil and, consequently, reduces the vertical deformation. 

The effect of reinforcement in reducing deformation of a soil mass can be 

illustrated by triaxial compression test results conducted on unreinforced and 

reinforced soil samples by Gray and Al-Refeai (1987) as shown in Figure 2.11. 

Figure 2.11 shows that the stiffness or tangent moduli of the unreinforced and 

reinforced specimens are almost the same until 1.5% of axial strain. In other words, 

the internal restraining effect by the geosynthetic reinforcement is insignificant at 
16

small strains. This is because the geosynthetic reinforcement requires some 

deformation in order to mobilize sufficient tensile force in the reinforcement. 

Figure 2.11 also shows that at small strains (0 to 1.5%), the stiffness of a 

reinforced soil is somewhat smaller than that in the unreinforced soil. Similar 

behavior has been reported in triaxial compression tests by Broms (1977). Wu (1989) 

has investigated this effect and concluded that the loss of compressive stiffness in the 

reinforced soil is due to compression of the reinforcement itself. The effect of 

compressibility of the reinforcement is pronounced in the triaxial tests because ratios 

of the reinforcement spacing to the reinforcement thickness in the triaxial tests are 

relatively small. The loss of stiffness at the small strains because of the 

compressibility of the reinforcement is negligible in field construction because ratios 

of the reinforcement spacing to the reinforcement thickness are much greater than 

those in the triaxial tests. 

Deformation of a GRS mass is of major concern when it is to be used in 

critical structures such as bridge piers and abutments. To limit the deformation of a 

GRS mass, a preloading concept is applied to increase the stiffness of the GRS 

structure (Tatsuoka et al., 1997). The preloading technique on a GRS mass takes 

advantage of the fact that soil stiffness is increased after it has been preloaded or 

prestressed. The preloaded GRS mass is also expected to behave nearly elastically in 

a reloading path similar to what has been observed in a preloaded soil. 

Preloading also mobilizes tensile strains in the geosynthetic reinforcement in a 

service condition--the so-called ratcheting mechanism (Tatsuoka et al., 1997). A 

simple model of a soil-geosynthetic composite shown in Figure 2.12 illustrates this 

mechanism. Under an applied pressure, σv, lateral deformation of the composite 

occurs and results in a tensile force in the reinforcement. Upon unloading, most of 

the lateral deformation of the soil does not rebound back. As a result, the 

reinforcement has been stretched and the tensile strains are mobilized. This 

mechanism also helps eliminating wrinkles that often occur during field placement of 

geosynthetic layers. 
17

Figure 2.9: Interface Friction Angle as a Function of Number of Repeated 

Loadings for Ottawa Sand on HPDE (After O’Rourke et al., 1990) 
18

Figure 2.10: Increased Confinement Concept of Soil Reinforcement 

(After Yang, 1974) 
19

Figure 2.11: Stress-Strain Relationships from Triaxial Compression Tests on 

Reinforced Sand (After Gray and Al-Refeai, 1987) 
20

Figure 2.12: Ratcheting Mechanism (After Tatsuoka et al., 1997) 
21

2.4.2 Preloaded GRS Structures 

 Since 1977, the preloading concept has been applied on the following four 

GRS structure: 

1. Preloaded/Prestressed GRS walls in University of Tokyo, Tokyo, Japan 

(Tatsuoka et al., 1997); 

2. Preloaded GRS pier in Turner-Fairbank Highway Research Center, 

McLean, Virginia, USA (Adams, 1997), referred to as the FHWA pier; 

3. Preloaded/Prestressed GRS bridge pier in Fukuoka City, Japan 

(Uchimura et al., 1998); 

4. Preloaded GRS bridge abutments in Black Hawk, Colorado, USA 

(Wu et al., 1999), referred to as the Black Hawk abutments. 

2.4.2.1 Preloaded/Prestressed GRS Walls 

Tatsuoka et al. (1997) proposed a new construction protocol, so-called 

preloaded/prestressed (PL/PS) reinforced soil. The main purpose was to make 

deformation of a GRS mass be nearly elastic and have a very high stiffness under 

applied loads. 

A schematic diagram of a PL/PS GRS structure is shown in Figure 2.13. 

Large preloading is applied by introducing tension into metallic tie rods that are 

intruded through the reinforced soil mass and fixed to the bottom reaction block. The 

tensile force in the tie rods and the corresponding compressive load in the backfill soil 

function as prestressing to maintain the vertical confining pressure and results in high 

stiffness in the vertical direction. 

A typical PL/PS loading path involves preloading, sustained loading, 

unloading to a desired prestress loading level, and reloading as shown in Figure 2.14. 

A vertical load is applied up to a stress level, b, and sustained for a period of time. 

After allowing the creep deformation during the preloading stage to occur (b to b ́), 

the load is reduced from b ́ to c as unloading. The stress level, c, is defined as an 

initial prestress level. The vertical deformation is maintained constant at the stress 

level, c, and, consequently, the prestress level decreases from c to c ́ due to plastic 

deformation of the GRS mass, known as the stress relaxation. A reloading stress path 

takes place from the stress level c ́ to d. 

 Full-scale loading tests of 5.4-m-high geogrid-reinforced walls were 

conducted at the University of Tokyo, Japan, to validate the PL/PS concept (Tatsuoka 

et al., 1997). The full-scale test results showed that the stiffness of the soil mass with 

compressive prestress was higher than that of the soil mass without prestress. 

Deformation of soil after preloading was nearly elastic for a relatively small load 

increment (Tatsuoka et al., 1997). 
22

 Figure 2.13: Schematic Diagram of Preloaded/Prestressed GRS Structure 

(After Tatsuoka et al., 1997) 
23

Figure 2.14: Typical Load Path of Preloaded/Prestressed GRS Structure 

(After Tatsuoka et al., 1997) 
24

2.4.2.2 FHWA Pier 

A detailed description of the FHWA pier has been presented by Adams 

(1997). A brief description of the project is given below. The GRS pier was 5.4 m 

high with base and top dimensions of 3.6 m x 4.8 m and 3.06 m x 4.26 m, 

respectively. The pier was constructed with a well-graded gravel (GW-GM per 

ASTM D2487) and reinforced with layers of geotextile sheets. The maximum dry 

density of the backfill was 24 kN/m3

, and the optimum moisture content was 5.0%, 

per AASHTO T180. The average backfill density from nuclear density tests was 22.8 

kN/m3. The reinforcement was a high-strength woven polypropylene geotextile, 

Amoco 2044. The vertical spacing of reinforcement was 0.2 m. Split face concrete 

(cinder) blocks, with dimensions of 0.2 m x 0.2 m x 0.4 m, were dry-stacked to form 

the facing. The front edge of each reinforcement sheet was placed between vertically 

aligned blocks to achieve a frictional connection between the reinforcement layer and 

the facing blocks. A schematic diagram of the pier is shown in Figure 2.15. 

 The loading mechanism of the GRS pier comprised hydraulic jacks and a 

specially designed reaction system, as shown in Figure 2.16. The reinforced soil 

mass was sandwiched between the top and bottom concrete pads, which were 

connected together with vertical steel rods. The hydraulic jacks were placed between 

the top concrete pads and the reaction frame. Upon applying pressure to the 

hydraulic jacks, the GRS pier was “squeezed” between the top and bottom pads. 
25

Figure 2.15: Principal Elements of FHWA Pier (After Adams, 1997) 
26

Figure 2.16: Preloading Assembly of FHWA Pier (After Adams, 1997) 
27

2.4.2.3 Preloaded/Prestressed GRS Walls 

A prototype 2.7 m-high PL/PS geogrid-reinforced soil bridge pier, as shown 

in Figure 2.17, was constructed at Fukuoka City, Japan, to support temporary railway 

girders. It has been opened to service since the summer of 1997. Behavior of the 

prototype PL/PS bridge pier during and after construction and in service was reported 

by Uchimura et al. (1998). The prototype pier showed very small transient and longterm deformations compared with a nearby geogrid-reinforced bridge abutment 

constructed without preloading/prestressing subject to the same transient load from a 

locomotive (Uchimura et al.,1998). 

2.4.2.4 Black Hawk Abutments 

A detailed description of the Black Hawk abutments has been presented by 

Wu et al. (1999). A brief description of the project is given below. The abutments 

were constructed in the mountain terrain above the city of Black Hawk, Colorado, to 

support a 36-m span steel arched bridge. The abutments were constructed with the 

on-site soil (the Road Base soil used in the SGP test in this study) and reinforced with 

layers of a woven geotextile (Amoco 2044) having a vertical spacing of 0.3 m. 

Material properties of the soil and the reinforcement are presented in Chapter 3. The 

facing was of rock-faced type. The wall face was built by tightly stacking the rocks in 

rows about 0.3 m in height. The front edge of each reinforcement sheet was placed 

between vertically aligned rocks at the wall face to form a frictional connection 

between the reinforcement layers and the facing rocks. 

 A series of sketches illustrating the geometry of the GRS abutments is shown 

in Figure 2.18. Each GRS abutment comprised a two-tier rock-faced GRS mass, two 

square footings (on the GRS base mass), and a strip footing (on the upper-tier GRS 

mass). Each abutment was constructed into a mountain slope on opposite sides of a 

stream valley with a silty stream deposit. The thickness of the silty soil layer was 

variable and considerably greater on the down slope side of the mountain. The slopes 

were excavated to remove the silty soil, which was considered unsuitable to support 

the abutments. The GRS abutments were supported on a stiff soil layer underneath 

the silty soil layer. 

 As viewed from the faces (due east and west) (see Figure 2.18), the base of 

the GRS mass was located at different depths of the excavated stiff soil. The variable 

thickness of the GRS base mass was between 1.5 m and 7.5 m for the east abutment 

and 1.5 m and 4.5 m for the west abutment. The width at the base of the GRS base 

mass was 5.5 m. The lower part of the GRS base mass was embedded in the ground, 

and the upper part was above the ground. Only the portion above ground was 

constructed with rock facing. The height of the rock-faced wall varied from 1.0 m to 

5.4 m in the east abutment and 1.0 m to 2.7 m in the west abutment. The upper-tier 

GRS mass was perched on the backside of each GRS base mass. The upper-tier GRS 

mass was 1.8 m thick and constructed in the same fashion as the GRS base mass. 
28

 The four square footings had a base area of 2.4 m x 2.4 m. The footing 

thickness was about 1.65 m. The final thickness depended on the amount of 

settlement due to preloading. The square footings on the west abutment were referred 

to as Footing #1 (F1) and #4 (F4). The square footings on the east abutment were 

referred to as Footing #2 (F2) and #3 (F3). The design load for each square footing 

was 865 kN, equivalent to a vertical pressure of 150 kPa. 

 As shown in Figure 2.19, the preloading assembly for each footing consisted 

of four 534-kN hollow-cored jacks ganged together with a manifold and connected to 

a hydraulic electric pump. Each jack was placed on top of the square footing and 

connected to a threaded rod by inserting the rod through the core of the jack. The 

jack was sandwiched between the square footing and the steel bearing plates capped 

with a nut threaded on the rod. On two jacks, 890-kN load cells were inserted 

between the steel bearing plate and the nut. Installation of the threaded rods occurred 

after construction of the GRS base mass. A survey located the perimeter of the 

square footings and four prescribed points within the perimeter of the footing. At the 

points, a reticulating air-percussion rotary drill rig bored 90-mm diameter holes 

through the GRS mass, the stiff soil layer, and into the underlying bedrock. The bond 

length was about 3.5 m within the bedrock. 

 To preload the GRS mass and the stiff soil layer underneath the footings, 

hydraulic oil was pumped into the hydraulic jacks. As the cylinders advanced, the 

GRS and the stiff soil were preloaded or “squeezed” between the footing and the 

bedrock. After the preloading, each borehole was sealed with a grout mix. 
29

 Figure 2.17: Prototype Preloaded/Prestressed GRS Bridge Pier 

 (After Uchimura et al., 1998)
30

 

 Figure 2.18: Black Hawk Abutments (After Wu et al., 1999) 
31

 

Figure 2.19: Preloading Assembly of Black Hawk Abutments 
32

2.5 Plane Strain Tests of Reinforced-Soil Mass 

 The behavior of reinforced soil has been studied by using triaxial and plane 

strain compression tests. Strictly speaking, the triaxial compression test is only 

applicable to a soil mass beneath the center line of a circular footing subject to 

vertical and concentric loads. Most GRS structures (e.g., retaining walls and 

embankments) are close to being in a plane strain condition. Moreover, in typical 

GRS structures, the geosynthetic reinforcement layers are placed with its stronger 

direction perpendicular to the longitudinal direction of the plane strain structure. For 

example, in GRS retaining walls, the stronger direction of a woven geotextile 

reinforcement is usually arranged to be perpendicular to the wall facing. Therefore, 

plane strain compression tests generally give a better simulation of actual GRS 

structures than triaxial compression tests. 

 Four plane strain tests conducted on the reinforced-soil masses by McGown et 

al. (1978), Tatsuoka and Yamauchi (1986), Whittle et al. (1992), and Boyle (1995) 

are reviewed in the following paragraphs. 

 McGown et al. (1978) employed a plane strain compression test apparatus to 

study the effect of inclusion properties on the behavior of sand. The specimens were 

Leighton Buzzard sand with and without inclusions of aluminium foil, aluminium 

mesh, and a non-woven melt bonded hetrofilament fabric. Specimen dimensions 

were 102 mm long, 102 mm high, and 152 mm deep (i.e., in the longitudinal 

direction). 

 The apparatus had rigid lubricated top and bottom platens. The plane strain 

condition was imposed by using two rigid lubricated side platens that were bolted 

across the 102-mm x 102-mm faces. The confining pressure was applied using 

vacuum and was kept constant during the tests. The test results were analyzed in 

terms of the vertical stress-strain relationships and the internal deformations measured 

by the stereo-viewing photogrammetric technique (Butterfield et al., 1970). 

The behavior of the sand reinforced with the extensible and inextensible 

inclusions is shown in Figure 2.20. The figures show the relationships of the 

principal stress ratio (σ1/σ3) versus axial strain of loose and dense sands with and 

without the inclusions. It is shown that the sands with the extensible inclusions were 

more ductile than those with the inextensible inclusions. Butterfield et al. (1970) 

concluded that the overall load-deformation behavior of the reinforced soil system 

was significantly influenced by the stiffness or the relative extensibility of the tensile 

inclusions. 

 Tatsuoka and Yamauchi (1986) conducted plane strain compression tests on 

reinforced Toyoura sand specimens. The specimen dimensions were 80 mm wide, 75 

mm high, and 20 mm deep (i.e., the longitudinal direction), as shown in Figure 2.21. 

The top and bottom sides of the specimen were lubricated. The side walls restraining 

deformation of the specimen were also lubricated. 
33

 The reinforcement materials were brass plates, non-woven geotextiles, and 

different types of rubbers. The average principal stress difference (σ′1/σ′3) versus 

average minor principal strain (ε3) relationships of the soil are shown in Figure 2.22. 

The stress-strain relationships are similar to those of the plane strain tests conducted 

by McGown et al. (1978) (of Figure 2.20), in that the sand reinforced with stiff 

materials (brass plates) was more brittle than the sand reinforced with relatively less 

stiff materials (geotextiles and rubbers). The test results also indicated that, in order 

to mobilize a sufficient degree of tensile restraint in the composite, the non-woven 

geotextiles required a larger soil deformation in the reinforcement direction than the 

stiffer reinforcement materials. 

 Whittle et al. (1992) devised an automated plane strain reinforcement (APSR) 

cell to study load transfer characteristics at working load levels of a reinforced-soil 

mass. Figure 2.23 shows a schematic diagram of the APSR cell. The soil specimen 

has dimensions of 570 mm high, 450 mm wide, and 150 mm deep (i.e., the 

longitudinal direction). The major principal stress (σ1< 500 kPa) was applied through 

two pressurized water bags mounted on moveable rigid platforms. A uniform lateral 

confinement (σ3< 50 kPa) was provided by air pressure. The maximum tensile stress 

in the reinforcement was measured at the end that was connected to a load cell. The 

stress in the reinforcement was induced by the stress developed in the confining soil 

resulting from the boundary stresses (σ1 and σ3 ). All contacted surfaces of the 

specimen to the apparatus were lubricated with silicone grease to minimize friction in 

the system. 

 Whittle et al. (1992) reported the results of a test performed on a dry Ticino 

sand reinforced with two-ply steel sheet inclusions. A number of strain gauges were 

mounted between the two thin steel sheets (0.13 mm thick) to obtain the strain 

distribution within the reinforcement. The test results are shown in Figure 2.24. The 

figure shows the relationships of the load in the reinforcement versus the applied 

stress ratio (R=σ1/σ3). It was concluded that the tensile stress in the reinforcement 

was a linear function of the stress ratio, R. It also showed that the maximum tensile 

stress occurred at the center of the inclusion and that the tensile stresses in the 

reinforcement were minimal when the stress ratio, R, was less than 2. 

 A plane strain unit cell device (UCD) was developed by Boyle (1995). The 

specimen dimensions were 200 mm high, 200 mm wide, and 100 mm deep (i.e., the 

longitudinal direction). Figure 2.25 shows schematic diagrams of the apparatus. The 

UCD was a load-controlled test apparatus. The vertical pressure was applied by the 

top and bottom air bladders to the surfaces of the specimen. The left instrument box 

was allowed to move freely in the horizontal direction. The lateral pressure was 

applied by the end bladder through the instrument box. The tensile forces at two ends 

of the reinforcement layer were measured by load cells. Stiff end plates that were 

linked to the clamps controlled that the soil and the reinforcement deform together in 

the horizontal direction. The vertical and the horizontal displacements, the major 
34

principal stress, and the tension at two ends of the reinforcement layer were measured 

directly. 

Two different sands, four woven geotextiles, two nonwoven geotextiles, and a 

steel sheet were employed in the study. Boyle (1995) reported similar results as those 

of the previous studies that the reinforcement improved the load carrying capacity of 

the dense cohesionless soil, as shown in Figure 2.26. The figure shows the 

relationships of the principal stress (σ1) versus lateral strain (ε3). The load carrying 

capacity of the soil specimen reinforced with geotextiles (reinforcing No.1 to 6) 

increased with the stiffness of the reinforcement that was presented in terms of the 

modulus at 5% strain. The sand reinforced with a steel sheet (No.7) showed 

significantly higher deformation modulus than those with the geotextile 

reinforcement before yielding occurred at about 0.3% of lateral strain. 

A comparison of the specimen size, soil type, reinforcement types, and 

instrumentation of the four plane strain compression tests of reinforced-soil masses 

reviewed in this section is presented in Table 2.1. A shortcoming of these triaxial and 

plane strain compression tests performed on the GRS mass is their reduced 

dimensions. The relatively small dimensions of the test specimens prohibit testing of 

a representative reinforced-soil specimen of a typical GRS structure. 
35

Figure 2.20: Behavior of a Unit Cell With and Without Inclusions: 

(a) Dense Sand and (b) Loose Sand (After McGown et al., 1978) 
36
37
38
39

Figure 2.24: Stress Distribution in a Steel Inclusion of the APSR Cell 

(After Whittle et al., 1992) 
40
41
42
43

3. Laboratory Tests on Soils, Geosynthetics, and Soil-Geosynthetic Interfaces

Laboratory tests were conducted to examine the behavior of a number of soils, 

geosynthetics, and soil-geosynthetic interfaces subject to monotonic loading and 

unloading-reloading cycle(s). The laboratory tests consisted of conventional triaxial 

compression (CTC) tests for soils, in-isolation load-extension (LE) tests for

geosynthetics, and direct shear (DS) tests for soil-geosynthetic interfaces. Each test 

category employed two types of loading sequences: monotonic loading and 

unloading-reloading cycle(s). The monotonic-loading tests were conducted to 

examine the behavior of the materials and the interfaces subject to monotonic loading 

and to provide reference properties for assessing effects of preloading on the 

deformation and strength behavior. The unloading-reloading tests were conducted to 

examine the behavior subject to unloading-reloading cycle(s) and to assess effects of 

preloading on the deformation and strength behavior. Test specimens used for the 

monotonic-loading tests were referred to as virgin specimens, whereas test specimens 

used for the unloading-reloading tests were referred to as preloaded specimens. 

This chapter presents test materials, test descriptions, specimen preparations, 

measurement, data reductions, test programs, test results, and discussions of test 

results of the laboratory tests.

3.1 Test Materials

3.1.1 Soils

Two types of granular soils were used in this study: an Ottawa sand and a 

“Road Base” soil, designated as S and RB, respectively. The Ottawa sand was 

chosen because of its well-defined properties. The Road Base soil was a granular 

material that is commonly used as backfill for GRS retaining walls. It was selected in 

this study to examine the behavior of a generic preloaded GRS mass consisting of a 

typical construction backfill. 

The Ottawa sand used in this study was a subround uniform sand, with its 

gradation curve shown in Figure 3.1. The specific gravity of the sand is 2.65. The 

maximum and minimum unit weights, per ASTM D854, were 17.65 kN/m3 and 15.34 

kN/m3, respectively. The Road Base soil used in this study was a dark brown, silty 

sand. It was a backfill material for the preloaded GRS abutments in Black Hawk, 

Colorado (Section 2.4.1.4). The soil was classified as SM-SC, per ASTM D2487. It 

has 12% of fine particles (passing #200 standard sieve). The gradation curve is 

shown in Figure 3.2. The plasticity index and the liquid limit were 6% and 27%, 

respectively. The maximum dry density was 18.75 kN/m3 with the optimum water 

content of 14.2%, per ASTM D698. The moisture content-dry unit weight 

relationship is shown in Figure 3.3.
44

Figure 3.1: Grain Size Distribution of Ottawa Sand
45

Figure 3.2: Grain Size Distribution of Road Base Soil

0

10

20

30

40

50

60

70

80

90

100

10 1 0.1 0.01

Grain Diameter (mm)

Percent Passing (%)
46

Figure 3.3: Moisture Content-Dry Unit Weight Relationship of Road Base Soil

17

17.5

18

18.5

19

8 10 12 14 16 18 20

Moisture Content (%)

Dry Unit Weight (kN/m

3

)

Max. Dry Unit Weight = 18.75 kN/m

3

O.M.C. = 14.2 %
47

3.1.2 Geosynthetics

Two types of geosynthetics, Amoco 2044 and Typar 3301, were used in this 

study. Amoco 2044 represents a strong reinforcement material, whereas Typar 3301 

represents a weak reinforcement material. 

Amoco 2044 is a woven polypropylene geotextile. The wide-width tensile 

strengths, as provided by the manufacturer, in both fill and warp directions are 70 

kN/m. Amoco 2044 was a reinforcement material used in the FHWA pier (Section 

2.4.1.2) and the Black Hawk abutments (Section 2.4.1.4). Some index properties of 

Amoco 2044 are shown in Table 3.1. Typar 3301 is a non-woven heat-bonded 

polypropylene geotextile. It was primarily used for filtration and drainage 

applications in actual applications. Some index properties of Typar 3301 are shown 

in Table 3.1.
48

Table 3.1: Some Index Properties of Geosynthetics

Geosynthetic Amoco 2044 Typar 3301

Manufacturing method Woven Non-Woven

Wide-width tensile strength 70 kN/m 6 kN/m

(ASTM D-4595) (fill and warp directions)

Elongation at break 8% (fill direction) 70%

(ASTM D-4595) 10% (warp direction)

Grab tensile 2.22 kN (fill direction) 0.53 kN

(ASTM D-4632) 2.67 kN (warp direction)

Elongation at break 20% 60%

(ASTM D-4632) (fill and warp directions)
49

3.2 Loading System

The loading system used in this study was the MTS-810 electro-hydraulic 

testing system. The MTS-810 testing system comprised a loading frame integrated 

with a data acquisition system and a control unit. The loading frame (MTS Model 

311.31) consisted of four vertical columns that joined a moveable crosshead and a 

fixed platen (see Figure 3.4). The crosshead was vertically adjustable to 

accommodate specimens of various heights. The vertical movement of the crosshead 

was controlled by hydraulic crosshead lifts. The crosshead, once in position, locked 

into place to prevent slippage during testing. The data acquisition system included a 

load cell with a maximum capacity of 1,000 kN (sensitivity = +0.04 kN) and LVDT 

(linear variable differential transformer) with a maximum displacement of 150 mm 

(sensitivity = +0.03 mm). The LVDT is an electromechanical device that provides an 

output voltage that is proportional to the displacement of a moveable core extension 

or a stylus. The LVDT was internally mounted on the hydraulic actuator to provide 

an indication of the actuator piston rod displacement. The MTS-810 loading system 

used the MTS458.20 MicroConsole as a control unit to control the servohydraulic 

system. 

The data acquisition system and the control unit were connected to an IBM 

personal computer. A BASIC software for the control unit and the data acquisition 

system developed at the University of Colorado at Denver was modified by the author 

for this study. The modified BASIC software provided the inputs (stress-controlled 

or strain-controlled modes) for the control unit and recorded the outputs (load and 

displacement) from the data acquisition system. All input parameters must be 

predetermined and programmed in the IBM personal computer before starting a test. 

For the stress-controlled mode, the failure load of the specimen needs to be estimated 

beforehand to set an upper bound for the loading magnitude input. It is to be noted 

that the stress-controlled mode must never be used to load the specimen to failure. 

This is because a premature failure may damage the testing system.

3.3 Loading Sequences

 In this study, the monotonic loading was applied in a strain-controlled mode at 

a constant strain rate. The unloading-reloading cycles were applied in a stresscontrolled mode at a constant loading rate. The unloading-reloading cycles were an 

array of different combinations of five loading paths: preloading (PL), unloading to a 

zero-load level (UL-Z), unloading to a prestressed load level (UL-PS), reloading from 

a zero-load level (RL-Z), and reloading from a prestressed load level (RL-PS). A

diagram illustrating the applied load versus time relationships for 1) PL, UL-Z, and 

RL-Z paths, and 2) PL, UL-PS, and RL-PS paths are shown in Figure 3.5. In this 

report, the term “applied load” is used to represent different quantities for different 

types of tests. It represents the deviator stress in CTC tests, the applied tensile load in 

LE tests, the shear stress in DS tests, and the vertical load from the MTS-810 loading 
50

device in SGP tests. The unloading load level (ULL) was equal to the zero-load level 

for the UL-Z and RL-Z paths, and the prestressed load level (PSL) for the UL-PS and 

RL-PS paths. The minimum unloading load level was the zero-load level. The zeroload level was considered the initial stress of the specimen; i.e., the applied load = 0.

As shown in Figure 3.5, the PL path begins at t = 0 and increases at a constant 

loading rate to a PLL. An unloading path (UL-Z or UL-PS path) follows the PL path. 

The UL-Z path involves a decrease of the loading magnitude from a preloading load 

level to a zero-load level (i.e., ULL = 0). The RL-Z path follows the UL-Z path. The 

UL-PS path involves a decrease of the loading magnitude from a preloading load 

level to a prestressed-load level (i.e., ULL = PSL). The RL-PS path follows the ULPS path. The preloading path resumes when the magnitude of the load in the 

reloading path exceeds the preloading load level.
51

Figure 3.4: MTS-810 Loading System
52

Figure 3.5: General Loading Sequences

UL

ULL

PLL

Applied Load

PL

RL

Time

Two unloading-reloading paths

1) When ULL = 0 => UL-Z, and RL-Z paths 

2) When ULL = PSL => UL-PS, and RL-PS paths
53

3.4 Conventional Triaxial Compression Tests for Soils

A series of CTC tests under monotonic loading and unloading-reloading 

cycles were conducted on the two soils described in Section 3.1.1. The purposes of 

the tests were to examine the behavior of the soils subject to unloading-reloading 

cycles and to calibrate soil model parameters in the finite element analysis and the 

SPR model (Sections 5.3 and 6.3).

3.4.1 Test Description

The CTC test was performed on an unsaturated soil specimen. The triaxial 

chamber was placed in the MTS loading device as shown in Figure 3.6. Confining 

pressure was applied to the specimen by pressurizing the water surrounding the 

specimen. The applied vertical load and the vertical displacement of the loading rod 

were recorded by a data acquisition system integrated with the MTS-810 loading 

device. The volume-change occurred during shear was measured by monitoring the 

volume change of water entering or leaving the triaxial chamber. 

3.4.2 Specimen Preparation and Test Procedure

The Ottawa sand specimen in the triaxial tests was 158 mm high and 71 mm 

in diameter. The specimen was prepared at a unit weight of 16.85 kN/m3 (+0.15 

kN/m3). The specimen preparation and the test procedure for the Ottawa sand are as 

follows:

1. Obtain the dry Ottawa sand from the batch.

2. Use o-rings to attach a 0.2-mm-thick rubber membrane to the base platen.

3. Place a porous stone at the base of the platen.

4. Place a metallic mold (a split-barrel type) around the rubber membrane and 

fold the top portion of the membrane down and over the mold.

5. Pour the sand in the mold by using 50-mm-diameter funnel with the opening 

diameter of 5 mm at a constant drop height of approximately 80 mm.

6. Place a porous stone on top of the specimen.

7. Place the top platen on the porous stone and roll the rubber membrane over 

the top platen and seal to the circumference of the top platen with o-rings.

8. Apply a vacuum pressure of 35 kPa on the specimen through the back 

pressure valve that is connected to the base of the specimen.

9. Remove the metallic mold and obtain the average height and average diameter 

of the specimen by using a stand ruler and a π−tape.

10. Place a lucite cylinder on the cell base.

11. Place the triaxial chamber in an MTS-810 loading frame.

12. Apply a predetermined confining pressure and open the back pressure valve.

13. After 15 minutes of consolidation with the confining pressure, start to apply 

shear stress at a prescribed strain or loading rate.
54

14. Record the vertical applied load, the axial displacement, and the volume 

change of the specimen during shear.

