Pham Thang Investigating Composite Behavior of Geosynthetic Reinforced Soil Mass Thesis

INVESTIGATING COMPOSITE BEHAVIOR OF GEOSYNTHETIC-

REINFORCED SOIL (GRS) MASS

by

Thang Quyet Pham

B.S., Hanoi University of Civil Engineering, 1993

M.S., Hanoi University of Civil Engineering, 2001

A thesis submitted to the

University of Colorado Denver

In partial fulfillment

of the requirements for the degree of

Doctoral of Philosophy

Civil Engineering

2009

Thang Quyet Pham (Ph.D., Civil Engineering)

“Investigating Composite Behavior of Geosynthetic-Reinforced Soil (GRS) Mass”

Thesis directed by Professor Jonathan T. H. Wu

ABSTRACT

A study was undertaken to investigate the composite behavior of a Geosynthetic

Reinforced Soil (GRS) mass. Many studies have been conducted on the behavior

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

geosynthetic reinforcement in a GRS mass has not been fully elucidated. Current

design methods consider the reinforcement in a GRS structure as “tiebacks” and

adopt a design concept the reinforcement strength, Tf, and reinforcement spacing,

Sv, have the same effects on the performance of a GRS structure. This has

encouraged the designers to use stronger reinforcement at larger spacing, as the

use of larger spacing will generally reduce time and effort in construction.

A series of large-size Generic Soil-Geosynthetic Composite (GSGC) tests were

designed and conducted in the course of this study to examine the behavior of

GRS mass under well-controlled conditions. The tests clearly demonstrated that

reinforcement spacing has a much stronger effect on the performance of GRS

mass than reinforcement strength. An analytical model was established to

describe the relative contribution of reinforcement strength and reinforcement

spacing. Based on the analytical model, equations for calculating the apparent

cohesion of a GRS composite, the ultimate load carrying capacity of a reinforced

DEDICATION

This thesis is dedicated to my loving parents, Lam Van Pham and Khoi

Thi Pham, who have continuously given me unlimited support in achieving all my

life goals.

ACKNOWLEDGMENTS

I would like to express my most sincere gratitude to my thesis advisor,

Professor Jonathan T.H. Wu, for his dedicated support and guidance throughout

the course of this study. His clear insight of the subject has made my study both a

great learning experience and a joy. I also wish to thank members of my thesis

committee, Professors Hon-Yim Ko, John McCartney, Brian Brady, and Ronald

Rorrer for their helpful comments.

A special thank-you is extended to Michael Adams of the Federal

Highway Administration for his enthusiastic assistance and expert technical

support of the GSGC tests. My gratitude also goes to Jane Li and Thomas Stabile

for their help with the GSGC tests. Without their help, I could not have

conducted five successful tests during my three-month stay at the Turner-Fairbank

Highway Research Center in McLean, Virginia.

I truly appreciate the help of a dear brother and a loyal partner, Dr. Sang

Ho Lee, a visiting professor from Kyungpook National University, South Korea,

who helped me with all my experiments, including those I conducted at the

Turner-Fairbank Highway Research Center.

Last but not least, I would like to thank my wife Thuy Vu and our three

young daughters for standing by me and for encouraging me every step of the

way.

I feel blessed to have all these nice people around me in the course of this

study. Without them, this thesis would not be a reality.

CONTENTS

Figures.......................................................................................................................... xi

Tables ...................................................................................................................... xviii

Chapter

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

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

1.2 Research Objectives ...........................................................................................4

1.3 Tasks of research ................................................................................................5

2. Literature Review...............................................................................................9

2.1 Mechanics of Reinforced Soil ............................................................................9

2.2 Composite Behavior of GRS Mass ..................................................................15

2.3 Compaction-Induced Stresses in an Unreinforced Soil Mass ..........................27

2.3.1 Lateral Earth Pressure Estimation by Rowe (1954) .........................................27

2.3.2 Stress Path Theory by Broms (1971) and Extension of Broms’ Work by Ingold (1979) ...................................................................................................31

2.3.3 Finite Element Analysis by Aggour and Brown (1974) ..................................36

2.3.4 Compaction-Induced Stress Models by Seed (1983) .......................................40

2.4 Compaction-Induced Stresses in a Reinforced Soil Mass ...............................62

2.4.1 Ehrlich and Mitchell (1994) .............................................................................62

2.4.2 Hatami and Bathurst (2006) .............................................................................65

2.4.3 Morrison et al. (2006) ......................................................................................66

2.5 Highlights on Compaction-Induced Stresses ...................................................68

3. Analytical Model for Calculating Lateral Displacement of a GRS Wall with Modular Block Facing .....................................................................................71

3.1 Review of Existing Methods for Estimating Maximum Wall Movement .......73

3.1.1 The FHWA Method (Christopher et al., 1989) ................................................74

3.1.2 The Geoservices Method (Giroud, 1989) ........................................................76

vii

3.1.3 The CTI Method (Wu, 1994) ...........................................................................77

3.1.4 The Jewell-Milligan Method ............................................................................78

3.2 Developing an Analytical Model for Calculating Lateral Movement and Connection Forces of a GRS Wall ...................................................................84

3.2.1 Lateral Movement of GRS Walls with Negligible Facing Rigidity ................85

3.2.2 Connection Forces for GRS walls with Modular Block Facing ......................87

3.2.3 Lateral Movement of GRS Walls with Modular Block Facing .......................92

3.3 Verification of Analytical Model .....................................................................93

3.3.1 Comparisons with the Jewell-Milligan Method for Lateral Wall Movement ..93

3.3.2 Comparisons of with Measured Data of Full-Scale Experiment by Hatami and Bathurst (2005 and 2006).................................................................................99

3.4 Summary ......................................................................................................103

4. The Generic Soil-Geosynthetic Composite (GSGC) Tests ............................104

4.1 Dimension of the Plane Strain GSGC Test Specimen ...................................104

4.2 Apparatus for Plane Strain Test .....................................................................119

4.2.1 Lateral Deformation .......................................................................................119

4.2.2 Friction ...........................................................................................................119

4.3 Test Material ..................................................................................................121

4.3.1 Backfill ...........................................................................................................121

4.3.2 Geosynthetics .................................................................................................128

4.3.3 Facing Block ..................................................................................................132

4.4 Test Program ..................................................................................................133

4.5 Test Conditions and Instrumentation .............................................................134

4.5.1 Vertical Loading System ................................................................................134

4.5.2 Confining Pressure .........................................................................................134

4.5.3 Instrumentation ..............................................................................................134

4.5.4 Preparation of Test Specimen for GSGC Tests .............................................143

4.6 Test Results ....................................................................................................163

4.6.1 Test 1-Unreinforced Soil ................................................................................163

4.6.2 Test 2-GSGC Test (T, Sv) ..............................................................................169

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4.6.3 Test 3-GSGC Test (2T, 2Sv) ..........................................................................187

4.6.4 Test 4-GSGC Test (T, 2Sv) ............................................................................199

4.6.5 Test 5-GSGC Test (unconfined with T, Sv) ...................................................211

4.7 Discussion of the Results ...............................................................................224

4.7.1 Effects of Geosynthetic Inclusion (Comparison between Tests 1 and 2) ......224

4.7.2 Relationship between Reinforcement Spacing and Reinforcement Strength (Comparison between Tests 2 and 3) .............................................................226

4.7.3 Effects of Reinforcement Spacing (Comparison between Tests 2 and 4) .....228

4.7.4 Effects of Reinforcement Strength (Comparison between Tests 3 and 4) .....230

4.7.5 Effects of Confining Pressure (Comparison between Tests 2 and 5) ............231

4.7.6 Composite Strength Properties ......................................................................233

5. Analytical Models for Evaluating CIS, Composite Strength Properties of a GRS Composite, and Required Reinforcement Strength ...............................235

5.1 Evaluating CIS in a GRS Mass ......................................................................236

5.1.1 Conceptual Model for Simulation of Fill Compaction of a GRS Mass .........236

5.1.2 A Simplified Model to Simulate Fill Compaction of a GRS Mass ................237

5.1.3 Model Parameters of the Proposed Compaction Simulation Model ..............239

5.1.4 Simulation of Fill Compaction Operation ......................................................241

5.1.5 Estimation of K2,c ...........................................................................................246

5.2 Strength Properties of GRS Composite .........................................................250

5.2.1 Increase Confining Pressure ..........................................................................251

5.2.2 Apparent Cohesion and Ultimate Pressure Carrying Capacity of a GRS Mass ...............................................................................................................257

5.3 Verification of the Analytical Model with Measured Data ...........................258

5.3.1 Comparison between the Analytical Model and GSGC Test Results............258

5.3.2 Comparison between the Analytical Model and Elton and Patawaran’s Test Data ...............................................................................................................261

5.3.3 Comparison of the Results between the Analytical Model and Finite Element Results ............................................................................................................266

5.4 Required Reinforcement Strength in Design .................................................268

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5.4.1 Proposed Model for Determining Reinforcement Force ...............................268

5.4.2 Comparison of Reinforcement Strength between the Analytical Model and Current Design Equation................................................................................270

5.4.3 Verification of the Analytical Model for Determining Reinforcement Strength ..........................................................................................................271

6 Finite Element Analyses ................................................................................275

6.1 Brief Description of Plaxis 8.2 .......................................................................275

6.2 Compaction-Induced Stress in a GRS Mass ..................................................278

6.3 Finite Element Simulation of the GSGC Tests ..............................................280

6.3.1 Simulation of GSGC Test 1 ...........................................................................287



6.4 FE Analysis of GSGC Test 2 under Different Confining Pressures and Dilation Angle of Soil-Geosynthetic Composites ..........................................300

6.5 Verification of Compaction-Induced Stress Model .......................................302

7. Summary, Conclusions and Recommendations .............................................308

7.1 Summary ........................................................................................................308

7.2 Findings and Conclusions ..............................................................................309

Appendix A ...............................................................................................................311

Appendix B ...............................................................................................................345

References ..................................................................................................................349

x

LIST OF FIGURES

Figure

1.1 Typical Cross-Section of a GRS Wall with Modular Block Facing ..................8

2.1 Concept of Apparent Cohesion due to the Presence of Reinforcement (Scholosser and Long, 1972) .........................................................................10

2.2 Concept of Apparent Confining Pressure due to the Presence of Reinforcement (Yang, 1972) ...........................................................................11

2.3 Strength Envelopes for Sand and Reinforced Sand (Mitchell and Villet, 1987) ................................................................................................................14

2.4 Triaxial Compression Tests (Broms, 1977) .....................................................16

2.5 Reinforced Triaxial Test Specimen (Elton and Patawaran, 2005) ...................17

2.6 Stress-Strain Curves of Samples Reinforced at Spacing of 12 in. and 6 in. in Large-Size Unconfined Compression Tests (Elton and Patawaran, 2005) ................................................................................................................18

2.7 Mini Pier Experiments (Adams, 1997) ............................................................19

2.8 Stress-Strain Curve (Adams, et al., 2007)........................................................20

2.9 Test Set-up of Large Triaxial Tests with 1,100 mm High and 500 mm in Diameter (Ziegler, et al., 2008) ........................................................................21

2.10 Large-Size Triaxial Test Results (Ziegler, et al., 2008) ...................................22

2.11 Vertical Stress Distribution at 6-kN Vertical Load of the GRS Masses with and without Reinforcement (Ketchart and Wu, 2001) .....................................24

2.12 Horizontal Stress Distribution at 6-kN Vertical Load of the GRS Masses with and without Reinforcement (Ketchart and Wu, 2001) .............................25

2.13 Shear Stress Distribution at 6-kN Vertical Load the GRS Masses with and without Reinforcement (Ketchart and Wu, 2001) ...........................................26

2.14 Schematic Illustration of Rowe’s Theory (Rowe, 1954) .................................29

2.15 Results of the Two-Directional Direct Shear Tests (Rowe, 1954) ..................30

2.16 Hypothetical Stress Path during Compaction (Broms, 1971) ..........................32

2.17 Residual Lateral Earth Pressure Distribution (Broms, 1971) ..........................34

xi

2.18 Hypothetical Stress Path of Shallow and Deep Soil Elements (Broms, 1971) ................................................................................................................35

2.19 A Sample Problem Analyzed by Aggour and Brown (1974) ..........................39

2.10 The First-Cycle K0-Reloading Model (Seed, 1983) ........................................41

2.21 Suggested Relationship between sinφ’ and α (Seed, 1983) .............................42

2.22 Typical K0-Reloading Stress Paths (Seed, 1983) .............................................43

2.23 K0-Unloading following Reloading (Seed, 1983) ............................................45

2.24 Unloading after Moderate Reloading (Seed, 1983) .........................................47

2.25 Basic Components of the Non-Linear K0-Loading/Unloading Model (Seed, 1983) ................................................................................................................49

2.26 Profile of against a Vertical Wall for a Single Drum Roller (Seed, 1983) ................................................................................................................50

',, pvchσΔ

2.27 Stress Path Associated with Placement and Compaction of a Typical Layer of Fill (Seed, 1983) ..........................................................................................51

2.28 Bi-Linear Approximation of Non-Linear K0-Unloading Model (Seed, 1983) ................................................................................................................52

2.29 Relationship between K2 and F in the Bi-Linear Unloading Model (Seed, 1983) ................................................................................................................52

2.30 Relationship between K3 and β 3 in the Bi-Linear Model (Seed, 1983) .........53

2.31 Basic Components of the Bi-Linear Model (Seed, 1983) ................................55

2.32 Compaction Loading/Unloading Cycles in the Bi-Linear Model (Seed, 1983) ................................................................................................................57

2.33 An Example Problem for Hand Calculation of Peak Vertical Compaction Profile (Seed, 1983) .........................................................................................60

2.34 Solution Results from the Bi-Linear Model and Non-Linear Model (Seed, 1983) ................................................................................................................61

2.35 Assumed Stress Path (Ehrlich and Mitchell, 1994) .........................................63

2.36 Compaction and Reinforcement Stiffness Typical Influence ..........................65

2.37 FE Model for FE Analysis (Morrison, et al., 2006) .........................................67

3.1 Basic Components of a GRS Wall with a Modular Block Facing ...................73

xii

3.2 Empirical Curve for Estimating Maximum Wall Movement during Construction in the FHWA Method (Christopher, et al., 1989) ......................75

3.3 Assumed Strain Distribution in the Geoservices Method ................................77

3.4 Stress Characteristics and Velocity Characteristics behind a Smooth Retaining Wall Rotating around the Toe (Jewell and Milligan, 1989) ............79

3.5 Major Zones of Reinforcement Forces in a GRS Wall and the Force Distribution along reinforcement with Ideal Length (Jewell and Milligan, 1989) ................................................................................................................80

3.6 Charts for Estimating Lateral Displacement of GRS Walls with the Ideal Layout (Jewell and Milligan, 1989) .................................................................83

3.7 Major Zones of Reinforcement Forces in a Reinforces Soil Wall (Jewell and Milligan, 1989) ..........................................................................................85

3.8 Forces acting on Two Facing Blocks at Depth zi .............................................88

3.9 Connection Forces in Reinforcement (q = 0) ...................................................91

3.10 Connection Forces in Reinforcement (q = 50) .................................................91

3.11 Comparison of Lateral Displacement Calculated by Jewell-Milligan Method and the Analytical Model, 0=bγ ......................................................95

3.12 Comparison of Lateral Displacement Calculated by Jewell-Milligan Method and the Analytical Model, 10=bγ ....................................................96



3.15 Configuration of a Full-Scale Experiment of a GRS Wall with Modular Block Facing (Hatami and Bathurst, 2005 and 2006)....................................100

3.16 Comparisons of Measured Lateral Displacement with Jewell-Milligan Method and the Analytical Model .................................................................102

4.1 Typical Geometric and Loading Conditions of a GRS Composite................107

4.2 Global Stress-Strain Curves for Soil-Geosynthetic Composites of Different Dimensions under a Confining Pressure of 0 kPa .........................................109

4.3 Global Volume Change Curves for Soil-Geosynthetic Composites of Different Dimensions under a Confining Pressure of 0 kPa ..........................110

xiii

4.4 Global Stress-Strain Curves for Soil-Geosynthetic Composites of Different Dimensions under a Confining Pressure of 30 kPa .......................................111

4.5 Global Volume Change Curves for Soil-Geosynthetic Composites of Different Dimensions under a Confining Pressure of 30 kPa ........................112

4.6 Global Stress-Strain Curves of the Unreinforced Soil under a Confining Pressure of 30 kPa ..........................................................................................114

4.7 Global Volume Change Curves of the Unreinforced Soil under a Confining Pressure of 30 kPa ..........................................................................................115

4.8 Specimen Dimensions for the GSGC Tests ...................................................116

4.9 Front View of the Test Setup .........................................................................117

4.10 Plan View of the Test Setup...........................................................................118

4.11 The Test Bin ...................................................................................................120

4.12 Grain Size Distribution of Backfill ................................................................124

4.13 Typical Triaxial Test Specimen before and after Test ...................................125

4.14 Triaxial Test Results ......................................................................................126

4.15 Mohr-Coulomb Failure Envelops of Backfill ................................................127

4.16 Uni-Axial Tension Test of Geotex 4x4 ..........................................................130

4.17 Load-Deformation Curves of the Geosynthetics ...........................................132

4.18 Locations of LVDTs and Digital Dial Indicator ............................................136

4.19 Strain Gauges on Geotext 4x4 Geotextile ......................................................138

4.20 Strain Gauges Mounted on Geotex 4x4 Geotextile .......................................139

4.21 Calibration Curve for Single-Sheet Geotex 4x4 ............................................141

4.22 Calibration Curve for Double-Sheet Geotex 4x4 ...........................................142

4.23 Applying Grease on Plexiglass Surfaces .......................................................145

4.24 Attaching Membrane .....................................................................................146

4.25 Placement of the First Course of Facing Block .............................................147

4.26 Compaction of the First Lift of Backfill ........................................................148

4.27 Placement of Backfill for the Second Lift .....................................................149

4.28 Placement of a Reinforcement Sheet .............................................................150

xiv

4.29 Completion of Compaction of the Composite Mass and Leveling the Top Surface with 5 mm-thick Sand Layer ............................................................151

4.30 Completed Composite Mass with a Geotextile Sheet on the Top Surface ....152

4.31 Covering the Top Surface of the Composite Mass with a Sheet of Membrane ......................................................................................................153

4.32 Removing Facing Blocks and Trimming off Excess Geosynthetic Reinforcement ................................................................................................154

4.33 Insertion of the Strain Gauge Cables though Membrane Sheet .....................155

4.34 Vacuuming the Composite Mass with a Low Pressure .................................156

4.35 Sealing the Connection between Cable and Membrane with Epoxy to Prevent Air Leaks ..........................................................................................157

4.36 Checking Air Leaks under Vacuuming ..........................................................158

4.37 The LVDTs on an Open Side of Test Specimen ............................................159

4.38 Location of Selected Points to Trace Internal Movements of Tests ..............160

4.39 Soil Dry Unit Weight Results during Specimen Preparation of Five GSGC Tests ...............................................................................................................161