The Road Base soil specimen in the CTC tests was 305 mm high and 152 mm 

in diameter. The specimen was prepared at a dry unit weight of 17.81 kN/m3 (+0.1 

kN/m3) with a water content of 12.2%. The specimen preparation and the test 

procedure for the Road Base soil are as follows:

1. Prepare the soil at the desired moisture content of 12.2% and cure overnight in 

a sealed container inside a high humidity room.

2. Use o-rings to attach a 0.3-mm-thick rubber membrane to the base platen.

3. Place a porous stone at the base of the platen.

4. Place a metallic mold (a split-barrel type) around the rubber membrane and 

fold the top portion of the membrane down and over the mold.

5. Compact the soil inside the mold in 12 layers by a 4-lb standard Proctor 

hammer at the prescribed density.

6. Place a porous stone on top of the specimen.

7. Place the top platen on the porous stone and roll the rubber membrane over 

the top platen and seal to the circumference of the top platen with o-rings.

8. Apply a vacuum pressure of 35 kPa on the specimen through the back 

pressure valve that is connected to the base of the specimen.

9. Remove the metallic mold and attach a second layer of rubber membrane to 

the specimen with o-rings on the top and base platens.

10. Obtain the average height and average diameter of the specimen by using a 

stand ruler and a π−tape.

11. Place a lucite cylinder on the cell base.

12. Fill the triaxial chamber with water.

13. Place the triaxial chamber in an MTS-810 loading frame.

14. Apply a predetermined confining pressure and open the back pressure valve.

15. After 1 hour of consolidation with the confining pressure, start to apply shear 

stress at a prescribed strain or loading rate.

16. Record the vertical applied load, the axial displacement, and the volume 

change of the specimen during shear.
55

Figure 3.6: Conventional Triaxial Compression Test Apparatus
56

3.4.3 Measurement and Test Data Reduction

The change in height of the specimen and the net applied axial load was 

measured by the data acquisition system of the MTS-810 testing system. The axial 

strain (εa) and the deviator stress (σ1-σ3) were calculated by the following formulas:

o

a

H

?H

e = [3.1]

Acorr

P

(s 1 −s 3) = [3.2]

( e )

A

A

a

o

corr

−

=

1

[3.3]

where DH = change in height of the specimen

Ho = specimen height after consolidation 

P = net applied axial load

Acorr = corrected area of the specimen during shear

Ao = area of the specimen after consolidation 

The volume change of the specimen was measured by monitoring the volume 

of water entering or leaving the triaxial cell to compensate for the change in volume 

of the specimen. A Validyne transducer (model DP15-30) was used to monitor the 

change of water level in a burette that was connected to the surrounding water in the 

triaxial cell. The Validyne transducer was connected to an IBM personal computer. 

The sensitivity of the transducer was 0.01 cm3. Corrections of the measured values 

from the transducer were made to account for expansions of the triaxial chamber and 

the tube and penetration of the loading ram into the triaxial chamber during shear. 

The volumetric strain (εv) was calculated by the following formula:

O

v

V

?V

e = [3.4]

where ΔV = volume change of the specimen

Vo = volume of specimen after consolidation 
57

3.4.4 Test Programs 

Test programs for the CTC tests are presented in Table 3.2 for the Ottawa 

sand and Table 3.3 for the Road Base soil. The test program was divided into two 

groups: monotonic-loading (M) tests and unloading-reloading (UR) tests. 

Designations of all the tests are shown in the tables. The monotonic-loading tests 

were conducted in a strain-controlled mode at a constant strain rate of 0.5% per 

minute. The unloading-reloading tests were conducted in a stress-controlled mode 

with various loading sequences at a constant loading rate of 10 kPa per minute and 

followed by a strain-controlled mode at a constant strain rate of 0.5% per minute until 

failure occurred. 
58

Table 3.2: CTC Test Program for the Ottawa Sand
59

Table 3.3: CTC Test Program for the Road Base Soil
60

3.4.5 Test Results and Discussions

The CTC test results and discussions of the test results are presented in the 

following sections. The general behavior was first described, followed by an 

assessment of the effects of preloading on deformation and shear strength of the soils.

3.4.5.1 General Behavior

The peak or maximum deviator stress generally corresponds to the failure 

state of the specimen. When the deviator stress continued to increase without 

showing a peak value, the deviator stress at 10% axial strain was considered the 

maximum deviator stress. A positive sign of the volumetric strain represents 

specimen dilation; whereas, a negative sign represents specimen contraction. 

Figures 3.7 and 3.8 show the results of the monotonic-loading CTC tests. The 

deviator stress increased with the axial strain until failure occurred. The Ottawa sand 

initially contracted during shear and started to dilate at axial strains less than 0.8%. 

Similar to the sand, the Road Base soil at lower confining pressures contracted 

initially and dilated after it reached certain axial strains. The Road Base soil 

experienced dilatancy at larger axial strains (1.2% and 6% at confining pressures of 

69 kPa and 207 kPa, respectively) than the Ottawa sand. At the confining pressure of 

345 kPa, the Road Base soil specimen did not show the dilatant behavior. 

Figures 3.9 to 3.14 show the results of the unloading-reloading CTC tests. 

The stress-strain curve was similar to the typical stress-strain curve of a soil specimen 

in the CTC test subject to primary loading, unloading, and reloading as described in 

Section 2.1.

The specimen was initially loaded to a preloading load level, then unloaded. 

Irrecoverable and recoverable deformations occurred when the specimen was 

unloaded. This behavior may be explained in terms of deformation of grains and 

sliding between grains (see, e.g., Makhlouf and Stewart, 1965; Ko and Scott, 1967; 

Lade and Duncan, 1976). The recoverable deformation was due to the elastic 

deformation of individual grains, whereas the irrecoverable deformation was 

primarily caused by the sliding between individual grains. In the primary loading, 

both the elastic deformation and sliding between grains occurred. Upon unloading, 

individual grains did not rebound to their original positions but remained 

approximately in their displaced positions. This behavior caused the irrecoverable 

deformation. 

During the initial unloading path in which the deviator stress started to reduce, 

it was observed that axial and volumetric strains still continued to behave in the same 

fashion as those in the PL path. Specifically, the downward deformation continued 

and the volume change behavior was in expansion for the Ottawa sand and in 

contraction for the Road Base soil. This behavior has been reported in cyclic triaxial 

tests as a rounded corner of hysteresis loops (Hyodo et al., 1994) and explained in 

terms of creep of a soil specimen by Tatsuoka and Shibuya (1991). The magnitude of 
61

the creep deformation was found to be more significant when the specimen was 

unloaded from a high preloading load level. 

It is the author opinion that the influence of soil creep at an initial unloading 

path is suppressed in an unloading-reloading CTC test conducted in a straincontrolled mode. This is believed to be a strain-controlled loading characteristic. 

Under the strain-controlled mode, the vertical deformation of the specimen is 

controlled by vertical movements of the loading rod. It is tacitly assumed that the 

specimen is in full contact with the loading rod. The unloading path begins when the 

loading rod movement is reversed. This unloading mechanism eliminates the 

possibility of the soil to continue the vertical downward deformation during the 

unloading path.

When the specimen was unloaded and reloaded from small to moderate 

preloading load levels, it behaved approximately linear-elastically. However, when 

the unloading path took place at a high preloading load level (i.e., close to failure), 

the linearity between stress and strain may not be assumed as a result of significant 

hysteresis loops. The hysteresis loop existed in all unloading-reloading portions of 

deviator stress-axial strain curves. The width of the hysteresis loop is typically larger 

at the high preloading load level. 
62

Figure 3.7: Test Results of Monotonic-Loading CTC Tests on Ottawa Sand

(Tests T-M-S1, 2, and 3)

0

200

400

600

800

1000

1200

0 2 4 6 8 10 12

Axial Strain (%)

Deviator Stress (kPa)

345 kPa

207 kPa

69 kPa

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 2 4 6 8 10 12

Axial Strain (%)

Volumetric Strain (%)

69 kPa

207 kPa

345 kPa
63

Figure 3.8: Test Results of Monotonic-Loading CTC Tests on Road Base Soil

(Tests T-M-RB1, 2, and 3)

0

200

400

600

800

1000

0 2 4 6 8 10 12 14

Axial Strain (%)

Deviator Stress (kPa)

345 kPa

207 kPa

69 kPa

-4

-3

-2

-1

0

1

2

3

0 2 4 6 8 10 12 14

Axial Strain (%)

Volumetric Strain (%)

 69 kPa

 207 kPa

345 kPa
64

Figure 3.9: Results of Test T-UR-S1 (Confining Pressure = 69 kPa)

0

50

100

150

200

250

0 2 4 6 8 10 12

Axial Strain (%)

Deviator Stress (kPa)

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 2 4 6 8 10 12

Axial Strain (%)

Volumetric Strain (%)
65

Figure 3.10: Results of Test T-UR-S2 (Confining Pressure = 207 kPa)

0

100

200

300

400

500

600

0 2 4 6 8 10 12

Axial Strain (%)

Deviator Stress (kPa)

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 2 4 6 8 10 12

Axial Strain (%)

Volumetric Strain (%)
66

Figure 3.11: Results of Test T-UR-S3 (Confining Pressure = 345 kPa)

0

200

400

600

800

1000

1200

0 2 4 6 8 10 12

Axial Strain (%)

Deviator Stress (kPa)

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 2 4 6 8 10 12

Axial Strain (%)

Volumetric Strain (%)
67

Figure 3.12: Results of Test T-R-RB1 (Confining Pressure = 69 kPa) 

0

50

100

150

200

250

300

0 2 4 6 8 10

Axial Strain (%)

Deviator Stress (kPa)

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

0 2 4 6 8 10

Axial Strain (%)

Volumetric Strain (%)
68

Figure 3.13: Results of Test T-UR-RB2 (Confining Pressure = 207 kPa) 

0

100

200

300

400

500

600

0.0 2.0 4.0 6.0 8.0 10.0 12.0

Axial Strain (%)

Deviator Stress (kPa)

-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

0.0 2.0 4.0 6.0 8.0 10.0 12.0

Axial Strain (%)

Volumetric Strain (%)
69

Figure 3.14: Results of Test T-UR-RB3 (Confining Pressure = 345 kPa) 

0

100

200

300

400

500

600

700

800

900

1000

0 2 4 6 8 10 12

Axial Strain (%)

Deviator Stress (kPa)

-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

0.0 2.0 4.0 6.0 8.0 10.0 12.0

Axial Strain (%)

Volumetric Strain (%)
70

 During reloading, reduction of reloading stiffness was observed when the 

reloading magnitude was approaching the preloading level. This behavior is referred 

to as the Bauschinger effect (see, e.g., Mendelson, 1968; Lubahn and Felgar, 1961). 

After the deviator stress exceeded the preloading load level, the stress-strain curve 

resumed the preloading path.

From the volumetric strain versus axial strain relationships, the Ottawa sand 

contracted, then dilated during the preloading path. When the reloading path took 

place, the dilation behavior continued during the initial stage of the unloading path. 

Then, contraction prevailed for the remaining of the unloading path. The contraction 

behavior upon unloading has been reported by Perriello-Zampelli (1983) on 

experiments performed on assemblies of glass sphere, and Perkins (1991) and Klosky 

(1997) on large-size CTC tests on lunar soil simulant. In the reloading path, the 

volume change behavior was similar to that of the preloading path. It started with 

contraction and changed to dilation when the reloading magnitude approached the 

preloading load level. 

The volume change behavior during unloading-reloading of the Road Base 

soil specimen was different from that of the Sand specimen. For the Road Base soil,

the specimen contracted during the preloading path. Upon unloading, the soil 

continued to contract and, then, dilated in a relatively small magnitude for the 

remaining unloading path. The soil started to contract again under the reloading path.

3.4.5.2 Effects of Preloading on Deformation and Shear Strength of Soils

To assess the effects of preloading on deformation behavior of the soils, a 

secant modulus at 50% of failure stress (E50) and a reloading modulus (ERL) are 

introduced. The secant modulus at 50% of failure stress was determined from a 

monotonic-loading CTC test. The reloading modulus was determined from the 

reloading portion of an unloading-reloading CTC test. 

The secant modulus at 50% of failure stress (E50) was defined as the slope of a 

deviator stress-axial strain curve at 50% of failure stress. E50 represents an average 

deformation modulus of a virgin specimen. It was used by Vermeer (1996) to model 

soil response in the finite element analysis. 

Depending on the unloading load level, the reloading modulus can be ERL-Z or 

ERL-PS. ERL-Z represents the reloading modulus when the specimen was reloaded from 

a zero-load level (i.e., RL-Z path). ERL-PS represents the reloading modulus when the 

specimen was reloaded from a prestressed load level (i.e., RL-PS path). From 

Figures 3.9 to 3.14, the slope of the deviator stress-axial strain curve in the reloading 

portion was found to be approximately linear until the reloading magnitude was about 

70% of the total stress difference during the unloading-reloading cycle. 

Both ERL-Z and ERL-PS were determined by a statistical approach from the 

reloading portions of the deviator stress-axial strain curve. A linear interpolation 

using least-squares regression was established by employing the reloading data 
71

between 0% and 70% of the total stress difference during the unloading-reloading 

cycle. The slope of the linear interpolation was the reloading modulus.

Figures 3.15 and 3.18 show the relationships of reloading modulus (ERL-Z and 

ERL-PS) versus 

f

PL

− )

− )

1 3

1 3

(

(

s s

s s

 of the Ottawa sand and the Road Base soil. The value of 

f

PL

− )

− )

1 3

1 3

(

(

s s

s s

 is an indication of the preloading load level with respect to the failure 

load. The average value of the reloading modulus at a given confining pressure was 

calculated and presented in the figures. It can be seen that the reloading modulus 

increased with increasing confining pressures. At the same confining pressure, the 

reloading moduli tended to reduce with increasing 

f

PL

− )

− )

1 3

1 3

(

(

s s

s s

. At 

f

PL

− )

− )

1 3

1 3

(

(

s s

s s

= 

0.8, the reloading modulus was about 0.85 to 0.95 of the average reloading modulus.

ERL-Z and ERL-PS were compared with E50 to examine the effects of preloading 

on deformation of the soils. Figures 3.19 and 3.20 show average deformation 

modulus versus confining pressure relationships of the Sand and the Road Base soil, 

respectively. As shown in Figures 3.19 and 3.20, E50 , ERL-Z , and ERL-PS increased 

with increasing confining pressures. At the same confining pressure, ERL-PS, ERL-Z, 

and E50 had the maximum, medium, and minimum values, respectively. The 

reloading modulus of the Ottawa sand was larger than E50 by factors of 1.5 to 3 for 

ERL-Z and 3 to 4 for ERL-PS. For the Road Base soil, the reloading modulus was larger 

than E50 by factors of 4.5 to 6.5 for ERL-Z and 6 to 9 for ERL-PS. These results indicate 

that 1) the preloaded specimen has much higher deformation modulus than the virgin 

specimen, and 2) the RL-SP path is more effective for increasing the deformation 

modulus than the RL-Z path. 

Effects of preloading on shear strength of the Ottawa sand and the Road Base 

soil were examined by a means of Mohr-Coulomb shear strength parameters (i.e.,

internal friction angle and cohesion). The shear strength parameters were determined 

from the p-q diagram at failure as shown in Figures 3.21 and 3.22. The friction angle 

of the Ottawa sand was 37.4° from the monotonic loading tests and 36.0° from the 

unloading-reloading tests. The friction angle and the cohesion of the Road Base soil 

were 31.4° and 32.9 kPa from the monotonic loading tests and 32.0° and 34.2 kPa 

from the unloading-reloading tests. These results indicate that the effects of

preloading on the shear strength of the soils are insignificant. This finding is 

consistent with Bishop and Eldin (1953), Lade and Duncan (1976), and Lambrechts 

and Leonard (1978). This behavior may be explained by the relatively large 

deformation that occurred before and during failure. The displacements of the soil 

grains during failure are probably large enough to erase the preloading effects.
72

Figure 3.15: ERL-Z versus 

f

PL

− )

− )

1 3

1 3

(

(

s s

s s

 Relationships of Ottawa Sand

0

50

100

150

200

250

300

350

0.0 0.2 0.4 0.6 0.8 1.0

(s 1 - s 3 ) PL/(s 1 - s 3) f

ERL-Z (MPa)

69 kPa

207 kPa

345 kPa

Avg. =326.4 MPa

Avg. =208.2 MPa
73

Figure 3.16: ERL-PS versus 

f

PL

− )

− )

1 3

1 3

(

(

s s

s s

 Relationships of Ottawa Sand

0

50

100

150

200

250

300

350

400

0.0 0.2 0.4 0.6 0.8 1.0

(s 1 - s 3) PL/(s 1 - s 3) f

ERL-PS (MPa)

69 kPa

207 kPa

345 kPa

Avg. =366.8 MPa

Avg. =311.4 Mpa
74

Figure 3.17: ERL-Z versus 

f

PL

− )

− )

1 3

1 3

(

(

s s

s s

 Relationships of Road Base Soil

0

50

100

150

200

250

0.0 0.2 0.4 0.6 0.8 1.0

(s 1 - s3) PL/(s 1 - s3)

 f

ERL-Z (MPa)

69 kPa

207 kPa

345 kPa

Avg. =177.1 MPa

Avg. =145.8 MPa

Avg. =84.1 MPa
75

Figure 3.18: ERL-PS versus 

f

PL

− )

− )

1 3

1 3

(

(

s s

s s

 Relationships of Road Base Soil

0

50

100

150

200

250

300

0.0 0.2 0.4 0.6 0.8 1.0

(s1 - s 3) PL/(s1 - s3) f

ERL-PS (MPa)

69 kPa

207 kPa

345 kPa

Avg. =248.3 MPa

Avg. =207.8 MPa
76

Figure 3.19: Deformation Modulus Versus Confining Pressure Relationships 

of Ottawa Sand

0

50

100

150

200

250

300

350

400

0 50 100 150 200 250 300 350 400

Confining Pressure (kPa)

Deformation Modulus (MPa)

E(50)

E(RL-Z)

E(RL-PS)
77

Figure 3.20: Deformation Modulus Versus Confining Pressure Relationships 

of Road Base Soil

0

50

100

150

200

250

300

0 50 100 150 200 250 300 350 400

Confining Pressure (kPa)

Deformation Modulus (MPa)

E(50)

E(RL-Z)

E(RL-PS)
78

Figure 3.21: p-q Diagram at Failure of Ottawa Sand

0

200

400

600

800

1000

0 200 400 600 800 1000

p = (s1 + s3) / 2 (kPa)

q = (

s1-s3)/2 (kPa)

Monotonic Loading Tests

Unloading-Reloading Tests
79

Figure 3.22: p-q Diagram at Failure of Road Base Soil 

0

200

400

600

800

1000

0 200 400 600 800 1000

p = (s1 + s3) / 2 (kPa)

q = (

s1-s3)/2 (kPa)

Monotonic Loading Tests

Unloading-Reloading Tests
80

3.5 In-Isolation Load-Extension Tests for Geosynthetics 

 A series of LE tests under monotonic loading and unloading-reloading cycles 

was conducted on the two geosynthetics described in Section 3.1.2. The purposes of 

the tests were to examine the behavior of the geosynthetics subject to unloadingreloading cycles and to calibrate geosynthetic model parameters in the finite element 

analysis and the SPR model (Sections 5.4 and 6.3). 

3.5.1 Test Description 

In the LE test, a geosynthetic specimen was subjected to uniaxial tensile force 

without soil confinement (i.e., in-isolation test). The in-isolation load-extension test 

is an “element” test. In an element test of geosynthetics, the specimen is subjected to 

a uniform stress-deformation condition and, as a result, can be considered 

independent of the specimen dimensions. The in-isolation load-extension tests were 

conducted in both strain-controlled and stress-controlled modes of loading. All tests 

were carried out using the MTS-810 testing system. 

3.5.2 Specimen Preparation and Test Procedure 

The test method specified by ASTM D4595, the wide-width tensile test, uses a 

200-mm wide specimen with a gauge length (length between the opposing grips) of 

100-mm. The specimen is subjected to a uniaxial tensile force at a constant strain rate 

of 10% per minute by using a pair of grips that cover the entire width of the test 

specimen. Yamauchi (1988) showed that the aspect ratio (the ratio of width to gauge 

length) of 2 in the ASTM wide-width tensile test produced a significant Poisson 

effect (i.e., necking) in nonwoven geotextiles and gave a weaker load-deformation 

response. 

 In this study, the geosynthetic specimen for Typar 3301 was 305 mm in width 

and 25 mm in gauge length. The grip portion was treated with a high strength epoxy 

(Unitex Propoxy A and B). A schematic diagram of the test specimen for Typar 3301 

is shown in Figure 3.23. After sample treatment, the test specimen was fixed to a pair 

of rigid grips attached to the MTS-810 loading device (see Figure 3.24). The grips 

consisted of two angle-shaped steel bases that were connected to the MTS-810 

loading device and two 25-mm by 38-mm by 305-mm rectangular steel bars. Before 

the test started, a pretension load of 45 N was applied, per ASTM D4595. 

For Amoco 2044, the epoxy-treated grip used in Typar 3301 was not 

sufficiently stiff to prevent slippage in the grip portion upon tensile load applications. 

Several gripping methods were examined. The wrapped-around gripping method was 

selected. The Amoco 2044 specimen was 200 mm in width and 100 mm in gauge 

length, per ASTM D4595, as shown in Figure 3.25. The overall length of the Amoco 

2044 specimen was 480 mm to accommodate the wrapped-around gripping method. 

The grip portion was treated with high-strength epoxy and two steel plates. The test 

specimen was wrapped around the rectangular steel bar, as shown in Figure 3.26. A 
81

pretension tensile load of 220 N was applied, per ASTM D4595, before starting the 

test. 

3.5.3 Measurement and Test Data Reduction 

For Typar 3301 specimens, the elongation and the applied tensile load were 

measured by the data acquisition system of the MTS-810 loading system. For Amoco 

2044 specimens, partial slippage occurred in the grip area. This is known as the endeffect. To eliminate the end-effect in the elongation measurement, a special 

technique was developed in this study that is described in the following paragraph. 

Two rows of small angles (25 mm x 25 mm) were first glued on one side of 

the specimen marking 100-mm gauge length on prescribed locations as shown in 

Figure 3.26. Four LVDTs were then mounted on the top of the gripping system. The 

stylus of each LVDT was in contact with the angle that was glued on the specimen. 

Elongation of the specimen was the change in distance between the two angles that 

were vertically aligned. The average elongation of two angle sets was used to 

calculate the axial strain. The LVDT readings were recorded by the DATAQ4500 

data acquisition system. The sensitivity of the LVDT was +0.005 mm. The applied 

tensile load was recorded by the data acquisition system of the MTS-810 loading 

system. 

The tensile load per unit length (T) and the axial strain of the specimen (εa) 

were calculated by the following formulas: 

 Wo

P T = [3.5] 

O

a L

∆L

ε = [3.6] 

where P = applied axial load (in tension) 

Wo = initial width of the specimen 

 (305 mm for Typar 3301 specimen and 200 mm for Amoco 

2044 specimen) 

∆L = elongation of the specimen 

Lo = gauge length 

(25 mm for Typar 3301 specimen and 100 mm for Amoco 

2044 specimen) 
82

Figure 3.23: Typar 3301 Specimen 

305 mm

25 mm
83

 Figure 3.24: LE Test Setup for Typar 3301 Specimen

Typar 3301 

Specimen

(a) Front View (b) Side View
84

Figure 3.25: Amoco 2044 Specimen 

Gage length = 100 mm

200 mm

480 mm

305 mm
85

Figure 3.26: LE Test Setup for Amoco 2044 Specimen 

Amoco 2044

Specimen

LVDT

Steel 

Angle

Steel 

Angle

LVDT

(a) Front View (b) Side View
86

4.5.4 Test Programs 

The test programs for the LE tests are presented in Table 3.4 for Typar 3301 

and Table 3.5 for Amoco 2044. The test program was divided into two groups: 

monotonic (M) tests and unloading-reloading (UR) tests. Designations of all the tests 

are shown in the tables. The monotonic tests were conducted in a strain-controlled 

mode at a constant strain rate of 10% per minute. The unloading-reloading (UR) tests 

were conducted in a stress-controlled mode with various loading sequences at a 

constant loading rate of 1.75 kN/m per minute, followed by a strain-controlled mode 

at a constant strain rate of 10% per minute up to failure. 
87

Table 3.4: LE Test Program for Typar 3301
88

Table 3.5: LE Test Program for Amoco 2044 
89

3.5.5 Test Results and Discussions 

The LE test results and discussions of the test results are presented in the 

following sections. The general behavior was first described, followed by an 

assessment of the effects of preloading on deformation and tensile strength of the 

geosynthetics. 

3.5.5.1 General Behavior

 To describe the load-deformation behavior of the geosynthetics, an ultimate 

tensile load (TULT) is defined. The ultimate tensile load is defined as either the actual 

peak tensile load or, if the tensile load continued to increase during the test, the 

tensile load at 100% axial strain. 

 Figures 3.27 and 3.28 present the tensile load versus axial strain relationships 

of the monotonic-loading LE tests of Typar 3301 and Amoco 2044, respectively. The 

ultimate tensile load of Typar 3301 was 7.0 kN/m at 100% axial strain without 

experiencing rupture failure. For Amoco 2044, two identical specimens were used 

for Test G-M-2044 to evaluate the gripping method and the new elongation 

measurement technique described in Section 3.5.2. As shown in Figure 3.28, the 

load-strain curves are almost identical before failure. The ultimate tensile loads of 

Specimens 1 and 2 were 67 kN/m and 72 kN/m, with a rupture failure along the 

center line of the specimen. The average ultimate tensile load was 69.5 kN/m. The 

tensile load at 5% strain was 36 kN/m. The ultimate tensile load and tensile load at 

5% strain, as provided by the manufacturer, are 70 kN/m and 38 kN/m, respectively. 

The gripping system is considered adequate for the LE test of Amoco 2044 geotextile. 

 The results of stress-controlled and strain-controlled parts of the unloadingreloading LE test are presented separately. The stress-controlled part was presented 

first. The result of the monotonic-loading LE test was superimposed in the loadstrain plot of the strain-controlled response for comparison. 

Figures 3.29 to 3.32 show the tensile load versus axial strain relationships of 

the unloading-reloading LE tests. Figures 3.29 and 3.30 are, respectively, the results 

of the stress-controlled and strain-controlled parts of Typar 3301. Figures 3.31 and 

3.32 are, respectively, the results of the stress-controlled and strain-controlled parts of 

Amoco 2044. In the stress-controlled part, the specimen was loaded under a loading 

rate of 1.75 kN/m per minute up to a preloading level, unloaded, and reloaded to 2 

kN/m for Typar 3301 and 10 kN/m for Amoco 2044, then unloaded. The specimen 

was subsequently subjected to a monotonic loading at a strain rate of 10% per minute 

(strain-controlled part) until failure occurred. 

From the results of the stress-controlled part, it is seen that the load-strain 

relationships of the primary loading, unloading, and reloading were non-linear. The 

irrecoverable strain occurred upon unloading. The hysteresis loop existed during 

unloading and reloading. 
90

The initiation point of the load-strain curve in the strain-controlled part was 

the irrecoverable strain of the stress-controlled part. The slope of the reloading curve 

changed significantly once the tensile load reached the preloading load level. The 

load-strain curve resembled the monotonic-loading curve after the tensile load 

exceeded the preloading load level. 

3.5.5.2 Effects of Preloading on Elongation and Tensile Strength of 

Geosynthetics 

The secant stiffness is introduced to examine the effects of preloading on 

deformation of the geosynthetics used in this study. The secant stiffness is defined as 

the secant slope of a tensile load-strain curve at a given tensile load. The secant 

stiffness was determined at the tensile load of 2 kN/m for Typar 3301 and 10 kN/m 

for Amoco 2044. The secant stiffness from the preloading path was 44.2 kN/m for 

Typar 3301 and 625 kN/m for Amoco 2044. The secant stiffness from the preloading 

path was used as a reference to calculate the stiffness ratio. The stiffness ratio is the 

ratio of the secant stiffness determined from the preloading and reloading load-strain 

curves at the same tensile load. 

Figure 3.33 shows the stiffness ratio versus 

ULT

PL

T

T relationships of Typar 3301 

and Amoco 2044. The ratio

ULT

PL

T

T is an indication of the relative magnitude of 

preloading load level. The stiffness ratio of Typar 3301 and Amoco 2044 appeared to 

reduce with increasing preloading load levels. The stiffness ratios at 

ULT

PL

T

T = 0.43, 

0.5, and 0.71 were, respectively, 1.7, 1.2, and 0.8 for Typar 3301. The stiffness ratios 

at 

ULT

PL

T

T = 0.29, 0.36, and 0.43 were, respectively, 2.3, 1.2, and 1.2 for Amoco 2044. 

This behavior indicates that preloading can have a detrimental effect on the 

geosynthetics if the preloading level exceeds a certain critical load level. For Typar 

3301 and Amoco 2044, the threshold load level was about half of the ultimate tensile 

load. 

 Figure 3.34 shows failure load ratio versus TPL/TULT relationships of Typar 

3301 and Amoco 2044. The failure load ratio was the ratio of ultimate loads of the 

preloaded specimen and the corresponding virgin specimen. It is shown that 

preloading reduced the ultimate load of the geosynthetics by about 5%. 
91

Figure 3.27: Tensile Load Versus Axial Strain Relationship, Test G-M-3301 

Figure 3.28: Tensile Load Versus Axial Strain Relationships, Tests G-M-2044-1, 2

0

1

2

3

4

5

6

7

8

0 20 40 60 80 100 120

Axial Strain (%)

Tensile Load (kN/m)

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14 16

Axial Strain (%)

Tensile Load (kN/m)

G-M-2044-1

G-M-2044-2
92

 Figure 3.29: Tensile Load Versus Axial Strain Relationships of 

Tests G-UR-3301-1, 2, and 3 (Stress-Controlled Part) 

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50

Axial Strain (%)

Tensile Load (kN/m)

(a) Test G-UR-3301-1

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50

Axial Strain (%)

Tensile Load (kN/m)

(b) Test G-UR-3301-2

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50

Axial Strain (%)

Tensile Load (kN/m)

(c) Test G-UR-3301-3
93

Figure 3.30: Tensile Load Versus Axial Strain Relationships of 

Test G-M-3301 and Tests G-UR-3301-1, 2, 3 (Strain-Controlled Part)

0

1

2

3

4

5

6

7

8

0 20 40 60 80 100 120

Axial Strain (%)

Tensile Load (kN/m)

G-M-3301

G-UR-3301-1

G-UR-3301-2

G-UR-3301-3
94

Figure 3.31: Tensile Load Versus Axial Strain Relationships of 

Tests G-UR-2044-1, 2, and 3 (Stress-Controlled Part) 

0

10

20

30

40

50

60

70

80

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

Axial Strain (%)

Tensile Load (kN/m)

(a) Test G-UR-2044-1

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14

Axial Strain (%)

Tensile Load (kN/m)

(b) Test G-UR-2044-2

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14

Axial Strain (%)

Tensile Load (kN/m)

(c) Test G-UR-2044-3
95

Figure 3.32: Tensile Load Versus Axial Strain Relationships of 

Test G-M-2044-1 and Tests G-UR-2044-1, 2 (Strain-Controlled Part) 

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14

Axial Strain (%)

Tensile Load (kN/m)

G-M-2044-1

G-UR-2044-1

G-UR-2044-2
96

Figure 3.33: Stiffness Ratio Versus

ULT

PL

T

T Relationships of 

Typar 3301 and Amoco 2044 

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.2 0.4 0.6 0.8 1.0

TPL/TULT

Stiffness Ratio

Typar 3301

Amoco 2044
97

Figure 3.34: Failure Load Ratio Versus

ULT

PL

T

T Relationships of Typar 3301 

and Amoco 2044 

0.50

0.75

1.00

1.25

1.50

0.0 0.2 0.4 0.6 0.8 1.0

TPL/TULT

Failure Load Ratio

Typar 3301

Amoco 2044
98

3.6 Direct Shear Tests for Soil-Geosynthetic Interfaces

A series of DS tests on the soil-geosynthetic interfaces was conducted under 

monotonic loading and unloading-reloading cycles. The purposes of the tests were to 

examine the behavior of the interfaces subject to unloading-reloading cycles and to 

calibrate interface model parameters in the finite element analysis and the SPR model 

(Sections 5.4 and 6.3).

3.6.1 Test Description

The DS test apparatus consisted of a pair of 60-mm by 60-mm by 20-mm deep 

shear boxes with a displacement-controlled loading system. The rate of shear 

displacement was 0.4 mm per minute. The constant normal stress was applied by a 

dead load. 

A geotextile specimen with dimensions of 60 mm x 60 mm was firmly glued 

to the top surface of a rigid wooden block. The wooden block with the geosynthetic 

specimen was placed inside the lower shear box. The thickness of the wooden block 

was modified several times to have the geosynthetic surface positioned at 0.1 mm 

above the horizontal surface of the lower shear box. The soil was placed in the upper 

shear box. 

The unloading and reloading paths of the DS test were manually controlled by 

reversal of the upper box displacement. In the preloading path, the upper box moved 

in one direction until a preloading shear stress level was reached. The movement 

direction of the upper box was then reversed to represent the unloading path. When 

the reversed shear stress in the unloading path was equal to the magnitude of the 

preloading shear stress level, the movement direction was reversed again to represent 

the reloading path.

The size of the DS test in this study was relatively small. The boundary 

effects could affect the test results to some degree. However, the test results with the 

60-mm-square direct shear box were expected to have insignificant boundary effects 

for two reasons. First, the dimensions of the direct shear box were approximately 100 

times the mean grain size (D50) of the soil specimen. This was in the range 

recommended by ASTM D3080 and by other researchers (Jewell and Wroth, 1987; 

Palmeira, 1988). Second, it was confirmed by O’Rourke et al. (1990) that the 

60-mm-square direct shear apparatus for Ottawa sand and HDPE gave results similar 

to those obtained from larger size direct shear apparatus. O’Rourke et al. (1990) 

conducted a series of direct shear tests on Ottawa sand and HDPE using 

a 60-mm- square shear box. They compared the test results with those obtained by 

using different sizes of direct shear boxes by Martin et al. (1984), Saxena and Wong 

(1984), and Williams and Houlihan (1987). It was found that all the direct shear test 

results were similar.
99

The DS tests were conducted on the interfaces between the Ottawa sand and 

Amoco 2044, and between the Road Base soil and Amoco 2044. The DS tests results 

of Typar 3301 and the Ottawa sand were readily available from Wu (1993). 

3.6.2 Specimen Preparation and Test Procedure

The specimen preparation and the test procedure of the interface tests are as 

follows:

1. Glue a 60-mm x 60-mm geosynthetic sheet on the top surface of a rigid 

wooden block.

2. Fit the rigid wooden block with the geosynthetic sheet inside the lower direct 

shear box.

3. Place the upper shear box on top of the lower shear box and tighten corner 

screws.

4. Place soil in the upper shear box. For the Road Base soil, the soil was 

compacted in the upper shear box by tamping. The Road Base soil used in the 

direct shear tests was minus #4 standard sieve material with a water content of 

12.2%. For the Ottawa sand, the sand was poured in the upper shear box and 

densified to a prescribed density by vibrating the direct shear box.

5. Place a rigid loading plate on top of the soil.

6. Remove the corner screws and lift the upper shear box up to have a 0.5 mm 

gap between the lower and upper shear boxes.

7. Apply a constant vertical load on the rigid loading plate.

8. Allow the specimen to compress until the vertical movement cease or 

becomes negligible.

9. Mount two LVDTs to measure the vertical movement of the rigid loading 

plate and the horizontal applied load.

10. Apply horizontal loads in a constant displacement mode.

3.6.3 Measurement and Test Data Reduction

The vertical deformation of the test specimen was recorded by an LVDT 

(sensitivity = +0.005 mm). The applied shear force was measured by the other LVDT 

(sensitivity = +8 N) attached to a proof ring. The LVDT measurement has been 

calibrated with the proof ring gauge to obtain the relationship between the LVDT 

displacement and the horizontal load. The LVDTs were connected to a DATAQ4500

data acquisition system. The horizontal movement of the upper box was calculated 

from the controlled displacement rate and time. The shear stress (τ.) along the soilgeosynthetic interface was calculated from the following formula:

O

h

A

F

t = [3.7]
100

where Fh = applied horizontal force

Ao = horizontal cross-sectional area of the specimen (assumed to 

 be constant and equal to the initial area) 

3.6.4 Test Programs

Test programs for the DS tests are presented in Table 3.6 for the Ottawa sand 

and Amoco 2044 interface and Table 3.7 for the Road Base soil and Amoco 2044 

interface. The test program was divided into two groups: monotonic-loading (M) 

tests and unloading-reloading (UR) tests. The monotonic-loading and unloadingreloading tests were conducted in a displacement-controlled mode at a constant 

displacement rate of 0.4 mm per minute. 
101

Table 3.6: DS Test Program for the Ottawa Sand and Amoco 2044 Interface
102

Table 3.7: DS Test Program for the Road Base Soil and Amoco 2044 Interface 
103

3.6.5 Test Results and Discussions

The DS test results and discussions of the test results are presented in the 

following sections. The general behavior was first described, followed by an 

assessment of the effects of preloading on relative displacement and shear strength of 

the soil-geosynthetic interfaces.

3.6.5.1 General Behavior

The relationships of shear stress versus horizontal displacement and vertical 

displacement versus horizontal displacement of the interface tests were plotted. 

Failure state was defined as the peak shear stress. In the vertical displacementhorizontal displacement plot, a positive sign represents specimen dilation, whereas a 

negative sign represents specimen contraction.

Figure 3.35 presents the DS test results of the Sand-Amoco 2044 interface. 

Figures 3.36 presents the DS test results of the Road Base soil-Amoco 2044 interface. 

The shear stress increased in a non-linear manner with increasing horizontal 

displacement. The unloading-reloading part of the curve was approximately linear. 

The reloading curve resembled the preloading curve after the reloading shear stress 

exceeded the preloading load level. The peak shear stress of the Ottawa sand-Amoco 

2044 interface was reached at smaller horizontal displacements (1 to 2 mm) than 

those of the Road Base soil-Amoco 2044 interface (3 to 6 mm). 

From the vertical displacement-horizontal displacement plots, the Ottawa 

Sand-Amoco 2044 specimen initially contracted and then dilated. Upon unloading, 

the specimen contracted. During reloading, the specimen exhibited similar volume 

change behavior as in the preloading path. The specimen contracted and dilated until 

failure. In the Road Base soil-Amoco 2044 specimen, contraction behavior prevailed 

in the preloading and unloading-reloading paths. 

3.6.5.2 Effects of Preloading on Relative Displacement and Shear Strength of 

Interfaces

The secant interface stiffness at 50% of failure stress (K50) and the reloading 

interface stiffness (KRL) are introduced to examine the effects of preloading on the 

relative displacement at the interfaces. K50 is defined as the secant slope of a shear 

stress-horizontal displacement curve at 50% of failure shear stress. K50 represents the 

average interface stiffness of the virgin soil-geosynthetic interface. KRL was 

determined from the reloading portions of the shear stress-horizontal displacement 

curve by a linear interpolation using least-square regression. KRL represents the 

average interface stiffness of the preloaded soil-geosynthetic interface.

Figures 3.37 and 3.38 show the interface stiffness versus normal stress 

relationships of the Ottawa sand-Amoco 2044 and Road Base soil-Amoco 2044 

interfaces, respectively. It is shown that KRL and K50 increased with increasing 

normal stresses. KRL was about 1.5 to 2 times as high as K50. 
104

Figures 3.39 and 3.40 show the peak shear stress versus normal stress 

relationships of monotonic-loading and unloading-reloading DS tests. A series of 

monotonic-loading DS tests was conducted to obtain shear strength envelopes for the 

interfaces under monotonic loading. It is shown that the effect of preloading on the 

shear strength of the interfaces was insignificant. This finding is in agreement with 

the results of direct shear tests by O’Rouke et al. (1990), as shown in Figure 2.9.
105

Figure 3.35: Results of Tests DS-UR-(S+2044)-1, 2, and 3

0

50

100

150

200

250

300

0 0.5 1 1.5 2 2.5 3 3.5

Horizontal Displacement (mm)

Shear Stress (kPa)

195 kPa

358 kPa

86 kPa

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.5 1 1.5 2 2.5 3 3.5

Horizontal Displacement (mm)

Vertical Displacement (mm)

86 kPa

195 kPa

358 kPa
106

Figure 3.36: Results of Tests DS-UR-(RB+2044)-1, 2, and 3

0

50

100

150

200

250

300

0 1 2 3 4 5 6 7

Horizontal Displacement (mm)

Shear Stress (kPa)

86 kPa

195 kPa

358 kPa

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0 1 2 3 4 5 6 7

Horizontal Displacement (mm)

Vertical Displacement (mm)

86 kPa

195 kPa

358 kPa
107

Figure 3.37: Interface Stiffness Versus Normal Stress Relationships of 

Ottawa Sand and Amoco 2044 Interface

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

0 50 100 150 200 250 300 350 400

Normal Stress (kPa)

Interface Stiffness (kN/m

3

)

K(50)

K(RL)
108

Figure 3.38: Interface Stiffness Versus Normal Stress Relationships of Road 

Base Soil and Amoco 2044 Interface

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

0 50 100 150 200 250 300 350 400

Normal Stress (kPa)

Interface Stiffness (kN/m3

)

K(50)

K(RL)
109

Figure 3.39: Peak Shear Stress Versus Normal Stress Relationships of Ottawa 

Sand and Amoco 2044 Interface

0

50

100

150

200

250

300

350

400

0 100 200 300 400

Normal Stress (kPa)

Peak Shear Stress (kPa)

Monotonic DS Tests

Unloading-Reloading DS Tests

Linear (Monotonic DS Tests)
110

Figure 3.40: Peak Shear Stress Versus Normal Stress Relationships of Road 

Base Soil and Amoco 2044 Interface

0

50

100

150

200

250

300

350

400

0 100 200 300 400

Normal Stress (kPa)

Peak Shear Stress (kPa)

Monotonic DS Tests

Unloading-Reloading DS Tests

Linear (Monotonic DS Tests)
111

3.7 Summary and Concluding Remarks

Laboratory tests were conducted to examine the behavior of different soils, 

geosynthetics, and soil-geosynthetic interfaces subject to monotonic loading and 

unloading-reloading cycle(s). The tests consisted of conventional triaxial 

compression (CTC) tests for soils, in-isolation load-extension (LE) tests for 

geosynthetics, and direct shear (DS) tests for soil-geosynthetic interfaces. Each test 

category employed two types of loading sequence: monotonic loading and unloadingreloading cycle(s). Test specimens used for the monotonic-loading tests were 

referred to as virgin specimens, whereas test specimens used for the unloadingreloading test were referred to as preloaded specimens. 

The test results showed that:

1. The stiffness of the soils increased due to preloading. The reloading stiffness was 

found to depend on the confining pressure and the unloading load level. At the 

same confining pressure, the reloading stiffness in the RL-PS path was higher 

than in the RL-Z path.

2. The stiffness of the preloaded geosynthetic specimen was higher than that of the 

virgin specimen, provided that the preloading load level was less than about 50% 

of the ultimate tensile strength. The reloading stiffness reduced with increasing 

preloading level.

3. The reloading stiffness of the preloaded interface was higher than that of the 

interface without preloading. The reloading stiffness of the interface increased 

with increasing normal stress applied on the interface.

4. Preloading did not affect the shear strength of the soils or the interfaces.

5. The tensile strength of the preloaded geosynthetic specimen was about 5% lower 

than that of the corresponding virgin specimen.
112

4. SGP Test Apparatus

In this study, a modified SGP test apparatus was devised for investigating the 

behavior of a generic GRS mass subject to monotonic loading and unloadingreloading cycles. The SGP test apparatus was the third generation of a SGP test 

device developed at the University of Colorado at Denver. Typically, the 

performance test is performed on a soil-reinforcement composite consisting of soil 

and horizontally placed layer(s) of geosynthetic reinforcement in a plane strain 

condition. The geosynthetic reinforcement and the confining soil are allowed to 

deform in an interactive manner upon load applications. The geosynthetic tensile 

stresses are induced by the stresses developed in the soil resulting from the selfweight of the soil and externally applied loads.

Conceptually, the SGP test specimen represents neither an element in a 

prototype GRS structure nor a reduced scale model of any prototype GRS structures. 

Generally speaking, the measured quantities of the SGP test, such as deformation and 

reinforcement strain, cannot be correlated directly to a prototype GRS structure. In 

this study, the results of the SGP test were used to 1) examine the effects of 

preloading on deformation and strength of a GRS mass, 2) evaluate the benefits of 

different unloading-reloading cycles, 3) verify a finite element analysis, 4) evaluate 

the simplified preloading-reloading (SPR) model developed in this study, and 5) 

develop a methodology to relate the behavior of a preloaded GRS mass to that of a 

proloaded GRS structure.

This chapter presents development of the modified SGP test, apparatus 

configurations, specimen preparations, test procedures, instrumentation, and test 

programs.

4.1 First and Second Generations of SGP Test Apparatus

4.1.1 First-Generation SGP Test

Wu and Helwany (1996) developed a soil-geosynthetic performance test to 

investigate long-term interactive behavior of soil-geosynthetic composites. A 

schematic diagram of the test device is shown in Figure 4.1, in which a reinforcedsoil mass was placed inside a rigid container with transparent plexiglass side walls. 

The reinforced-soil mass comprised a sheet of geosynthetic reinforcement, two 

flexible steel plates, and confining soil. The confining soil confined the geosynthetic 

reinforcement at both top and bottom. The two ends of the geosynthetic 

reinforcement were securely attached to the two vertical steel plates at their midheight. The transverse direction of the reinforced-soil mass was fitted between two 

lubricated plexiglass sidewalls of a rigid container in such a manner that 

reinforced-soil mass was restrained from movement in the direction perpendicular to 

the plexiglass sidewalls (i.e., in a plane strain configuration). On the top surface of 

the confining soil, another sheet of geosynthetic was used to connect the top edge of 
113

the vertical steel plates. Upon the application of a surface load, the geosynthetic 

reinforcement and its confining soil will deform interactively over time.

To maintain the plane strain condition throughout the test, the interface 

adhesion between the rigid plexiglass and the soil was minimized to nearly 

frictionless. This was accomplished by creating a lubrication layer at the interface of 

the plexiglass sidewall and the soil. The lubrication layer consisted of a 

0.2-mm-thick membrane and a thin layer of silicon grease. This technique was 

developed at the University of Tokyo by Tatsuoka and his associates and has been 

used successfully in many property tests, reduced-scale model tests, and full-scale 

tests (Tatsuoka et al., 1984; Wu, 1992; Ling and Tatsuoka, 1993)

4.1.2 Second-Generation SGP Test Apparatus

The second-generation soil-geosynthetic performance test apparatus was 

developed by Ketchart and Wu (1996). The new apparatus was devised to simplify 

the sample preparation procedure and load application. A schematic diagram of the 

long-term performance test apparatus is shown in Figure 4.2. The test specimen was 

reduced to 300 mm high, 600 mm wide and 300 mm long. The longitudinal direction 

of the test specimen was in a state of unconfined condition, whereas in the 

first-generation apparatus it was supported by flexible steel plates. During sample 

preparation, the longitudinal sides of the reinforced-soil mass were restrained from 

movement by two moveable plexiglass plates. With the aid of a pair of air cylinders, 

the moveable plates were released immediately before testing. Thus, the soilgeosynthetic composite was allowed to deform in an unconfined condition along the 

longitudinal direction. Also, unlike in the first-generation test, the geosynthetic 

reinforcement at the mid-height was simply laid horizontally without any artificial 

restraints at the ends. A sustained vertical load was applied to the top surface of the 

specimen with a self-contained loading mechanism.

4.2 Modified SGP Test Apparatus

 A schematic diagram of various components of the modified SGP test 

apparatus is shown in Figure 4.3. The test apparatus was manufactured by the 

Turner-Fairbank Highway Research Center of the Federal Highway Administration. 

Figure 4.4 depicts the new SGP test apparatus with a specimen on the MTS-810 

loading apparatus. Each of the components is described in the following sections.

4.2.1 Apparatus Configurations

In the modified SGP test, a generic GRS mass was placed inside a rigid 

container as shown in Figure 4.5. Dimensions of the specimen were designated as W 

(width), H (height), and D (depth) in the plane strain direction. The dimensions of the 

SGP test specimen employed in this study were 610 mm (24 in) high, 254 mm (10 in) 

wide (W), and 565 mm (22.25 in) deep (D). The test specimen comprised a soil with 
114

three layers of reinforcement at the bottom, mid-height, and top. The transverse 

direction (plane strain direction) of the test specimen was fitted between two 

lubricated acrylic sidewalls of the rigid container. The test specimen was restrained 

from movement in the direction perpendicular to the sidewalls (i.e., plane strain 

direction). The longitudinal direction of the test specimen was unrestrained. 

The rigid container had two side panels, six transverse bars, and two base 

plates. The sidewall panel had dimensions of 890 mm by 915 mm. Each side panel 

consisted of a 13-mm-thick transparent acrylic panel reinforced by 3.2-mm-thick, 

50.8-mm-square steel tubes with center to center spacing of 216 mm in both 

horizontal and vertical directions. The transverse bars were rigidly connected with 

the sidewalls to form a container, as shown in Figure 4.6. The height of the sidewall 

panels can be increased to 1090 mm by using sidewall extensions with two additional 

transverse bars across the top of the sidewall extensions. 

Figures 4.7 and 4.8 show, respectively, the plan view and cross section of the 

modified SGP test apparatus with a test specimen (without reinforcement layers). 

Figure 4.7 depicts the sidewall panels, transverse bars, extension transverse bar, and 

horizontal removable panels with horizontal constraint assemblies. Figure 4.8 shows 

the cross section A-A from the top view. Figure 4.8 depicts, from the bottom up, a 

lower base plate, an upper base plate, six horizontal removable panels (three on each 

side) with horizontal constraint configurations, a sidewall panel, six main transverse 

bars, an extension sidewall panel, and two extension transverse bars. The test 

specimen was situated on top of the upper base plate. The upper base plate was a 25-

mm-thick, 915-mm by 565-mm steel plate. The lower base plate was a 25-mm-thick, 

457-mm by 565-mm steel plate with a 25-mm-thick, 150-mm-diameter steel ring at 

the center (see Figure 4.8). The lower steel plate was placed on the lower actuatorloading rod of the MTS-810 loading device during load applications. The center ring 

of the lower steel plate was designed to ensure that the vertical load from the 

actuator-loading rod was applied to the center of the test specimen.

The horizontal removable panel consisted of a 8-mm-thick steel plate 

reinforced with two vertical and three horizontal 3.2-mm-thick, 25-mm by 50-mm 

rectangular tubes. The horizontal removable panels were used during specimen 

preparation. They were set perpendicular to the sidewall panels to form a cuboid 

space for the specimen.

During the specimen preparation, a horizontal constraint assembly restrained 

the horizontal removable panels from horizontal movement. The horizontal 

constraint assembly comprised a 8.5-mm-thick circular plate and a 8-mm-diameter 

rod threaded through the transverse bar (see Figures 4.7 and 4.8). The threaded rod 

controlled the horizontal position of the circular plate. The circular plate was set to 

touch and restrain the horizontal bars of the horizontal removable panel during the 

specimen preparation. The horizontal removable panels were removed after 

completing specimen preparation.
115

The modified SGP test apparatus was designed to accommodate specimens 

with maximum dimensions of 915 mm (36 in) high (H), 508 mm (20 in) wide (W), 

and 565 mm (22.25 in) deep (D). The dimensions of the SGP test specimen 

employed in this study were 610 mm (24 in) high, 254 mm (10 in) wide (W), and 565 

mm (22.25 in) deep (D). Note that the depth of the specimen was limited by the 

clearance of the MTS-810 loading frame. The main factors used to determine the 

overall specimen dimensions are as follows:

1. Backfill Particle Size: To reduce the particle size effects, the dimensions of 

a generic GRS mass should be at least 6 times larger than 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) (Jewell,1993). The recommended 

maximum particle size for the backfill of GRS structures is 19 mm (Elias and 

Christopher, 1996). The specimen dimension, therefore, should be at least 120 mm.

2. Reinforcement Spacing: The reinforcement spacing plays an important role 

in the deformation behavior of GRS structures (Adams, 1999) and the load-transfer 

mechanism of reinforced-soil masses (Abramento and Whittle, 1993). The height (H) 

of a generic GRS mass should be able to accommodate the typical reinforcement 

spacing with the recommended maximum spacing of 800 mm (Elias and Christopher, 

1996). 

3. Size of Reinforcement Sheet: The specimen depth in plane strain direction 

(D) and the specimen width (W) should be large enough to accommodate typical 

geosynthetic reinforcement (e.g., polymer grids, woven and non-woven geotextiles). 

Ideally, the reinforcement size used in the SGP test should represent a “very large” 

sheet of reinforcement. For polymer grids, enough grid “cells” are required for a 

good representation of the polymer grid specimen. For non-woven geotextiles, the 

aspect ratio of the reinforcement specimen (i.e., the ratio of width to length) should be 

at least 2 to alleviate significant necking effects.

4.2.2 Boundary Conditions 

The transverse direction (plane strain direction) of the test specimen was fitted 

between two lubricated acrylic sidewalls of the rigid frame. The test specimen was 

restrained from movement in the direction perpendicular to the sidewalls (i.e., plane 

strain condition). The longitudinal direction of the test specimen was unrestrained. 

On the top of the specimen was a rigid loading plate. The vertical load was applied 

on the rigid loading plate by the MTS-810 testing system. 

All contacted surfaces of the specimen with the SGP test apparatus and the 

rigid loading plate were lubricated to minimize the interface friction. The lubrication 

layer consisted of a 0.5-mm-thick latex membrane and a thin layer of silicone grease.

The specimen surface was vacuum-sealed with a 0.5-mm-thick rubber 

membrane for confining pressure application. The confining pressure was applied by 

vacuuming. A small-diameter flexible plastic tube connected to a suction machine 
116

was attached to one unrestrained side of the specimen (see Figure 4.4). The 

maximum confining pressure that can be applied by such a system is the atmospheric 

pressure. The applied confining pressure was controlled by a gauge connected to a 

suction machine.
117
118
119

Figure 4.4: Modified SGP Test Apparatus on MTS-810 Loading System

Before Testing
120

Figure 4.5: Specimen Dimensions of Modified SGP Test

Base reinforcement layer

Soil

Soil

Middle reinforcement layer

Top reinforcement layer

D = 565 mm

H

W

Rigid container

915 mm

In this study , H = 610 mm and W = 254 mm

890 mm
121

Figure 4.6: Rigid Container of Modified SGP Test Apparatus
122

1 = Horizontal Constraint

2 = Reinforced Steel Tube

3 = Transparent Acrylic Panel

4 = Horizontal Removable Panel

5 = Extension Transverse Bar

6 = Transverse Bar

Figure 4.7: Top View of Modified SGP Test Apparatus

5

6

1 2 3 4
123

Figure 4.8: Cross Section of Modified SGP Test Apparatus (Section A-A)

1 = Extension 

 Transverse Bar

2 = Extension Side 

 Wall Panel

3 = Side Wall Panel

4 = Transverse Bar

5 = Horizontal 

 Removable Panel

6 = Upper Base Plate 

7 = Lower Base Plate

 

7 6

1

2

3

4

TEST

SPECIMEN

5
124

4.2.3 Specimen Preparation and Test Procedure

4.2.3.1 Sand Specimen

The sand was placed inside the modified SGP test apparatus at a constant 

density of 16.85 kN/m3 (+0.5 kN/m3) by an air-pluviation method using a hopper 

designed for construction of the Denver wall (Wu, 1993). The hopper dispensed sand 

uniformly as it traveled in a pendulum motion over the SGP test apparatus (see Figure 

4.9). During specimen preparation, the hopper was raised incrementally as the 

specimen height increased to ensure a constant height of pluviation. The opening size 

of the hopper is adjustable by a linkage control attached to the handle of the hopper. 

Factors affecting the sand density in the air-pluviation method are the size of 

opening of the hopper, the height of pluviation, and the swing rate. To achieve the 

prescribed sand density, a trial-and-error process was employed to determine the 

appropriate opening size, the height of pluviation, and the swing rate of the hopper. 

The sand was dispensed from the hopper into two 100-mm-diameter Proctor molds 

placed 80 mm apart at the various opening sizes, heights of pluviation, and swing 

rates. It was found that the sand density decreased with the increase of the opening 

size and the swing rate and increased with the increase of the height of pluviation. In 

this study, the opening size of 2 mm, the height of pluviation of 1.0 m, and the swing 

rate of approximately 2 seconds per swing were used to obtain the targeted density.

The rubber membrane used for the sand specimen was prepared prior to 

sample preparation. The rubber membrane was cut to a special shape and folded to 

form a 254-mm by 565-mm by 915-mm bag. The edges of the rubber membrane 

were glued together by a clear silicone sealant.

The specimen preparation and the test procedure for the SGP test with the Ottawa 

sand are as follows:

1. Lubricate the entire base and sidewall surface areas with a silicone grease.

2. Install the moveable rigid panels to form a cuboid space for the specimen.

3. Apply a thin layer of silicone grease on the inner surfaces of the moveable rigid 

panels.

4. Place the rubber membrane bag in the cuboid space of the apparatus.

5. Remove the air bubbles trapped between the rubber membrane and the contacted 

surface.

6. Connect the small-diameter vacuuming tube to the rubber membrane.

7. Place the bottom reinforcement layer (for a test with reinforcement).

8. Place a large cardboard with a 254-mm by 565-mm rectangular slot on top of the 

apparatus to prevent spilling of the sand outside the cuboid space.

9. Raise the hopper filled with the sand to a prescribed drop height.

10. Start dispersing the sand with a pendulum motion of the hopper.

11. Move the hopper up incrementally to maintain a constant height of pluviation.

12. Place the middle reinforcement layer at mid-height and continue dispersing the 

sand until full-height is reached.
125

13. Place the top reinforcement layer on top of the soil specimen.

14. Remove the hopper and the cardboard.

15. Fold the rubber membrane bag to cover the top surface of the specimen.

16. Seal the rubber membrane connection.

17. Place the modified SGP test apparatus on a fork lift.

18. Move the test apparatus to the testing area and place it in the MTS-810 loading 

device.

19. Apply a vacuum pressure of 69 kPa to maintain the specimen shape.

20. Remove the horizontal removable panels.

21. Place the rigid loading plate on top of the specimen.

22. Glue 25-mm by 25-mm plastic pieces on the unrestrained surface of the specimen 

at 152 mm, 305 mm, and 458 mm from the specimen base. The square plastic 

pieces serve as smooth and rigid targets for the horizontal LVDTs.

23. Apply a vertical seating load of 3.5 kPa on the specimen.

24. Set the initial values for all instruments.

25. Start applying the vertical load in accordance with the prescribed loading 

sequence and record the performance of the test specimen.