4.40 Soil Mass at Failure of Test 1 ........................................................................164

4.41 Results of Test 1-Unreinforced Soil Mass .....................................................165

4.42 Lateral Displacements on the Open Face of Test 1 .......................................166

4.43 Internal Displacements of Test 1 ...................................................................167

4.44 Composite Mass at Failure of Test 2 .............................................................170

4.45 Close-up of Shear Bands at Failure of Area A in Figure 4.44 .......................171

4.46 Failure Planes of the Composite Mass after Testing in Test 2 ......................172

4.47 Results of Test 2-Reinforced Soil Mass .........................................................173



4.50 Locations of Strain Gauges Geosynthetic Sheets in Test 2 ...........................178

4.51 Reinforcement Strain Distribution of the Composite Mass in Test 2 ............179

4.52 Aerial View of the Reinforcement Sheets Exhumed from the Composite Mass after Test 2 ............................................................................................184

4.53 Location of Rupture Lines of Reinforcement in Test 2 .................................185

xv

4.54 Composite Mass after Testing of Test 3 ........................................................189

4.55 Global Stress-Strain Relationship of Test 3 ...................................................190















4.70 Composite Mass after Failure of Test 5 .........................................................213



4.73 Lateral Displacements on the Open Face of Test ..........................................216






5.1 Conceptual Stress Path for Compaction of a GRS Mass ...............................237

xvi

5.2 Stress Path of the Proposed Simplified Model for Compaction of a GRS Mass ...............................................................................................................238

5.3 Locations of Compaction Loads and Stress Paths during Compaction at Depth a along Section I-I as Compaction Loads Moving toward Section I-I....................................................................................................................243

5.4 Locations of Compaction Loads and Stress Paths during Compaction at Depth a along Section I-I as Compaction Loads Moving away from Section I-I....................................................................................................................244

5.5 Stress Path at Depth a when Subject to Multiple Compaction Passes ...........245

5.6 Stress Path of the Proposed Model for Fill Compaction of a GRS Mass ......246

5.7 Concept of Apparent Confining Pressure and Apparent Cohesion of a GRS Composite ......................................................................................................250

5.8 An Ideal Plane-Strain GRS Mass for the SPR Model....................................254

5.9 Equilibrium of Differential Soil and reinforcement Elements .......................254

5.10 Reinforced Soil Test Specimen before Testing (Elton and Patawanran, 2005) ..............................................................................................................262

5.11 Backfill Grain Size Distribution before and after Large-Size Triaxial Tests (Elton and Patawanran, 2005) ........................................................................263

5.12 Large-Size Triaxial Test Results (Elton and Patawanran, 2005) ...................263

6.1 Distribution of Residual Lateral Stresses of a GRS mass with Depth due to Fill Compaction .............................................................................................279

6.2 Comparison of Results for GSGC Test 1 .......................................................288

6.3 Comparison of Lateral Displacement at Open Face of GSGC Test 1 ...........289

6.4 Comparison of Global Stress-Strain Relationship of GSGC Test 2 ..............291


6.6 Comparison of Internal Displacements of GSGC Test 2 ...............................293

6.7 Comparison of Reinforcement Strains of GSGC Test 2 ................................294

6.8 Comparison of Global Stress-Strain Relationship of GSGC Test 3 ..............296


6.10 Comparison of Internal Displacements of GSGC Test 3 ...............................298

6.11 Comparison of Reinforcement Strains of GSGC Test 3 ................................299

6.12 FE analyses of Test 2 with Different Confining Pressures ............................301

xvii

6.13 FE Mesh to Simulate CIS of a Reinforced Soil Mass ....................................304

6.14 Lateral Stress Distribution of a GRS Mass from FE Analyses ......................305

6.15 Comparison of Residual Lateral Stresses of a GRS Mass due to Fill Compaction between FE Analyses and Analytical Model ............................306

6.16 Comparison of Residual Lateral Stresses of a GRS Mass due to Fill Compaction between FE Analyses with Coarse Mesh and Analytical Model .............................................................................................................307

xviii

LIST OF TABLES

Table

2.1 Properties of material for the mini pier experiments (Adams, et al., 2007) ....19

2.2 None-Linear K0-loading/unloading model parameters (Seed, 1983) ..............48

2.3 Bi-Linear K0-loading/unloading model parameters (Seed, 1983) ...................54

4.1 Conditions and properties of material used in FE analyses ...........................108

4.2 Summary of some index properties of backfill ..............................................123

4.3 Summary of Geotex 4x4 properties ...............................................................128

4.4 Properties of Geotex 4x4 in fill-direction ......................................................131

4.5 Test program form the GSGC Tests ..............................................................133

4.6 Dimensions of the GSGC Test Specimens before Testing ............................162

4.7 Some Test Results for Test 1 .........................................................................168





4.12 Comparison between Test 1 and Test 2 .........................................................225

4.13 Comparison between Test 2 and Test 3 with the same Tf/Sv ratio .................227




4.17 Comparison of strength properties of five GSGC Tests ...............................234

5.1 Model parameters for the proposed compaction simulation model ...............240

5.2 Values of factor r under different applied pressure and reinforcement lengths ............................................................................................................256

5.3 Comparison of the results between the analytical model and the GSGC tests ................................................................................................................259

xix

xx

5.4 Comparison of the results between Schlosser and Long’s method and GSGC tests ................................................................................................................260

5.5 Comparison of the results between the analytical model and Elton and Patawaran’s tests (2005) ................................................................................264

5.6 Comparison of the results between Schlosser and Long’s method and Elton and Patawaran’s tests (2005) .........................................................................265

5.7 Comparison of the results between the analytical model and the FE results for GSGC Test 2 ..................................................................................................267

5.8 Comparison of reinforcement forces between proposed model and current design equation for a GRS wall .....................................................................272

5.9 Comparison of reinforcement forces between proposed model and the GSGC tests ................................................................................................................273

5.10 Comparison of reinforcement forces between proposed model and test data from Elton and Patawaran (2005) ..................................................................274

6.1 Parameters and properties of the GSGC Tests used in analyses ....................282

6.2 The steps of analysis for the GSGC Tests .....................................................284

1. INTRODUCTION

1.1 Problem Statement

Over the past two decades, Geosynthetic-Reinforced Soil (GRS) structures, including

retaining walls, slopes, embankments, roadways, and load-bearing foundations, have

gained increasing popularity in the U.S. and abroad. In actual construction, GRS

structures have demonstrated a number of distinct advantages over their conventional

counterparts. GRS structures are generally more ductile, more flexible (hence more

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

permeability backfill, easier to construct, require less over-excavation, and more

economical than conventional earth structures (Wu, 1994; Holtz, et al., 1997;

Bathurst, et al., 1997).

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

applications than other types of reinforced soil structures. A GRS wall comprises two

major components: a facing element and a geosynthetic-reinforced soil mass. Figure

1.1 shows the schematic diagram of a typical GRS wall with modular block facing.

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

different materials. The other component of a GRS wall, a geosynthetic-reinforced

soil mass, however, is always a compacted soil mass reinforced by layers of

geosynthetic reinforcement.

It is a well-known fact that soil is weak in tension and relatively strong in

compression and shear. In a reinforced soil, the soil mass is reinforced by

1

incorporating an inclusion (or reinforcement) that is strong in tensile resistance.

Through soil-reinforcement interface bonding, the reinforcement restrains lateral

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

for dilation, and consequently increases the stiffness and strength of the soil mass.

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

interactive behavior between soil and reinforcement in a GRS mass has not been fully

elucidated. This has resulted in design methods that are fundamentally deficient in a

number of aspects (Wu, 2001). Perhaps the most serious deficiency with the current

design methods is that they ignore the composite nature of the reinforced soil mass,

and simply consider the reinforcement as “tiebacks” that are being added to the soil

mass. In current design methods, the reinforcement strength is determined by

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

at-rest pressure that is assumed to be unaffected by the configuration of the

reinforcement. Specifically, the design strength of the reinforcement, Τrequired, has

been determined by multiplying an assumed lateral earth pressure at a given depth,

σh, by a prescribed value of reinforcement spacing, Sv, and a safety factor, Fs, i.e.,

svhrequired FST ∗∗= σ (1.1)

Equation 1.1 implies that, as along as the reinforcement strength is kept linearly

proportional to the reinforcement spacing, all walls with the same σh (i.e., walls of a

given height with the same backfill that is compacted to the same density) will behave

the same. In other words, a GRS wall with reinforcement strength of T at spacing Sv

will behave the same as one with reinforcement strength of 2*T at twice the spacing

2*Sv. Note that Equation 1.1 has very important practical significance. It has

encouraged designers to use stronger reinforcement at larger spacing, because the use

2

of larger spacing will generally reduce time and effort in construction.

A handful of engineers, however, have learned from actual construction that Equation

1.1 cannot be true. They realized that reinforcement spacing appears to play a much

greater role than reinforcement strength in the performance of a GRS wall.

Researchers at the Turner-Fairbank Highway Research Center have conducted a

series of full-scale experiments (Adams, 1997; Adams, et al., 2007) in which a weak

reinforcement at small spacing and a strong reinforcement (with several times the

strength of the weak reinforcement) at twice the spacing were load-tested. The

former was found to be much stronger than the latter. An in-depth study on the

relationship between reinforcement spacing and reinforcement stiffness/strength

regarding their effects on the behavior of a GRS mass is of critical importance to the

design of GRS structures and is urgently needed.

The effects of CIS in unreinforced soil masses and earth structures have been the

subject of study by many researchers, including Rowe (1954), Broms (1971), Aggour

and Brown (1974), Seed (1983), and Duncan, et al. (1984, 1986, 1991, and 1993).

These studies indicated that the CIS would increase significantly the lateral stresses in

soil (also known as the “locked-in” lateral stresses or “residual” lateral stresses),

provided that there was sufficient constraint to lateral movement of the soil during

compaction. The increase in lateral stresses will increase the stiffness and strength of

the compacted soil mass.

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

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

bonding between the soil and reinforcement will increase the degree of restraint to

lateral movement of the soil mass during fill compaction. With greater restraint to

lateral movement, the resulting locked-in lateral stresses are likely to become larger.

3

In numerical analysis of earth structures, the effects of CIS has either been overly

simplified (e.g., Katona, 1978; Hatami and Bathurst, 2005 and 2006; Morrison, et al.,

2006), or in most other studies, totally neglected. In the case of GRS walls, failure to

account for the CIS may be a critical culprit that has lead to the erroneous conclusion

by many numerical studies that Equation 1.1 is valid. Evaluation of compaction-

induced stresses in GRS structures is considered a very important issue in the study of

GRS structures.

In addition, GRS walls with modular block facing is rather “flexible”, hence the

design of these structures should consider not only the stresses in the GRS mass, but

also the deformation. Jewell-Milligan method (1989), recognized as the best

available method for estimating lateral movement of GRS walls applies only to walls

with little or no facing resistance. With increasing popularity of GRS walls with

modular block facing where facing rigidity should not be ignored, an improvement

over the Jewell-Milligan method for calculating lateral wall movement is needed.

1.2 Research Objectives

The objectives of this study were four-fold. The first objective was to investigate the

composite behavior of GRS masses with different reinforcing configurations. The

second objective was to examine the relationship between reinforcement strength and

reinforcement spacing regarding their effects on the behavior of a GRS mass. The

third objective was to develop an analytical model for evaluation of compaction-

induced stresses in a GRS mass. The fourth objective was to develop an analytical

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

4

1.3 Tasks of Research

To achieve the research objectives outlined above, the following tasks were carried

out in this study:

Task 1: Reviewed previous studies on: (a) composite behavior of a GRS mass, (b)

compaction-induced stresses in a soil mass, and (c) reinforcing mechanism

of GRS structures.

Previous studies on composite behavior of a GRS mass were reviewed. The

review included theoretical analyses and experimental tests. Compaction-

induced stresses in an unreinforced soil mass that have been undertaken by

different researchers were also reviewed, including simulation models for

fill compaction. In addition, a literature study on reinforcing mechanisms of

GRS structures was conducted.

Task 2: Developed a hand-computation analytical model for simulation of

compaction-induced stresses in a GRS mass.

An analytical model for simulation of Compaction-Induced Stresses (CIS) in

a GRS mass was developed. The compaction model was developed by

modifying an existing fill compaction simulation model for unreinforced

soil. The model allows compaction-induced stress in a GRS mass to be

evaluated by hand computations. The CIS was implemented into a finite

element computer code for investigating performance of GRS structures.

Task 3: Developed an analytical model for the relationship between reinforcement

strength and reinforcement spacing, and derived an equation for calculating

composite strength properties.

An analytical model for the relationship between reinforcement strength and

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

5

stress concept for GRS mass (Ketchart and Wu, 2001), an equation for

calculating the composite strength properties of a GRS mass was derived.

The model represents a major improvement over the existing model that has

been used in current design methods, and more correctly reflects the role of

reinforcement spacing versus reinforcement strength on the behavior of a

GRS mass. The equation allows the strength properties of a GRS mass to be

evaluated by a simple method.

Task 4: Designed and conducted laboratory experiments on a generic soil-

geosynthetic composite to investigate the performance of GRS masses with

different reinforcing conditions.

A generic soil-geosynthetic composite (GSGC) plane strain test was

designed by considering a number of factors learned from previous studies.

A series of finite element analyses were performed to determine the

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

change behavior representative of a very large soil-geosynthetic composite

mass. Five GSGC tests with different reinforcement strength, reinforcement

spacing, and confining pressure were conducted. These tests allow direct

observation of the composite behavior of GRS mass in various reinforcing

conditions. They also provide measured data for verification of analytical

and numerical models, including the models developed in Tasks 2 and 3, for

investigating the behavior of a GRS mass.

Task 5: Performed finite element analyses to simulate the GSGC tests and analyze

the behavior of GRS mass.

Finite element analyses were performed to simulate the GSGC tests

conducted in Task 4. The analyses allowed stresses in the soil and forces in

the reinforcement to be determined. They also allowed the behavior of GRS

6

composites under conditions different from those employed in the GSGC

tests of Task 4 to be investigated.

Task 6: Verified the analytical models developed in Tasks 2 and 3 by using the

measured data from the GSGC tests and relevant test data available in the

literature.

The compaction model developed in Task 2 was employed to determine the

CIS for the GSGC tests; the results were then incorporated into a finite

element analysis to calculate the global stress-strain relationship and

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

relevant test data available in the literature, and results from FE analyses

were also used to verify the analytical models developed in Task 3 for

calculating composite strength properties of a GRS mass and for calculating

required tensile strength of reinforcement based on the forces induced in the

reinforcement.

Task 7: Developed an analytical model for predicting lateral movement of GRS

walls with modular block facing.

An analytical model was developed for predicting the lateral movement of

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

model for reinforced soil walls without facing (Jewell and Milligan, 1989).

The results obtained from the model were compared with measured data

from a full-scale experiment of a GRS wall with modular block facing.

7

8

Figure 1-1: Typical Cross-Section of a GRS Wall with Modular Block Facing

2. LITERATURE REVIEW

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

reinforcement. These layers are typically placed in the horizontal direction at vertical

spacing of 8 in. to 12 in. Under vertical loads, a GRS mass exhibits significantly

higher stiffness and strength than an unreinforced soil mass. This Chapter presents a

review of previous studies on the mechanics of reinforced soil, the composite

behavior of a Geosynthetic-Reinforced Soil (GRS) mass, and Compaction-Induced

Stresses (CIS) in a reinforced soil mass.

2.1 Mechanics of Reinforced Soil

In thee literature, three concepts have been proposed to explain the mechanical

behavior of a GRS mass: (1) the concept of enhanced confining pressure (Yang,

1972; Yang and Singh, 1974; Ingold, 1982; Athanasopoulos, 1994), (2) the concept of

enhanced material properties (Scholosser and Long, 1972; Hausmann, 1976; Ingold,

1982; Gray and Ohashi, 1983; Maher and Woods, 1990; Athanasopoulos, 1993; Elton

and Patawaran, 2004 and 2005), and (3) the concept of reduced normal strains (Basset

and Last, 1978).

The mechanics of a GRS mass has been explained by Schlosser and Long (1972) and

Yang (1972) by two concepts: (a) concept of apparent cohesion, and (b) concept of

apparent confining pressure.

9

a) Concept of apparent cohesion

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

from σ1 to σ1R (with an apparent cohesion cR’) due to the presence of the

reinforcement, as shown by the Mohr stress diagram in Figure 2.1. If a series of

triaxial tests on unreinforced and reinforced soil elements are conducted, the failure

envelops of the unreinforced and reinforced soils shall allow the apparent cohesion

cR’ to be determined. Yang (1972) indicated that the φ value for unreinforced sand

and reinforced sand were about the same as long as slippage at the soil-reinforcement

interface did not occur.

Figure 2.1: Concept of Apparent Cohesion due to the Presence of Reinforcement (Scholosser and Long, 1972)

10

b) Concept of increase of apparent confining pressure

In this concept, a reinforced soil is said to increase its axial strength from σ1 to σ1R

(with an increase of confining pressure Δσ3R), as shown in Figure 2.2, due to the

tensile inclusion. The value of Δσ3R can also be determined from a series of triaxial

tests, again by assuming that φ will remain the same.

Figure 2.2: Concept of Apparent Confining Pressure due to the Presence of Reinforcement (Yang, 1972)

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

be determined with only the strength data for the unreinforced soil as follows

(Schlosser and Long, 1972):

11

(1) Consider a reinforced soil mass with equally spaced reinforcement of strength

Tf (vertical spacing = Sv), it is assumed that the increase in confining pressure

due to the tensile inclusion Δσ3R is:

3f

Rv

TS

σΔ = (2.1)

(2) From Figure 2.1 and Figure 2.2 and using Rankine’s earth pressure theory to

equate the principal stress at failure σ1R,

Referring to Figure 2.1, '

1 3 2R C P RK c Kσ σ= + P (2.2)

Referring to Figure 2.2,

PRR K31 σσ = (2.3)

Knowing

RCR 333 σσσ Δ+= (2.4)

Equation 2.3 can be written as:

( PRCPRR KK 3331 )σσσσ Δ+== (2.5)

Equating Equations 2.2 to Equation 2.5, we obtain

2' 3' PR

R

Kc

σΔ= (2.6)

(3) Substituting equation 2.1 into equation 2.6,

v

PfR S

KTc

2'= (2.7)

Equation 2.7 may be very useful for evaluating the stability of a reinforced soil mass.

Given a granular soil with strength parameters c (c = 0) and φ, Equation 2.7 allows

the strength parameters of a reinforced soil mass (cR’ and φR) to be determined as a

function of T and Sv.