4.2.3.2 Road Base Soil Specimen

The Road Base soil was compacted in the modified SGP test apparatus in 24 

lifts to provide adequate compaction (see Figure 4.10). The specimen was prepared 

at a dry density of 17.81 kN/m3 (+0.15 kN/m3). The compaction was carried out by a 

4-lb standard Proctor hammer (ASTM D698). The method of weight-volume 

allocation was used to control the uniform density of the specimen. The total weight 

of the test specimen was divided into 24 equal soil portions. Each soil portion was

compacted in the SGP test apparatus until the prescribed density was obtained. The 

density of each lift was calculated from the volume of the specimen for one lift and 

the allocated portion of the soil. 

The rubber membrane used for the Road Base specimen was cut to a 

prescribed size and folded to form a cuboid shape. The edges of the rubber 

membrane were glued together by a clear silicone sealant. After the Road Base soil 

had already been compacted, the folded rubber membrane was used to cover and 

vacuum-seal the Road Base soil specimen

The specimen preparation and the test procedure for the modified SGP test 

with the Road Base soil were similar to those of the Ottawa sand. The difference was 

the soil placement method. The air-pluviation method was employed for the Ottawa 

sand specimens, whereas the dynamic compaction by a standard Proctor hammer was 

used for the Road Base soil specimens. The specimen preparation and the test 

procedure for the SGP test with the Road Base soil are as follows:

1. Lubricate the entire base and sidewall surface areas with a silicone grease.

2. Install the moveable rigid panels to form a cuboid space for the specimen.
126

3. Place rubber membranes over the lubricated base and sidewall areas.

4. Remove the air bubbles trapped between the rubber membrane and the contacted 

surface.

5. Place the bottom reinforcement layer (for a test with reinforcement).

6. Start compacting the Road Base soil in 25-mm-thick lifts.

7. Place the middle reinforcement layer at the mid-height and continue compacting 

the Road Base soil to full-height.

8. Place the top reinforcement layer on top of the soil specimen.

9. Place the SGP test apparatus on a fork lift.

10. Move the test apparatus to the testing area and place it in the MTS-810 loading 

device.

11. Remove the horizontal removable panels.

12. Cover and vacuum-seal the specimen with the pre-prepared rubber membrane.

13. Connect the vacuuming tube to the rubber membrane.

14. Apply a vacuum pressure of 34.5 kPa.

15. Place the rigid loading plate on top of the specimen.

16. Glue 25-mm by 25-mm plastic pieces on the unrestrained surface of the specimen 

at 152 mm, 305 mm, and 458 mm from the specimen base. The square plastic 

pieces serve as smooth and rigid targets for the horizontal LVDT.

17. Apply a vertical seating load of 3.5 kPa on the specimen.

18. Set the initial values for all instruments.

19. Start applying the vertical load in accordance with the prescribed loading 

sequence and record the performance of the test specimen.

4.2.4 Instrumentation 

The instrumentation layout for the modified SGP test is shown in Figure 4.3. 

The vertical deformation of the specimen (i.e., vertical displacement of the rigid 

loading plate) and the applied vertical load were measured by the internal LVDT and 

the load cell, respectively, of the data acquisition system of the MTS-810 loading 

system. A total of six LVDTs (three on each side) were used to measure the 

horizontal deformation of the specimen in the direction perpendicular to the plane 

strain direction. Three LVDTs were installed on each side of the specimen at 152 

mm (point B, Figure 4.3), 305 mm (point M, Figure 4.3), and 458 mm (point T, 

Figure 4.3) from the base or at 1⁄4, 1⁄2, and 3⁄4 points of the specimen height. The 

sensitivity of the horizontal LVDT was +0.005mm. 

In one test with the Road Base soil and Amoco 2044 reinforcement, nine 

strain gauges were mounted on the middle reinforcement layer (see Figure 4.11). The 

gauges were installed to measure strains in the fill direction of the reinforcement, 

which was oriented perpendicular to the plane strain direction.

The strain gauges were mounted by a “patch” procedure. A strain gauge was 

first mounted on a 25-mm x 76-mm patch. The patch was a weak heat-bonded non-
127

woven geotextile. Each strain gauge was glued to the geotextile patch only at the two 

ends to avoid inconsistent local stiffening of the geotextile because of adhesive 

(Billiard and Wu, 1991). The geotextile patch (with a strain gauge mounted) was 

then attached to the geotextile reinforcement at a prescribed location. A 

microcrystalline wax and a Neoprene rubber patch were applied over the gauge to 

protect it from soil moisture and possible mechanical damage during compaction and 

during testing. Due to the presence of the lightweight geotextile patch, calibration 

was needed. A wide-width tensile test was performed to correlate the recorded strains 

to actual strains of the geotextile reinforcement. Figure 4.12 shows the wide-width 

tensile test performed on the Amoco 2044 specimen with two strain gauges mounted 

on one side. The calibration curves are shown in Figure 4.13.
128

Figure 4.9: Specimen Preparation for Ottawa Sand Specimen
129

Figure 4.10: Specimen Preparation for Road Base Soil Specimen 
130

Figure 4.11: Strain Gauge Layout

155 mm

89 mm

Amoco 2044 

Reinforcement Layer

89 mm

L3 M3

L2 M2

127 mm 155 mm

L1 M1

R3

R2

38 mm

127 mm

R1

38 mm

Strain Gauge
131

Figure 4.12: Strain Gauge Calibration with LE Test
132

Figure 4.13: Calibration Curve for Strain Gauges

y = 3.0841x

R

2

 = 0.975

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8 1 1.2

Average Strain from LVDT (%)

Measured Voltage from Strain Gauge (Volt)
133

4.3 Test Programs

Test programs for the SGP tests are presented in Table 4.1 for the Ottawa sand 

and Table 4.2 for the Road Base soil. The test program was divided into two groups: 

monotonic-loading (M) tests and unloading-reloading (UR) tests. The monotonic 

tests were conducted in a strain-controlled mode at a constant strain rate of 0.5% per 

minute. The unloading-reloading (UR) tests were conducted in a stress-controlled 

mode with various loading sequences at a constant loading rate of 10 kPa per minute, 

followed by a strain-controlled mode at a constant strain rate of 0.5% per minute up 

to failure. 

The monotonic loading SGP test program was designed for the following 

purposes:

1. To examine the reinforcing effects during the monotonic loading 

Tests P-M-S vs. P-M-(S+3301) and P-M-(S+2044); and Tests P-M-RB vs. P-M-

(RB+2044).

2. To provide a reference for an assessment of the effects of preloading on the GRS 

mass.

The unloading-reloading SGP test program was designed for the following 

purposes:

1. To examine the effects of preloading on the GRS mass

Tests P-M-(S+2044) vs. P-UR-(S+2044)-1; and Tests P-M-(RB+2044) vs. P-UR-

(RB+2044).

2. To examine the effects of different types of unloading-reloading cycles

For RL-Z path vs. RL-PS path: Tests P-UR-(S+2044)-1 vs. P-UR-(S+2044)-3; 

and Tests P-UR-(RB+2044). For multiple unloading-reloading cycles at the 

working load level: Tests P-UR-(S+2044)-2 and P-UR-(RB+2044). The working 

load level is defined as the vertical load with a magnitude less than the PLL.

3. To examine the effects of preloading magnitude on the GRS mass

Tests P-UR-(S+2044)-1 vs. P-UR-(S+2044)-2; and Test P-UR-(RB+2044)).

4. To examine the reinforcing effects during the unloading-reloading cycles

Tests P-UR-S vs. P-UR-(S+2044)-1; and Tests P-UR-RB vs. P-UR-(RB+2044).
134

Table 4.1: SGP Test Program for the Ottawa Sand Specimen
135

Table 4.1: SGP Test Program for the Ottawa Sand Specimen (Continued)
136

Table 4.2: SGP Test Program for the Road Base Soil Specimen
137

5. Behavior of GRS Mass Subject to Monotonic Loading and UnloadingReloading Cycles and Finite Element Analysis

This chapter presents experimental results and finite element analyses of the 

modified SGP tests conducted in this study. A total of 11 SGP tests were conducted 

to investigate the behavior of GRS masses subject to monotonic loading and 

unloading-reloading cycles. The finite element analyses were conducted to determine 

the stress distribution of a GRS mass in the SGP test.

To present the SGP test results, the following terms and symbols were used:

Vertical load = applied vertical load from the MTS-810 loading 

 system

Vertical displacement = vertical displacement of the rigid loading plate

Horizontal displacement = sum of the horizontal displacements on two sides 

 of the specimen at a particular height

Average horizontal 

displacement = average horizontal displacement of three measured 

 locations along the specimen height

Sand mass = Ottawa sand specimen without reinforcement 

Road Base soil mass = Road Base soil specimen without reinforcement

GRS mass = soil specimen with reinforcement

Preloading curve = load-displacement curve during preloading 

Unloading curve = load-displacement curve during unloading

Reloading curve = load-displacement curve during reloading

PL = preloading

UL = unloading

RL = reloading

PLL = preloading load level

ULL = unloading load level

PSL = prestressed load level

WLL = working load level

5.1 Monotonic-Loading SGP Test Results and Discussions

The monotonic-loading SGP test results and discussions of the test results are 

presented in this section. The discussions are focused primarily on the comparison of 

the test results of the soil mass with and without reinforcement. Figure 5.1 shows 

plots of the vertical and horizontal (at mid-height) displacements versus the vertical 

load of the Road Base soil mass without reinforcement (Test P-M-RB) and with 

Amoco 2044 geotextile reinforcement (Test P-M-(RB+2044)). Figure 5.2 shows 

plots of the vertical and horizontal (at mid-height) displacements versus the vertical 

load of the Ottawa sand mass without reinforcement (Test P-M-S), with Typar 3301 
138

geotextile reinforcement (Test P-M-(S+3301)), and with Amoco 2044 geotextile 

reinforcement (Test P-M-(S+2044)).

The test results show that, at the same vertical load, the GRS mass 

experienced less vertical and horizontal displacements than the soil mass. At 10-kN 

vertical load, the Road Base soil mass and the corresponding GRS mass had vertical 

displacements of 6.36 mm and 4.58 mm, respectively, and horizontal displacements 

of 2.11 mm and 0.69 mm, respectively. At 35-kN vertical load, the Ottawa sand 

mass had a vertical displacement of 9.90 mm; with Typar 3301 reinforcement the 

vertical displacement was 7.59 mm, and with Amoco 2044 reinforcement it was 7.63 

mm. The horizontal displacement of Test P-M-S was not available due to 

measurement errors. 

The GRS masses also had higher failure loads. The Road Base soil mass had 

a failure load of 11.3 kN, whereas the corresponding GRS mass had a failure load of 

16.9 kN. The Sand mass had a failure load of 37.4 kN; with Typar 3301 

reinforcement the failure load was 44.7 kN, and with Amoco 2044 reinforcement it 

was 53.0 kN. These results demonstrate the reinforcing effects resulting from 

reinforcement layers in the GRS mass. 

It is seen in Figure 5.2 that the initial vertical stiffness of the GRS mass with 

Typar 3301 was somewhat smaller than that of the Sand mass. This behavior, 

referred to as loss of compressive stiffness has been reported in triaxial and plane 

strain tests of GRS specimens (see, e.g., Broms, 1977; Holtz et al., 1982). It was 

explained by Wu (1989) and described in Section 2.4.1. 

At small displacements, the soil and GRS masses showed almost identical 

deformation responses (see Figures 5.1 and 5.2). The reinforcement prohibited the 

specimen deformation after some vertical and horizontal displacements had occurred. 

This behavior can be explained by the load transfer mechanism of the GRS mass. 

Under a vertical load, the GRS mass deformed in both vertical and horizontal 

directions. The horizontal deformation induced the restraining effect from the 

reinforcement through interface friction. However, in a range when deformation was 

small, the magnitude of the horizontal deformation may not be sufficient to mobilize 

the restraining effect. This results in the same deformation response of the soil and 

GRS masses at small strains. In the Road Base soil mass with and without 

reinforcement, the required vertical and horizontal displacements were 2.0 mm and 

0.5 mm, respectively. The magnitude of the required deformation depends on the 

stiffness of the soil, reinforcement, and interface. 

The horizontal displacements at Points B, M, and T (i.e., 1⁄4, 1⁄2, and 3⁄4 of the 

specimen height, see Figure 4.3) of the Road Base soil and GRS masses at 4-kN, 

8-kN, and 11-kN vertical loads were shown in Figure 5.3. Figure 5.3 clearly 

illustrates the reinforcing effects in reducing the horizontal deformation. The Road 

Base soil mass showed the largest horizontal movement at Point B and the least 

movement at Point T. For the GRS mass, Points T and B showed comparable 
139

horizontal displacements. The smallest horizontal displacement occurred at Point M. 

At the vertical load of 11 kN, the horizontal displacements at Points T, M, and B 

were, respectively, 2.27 mm, 4.04 mm, and 6.63 mm in the Road Base soil mass. The 

corresponding displacements were 1.67 mm, 0.81 mm, and 1.44 mm in the GRS 

mass.

Two types of failure modes, a diagonal shear failure and a wedge-type shear 

failure, were observed in these SGP tests. Figure 5.4 shows sketches of both failure 

modes. Figures 5.5 and 5.6 depict the specimens after failure for Tests P-M-RB and 

P-UR-(RB+2044), which show, respectively, the diagonal shear failure and wedgetype shear failure modes.

The first failure mode involved a single shear plane across a diagonal 

direction of the specimen. This failure mode occurred in the Sand and Road Base soil 

masses and the Sand mass with a weak reinforcement (Typar 3301). As shown in 

Figures 5.5, the shear band was evident along the diagonal direction from the top to 

the bottom of the specimen. In the test with Typar 3301 reinforcement, the middle 

reinforcement layer ruptured along the center line. The rupture location was 

approximately the intersection of the shear plane and the middle reinforcement layer. 

The reinforcement delayed a full development of the diagonal shear plane and, hence, 

increased the load carrying capacity of the soil mass.

The second failure mode was a wedge-type shear failure (see Figure 5.6). It 

occurred in the GRS mass with a strong reinforcement (Amoco 2044). The specimen 

experienced the wedge-type shear failure in the lower part of the specimen without 

reinforcement rupture. It appears that the strong reinforcement had altered the failure 

mode from the diagonal shear failure mode to the wedge-type shear failure mode. 
140

Figure 5.1: Vertical Load Versus Displacement Relationships of 

Tests P-M-RB and P-M-(RB+2044)

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20 25 30 35 40

Vertical Displacement (mm)

Vertical Load (kN)

P-M-RB

P-M-(RB+2044)

0

2

4

6

8

10

12

14

16

18

20

0 2 4 6 8 10 12

Horizontal Displacement at Pt. M (mm)

Vertical Load (kN)

P-M-RB

P-M-(RB+2044)
141

Figure 5.2: Vertical Load Versus Displacement Relationships of 

Tests P-M-S, P-M-(S+3301), and P-M-(S+2044)

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35 40

Vertical Displacement (mm)

Vertical Load (kN)

P-M-S

P-M-(S+3301)

P-M-(S+2044)

0

10

20

30

40

50

60

0 2 4 6 8 10 12

Horizontal Displacement at Pt. M (mm)

Vertical Load (kN)

P-M-(S+3301)

P-M-(S+2044)
142

Figure 5.3: Horizontal Displacements of Points T, M, and B at 4-kN, 8-kN, 

and 11-kN Vertical Loads

0

100

200

300

400

500

600

0 2 4 6 8 10

Horizontal Displacement (mm)

Specimen Height (mm)

RB(4kN)

RB+2044(4kN)

RB(8kN)

RB+2044(8kN)

RB(11kN)

RB+2044(11kN)
143

Figure 5.4: Two Failure Modes in SGP Tests

Diagonal shear failure

 Soil mass

Wedge-type

shear failure

GRS mass with 

strong reinforcement 

layers (e.g., Amoco 2044)

GRS mass with 

weak reinforcement 

layers (e.g.,Typar 3301)
144

Figure 5.5: Diagonal Shear Failure
145

Figure 5.6: Wedge-Type Shear Failure
146

5.2 Unloading-Reloading SGP Test Results and Discussions

A series of plots of the vertical load versus displacement relationships for 

unloading-reloading SGP tests is shown in Figures 5.7 to 5.10 for the Sand and GRS 

masses and in Figures 5.11 and 5.12 for the Road Base soil and GRS masses. A 

detailed description of the loading sequences for the tests was given in Section 4.3. 

The full-scale load test results of the FHWA pier were presented in Figure 5.13 and 

compared with the SGP test results. The load test results of the FHWA pier were 

adapted from Adams (1997).

From the results of the unloading-reloading SGP tests and the load test of the 

FHWA pier, the following observations were made.

1. Displacements During the PL Path: Both the SGP test and the FHWA pier 

showed vertical settlements and horizontal expansions under the PL path. After the 

SGP test specimen was unloaded and reloaded, the load-displacement curve resumed 

the preloading curve after the vertical load exceeded the PLL (see Figures 5.7 to

5.12). The preloading curve in the unloading-reloading SGP test was similar to the 

load-displacement curve of the corresponding monotonic SGP test (Test P-M-S vs. 

Test P-UR-S, Test P-M-RB vs. Test P-UR-RB, Test P-M-(S+2044) vs. Tests P-UR-

(S+2044)-1 and P-UR-(S+2044)-2, and Test P-M-(RB+2044) vs. Test P-UR-

(RB+2044)). This behavior indicates that the preloading curve of the soil mass with 

and without reinforcement is almost unaffected by the previous unloading-reloading 

cycles that occur at lower stress level. In the FHWA pier, the vertical loads in the RL 

path did not exceed the PLL.

2. Displacements During the Initial Stage of the UL Path: During the initial 

stage of the unloading path (from PLL to 0.95⋅PLL in the Sand and GRS masses and 

from PLL to 0.9⋅PLL in the Road Base soil and GRS masses), the SGP test specimen 

continued to deform in the same manners as in the PL path (i.e., settled and 

horizontally expanded). This behavior indicates potential creep deformation of the 

specimen at the PLL. This behavior was more pronounced in the Road Base soil than 

the Sand, in the horizontal movement than the vertical movement, and at the higher 

PLL than the lower PLL. The similar deformation behavior was also observed during 

the initial unloading path in the CTC tests of the soils (see Section 3.4.5.1). There 

was no data available during the unloading path of the FHWA pier.

3. Displacements During the UL Path After Passing the Initial Stage: For the 

rest of the unloading path, the SGP test specimen and the FHWA pier rebounded 

toward returning to the original shape. Both the SGP test specimen and the FHWA 

pier expanded vertically and contracted horizontally. After unloading, the 

irrecoverable deformation occurred in both vertical and horizontal directions of the 

SGP test specimen and the FHWA pier.

4. Unloading Stiffness: The unloading stiffness was approximately constant 

until the vertical load was reduced to a certain load level, referred to as the unloading 

threshold load. Below the unloading threshold load, the unloading stiffness became 
147

much smaller. In other words, the specimen experienced a significant increase in the 

swelling rate at the unloading threshold load. 

The unloading threshold load can be determined as the point of intersection of 

two straight lines tangent to the upper and lower portions of the unloading curve. The 

test data showed that the unloading threshold load was nearly the same for the soil 

mass with or without reinforcement, as shown in Figures 5.7, 5.8, 5.11, and 5.12. The 

unloading threshold load was found to be 0.15⋅PLL for the Sand and GRS masses 

(see Figures 5.7 and 5.8) and 0.25⋅PLL for the Road Base soil and GRS masses (see 

Figures 5.11 to 5.12). It was observed that reduction of the unloading stiffness below 

the unloading threshold load was more pronounced in the Sand specimens than the 

Road Base soil specimens. It is to be noted that in the UL-PS paths, the soil and GRS 

masses did not show this deformation behavior during unloading. This is because the 

ULL of the UL-PS paths (i.e., ULL=PSL) was higher than the unloading threshold 

load. The unloading threshold load will be used as a criterion for differentiating 

between the reloading stiffness of the RL-PS path and the RL-Z path in the simplified 

preloading-reloading (SPR) model. The SPR model will be described in detail in 

Chapter 6.

5. Displacements During the RL Path of the Sand: During the RL path, the 

Sand and GRS masses showed vertical settlements and horizontal expansions similar 

to the deformation behavior during the PL path. The vertical reloading curve of the 

RL-Z path of the Sand and GRS masses showed small stiffness at the initial stage. 

The vertical reloading stiffness gradually increased with the reloading magnitude 

until a vertical load was 0.15⋅PLL (see Figures 5.7, 5.8, and 5.9). After 0.15⋅PLL 

vertical load, the test specimens behaved approximately linearly. When the reloading 

magnitude approached the PLL, the reloading stiffness started to decrease. This 

behavior is known as the Bauschinger effect, as described in Section 3.4.5.

The small vertical stiffness during the initial stage of the RL-Z path is referred 

to as the reduced reloading stiffness. From Figures 5.7, 5.8, and 5.9, it appears that 

the reduced reloading stiffness behavior started from the ULL (i.e., the zero-load 

level for the RL-Z path), and ended at a reloading magnitude approximately equal to 

the unloading threshold load. The horizontal deformation during the RL-Z path did 

not show the reduced reloading stiffness. The FHWA pier (see Figure 5.13) and the 

Road Base soil and GRS masses (see Figures 5.11 and 5.12) also showed the reduced 

reloading stiffness in a vertical direction but not as obviously as in the Sand 

specimen. For the specimen under the RL-PS path, the reduced reloading stiffness 

did not occur in either vertical or horizontal directions. This interesting deformation 

characteristic is explained in the following paragraphs on the basis of the concept of 

principal stress rotation. 

It is a well-known fact that principal stress rotation affects deformation 

response of many soils. This phenomenon is known as stress-induced stiffness 

anisotropy (e.g., Arthur et al., 1977; Mould et al., 1982). Mould (1983) conducted a 
148

series of tests on Leighton Buzzard sand with a multiaxial cubical device. The 

specimen was first loaded and unloaded along the same stress path. In the subsequent 

reloading, the major principal stress was rotated 90° relative to its initial direction. It 

was found that the reloading response of the soil was softer than the virgin loading 

response. Also, the stiffness of the reloading curve decreased with increasing 

preloading level. 

The vertical displacement of the SGP test specimen was a response of a 

particular boundary problem. The reduced reloading stiffness was most likely due to 

the reduction of vertical stiffness of a portion of soil in the specimen resulting from 

rotations of the principal stress directions. The principal stress rotation in some part 

of the SGP test specimen is explained in the following paragraphs and shown in 

Figure 5.14.

It is assumed that directions of compressive major and minor principal 

stresses are parallel to the vertical and horizontal axes, respectively. At the initial 

stage, the initial vertical and horizontal stresses (Point A in Figure 5.14) are, 

respectively, major and minor principal stresses. Under a vertical load, the vertical 

and horizontal stresses increased from Point A to B. Upon unloading to a zero-load 

level, the vertical stress was reduced to the initial vertical stress (Point C). Note that 

there exists a residual or “locked-in” horizontal stress (see Figure 5.14). The sum of 

the residual and initial horizontal stresses in some particular area may be larger than 

the vertical stress and causes rotations of the principal stress. As a result, the vertical 

stiffness of such an area in a subsequent vertical reloading (Point C to D) was small 

initially. The vertical stiffness gradually increases with the reloading magnitude as 

the major principal stress rotates back to the vertical direction. The unloading 

threshold load may be considered as the dividing point along the unloading path 

(Point B to C). When the vertical load is reduced below the unloading threshold load, 

the horizontal stress in a portion of the specimen becomes the major principal stress 

and results in softening of the vertical unloading stiffness and reducing of the 

subsequent vertical reloading stiffness.

Figure 5.14 also shows the stress path for an RL-PS path. In the RL-PS path, 

the test specimen is unloaded from Point B′ to C′. During unloading, both the vertical 

and horizontal stresses decreased along the same stress path as in the unloading path 

of the RL-Z path. However, unlike the unloading path of the RL-Z path, the 

magnitude of the vertical stress from Point B′ to C′ remains larger than the horizontal 

stress. Therefore, from Point B′ to C′, there is no principal stress rotation from a 

vertical direction to a horizontal direction. As a result, the reduced reloading stiffness 

did not occur in the subsequent reloading path from Point C′ to D′ (i.e., RL-PS path).

It should be pointed out that the stress paths presented in Figure 5.14 were 

assumed and were not from actual measurement. The above explanation for the 

reduced reloading stiffness may be validated by conducting a numerical analysis of 

the unloading-reloading behavior. Such a numerical analysis requires a constitutive 
149

soil model that can account for the stress-induced stiffness anisotropy such as the 

nesting surface models (see, e.g., Mroz, 1967; Provost, 1981).

6. Displacements During the RL Path for the Road Base Soil: After the UL 

path in which the rebounding deformation occurred, the SGP test specimen was 

subjected to the RL path. During the RL path, the Road Base soil and GRS masses 

showed vertical settlements and horizontal expansion similar to the deformation 

behavior during the PL path. The test specimens behaved approximately linearly 

during the RL path. When the reloading magnitude approached the PLL, the 

reloading stiffness started to decrease (i.e., the Bauschinger effect). 

During the initial reloading path when the UL path took place at a high PLL 

(PLL = 11.5 kN), the rebounding deformation from the unloading path still persisted 

(see Figure 5.12). The GRS mass continued to rebound vertically and horizontally 

against the vertical reloading. This behavior was more significant in the horizontal 

direction than in the vertical direction.

The FHWA pier showed a similar rebounding behavior. As shown in Figure 

5.13, the pier continued rebounding in both vertical and horizontal directions after 

unloading to zero. It is believed that the rebounding deformation caused a stiffer 

reloading response upon reloading until the reloading load was about 80 kPa. This is 

because the vertical reloading load was applied against the vertical rebounding 

deformation of the pier.

7. Displacement During the RL-Z Path Versus the RL-PS Path: The vertical 

reloading curve of the RL-PS path showed higher stiffness than that of the RL-Z path 

for the Road Base soil and GRS masses (see Figures 5.11 and 5.12) and the Sand and 

GRS masses (see Figures 5.8 and 5.10). This behavior also showed in the unloadingreloading CTC tests of soils and is illustrated in Figures 3.19 and 3.20 (Section 3.4.5). 

A comparison of the displacement during the RL-Z path versus the RL-PS path will 

be presented later in Section 5.3.1.

8. Reinforcement Strains During Unloading-Reloading Cycles: The strains in 

the middle reinforcement layer of Test P-UR-(RB+2044) were measured by strain 

gauges. Of a total of 9 strain gauges, only gauges R-2 and R-3 (see Figure 4.11 for 

gauge locations) operated properly. This may due to mechanical damage of the 

gauges during specimen preparation by compaction. The specimen was compacted 

by a standard 4-lb Proctor hammer with 25-mm-thick compaction lifts. It was learned 

afterwards that the thickness of the compaction lift should be at least 200 mm to 

minimize possible mechanical damage. The 200-mm thickness is based on the 

reinforcement spacing of the FHWA pier. A total of 84 strain gauges were mounted 

on the reinforcement layers of the FHWA pier by the same technique employed in 

this study. Most of the gauges survived during construction and subsequent loading 

tests. The measured strains correlated well with the measured lateral displacements 

(Adams, 1997).
150

Due to the limited number of workable strain gauges, the measured strains 

were interpreted qualitatively. Figure 5.15 shows the relationship of the measured 

tensile strains from gauge R-3 (see Figure 4.11 for location) versus the vertical load. 

Generally speaking, the load-strain curve was similar to the load-horizontal 

displacement curve shown in Figure 5.12. The strain increased with increasing 

vertical loads. The load-strain curve showed horizontal creep behavior in the initial 

stage of the unloading path, and the tensile strains reduced during unloading. In the 

initial stage of reloading, the strains continued to reduce. This behavior conforms to 

the load-horizontal displacement behavior that the specimen continued to contract in 

the initial stage of reloading. 

The irrecoverable strain was evident during unloading. The irrecoverable 

tensile strain has important implications for a preloaded GRS mass. First, it confirms 

the ratcheting mechanism (Tatsuoka et al., 1997), as explained in Section 2.4, in a 

preloaded GRS mass. Second, it indicates that there exists a residual or “locked-in” 

horizontal compressive stress in the soil after unloading because of the residual 

tensile forces of the reinforcement.