12

It should be noted that the validity of Equation 2.7 is rather questionable. There is a

key assumption involved in the derivation -- the assumption of v

fR S

T=Δ 3σ (this

expression implies that an increase in “Tf” has the same effect as a proportional

decrease in “Sv”.) Figure 2.3 shows the strength envelopes for sand and reinforced

sand based on the studies of Schlosser and Long (1972), Yang (1972), and Hausmann

(1976). Note that the increase in confining pressure was vT SR /3 =Δσ (see Figure

2.2) based on the explanation given by Schlosser and Long (1972) and Yang (1972);

and it was vT SR /3 ≤Δσ in Hausmann’s study (1976), where . fT TR ≡

13

Figure 2.3: Strength Envelopes for Sand and Reinforced Sand (Mitchell and Villet, 1987)

14

2.2 Composite Behavior of GRS Mass

The behavior of soil-geosynthetic composites have been investigated through

different types of laboratory experiments, including: small-size triaxial compression

tests with the specimen diameter no greater than 6 in. (Broms, 1977; Gray and Al-

Refeai, 1986; Haeri et al., 2000; etc), large-size triaxial compression tests (Ziegler et

al., 2008), large-size unconfined compression tests (Elton and Patawaran, 2005),

unconfined compression tests with cubical specimens (Adams, 1997 and Adams et

al., 2007), and plane strain tests (Ketchart and Wu, 2001).

Figure 2.4 shows the effects of reinforcement layers on the stiffness and strength of

soil-geosynthetic composites conducted by Broms (1977). For unreinforced soil

specimen (number 1 in Figure 2.4) and the specimen with reinforcement at the top

and bottom (number 2 in Figure 2.4), the stress-strain curves are nearly the same.

This suggests that unless the reinforcement is placed at locations where lateral

deformation of the soil occurs, there will not be any reinforcing effect. For the

specimens with 3 and 4 layers, the stiffness and strength of the composites are

significantly higher as the reinforcement effectively restrains lateral deformation of

the soil.

15

Figure 2.4: Triaxial Compression Tests (Broms, 1977)

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

the reinforcement in these tests is very small compared with the typical field

installation, and factors such as gravity, soil arching, and compaction-induced stresses

are not simulated properly. For these reasons, a number of larger-size triaxial tests

and plane strain test specimens have been conducted. Elton and Patawaran (2005)

conducted seven unconfined compression tests on 2.5 ft diameter and 5 ft high

16

specimens with different types of reinforcement and spacing (see Figure 2.5). Six

types of reinforcement were used in the tests with spacing of 6 in. and 12 in. Figure

2.6 shows the stress-strain curves of the specimens reinforced by TG500 at spacing of

12 in. and 6 in. It can be seen that the strength of the soil-geosynthetic composite was

much higher at 6 in. spacing than at 12 in. spacing.

(a) (b)

Figure 2.5: Unconfined Test Specimen (a) before and (b) after Testing

(Elton and Patawaran, 2005)

17

Stress - Strain curves

0

50

100

150

200

250

300

0 5 10 15 20 25 30

Vertical Strain εv (%)

Stre

ss (k

Pa)

TG500-12 (Spacing = 12 in.)

TG500 (Spacing = 6 in.)

Figure 2.6: Stress- Strain Curves of Specimens Reinforced at Spacing of 12 in. and 6 in. in Large-Size Unconfined Compression Tests

(Elton and Patawaran, 2005)

Five unconfined “mini pier” experiments were conducted by Adams and his

associates (Adams, 1997 and Adams et al., 2007). The dimensions of the specimen

were 2.0 m high, 1.0 m wide and 1.0 m deep. The test results showed that the load-

carrying capacity is affected strongly by the spacing of the reinforcement, and not

significantly affected by the strength of the reinforcement. Figure 2.7 shows a photo

of the mini pier experiment and Table 2.1 shows the material properties and test

conditions for the tests. The stress-strain curves from the tests are presented in Figure

2.8. From the Figure, the effect of reinforcement spacing and reinforcement strength

on the behavior of the mini piers can be seen by comparing the difference between

curve B (at 0.4 m spacing) and curve D (at 0.2 m spacing) and the difference between

curve C (reinforcement strength = 21 kN/m) and curve D (reinforcement strength =

70 kN/m). The effect of reinforcement spacing is much more pronounced than the

effect of reinforcement strength.

18

Figure 2.7: Mini Pier Experiments (Adams, 1997)

Table 2.1: Properties of materials for the mini pier experiments (Adams et al., 2007)

19

Figure 2.8: Stress-Strain Curves of Mini-Pier Experiments (Adams et al., 2007)

Figure 2.9 shows the setup of the large-size triaxial tests conducted by Ziegler et al.

(2008). The specimens were 0.5 m in diameter and 1.1 m high. The results also

show that the behavior of the GRS specimens was strongly affected by reinforcement

spacing. Figure 2.10 shows the relationship between applied loads and vertical

strains of the test specimens. The strength of the specimen increases with increasing

number of reinforcement layers. The stiffness of the specimen also increases with

increasing number of reinforcement layers for strains more than about 1%. Below

1%, the stiffness is not affected by the reinforcement layers.

20

Figure 2.9: Test Setup of Large-Size Triaxial Tests with Specimens of 1100 mm High and 500 mm in Diameter (Ziegler et al., 2008):

a) Schematic Diagram, and b) A Photo of the Large-Size Triaxial Test

21

Figure 2.10: Large-Size Triaxial Test Results (Ziegler et al., 2008)

The behavior of soil-geosynthetic composites have also been investigated through

numerical analysis. Examples of these studies include Lee, 2000; Chen et al., 2000;

Holtz and Lee, 2002; Zhang et al., 2006; Ketchart and Wu, 2001; and Vulova and

Leshchinsky, 2003.

Vulova and Leshchinsky (2003) conducted a series of analyses using a two-

dimensional finite difference program FLAC Version 3.40 (1998). From the analysis,

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

behavior of GRS walls. The analysis of GRS walls with reinforcement spacing varied

from 0.2 m to 1.0 m showed that the critical wall height (defined as a general

characteristic of wall stability) always increased when reinforcement spacing

22

decreased. Reinforcement spacing also controls the mode of failure of GRS walls. In

these analyses, compaction induced stresses in soil were not included.

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

were made by Ketchart and Wu (2001). The reinforcement was a medium strength

woven geotextile (with wide-width strength = 70 kN/m), the backfill was a

compacted road base material, and the reinforcement spacing was 0.3 m. Figures

2.11, 2.12 and 2.13 present the vertical, horizontal, and shear stress distributions,

respectively, at a vertical load of 6 kN. It is noted that the presence of the

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

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

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

reinforcement and reduced with the increasing distance from the reinforcement. The

extent of appreciable influence was only about 0.1~ 0.15 m from the reinforcement.

With the increased lateral stress, the stiffness and strength of the soil will become

larger. They emphasized the importance of keeping reinforcement spacing to be less

than 0.3 m for GRS walls.

23

Figure 2.11: Vertical Stress Distribution at 6-kN Vertical Load of the GRS Masses

(a) with and (b) without Reinforcement (Ketchart and Wu, 2001)

24

Figure 2.12: Horizontal Stress Distribution at 6-kN Vertical Load of the GRS Masses (a) with and (b) without Reinforcement (Ketchart and Wu, 2001)

25

Figure 2.13: Shear Stress Distribution at 6-kN Vertical Load the GRS Masses (a) with and (b) without Reinforcement (Ketchart and Wu, 2001)

26

2.3 Compaction-Induced Stresses in an Unreinforced Soil Mass

Many studies have been conducted to address the compaction-induced stresses (CIS)

in a soil mass. As early as 1934, Terzaghi noted that compaction significantly

affected lateral earth pressures. Rowe (1954) calculated lateral earth pressures for

conditions of wall deflection intermediate between the at-rest and fully active and

fully passive states. Rowe’s work did not directly address CIS, but it contributed

strongly to the later study by Broms (1971) on compaction-induced earth pressures.

Seed (1983), and Seed and Duncan (1984) had developed a simulation model called

the "bi-linear hysteretic loading/unloading model" to simulate the compaction effect

on vertical, non-deflecting structures. Duncan and Seed (1986) and Duncan et al.

(1991) also developed a procedure to determine lateral earth pressure due to

compaction. The studies were considered to have a strong impact on the

determination of CIS.

2.3.1 Lateral Earth Pressure Estimation by Rowe (1954)

This study was not directly related to CIS, but it addressed lateral earth pressures for

conditions of wall deflection intermediate between the at-rest and fully active and

fully passive states. Rowe’s stress-strain theory for calculations of lateral pressures

exerted on structures by cohesionless soils was based on the following hypotheses:

• The degrees of mobilization of the soil friction angle φ and the soil-wall

friction angle δ depend on the degrees of interlocking of the soil grains,

which in turn depend on the fractional movement of the shear planes or

slip strain (defined as the ratio of relative shear displacement to total slip

plane length). The friction angle developed increases from a relatively

low value to a higher limiting or ultimate value as slip strain increases.

27

• Earth pressures acting on a retaining wall or structure may be calculated

by conventional limiting equilibrium methods (i.e., gravity analyses of

sliding wedges) using the developed fractional φ and δ values.

The basic mechanics of Rowe’s theory are illustrated schematically in Figure 2.14.

The analysis is essentially a simple Coulomb analysis of sliding wedges. A sample

wedge adjacent to a wall or structures is considered as shown in Figure 2.14(a).

When the structure deflects, slip strain occurs along planes AB and AC as shown in

the figure. Assuming no soil compression, slip strain along each plane was calculated

as the ratio of shear displacement along the plane to the length of the plane. The

forces acting on the typical sliding wedge were shown in Figure 2.14(b).

28

Figure 2.14: Schematic Illustration of Rowe’s Theory (Rowe, 1954)

Rowe substantiated his theory by performing a series of direct shear tests on different

sands, recording the friction angle developed at various levels of slip strain, and using

these values to calculate lateral earth pressures for sample problems. Figure 2.15

shows some results of these tests. By considering “tamping” or compaction as

application and removal of a surcharge pressure γh0 (γ = unit weight of soil, h0 =

29

surcharge head), he postulated that slip strains would be induced by the load

application. Rowe suggested that in the compression and shear tests, unloading

results in relatively small strain reversals. Thus, after tamping a fill behind a wall, the

lateral pressure will be almost as great as the value, which acted under the

preconsolidation pressure. From that, the pressure coefficient (K0') could be

expressed as:

⎟⎠⎞

⎜⎝⎛ +=

hh

KK 00

'0 1 (2.8)

where h0 is the surcharge head removed and h is the overburden head ( γσ /vh = ). In

any case, (KP = coefficient of passive earth pressure at limiting condition). PKK ≤0

Figure 2.15: Results of the Two-Directional Direct Shear Tests (Rowe, 1954)

30

It is interesting to note the similarity between Rowe’s early equation for residual,

compaction-induced lateral earth pressures and an equation proposed later by Schmidt

(1967) to explain residual lateral earth pressures resulting from overconsolidation of

soils under conditions of no lateral strain (i.e., the K0-condition). Schmidt's equation

which empirically allow for some degree of relaxation of lateral stresses following

surcharge removal, can be expressed as:

α

⎟⎠⎞

⎜⎝⎛ +=

hh

KK 00

'0 1 (2.9)

where: α = 0.3 to 0.5 for most sands α = 1.2 sinφ' for initially normally consolidated clays

2.3.2 Stress Path Theory by Broms (1971) and Extension of Broms’ Work by

Ingold (1979)

Broms (1971) developed a stress path theory to explain residual lateral earth presses

on rigid, vertical, non-yielding structures resulting either from compaction or

surcharge loading, which is subsequently removed. The theoretical basis for Broms'

theory is illustrated in Figure 2.16. An element of soil at some depth is considered to

exist at some initial stress state represented by point A with horizontal and vertical

effective stresses of ho'σ and vo'σ . Compaction of the soil is considered as a process

of loading followed by unloading. When the overburden pressure is increased (i.e.,

loading), there is a little change in lateral pressure until the ratio of lateral to vertical

effective stresses is equal to K0 (denoted by point B in Figure 2.16) where K0 is the

coefficient of earth pressure at rest. Thereafter, increased vertical stress is

accompanied by an increased lateral stress according to vh K '' 0 σσ = , corresponding

to primary (or virgin) loading. When the overburden pressure is subsequently

decreased (say, from point C) the corresponding decrease in lateral pressure is small

31

until the ratio of lateral to vertical effective stresses is equal to some limiting constant

K1 (denoted by point D in Figure 2.16). Thereafter, continued decrease in vertical

pressure is accompanied by a decrease in lateral stress according to vh K '' 1σσ = . This

idealized stress path is in agreement with the earlier hypothesis of Rowe (1954) that

stress relaxation with unloading is negligible until some limiting condition, defined

by the K1-line, is reached. By following this type of stress path, an element of soil

can be brought to a final state represented by an effective coefficient Keffective varying

. Having made this idealized assumption of the stress path, Broms

then postulated that the actual stress path followed by a real soil element might be as

represented by the dash line in Figure 2.17. Rowe (1954) as well as Ingold (1979)

suggested that K1 = KP (the coefficient of passive earth pressure) reasoning that the

limiting condition reached is essentially a form of passive failure.

10 KKK effective ≤≤

C

D

B

A

E

σh =K0 σv

Assumed relationship

σh =K1 σvσ'h0

σ'v0

Effe

ctiv

e ov

erbu

nden

pre

ssur

e, σ

v

/K0

σ'h0

Actual relationship

Effective lateral earth pressure, σh

Figure 2.16: Hypothetical Stress Path during Compaction (Broms, 1971)

32

By employing this theory to estimate the lateral pressure exerted on a vertical, rigid,

non-yielding structure with a compacted fill, Broms considered the compaction plant

to present a load applied to the fill surface inducing vertical stresses which may be

approximated as twice as those calculated by Boussinesq stress equation for an

infinite half space. Lateral earth pressures acting against the wall were then

calculated as vh K '' 0σσ = . The resulting horizontal stress distribution calculated for a

10.2 metric ton smooth wheel roller is presented as line 1 in Figure 2.17(a).

33

Figure 2.17: Residual Lateral Earth Pressure Distributions (Broms, 1971)

34

Figure 2.18(a) shows the loading path for a soil element at a shallow depth z < zcr ,

where zcr is a critical depth that will be addressed later. The soil is loaded from points

A’ to C’, then latter stages of unloading following the vertical path to point D’ and

then following the stress path vh K '' 1σσ = to point E’, resulting in a final condition

. 10 ' KK =

Figure 2.18(b) shows the loading path for a soil element at deeper depth z > zcr. After

loading from A’’ to C’’, the unloading to E’’ is not sufficient to bring the soil element

to the limiting condition vh K '' 1σσ = at point D’’ because the vertical stress at point A

is greater than that at point D’’.

Figure 2.18: Hypothetical Stress Paths of Shallow and Deep Soil Elements (Broms, 1971)

35

Following the process above and knowing values of K0 and K1, a residual lateral

pressure distribution, as shown by the shaded area in Figure 2.17(a), can be

determined. The line 23 in Figure 2.17(a) represents the residual stresses for

elements below zcr and line 02 represents the limiting condition vh K '' 1σσ = . Point 2,

where these two lines intersect, occurs at a depth zcr called the critical depth.

By considering the backfill process as the placement of a series of soil layers each

deposited and then compacted one after the other, the compaction-induced lateral

pressure for each new layer will be surpassed in magnitude by the at-rest earth

pressures due to the static overburden. A stress distribution as shown in Figure

2.17(b) can be calculated. This type of lateral pressure distribution may be

generalized as shown in Figure 2.17(c).

Ingold (1979) applied the extension of Broms’ theory in cases where wall deflection

during backfilling were sufficient to induce an active condition in the lower layers of

a backfill which is deposited and compacted in lifts by assuming the virgin loading

path to be vAh K '' σσ = instead of Broms’ vh K '' 0σσ = . Ingold postulated that passive

failure controlled the other limiting condition, therefore K1 = KP.

2.3.3 Finite Element Analysis by Aggour and Brown (1974)

Aggour and Brown (1974) were the first to model compaction-induced lateral earth

pressure by two-dimensional finite element analysis. Aggour and Brown's analysis

involved the following steps for simulation of compaction operation:

1. A layer of soil elements adjacent to a wall was modeled with some initial

modulus E1.

36

2. Compaction was modeled as some increased vertical load acting uniformly

over the entire surface of the soil. Simultaneously the soil modulus is

increased to some new and stiffer value E2 to reflect the increase in density

during compaction.

3. The compaction load was then removed. The resulting strains, deflections,

and stress redistributions were modeled using a stiffer unloading modulus Eu2.

4. A new layer of fill with modulus E1 was added to the top of the preceding

layer. This increased the vertical stresses in the underlying layer. These

increased stresses in the underlying were modeled using the soil modulus E2.

5. A surface load to model compaction of the new layer was applied, increasing

the stresses in both these soil layers, and the modulus was increased to E2.

6. The compacting load was removed and the resulting wall deflections, strains

and stress redistributions were modeled using the modulus Eu2 for both soil

layers.

7. The entire process was then incrementally repeated for subsequent soil layers.

Figure 2.19 shows a sample problem analyzed by Aggour and Brown using the

procedure above. Figure 2.19(a) shows the method used to model the soil moduli.

The effects of increased numbers of compaction 'passes' were modeled by increasing

the soil modulus E2. The soil modulus was greater for unloading than for reloading.

The geometry and material properties used in the sample problem are shown in

Figure 2.19(b). Compaction loading was modeled as a uniform unit surface pressure

of unit width acting at all points along the full length of the fill, from the wall to the

right-hand boundary of the finite element mesh. The fill materials were placed in five

4-ft lifts. The interface between soil and wall was assumed to remain bonded at all

time.

37

The results of this analysis are shown in Figure 2.19(c). These results indicate:

• Increased wall deflections with increased compactive effort (increased number

of passes was modeled by increases E2 values)

• Increased residual lateral pressures near the top of the wall with increased

compactive effort.

The second sample problem analyzed by Aggour and Brown used the same soil and

wall geometry, but this time only the last soil lift placed was compacted. The results

of this analysis are shown in Figure 2.19(d). The effects of the compaction of the last

soil layer were: increased wall deflections, and increased residual lateral earth

pressures near the top of the wall. These results were found to be in agreement, on a

qualitative basis, with field and scale-model observations of the effects of compaction

on structural deflections and residual lateral earth pressures. The analyses suggest the

potential value of finite element analysis for determining compaction-induced earth

pressures on yielding structures.

38

Figure 2.19: A Sample Problem Analyzed by Aggour and Brown (1974)

39

2.3.4 Compaction-Induced Stress Models by Seed (1983)

Seed (1983) proposed a method to estimate the effects of CIS and associated

deflections. Seed's study will be summarized in detail as it represents the most in-

depth study on the subject of CIS. Seed’s study involved the following three areas:

• Compaction induced stresses due to different stress paths, including the first-

cycle K0–reloading stress path, typical K0–reloading stress path, multi-cycle

K0-unloading/reloading stress path, and K0-unloading following reloading

stress path.

• The nonlinear and bi-linear hysteretic loading/unloading compaction models

for simulation of fill compaction behind vertical, non-deflecting structures.

• Finite element analysis of fill compaction using the non-linear and bi-linear

models.

a) First-Cycle K0-Reloading Stress Path and Typical K0-unloading/Reloading

Stress Path

Seed (1983) proposed what is termed “first-cycle K0-reloading model,” as shown in

Figure 2.20. The model was derived from fitting available data. Upon loading, the

stress path is assumed to follow the K0-line to point A (see Figure 2.20), after which

the unloading stress path is followed by ( )αOCRKK 00' = to an arbitrary point B prior

to reloading. Reloading is then assumed to follow a linear path to point R, the

intersection of the reloading path with the K0-line, and again to follow the K0-line

thereafter. Point R, the intersecting point of the reloading path with the virgin loading

path is determined as: *

, ,min'h r hσ σ β= + ∗Δ (2.10)

40

rhrvK

,*

0

,* 1 σσ = (2.11)

In which Δ is the decrease in horizontal effective stress from the maximum loading at

point A to the minimum unloading at point B, β is assumed constant regardless of the

degree of unloading which precedes reloading (Figure 2.20), σ’h,min is minimum

horizontal stress, σ*v,r σ*

h,r are vertical and horizontal residual stress after compaction.

The unloading curve from point A to point B in Figure 2.20, can be estimated by

. The value α can be estimated by Equation 2.12 or by Figure 2.21: ( αOCRKK 00' = )

'sin974.0018.0 φα += (2.12)

Figure 2.20: The First-Cycle K0-Reloading Model (Seed, 1983)

41

Figure 2.21: Suggested Relationship between sinφ' and α (Seed, 1983)

42

Some typical results of using the model are illustrated in Figure 2.22. In this figure, β

remains constant but Δ varies with magnitude of unloading.

Figure 2.22: Typical K0-Reloading Stress Paths (Seed, 1983)

In Figures 2.21 and 2.22, K1-line is at the limiting condition and defined as:

φφ σ ,13

,11 ''2 KcKK +=

(2.13)

⎟⎠⎞

⎜⎝⎛ +=

2'45tan 02

,1φ

φK (2.14)

where K1, φ’ = coefficient of passive lateral earth pressure, and φ’ = effective internal

friction angle of soil.

43

b) Multi-Cycle K0-Unloading/Reloading Stress Path and K0-Unloading

Following Reloading Stress Path.

Seed (1983) proposed another model for multi-cycle K0-unloading/reloading

conditions. The values α and β are assumed to remain constant regardless of the

number of loading-reloading cycles. The model is illustrated in Figure 2.23.

Three situations of unloading were considered. The first situation, as shown in Figure

2.23(a), is for unloading after significant loading, and can be described as follows:

1. Loading by following the K0-line to point A;

2. Unloading by following the K0’-line, with ( )αOCR , to point B; KK 00 '=

3. Reloading through point R then to point C, passing through previous

maximum loading point A;

4. Subsequent loading-unloading path is assumed to follow an α-type path CD.

44

Figure 2.23: K0-unloading following Reloading (Seed, 1983)

45

The second situation, unloading after intermediate reloading, is shown in Figure

2.23(b), and can be described as follows:

1. Loading by following the K0-line to point A;

2. Unloading by following the K0’-line, with ( )αOCR , to point B; KK 00 '=

3. Reloading through point R to point C on the virgin K0-line, but at a stress less

than the maximum previous loading point A;

4. Subsequent loading-unloading path is assumed to follow an α*-type path CD

( αα ≥* ).

The third situation, unloading after moderate reloading, is shown in Figure 2.24. In

this situation, the stress again begins with loading to point A and unloading to point

B, then reloading to point C. In this situation, the stress state at point C is not

sufficient to reach a stress state on the K0-line. Subsequent loading is then modeled

as follows:

1. Point C is projected vertically down to point C’ on the K0-line, and point B is

projected vertically down through the same distance to point B’;

2. From point C’ unloading to point B’ by following a α*-type ( αα ≥* ) path;

3. The actual unloading path is assumed to be “parallel” to the imaginary path

above (dash lines).

Note that in this situation, point B is the “current” minimum stress point.

46

Figure 2.24: Unloading after Moderate Reloading (Seed, 1983)

c) Non-Linear, Multi-Cycle K0-Unloading/Reloading Compaction Model

The non-linear, multi-cycle K0-unloading/reloading model was developed based on

the stress paths described in Sections (a) and (b) above. The model requires five

material parameters: α, β, K0, K1,φ and c’. The name of each model parameter,

recommended limits of each parameter, and the correlations with φ’ are given in

Table 2.2.

47

Table 2.2: Non-linear K0-loading/unloading model parameters (Seed, 1983)

Parameter Name Recommended Limits

Method of Estimation Based on φ’

α Unloading coefficient 10 ≤≤ α

β Reloading coefficient 10 ≤≤ β 6.0≅β

K0 Coefficient of at-rest lateral earth pressure for virgin loading

10 0 ≤≤ K 'sin10 φ−≅K

K1,φ Frictional component of limiting coefficient of at-rest lateral earth pressure for unloading

PKKK ≤≤ φ,10

⎟⎠⎞

⎜⎝⎛ +≅

2'45tan 2

,1φ

φK

c’ Effective stress strength envelope cohesion intercept

--

--

Note: K1 = Limiting coefficient of at-rest lateral pressure for unloading

vh K '' 1lim, σσ = and ',13

',11 ''2

φφ σKcKK B+=

KP = Coefficient of passive lateral earth pressure

Basic component of the non-linear K0-loading/unloading model is described in Figure

2.25. In the figure, the K1- line is the stress path at limiting condition; K0 – line is

virgin or initial stress path; MPLP is maximum loading point; RMUP is residual

minimum unloading point; RMLP is residual maximum loading point; point R is at

residual condition after compaction.

48

Figure 2.25: Basic Components of the Non-Linear K0-Loading/Unloading Model (Seed, 1983)

The term Δσ'h,vc,p (same as “Δ” in Figure 2.25; the subscripts “h” denotes horizontal,

“vc” denotes virgin compression, and “p” denotes peak) is referred to as the peak

change in lateral stress induced by compaction (loading only). The value of Δσ'h,vc,p

resulted from surficial loading can be obtained from simple elastic solution, such as

Boussinesq’s solution (1885), by assuming the soil is previously uncompacted (i.e., a

“virgin” soil) and by varying the type and location of the compaction plant.

Boussinesq’s solution is for a semi-infinite mass. For any point along a vertical non-

deflecting wall, the change in lateral stress will be twice as much as the values

obtained from Boussinesq’s solution.

49

Figure 2.26 (a) shows the distribution of Δσ'h,vc,p for loads applied at different

distances under the condition that the soil is not underlain by a rigid base. The

distribution of Δσ'h,vc,p under the condition that the soil is underlain by a rigid base at

a depth of 6 ft is shown in Figure 2.26(b). In the latter case, attenuation of Δσ'h,vc,p

with depth beyond the maximum point is followed by an increase with depth when a

rigid base is approached. Figure 2.27 shows stress path associated with placement

and compaction of a typical layer of fill. For a typical layer of fill at point A, stress in

soil at this point is increased to point B (because of the soil weight of this layer), and

then to point D and C due to compaction loading. For the unloading path, stress at

point C then reduced to point D (the vertical load, Δσ’v,0 is remained because of the

soil weight of this layer). After compaction, Δσ’h,r is residual horizontal stress in soil

at this layer.

Figure 2.26: Profiles of Δσ'h,vc,p against a Vertical Wall for a Single Drum Roller

50

Figure 2.27: Stress Path associated with Placement and Compaction of a Typical

Layer of Fill (Seed, 1983)

d) Simplified Bi-Linear Approximation to the Non-Linear Model

In this model, the “α-type” non-linear unloading model for the first-cycle unloading

is approximated by a bi-linear unloading path, as shown by the dashed lines in Figure

2.28. The relationship between K2 and F (as defined in Figure 2.29) in the bi-linear

unloading model is shown in Figure 2.29. Figure 2.30 shows the relationship

between K3 (slope of reloading path) and β3 (as defined in Figure 2.30) of the model.

The bi-linear K0-loading/unloading model parameters are described in Table 2.3.

51

Figure 2.28: Bi-Linear Approximation of Non-linear K0-unloading Model

Figure 2.29: Relationship between K2 and F in the Bi-Linear Unloading Model (Seed, 1983)

52

Figure 2.30: Relationship between K3 and β3 in the Bi-Linear Model (Seed, 1983)

53

Table 2.3: Bi-linear K0-loading/unloading model parameters (Seed,1983)

Parameter Name Recommended Limits

Method of Estimation Based on φ’

K0 Coefficient of at-rest lateral earth pressure for virgin loading

10 0 ≤≤ K

Same as non-linear model

(Recommended 'sin10 φ−≅K )

K1,φ’,B Frictional component of limiting coefficient of at-rest lateral earth pressure for unloading

PKKK ≤≤ 10

',1,',1 32

ϕφ KK B ≅

⎟⎠⎞

⎜⎝⎛ +≅

2'45tan 2

',1φ

φoK

cB’ Effective stress strength envelope Cohesion Intercept

0'≥Bc

' 8.0' ccB ≅

F

or

K2

( FKK −= 102 )

- Fraction of peak lateral compaction stress retained as residual stress for virgin soil

- Incremental coefficient of at-rest lateral earth pressure for reloading

10 ≤≤ F

020 ≥≥ KK

- F (or K2) should be chosen such that the bi-linear unloading stress path intersects the α-type non-linear unloading stress path at a suitable OCR. Recommended:

( )( )1

1−

−−=

OCROCROCRF

α

Where a suitable OCR for “matching” the bi-linear and non-linear unloading curves is typical . 5≅OCR

K3 Incremental coefficient of at-rest lateral earth pressure for reloading

030 KK ≤≤ ( )( )FKKK −=≅ 1023

Note: vh K '' 1lim, σσ = , BB

B KcKK ,',13

,',11 ''2

φφ σ+= , ',1,',1 3

2φφ KK B ≅ , and . PKK =',1 φ

54

Figure 2.31 shows the basic components of the bi-linear model. Virgin loading is

assumed to follow the K0-line in the same manner as in the non-linear model.

Unloading initially follows a linear stress path according '' 2 vh K σσ Δ=Δ until a K1-

type of limiting condition is reached, at which point further unloading follows a linear

stress path according to '' 1 vh K σσ Δ= . Reloading follows a linear stress path

according to 'v' 3h K σσ Δ=Δ until the virgin K0-loading stress path is regained, after

that further reloading follows the virgin stress path.

Figure 2.31: Basic Components of the Bi-linear Model (Seed,1983)

From Figure 2.31, the parameters of bi-linear model can be calculated as:

'.' ,, phrh F σσ Δ=Δ (2.15)

( )( )1

110

2

−−

−=−=OCR

OCROCRKKF

α

(2.16)

55

( )30

2

233

11 β

β

−−=

KK

KK (2.17)

56

Figure 2.32: Compaction Loading/Unloading Cycles in the Bi-Linear Model (Seed, 1983)

57

Seed (1983) also developed a simplified hand calculation procedure for computing

the CIS. The procedure can be described by the following steps:

1. Calculate the peak lateral compaction pressure profile (i.e., Δσ'h,vc,p vs. depth

relationship) by the method described in Section c, as shown in Figure

2.32(b).

2. Multiply the Δσ'h,vc,p values with the bi-linear model parameter F.

3. Calculate the lateral residual stress as ',, . 0, '' pvchvrh FK σσσ Δ+=

4. Reduce the near-the-surface portion of the σ’h,r distribution with

'' ,',1, vBrh K σσ φ≤ at all depths.

5. Increase the residual effective stress distribution such that '' 0, vrh K σσ ≥ at all

depths.

Figure 2.33 shows an example problem given by Seed (1983) to show how to

determine the compaction-induced lateral pressure on a vertical non-deflecting

structure using bi-linear model and non-linear model. The material parameters of the

models based on the given angle of friction (φ = 35o) are shown in Table 2.4.

Table 2.4: Material parameters for non-linear and bi-linear models

Non-linear model parameters Bi-linear model parameters

K0 = 1 - sinφ' = 0.43

21, '

'tan 45 3.692

oK φφ⎛ ⎞= − =⎜ ⎟

⎝ ⎠

63.0=α (from Figure 2.20)

6.0=β (assumed)

c' = 0

K0 = 1 - sinφ' = 0.43

46.232

',1,',1 == φφ KK B

44.015

551 =−−

−=α

F

24.023 == KK

c'B = 0

58

Figure 2.34 shows the residual lateral stresses as a result of unloading due to fill

compaction and the at-rest earth pressure. The results of the bi-linear model (the solid

line) and the non-linear model (the bold dots) are approximately the same.

59

Figure 2.33: An Example Problem for Hand Calculation of Peak Vertical Compaction Profile (Seed, 1983)

60

Figure 2.34: Solution Results from the Bi-Linear Model and the Nonlinear Model (Seed, 1983)

The compaction models developed by Seed (1983) has been used to determine the

CIS for full-scale experiments and reported by Duncan and Seed (1986) and Duncan

et al. (1986). The papers showed that, the CIS could be calculated based on either the

simplified method (i.e., the bi-linear model) or the non-linear model with the aid of

finite element analysis. They have shown that the resulting lateral earth pressures

determined by the models are in good agreement with measured data.

61

2.4 Compaction-Induced Stresses in a Reinforced Soil Mass

of previous studies on GRS masses

cluding the effects of CIS is presented below.

4.1 Ehrlich and Mitchell (1994)

fecting the

the procedure are:

ion lift was subjected to only one cycle of loading, as shown

Figure 2.35.

stress-state condition at the end of construction. Ehrlich and Mitchell (1994) noted

Many researchers and practicing engineers have suggested that if a granular backfill

is well compacted, a GRS mass can usually carry a great deal of loads and experience

little movement. A handful of studies on performance of GRS structures have used

simplified, and somewhat arbitrary, procedures to simulate the effects of fill

compaction. In all other studies, the compaction-induced stresses (CIS) in the fills

have been ignored completely. The CIS in a GRS mass is likely to be more

pronounced than those induced in an unreinforced soil mass because soil-

reinforcement interface friction tends to restrain lateral deformation of the soil mass

and results in greater values of CIS. A review

in

2.

Ehrlich and Mitchell (1994) presented a procedure to include CIS in the analysis of

reinforced soil walls and noted that CIS was a major factor af

reinforcement tensions. The assumptions involved in

• The stress path was as shown in Figure 2.35.

• With the multi-cycle operations of soil placement and compaction during

construction, the soil surrounding the reinforcement maximum tension point

in each compact

in

Loading due to the weight of overlying soil layers plus some equivalent increase in

the stress state induced by the compaction operations is shown as paths 1 to 3 in

Figure 2.35. This is followed by unloading along paths 3 to 5 to the final residual

62

that by following this procedure, the stresses in each layer were calculated only once

and that each layer calculation was independent of the others.

The specific values of σ’z and σ’zc at point 3 in Figure 2.35 represent the maximum

stress applied to the soil at a given depth during the construction process. The

maximum past equivalent vertical stress, including compaction at the end of

construction (σ’zc), can be estimated using a new procedure, based on the method

given by Duncan and Seed (1986) for conventional retaining walls.

Figure 2.35: Assumed Stress Path (Ehrlich and Mitchell, 1994)

In Figure 2.35, the value of σ’zc can be estimated as the following:

0

''

Kxp

zc

σσ = (2.18)

where:

'sin10 φ−=K (Jaky, 1944) (2.19)

63

( )LQN

K Axpγγ

νσ'5.0

1' 0 += (2.20)

and Q = maximum vertical operating force of the roller drum

L = length of the roller drum

γ = effective soil unit weight.

0

00 1 K

K−

=υ (Poisson’s ratio under K0-condition) (2.21)

⎥⎦

⎤⎢⎣

⎡−⎟

⎠⎞

⎜⎝⎛ +⎟

⎠⎞

⎜⎝⎛ += 1

2'45tan

2'45tan 4 φφ

γooN (bearing capacity factor) (2.22)

Figure 2.36 shows the effects of CIS on compaction and reinforcement stiffness in

GRS walls. The conclusions drawn by Ehrlich and Mitchell from their study are:

- The soil shearing resistance parameters, the soil unit weight, the depth, the

relative soil-reinforcements stiffness index, Si, and compaction are the

major factors determining reinforcement tensions (typical Si for metallic

reinforcement: 0.500-3.200; plastic reinforcement: 0.030-0.120 and

geotextile reinforcement: 0.003-0.012);

- Increasing Si, usually means increased lateral earth pressure and

reinforcement tension, but at shallow depths the opposite effect can occur

depending on compaction conditions;

- The coefficient of horizontal earth pressure, K, can be greater than K0 at

the top of the wall and be greater than KA to depths of more than 6.1 m (20

ft) depending on the relative soil-reinforcements stiffness index, and the

compaction load; and

- K0 is the upper limit for the coefficient of horizontal earth pressure, K, if

there is no compaction of the backfill.

64

Figure 2.36: Compaction and Reinforcement Stiffness Typical Influence (Ehrlich and Mitchell, 1994)

2.4.2 Hatami and Bathurst (2006)

Hatami and Bathurst (2006) noted that fill compaction has two effects on the soil: (1)

increase the lateral earth pressure, (2) reduce the effective Poisson’s ratio. They

suggested that the first effect can be modeled in a numerical analysis by applying a

uniform vertical stress (8 kPa, and 16 kPa depending on compaction load) to entire

surface of each newly placed soil layer before analysis and removed it afterwards.

This procedure was based on a recommendation by Gotteland et al. (1997).

Gotteland et al. simulated the compacting effect by loading and unloading of a

uniform surcharge of 50 kPa and 100 kPa on the top of the wall.

65

For the second effect of compaction on the reduction of Poisson’s ratio, Hatami and

Bathurst used the numerical simulation to find νmin from matching measured and

analysis data. The results (wall lateral movement and reinforcement forces) obtained

from the numerical analysis including compaction effect were in a very good

agreement with the measured data.

In their numerical analyses, the compaction effects were also account for by

increasing the elastic modulus number, Ke value from triaxial test results by a factor

of 2.25 for Walls 1 and 2. In other words, the elastic modulus was increased by the

factor of 2.25 for Walls 1 and 2.

2.4.3 Morrison et al. (2006)

Morrison et al. (2006) simulated the effects of fill compaction of shored mechanically

stability earth (SMSE) walls. A 50 kPa inward pressure was applied to the top,

bottom and exposed faces of each lift to simulate the effects of fill compaction. The

inward pressure was then reduced to 10 kPa on the top and bottom of a soil lift prior

to placement of the next lift to simulate vertical relaxation or unloading following

compaction. The inward pressure acting on the exposed face was maintained at 50

kPa as this produced the most reasonable model deformation behavior compared with

that observed in the field-scale test. They considered that the inward maintained

pressures are "locking-in" stresses in soil due to compaction.

The stiffness of soil was increased by the factor of ten (10) to consider the

compaction-induced stresses in the GRS mass. This factor in Hatami and Bathurst

(2006) was about 2.25.