9. Effects of PLL Magnitude on Displacements in the RL Paths: The 

reloading curves under different PLL magnitudes of the GRS mass with the Sand 

(Tests P-UR-(S+2044)-1 and P-UR-(S+2044)-2) were almost identical (see Figure 

5.16). The PLL magnitude was 28 kN in the former and 43 kN in the latter. The same 

behavior is also shown in the Road Base soil with and without reinforcement in which 

several PLL magnitudes were employed for the RL-Z and RL-PS paths. This 

indicates that the PLL magnitude does not affect the reloading deformation of the 

GRS mass except during the initial stage of the RL-Z path for the GRS mass with the 

Road Base soil, which showed some rebounding deformation following a high PLL.
151

Figure 5.7: Vertical Load Versus Displacement Relationships of

Test P-UR-S 

0

5

10

15

20

25

30

35

40

45

0 1 2 3 4 5 6 7 8

Avg. Horizontal Displacement (mm)

Vertical Load (kN)

0

5

10

15

20

25

30

35

40

45

0 2 4 6 8 10 12 14 16 18 20

Vertical Displacement (mm)

Vertcial Load (kN)
152

Figure 5.8: Vertical Load Versus Displacement Relationships of

Test P-UR-(S+2044)-1 

0

5

10

15

20

25

30

35

40

45

50

55

60

0 1 2 3 4 5 6 7 8

Avg. Horizontal Displacement (mm)

Vertical Load (kN)

0

5

10

15

20

25

30

35

40

45

50

55

60

0 2 4 6 8 10 12 14 16 18

Vertical Displacement (mm)

Vertcial Load (kN)
153

Figure 5.9: Vertical Load Versus Displacement Relationships of

Test P-UR-(S+2044)-2 

0

5

10

15

20

25

30

35

40

45

50

55

60

0 5 10 15 20

Vertical Displacement (mm)

Vertcial Load (kN)

0

5

10

15

20

25

30

35

40

45

50

55

60

0 2 4 6 8

Avg. Horizontal Displacement (mm)

Vertical Load (kN)
154

Figure 5.10: Vertical Load Versus Displacement Relationships of

Test P-UR-(S+2044)-3

0

5

10

15

20

25

30

35

40

45

0.00 2.00 4.00 6.00 8.00

Avg. Horizontal Displacement (mm)

Vertical Load (kN)

0

5

10

15

20

25

30

35

40

45

0 2 4 6 8 10 12 14 16 18 20

Vertical Displacement (mm)

Vertcial Load (kN)
155

Figure 5.11: Vertical Load Versus Displacement Relationships of

Test P-UR-RB 

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18

Vertical Displacement (mm)

Vertcial Load (kN)

0

2

4

6

8

10

12

14

0 2 4 6 8 10

Avg. Horizontal Displacement (mm)

Vertical Load (kN)
156

Figure 5.12: Vertical Load Versus Displacement Relationships of

Test P-UR-(RB+2044) 

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18

Vertical Displacement (mm)

Vertcial Load (kN)

0

2

4

6

8

10

12

14

0 2 4 6 8 10

Avg. Horizontal Displacement (mm)

Vertical Load (kN)
157

Figure 5.13: Vertical Applied Pressure Versus Displacement Relationships of

the FHWA Pier

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80 100

Displacement (mm)

Vertical Applied Pressure (kPa)

Vertical

Horizontal
158

Figure 5.14: Conceptual Stress Diagrams for the RL-Z and RL-PS Paths 

Initial 

Vertical Stress

Time

C'

A, A' Initial Horizontal

Stress

RL-Z Path

A C

Vertical Stress

B

Residual Horizontal

Stress C

Horizontal Stress

Time

Vertical Stress

D D'

RL-PS Path

A'

C'

Vertical Stress

B'

D

D'

B, B'
159

Figure 5.15: Vertical Load Versus Reinforcement Strain Relationship of Test 

P-UR-(RB+2044), Gauge R-3 (see Figure 4.11 for gauge location)

0

2

4

6

8

10

12

14

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

Measured Strain (%)

Vertical Load (kN)
160

10. Multiple Unloading-Reloading Cycles at a Working Load Level: Three 

tests were conducted in such a manner that the specimen was subjected to multiple 

loading-unloading cycles at a “working” load level. The specimen was subjected to 

five reloading-unloading cycles at 15 kN (0.35% of PLL) in Test P-UR-(S+2044)-2 

(see Figure 5.9), at 3.6 kN (50% of PLL) in Test P-UR-RB (see Figure 5.11), and at 

7.2 kN (60% of PLL) in Test P-UR-(RB+2044) (see Figure 5.12). From the figures, 

it is seen that the load-displacement curves under the multiple unloading-reloading 

cycles at working load levels approximately coincided with one another. This 

indicates that the deformation response of the soil and GRS masses is not influenced 

by multiple reloading-unloading cycles at working load levels. This behavior was 

also observed in the FHWA pier and the Black Hawk abutments (see Figures 7.1, 7.5, 

and 7.6 in Chapter 7). Adams (1997) and Wu et al. (1999) stated that the effects of 

preloading in reducing the deformation of the structure were minute in subsequent 

reloading cycles.

11. Hysteresis Loops: Hysteresis loops existed in all unloading-reloading 

cycles (see Figures 5.7 to 5.12). The hysteresis loop is an indication of energy 

dissipation during an unloading-reloading cyc le. The area of the hysteresis loop can 

be used to determine a damping ratio of a soil. A detailed analysis of the hysteresis 

loops may be carried out in future studies of the dynamic behavior of preloaded GRS 

masses. Only general observations of the hysteresis loop were made in this study. It 

is seen that the hysteresis loop area increased when the unloading-reloading cycle 

took place at the higher PLL. As shown in Figures 5.11 and 5.12, at the comparable 

PLL, the area of hysteresis loop was smaller for unloading-reloading cycles 

performed at a prestressed load level (i.e., UL-PS and RL-PS paths) than at zero-load 

level (i.e., UL-Z and RL-Z paths).

5.3 Effects of Preloading on Deformation and Strength of GRS Mass

Effects of preloading on deformation and strength of GRS masses were 

assessed in the following sections.

5.3.1 Effects of Preloading on Deformation

To assess the effects of preloading on deformation, the displacements of 

monotonic loading SGP tests were compared with reloading displacements of the 

unloading-reloading SGP tests. In comparing the displacements, the displacements of 

the monotonic-loading and unloading-reloading tests were presented in the same plot. 

In the plot, the reloading displacement was referenced to the deformed shape of the 

test specimen after the end of the unloading path. The reloading displacement was 

considered as the displacement of a preloaded specimen, whereas the displacement 

under monotonic loading was considered as the displacement of a virgin specimen.

The displacements under monotonic loading and reloading paths of the GRS 

masses with the Sand are presented in Figure 5.16. Figure 5.16 shows the vertical 
161

and average horizontal displacements versus vertical load relationships for Test P-M-

(S+2044) (for monotonic loading), Tests P-UR-(S+2044)-1 and 2 (for the RL-Z path), 

and Test P-UR-(S+2044)-3 (for the RL-PS path). The displacements of the 

monotonic loading were compared with those of the RL-Z and RL-PS paths.

It can be seen that, at the same vertical load, the preloaded specimen 

experienced less vertical and horizontal displacements than the virgin specimen. The 

RL-PS path showed higher stiffness than the RL-Z path in the vertical direction, but 

the stiffness was similar in the horizontal direction for vertical loads less than 20 kN. 

At a vertical load of 20 kN, the vertical and horizontal displacements of the virgin 

specimen were 4.05 mm and 0.26 mm, respectively. At the same vertical load, the 

vertical and horizontal displacements of the preloaded specimen were 1.23 mm and 

0.02 mm, respectively, in the RL-Z path and 0.56 and 0.05, respectively, in the RLPS path. A similar reduction of the displacements upon preloading was observed in 

the GRS masses with the Road Base soil as shown in Figures 5.33 and 5.34.

Figure 5.17 shows the vertical and average horizontal displacements versus 

vertical load relationships for Test P-M-(RB+2044) (for monotonic loading) and Test 

P-UR-(RB+2044) (for the RL-Z and RL-PS paths). The RL-PS paths include two 

tests with different prestressed load levels (PSL). The value of PSL was 1.5 kN for 

the RL-PS1 path and 4.5 kN for the RL-PS2 path. The displacements of the 

monotonic loading were compared with those of the RL-Z, RL-PS1, and RL-PS2 

paths. 

The preloaded specimen showed stiffer deformation responses in both vertical 

and horizontal directions. At the same vertical load, the RL-PS2 path yielded the 

least value of the vertical displacement, followed by the RL-PS1 path, then the RL-Z 

path. This indicates that the vertical stiffness of the preloaded GRS mass increases 

with the prestressed load level (PSL) or the unloading load level (ULL). The 

horizontal displacements of all reloading paths were comparable. At a vertical load 

of 4 kN, the vertical and horizontal displacements of the virgin specimen were 1.79 

mm and 0.18 mm, respectively. At the same vertical load, the corresponding 

displacements of the preloaded specimen were 0.82 mm and –0.02 mm in the RL-Z 

path, 0.56 mm and 0.03 mm in the RL-PS1 path, and 0.33 mm and 0.01 mm in the 

RL-PS2 path. 

Effects of reinforcement (i.e., the reinforcing effect) during the reloading 

paths were also examined. A series of plots comparing the reloading displacements 

of the soil and GRS masses was shown in Figures 5.18 to 5.20. Figure 5.18 compares 

the displacements under the RL-Z path of the Sand mass with and without 

reinforcement. Figure 5.19 compares the displacements under the RL-Z path of the 

Road Base soil mass with and without reinforcement. Figure 5.20 compares the 

displacements under the RL-PS path of the Road Base soil mass with and without 

reinforcement. It can be seen that the soil mass with and without reinforcement 

showed nearly identical vertical and horizontal reloading curves in some cases. In 
162

other cases, the soil mass with reinforcement showed slightly stiffer response. This 

indicates that the effect of reinforcement is insignificant during the reloading path.

5.3.2 Effects of Preloading on Strength 

 Table 5.1 presents the peak vertical loads (i.e., the failure load) of the SGP 

tests conducted in this study. The peak loads of the preloaded specimens were 

slightly higher than those of the corresponding virgin specimens. The differences 

were in the range of 5% except for the Road Base soil specimen with reinforcement. 

The preloaded Road Base soil specimen with Amoco 2044 showed about 20% lower 

peak load than that of the corresponding virgin specimen. This may be because of the 

slight differences in the degree of compaction and water content.

The failure mode of the preloaded and virgin specimens was also similar. 

Tests P-UR-S and P-UR-RB showed a diagonal shear failure (see Section 5.1 for 

definition), whereas Tests P-UR-(S+2044)-1,2 and P-UR-(RB+2044) showed the 

wedge-type shear failure (see Section 5.1 for definition). Note that the reloading to 

failure load of Test P-UR-(S+2044)-3 was not available due to measurement errors.
163

Figure 5.16: Vertical Load Versus Displacements of Virgin Specimen from

Test P-M-(S+2044) and Preloaded Specimens from Tests P-UR-(S+2044)-

1,2,3

0

5

10

15

20

25

30

35

40

45

50

0 2 4 6 8 10 12

Vertical Displacement (mm)

Vertical Load (kN)

P-M-(S+2044)

P-UR-(S+2044)-1

P-UR-(S+2044)-2

P-UR-(S+2044)-3

0

5

10

15

20

25

30

35

40

45

50

0 0.5 1 1.5 2 2.5 3 3.5

Avg. Horizontal Displacement (mm)

Vertical Load (kN)

P-M-(S+2044)

P-UR-(S+2044)-1

P-UR-(S+2044)-2

P-UR-(S+2044)-3
164

Figure 5.17: Vertical Load Versus Displacements of Virgin Specimen from

Test P-M-(RB+2044) and Preloaded Specimen from Test P-UR-(RB+2044) 

0

2

4

6

8

10

12

-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Vertical Displacement (mm)

Vertical Load (kN)

RL-Z

RL-PS1

RL-PS2

P-M-(RB+2044)

0

2

4

6

8

10

12

-0.5 0 0.5 1 1.5 2 2.5

Avg. Horizontal Displacement (mm)

Vertical Load (kN)

RL-Z

RL-PS1

RL-PS2

P-M-(RB+2044)
165

Figure 5.18: Vertical Load Versus Reloading Displacement Relationships 

(RL-Z path) of Tests P-UR-S and P-UR-(S+2044)-1

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5

Vertical Displacement (mm)

Vertical Load (kN)

P-UR-S

P-UR-(S+2044)-1

0

5

10

15

20

25

30

35

-0.05 0 0.05 0.1 0.15 0.2 0.25

Avg. Horizontal Displacement (mm)

Vertical Load (kN)

P-UR-S

P-UR-(S+2044)-1
166

Figure 5.19: Vertical Load Versus Reloading Displacement Relationships

(RL-Z path) of Tests P-UR-RB and P-UR-(RB+2044)

0

1

2

3

4

5

6

7

8

-0.05 0 0.05 0.1 0.15 0.2

Avg. Horizontal Displacement (mm)

Vertical Load (kN)

P-UR-RB

P-UR-(RB+2044)

0

1

2

3

4

5

6

7

8

0 0.5 1 1.5 2 2.5 3

Vertical Displacement (mm)

Vertical Load (kN)

P-UR-RB

P-UR-(RB+2044)
167

Figure 5.20: Vertical Load Versus Reloading Displacement Relationships

(RL-PS path) of Tests P-UR-RB and P-UR-(RB+2044)

0

1

2

3

4

5

6

7

8

0 0.5 1 1.5 2 2.5

Vertical Displacement (mm)

Vertical Load (kN)

P-UR-RB

P-UR-(RB+2044)

0

1

2

3

4

5

6

7

8

-0.05 0 0.05 0.1 0.15 0.2

Avg. Horizontal Displacement (mm)

Vertical Load (kN)

P-UR-RB

P-UR-(RB+2044)
168

Table 5.1: Summary of Failure Loads of the SGP Tests

Test Soil Reinforcement Peak

Vertical Load

(kN)

P-M-S S - 37.4

P-UR-S S - 38.2

P-M-RB RB - 11.3

P-UR-RB RB - 11.8

P-M-(S+3301) S Typar 3301 44.7

P-M-(S+2044) S Amoco 2044 53

P-UR-(S+2044)-1 S Amoco 2044 55.2

P-UR-(S+2044)-2 S Amoco 2044 56

P-UR-(S+2044)-3 S Amoco 2044 N/A

P-M-(RB+2044) RB Amoco 2044 16.9

P-UR-(RB+2044) RB Amoco 2044 13.1
169

5.4 Finite Element Analysis of the SGP Test

Finite element analyses were conducted to examine the stress distribution of a 

GRS mass in the SGP test subject to monotonic loading. The analysis results and the 

SGP test results provided a basis for developing the simplified preloading-reloading 

(SPR) model. A finite element analysis for the unloading-reloading SGP tests was 

not conducted because the results of the SGP tests and the finite element analyses of 

the monotonic-loading SGP tests were judged to be sufficient for developing the SPR 

model.

The program SSCOMPPC (a finite element analysis program for evaluation of 

soil-structure interaction and compaction Effects) was used. The SSCOMPPC has 

been used with success to predict reinforced-soil wall behavior (Collin, 1986; Adib, 

1988; Jaber, 1989). The following subsection briefly describes the program, the

material and interface behavior models, and determination of the model parameters. 

A detailed description of the program can be found in the SSCOMPPC manual by 

Boulanger et al.(1991).

5.4.1 Program Description

The program SSCOMPPC is a general purpose, plane strain, soil-structure 

interaction finite element program for static analysis of geotechnical problems. The 

program SSCOMPPC is the PC version of the program SSCOMP (Seed and Duncan, 

1984). 

The program calculates stresses, strains, and displacements in soil elements, 

and internal forces and displacements in structural elements by simulating the actual 

sequence of construction operations in a number of steps. The nonlinear and stressdependent stress-strain properties of the soils are approximated by varying the values 

of modulus and Poisson’s ratio in accordance with calculated stresses by using the 

modified hyperbolic model (Duncan et al., 1980). The structural materials are 

assumed to behave linearly. 

An increment of an analysis may be placement of a layer of fill, compaction 

of a layer of fill, or application of loads. For an increment of analysis, two iterations 

are performed. The first iteration uses soil modulus and Poisson’s ratio values based 

on the stresses in each soil element at the beginning of the increment. The second 

iteration uses adjusted soil modulus and Poisson’s ratio values based on the average 

stresses during the increment.

5.4.2 Material and Interface Behavior Models

5.4.2.1 Soil Behavior Model

The hyperbolic stress-strain model for soils was first proposed by Kondner 

(1963) and modified by Duncan and Chang (1970) and Duncan et al. (1980). It has 

been widely used in finite element analysis of different earth structures (Duncan, 

1994). Ko and Sture (1981) pointed out some limitations inherent in the model. The 
170

model is based on the generalized Hooke’s law for isotropic material. As a result, it 

is not capable of modeling shear dilatancy (i.e., volume change during shear) of soils. 

If the loading path deviates significantly from that of triaxial compression, the strains 

predicted by the model may not be accurate. Another limitation is that the model 

does not realistically model at and after peak responses of soils (Duncan, 1994). 

In spite of the aforementioned limitations, the model has several advantages 

that lead to its popularity in geotechnical engineering applications. First, the model 

parameters are easily understood and can be related to the deformation behavior of 

the soil. Second, only standard triaxial compression tests are needed for 

determination of the model parameters. Third, the large database of the model 

parameters is available in the literature for a wide variety of soil types under both 

drained and undrained conditions. Duncan (1994) suggested that the model is 

adequate under the following conditions:

1. The factor of safety against global stability is high enough.

2. If local failure occurs, it does not control behavior in any region where accurate 

results are needed.

3. The conditions analyzed are either fully drained (and analyzed in terms of 

effective stress) or completely undrained (and analyzed in terms of total stress).

The hyperbolic stress-strain model appears to be adequate for the 

determination of the pre-peak stress distributions of the GRS mass in the monotonicloading SGP test. The finite element analyses were only conducted on the Road Base 

soil mass with and without reinforcement because of the limitation of the soil model 

to simulate the shear dilatancy behavior of the medium-dense Ottawa sand.

The nonlinear soil behavior model employed in the program SSCOMPPC is 

the modified hyperbolic stress-strain model (Duncan et al., 1980; Seed and Duncan, 

1984). The hyperbolic soil model parameters and the recommended methods for 

obtaining the parameters are presented in detail in Duncan et al. (1980). A brief 

description of the hyperbolic model parameters and parameter determination is 

presented below.

The hyperbolic soil model is a nonlinear (hyperbolic) incremental stress-strain 

and bulk modulus model. The model assumes that stress-strain curves for soils can 

be approximated as hyperbolas. 

The soil material is considered as an isotropic elastic material. The nonlinear 

stress-strain relation is represented by the following hyperbolic relationship (see 

Figure 5.21):

Ei ( )ult

1

1 3

1 3

1

1

s s

e

e

s s

−

+

− = [5.1] 

where s1-s3 = deviator stress

Ei = tangent Young’s modulus at the origin (σ1-σ3 = 0)
171

e1 = major principal strain (axial strain in a 

 triaxial compression test)

(s1-s3)ult = hyperbolic asymptotic value of s1-s3

The parameters Ei and (s1-s3)ult are functions of the confining stress and can 

be expressed as:

n

a

i a

P

E K P ( )

s3

= ⋅ ⋅ [5.2] 

and

(1 sin )

2 cos 2 sin

( )

3

1 3

f

f s f

s s

⋅ −

⋅ ⋅ + ⋅ ⋅

− =

f

ult R

c

[5.3]

where K and n = primary loading model parameters relating the initial 

 modulus, Ei, to the confining stress, s3

Pa = atmospheric pressure

f = internal angle of friction (Mohr-Coulomb failure 

 criterion);

c = shear strength intercept (Mohr-Coulomb failure 

 criterion); 

Rf = failure ratio, defined as: Rf = (s1-s3)f / (s1-s3)ult 

(s1-s3)f = deviator stress at failure determined by Mohr- 

 Coulomb failure criterion;

The instantaneous slope of the hyperbolic stress-strain curve is the tangential 

modulus, Et, which can be expressed as:

n

a

a

f

t f

P

E R P ( )

( )

( )

1

3

2

1 3

1 3 s

s s

s s

⋅ ⋅

















−

−

= − ⋅ [5.4] 

Unloading is modeled as linear and elastic. The unloading-reloading modulus 

is a function only of the confining stress as

n

a

ur ur a

P

E K P ( )

s3

= ⋅ ⋅ [5.5]

where Kur = unloading model parameter 

The second elastic parameter used in the modified hyperbolic model is a 

stress-dependent bulk modulus. The bulk modulus, B, is assumed to be a function of 

the confining pressure and can be expressed as:
172

m

a

b a

P

B K P ( )

s3

= ⋅ ⋅ [5.6] 

where Kb and m = Bulk modulus model parameters relating the bulk

 modulus, B, to the confining pressure, s3

In a triaxial compression test, the volumetric strain can be related to the axial 

strain by the following equation:

v a

e = (1− 2n )⋅ e [5.7]

where n = Poisson’s ratio

The bulk modulus, B, can be expressed in terms of Et and ν as:

3⋅(1− 2n )

=

Et B [5.8] 

From Eq. 5.7 and 5.8, the following equation can be derived:

a

t

v

B

E

e ⋅Δe

⋅

Δ =

3

[5.9] 

At least three triaxial tests are needed to obtain the hyperbolic model 

parameters. The initial modulus, Ei, and the hyperbolic asymptotic value, (σ1-σ3)ult, 

from each triaxial test are first determined. The parameters Ei and (σ1-σ3)ult are 

determined by plotting ε1/(σ1-σ3) versus ε1. A linear regression can be used to obtain 

the best fitting straight line for each test. 

The parameters K and n can be determined by plotting Ei/Pa versus σ3/Pa on a 

log-log scale. The best-fit straight line is drawn. The value of K is equal to the value 

of Ei/Pa where σ3/Pa is equal to unity of the best-fit line. The value of n is the slope of 

the line.

The value of Kur is determined by assuming that the modulus exponent, n, for 

unloading-reloading was the same as that of primary loading. Eq. 5.5 can be written 

in the following form:

n

a

a

ur

ur

P

P

E

K

( )

s3

⋅

= [5.10]
173

The unloading-reloading modulus (Eur) can be determined from the deviator 

stress versus axial strain relationship of each triaxial test. The scattered values of Kur

are averaged to give a representative value of Kur.

Two steps are involved in determining the values of Kb and m. First, the bulk 

modulus (B) from each triaxial test was determined by the following equation:

v

B

e

s s

⋅

−

=

3

( ) 1 3

[5.11]

The bulk modulus is determined at (σ1-σ3) = 0.7 (σ1-σ3)f and the 

corresponding value of εv. Second, the values of Kb and m are determined by plotting 

the values of B/Pa versus σ3/Pa on a log-log scale. The best-fit straight line is drawn. 

The value of Kb is equal to the value of B/Pa where σ3/Pa is equal to unity of the bestfit line. The value of m is the slope of the line. 

5.4.2.2 Geosynthetic Behavior Model

The geosynthetic reinforcement was modeled by using linear-elastic onedimensional bar elements that had axial stiffness but no flexural stiffness. The 

material properties can be obtained from the uniaxial load-extension test of the 

geosynthetic. Input for the bar element includes Young’s modulus and crosssectional area. 

The linear-elastic idealization is not realistic in some geosynthetics that show 

a significant nonlinear load-strain relationship under the anticipated stress range. 

Nonlinear relationships, as proposed by Ling and Tatsuoka (1992) or Chou and Wu 

(1993), may be used to model the non-linear behavior. The nonlinear model for a 

geosynthetic is typically established from a uniaxial load-extension test, either in a 

confined or unconfined condition, conducted at a constant strain rate. It must be 

noted that the load-strain relationship of some geosynthetics is strain-rate dependent. 

If the strainrate of the load-extension test for such a geosynthetic is significantly 

different from the GRS structure, a significant error may occur. 

In this study, the reinforcement strains in the SGP test were expected to be 

relatively small (typically less than 1%). This was later confirmed by the measured 

strains of Test P-UR-(RB+2044) presented in Section 5.2. The load-extension test 

results obtained under stress- and strain-controlled modes showed that the load-strain 

relationship of Amoco 2044 reinforcement was approximately linear for strains less 

than 1%, and the behavior was strain-rate independent.

5.4.2.3 Soil-Geosynthetic Interface Model

The soil-geosynthetic interface is modeled by an assembly of nonlinear 

hyperbolic interface elements with normal and tangential springs (i.e., the method of 

stiffness). The interface element based on the method of stiffness has been widely 

used in the finite element analysis of soil-structure interaction problems. It was first 
174

introduced by Goodman et al. (1968) for finite element analysis of jointed rock 

masses. The interface elements in the program SSCOMPPC are based on a nonlinear 

interface element that was developed by Clough and Duncan (1969).

The interface model consists of two parallel nodal links, as shown in Figure 

5.22. Each nodal link comprises a normal spring and a shear spring. The properties 

of the interface element consist of a normal stiffness (of the normal springs), Kn, and 

a tangent shear stiffness (of the shear springs), Kst. The normal stress, σn, and the 

shear stress, τ, acting on the element are related to the normal and shear stiffness by 

the following equations:

Kn Δn = sn⋅ [5.12] 

⋅Δ = t Kst s[5.13] 

in which Dn is the average relative normal displacement across the element, and Ds is 

the average relative shear displacement along the element. 

The linear elastic normal stiffness, Kn, controls the opening and the 

compressing of the interface element between two adjacent two-dimensional 

elements. The normal stiffness is specified by a dimensionless coefficient as:

w

n

n

K

k

g

= [5.14] 

in which Kn is the normal stiffness, kn is the input normal spring coefficient 

(dimensionless), and gw is the unit weight of water. For compressive loading, the 

overlapping (or penetration) of the two-dimensional elements can be minimized by 

using a large normal spring stiffness. The analysis is carried out by using a “fixed” 

condition initially (i.e., assuming a “large” kn value). In the case of tension, the 

normal spring stiffness is set to zero by SSCOMPPC.

The shear behavior of the interface is modeled by a hyperbolic relationship 

between the shear stress and the relative shear displacement at the interface, as shown 

in Figure 5.22. The equations that describe the hyperbolic model for the shear 

behavior are as follows:

(a) Primary Loading and Reloading:

2

tan

1

















+ ⋅

⋅

− 















= ⋅ ⋅

s d

s t

g

n

f

n

a

n

st s w

c

R

P

K k [5.15] 

in which Kst is the tangent shear stiffness, ks is the input shear spring coefficient 

(dimensionless), n and Rf are experimentally determined constants, gw is the unit 
175

weight of water, Pa is the atmospheric pressure, d is the interface frictional angle, c is 

the interface cohesion, and sn and t are the normal stress and shear stress acting on 

the interface, respectively.

(b) Unloading:

n

a

n

st ur w

P

K k

















= ⋅ ⋅

s

g [5.16] 

in which kur is the input unloading shear spring coefficient (dimensionless).

The values of ks, kur, n, and Rf for an interface can be determined from laboratory 

tests, such as direct shear tests or other appropriate tests. The tests should be 

conducted between the relevant materials for the range of stresses expected in the 

application.

Wu (1993) pointed out two problems associated with the interface models 

using the method of stiffness. The first problem relates to determination of the value 

of shear spring stiffness, Kst. The value of Kst is typically determined by laboratory 

interface shear tests such as direct shear tests or pullout tests. These laboratory shear 

tests are model tests. The results of the model tests depend on the geometric 

conditions of the tests (e.g., specimen size). Therefore, the value of Kst is a function 

of the specimen size, among other variables. This implies that correct values of Kst

must be deduced from an interface shear test of which the specimen size is nearly 

equal to the length of the interface segment in the finite element discretization. 

The second problem relates to numerical difficulties that may arise in this 

approach. To minimize penetration between contacting nodes, a large normal spring 

stiffness is used. If the value of the normal spring stiffness is too small, significant 

penetration will occur, which is kinemetically incorrect. On the other hand, if the 

value of the normal spring stiffness is too large, the truncation error may become too 

large and the resulting stresses can be in significant error.

In this study, the first problem addressed by Wu (1993) was alleviated by 

compromising the length of the interface elements in the finite element discretization 

with the size of the specimen in the direct shear tests. The uniform length of the 

interface elements in the finite element discretization was about 20% of the specimen 

width of the direct shear tests. To prevent penetration of the contacting nodes and 

avoid the truncation error, the value of normal spring stiffness recommended by the 

SSCOMPPC manual was used.

5.4.3 Determination of Model Parameters

The model parameters needed for the analysis were determined by the 

recommended procedures described in Section 5.2.2. Results of the conventional 

triaxial compression (CTC) tests, the in-isolation load extension (LE) tests, and the 

direct shear tests (DS) were used. 
176

5.4.3.1 Soil Model Parameters

The soil model parameters for the Road Base soil were first determined from 

three CTC tests by the recommended procedure by Duncan et al. (1980). They were 

then adjusted to fit the deformation responses of the Road Base soil mass in the SGP 

test. Table 5.2 shows the parameters of the hyperbolic stress-strain model for the 

Road Base soil.

The hyperbolic model parameters shown in Table 5.1 were used to backcalculate the results of the CTC tests. The model-simulated results as compared with 

the CTC test results are shown in Figure 5.23. The agreement between the two is 

considered acceptable.

5.4.3.2 Geosynthetic Model Parameters

The secant slope at 1% was used to represent the axial stiffness of the 

geosynthetic. From the load-strain relationship of Amoco 2044 geosynthetic, the 

secant slope at 1% strain was determined to be equal to 1,000 kN/m. In the analysis, 

the values of Young’s modulus of 1,000 kN/m2 and cross-sectional area of 1 m2/m 

were assigned. These values give an axial stiffness value of 1,000 kN/m.

5.4.3.3 Soil-Geosynthetic Interface Model Parameters

The hyperbolic interface model parameters for the soil were determined from 

three unloading-reloading DS tests by a me thod similar to that used for the hyperbolic 

soil parameters. Table 5.2 shows the parameters of the hyperbolic interface model for 

the Road Base soil with Amoco 2044 geosynthetic. The hyperbolic model parameters 

shown in Table 5.2 were used to back-calculate the results of the DS tests. The 

model-simulated results as compared with the direct shear test results are shown in 

Figure 5.24. It is seen that the agreement between the two is good.

5.4.4 Finite Element Modeling 

The reinforced soil specimen in the SGP test was modeled as a plane-strain 

two-dimensional problem in the finite element analysis. Four types of elements were 

used in the analysis:

1. Soil Elements: The soil elements in the SSCOMPPC program are four-noded, 

isoparametric elements.

2. Bar Elements: The bar elements are two-noded elements with axial stiffness only. 

These elements were used to model the geosynthetic reinforcement layers. 

3. Interface Elements: The interface elements are zero-thickness elements that consist 

of two pairs of normal and shear springs. These elements were used to model the 

soil-geosynthetic interfaces and the lubrication layers. For lubrication layers, the 

friction angle was assumed to be 1.5°. 