66

Figure 2.37 shows the model for finite element analysis by Morrison et al. (2006).

The figure shows the simulation of fill compaction of lift 5 by the applying uniform

pressures.

Figure 2.37: Finite Element Model for Finite Element Analysis (Morrison et al., 2006)

67

The results of the lateral movement and reinforcement forces showed a good

qualitative agreement with the measured data. However, general application of the

procedure may be questionable because neither the method of analysis nor the

magnitude of the applied inward pressure was properly justified.

2.5 Highlights on Compaction-Induced Earth Pressures in the Literature

A number of important highlights regarding compaction-induced lateral earth

pressures in the literature are summarized below:

1. Compaction of soil against a rigid, vertical, non-yielding structure appears to

result in the following residual lateral pressure distribution: (a) the lateral

pressures near the surface increase rapidly with depth, exceeding the at-rest

value, but limited a passive failure, (b) at intermediate depths, the lateral

pressures exceed the at-rest value, increase less rapidly with depth or remain

fairly constant with depth, and (c) at greater depths, the lateral pressures

appear to be the simple at-rest pressures, showing no affects of compaction

(Broms, 1971, Seed, 1983).

2. Compaction of soil against deflecting structures appears to increase near

surface.

3. The compaction-induced residual earth pressures are significant affected by

the compaction equipments. For compaction by small hand-operated rollers,

the increase in the lateral pressure occurs within a depth of about 3 to 4m, but

for very large rollers, the effect of compaction can be up to 15 to 25 m

(Duncan and Seed, 1986).

4. Structural deflections away from the soil, which occur during fill placement

and compaction, will reduce the residual lateral earth pressures. Reduction in

pressures appears to occur more rapidly in heavily compacted cohesionless

soil (Seed, 1983).

68

5. Compaction-induced residual lateral earth pressures in cohesive soils appear

to dissipate with time, even against non-deflecting structures, and eventually

approach at-rest values.

6. There is some evidence suggesting that the direction of rolling with the

compactor can have a significant effect in compaction-induced earth pressures

(Erhlich and Mitchell, 1993).

7. Field observations indicate that available overburden pressures are sufficient

that possible passive failure does not limit residual lateral earth pressure, a

high percentage of the peak lateral earth pressures induced during compaction

may be retained as residual pressures. In previously compacted soil, however,

additional compaction can result in only small increases in peak pressures, and

a negligible fraction of this (Aggour and Brown, 1974).

8. A number of simulation models have been proposed to explain and to evaluate

the residual lateral earth pressures induced by compaction. Common to all of

these theories is the idea that compaction represents a form of over-

consolidation wherein stresses resulting from a temporary or transient loading

condition are retained to some extent following removal of this peak load.

9. Many researchers, including Rowe (1954), Broms (1971), Gotteland et al.

(1997), and Hatami and Bathurst (2006), have simulated fill compaction by

application and removal of a surficial surcharge pressure.

10. Broms (1971) proposed a theory to calculate compaction-induced residual

lateral earth pressures against a rigid, vertical, frictionless, non-yielding wall.

The simulation results somewhat agree with available field data for walls

sustaining minimal deflections. Broms assumed that: (a) unloading results in

no decrease in lateral stress until a limiting passive failure-type condition is

reached, and (b) reloading results in no increase in lateral stress until the

virgin K0-loading stress path is regained. This type of model does not predict

well the peak lateral stresses induced by fill compaction, and is not suited for

69

70

computing lateral stresses induced by a surficial compaction plant of finite

lateral dimensions (not entire the surface). But Broms’ theory is very easy to

apply. Some researchers have adopted this theory for analysis of GRS

structures, including Gotteland et al. (1997), Hatami and Bathurst (2006), and

Morrison et al. (2006).

11. Seed (1983) developed two models for simulation of fill compaction: a non-

linear model and a bi-linear model. They are well suited for simulation of

compaction operation in GRS structures. The simulation results of the two

models are rather similar, and both agree well with measured data of

unreinforced earth retaining walls. The bi-linear model is easy to apply by

using hand calculation. Both models, bi-linear and non-linear models, are

based on the K0 condition. These are very useful to estimate CIS for soil only.

To use it for GRS structures, in-depth studies need to be carried out.

3. AN ANALYTICAL MODEL FOR CALCULATING LATERAL

DISPLACEMENT OF A GRS WALL WITH MODULAR BLOCK

FACING

Over the past two decades, Geosynthetic-Reinforced Soil (GRS) walls have gained

increasing popularity in the U.S. and abroad. In actual construction, GRS walls have

demonstrated a number of distinct advantages over the conventional cantilever and

gravity retaining walls. GRS walls are generally more ductile, more flexible (hence

more tolerant to differential settlement and to seismic loading), more adaptable to

low-permeability backfill, easier to construct, require less over-excavation, and

significantly more economical than conventional earth structures (Wu, 1994; Holtz

et al., 1997; Bathurst et al., 1997).

A GRS wall comprises two major components: a facing element and a GRS mass.

The facing element of a GRS wall have been constructed with different types of

material and in different forms, including wrapped geotextile facing, timber facing,

modular concrete block facing, precast concrete panel facing, and cast-in-place rigid

facing. Among the various facing types, modular concrete block facing has been

most popular in North America, mainly because of its ease of construction, ready

availability, and lower costs. The other component of a GRS wall, a GRS mass,

however, is always a compacted soil mass reinforced with layers of geosynthetic

reinforcement. Figure 3.1 shows the schematic diagram of a typical GRS wall with

modular block facing.

Current design methods for GRS walls consider only the stresses and forces in the

wall system. Even though a GRS wall with modular block facing is a fairly “flexible”

71

wall system, movement of the wall is not accounted for in current designs. A number

of empirical and analytical methods have been proposed for estimating lateral

movement of GRS walls. Most these methods, however, do not address the rigidity

of the facing although many full-scale experiments, numerical analysis, and field

experience have clearly indicated the importance of facing rigidity on wall movement

(e.g., Tatsuoka, et al., 1993; Rowe and Ho, 1993; Helwany et al., 1996; Bathurst et

al., 2006).

The prevailing methods for estimating the maximum lateral displacement of GRS

walls include: the FHWA method (Christopher, et al., 1989), the Geoservices method

(Giroud, 1989), the CTI method (Wu, 1994), and the Jewell-Milligan method (1989).

Among these methods, the Jewell-Milligan method has been found to give the closest

agreement with finite element analysis (Macklin, 1994). The Jewell-Milligan

method, however, ignores the effect of facing rigidity. Strictly speaking, the method

is only applicable to reinforced soil walls where there is little facing rigidity, such as a

wrapped-faced GRS wall.

A study aiming at developing an analytical model for calculating lateral movement of

a GRS wall with modular block facing was undertaken. The analytical model

modifies the Jewell-Milligan method (1989) to include the rigidity of facing element.

To verify the analytical model, the lateral wall displacements calculated by the

analytical model were compared with the results of the Jewell-Milligan method

(1989) for GRS walls with negligible facing rigidity. In addition, the lateral wall

displacements obtained from the analytical model were compared with the measured

data of a full-scale experiment of GRS wall with modular block facing (Hatami and

Bathurst, 2005 & 2006).

72

In addition to lateral displacement profiles, an equation for determining facing

connection forces (i.e., the forces in reinforcement immediately behind the facing) is

introduced.

Soil

Reinforcement

H

q

.L

Facing block

Sv

Figure 3.1: Basic Components of a GRS Wall with a Modular Block Facing.

3.1 Review of Existing Methods for Estimating Maximum Wall Movement

The most prevalent methods for estimating the maximum lateral displacement of

GRS walls are the FHWA method (Christopher, et al., 1989), the Geoservices method

(Giroud, 1989), the CTI method (Wu, 1994), and the Jewell-Milligan method (1989).

A summary of each method is presented below.

73

3.1.1 The FHWA Method (Christopher, et al., 1989)

The FHWA method correlates L/H ratio (L = reinforcement length, H = wall height)

with the lateral displacement of a reinforced soil wall during construction. Figure 3.2

shows the relationship between L/H and δR, the empirically derived relative

displacement coefficient. Based on 6 m high walls, the δR value is to increase 25%

for every 20 kPa of surcharge. For the higher walls, the surcharge effect may be

greater. The curve in Figure 3.2 has been approximated by a fourth-order polynomial

as:

For 0.3 1.175LH

≤ ≤ ,

471.945.3516.5725.4281.11234

+⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛=

HL

HL

HL

HL

Rδ (3.1)

For extensible reinforcement, the maximum lateral wall displacement, δmax, can be

calculated from by the following equation (δmax is in units of H):

⎟⎠⎞

⎜⎝⎛=

75maxH

Rδδ (3.2)

74

Figure 3.2: Empirical Curve for Estimating Maximum Wall Movement During Construction in the FHWA Method (Christopher, et al., 1989)

75

The FHWA method was developed empirically by determining a displacement

“trend” from numerical analysis and adjusting the curve to fit with field measured

data. The method provides a quick estimate of the maximum lateral displacement.

Note that the maximum lateral displacement, δR, as obtained from Figure 3.2 has been

corrected for the wall with different height and surcharge.

3.1.2 The Geoservices Method (Giroud, 1989)

The Geoservices method relies on limit-equilibrium analyses to calculate the length

of the required reinforcement to satisfy a suggested factor of safety with regard to

three presumed external failure modes (e.g., bearing capacity failure, sliding and

overturning). The method provides a procedure for calculating the lateral wall

displacement.

The lateral displacement is calculated by first choosing a strain limit for the

reinforcement. This strain limit is usually less than 10 % and will depend on a

number of factors such as the type of wall facing, the displacement tolerances and the

type of geosynthetic to be used as reinforcement. Concrete facing panels, for

example, would not allow much lateral displacement without showing the signs of

distress. Therefore a low strain limit (1 to 3 %) should be selected.

Geosynthetics have a wide range of material properties depending on, among other

factors, the way they are manufactured. Non-woven geotextile exhibits low modulus

characteristics and if chosen as reinforcement for a wall, design would necessarily

imply that a large design strain is to be considered.

76

Once the strain limit has been selected, the method then assumes a distribution of

strain in the reinforcement, as shown in Figure 3.3 for calculating wall movement.

The horizontal displacement, δh, then becomes:

2Ld

hε

δ = (3.3)

where εd = strain limit (εmax), and L = reinforcement length.

Φ/2

Rankine Surface

Strain Distribution

Reinforcement

εmax

Figure 3.3: Assumed Strain Distribution in the Geoservices Method

3.1.3 The CTI Method (Wu, 1994)

Differing from all other design methods based on ultimate-strength of the

geosynthetic reinforcement, the CTI method is a service-load based design method.

77

The requirements of reinforcement are made in terms of stiffness at a design limit

strain as well as the ultimate strength.

In most cases, the designer will select a design limit strain of 1% to 3% for the

reinforcement. The maximum lateral displacement of a wall, δmax, can be estimated

by the following empirical equation:

⎟⎠⎞

⎜⎝⎛=

25.1maxH

dεδ (3.4)

where εd = design limit strain (typically 1 % to 3 % for H ≤ 30 ft) and H =

wall height.

If the maximum wall displacement exceeds a prescribed tolerance for the wall, a

smaller design limit strain should be selected so that the maximum lateral

displacement of the wall will satisfy the performance requirement. Equation 3.4

applies only to walls with very small facing rigidity, such as wrapped-faced walls.

Walls with significant facing rigidity will have smaller maximum lateral

displacement. For example, a modular block GRS walls will have δmax about 15%

smaller than that calculated Equation 3.4.

3.1.4 The Jewell-Milligan Method

Jewell (1988) and Jewell and Milligan (1989) proposed a procedure for calculating

wall displacement based on analysis of stresses and displacements in a reinforced soil

mass. The method describes a link between soil stresses (stress fields) in a reinforced

soil mass in which a constant mobilized angle of friction is assumed with the resulting

displacements (velocity fields). There are two parameters for plane-strain plastic

deformation of soil: the plane strain angle of friction, φps, and the angle of dilation, ψ.

78

The planes on which the maximum shearing resistance φps is mobilized are called the

“stress characteristics” and are inclined at ( )2/450psφ+ to the direction of major

principal stress, as shown in Figure 3.4(a). The directions along which there is no

linear extension strain in the soil are called the “velocity characteristics” and are

inclined at ( )2/450 ψ+ to the direction of major principal stress, as shown in Figure

3.4(b).

Figure 3.4: (a) Stress Characteristics and (b) Velocity Characteristics behind a Smooth Retaining Wall Rotating about the Toe (Jewell and Milligan, 1989).

Jewell and Milligan (1989) noted from limiting equilibrium analyses that there are

three important zones in a reinforced soil wall, as illustrated in Figure 3.5(a). The

boundary between zone 1 and 2 is at an angle ( )2/450 ψ+ to the horizontal, and

between zone 2 and 3 at an angle φds. Large reinforcement forces are required in zone

1 to maintain stability across a series of critically inclined planes. In zone 2, the

required reinforcement forces reduce progressively.

79

The assumptions of the Jewell-Milligan method for "ideal length" of reinforcement

are:

• The reinforcement length at every layer extends to the back of zone 2, so

called "ideal length".

• The horizontal movement of the facing may be calculated by assuming the

horizontal deflections starting at the fixed boundary between zones 2 and 3

and working to the face of the wall.

• The stability on the stress characteristics and the velocity characteristics is

equally critical in soil and hence reinforcement must provide equilibrium for

both. The consequence is that behind the Rankine active zone in a reinforced

soil wall, the equilibrium is governed by φds mobilized on the velocity

characteristics.

Figure 3.5: Major Zones of Reinforcement Forces in a GRS Wall and the Force Distribution along Reinforcement with Ideal Length (Jewell and Milligan, 1989).

80

In Figure 3.5, the maximum horizontal resultant force required for equilibrium, Prm, is

equal to the active force Pa:

⎟⎟⎠

⎞⎜⎜⎝

⎛+== HqHKPP saarm 2

2γ (3.5)

in which, γ = unit weight of the soil; H = wall height; qs = uniform surcharge;

Ka = active earth pressure coefficient that can be expressed as:

⎟⎠⎞

⎜⎝⎛ +

⎟⎠⎞

⎜⎝⎛ −+

=+−

=

245tan

245tan

)sin1()sin1(

ψ

φψ

φφ ds

ps

psaK (3.6)

The required reinforcement force Pr in zone 2 at an angle θ, as shown in Figure

3.5(b), can be estimated from the maximum reinforcement force Prm as:

θ

φθtan

)tan(

a

ds

rm

r

KPP −

= (3.7)

The results of the displacement analyses have been presented in the form of design

charts as shown in Figure 3.6. The charts can be used to determine the distribution of

lateral wall displacement along the wall face for different values of mobilized internal

friction φps and angles of dilation ψ.

To estimate the horizontal deflection at the GRS wall face for reinforcement with the

ideal length and uniform spacing, the charts as shown in Figure 3.6 can be used. The

horizontal deflection at the wall face depends on the wall height H, the mobilized soil

shearing resistance φds, the reinforcement force Pr, and the reinforcement stiffness K.

81

The charts in Figure 3.6 can be used to obtain a dimensionless factor,base

h

HPKδ , and

then the horizontal displacement δh can be calculated from this factor. The

reinforcement occurs at the base of the wall, Pbase, in the dimensionless factor above,

can be calculated by

( )svabase qHsKP += γ (3.8)

82

Figure 3.6: Charts for Estimating Lateral Displacement of GRS Walls with the Ideal Length Layout (Jewell and Milligan, 1989)

83

3.2 Developing an Analytical Model for Calculating Lateral Movement and

Connection Forces of a GRS Wall

Jewell and Milligan (1989) have presented design charts for estimating deformation

of reinforced soil walls where the rigidity of the facing can be ignored. Ho and Rowe

(1997) and Rowe and Ho (1993, 1998) pointed out that there is little variation in the

reinforcement forces and the lateral wall deformation when the reinforcement length

to wall height ratio, L/H, is equal to or greater than 0.7 (Note: L/H = 0.7 is commonly

used in practice and it is also suggested by the AASHTO). Based on a series of

numerical analyses of GRS walls, Rowe and Ho (1998) also showed that the

maximum lateral deformation obtained by the Jewell-Milligan method with an ideal

reinforcement length, as defined by Jewell and Milligan (1989), is generally in good

agreement with the numerical results for L/H = 0.7. For this reason, the Jewell-

Milligan method, with the ideal reinforcement length, can be used to estimate lateral

movement of a reinforced soil wall with L/H ≥ 0.7. The analytical model developed

in this study for GRS walls with modular block facing was base on Jewell-Milligan

method. The method is applicable to GRS walls with L/H ≥ 0.7.

The derivation of the analytical model is given below. It begins with the derivation of

the equations in the Jewell-Milligan method for predicting deformation of a

reinforced soil wall with negligible facing rigidity, followed by the derivation of the

equations for determining connection forces in the reinforcement for walls with

modular block facing, and ends with the equations for calculating lateral movement

of GRS walls with modular block facing.

84

3.2.1 Lateral Movement of GRS Walls with Negligible Facing Rigidity

Figure 3.7 shows the three major zones in a GRS wall and the force distribution in the

reinforcement at depth zi, used by Jewell and Milligan (1989) to develop an analytical

model for determination of wall deformation. Jewell and Milligan (1989) have

presented design charts based on the analytical model (without giving the derivation).

The following derivation is presented for completeness and for easier reference when

showing the derivation of the analytical model developed for this study.

Pr m

H

z

(H - z )

i

i

Reinforcement

Zone 3

Zone 1Zone 2

x

z

L Lzone-1 zone-2

L

45 + ψ/2 φds

i

Figure 3.7: Major Zones of the Reinforcement Force in a Reinforced Soil Wall (Jewell and Milligan, 1989)

The horizontal movement, Δh, of the wall face at depth zi can be evaluated as:

(3.9) 21 −− Δ+Δ=Δ zonezoneh

1inf0 inf

1

1

−− ∫−

==Δ zonere

rmL

re

rmzone L

KP

dxKPzone

(3.10)

85

∫−−

−

+

−− ⎟⎠⎞

⎜⎝⎛≈=Δ

21

1

2infinf

2 21zonezone

zone

LL

Lzone

re

rm

re

rzone L

KP

dxK

P (3.11)

where Kreinf stiffness of the reinforcement

Prm maximum reinforcement force at depth zi

Lzone-1 reinforcement length in Zone 1 at depth zi

Lzone-2 reinforcement length in Zone 2 at depth zi

Substituting Equation 2.10 and Equation 3.11 into Equation 3.9, we get

⎟⎠⎞

⎜⎝⎛ +=Δ −− 21

inf 21

zonezonere

rmh LL

KP

(3.12)

Since

( ) ⎟⎠⎞

⎜⎝⎛ −−=− 245tan1

ψoizone zHL (3.13)

and

( ) ( ) ⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −−−−=− 245tan90tan2

ψφ ods

oizone zHL (3.14)

Therefore, substituting Equation 3.13 and Equation 3.14 into Equation 3.12 leads to

( ) ( ) ( )⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −−−−+⎟

⎠⎞

⎜⎝⎛ −−=Δ

245tan90tan

21

245tan

inf

ψφψ ods

oi

oi

re

rmh zHzH

KP

(3.15)

Rearranging Equation 3.15, we have

( ) ( )⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −−−+⎟

⎠⎞

⎜⎝⎛ −−=Δ

245tan90tan

21

245tan

inf

ψφψ ods

ooi

re

rmh zH

KP

(3.16)

or

( ) ( )⎭⎬⎫

⎩⎨⎧

⎥⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −−=Δ ds

ooi

re

rmh zH

KP

φψ 90tan2

45tan21

inf

(3.17)

86

The value of Δh, lateral displacement of a GRS wall at depth zi, can be calculated

directly from the following equation:

( ) ⎥⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=Δ )90tan(

245tan

21 00

infdsi

re

rmh zH

KP

φψ (3.18)

where Kreinf stiffness of the reinforcement

Prm maximum reinforcement force at depth zi

H wall height

φds effective direct shear friction angle of soil

ψ angle of dilation of soil

Prm reinforcement force in zone 1 or connection force (will be

discussed in Section 2.2)

3.2.2 Connection Forces for GRS walls with Modular Block Facing

The connection forces, Prm in Equation 3.18, are defined as the forces in the

reinforcement at the back face of the wall facing. The assumptions made for the

determination of the connection forces include:

• The wall face is vertical or nearly vertical.

• There is only friction connection between adjacent facing blocks (i.e., there is

no additional mechanical connection elements, such as lips, keys, or pins).

• A uniform surcharge is being applied over the entire horizontal crest of the

wall.

• Each facing block is a rigid body, i.e., movement is allowed, but not the

deformation. As a facing block moves, the frictional resistance, F, between

two adjacent blocks will reach Fmax.

87

Consider the reinforcement at depth zi, sandwiched between two adjacent facing

blocks, as shown in Figure 3.8. The frictional forces above and below these blocks

are Fi-1 and Fi+1. The horizontal resultant force of lateral earth pressure acting on the

two facing blocks is Pi. The tensile connection force in the reinforcement at depth zi

is Ti.

Sv

± Fi+1

b

± Fi-1

Ti

reinforcement

Ni-1

Wi

Ni+1

Ffi

Pi

Top of the wall

Zi

Figure 3.8: Forces Acting on Two Facing Blocks at Depth zi

The tensile connection force Ti in the reinforcement will be:

) (3.19) ( 11 −+ −±= iiii FFPT

where ( vishi SqzKP += )γ (3.20)

If Ti should be set equal to 0, as geosynthetic reinforcement can

resist only tensile forces, i.e., Ti is always ≥ 0.

,0)( 11 <−± −+ iii FFP

From Figure 3.8,

δtan)( 11 −+ −±= iiii NNPT ; 0=iT if 0≤iT (3.21)

where Ni+1 and Ni-1 are normal forces on the top and the bottom of the two adjacent

blocks.

δtan)( fiiii FWPT +±= (3.22)

88

or,

δβγ tan)tan( vvbii SpbSPT +±= (3.23)

where

Ffi frictional resultant force between wall facing and soil

γb unit weight of facing block

b width of facing block

Sv reinforcement spacing

δ friction angle between modular block facing elements (δ can be the

friction angle between facing blocks if there is no reinforcement

between the blocks, or it can be the friction angle between facing

block and geosynthetic if there is reinforcement sandwiched between

blocks)

β friction angle between back face of wall and soil

p average net earth pressure acting on the facing, due to earth pressure

on the facing and the pressure caused by the reinforcement force. The

value of p can be estimated as:

δγ tan11 bS

FFp bv

ii =−

= −+ (3.24)

Substituting Equation 3.24 into Equation 3.23, Ti , the connection force at depth zi,

can be determined as:

δβδγγ tan)tantan( vbvbii bSbSPT +±= (3.25)

or,

( ) δβδγγγ tan)tantan( vbvbvishi bSbSSqzKT +±+= (3.26)

Therefore, the tensile connection force in the reinforcement at depth zi can be

expressed as:

( ) )tantan1(tan βδδγγ +±+= vbvishi bSSqzKT ; T = 0 if T ≤ 0 (3.27)

89

Note that if the friction between the back face of the wall facing and the soil behind

the wall is ignored, the connection force at depth zi becomes:

( ) ( )( )δγγ tanvbvishi bSSqzKT ±+= ; T = 0 if T ≤ 0 (3.28)

Calculating the reinforcement connection forces in a GRS wall with modular block

facing by a simple equation can reduce considerable amount of work for designing a

GRS wall. To design GRS walls with segmental facing, the connection forces are

concerned. A series of experimental tests to measure the connection forces were

conducted from many researchers. According to their results, if the blocks are heavy

and well connected, the GRS walls with block facing would perform very well

(Hatami and Bathurst, 2005 and 2006). A simple way to estimate the connection

forces of reinforcement in the GRS walls with block facing will be presented. The

values of the connection forces can be estimated by using the equation below for a

typical GRS wall with modular block facing:

( ) ( )( )δγγ tanvbvishi bSSqzKT −+= (3.29)

The resistant connection force at depth zi at facing can be estimated by:

)(tan2 δγ ibr bzF = (3.30)

The comparison of connection forces and maximum friction capacity at facing blocks

are shown in Figure 3.9 and 3.10.

90

Connection force

0

0.5

1

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30

Connection force (kN)D

epth

(m)

Proposedmethod

Maximumfrictioncapacity atfacing

Figure 3.9: Connection Forces in Reinforcement (q = 0) (The Data of the Wall are from Section 3.3.1 with ψ = 150)

Connection force

0

0.5

1

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30 35 40

Connection force (kN)

Dep

th (m

)

Proposedmethod

Maximumfrictioncapacity atfacing

Figure 3.10: Connection Forces in Reinforcement (q = 50 kN/m) (The Data of the Wall are from Section 3.3.1 with ψ = 150)

91

Figures 3.9 and 3.10 show the values of connection forces with the maximum

connection friction forces with the surcharge of zero and 50 kN/m. For most of the

cases, the lightweight blocks (without strong key connections between block and

block) can be used for GRS walls. With the heavy surcharge, some blocks at the top

of the walls may be unstable as shown in Figure 3.10.

3.2.3 Lateral Movement of GRS Walls with Modular Block Facing

From Equation 3.18 and Equation 3.29, the displacement of a GRS wall with modular

block facing at depth zi can be determined by:

( ) ( ) ⎥⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −−⎟⎟

⎠

⎞⎜⎜⎝

⎛ +−+=Δ )90tan(

245tan

)tantan1(tan5.0 00

infdsi

re

vbvishi zH

KbSSqzK

φψβδδγγ

(3.31)

Equation 3.31 is referred to as the analytical model in this study. When there is the

frictional resistance between the back face of the wall facing and the soil can be

ignored, the displacement of the wall at depth zi will reduce to:

( ) ( )( ) ( ) ⎥⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −−⎟⎟

⎠

⎞⎜⎜⎝

⎛ −+=Δ )90tan(

245tan

tan5.0 00

infdsi

re

vbvishi zH

KbSSqzK

φψδγγ

(3.32)

Note that the lateral movement calculated by Equation 3.32 will be slightly larger

than those calculated by Equation 3.31.

92

3.3 Verification of the Analytical Method

To verify the analytical model developed in this study, the model calculation results

were first compared with the Jewell-Milligan method for GRS walls with negligible

facing rigidity. The model calculation results were then compared with measured

data from a full-scale experiment.

3.3.1 Comparisons with the Jewell-Milligan Method for Lateral Wall

Movement

The model calculation results of wall movement from the analytical model were first

compared with the results of the Jewell-Milligan method (1989) using an example.

The conditions of the wall in this example are as follows:

• Wall height H = 4.0 m.

• Geosynthetic reinforcement: vertical spacing Sv = 0.4 m, stiffness Kreinf = 200

kN/m.

• Backfill: free-draining granular soil, unit weight γs = 18 kN/m3, cohesion c =

0, friction angle φds = 35o, dilation angle ψ = 5o.

• Facing: modular concrete blocks, width b = 0.3 m, unit weight γb = 0, 20, and

30 kN/m3.

• Interface between adjacent blocks: cohesion, c = 0; friction angle, δ = 25o.

• Interface friction between back face of facing and soil, β = 0o.

The Results of the comparisons between the analytical model and the Jewell-Milligan

method are showed in Figures 3.11 to 3.14 for different weights of facing blocks (unit

weight of block γb = 0, 10, 20, and 30 kN/m3, respectively), each with different values

93

of surcharge pressure (q = 0, 10, and 50 kN/m; Note: q = 10 kN/m represents a typical

surcharge for highway design). These Figures indicate that, for all facing conditions

(i.e., for different values of γb), the effect of surcharge on wall movement is very

significant. The deformed shape of the wall face is rather different at q = 0 and q =

50 kN/m. At q = 0, the wall bulges at the mid-height, but as the surcharge increases,

the top of the wall face begins to move outward. At q = 50 kN/m, the largest wall

movement occurs near the top of the wall.

As can be seen from Figure 3.11, when the facing block is weightless, i.e., unit

weight of facing block γb = 0, the analytical model give nearly identical lateral wall

movement to the Jewell-Milligan method. This is to be expected because facing

rigidity is ignored in the Jewell-Milligan method. The Figures show that as the facing

blocks becomes heavier (i.e., as the unit weight of the blocks increases), the wall

movement becomes smaller. When a heavy facing block (γb = 30 kN/m3) is used, the

maximum lateral wall movement can be as much as 35% smaller than a wall with

negligible facing rigidity.

94

q = 0

00.40.81.21.6

22.42.83.23.6

4

0 20 40 60

Lateral Displacement (mm)

Dep

th fr

om th

e To

p (m

)Analytical model

Jew ell-Milliganmethod

q = 10 kN/m

00.40.81.21.6

22.42.83.23.6

4

0 20 40 60


Dep

th fr

om th

e To

p (m

)

Analytical model


q = 50 kN/m

00.40.81.21.6

22.42.83.23.6

4

0 20 40 60


Dep

th fr

om th

e To

p (m

)

Analytical model


Figure 3.11: Comparison of Lateral Displacement Calculated by the Jewell-Milligan Method and the Analytical Model, γb = 0 kN/m3

95

q = 0

00.40.81.21.6

22.42.83.23.6

4

0 20 40 60


Dep

th fr

om th

e To

p (m

)Analytical model


q = 10 kN/m

00.40.81.21.6

22.42.83.23.6

4

0 20 40 60


Dep

th fr

om th

e To

p (m

)

Analytical model


q = 50 kN/m

00.40.81.21.6

22.42.83.23.6

4

0 20 40 60


Dep

th fr

om th

e To

p (m

)

Analytical model



96

q = 0

00.40.81.21.6

22.42.83.23.6

4

0 20 40 60


Dep

th fr

om th

e To

p (m

)Analytical model


q = 10 kN/m

00.40.81.21.6

22.42.83.23.6

4

0 20 40 60


Dep

th fr

om th

e To

p (m

)

Analytical model


q = 50 kN/m

00.40.81.21.6

22.42.83.23.6

4

0 20 40 60


Dep

th fr

om th

e To

p (m

)

Analytical model



97

q = 0

00.40.81.21.6

22.42.83.23.6

4

0 20 40 60


Dep

th fr

om th

e To

p (m

)Analytical model


q = 10 kN/m

00.40.81.21.6

22.42.83.23.6

4

0 20 40 60


Dep

th fr

om th

e To

p (m

)

Analytical model


q = 50 kN/m

00.40.81.21.6

22.42.83.23.6

4

0 20 40 60


Dep

th fr

om th

e To

p (m

)

Analytical model



98

3.3.2 Comparisons with Measured Data of Full-Scale Experiment by Hatami

and Bathurst (2005 and 2006)

Figure 3.15 shows the configuration a full-scale experiment of GRS wall with

modular block facing. It is one of a series of laboratory experiments conducted by

Hatami and Bathurst (2005 and 2006), and was referred to as “wall 1” by the authors.

The parameters of the GRS wall are summarized below:

• Wall height H = 3.6 m high with a facing batter of 8° from the vertical and

seated on a rigid foundation.

• Soil: a clean uniform beach sand, γs = 16.8 kN/m3, φps = 44o, ψ = 11o, and c =

2 kPa.

• Geosynthetic reinforcement: a weak biaxial polypropylene (PP) geogrid,

vertical spacing = 0.6 m, reinforcement stiffness = 115 kN/m, ultimate

strength = 14 kN/m.

• Facing: solid masonry concrete blocks (300 mm wide by 150 mm high by 200

mm deep) with a shear key on the top surface of block, and γb = 20 kN/m3.

• Interface between facing blocks: δb-b = 57o and cb-b = 46 kPa.

Because the analytical model requires that the direct shear friction angle be used in

model calculations, and it also assumes a vertical wall face, the direct shear friction

angle of the soil and the facing batter factor were determined before using the

analytical model to evaluate the lateral movement of the facing.

(a) Direct shear friction angle:

ooo

oo

ps

psds 40

11sin44sin111cos44sin

sinsin1cossin

tan =−

=−

=ψφ

ψφφ (3.34)

99

(b) Empirical facing batter factor, Φ , from Allen and Bathurst (2001), with facing

batter of 8o: fb

88.0=⎟⎠

⎜⎝ avh

fb K

In the above equation, Kabh is the horizontal component of the active earth pressure

coefficient accounting for wall face batter, Kavh is the horizontal component of the

active earth pressure coefficient for a vertical wall, and d is a constant coef

⎟⎞

⎜⎛

=Φd

abhK (3.35)

ficient.

Allen and Bathurst (2001) found that the value of d = 0.5 would yield the best fit for

available Tmax data, and recommended using d = 0.5 for determination of Φfb.

Figure 3.15: Configuration of a Full-Scale Experiment of GRS Wall with Modular

Block Facing (Hatami and Bathurst, 2005 and 2006)

100

Figure 3.16 shows lateral movement of the GRS wall under surcharge pressures of 50

kN/m and 70 kN/m for: (a) mean value of measured displacement (Hatami and

Bathurst, 2006), (b) the Jewell-Milligan method, and (c) the analytical model (present

study). The Figure shows that the lateral movement calculated by the analytical

model is in very good agreement with the measured values. It is seen that that lateral

wall movement given by the analytical model agrees much better with the measured

values than that calculated by the Jewell-Milligan method for both surcharge

pressures. The lateral movement obtained by the Jewell-Milligan method was as

much as 3.5 times as large as the measured movement. Note that the analytical

odel, not unlike the Jewell-Milligan method, produced a displacement profile that

had lower bending stiffness than the measured profile. However, considering that the

analytical model is a simplified model, the simulation is considered adequate.

m

101

q = 50 kN/m

0

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

0 30 60 90 Lateral Displacement (mm)

Dep

th fr

om th

e To

p (m

)

Analyticalmodel


Averagemeasured

q = 70 kN/m

0

0.4

0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

0 30 60 90 Lateral Displacement (mm)

Dep

th fr

om th

e To

p (m

)

Analyticalmodel


Averagemeasured

Figure 3.16: Comparisons of Measured Lateral Displacements with Jewell-Milligan Method and the Analytical Model

102

103

3.4 Summary

An analytical model has been developed to predict the profile of lateral movement of

a GRS wall with modular block facing. The connection forces in the reinforcement

can also be determined by a simple equation. The analytical model has been verified

through comparisons with Jewell-Milligan’s method. Jewell-Milligan’s method is

only a special case of the analytical model for GRS walls with negligible facing

rigidity. Comparisons were also made with a full-scale experiment of GRS wall with

modular block facing. It is shown that the analytical model offers a simple and

improved tool for predicting lateral movement of a GRS wall with modular block

facing.

4. THE GENERIC SOIL-GEOSYNTHETIC COMPOSITE (GSGC) TESTS

The understanding of soil-geosynthetic composite behavior in reinforced soil

structures has been lacking. As a result, current design methods have simply

considered the geosynthetics as added tensile elements, and have failed to account for

the interaction between soil and geosynthetics. A series of laboratory tests, referred

to as the “Generic Soil-Geosynthetic Composite” tests, or GSGC tests, were designed

and conducted to (a) examine the behavior of a generic soil-geosynthetic composite

with varying spacing and strength of reinforcement, (b) provide test data for verifying

the analytical model for calculating strength properties of a GRS composite as

described in Chapter 5, and (c) provide test data for calibration of Finite Element (FE)

model for a GRS mass. The GSGC tests were conducted at the Turner-Fairbank

Highway Research Center (TFHRC), Federal Highway Administration (FHWA) in

Mclean, Virginia.

4.1 Dimensions of the Plane Strain GSGC Test Specimen

A soil mass reinforced by layers of geosynthetic reinforcement is not a uniform mass.

To investigate the behavior of soil-geosynthetic composites by conducting laboratory

tests, it is necessary to determine the proper dimensions of the test specimen so that

the test will provide an adequate representation of soil-geosynthetic composite

behavior. Also, since most GRS structures resemble a plane strain condition, the test

specimen needs to be tested under a plane strain condition.

A number of factors were considered prior to determining the test specimen dimensions

of the GSGC test, including:

104

- Plane Strain Condition: As most GRS structures resemble a plane strain

condition, the test should be conducted in a plane strain condition.

- Backfill Particle Size: To alleviate the particle size effects on the test

specimen, the dimensions of a generic GRS mass should be at least 6 times as

large as the maximum particle size of the soil specimen, as suggested by the

U.S. Army Corps of Engineers, and 15 times larger than the average

particle size (D50) (Jewell, 1993). The recommended maximum particle

size for the backfill of GRS structures is 19 mm or ¾ in. (Elias and

Christopher, 1996). The specimen dimension, therefore, should be at least

120 mm.

- 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 of 200 mm to 300 mm for GRS walls.

- Size of Reinforcement Sheet: The specimen dimensions in the plane strain

direction, referred to as the “width” (W) and in the longitudinal direction,

referred to as Length (L) should be sufficiently large to provide adequate

representation of the geosynthetic reinforcement. For polymer grids, enough

grid “cells” need to be included for a good representation of the polymer grid.

For nonwoven geotextiles, the aspect ratio of the reinforcement specimen

(i.e., the ratio of width to length) should be sufficiently large (say, greater

than 4) to alleviate significant “necking” effect. There will be little “necking”

effect for woven geotextiles, regardless of the aspect ratio.

A series of finite element analyses, using the computer code PLAXIS 8.2, were

conducted to examine the effect of specimen dimensions on the resulting global

stress-strain and volume change relationships of the composites. The objective of the

105

finite element analyses was to determine proper dimensions of a generic soil-

geosynthetic composite that will produce load-deformation behavior sufficiently close

to that of a large mass of soil-geosynthetic composite, referred to as the reference

composite.

Figure 4.1 shows the typical geometric and loading conditions of the GSGC tests.