4. Beam Elements: The beam elements are two-node elements with axial, bending, 

and shear stiffness. These elements were used to model the rigid loading plate. 
177

Relatively large values were assigned to the material properties to simulate large 

rigidity of the loading plate.

Figure 5.25 shows the finite element discretizations for the analysis of the 

SGP test with and without reinforcement. Only one-half of the geometry was 

analyzed due to symmetry.

The finite element mesh of the soil mass consisted of 462 nodes, 400 soil 

elements, 10 beam elements for the loading plate, and 10 interface elements for the 

lubrication layer between the loading plate and the soil. The finite element mesh of 

the soil mass with reinforcement consisted of 506 nodes, 400 soil elements, 10 beam 

elements for the rigid loading plate, 30 bar elements for the reinforcement layers, 10 

interface elements for the lubrication layer between the loading plate and the top 

reinforcement layer, and 40 interface elements for the soil-reinforcement interfaces.

The specimen preparation was modeled by 24 construction increments. The 

confining pressure was applied in equal increments of 3.45 kPa up to a total confining 

pressure of 34.5 kPa. A vertical pressure of 5 kPa was applied to represent the weight 

of the loading plate and the seating load. The vertical load was applied in equal 

increments of 6.9 kPa on the beam elements. It is to be noted that the program 

SSCOMPPC defines failure of a soil element by using a stress level, 

SL= (σ1-σ3)/(σ1-σ3)f. Failure of an element is said to occur when the stress level is 

unity. At failure, the program was coded to set the value of the tangential modulus, 

Et, to a very small value. 

5.4.5 Comparison of Finite Element Analyses with SGP Test Results 

Figures 5.26 and 5.27 show the measured and calculated values of the vertical 

and average horizontal displacements of Tests P-M-RB (Road Base soil mass) and PM-(RB+2044) (GRS mass), respectively. The measured values are in good 

agreement with the calculated values except at high vertical loads (i.e., near failure) 

of Test P-M-(RB+2044). This is due to a limitation of the soil model to model the 

near-failure behavior of the soil, as discussed in Section 5.4.2.1. At 10-kN vertical 

load, the measured and calculated values of the GRS mass were, respectively, 4.6 mm 

and 5.0 mm for the vertical displacements, and 1.0 mm and 1.8 mm for the average 

horizontal displacements. Figure 5.28 shows strain distributions in the middle 

reinforcement layer at vertical loads of 2 kN, 4 kN, and 6 kN. The maximum strain 

occurs at the center line of the reinforcement and gradually reduces toward the end at 

all the loads. The maximum reinforcement strains were 0.038% at 2 kN, 0.081% at 4 

kN, and 0.129% at 6 kN. The reinforcement strains were not measured in Test P-M-

(RB+2044). However, the calculated strains are of the same order of magnitude as 

the measured strains in the preloading path prior to the first unloading-reloading cycle 

from Test P-UR-(RB+2044). Tests P-UR-(RB+2044) and P-M-(RB+2044) had the 

same soil and reinforcement types. The average measured strains at 2 kN, 4 kN, and 

6 kN were 0.015%, 0.067%, and 0.152%, respectively.
178

In conclusion, the calculated values of displacements and reinforcement 

strains are in good agreement with the measured values. Some discrepancies 

occurred at the near-failure state for the specimen with geosynthetic reinforcement.
179

Figure 5.21: Hyperbolic Model of Stress-Strain Behavior (After Duncan and Chang, 

1970)
180

Figure 5.22: Component of Interface Elements and Hyperbolic Shear Stress-Relative 

Shear Displacement (After Clough and Duncan, 1969)
181

Table 5.2: Summary of Hyperbolic Soil Parameters for Finite Element 

Analysis

Property Symbol Value

Unit weight γ 20.25 kN/m3

Modulus number K 220

Modulus exponent n 0.48

Failure ratio Rf 0.7

Bulk modulus number Kb 172

Bulk modulus exponent m -0.33

Cohesion c 6.9 kPa

Friction angle φ 31.3 degrees

Table 5.3: Summary of Interface Properties for Finite Element Analysis

Property Symbol Value

Interface adhesion c 21 kPa

Interface friction φ 32 degrees

Normal spring coefficient kn 1x108

Shear spring coefficient kst 22,280

Shear exponent n 0.128

Failure ratio Rf 0.86
182

Figure 5.23: Calculated Versus Measured CTC Test Results of Road Base 

Soil 

0

200

400

600

800

1000

1200

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

Axial Strain (%)

Deviator Stress (kPa)

69 kPa(Measured)

207 kPa(Measured)

345 kPa (Measured)

69 kPa (Calculated)

207 kPa (Calculated)

345 kPa (Calculated)

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

Axial Strain (%)

Volumetric Strain (%)

69 kPa(Measured)

207 kPa(Measured)

345 kPa(Measured)

69 kPa(Calculated)

207 kPa(Calculated)

345 kPa(Calculated)
183

Figure 5.24: Calculated Versus Measured DS Test Results of Road Base Soil 

and Amoco 2044 Interface 

0

50

100

150

200

250

300

0 1 2 3 4 5 6 7 8

Horizontal Displacement (mm)

Shear Stress (kPa)

86 kPa (Measured)

195 kPa (Measured)

358 kPa (Measured)

86 kPa (Calculated)

195 kPa (Calculated)

358 kPa (Calculated)

Normal Stress
184

Figure 5.25: Finite Element Discretizations of SGP Test Specimens 

Loading Plate

Vertical Load

Reinforcement

Reinforcement

Vertical Load

Reinforcement

Loading Plate

(a) Finite element discretization 

 of a soil mass in the SGP test

(b) Finite Element Discretization 

 of a GRS mass in the SGP test
185

Figure 5.26: Measured and Calculated Vertical and Average Horizontal 

Displacements of Test P-M-RB 

0

2

4

6

8

10

12

14

0 5 10 15 20

Displacement (mm)

Vertical Load (kN)

Vertical (Measured)

Vertical (Calculated)

Avg. Horizontal (Measured)

Avg. Horizontal (Calculated)
186

Figure 5.27: Measured and Calculated Vertical and Average Horizontal 

Displacements of Test P-M-(RB+2044) 

0

2

4

6

8

10

12

14

16

18

0 5 10 15 20 25 30

Displacement (mm)

Vertical Load (kN)

Vertical (Measured)

Vertical (Calculated)

Avg. Horizontal (Measured)

Avg. Horizontal (Calculated)
187

Figure 5.28: Calculated Strain Distributions in the Middle Reinforcement 

Layer

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 20 40 60 80 100 120

Distance from Center Line (mm)

Reinforcement Strain (%)

2 kN

4 kN

6 kN
188

5.4.6 Stresses in GRS Mass in the SGP Test

The stress distributions of the soil mass with and without reinforcement in the 

SGP test were compared. Figures 5.29, 5.30, and 5.31 present, respectively, the 

vertical, horizontal, and shear stress distributions at a vertical load of 6 kN. The 

stress intensity, shown by different colors, in half of the specimen geometry is 

illustrated. It is seen that the vertical stress distributions of the specimen with and 

without reinforcement are almost identical, whereas the horizontal and the shear 

stress distributions are distinctly different. The vertical stress at any given height was 

approximately the sum of the confining pressure and the vertical stresses due to the 

external load, the self-weight of the soil, the weight of the loading plate, and the 

seating load.

The horizontal stresses were rather uniform in the specimen without 

reinforcement and were equal to the confining pressure of 34.5 kPa. With the 

presence of three reinforcement layers, the horizontal stress distribution was quite 

different. A high horizontal stress of about 50 kPa occurred adjacent to the 

reinforcement and gradually reduced away from the reinforcement location. 

The shear stress in the specimen without reinforcement was nearly zero. 

Some shear stresses occurred near the reinforcement in the specimen with 

reinforcement. On each reinforcement layer, the shear stresses vary along the 

horizontal direction with a minimum value of almost zero at the centerline and a 

maximum value of about 10 kPa at the end. Such a shear stress distribution is similar 

to the calculated shear stress distribution by Ashwamy et al. (1998) of reinforced-soil 

specimens in a conventional triaxial compression test. 

It is to be noted that the shear stresses at mid-height between two vertically 

adjacent reinforcement layers are almost zero. This behavior has been referred to as a 

shear stress reversal by Smith (1977). Adib (1988) and Sawicki (1998) applied the 

shear stress reversal concept in their simplified models to calculate reinforcement 

tensions in reinforced-soil retaining walls. In this study, the shear stress reversal 

concept was employed in the development of the SPR model to estimate the 

deformation behavior. This will be described in detail in Chapter 6.

To quantify the reinforcing effect, a minor principal stress ratio is introduced. 

The minor principal stress ratio is defined as the ratio of the compressive minor 

principal stress in a specimen with reinforcement to that of the specimen without 

reinforcement. The minor principal stress ratio gives a direct indication of the 

increase in the minor principal stresses resulting from the reinforcement. 

Figure 5.32 shows a distribution of the minor principal stress ratio. As shown 

in Figure 5.32, the maximum value of minor principal stress ratio of about 1.4 to 1.5 

occurred near the reinforcement and reduced with the distance from the reinforcement 

location. The minor principal stress ratio was near unity (i.e., no reinforcing effects) 

around the middle area of two adjacent reinforcement layers. 
189

Based on the finite element analyses, it can be concluded that the presence of 

the reinforcement altered the horizontal and shear stress distributions but not the 

vertical stress distribution. The horizontal and shear stresses increased significantly 

near the reinforcement and resulted in an increase of the minor principal stress. By 

increasing the minor principal stress, deformation stiffness and shear strength of the 

soil were also increased. The reinforcing effect, as quantified by the minor principal 

stress ratio, was the largest near the reinforcement and reduced with increasing 

distance from the reinforcement.
190

Figure 5.29: Vertical Stress Distributions at 6-kN Vertical Load of 

Tests P-M-RB and P-M-(RB+2044)

20 60 100

Distance from Center Line (mm)

50

100

150

200

250

300

350

400

450

500

550

600

Specimen Height (m

m)

80

85

90

95

100

(b) Vertical Stress at 6 kN

 of Test P-M-(RB+2044)

20 60 100

Distance from Center Line (mm)

50

100

150

200

250

300

350

400

450

500

550

600

Specimen Height (m

m)

(a) Vertical Stress at 6 kN

 of Test P-M-RB

Stress Intensity (kPa)
191

Figure 5.30: Horizontal Stress Distributions at 6-kN Vertical Load of 

Tests P-M-RB and P-M-(RB+2044)

20 60 100

Distance from Center Line (mm)

50

100

150

200

250

300

350

400

450

500

550

600

Specimen Height (m

m)

34

38

42

46

50

(b) Horizontal Stress at 6 kN

 of Test P-M-(RB+2044)

Stress Intensity (kPa)

20 60 100

Distance from Center Line (mm)

50

100

150

200

250

300

350

400

450

500

550

600

Specimen Height (m

m) (a) Horizontal Stress at 6 kN

 of Test P-M-RB
192

Figure 5.31: Shear Stress Distributions at 6-kN Vertical Load of 

Tests P-M-RB and P-M-(RB+2044)

20 60 100

Distance from Center Line (mm)

50

100

150

200

250

300

350

400

450

500

550

600

Specimen Height (m

m)

0.0

2.0

4.0

6.0

8.0

10.0

(b) Shear Stress(xy) at 6 kN

 of Test P-M-(RB+2044)

Stress Intensity (kPa)

20 60 100

Distance from Center Line (mm)

50

100

150

200

250

300

350

400

450

500

550

600

Specimen Height (m

m)

(a) Shear Stress(xy) at 6 kN

 of Test P-M-RB
193

Figure 5.32: Distribution of Minor Principal Stress Ratio at 6-kN Vertical 

Load of Test P-M-(RB+2044)

20 60 100

Distance from Center Line (mm)

50

100

150

200

250

300

350

400

450

500

550

600

S

p

e

cim

en H

eight (m

m)

1.00

1.10

1.20

1.30

1.40

1.50

Stress Ratio
194

5.5 Summary and Concluding Remarks

A total of 11 SGP tests were carried out to investigate the behavior of a GRS 

mass subject to monotonic loading and unloading-reloading cycles. The SGP tests 

were conducted on the soil mass with and without reinforcement. The monotonicloading test program was designed to examine the reinforcing effects during 

monotonic loading and to provide a reference for an assessment of the effects of 

preloading on GRS masses. The unloading-reloading test program was designed to 

examine the effects of preloading, different types of the unloading-reloading cycles 

(i.e., RL-Z and RL-PS paths), the effects of preloading magnitude, and the reinforcing 

effects during the unloading-reloading cycles. The finite element analyses were 

conducted to examine the stress distribution in a GRS mass in the SGP test.

The monotonic-loading SGP tests showed that:

1. Due to the reinforcing effects imposed by the reinforcement, a soil mass with 

reinforcement had higher stiffness and strength than without reinforcement. The 

vertical stiffness of the soil mass with reinforcement was about 30% higher than 

without reinforcement.

2. Some vertical and horizontal deformations were required to mobilize the 

reinforcing effects. Before the reinforcing effect was fully mobilized, the soil 

mass with and without reinforcement showed comparable deformations. For the 

Road Base soil mass with or without reinforcement, the required vertical and 

horizontal displacements to fully mobilize the reinforcing effect were 2.0 mm and 

0.5 mm, respectively. 

The unloading-reloading SGP tests showed that:

1. With preloading, the stiffness of the GRS mass increased significantly. For the 

GRS mass comprising the Ottawa sand and Amoco 2044 geotextile 

reinforcement, the stiffness increased by factors of 3 to 7 in the vertical direction, 

and about 7 in the horizontal direction. For the GRS mass comprising the Road 

Base soil and Amoco 2044 geotextile reinforcement, the stiffness increased by 

factors of 2 to 5 in the vertical direction, and about 3 in the horizontal direction.

2. The magnitude of the preloading load level did not appear to affect the reloading 

stiffness except at the initial stage of the reloading path. During the initial stage 

of the reloading path, the rebounding deformation continued if the test specimen 

was unloaded from a high preloading load level to a zero-load level. Similar 

rebounding deformation behavior was also observed in the FHWA pier after 

unloading had completed.

3. The RL-PS path showed higher vertical reloading stiffness than the RL-Z path. 

The vertical reloading stiffness increased with increasing prestressed load level. 

In the horizontal direction, the stiffness of both the RL-Z and RL-PS paths was 

comparable.
195

4. The unloading and reloading curves of the multiple unloading-reloading at 

working load levels nearly coincided with one another. This behavior was also 

observed in the FHWA pier and the Black Hawk abutments.

5. The reinforcing effect was insignificant during the reloading path.

6. Preloading did not appear to affect the load carrying capacity of the GRS mass.

The finite element analysis showed that:

1. The presence of the reinforcement layers in the soil mass altered the horizontal 

and shear stress distributions but not the vertical stress distribution. 

2. The horizontal and shear stresses increased significantly near the reinforcement 

and resulted in an increase of the minor principal stress. With the increasing 

minor principal stress, the deformation stiffness and shear strength of the soil 

were subsequently increased. The reinforcing effect, as quantified by the increase 

of the minor principal stress, was the largest near the reinforcement and reduced 

with the increasing distance from the reinforcement.
196

6. Simplified Preloading-Reloading Model for GRS Mass

A simplified model, referred to as the simplified preloading-reloading (SPR) 

model, was developed and is presented in this chapter. The purpose of the model is to 

provide a simple model for estimating deformation of a GRS mass subject to 

monotonic loading or preloading and subsequent reloading. 

The SPR model consists of two principal modules: a load-transfer module and 

a deformation module. The load-transfer module can be used to calculate the average 

stresses in a GRS mass. The deformation module can be used to calculate the vertical 

and horizontal deformations of a GRS mass on the basis of the average stresses from 

the load-transfer module. 

6.1 Load-Transfer Module

The purpose of the load-transfer module is to quantify the stress distribution in 

a GRS mass. The stress distributions in a GRS mass are typically non-uniform, as 

illustrated by the finite element analyses in Section 5.4.6. The load-transfer module 

assumes the uniform stresses. The uniform stresses determined by the module can be 

considered as average vertical and horizontal stresses (σv andσh ) in a GRS mass. 

The average stresses are determined by a load-transfer analysis developed from the 

elastic analysis of an idealized plane-strain GRS mass. 

The following sections present the load-transfer analysis, verification of the 

load-transfer analysis with experimental and numerical results, and formulations of 

the average stresses in a GRS mass.

6.1.1 Load-Transfer Analysis

The load-transfer analysis is based on the elastic analysis of reinforcement 

tensions in a GRS mass. Figure 6.1 shows the idealized geometry of a plain-strain 

GRS mass. The reinforced-soil mass consists of a horizontal reinforcement layer 

embedded in a soil at mid-height. The reinforced-soil mass is subjected to uniform 

compressive vertical pressure (Pv) and horizontal pressure (Ph) along the top and 

lateral surfaces. Tensile forces in the reinforcement are induced by the stresses 

developed in the soil from externally applied pressures, Pv and Ph. Figure 6.2 shows 

differential elements of the soil and the reinforcement for the equilibrium equations.
197

Figure 6.1: An Idealized Plane-Strain GRS Mass for the SPR Model

SOIL

A REINFORCEMENT

s

 = Sv

L

SOIL

Pv

Ph
198

Figure 6.2: Equilibrium of Differential Soil and Reinforcement Elements 

(Reproduced from Hermann and Al-Yassin, 1978)

Soil Element

dx

τ(x)

σx

Reinforcement Element

τ(x)

dx

σx + dσx

F(x) F(x) + dF
199

The following presents the elastic solution for the reinforcement tension. It is 

extended from the solution given by Adib (1988), who modified the solution by 

Hermann and Al-Yassin (1978). The following assumptions were made in obtaining 

the solutions. 

1) The soil and the reinforcement behave as linear, isotropic, and elastic materials.

2) The soil and the reinforcement are linked together through an elastic soilreinforcement interface.

3) There is no axial force at the end of the reinforcement (i.e., F(x=L) = 0).

4) The horizontal stress in the soil and the reinforcement tension do not vary in the 

vertical direction.

5) The vertical stress in the soil is constant and equal to the boundary vertical 

pressure.

6) There is no relative horizontal displacement in the soil along the vertical 

direction.

Let U(x) = displacement function of the soil in the x direction

V(x) = displacement function of the reinforcement in the x direction

W(x) = displacement function of the soil-reinforcement interface element in 

 the x-direction

W (x) = U( x) −V( x) [6.1]

Equilibrium Equations

For the condition given in Figure 6.1, the following equilibrium equations can 

be derived. The normal stress is taken as positive for tension and negative for 

compression.

1) Equilibrium of the differential soil element as shown in Figure 6.2:

d A k p W x dx x s i s ⋅ = ⋅ ⋅ ( ) ⋅ [6.2(a)] 

 or

s

x i

A

k p W x

dx

d ⋅ ⋅ ( )

=

s

[6.2(b)] 

where ki = stiffness of the interface element

p = perimeter of the reinforcement that is in contact with the soil

As = area of the soil = Sv

Note that the term ki×W(x) is the shear stress along the interface.

2) Equilibrium of the differential reinforcement element:

dF x k p W x dx i( ) = − ⋅ ⋅ ( ) ⋅ [6.3(a)] 
200

or

( )

( )

k p W x

dx

dF x

i = − ⋅ ⋅ [6.3(b)] 

Stress-Strain Relationships

1. Soil 

For plane strain condition (with z-axis being the longitudinal direction):

e z = 0 [6.4(a)] 

( ) s z n s s x +s y = ⋅ [6.4(b)] 

In x-direction:

( ( ))

1

x s z y

s

x

E

e = ⋅ s −n ⋅ s +s [6.5(a)] 

where ns = Poisson’s ratio of the soil

Es = Young’s modulus of the soil

Subsitute Eq. 6.4(b) into Eq. 6.5(a) to yield:

( ) x s s s y

s

x

E

e = ⋅ s ⋅(1−n ) −n ⋅(1+n ) ⋅s

1 2

[6.5(b)]

Rearrange Eq. 6.5(b), 

x

s

s

y

s

s

x

E

e

n

s

n

n

s ⋅

−

⋅ +

−

=

(1 ) (1 )

2

[6.5(c)] 

2. Reinforcement

The reinforcement tension can be expressed as:

Ar Er r F(x) = ⋅ ⋅ e [6.6] 

Strain-Displacement Relationships

1. Soil 

Soil strain in the x-direction:

dx

dU x

x

( )

e = [6.7(a)] 

where Er = Young’s modulus of the reinforcement

Ar = cross-sectional area of the reinforcement
201

er = strain in the reinforcement

Substitute Eq. 6.7(a) into Eq. 6.5(c) and differentiate with respect to x to yield:

2

2

2

( )

(1 ) dx

E d U x

dx

d

s

x s

⋅

−

=

n

s

[6.7(b)]

2. Reinforcement

Reinforcement strain:

dx

dV x

r

( )

e = [6.8(a)] 

Substitute Eq. 6.8(a) into Eq. 6.6 and differentiate with respect to x to yield:

2

2

( ) ( )

dx

d V x

A E

dx

dF x

r r = ⋅ ⋅ [6.8(b)] 

or

















= ⋅ ⋅ − 2

2

2

2

( ) ( ) ( )

dx

d W x

dx

d U x

A E

dx

dF x

r r

[6.8(c)] 

From Eq.6.2(b) and Eq. 6.7(b):

2

2

2

( )

(1 )

( )

dx

E d U x

A

k p W x

dx

d s

s

x i

⋅

−

=

⋅ ⋅

=

n

s

[6.9(a)] 

Rearrange Eq. 6.9(a):

( )

( ) (1 )

2

2

2

k p W x

dx E A

d U x

i

s s

s

⋅ ⋅ ⋅

⋅

−

=

n

[6.9(b)] 

From Eq. 6.3(b) and Eq. 6.8(c):

















= − ⋅ ⋅ = ⋅ ⋅ − 2

2

2

2

( ) ( )

( )

( )

dx

d W x

dx

d U x

k p W x A E

dx

dF x

i r r

[6.10] 

Substitute Eq. 6.9(b) into Eq. 6.10 to yield:

















⋅ ⋅ ⋅ −

⋅

−

− ⋅ ⋅ = ⋅ ⋅

2

2 2

( )

( )

(1 )

( )

dx

d W x

k p W x

E A

k p W x A E i

s s

s

i r r

n

[6.11(a)] 
202

Rearrange Eq. 6.11(a):

( )

( ) 1 (1 )

2

2

2

W x

A E E A

k p

dx

d W x

s s

s

r r

i

⋅

















⋅

−

+

⋅

= ⋅ ⋅

n

[6.11(b)] 

Introduce

















⋅

−

+

⋅

= ⋅ ⋅

s s

s

r r

i

A E E A

k p

1 (1 )

2

2 n

a [6.12] 

Eq. 6.11(b) can be expressed as:

( )

( ) 2

2

2

W x

dx

d W x

=a ⋅ [6.13] 

The solution of Eq. 6.13 can be expressed in the following form:

W (x) = a ⋅ cosh(a ⋅ x) + b ⋅sinh( a ⋅ x) [6.14] 

Substitute Eq. 6.14 into Eq. 6.9(b) to solve for the soil displacement function:

( cosh( ) sinh( ))

( ) (1 )

2

2

2

k p a x b x

dx E A

d U x

i

s s

s

⋅ ⋅ ⋅ ⋅ ⋅ + ⋅ ⋅

⋅

−

= a a

n

[6.15] 

Introduce

k p

E A

i

s s

s

⋅ ⋅

⋅

−

=

(1 )

2

n

b [6.16] 

Eq. 6.15 can be expressed as:

( cosh( ) sinh( ))

( )

2

2

a x b x

dx

d U x

= b ⋅ ⋅ a ⋅ + ⋅ a ⋅ [6.17] 

and
203

dxdx (a x b x ) c x d

dx

d U x

U x = = ⋅ ⋅ ⋅ + ⋅ ⋅ + ⋅ + ∫∫ cosh( ) sinh( )

( )

( )

2 2

2

a a

a

b

[6.18] 

where a, b, c, and d are integration constants.

The above derivations were taken from Hermann and Al-Yassin (1978) and 

Adib (1988). The extension of the solution is presented below.

Impose the following four boundary conditions to solve for U(x): 

1. The displacement of the soil at x = 0 is zero:

U(x=0) = 0

2. The displacement of the interface element at x = 0 is zero:

W(x=0) = 0

3. The force in the reinforcement at x = L is zero:

F(x=L) = 0

4. The horizontal stress in the soil at x = L is the lateral boundary pressure:

σx(x=L) = -Ph

From condition (2) and Eq. 6.14, 

a = 0 [6.19(a)] 

From condition (1) and Eq. 6.18,

d = 0 [6.19(b)] 

From condition (3) and Eq. 6.6, 

cosh( ) (1 )

2 a

b

c = b⋅a ⋅ a ⋅ L ⋅ − [6.19(c)] 

From condition (4) and Eq. 6.5(c), 

cosh( )

(1 )

)

1

(

2

L

b

E

c P P

s

s

v

s

s

h

⋅ ⋅

⋅

−















 −

⋅

















⋅

−

= − + a

a

n b

n

n

[6.19(d)] 

Solve for b and c from Eq. 6.19(c) and 6.19(d), 

cosh( )

(1 ) 1

)

1

(

2

E L

b P P

s

s

v h

s

s

⋅ ⋅

⋅

−

⋅

















⋅ −

−

=

a a

n

n

n

[6.19(e)] 
204

(1 )

(1 )

)

1

(

2

2

a

n b

n

n

⋅ −

−

⋅

















⋅ −

−

=

s

s

v h

s

s

E

c P P [6.19(f)]

The Force in the Reinforcement

From Eq. 6.6,













= ⋅ ⋅ = ⋅ ⋅ −

dx

dW x

dx

dU x

F x Ar Er r Ar Er

( ) ( )

( ) e [6.20(a)]

The force in the reinforcement can be expressed as:

















⋅

⋅

⋅ −











⋅ −















 −

⋅

















⋅ −

−

= ⋅ ⋅

cosh( )

cosh( )

1 1

(1 )

)

1

( ) (

2

2

L

x

E

F x A E P P

s

s

v h

s

s

r r

a

a

a

n b

n

n

 [6.20(b)] 

The maximum force in the reinforcement occurs at x = 0 and can be expressed as:

















⋅

⋅ −











⋅ −















 −

⋅

















⋅ −

−

= ⋅ ⋅

cosh( )

1

1 1

(1 )

)

1

(

2

2

max E L

F A E P P

s

s

v h

s

s

r r

a a

n b

n

n

 [6.20(c)] 

The Horizontal Stress in the Soil

From Eq. 6.5(c):

dx

E dU x

P

E

s

s

v

s

s

x

s

s

y

s

s

x

( )

(1 )

)

1

(

(1 )

)

1

(

2 2

⋅

−

⋅ +

−

⋅ = −

−

⋅ +

−

=

n n

n

e

n

s

n

n

s [6.21(a)] 

The horizontal stress in the soil can be expressed as:

















+ −

⋅

⋅

⋅ ⋅

















⋅ −

−

⋅ + 















−

= − (1 )

cosh( )

cosh( )

)

1

(

1

2 2 a

b

a

a

a

b

n

n

n

n

s

L

x

P Pv Ph

s

s

v

s

s

x

[6.21(b)] 

6.1.2 Comparison of Load-Transfer Analysis with Experimental and Numerical 

Analysis Results of the APSR Test

To evaluate validity of the load-transfer analysis presented in Section 6.1.1, 

the closed-form solution for reinforcement tension (Eq. 6.20(b)) was used to predict 

the reinforcement tension in the APSR cell developed by Whittle et al. (1992). The 

results of the load-transfer analysis were compared with the experimental results by 

Whittle et al. (1992) and the numerical results from finite-element analyses of the 

APSR cell by Abramento and Whittle (1993).
205

A description of the APSR cell was given in Chapter 2. Figure 6.3 shows the 

schematic diagrams of the APSR test specimen subject to boundary stresses and 

displacements. In the APSR cell, the test specimen consisted of a sand with an 

inclusion at mid-height. The specimen was subjected to uniform boundary stresses 

under plane strain condition. By comparing Figures 6.1 and 6.3, it can be seen that 

the idealized plane-strain GRS mass shown in Figure 6.1, used to develop the loadtransfer analysis, can be used as an APSR cell specimen subject to uniform applied 

pressures. It was assumed that the horizontal stress on the vertical plane at the free 

end of the reinforcement was uniform and equal to the horizontal boundary stress. 

Eq. 6.20(b) was employed to predict the measured reinforcement tensions in 

the APSR cell. The soil was a Ticino sand with a void ratio of 0.63+0.02 and relative 

density of 75%. The reinforcement was a 0.25-mm-thick, 360-mm-long steel sheet 

with strain gauges mounted along the length. The elastic properties of the soil and the 

reinforcement were given by Abramento (1993). For the interface stiffness, the 

equation suggested by Hermann and Al-Yassin (1978) was used. The equation 

related the interface stiffness (ki) to the shear modulus of the soil (Gs) and the 

reinforcement spacing (Sv) as follows:

v

s

i

S

G

k

⋅

=

6

[6.22]

The equation 6.22 is applicable for both SI and British units. The input parameters 

for the load-transfer analysis are presented in Table 6.1.

Figure 6.4 shows comparisons of the predicted and measured values of the 

reinforcement tensions along the reinforcement length for vertical to horizontal 

pressure ratios (

h

v

P

P

) of 3 and 6. In the figure, the normalized axial stress of the 

reinforcement (

Ar Pv

F x

⋅

( )

) was plotted versus the normalized distance from the fixed 

end of the reinforcement (

L

x

). Very good agreements between the measured and 

predicted distributions and magnitudes of the reinforcement tensions are noted. Both 

the measured and predicted tensile force distributions showed the maximum values at 

the fixed end of the reinforcement and gradually reduced toward the free end of the 

reinforcement. At 

L

x

= 0 ( i.e., at the fixed end) and = 6

h

v

P

P

, the measured and 
206

predicted normalized axia l stresses were 358. At 

L

x

= 0.4 of the same pressure ratio, 

the measured and predicted normalized axial stresses were 320 and 307, respectively.