The reference soil-geosynthetic composite is taken as a reinforced soil mass of

dimensions 7.0 m (23 ft) high and 4.9 m wide in a plane strain condition. Four

different dimensions of GRS composites were analyzed: specimen heights, H = 7.0

m, 2.0 m, 1.0 m and 0.5 m, while the width, W, of the test specimen was kept as

0.7*H. In these analyses, the soil was a dense sand. The sand was reinforced by a

medium-strength woven geotextile (Geotex 4x4) at 0.2 m vertical spacing. Table 4.1

lists the conditions and properties of the soil and reinforcement used in the analyses.

The global stress-strain curves obtained from the analyses are shown in Figures 4.2

and 4.4 for confining pressures, σc, of 0 and 30 kPa, respectively (note: a confining

pressure of 30 kPa is representative of the lateral stress at the mid-height of a 7.0 m

high wall). The corresponding global volume change curves are shown in Figures 4.3

and 4.5. The global vertical strain, εv, was calculated by the following equation:

%100⎟⎠⎞

⎜⎝⎛ Δ

=HH

vε (4.1)

where HΔ = total vertical displacement of the specimen; H = initial height of the specimen.

Figures 4.2 and 4.4 indicate that the composite with height H = 2.0 m, width W = 1.4

m, and under a confining pressure of 30 kPa yields stress-strain and volume change

relationships that are sufficiently close to those of the reference composite. Specimen

106

sizes with heights H = 1.0 m and 0.5 m appear too small for providing an adequate

representation of the reference composite.

Soil

Reinforcement

Sv = 0.2 m

H

σv

W = 0.7 H

σcσc

Figure 4.1: Typical Geometric and Loading Conditions of a GRS Composite

107

Table 4.1: Conditions and properties of the backfill and reinforcement used in F.E. analyses

Description

Soil

A Dense sand: unit weight = 17 kN/m3; cohesion = 5 kPa;

angle of internal friction, φ = 38o; angle of dilation, ψ = 8o; soil

modulus, E50 = 40,000 kPa; Poisson’s ratio = 0.3.

Reinforcement Geotex 4x4: axial stiffness, EA = 1,000 kN/m; ultimate

strength, Tult = 70 kN/m; reinforcement spacing = 0.2 m.

Confining

Pressure

Constant confining pressures of 0 and 30 kPa.

108

0

500

1000

1500

2000

0 5 10 15 20 25

Global Vertical Strain εv (%)

σv- σ

h (kP

a)

7.0 m x 4.9 m

2.0 m x 1.4 m

1.0 m x 0.7 m

0.5 m x 0.35 m

Specimen Dimensions:

Figure 4.2: Global Stress-Strain Curves for Soil-Geosynthetic Composites of Different Dimensions under a Confining Pressure of 0 kPa

109

-2

-1

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16


Glo

bal V

olum

etric

Str

ain

ΔV/

V (%

)

7.0 m x 4.9 m

2.0 m x 1.4 m

1.0 m x 0.7 m

0.5 m x 0.35 m


Figure 4.3: Global Volume Change Curves for Soil-Geosynthetic Composites of Different Dimensions under a Confining Pressure of 0 kPa

110

0

500

1000

1500

2000

0 5 10 15 20 25


σv- σ

h (kP

a)

7.0 m x 4.9 m

2.0 m x 1.4 m

1.0 m x 0.7 m

0.5 m x 0.35 m


Figure 4.4: Global Stress-Strain Curves for Soil-Geosynthetic Composites of Different Dimensions under a Confining Pressure of 30 kPa

111

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10 12 14 16


Glo

bal V

olum

etric

Str

ain

ΔV/

V (%

)

7.0 m x 4.9 m

2.0 m x 1.4 m

1.0 m x 0.7 m

0.5 m x 0.35 m


Figure 4.5: Global Volume Change Curves for Soil-Geosynthetic Composites of Different Dimensions under a Confining Pressure of 30 kPa

112

For comparison purposes, additional analyses were conducted on unreinforced soil.

Figures 4.6 and 4.7 show, respectively, the global stress-strain curves and global

volume change curves of the soil masses without any reinforcement for the different

specimen dimensions. The results indicate that the specimen height as small as 0.5 m

will yield nearly the same stress-strain and volume change relationships as the

reference soil mass of height = 7.0 m when reinforcement is not present.

113

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

0 1 2 3 4 5 6


σv- σ

h (k

Pa)

7.0 m x 4.9 m

2.0 m x 1.4 m

1.0 m x 0.7 m

0.5 m x 0.35 m


Figure 4.6: Global Stress-Strain Curves of the Unreinforced Soil Under a Confining Pressure of 30 kPa

114

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6


Glo

bal V

olum

etric

Str

ain

ΔV/V

(%)

7m x 4.9m

2m x 1.4m

1m x 0.7m

0.5m x 0.35m

Specimen Dimensions

Figure 4.7: Global Volume Change Curves of the Unreinforced Soil Under a Confining Pressure of 30 kPa

115

Based on the results of the finite element analyses, a specimen height of 2.0 m, and

depth of 1.4 m, with 0.2 m reinforcement spacing, was selected as the specimen

dimensions for the GSGC tests. The actual specimen dimensions for the GSGC tests

are shown in Figures 4.8. Figures 4.9 and 4.10 show, respectively, the front and plan

views of the GSGC test setup.

Reinforcement

Sv = 0.2 m

H =

2.0

m

L = 1.2 m

W = 1.4 m

Figure 4.8: Specimen Dimensions for the GSGC Tests

116

160.00

81.6

5

Load cell LC1 (1000 kip)

11.38

108.00

2.625'' steel plate

70.0

0

36.00

1

3.00

1.50

6.00

6.00

5.0

2.6 6.0

76.2

5

134.

63

33.0

0

30.0

0

2.87

70.00

74.25

53.375

74.00

A 2

7.63

36.00

3

11.38

30.7

5

51.9

8

(Note: All Dimensions in Inches)

49.00

jack

12.2

5

Load cell LC2 (300 kip)

2'' steel plate

12.00

25.1

9

1.94 4.00

12.0

0

1.12

5.622.63

16.93

12.25

16.93

34.00

26.00

2.00

A

2.00

steel plate (26''x32.5''x2'')

concrete pad (49''x41 3/8''x12'')

concrete block (7.625''x7.625''x15.625'')

9.63

steel plate (43''x34''x2'')

steel plate (43''x34''x2'')

D=1.125''

FRONT VIEW

Figure 4.9: Front View of the Test Setup

117

36.00 108.00 36.00

PLAN

75.8

7

36.9

436

.94

74.0017.00 17.00

36.0

0

Open Face: Concrete blocks (7.625''x7.625''x15.625'') would be removed before testing

26.63

1 3

A

2

23.25

21.5

0

19.50

47.00

47.0

0

47.00

53.375 26.63

47.0

0

7.63

1.25

Rigid frame

Anchor

Specimen

(Note: All Dimensions in Inches)

Figure 4.10: Plan View of the Test Setup

118

4.2 Apparatus for Plane Strain Test

To maintain a plane strain condition for the GSGC specimens throughout the tests,

two major factors were considered: (1) the test bin needs to be sufficiently rigid to

have negligible lateral deformation in the longitudinal direction (i.e. the length

direction, L), and (2) the friction between the backfill and the side panels of the test

bin needs to be minimized to nearly zero.

4.2.1 Lateral deformation

Five GSGC masses were tested inside a test bin. The test bin was designed to

experience little deformation for a surcharge pressure of up to 2,800 kPa. The test bin

is shown in Figure 4.1. The details of the test bin and the design calculations are

presented in Appendix B.

4.2.2 Friction

Two transparent plexiglass panels were attached inside steel tubing frame to form the

side surfaces of the test bin. To minimize the friction between the plexiglass and the

backfill in these surfaces, a lubrication layer was created inside surfaces of the

plexiglass panels. The lubrication layer consisted of a 0.5 mm-thick latex membrane

and an approximate 1 mm-thick lubrication agent (Dow Corning 4 Electrical

Insulating Compound NSF 6). This procedure has been successful in many plane

strain tests conducted by Professor Tatsuoka at University of Tokyo and Professor

Wu at University of Colorado Denver. The friction angle between the lubricant layer

and the plexiglass as determined by direct shear test was less than one (1) degree.

119

Figure 4.11: The Test Bin

120

4.3 Test Material

The backfill and geotextile reinforcement employed in the tests are described as

follows.

4.3.1 Backfill

The backfill was a crushed Diabase from a source near Washington D.C. Before

conducting the GSGC tests, a series of laboratory tests were performed to determine

the properties of the backfill, including:

• Gradation test

• Specific gravity and absorption test of the coarse aggregates

• Moisture-Density tests (Proctor compaction) with rock correction

• Large-size triaxial tests with specimen diameter of 152 mm (6 in.)

The details of these tests are presented in Appendix A. A summary of some index

properties is given in Table 4.2. The grain size distribution of the soil is shown in

Figure 4.12. Two gradation tests were performed. The results agree well with each

other.

Four triaxial tests were conducted at confining pressures of 5 psi, 15 psi, 30 psi, and

70 psi, and the results were compared with those performed by Ketchart et al. on the

same soil. The soil specimen was approximately 6 in. in diameter and 12 in. in

height. The shapes of a typical specimen before and after failure are shown in Figure

4.13. Figure 4.14 presents the stress-strain curves and volume change curves of the

tests. The stress-strain curves obtained by Ketchart et al. are also included for

comparisons and for furnishing a more complete set of data. The stress-strain

relationships agree well in trend with those by Ketchart et al. The Mohr-Coulomb

121

failure envelops of the backfill are shown in Figure 4.15. For confining pressures

between 0 and 30 psi, the strength parameters are: c = 10.3 psi, φ = 50o. For

confining pressures between 30 and 110 psi, the strength parameters are: c = 35.1 psi,

φ = 38o.

122

Table 4.2: Summary of some index properties of backfill

Classification Well graded gravel: A-1a, per AASHTO M-15; and

GW-GM, per ASTM D2487.

Maximum Dry Unit Weight 24.1 kN/m3 (153.7 lb/ft3)

Optimum Moisture Content 5.2 %

Specific Gravity of Soil

Solids

3.03

123

0

10

20

30

40

50

60

70

80

0.010.1110100

Grain size (mm)

Perc

ent f

iner

(%)

Test 1

Test 2

Figure 4.12: Grain Size Distribution of Backfill

124

(a) (b)

Figure 4.13: Typical Triaxial Test Specimen (a) before and (b) after Test

125

Deviatoric Stress versus Axial Strain Relationships

0

50

100

150

200

250

300

350

400

450

500

550

600

0 1 2 3 4 5 6 7 8 9 10 11

Axial Strain (%)

Dev

iato

ric

Stre

ss (p

si)

5 psi

15 psi

30 psi

70 psi

70 psi - Ketchart

110 psi - Ketchart

(a)

Volumetric Strain versus Axial Strain

-0.4

-0.2

0

0.2

0.4

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Axial Strain (%)

Volu

met

ric

Stra

in (%

)

5 psi

30 psi

(b)

Figure 4.14: Triaxial Test Results:

(a) Stress-Strain Curves of Backfill at 24.1 kN/m3 Dry Density and 5.2% Moisture (b) Volume Change Curves of Backfill at Confining Pressures of 5 psi and 30 psi

126

σ3 = 15 psi

σ3 = 30 psi

Shea

r St

rees

s (ps

i)

Normal Stress (psi)

σ3 = 5 psi

σ3 = 70 psi

σ3 = 110 psi

433265172 61698300

C2 = 35.1 psi

C1 = 10.3 psi

Figure 4.15: Mohr-Coulomb Failure Envelops of Backfill

127

4.3.2 Geosynthetics

The geosynthetic used in the experiments was Geotex 4x4 manufactured by Propex,

Inc. (formally known as Amoco 2044). This geosynthetic is a woven polypropylene

geotextile, with its strength properties provided by the manufacture shown in Table

4.3.

Table 4.3: Summary of Geotex 4x4 properties provided by the manufacture

Property Test Method Machine Direction

(Wrap Direction)

Cross-Direction

(Fill Direction)

Tensile Strength

(Grab)

ASTM D-4632 2.67 kN

(0.6 kips)

2.22 kN

(0.5 kips)

Wide-Width

Tensile Ultimate

Strength

ASTM D-4595 70 kN/m

(400 lb/in.)

70 kN/m

(400 lb/in.)

Wide-Width

Strength at 5%

Strain

ASTM D-4595 21 kN/m

(121 lb/in.)

38 kN/m

(217 lb/in.)

Wide-Width

Ultimate

Elongation

ASTM D-4595 10 % 10 %

Puncture ASTM D-4833 0.8 kN (170 lb)

Trapezoid

Tearing Strength

ASTM D-4533 1.11 kN (250 lb)

128

Two types of geosynthetics were used for the experiments: a single-sheet of Geotex

4x4, and a double-sheet Geotex 4x4 (by gluing two sheets of Geotex 4x4 together

using 3M Super 77 spray adhesive). The use of the double-sheet was to create a

geosynthetic that is approximately twice as stiff (and as strong), yet maintaining the

same interface condition as that of the single-sheet geosynthetic. Geotex 4x4

geotextile has been used in the construction of hundreds of production GRS walls and

in many full-scale experiments, including the FHWA GRS pier (Adams, 1997),

Havana Yard Test abutment and pier (Ketchart and Wu, 1997), Blackhawk preloaded

GRS bridge abutment (Ketchart and Wu, 1998), and NCHRP test abutments (Wu, et

al., 2006).

Uniaxial tension tests were performed on both types of geosynthetic to determine the

load-deformation behavior using specimen dimensions of Width = 305 mm (12 in.)

and Length = 152 mm (6 in.), see Figure 4.16. The stiffness and strength of the two

geosynthetics are shown in Table 4.4 and load-deformation curves are shown in

Figure 4.17. It is seen that the stiffness and the strength of the double-sheet Geotex

4x4 are approximately twice as much as those of the single-sheet Geotex 4x4, with

the breakage strain being almost the same.

129

Figure 4.16: Uni-Axial Tension Test of Geotex 4x4

130

Table 4.4: Properties of Geotex 4x4 in fill-direction

Geosynthetics Wide-Width Tensile Strength,

per ASTM 4595

Stiffness (kN/m) at

1% Strain

Ultimate Strength (kN/m)

(% at break)

Single-Sheet

Geotex 4x4

1,000 70 (12 %)

Double-Sheet

Geotex 4x4

1,960 138 (12 %)

131

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Axial Strain (%)

Tens

ile L

oad

(kN

/m)

Single-Sheet

Double-Sheet

Figure 4.17: Load-Deformation Curves of the Geosynthetics

4.3.3 Facing Block

Blocks used for the facing of the GSGC mass during specimen preparation were

hollow concrete blocks with the dimensions of 397 mm x 194 mm x 194 mm (15.625

in. x 7.625 in. x 7.625 in.) and with the average weight of 18.1 kg/block (40

lbs/block).

132

4.4 Test Program

The test program comprises five GSGC tests, with their test conditions shown in

Table 4.5. The plate compactor, MBW - GP1200, used for the tests has the following

specifications: weight = 120 lbs; plate dimensions = 12 in. x 21 in.; centrifugal force

= 1,500 lbf; rotation speed = 5000 vpm; and moving speed = 70 ft/min.

Table 4.5: Test program for the GSGC tests

Test

Designation

Geosynthetic

Reinforcement

Confining

Pressure

Wide-Width

Strength of

Reinforcement

Reinforcement

Spacing, Sv

Test 1 None 34 kPa None No

reinforcement

Test 2 Geotex 4x4 34 kPa T = 70 kN/m Sv = 0.2 m

Test 3 Double-Sheet

Geotex 4x4

34 kPa T = 140 kN/m Sv = 0.4 m

Test 4 Geotex 4x4 34 kPa T = 70 kN/m Sv = 0.4 m

Test 5 Geotex 4x4 0

(unconfined)

T = 70 kN/m Sv = 0.2 m

133

4.5 Test Conditions and Instrumentation

4.5.1 Vertical Loading System

The vertical loads were applied to the test specimens by using a 1,000,000-pound

capacity loading frame with a 1,000,000-pound hydraulic jack. Loads were measured

by load cells and by hydraulic jack pressure gauges. For Test 1, two load cells of

100,000 pounds and 300,000 pounds were used to measure the loads. For Tests 2 to

5, a 1,000,000 pound load cell was used to measure the loads. A 12 in.-thick concrete

pad was placed on top of the specimen before loading. Vertical loads were applied in

equal increments with ten-minute elapsed time between increments to allow time for

equilibrium. The elapsed time also allow manual recording of displacements of the

test specimen. The vertical loads were applied until a failure condition was reached

to determine the strength of the composite specimen. The applied pressures on the

composite specimens were determined from the applied vertical loads divided by the

surface areas of the composite specimens.

4.5.2 Confining Pressure

The confining pressure on the test specimens was applied by vacuuming. The entire

surface area of the test specimen was vacuum-sealed with a 0.5-mm thick latex

membrane. A prescribed confining pressure of 34 kPa (5 psi) for tests 1 to 4 was applied

by connecting the latex membrane to a suction device through two 6-mm diameter

flexible plastic tubes. Only Test 5 was conducted without confining pressure.

4.5.3 Instrumentation

The specimens were instrumented to monitor their performance during tests. The

instruments used include:

134

a. Vertical Movement

Three Linear Variable Displacement Transducers (LVDT) and two digital dial

indicators were installed on the top of the concrete pad to measure the vertical

movement of the specimen during loading. The vertical movement was measured

along the top surface of the concrete pad.

b. Lateral Movement

Ten LVDTs and two digital dial indicators were installed along the height of the

specimen (two open sides of the specimen) to measure the lateral movement of the

specimen. The location of the LVDTs and digital dial indicators are shown in Figure

4.18. Figure 4.37 shows the LVDTs on a test specimen to monitor the lateral

movement.

c. Internal Movement

The internal movement of the soil at selected points in the soil mass was traced by

marking the locations of pre-selected points on a 2 in. x 2 in. grid system drawn on

the membrane. The locations of the selected points for the tests are depicted in Figure

4.38.