The load-transfer analysis was also performed to predict the maximum 

normalized axial stress (i.e., at 

L

x

= 0) of a hypothetical APSR test specimen for 

different material properties and reinforcement lengths. The predictions were 

compared with the values computed from the finite element analyses conducted by 

Abramento and Whittle (1993) using the ABAQUS finite element program. It was 

assumed in the finite element analysis that the reinforcement was fully bonded with 

the soil. 

Table 6.3 shows a comparison of the maximum normalized axial stress 

of the reinforcement (

Ar Pv

F

⋅

max ) for different material properties and reinforcement 

lengths. The properties for the finite element analysis and the load-transfer analysis 

are given in Table 6.2. The difference between values calculated from the loadtransfer analysis and the finite element analysis was within 5%. These experimental 

and numerical comparisons validate the load-transfer analysis for analyzing 

reinforcement tension in the GRS mass.
207

Figure 6.3: Schematic Diagrams of the APSR Cell (After Whittle et al., 1991)
208

Table 6.1: Input Parameters for Load-Transfer Analysis of the APSR Test Specimen 

(Data from Abramento, 1993)

Property Symbol Unit Value

Shear modulus of soil Gs kN/m26,000

Poisson's ratio of soil νs 0.35

Cross-sectional area of soil As m

2

0.57

Reinforcement modulus Er kN/m22.07x108

Cross-sectional area of reinforcement Ar m

2

2.54x10-4

Reinforcement length L m 0.36

Perimeter of reinforcement p m 2
209

Figure 6.4: Predicted and Measured Normalized Reinforcement Stress 

Distributions in the APSR Cell

0

50

100

150

200

250

300

350

400

0 0.2 0.4 0.6 0.8 1

Normalized Distance from the Fixed End of the Reinforcement

x/L

Normalized Axial Stress in the Reinforcement, 

(F(x)/Ar)/Pv

Measured, Pv/Ph=3

Predicted, Pv/Ph=3

Measured, Pv/Ph=6

Predicted, Pv/Ph=6
210

Table 6.2: Reference Properties for Comparison of Maximum Normalized 

Reinforcement Stress for Table 6.3 (Data from Whittle et al., 1991)

Property Symbol Unit Value

Young's modulus of soil Es kN/m2104

Poisson's ratio of soil νs 0.3

Cross-sectional area of soil As m

2

0.57

Stiffness ratio of soil and reinforcement Er/Gs 103

Reinforcement thickness t m 10-3

Reinforcement length L m 1.0

Perimeter of reinforcement P m 2.0

Applied pressure ratio Pv/Ph 10
211

Table 6.3: Comparison of Maximum Normalized Reinforcement Stress (

Ar Pv

F

⋅

max ), 

from Finite Element Analysis and Load-Transfer Analysis

L = 0.5 m

Er/Gs νs = 0.3 νs = 0.5

Finite Load-Transfer Finite Load-Transfer

Element Analysis Element Analysis

Analysis Analysis

10210.9 10.8 21.8 21.5

10363.6 63.6 135 136

104115 115 264 268

L = 100 m

Er/Gs νs = 0.3 νs = 0.5

Finite Load-Transfer Finite Load-Transfer

Element Analysis Element Analysis

Analysis Analysis

10210.9 10.8 21.8 21.6

10374.4 71.2 163 156

104168 161 438 418
212

6.1.3 Average Stresses in GRS Mass

Based on the load-transfer analysis, the average vertical and horizontal 

stresses in a GRS mass are introduced. The average vertical and horizontal stresses 

are needed in the deformation module for estimating deformations of a GRS mass. 

Uniform vertical and horizontal stresses are assumed for the average stresses. 

The average vertical stress,σv, is assumed to be equal to the boundary 

vertical pressure, i.e.,

v s v = P [6.23] 

Compressive stress is taken as positive and tensile stress as negative.

The average horizontal stress,σh, is defined as:

L

x dx

L

x

h

∫

=

0

s ( )

s [6.24(a)] 

By substituting σx(x) from Eq. 6.21(b) into Eq. 6.24(a) and performing integration, 

the average horizontal stress is obtained as: 













−

⋅

⋅

⋅ + ⋅

















⋅ −

−

⋅ −

−

= 1)

tanh( )

) 1 (

1

) (

1

(

2

L

L

P Pv Ph

s

s

v

s

s

h

a

a

a

b

n

n

n

n

s [6.24(b)] 

6.2 Deformation Module

This section presents the deformation module of the SPR model. The average 

stress-displacement diagram is first described, followed by the equations used to 

calculate the vertical and horizontal displacements.

6.2.1 Average Stress-Displacement Diagram

The average stress-displacement diagram is a conceptual diagram that 

provides a graphical representation of the average stress path and the corresponding 

displacements of an idealized plane-strain GRS mass under monotonic loading and 

unloading-reloading cycles. The average vertical stress (s v ) was plotted versus the 

average horizontal pressure (s h ), and the corresponding vertical displacement (δv) 

and horizontal displacement (δh). All the average stresses in the average stressdisplacement diagram are in compression. 

 Figure 6.5 shows the average stress-displacement diagrams of a GRS mass 

subject to monotonic loading. Initially, a GRS mass is subjected to initial applied 

boundary pressures of Pv,i and Ph,i. The initial average vertical and horizontal stresses 

(s v,i and s h,i) in the average stress diagram are equal to Pv,i and Ph,i, respectively. 
213

The GRS mass is subsequently subjected to an increase in the vertical 

boundary pressure while the horizontal boundary pressure remains constant (ΔPh = 0). 

This results in average stress changes of Δσv,ML and Δσh,ML (from Point 1 to 2 in 

the vertical stress versus horizontal stress plot) and corresponding displacements of 

δv,ML and δh,ML (from Point 1 to 2 in the vertical stress versus displacement plot). The 

GRS mass settles vertically and expands laterally during monotonic loading.

Figure 6.6 shows the average stress-displacement diagrams of a GRS mass 

subject to an unloading-reloading cycle. Initially, a GRS mass is subjected to initial 

applied boundary pressures of Pv,i and Ph,i. The initial average vertical and horizontal 

stresses (s v,i and s h,i) in the average stress diagram are equal to Pv,i and Ph,i, 

respectively. The GRS mass is preloaded to a preloading load level (from Point 1 to 

2 in the vertical stress versus horizontal stress plot), unloaded to the unloading load 

level (from Point 2 to 3), and reloaded (from Point 3 to 4). The diagram represents 

the (UL-Z)+(RL-Z) cycle forσv,UL= 0 (i.e., ULL = 0) and the (UL-PS)+(RL-PS) 

cycle for σv,UL≠ 0 (i.e., ULL = PSL).

For simplification, it is assumed that unloading and reloading stress paths in 

the average stress diagram are identical. The difference betweenσh at Points 1 and 3 

is the residual or “locked-in” horizontal stress, as shown in Figure 6.6. The existence 

of the residual horizontal stress in a GRS mass was confirmed by the irrecoverable 

reinforcement strain measured in Test P-UR-(RB+2044). The irrecoverable 

reinforcement strain implies that there is residual tension in the reinforcement and 

residual horizontal compression in the soil.

Displacements of a GRS mass during preloading, unloading, and reloading are 

shown in the average vertical stress versus displacement plots. The GRS mass settles 

vertically and expands laterally during preloading (from Point 1 to 2), expands 

vertically and contracts laterally (i.e., rebound) during unloading (from Point 2 to 3), 

and settles vertically and expands laterally during reloading (from Point 3 to 4).

In this study, only the average stress changes and displacements of monotonic 

loading and reloading paths were considered. The average stresses were defined in 

Section 6.1.3. The expressions for the vertical and horizontal displacements are 

presented in the following section.

6.2.2 Vertical and Horizontal Displacements

In this chapter, the vertical displacement at the top of the GRS mass is 

referred to as the vertical displacement (δv) and the horizontal displacement at the 

free end of the reinforcement is referred to as the horizontal displacement (δh) of the 

GRS mass. In calculating δv and δh, the average stresses,σv andσh, calculated by 

Eq. 6.23 and 6.24(b) are used. 

The vertical displacement is calculated by the following equation:

v v Sv d = e ⋅ [6.25] 
214

where Sv = height of the GRS mass

ev = vertical strain of the GRS mass and given as:

















⋅

−

⋅ −

−

= h

s

s

v

s

s

v

E

s

n

n

s

n

e

(1 )

(1 )

2

[6.26] 

The horizontal displacement is calculated by integrating the reinforcement 

strain along the reinforcement length. 

dx

A E

F x

x dx

L L

r r

h ∫ r ∫

⋅

= =

0 0

( )

d e ( ) [6.27(a)] 

By subsituting F(x) from Eq. 20(b) into Eq. 6.27(a) and performing integration, δh is 

obtained as:











 ⋅

⋅ −











⋅ −















 −

⋅

















⋅ −

−

=

a

a

a

n b

n

n

d

tanh( )

1

1

)

1

(

2

2

L

L

E

P P

s

s

v h

s

s

h

[6.27(b)]
215

Figure 6.5 : Average Stress-Displacement Diagram for Monotonic Loading
216

Figure 6.6: Average Stress-Displacement Diagram for Unloading and Reloading
217

6.3 Comparison of SPR Model Prediction with SGP Test Results 

To evaluate the SPR model, the SPR model was used to predict the vertical 

and horizontal displacements of the GRS mass in the SGP test, referred to as the 

SGP-GRS mass. The following sections present the application of the SPR model to 

the SGP test, the selection of material and interface properties, and the comparison. 

6.3.1 Application of SPR Model to SGP Test

Due to some differences in the configurations of the idealized plane-strain 

GRS mass (Figure 6.1) and the SGP-GRS mass (Figure 6.7), some assumptions were 

made to apply the SPR model on the SGP-GRS mass. From the finite element 

analysis of the SGP-GRS mass presented in Chapter 5, it was learned that a zeroshear plane can be assumed on the horizontal plane at mid-height between two 

vertically adjacent layers of reinforcement. The zero-shear plane assumption allowed 

a simplified analysis of the average stresses in the SGP-GRS mass. The SGP-GRS 

mass was divided into three layers, referred to as Layers T (top), M (middle), and B 

(bottom), with the zero-shear planes as border lines (see Figure 6.7). 

The average stresses of each layer were determined separately by the SPR 

model. The average vertical stress of each layer was the sum of the vertical boundary 

pressure (Pv) and the vertical stress from the self-weight of the soil at mid-height of 

the layer. The boundary vertical pressure was assumed to be uniform along the 

horizontal plane. This assumption was justified based on the result of the finite 

element analysis (see Figure 5.30). The average horizontal stress was calculated by 

Eq. 6.24(b). Note that the reinforcement perimeter (p) of Layers T and B was half of 

the perimeter of Layer M since the latter has twice the contact areas between the soil 

and the reinforcement. 

The vertical displacement of each layer was calculated by Eq. 6.25. The 

vertical displacement of the SGP-GRS mass was the sum of the vertical 

displacements of Layers T, M, and P. The horizontal displacement at mid-height of 

the SGP-GRS mass was equal to the horizontal displacement of Layer M and was 

given by Eq. 6.27(b).
218

Figure 6.7: SGP-GRS Mass

In this study: H = 610 mm and L = 127 mm

Layer B

Layer M

Layer T

H/4

H

H/2

H/4

L

Zero-Shear 

Plane

Zero-Shear 

Plane
219

6.3.2 Determination of Material and Interface Properties

Determination of the soil, geosynthetic, and interface properties for the SPR 

model are presented below. The subscripts ML and RL represent monotonic loading 

path and reloading path, respectively.

6.3.2.1 Soil 

For monotonic loading, a hyperbolic average stress-strain relationship based 

on the hyperbolic soil model proposed by Duncan et al. (1980) was used. The 

tangential Young’s modulus and Poisson’s ratio for each load increment are given as 

follows.

n

a

h ML

a

h ML

v ML h ML f

s ML P

K P

c

R

E

















⋅ ⋅ ⋅

















⋅ ⋅ + ⋅ ⋅

⋅ − ⋅ −

= −

,

2

,

, ,

,

2 cos 2 sin

(1 sin ) ( )

1

s

f s f

f s s

[6.28] 

















⋅

= −

s ML

s ML

s ML B

E

,

,

,

6

n 0.5 [6.29] 

where Bs,ML = bulk modulus of the soil during monotonic loading

1

,

,

m

a

h ML

s ML b a

P

B K P

















= ⋅ ⋅

s

[6.30]

The parameters for the soil model were determined by the procedure 

recommended by Duncan et al. (1980) and calibrated with the results of the SGP test 

without reinforcement. The calibration was conducted by using the SPR model 

assuming very small reinforcement stiffness to simulate the soil mass without 

reinforcement.

For the reloading path, the reloading modulus, Eq. 5.5, suggested by Duncan 

et al. (1980) was first examined. Based on Eq. 5.5, the reloading modulus for a soil is 

only a function of the minor principal stress (σ3), or the confining pressure in the 

CTC test. This implies that the reloading modulus at a given confining pressure is a 

constant whether the specimen is reloaded from a zero-load level (RL-Z path) or a 

prestressed load level (RL-PS path). However, from the CTC test results, the 

reloading modulus of the RL-PS path was consistently higher than that of the RL-Z 

path (see Figures 3.19 and 3.20). Therefore, the reloading modulus given by Duncan 

et al. (1980) was considered inadequate to model the reloading deformation of the 

GRS mass. 

Tatsuoka and his associates at the University of Tokyo performed extensive 

laboratory tests on rectangular prism soil specimens to determine the elastic Young’s 

modulus of soils. The elastic modulus in a certain direction (i.e., vertical or 
220

horizontal) was obtained at very small strains (on the order of 0.001%) by applying 

very small cyclic stresses in that direction. The strains were measured by local 

deformation transducers (Goto et al., 1991) to eliminate effects of bedding error. 

They have found that the tangent elastic Young’s modulus in a certain direction is a 

unique function of the operative normal stress in that direction (Kohata et al., 1994; 

Tatsuoka and Kohata, 1995; Hoque et al., 1995). Tatsuoka et al. (1997) proposed the 

following empirical relationship for the vertical elastic Young’s modulus based on the 

laboratory test results by Dong et al. (1994).

m

o

v

o

e e

E E 















= ⋅

s

s

( ) [6.31] 

where E

e

 is the elastic Young’s modulus in the vertical direction at a vertical stress 

sv, (Ee)o is the value of E

e

 when sv is equal to a reference value so, and m is the 

power number. The tests were conducted at confining pressures of 19.6 kPa and 78.5 

kPa.

In this study, the reloading modulus from the CTC tests was examined. It was 

found that a power law can be used to relate the reloading modulus (ERL) to the 

vertical unloading stress (σv,UL) as shown in Eq. 6.32. The vertical unloading stress 

was the sum of the confining pressure and the deviator stress at the end of the 

unloading path. 

q

a

ref v UL

RL RL P

E E 















= ⋅

s ,

[6.32] 

where E

ref

RL = reference reloading modulus, ERL when sv,UL = Pa

q = exponent number

However, it was found that Eq. 6.32 cannot account for the increasing of 

reloading stiffness due to prestress in the SGP test. Based on the SGP test results, an 

empirical coefficient λ was introduced to account for the effect of the prestressed load 

level (PSL). Eq. 6.32 was modified as follows:

q

a

ref v UL

RL RL P

E E

















= ⋅ ⋅

s ,

l [6.33] 

where l = empirical coefficient to account for the effect of prestress 

level

(l = 1 for the RL-Z path, PSL = 0) 

 `sv,UL = average vertical unloading stress
221

The parameters E

ref

RL and q were determined from the CTC tests and 

calibrated with the results of the SGP test without reinforcement (Tests P-UR-S and 

P-UR-RB) under the RL-Z path (PSL = 0 and l = 1). The parameter l was obtained 

from the results of the SGP test without reinforcement (Test P-UR-RB) under the RLPS path. For the Sand specimen, Test P-UR-(S+2044)-3 was used to determine the 

parameter λ. The unloading threshold load, as described in Section 5.2, was used as a 

criterion for differentiating the RL-Z path and the RL-PS path. The SPR model 

assumed the RL-Z path (i.e., λ = 1) when the unloading load level was less than the 

unloading threshold load, and otherwise assumed the RL-PS path.

The reloading Poisson’s ratio (νs,RL ) is calculated from the following 

equation:

















⋅

= −

s RL

s RL

s RL B

E

,

,

,

6

n 0.5 [6.34] 

where Bs,RL = bulk modulus of the soil during reloading

2

,

, ,

m

a

h RL

s RL b RL a

P

B K P

















= ⋅ ⋅

s

[6.35] 

The isotropic compression test may be conducted to determine change of bulk 

modulus due to preloading. However, such a test was not available for the soils in 

this study. It was assumed that Kb,ML= Kb,RL and m1=m2.

A summary of the soil properties for the SGP-GRS mass is presented in Table 

6.4. 
222

Table 6.4: Summary of Soil Properties for the SPR Model

(a) Ottawa Sand

Property Symbol Value

Unit weight (kN/m3) γ 16.8

Monotonic Loading

Modulus number K 350

Modulus exponent n 0.5

Failure ratio Rf 0.7

Bulk modulus number Kb 675

Bulk modulus exponent m1 0.4

Cohesion (kPa) c -

Friction angle (degree) φ 40.6

Reloading Path

Reference modulus number E

ref

RL 70000

Reloading modulus exponent q 0.2

Prestress-level coefficient λ 2.0

Bulk modulus number Kb,RL 675

Bulk modulus exponent m2 0.4
223

Table 6.4: Summary of Soil Properties for the SPR Model (Continued)

(b) Road Base Soil

Property Symbol Value

Unit weight (kN/m3) γ 20.25

Monotonic Loading

Modulus number K 220

Modulus exponent n 0.48

Failure ratio Rf 0.7

Bulk modulus number Kb 172

Bulk modulus exponent m1 -0.33

Cohesion (kPa) c 6.9

Friction angle (degree) φ 31.3

Reloading Path

Reference modulus number E

ref

RL 27000

Reloading modulus exponent q 0.58

Prestress-level coefficient λ 1.4

Bulk modulus number Kb,RL 172

Bulk modulus exponent m2 -0.33
224

6.3.2.2 Geosynthetic

The reinforcement stiffness (Er⋅Ar) for the SPR model can be obtained from 

the load-extension test of the geosynthetic. The secant stiffness (J) in the range of the 

expected reinforcement strain should be used. The SPR model allows the use of 

different values of reinforcement stiffness (Er) during the preloading and reloading 

paths. In the SGP tests, the measured reinforcement strains of Amoco 2044 

reinforcement were relatively small (in the range of 0 to 0.5%). An unloadingreloading LE test was conducted to determine the reloading modulus at small strains 

of Amoco 2044 geosynthetic. The test result is shown in Figure 6.8. It shows that, 

for strain less than 0.5%, the secant stiffness of the preloading and reloading paths is 

approximately the same. The stiffness of 1,000 kN/m was used for the Amoco 2044 

reinforcement.

6.3.2.3 Soil-Geosynthetic Interface

The interface stiffness (ki) in the SPR model can be determined from direct 

shear tests of the interface between the soil and geosynthetic reinforcement. Based on 

the results of the interface direct shear tests conducted in this study (see Section 

3.6.5), the following equations are proposed.

1

, 1

p

a

n

i ML ds w

P

k k 















= ⋅ ⋅

s

g [6.36] 

2

, 2

p

a

n

i RL ds w

P

k k 















= ⋅ ⋅

s

g [6.37] 

where ki,ML and ki,RL = monotonic-loading and reloading interface stiffness

kds1 and kds2 = interface stiffness number

p1 and p2 = interface exponent

gw = unit weight of water

sn = normal stress on the interface

The monotonic-loading interface stiffness (ki,ML) can be determined from a 

plot of K50/γw versus σn/Pa on a log-log scale. In the same fashion, the reloading 

interface stiffness (ki,RL) can be determined from a plot of KRL/γw ratio versus the 

σn/Pa on a log-log scale. A summary of the interface properties for the SGP-GRS 

mass is presented in Table 6.5.
225

Figure 6.8: Tensile Load Versus Axial Strain Relationship of Amoco 2044 

at Small Strain

0

10

20

0 1 2 3

Axial Strain (%)

Tensile Load (kN/m)
226

Table 6.5: Summary of Interface Properties for the SPR Model

Symbol Value

Ottawa Sand + Amoco 2044 Reinforcement

ML interface stiffness number kds1 17,450

ML interface stiffness exponent p1 0.28

RL interface stiffness number kds2 25,290

RL interface stiffness exponent p2 0.24

Road Base Soil + Amoco 2044 

Reinforcement

ML interface stiffness number kds1 11,110

ML interface stiffness exponent p1 0.45

RL interface stiffness number kds2 19,690

RL interface stiffness exponent p2 0.31
227

6.3.3 Calculation Example

The change in the average stresses and the corresponding change in the 

vertical and horizontal displacements of the SGP-GRS mass were formulated in an 

incremental form to simulate the stress-dependent properties of the soil and the

interface. Note that during the vertical load application, the boundary horizontal 

pressure remained constant (ΔPh = 0). 

v Δsv = ΔP [6.38] 













−

⋅

⋅

⋅ + ⋅

















⋅ Δ

−

⋅ Δ −

−

Δ = 1)

tanh( )

) 1 (

1

) (

1

(

2

L

L

P Pv

s

s

v

s

s

h

a

a

a

b

n

n

n

n

s [6.39] 

v

h

s

s

v

s

s

v S

E

⋅

















⋅ Δ

−

⋅ Δ −

−

Δ = s

n

n

s

n

d

(1 )

(1 )

2

[6.40] 











 ⋅

⋅ −











⋅ − 













 −

⋅

















⋅ Δ

−

Δ =

a

a

a

n b

n

n

d

tanh( )

1

1

)

1

(

2

2

L

L

E

P

s

s

v

s

s

h

[6.41] 

The calculations of the average stresses and displacements were performed by 

a spreadsheet program. An example calculation for Layer M of the SGP-GRS mass is 

presented in Table 6.6. The spreadsheet consists of the input in the upper area and the

computation in the lower area. The properties of the soil, the reinforcement, and the 

interface must be provided as the input. 

Columns 1 to 33 performed calculations based on Eq. 6.38 to 6.41. Columns 

1 and 2 are the vertical boundary pressures. Column 3 is the vertical stress resulting 

from self-weight of the soil. Column 4 is the confining pressure applied prior to the 

vertical load from the loading device. Columns 5 and 6 give the average vertical and 

horizontal stresses of each step. Columns 7 and 8 are the average vertical and 

horizontal stresses used to calculate the soil and the interface properties of each 

increment. Columns 9 to 22 are the calculation parameters. Column 23 gives the 

average horizontal stress as a result of the incremental vertical boundary pressure. 

The horizontal stress value in Column 23 is added to the average horizontal stress in 

the previous step. Note that iterations are needed in each increment for calculation of 

the average horizontal stress. This is because the soil and the interface properties are 

a function of the average horizontal stress which, in turn, is a function of the 

properties of the soil and the interface. Columns 24 to 28 calculate the vertical 

displacement. Columns 29 to 33 calculate the horizontal displacement.
228

Table 6.6: Calculation Example of SPR Model for SGP-GRS Mass

Calculating Vertical and Horizontal Displacements of SGP-GRS Mass by the SPR 

Model

By: Kanop Ketchart, Dept. of Civil Eng., U of Colorado at Denver

Input

Soil: Middle Layer

f = 31.3 degree

 c = 6.9 kPa

g = 20.25 kN/m3

z midheight= 0.3 m

K = 220

n = 0.48

Kb = 172

m = -0.33 β = ki*p*(1-n

2

)/EsAs

E

ref

RL = 27000 a

2 = kip(1/ErAr+(1-n2

)/EsAs)

q = 0.58

Rf = 0.7

Reinforcement: Stiffness ErAr = 1000 kN/m Interface: kds = 11110

Perimeter p = 2 m p = 0.45

Vertical 

spacing

Sv = AS = 0.3 m

Length L = 0.127 m
229

Table 6.6: Calculation Example of SPR Model for SGP-GRS Mass (Continued)

1 2 3 4

Step i Increment D Pv Pv g*z PC

(mid-height)

(kPa) (kPa) (kPa) (kPa)

1 0.000 6.075 34.5

1 9

2 9.000 6.075 34.5

2 9

3 18.000 6.075 34.5

5 6 7 8 9 10

sv sh sv,avg sh,avg (sv,avg-sh,avg) (sv,avg-sh,avg)f

=(Pv+g*z+PC) = sh,i+D sh, i-j =(sv,j+sv,i)/2 =(sh,j+sh,i)/2

(kPa) (kPa) (kPa) (kPa) (kPa) (kPa)

40.58 34.50

45.08 34.80 10.28 99.71

49.58 35.09

54.08 35.44 18.63 101.10

58.58 35.79

11 12 13 14 15 16

SL Ei Es=Et B n ki

(kPa) (kPa) (kPa) (kN/m3)

0.103093831 13,254 11,410 24,368 0.42 77,622 

0.18430997 13,372 10,144 24,221 0.43 84,249 
230

Table 6.6: Calculation Example of SPR Model for SGP-GRS Mass (Continued)

17 18 19 20

Step i Increment a

2

a b n/(1-n)

1

1 192.52 13.8752 37.27719 0.729982

2

2 213.62 14.61571 45.12177 0.754998

3

21 22 23

b/a2

(tanh(a*L)/a*L-1) D sh, i-j

(kPa)

0.193626 -0.465004548 0.592

0.211226 -0.486947193 0.699
231

Table 6.6: Calculation Example of SPR Model for SGP-GRS Mass (Continued)

Vertical Displacement

24 25 26 27 28

Step i

Increment Dsv Dsh D ever ever S total

(kPa) (kPa) (mm)

1 0 0

1 9.00 0.592 0.000617218

2 0.00061722 0.1851654

2 9.00 0.699 0.00068064

3 0.00129786 0.38935751

Horizontal Displacement (sum of two sides)

29 30 31 32 33

Step i

Increment (1-n2

)/Es

(1-b/a2) (L+tanh(a*L)/a) D dhor dhor

(mm) (mm)

1 0.0000

1 7.204E-05 0.806374 0.059055578 0.045075 

2 0.0451

2 8.034E-05 0.788774 0.061842293 0.053256 

3 0.0983
232

6.3.4 Comparison of SPR Model Prediction with SGP Test Results

The predicted and measured displacements of the SGP-GRS mass under the 

monotonic loading and reloading paths are presented. The SPR model was not used 

to predict the displacements near the failure load of the specimen because there was a 

high possibility of local failure in some areas of the specimen near the failure load. 

The SPR model, which is based on average stress fields, cannot model local soil 

failure. A stress level (SL) of 0.85 was set as the threshold level above which the 

SPR model is deemed not applicable.

Figures 6.9 and 6.10 show a comparison of the predicted and measured 

displacements of the GRS masses with the Sand and Road Base soil under monotonic 

loading. The predicted and measured displacements are in very good agreement. At 

42.5-kN vertical load, the predicted vertical and horizontal displacements of the GRS 

mass with the Sand were 9.5 mm and 2.1 mm as compared with the measured values 

of 9.9 mm and 2.2 mm, respectively. At 13-kN vertical load, the predicted vertical 

and horizontal displacements of the GRS mass with the Road Base soil were 5.4 mm 

and 0.9 mm as compared with the measured values of 6.1 mm and 1.1 mm, 

respectively.

A comparison of the predicted and measured displacements of the GRS 

masses under RL paths are presented in Figures 6.11 to 6.14. The reloading 

displacements were referenced to the deformed shape of the specimen at the end of 

the unloading path. 

Figures 6.11 and 6.12 show the displacements under, respectively, the RL-Z 

and RL-PS paths for the GRS masses with the Sand. The reduced vertical reloading 

stiffness at the initial RL-Z path, as described in Section 5.2, was modeled 

empirically base on the observations. At the vertical load of zero to 0.05⋅PLL of the 

RL-Z path, the reloading modulus of the soil was empirically reduced to 30% (i.e.,

70% reduction) of the reloading modulus calculated by Eq. 6.24. The reduction of 

reloading modulus was not used in the RL-PS path. The predicted and measured 

values for the Sand specimen during reloading paths are considered acceptable with 

some discrepancies in the horizontal displacements during initial RL-Z path. At a 

vertical load of 20 kN, the predicted and measured vertical displacements were, 

respectively, 1.34 mm and 1.23 mm for the RL-Z path, and 0.56 mm and 0.56 mm for 

the RL-PS path. The predicted and measured horizontal displacements were, 

respectively, 0.16 mm and 0.02 mm for the RL-Z path, and 0.02 mm and 0.05 mm for 

the RL-PS path. 

The displacements under the RL-Z path of the GRS mass with the Road Base 

soil are shown in Figure 6.13. Figure 6.14 and 6.15 shows the displacements under 

the RL-PS path. During the initial stage of the RL-Z path, the specimen continued to 

rebound in both vertical and horizontal directions. To model this behavior, an 

empirical procedure was performed. Negative values of predicted displacements 

were used to represent rebounding deformation. From observation, negative vertical 
233

displacements occurred from the vertical load of zero to 0.05⋅PLL and negative 

horizontal displacements from the vertical load of zero to 0.3⋅PLL. The RL-PS paths 

show the rebounding deformation only in the horizontal direction. The empirical 

procedure for the rebounding deformation was also used for horizontal displacements 

of the RL-PS path. With the empirical procedure for rebounding deformation, the 

SPR model appears to give a good overall simulation of the displacements in the GRS 

mass with the Road Base soil during RL-Z and RL-PS paths. At a vertical load of 4 

kN, the predicted and measured vertical displacements were, respectively, 0.73 mm 

and 0.82 mm for the RL-Z path, 0.53 mm and 0.56 mm for the RL-PS1 path, and 0.47 

mm and 0.33 mm for the RL-PS2 path. The predicted and measured horizontal 

displacements were, respectively, -0.05 mm and -0.02 mm for the RL-Z path, 0.02 

mm and 0.03 mm for the RL-PS1 path and 0.01 mm and 0.01 mm for the RL-PS2 

path.
234

Figure 6.9: Predicted Versus Measured Vertical and Horizontal 

Displacements of Test P-M-(S+2044)

0

10

20

30

40

50

60

0 5 10 15 20 25 30

Displacement (mm)

Vertical Load (kN)

Measured (Vertical)

Predicted (Vertical)

Measured (Horizontal)

Predicted (Horizontal)
235

Figure 6.10: Predicted Versus Measured Vertical and Horizontal

Displacements of Test P-M-(RB+2044)

0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20 25

Displacement (mm)

Vertical Load (kN)

Measured (Vertical)

Predicted (Vertical)

Measured (Horizontal)

Predicted (Horizontal)
236

Figure 6.11: Predicted Versus Measured Reloading Vertical and Horizontal 

Displacements of Test P-UR-(S+2044), RL-Z path 

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5

Displacement (mm)

Vertical Load (kN)

Measured (Vertical)

Predicted (Vertical)

Measured (Horizontal)

Predicted (Horizontal)
237

Figure 6.12: Predicted Versus Measured Reloading Vertical and Horizontal 

Displacements of Test P-UR-(S+2044), RL-PS path

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3

Displacement (mm)

Vertical Load (kN)

Measured (Vertical)

Predicted (Vertical)

Measured (Horizontal)

Predicted (Horizontal)
238

Figure 6.13: Predicted Versus Measured Reloading Vertical and Horizontal 

Displacements of Test P-UR-(RB+2044), RL-Z path

0

2

4

6

8

10

12

-0.5 0 0.5 1 1.5 2 2.5 3

Displacement (mm)

Vertical Load (kN)

Measured (Vertical)

Predicted (Vertical)

Measured (Horizontal)

Predicted (Horizontal)
239

Figure 6.14: Predicted Versus Measured Reloading Vertical and Horizontal 

Displacements of Test P-UR-(RB+2044), RL-PS1 path 

0

1

2

3

4

5

6

-0.5 0 0.5 1 1.5 2

Displacement (mm)

Vertical Load (kN)

Measured (Vertical)

Predicted (Vertical)

Measured (Horizontal)

Predicted (Horizontal)
240

Figure 6.15: Predicted Versus Measured Reloading Vertical and Horizontal 

Displacements of Test P-UR-(RB+2044), RL-PS2 path

0

1

2

3

4

5

6

7

-0.5 0 0.5 1 1.5 2

Displacement (mm)

Vertical Load (kN)

Measured (Vertical)

Predicted (Vertical)

Measured (Horizontal)

Predicted (Horizontal)
241

6.4 Parametric Study on Deformation of GRS Mass

A parametric study was carried out by the SPR model to examine the 

influences of the soil, reinforcement, and interface on the deformation behavior of a 

GRS mass. The baseline properties for the materials used in the parametric study are 

presented in Table 6.7. These properties were used in all displacement calculations 

except the parameter being investigated. Three parameters were investigated: the soil 

stiffness (Es), the reinforcement stiffness (Er⋅Ar), and the interface stiffness (ki).

The displacement ratio and the stiffness ratio are introduced to simplify the 

presentation of the results. The displacement ratio is defined as the ratio of the 

displacement of a GRS mass with the varied parameter to the displacement of the 

GRS mass with the baseline properties. The stiffness ratio is defined as the ratio of 

the varied parameter to the baseline value of the stiffness.

Figure 6.16 shows the relationships between vertical displacement ratio and 

stiffness ratios of the soil, the reinforcement, and the interface. Each stiffness ratio 

was varied from 1 to 10. The figures show that the reduction of the vertical 

displacements was far more pronounced with increasing soil stiffness than 

reinforcement stiffness. The change in the interface stiffness shows little effect. At a 

stiffness ratio of 2, the vertical displacement ratios due to the increase of soil, 

reinforcement, and interface stiffnesses were, respectively, 0.5, 0.98, and 1.0. At a 

stiffness ratio of 5, the vertical displacement ratios due to the increase of soil, 

reinforcement, and interface stiffnesses were, respectively, 0.2, 0.96, and 1.0.

Figure 6.17 shows the relationships between horizontal displacement ratio and 

the stiffness ratio of the soil, reinforcement, and interface. Similar to the vertical 

displacement, the horizontal displacements reduced with increasing soil and 

reinforcement stiffnesses. Increasing the soil stiffness has a more significant effect 

than increasing the reinforcement stiffness. The change in the interface stiffness 

shows little effect. At a stiffness ratio of 2, the horizontal displacement ratios due to 

the increase of soil, reinforcement, and interface stiffness were, respectively, 0.55, 

0.8, and 1.0. At a stiffness ratio of 5, the horizontal displacement ratios due to the 

increase of soil, reinforcement, and interface stiffness were, respectively, 0.25, 0.5, 

and 1.0.

These results have an important practical implication in selecting a method to 

reduce the settlement of a GRS mass. Either employing a stiffer reinforcement or 

increasing the soil stiffness can reduce the settlement of a GRS mass. Figure 6.16 can 

be used as a guide for reducing settlement. This finding supports the use of a 

preloading technique for reducing post-construction settlement of a GRS structure.
242

Table 6.7: Properties for the Baseline GRS Mass

Property Symbol Unit Value

Young's Modulus of soil Es kN/m2104

Poisson's ratio of soil ν 0.3

Cross sectional area of soil As m

2

0.3

Reinforcement stiffness ErAr kN/m 103

Reinforcement length L m 3

Perimeter of reinforcement p m 2.0

Interface stiffness ki kN/m33x104

Applied pressure ratio Pv/Ph 5
243

Figure 6.16: Vertical Displacement Ratio Versus Stiffness Ratio 

Relationships

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 2 3 4 5 6 7 8 9 10 11 12

Stiffness Ratio

Vertical Displacement Ratio

Soil Stiffness

Reinforcement Stiffness

Interface Stiffness
244

Figure 6.17: Horizontal Displacement Ratio Versus Stiffness Ratio 

Relationships

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 2 3 4 5 6 7 8 9 10 11 12

Stiffness Ratio

Horizontal Displacement Ratio

Soil Stiffness

Reinforcement Stiffness

Interface Stiffness
245

6.5 Summary and Concluding Remarks

A simplified preloading-reloading (SPR) model was developed and presented 

in this chapter. The purpose of the model was to provide a simple tool for estimating 

the deformation of a GRS mass subject to monotonic loading or preloading and 

subsequent reloading. The SPR model consists of two principal modules: a loadtransfer module and a deformation module. The load-transfer module is based on the 

elastic analysis of the load-transfer mechanism in an idealized plane-strain GRS mass. 

The load-transfer module assumes uniform stresses, referred to as the average 

stresses, in a GRS mass. The deformation module used the average stresses 

determined from the load-transfer module to calculate the vertical and horizontal 

displacements of the GRS mass.

The SPR model was evaluated by comparing its results with experimental and 

numerical analysis results of the APSR test (Whittle et al., 1992; Abramento and

Whittle, 1993) and the SGP test results conducted in this study. The comparison 

yielded satisfactory results. Although further verification is still needed, the SPR 

model appears to be a valid tool for estimating the deformation of GRS masses.

To examine the influences of increasing stiffness of soil, reinforcement, and 

interface on the deformation behavior of a GRS mass, a parametric study was 

conducted by the SPR model. The parametric study showed that vertical 

displacement of the GRS mass was significantly reduced by increasing soil stiffness. 

The effect of increasing reinforcement stiffness was much smaller, whereas the effect 

of increasing the interface stiffness was negligible. This finding supports the benefits 

of employing a preloading technique in reducing post-construction settlement of GRS 

structures.
246

7. Correlation Between SGP Test and Preloaded GRS Structure

This chapter describes correlations between the results of SGP tests and 

preloaded GRS structures. Two preloaded GRS structures and the corresponding 

SGP tests were examined. The first was the FHWA pier (Adams, 1997) and the 

performance test conducted by the second-generation SGP test prior to construction. 

The second was the Black Hawk abutments (Wu et al., 1999) and the modified SGP 

test. Both SGP tests were conducted with the same soil and reinforcement as those 

used in the preloaded GRS structures. The correlations were made in terms of 

normalized values of loads and displacements. 

It should be noted that deformation behavior of a GRS structure depends on 

various factors such as soil, reinforcement, reinforcement spacing, facing rigidity, 

geometry, soil placement condition, and construction sequence. The SGP test is 

capable of simulating the soil, the reinforcement, and the reinforcement spacing only. 

An absolute correlation, therefore, is not feasible. The attempt here is to establish the 

correlation for a construction protocol and a facing type (segmental concrete blocks 

with no pins for the FHWA pier and rock-faced type for the Black Hawk abutment).

7.1 FHWA Pier

The project description of the FHWA pier was presented in Chapter 2. The 

pier was load-tested on July 3, 1996, and July 23, 1996, which were referred to as the 

first and the second load tests. For each load test, The loading sequences consisted of 

two paths: preloading and reloading paths. In the first load test, the GRS pier was 

incrementally loaded up to 900 kPa and unloaded to zero. In the reloading path, the 

load was increased to 415 kPa and unloaded to zero. Note that the maximum loads in 

both preloading and reloading paths were much higher than the suggested maximum 

contact pressure of 200 kPa for mechanically stabilized bridge abutments (Elias and 

Christopher, 1997). In the second load test, the GRS pier was incrementally loaded 

up to 780 kPa and unloaded to zero. In the reloading path, the pier was loaded up to 

780 kPa. 

7.1.1 Load Test Results

The results of the first and the second load tests were compared to examine 

effects of preloading. In this section, the term “vertical displacement” refers to the 

average settlement of the loading pad; the term “horizontal displacement” refers to 

the horizontal displacement at mid-height of the wall faces; and the reloading 

displacement was referenced to the deformed shape of the pier at the end of 

unloading. The preloading and reloading paths of the first load test were designated 

as the preloading and first reloading paths. The preloading and reloading paths of the 

second load test were designated as the second and third reloading paths.
247

Figure 7.1 shows the relationship between the vertical applied pressure and 

displacements of the FHWA pier in the four loading paths. It can be seen that 

preloading reduced the vertical displacements of the FHWA pier. The vertical 

displacement at 200 kPa was 14.6 mm in the preloading path and 8.1 mm in the first 

reloading path. Figure 7.1 also shows that the reduction in vertical settlement was 

insignificant in the subsequent reloading paths (i.e., in the second and third reloading 

paths). Figure 7.1 shows the vertical applied pressure versus horizontal displacement 

relationships in the four loading paths. It shows that the horizontal movement for all 

loading paths was practically the same until the vertical pressure exceeds 400 kPa. 

The horizonatal displacements reduced somewhat due to preloading when the vertical 

pressure was higher than 400 kPa. The preloading effect in the horizontal direction, 

after the pressure exceeded 400 kPa, was not as significant as in the vertical direction. 

The horizontal displacement at 580 kPa was 13.9 mm in the preloading path and 11.1 

mm in the second reloading path.

7.1.2 SGP Test Results

The test specimen of the SGP test was prepared by employing the same soil 

and geosynthetic reinforcement as those used in actual construction of the FHWA 

pier. The test was conducted prior to construction of the pier by Sam Yu and Damin 

Shi at the University of Colorado at Denver. The soil was compacted to 23 kN/m3 

with a water content of 4.1%. The reinforcement sheets were placed at bottom, midheight, and top of the test specimen. The test specimen in the performance test was 

also subjected to two loading paths: preloading and reloading paths. In the preloading 

path, the load was increased at a constant rate of 10.5 kPa/min to 689 kPa and 

unloaded to zero. In the reloading path, the load was increased at the same rate as in 

the preloading path until failure occurred.

Figure 7.2 shows the results of the SGP tests. The vertical and the horizontal 

displacements were plotted versus the vertical load. The effects of preloading in 

reducing the displacement of the SGP test specimen are similar to those measured in 

the FHWA pier. The vertical displacement of the SGP test specimen reduced upon 

preloading. The vertical displacement at 120 kN was 3.3 mm in the preloading path 

and reduced to 2.0 mm in the reloading path. In the horizontal direction, the 

preloading effect was negligible until the specimen was loaded to about 70 kN.

7.1.3 Correlation Between SGP Test and FHWA Pier

To correlate the results of the SGP test to the FHWA pier, two terms were 

introduced: applied load level and improvement ratios. Applied load level is defined 

as the ratio of a given applied load to the ultimate load. Improvement ratio is defined 

as the ratio of the preloading and reloading displacements at the same applied load. 

The improvement ratios in the vertical and horizontal directions are designated as 

VIR and HIR, respectively.
248

The ultimate load of the test was 420 kN (see Figure 7.2). For the FHWA 

pier, the ultimate load was judged to be 915 kPa, at which the pier showed significant 

cracks in the facing blocks (Adams, 1997).

Figures 7.3 and 7.4 show, respectively, the vertical and horizontal 

improvement ratios of the SGP test and the FHWA pier at different applied load 

levels. Despite the large differences in the geometry and boundary conditions 

between the two structures, the improvement ratios of the SGP test specimen and the 

FHWA pier are both in the same range of 1.7 to 2.0 for the vertical direction and 1.0 

to 1.2 for the horizontal direction. At an applied load level of 0.2, the VIR and HIR 

of the SGP test specimen are 1.7 and 1.1, respectively. At the same applied load 

level, the FHWA pier has the VIR of 1.8 and the HIR of 1.0. 
249

Figure 7.1: Vertical Applied Pressure Versus Displacement Relationships of 

the FHWA Pier

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60 80 100

Vertical Displacement (mm)

Vertical Applied Pressure (kPa)

Primary Loading

1st Reloading

2nd Reloading

3rd Reloading

0

100

200

300

400

500

600

700

800

900

1000

0 10 20 30 40

Horizontal Displacement (mm)

Vertical Applied Pressure (kPa)

Primary Loading

1st Reloading

2nd Reloading
250

Figure 7.2: Vertical Load Versus Displacement Relationships of the SPG Test

0

50

100

150

200

250

300

350

400

450

0 5 10 15 20 25

Vertical Displacement (mm)

Vertical Load (kN)

Primary Loading

Reloading

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12

Horizontal Displacement (mm)

Vertical Load (kN)

Primary Loading

Reloading
251

Figure 7.3: Vertical Improvement Ratio Versus Applied Load Level 

Relationships of the FHWA Pier and SGP Test

0

1

2

3

4

5

0.00 0.20 0.40 0.60 0.80 1.00

Applied Load Level

Vertical Improvement Ratio

FHWA Pier

SGP Test
252

Figure 7.4: Horizontal Improvement Ratio Versus Applied Load Level 

Relationships of the FHWA Pier and SGP Test

0

1

2

3

4

5

0.00 0.20 0.40 0.60 0.80 1.00

Applied Load Level

Horizontal Improvement Ratio

FHWA Pier

SGP Test
253

7.2 Black Hawk Abutments

The project description of the Black Hawk abutments was given in Chapter 2. 

Differing from the FHWA pier, the Black Hawk abutments were a production project. 

The abutments were preloaded to reduce anticipated differential post-construction 

settlement due to largely different thickness of the GRS masses. The abutments were 

preloaded in October 1997. The loading sequence consisted of primary loading and 

three cycles of reloading. During primary loading, increasing vertical loads were 

incrementally applied up to 245 kPa (1.6 times the design load of 150 kPa) and then 

unloaded to zero. Three loading-unloading cycles were applied following the primary 

loading. In the reloading cycles, the applied pressure was approximately the design 

load of 150 kPa.

7.2.1 Full-Scale Preloading Results

Figures 7.5 and 7.6 show vertical applied pressure versus average settlement 

relationships of Footings #1 and #3 (for footing descriptions, see Section 2.4.1.4). 

The average settlement was calculated from the settlements at four corners of each 

footing. The vertical load-settlement behavior of the footings shows the effect of 

preloading in reducing footing settlement. At 150 kPa, the average settlements of 

Footings #1 and #3 were, respectively, 13.3 mm and 28.0 mm. At the same vertical 

pressure, the average settlements of Footings #1 and #3 reduced to, respectively, 2.8 

mm and 4.2 mm. The differences of the settlements between Footing #1 and Footing 

#3 were due to different thickness of the GRS masses and different boundary 

conditions (where the footing was positioned with respect to the rock-faced wall). 

Figures 7.5 and 7.6 also show that the settlements in all the reloading paths were 

comparable and much smaller than the settlement in the primary loading. This 

indicates that the preloading effect is insignificant in subsequent reloading paths. 

This behavior was also observed in the FHWA pier and the SGP tests.

7.2.2 SGP Test Results

A series of the modified SGP tests were conducted on the Road Base soil 

with Amoco 2044 reinforcement. The test results were presented in Chapter 5. 

Figure 7.7 shows the vertical load versus vertical displacement relationships of the 

SGP tests (Tests P-M-(RB+2044) and P-UR-(RB+2044)). The predicted values from 

the SPR model described in Chapter 6 are also included. Both the measured and 

predicted displacements showed the effect of preloading in reducing the vertical 

displacements.

7.2.3 Correlation Between the Modified SGP Test and Black Hawk Abutments

The correlation between the modified SGP tests and the Black Hawk 

abutments is presented. The ultimate load of the footing was determined by assuming 
254

a hyperbolic relationship between the vertical pressure and the average settlement. 

The ultimate loads of Footings #1 and #3 were 370 kN and 330 kN, respectively.

The vertical improvement ratios of the footings were compared with those 

from the SGP tests and the SPR model, as shown in Figure 7.8. The VIR values from 

the SGP test and the SPR model were smaller than the measured data. At an applied 

load level of 0.25, the VIF values from the SGP tests and the SPR model were 2.3 and 

1.8, respectively; whereas, the measured data of Footings #1 and #3 showed that the 

VIR values were about 3.6. 

The large discrepancy in the VIR values is attributed to the difference in the 

placement density. In the FHWA pier, the field density was closely monitored by 

field density tests to ensure uniformity. The field density of the Black Hawk 

abutments was controlled by experience without field density measurement. As a 

result, the field density was not as well controlled and not as uniform as the FHWA 

pier. The field density was most likely lower than in the SGP test (95% R.C. 

Standard Proctor). The lower density led to a large compression of the backfill 

during preloading, hence, higher VIR values. 
255

Figure 7.5: Vertical Applied Pressure Versus Average Settlement Relationships of 

Footing #1 of the Black Hawk Abutments

0

50

100

150

200

250

300

0 5 10 15 20 25 30 35

Average Settlement (mm)

Vertical Applied Pressure (kPa)

Preloading

1st Reloading

2nd Reloading

3rd Reloading
256

Figure 7.6: Vertical Applied Pressure Versus Average Settlement 

Relationships of Footing #3 of the Black Hawk Abutments

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70

Settlement (mm)

Vertical Applied Pressure (kPa)

Preloading

1st Reloading

2nd Reloading

3rd Reloading
257

Figure 7.7: Predicted and Measured Vertical Load Versus Vertical 

Displacement of the Modified SGP Tests

0

2

4

6

8

10

12

-0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5

Vertical Displacement (mm)

Vertical Load (kN)

RL-Z path (Measured)

P-M-(RB+2044) (Measured)

RL-Z path (Predicted)

P-M-(RB+2044) (Predicted)
258

Figure 7.8: Vertical Improvement Ratio Versus Applied Load Level 

Relationships of the Black Hawk Abutments and SGP Tests 

0

1

2

3

4

5

6

7

8

9

10

0.00 0.20 0.40 0.60 0.80 1.00

Applied Load Level

Vertical Improvement Ratio

Footing #1

Footing #3

SGP Test

SPR Model
259

7.3 Summary and Concluding Remarks

The vertical and horizontal improvement ratios (VIR and HIR) from the SGP 

test correlated quite well with those of the FHWA pier despite the large differences in 

geometry and boundary conditions between them. The difference in VIR and HIR 

between the SGP test and the FHWA pier was within 10%. In the Black Hawk 

abutments, the SGP tests and the SPR model give about 40% lower VIR values than 

the VIR from the measured data. The difference is believed to be due to the 

uncertainty in the placement density and moisture of the backfill in the abutments.

The degree of reduction in the settlement due to preloading of GRS structures 

may be assessed with reasonable accuracy by conducting a SGP test or simply using 

the SPR model. Additional validation is still needed as more reliable field-measured 

data of preloaded GRS structures become available. 
260

8. Summary, Conclusions, and Recommendations

8.1 Summary

A study was undertaken to investigate the behavior of a geosyntheticreinforced soil (GRS ) mass subject to preloading and to develop a simplified 

analytical model for estimating deformation of a preloaded GRS mass. Since 1997, 

preloading has been applied to a number of full-scale GRS structures. The preloading 

has been shown to reduce settlements in the subsequent loading paths. However, the 

behavior of a preloaded GRS mass has not yet been fully elucidated. Specifically, 

two important questions remain unanswered:

1. What is the appropriate loading magnitude and loading sequence to effectively 

preload a GRS mass?

2. How much deformation is to be expected in a preloaded GRS mass?

To seek answers to these questions, a systematic study was conducted. 

Specifically, the following four tasks were carried out:

Task 1: Conduct laboratory tests to examine the behavior of different soils, 

geosynthetics, and soil-geosynthetic interfaces subject to monotonic loading and 

unloading-reloading. The test programs included conventional triaxial tests on soils, 

in-isolation load-extension tests on geosynthetics, and direct shear tests on soilgeosynthetic interfaces. The soils were an Ottawa sand and a Road Base soil. The 

Road Base soil was a granular material commonly used as backfill for GRS 

structures. The geosynthetics were a woven polypropylene geotextile, Amoco 2044, 

as a strong reinforcement and a non-woven heat-bonded polypropylene geotextile, 

Typar 3301, as a weak reinforcement.

Task 2: Conduct laboratory tests to examine the behavior of generic GRS masses 

subject to monotonic loading and unloading-reloading. The tests were conducted by 

a modified soil-geosynthetic performance (SGP) test devised in this study. Vertical 

and horizontal deformations of the test specimen were measured. In one test, strain 

gauges were installed to measure strains in the reinforcement. A finite element 

analysis was conducted to examine the stress distribution of a GRS mass in the SGP 

test under monotonic loading.

Task 3: Develop a simplified analytical model, referred to as the simplified 

preloading-reloading (SPR) model, for estimating deformation of a preloaded GRS 

mass. The SPR model consists of two principal modules: a load-transfer module and 

a deformation module. The load-transfer module is based on the elastic analysis of an 

idealized plane-strain GRS mass. The load-transfer module can be used to calculate 

the average stresses in a GRS mass. The deformation module can be used to calculate 

the vertical and horizontal deformations of a GRS mass based on the average stresses 

from the load-transfer module. The SPR model was verified by the results of 

experimental tests and numerical analysis of the APSR test and by the results of the 

SGP tests conducted in this study. 
261

Task 4: Examine the correlations between the SGP test and preloaded GRS structures. 

The correlations were made with normalized loads and normalized displacements, 

referred to as the vertical and horizontal improvement factors (VIR and HIR). Two 

full-scale GRS structures, the FHWA pier and the Black Hawk abutments, and 

corresponding SGP tests were used to examine the correlations.

8.2 Findings and Conclusions

The findings and conclusions of this study are organized into four groups, 

namely: (1) laboratory tests of soils, geosynthetics, and interfaces, (2) SGP tests and 

finite element analysis, (3) the simplified preloading-reloading (SPR) model, and (4) 

correlations between SGP test and preloaded GRS structures.

(1) Laboratory Tests of Soils, Geosynthetics, and Interfaces

1. The stiffness of the soils increased as a result of preloading. The reloading 

stiffness was found to depend on the confining pressure and the unloading load 

level. At the same confining pressure, the reloading stiffness of the RL-PS path 

was higher than in the RL-Z path. The RL-Z path was a reloading path that 

initiated from a zero-load level, whereas the RL-PS path was a reloading path that 

initiated from a prestressed load level.

2. The stiffness of the preloaded geosynthetic specimen was higher than that of the 

corresponding virgin specimen, provided that the preloading load level was less 

than about 50% of the ultimate tensile strength. The reloading stiffness reduced 

with increasing preloading load level.

3. The reloading stiffness of the preloaded interface was higher than that of the 

interface without preloading. The reloading stiffness of the interface increased 

with normal stress applied on the interface.

4. The preloading did not affect the shear strength of the soils or the interfaces.

5. The tensile strength of the preloaded geosynthetic specimen was only about 5% 

lower than that of the corresponding virgin specimen.

(2) SGP Tests and Finite Element Analysis

(A) Monotonic-Loading SGP Tests 

1. Due to the reinforcing effects imposed by the reinforcement, a soil mass with 

reinforcement had higher stiffness and strength than without reinforcement. The 

stiffness of the soil mass with reinforcement was about 30% higher than without 

reinforcement.

2. Some vertical and horizontal deformations were required to mobilize the 

reinforcing effects. Before the reinforcing effect was fully mobilized, the soil 

mass with and without reinforcement showed comparable deformations. For the 

Road Base soil mass with or without reinforcement, the required vertical and 

horizontal displacements to fully mobilize the reinforcing effect were 2.0 mm and 

0.5 mm, respectively. 
262

(B) Unloading-Reloading SGP Tests

1. With preloading, the stiffness of the GRS mass increased significantly. For the 

GRS mass comprising the Ottawa sand and Amoco 2044 geotextile 

reinforcement, the stiffness increased by factors of 3 to 7 in the vertical direction, 

and about 7 in the horizontal direction. For the GRS mass comprising the Road 

Base soil and Amoco 2044 geotextile reinforcement, the stiffness increased by 

factors of 2 to 5 in the vertical direction, and about 3 in the horizontal direction.

2. The magnitude of the preloading load level did not appear to affect the reloading 

stiffness except at the initial stage of the reloading path. During the initial stage 

of the reloading path, the rebounding deformation continued if the test specimen 

was unloaded from a high preloading load level to a zero-load level. Similar 

rebounding deformation behavior was also observed in the FHWA pier after 

unloading had completed.

3. The RL-PS path showed higher vertical reloading stiffness than the RL-Z path. 

The vertical reloading stiffness increased with increasing prestressed load level. 

In the horizontal direction, the RL-Z and RL-PS paths showed comparable 

horizontal reloading stiffness.

4. The unloading and reloading curves of the multiple unloading-reloading at 

working load levels nearly coincided with one another. This behavior was also 

observed in the FHWA pier and the Black Hawk abutments.

5. The reinforcing effect was insignificant during the reloading path.

6. Preloading did not appear to affect the load carrying capacity of the GRS mass.

(C) Finite Element Analysis

1. The presence of the reinforcement layers in the soil mass altered the horizontal 

and shear stress distributions but not the vertical stress distribution. 

2. The horizontal and shear stresses increased significantly near the reinforcement 

and resulted in an increase of the minor principal stress. With the increasing 

minor principal stress, the deformation stiffness and shear strength of the soil 

were subsequently increased. The reinforcing effect, as quantified by the increase 

of the minor principal stress, was largest near the reinforcement and reduced with 

the increasing distance from the reinforcement.

(3) Simplified Preloading-Reloading (SPR) Model

1. The SPR model is capable of predicting experimental and numerical analysis 

results of the APSR test and the SGP test conducted in this study. Although 

further verification is still needed, the SPR model appears to be a simple and valid 

tool for estimating the deformation of GRS masses.

2. The parametric study carried out by the SPR model showed that the vertical 

displacement of the GRS mass was significantly reduced by increasing the soil 

stiffness. The effect of increasing the reinforcement stiffness was much smaller, 

whereas the effect of the interface stiffness was negligible. This finding supports 
263

the benefits of employing a preloading technique in reducing post-construction 

settlement of GRS structures.

(4) Correlations Between SGP Test and Preloaded GRS Structures

1. The vertical and horizontal improvement ratios (VIR and HIR) from the SGP test 

correlated quite well with those of the FHWA pier despite the large differences in 

the geometry and boundary conditions between them. The difference in VIR and 

HIR from the SGP test and the FHWA pier was within 10%. In the Black Hawk 

abutments, the SGP tests and the SPR model gave about 40% lower VIR values 

than the VIR from the measured data. The difference is believed to be due to the 

uncertainty in the placement density and moisture of the backfill in the abutments.

2. The degree of reduction in the settlement due to preloading of GRS structures 

may be assessed with reasonable accuracy by conducting a SGP test or simply 

using the SPR model. Additional validation is still needed as more reliable fieldmeasured data of preloaded GRS structures become available. 

8.3 Recommendations

1. Effects of preloading on creep deformation of GRS structures should be 

investigated. Accelerated creep tests of a generic GRS mass can be conducted by 

the SGP test in an elevated temperature incubator, as demonstrated by Ketchart 

and Wu (1996). It was observed in the FHWA pier that preloading reduced the 

creep deformation in the subsequent loading paths (Adams, 1997). Tatsuoka et 

al. (1997) also reported the reduction of creep deformation in the full-scale test of 

preloaded GRS walls. A systematic study on creep deformation is needed.

2. The SPR model should be further evaluated with different types of soils and 

geosynthetics. The strain-rate dependent properties of some geosynthetics and the 

soil model that can account for creep and stress-induced anisotropy may be 

incorporated in the SPR model.
264

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