135

FRONT VIEWSIDE VIEW

Cross Section A-A

TOP VIEW

72.25'' (1835.15) 47.37'' (1203.32)

1-1/4''

73.72 (1872.49)

55.12'' (1400)

5.35''

11.37

(288

.92)

10.4

(264

.16)

11.37

(288

.92)

11.37

(288

.92)

11.37

(288

.92)

11.37

(288

.92)

11.37

(288

.92)

76.3'

' (193

8)

81.65

'' (20

73.91

)

304.8

13.0

(332

.1)13

.0(3

32.1)

11.0

(297

.4)13

.0(3

32.1)

2.34

(59.4

9)

LVDT

Dial Indicator

13.0

(332

.1)30

4.82.3

4(5

9.49)

11.0

(297

.4)13

.0(3

32.1)

13.0

(332

.1)

Dial Indicator

LVDT

13.0

(332

.1)

81.65

'' (20

73.91

)

76.3'

' (193

8)

13.0

(332

.1)

304.8

304.8

Dial Indicator

13.0

(332

.1)13

.0(3

32.1)

11.0

(297

.4)2.3

4(5

9.49)

5.35'' 55.12'' (1400)

72.25'' (1835.15)

2.34

(59.4

9)11

.0(2

97.4)

13.0

(332

.1)13

.0(3

32.1)

LVDT LVDT

Dial Indicator

GSGC MASS

13.0

(332

.1)

11.37

(288

.92)

81.65

'' (20

73.91

)

76.3'

' (193

8)

304.8

10.4

(264

.16)

13.0

(332

.1)13

.0(3

32.1)

11.0

(297

.4)2.3

4(5

9.49)

11.37

(288

.92)

11.37

(288

.92)

11.37

(288

.92)

11.37

(288

.92)

11.37

(288

.92)

Dial Indicator

2''

LVDT

LVDTs on the open side

Dial Indicator on the open side

6''

Dial Indicator on the top surface

LVDT on the top surface

LVDT on the top surface (the location can be adjusted dependent on the size of the loading system)

Footing on the top of GRS specimen

AJack

Center line

6''

Dial Indicator

4''4''

Dial Indicator on the top surface

Location of LVDTs and Dial Indicators

Figure 4.18: Locations of LVDTs and Digital Dial Indicators

136

d. Reinforcement Strain

To measure the strains in the geotextile, a number of high elongation strain gauge

(type EP-08-250BG-120), manufactured by Measurements Group, Inc., were used.

Each strain gauge was glued to the geotextile only at two ends to avoid inconsistent

local stiffening of geotextile due to the adhesive. The strain gauge attachment

technique was developed at the University of Colorado Denver. The gauge was first

mounted on a 25 mm by 76 mm patch of a lightweight nonwoven geotextile (see

Figure 4.19). A Microcystalline wax and a rubber coating (M-Coat B, Nitrile Rubber

coating) were used to protect the gauges from moisture. To check the effectiveness

of the moisture-protection technique, the geotextile specimens with the strain gauges

were tested after immersing in water for 24 hours. Before placing the reinforcement

sheet in the test specimen, an M-Coat FB-2, 6694, Butyl Rubber Tape was used to

cover the gauges to protect the gauges during compaction (see Figure 4.19). To

measure the strain distribution of the reinforcement, six strain gauges were mounted

on each Geotex 4x4 sheet (see Figure 4.20).

137

(a) (b)

Figure 4.19: Strain Gauge on Geotex 4x4 Geotextile: (a) Before Applying Protection Tape (b) After Applying Protection Tape (M-Coat FB-2, 6694, Butyl Rubber Tape).

138

Figure 4.20: Strain Gauges Mounted on Geotex 4x4 Geotextile

139

Due to the presence of the light-weight geotextile patch, calibration of the strain

gauge is needed. The calibration tests were performed to relate the strain obtained

from the strain gauge to the actual strain of the reinforcement. Figures 4.21 and 4.22

show the calibration curves along the fill direction of Geotex 4x4 geotextile for the

single-sheet and the double-sheet specimens, respectively.

140

y = 1.172xR2 = 0.9913

0

1

2

3

4

5

6

0 1 2 3 4 5Strain from Strain Gage (%)

Stra

in fr

om In

stro

n M

achi

ne (%

)

Figure 4.21: Calibration Curve for Single-Sheet Geotex 4x4

141

y = 1.078xR2 = 0.9986

0

1

2

3

4

5

6

0 1 2 3 4 5

Strain from Strain Gauge (%)

Stra

in fr

om In

stro

n M

achi

ne (%

)

Figure 4.22: Calibration Curve for Double-Sheet Geotex 4x4

142

4.5.4 Preparation of Test Specimen for GSGC Tests

The preparation procedure of a typical composite mass with the dimensions of 2.0 m

(H) x 1.4 m (D) x 1.2 m (L) is described as follows:

1. Mark the anticipated location of the GSGC mass on the plexiglass;

2. Apply approximately 1-mm thick lubricating agent (Dow Corning 4

Electrical Insulating Compound NSF 61) evenly on the inside surfaces

of the plexiglass (see Figure 4.23);

3. Attach a sheet of membrane (with 51 mm x 51 mm grid system pre-

drawn on membrane) over each plexiglass and at the bottom of the

specimen (see Figure 4.24);

4. Lay a course of the facing blocks on the open sides of the specimen (see

Figure 4.25);

5. Place the backfill in the test bin and compact in 0.2 m lifts (see Figures

4.26 and 4.27); check and adjust (if needed) the backfill moisture before

compaction to achieve the target moisture of 5.2%;

6. Check the water content and dry unit weight of each lift by using a

nuclear density gauge, Troxler 3440, by the direct transmission method

(note: the measured dry unit weights of five tests are shown in Figure

4.39);

7. Place the next layer of geosynthetic reinforcement (with strain gauges

already mounted) covering the entire top surface area of compacted fill

and the facing blocks (see Figure 4.28);

8. Repeat steps 4 to 8 until the full height of the composite mass is reached;

9. Sprinkle a 5 mm-thick fine sand layer over the top surface of the

completed composite mass to level the surface and protect the

membrane from being punctured by gravels in the backfill (see Figure

4.29);

143

10. Place a geosynthetic sheet on top of the composite mass (see Figure

4.30);

11. Glue a sheet of membrane to the top edge of the side membrane sheets

(see Figure 4.31);

12. Remove all facing blocks and trim off the excess geotextile (see Figure

4.32);

13. Insert strain gauge cables through the plastic openings that were already

attached on the membrane sheets at prescribed locations (see Figure

4.33);

14. Glue membrane sheets to enclose entire composite mass;

15. Apply vacuum to the composite mass at a low pressure of 14 kPa (see

Figure 4.34);

16. Seal the connection between cables and membrane with epoxy to

prevent air leaks (see Figure 4.35). The low vacuum pressure allows the

epoxy to seal the connection well;

17. Raise the vacuum pressure to 34 kPa and check air leaks under

vacuuming (see Figure 4.36) and measure the specimen dimensions (see

Table 4.6 for specimen dimensions of five tests).

144

Figure 4.23: Applying Grease on Plexiglass Surfaces

145

Figure 4.24: Attaching Membrane

146

Figure 4.25: Placement of the first Course of Facing Block

147

Figure 4.26: Compaction of the First Lift of Backfill

148

Figure 4.27: Placement of Backfill for the Second Lift

149

Figure 4.28: Placement of a Reinforcement Sheet

150

Figure 4.29: Completion of Compaction of the Composite Mass and Leveling the Top Surface with 5 mm-thick Sand Layer

151

Figure 4.30: Completed Composite Mass with a Geotextile Sheet on the Top Surface

152

Figure 4.31: Covering the Top Surface of the Composite Mass with a Sheet of Membrane

153

Figure 4.32: Removing Facing Blocks and Trimming off Excess Geosynthetic Reinforcement

154

Figure 4.33: Insertion of Strain Gauge Cables through the Membrane Sheet

155

Figure 4.34: Vacuuming the Composite Mass with a Low Pressure

156

Figure 4.35: Sealing the Connection between Cable and Membrane with Epoxy to Prevent Air Leaks

157

Figure 4.36: Checking Air Leaks under Vacuuming

158

Figure 4.37: The LVDT’s on an Open Side of Test Specimen

159

2.50

2.5024.50

42.0

0

66.0

0

16.0

0

1 2 3

4 5 6

7 8 9

2x2'' Grid System

10.2

5

60.2

5

34.2

5

32.50

54.0

0

16.0

0

42.0

0

31.383.38

3.38

4

7

10.3

5

10

1

65

34.3

5

8 9

2x2'' Grid System

11

2 3

(b): Tests 3,4 and 5

Width

Width

Hei

gth

= 76

.25

in. (

Test

1),

76.3

5 in

. (Te

st 2

)H

eigh

t = 7

6.30

in.

15.38

(a): Tests 1 and 2

Figure 4.38: Locations of Selected Points to Trace Internal Movement of (a) Tests 1 and 2 and (b) Tests 3, 4 and 5

160

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

15 18 21 24 27 30

Dry Unit Weight (kN/m3)

Spec

imen

Hei

ght (

m)

Test 1

Test 2

Test 3

Test 4

Test 5

Figure 4.39: Soil Dry Unit Weight Results during Specimen Preparation of the Five

Tests

161

Table 4.6: Dimensions of the GSGC specimens before loading

Test Height, m (in.)

Width, m (in.)

Length, m (in.)

Test 1 1.937 (76.25) 1.448 (57.00) 1.194 (47.00)

Test 2 1.939 (76.35) 1.372 (54.00) 1.187 (46.75)

Test 3 1.939 (76.35) 1.346 (53.00) 1.187 (46.75)

Test 4 1.938 (76.30) 1.492 (58.75) 1.187 (46.75)

Test 5 1.939 (76.35) 1.245 (49.00) 1.187 (46.75)

162

4.6 Test Results

4.6.1 Test 1 – Unreinforced Soil

This test is perhaps the largest plane strain test for soil with a confining pressure.

Test 1 was conducted as the base line for the other four GSGC tests.

The loading sequence of the soil mass was:

• Loading up to a vertical pressure of 250 kPa (nearly 1% vertical strain)

• Unloading to zero

• Reloading until a failure pressure of 770 kPa was reached.

The soil mass at failure is shown in Figure 4.40. Figure 4.41 shows the global

vertical stress-strain and volume change relationships of the soil mass. The average

lateral displacements, measured by LVDT’s, on the open faces of the soil mass under

different vertical stresses are presented in Figure 4.42. The internal displacements of

the soil at selected points under vertical applied pressures of 190 kPa, 310 kPa, 620

kPa, and 770 kPa are shown in Figure 4.43. The test results of Test 1 for

unreinforced soil are summarized in Table 4.7.

163

Figure 4.40: Soil Mass at Failure of Test 1

164

0

100

200

300

400

500

600

700

800

900

0 1 2 3 4 5Global Vertical Strain (%)

App

lied

Vert

ical

Str

ess

(kPa

)

6

(a)

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3 3.5

Global Vertical Strain (%)

Volu

met

ric S

train

(%)

(b)

Figure 4.41: Test 1-Unreinforced Soil Mass:

(a) Global Vertical Stress-Vertical Strain Relationship (b) Global Volume Change Strain Relationship

165

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

0 10 20 30 40 50


Spec

imen

Hei

ght (

m)

200 kPa

400 kPa

600 kPa

770 kPa

700 kPa

Applied Pressure:

Figure 4.42: Lateral Displacements on the Open Face of Test 1

166

76.2

5

Test 1

57.00

2.502.50

42.0

0

66.0

0

16.0

0

1

2'' x 2'' Grid System

10.2

5

34.2

5

32.50

4 5 6

2 3

8 97

Before Loading

190 kPa (75 kips)

310 kPa (120 kips)

620 kPa (240 kips)

770 kPa (300 kips)

Legend:

(All Displacements in inches, Drawn to Scale of the Soil Mass)

Note:

Figure 4.43: Internal Displacements of Test 1

167

Table 4.7: Some test results of Test 1

Test 1

Test Conditions

Geosynthetic Reinforcement None

Wide-Width Strength of Reinforcement None

Reinforcement Spacing No Reinforcement

Confining Pressure 34 kPa

Test Results

Applied Stress at Vertical Strain of 1% 335 kPa (48.6 psi)

Ultimate Applied Pressure 770 kPa (112 psi)

Vertical Strain at Failure 3 %

Maximum Lateral Displacement of the Open Face at Failure 47 mm

Stiffness at 1% vertical strain (Eat 1%) 33,500 kPa

Stiffness for Unloading-Reloading (Eur) 87,100 kPa

168

4.6.2 Test 2 – GSGC Test (T, Sv)

In this test, the GSGC mass was reinforced by nine sheet of single-sheet Geotex 4x4

with spacing of 0.2 m. The soil layer was compacted at 0.2 m-thick lifts. Each

reinforcement sheet was mounted with 54 strain gauges.

The failure load in this test was 1,000,000 pounds. All nine reinforcement sheets

were ruptured after testing. The composite mass after testing is shown in Figure 4.44.

The shear bands of the composite mass after testing are visible through the diagonal

lines of the mass (see Figures 4.44 and 4.45). Along the shear bands, the square grids

of 51 mm by 51 mm (2 in. by 2 in.) were severely distorted after testing (Figure 4.45).

These shear bands correspond exactly with the failure surfaces seen in Figure 4.46.

The location of rupture lines of all reinforcement sheets in the GSGC mass can be

seen in Figures 4.52 and 4.53.

The measured data of Test 2 are highlighted as bellows:

• Global stress-strain relationship: Figure 4.47 shows the global stress-strain

relationship of the composite up to and post failure. The maximum applied

vertical pressure was about 2700 kPa, where the corresponding vertical

displacement was 125 mm (6.5% vertical strain).

• Lateral displacement: The average lateral displacement profiles are on the

open faces of the composite under different vertical pressures shown in Figure

4.48. The lateral displacements were nearly uniform along the height of the

composite up to a pressure of about 600 kPa. At vertical pressures between

770 kPa and 1,500 kPa, the maximum lateral displacement occurred at about

3/8 H (H = the height of the composite mass) from the base. The locations of

the maximum displacements were about the same as those of Test 1

(unreinforced).

169

Figure 4.44: Composite Mass at Failure of Test 2

170

Figure 4.45: Close-Up of Shear Bands at Failure of Area A in Figure 4.44

171

Figure 4.46: Failure Planes of the Composite Mass after Testing in Test 2

172

0

500

1,000

1,500

2,000

2,500

3,000

0 1 2 3 4 5 6 7 8 9


App

lied

Verti

cal S

tress

(kPa

)

(a)

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

00 1 2 3 4 5 6


Vol

umet

ric

Stra

in (%

)

7

(b)

Figure 4.47: Test 2-Reinforced Soil Mass:

(a) Global Vertical Stress-Vertical Strain Relationship (b) Global Volume Change Strain Relationship

173

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

0 10 20 30 40 50 60 70


Spec

imen

Hei

ght (

m)

200 kPa

400 kPa

600 kPa

770 kPa

1000 kPa

1250 kPa

1500 kPa

1750 kPa

2000 kPa

2250 kPa

2500 kPa

2700 kPa

Applied Pressure:


174

The maximum lateral displacement at the mid-height of the composite under

the applied pressure of 2,700 kPa was 60 mm.

• Internal displacement: The internal displacements of the composite mass at

selected points under vertical applied pressures of 270 kPa to 2,700 kPa, at an

increment of 270 kPa are shown in Figure 4.49. At points 1 (and 3), 4 (and 6),

and 7 (and 9) near the open faces, the displacements moved downward and

outward with an angle, measured after testing, of about 67o, 47o, and 31o,

respectively, to the horizontal. The vertical displacements of the points at the

upper part of the soil mass were greater than those at the lower part. Along

the center line, there were only vertical displacements (Points 2, 5 and 8).

There was almost no displacement at Point 8 near the bottom and at the center

line. The maximum lateral displacement in the soil body was 60 mm at the

mid height on the open sides, and the maximum vertical displacement was

125 mm at the top of the specimen.

• Reinforcement strain: Figure 4.50 shows the locations of the strain gauges on

the geosynthetic sheets. The strain in the reinforcement of the GSGC mass is

shown in Figure 4.51. Most of the strain gauges performed well at strains less

than 4%. All reinforcement layers were found ruptured after the test

completed. The locations of the rupture lines can be seen from the aerial view

of the reinforcement sheets exhumed from the composite after testing (see

Figure 4.52). Based on the locations of the rupture lines, the rupture planes

can be constructed as shown in Figure 4.53. Note that this agrees perfectly

with the shear bands in Figure 4.46. The maximum strain in reinforcement at

ruptured was about 12 %, while the measured data from strain gauges were

only less than 4 %. From the strain distribution in Figure 4.51, the locations

of the maximum strain in reinforcement were different between layers. In

reinforcement layers near at the mid height of the GSGC mass (0.8 m and 1.0

175

m from the base), the maximum reinforcement strains were close to the

centerline, while the reinforcement layers at near the top and the base of the

GSGC mass (0,2 m and 1.8 m from the base), the maximum reinforcement

strains were at about 0.3 m from the edge of the composite mass. The

maximum strain locations in all reinforcement layers were at the ruptured

lines of reinforcement that can be seen in Figures 4.52 and 4.53.

• The test results of Test 2 are summarized in Table 4.8.

176


76.3

5

Test 2

54.00

3.00

3.00

38.0

0

66.0

0

16.0

0

1 2 3

4 5 6

7 8 9

10.3

5

38.3

5

31.00

Before Loading

270 kPa

540 kPa

2,700 kPa

...

Legend:

(All Displacements in inches, Drawn to Scale of the Composite Mass)

Note:


177

Strain Gages

11.00 8.00 8.00 8.00 8.00 11.00

54

7.63

7.63

7.63

7.63

7.63

7.63

7.63

7.63

7.63

7.63

Sheet No 9

Sheet No 8

Sheet No 7

Sheet No 6

Sheet No 5

Sheet No 4

Sheet No 3

Sheet No 2

Sheet No 1

Reinforcement

(Note: All Dimensions in inches)

Figure 4.50: Locations of Strain Gauges on Geosynthetic sheets in Test 2

178

0

0.5

1

1.5

2

2.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Distance from the Edge of the Composite Mass (m)

Stra

in (%

)

200 kPa400 kPa

600 kPa800 kPa

1000 kPa1250 kPa

1500 kPa

Applied Pressure:

(a)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

)

200 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

1250 kPa

1500 kPa

Applied Pressure:

(b)

Figure 4.51: Reinforcement Strain Distribution of the Composite Mass in Test 2:

(a) Layer 1, at 0.2 m from the Base (b) Layer 2, at 0.4 m from the Base

179

00.5

11.5

22.5

33.5

44.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

)

200 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

1250 kPa

1500 kPa

Applied Pressure:

(c)

0

0.5

1

1.5

2

2.5

3

3.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

)

200 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

Applied Pressure:

(d)

Figure 4.51 (continued): Reinforcement Strain Distribution of the Composite

Mass in Test 2: (c) Layer 3, at 0.6 m from the Base (d) Layer 4, at 0.8 m from the Base

180

0

0.5

1

1.5

2

2.5

3

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

) 200 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

Applied Pressure:

(e)

0

0.5

1

1.5

2

2.5

3

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

) 200 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

Applied Pressure:

(f)

Figure 4.51 (continued): Reinforcement Strain Distribution of the Composite Mass in Test 2:

(e) Layer 5, at 1.0 m from the Base (f) Layer 6, at 1.2 m from the Base

181

00.5

11.5

22.5

33.5

4

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

)

200 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

1250 kPa

Applied Pressure:

(g)

0

0.5

1

1.5

2

2.5

3

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

)

200 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

1250 kPa

Applied Pressure:

(h)

Figure 4.51 (continued): Reinforcement Strain Distribution of the Composite

Mass in Test 2: (g) Layer 7, at 1.4 m from the Base (h) Layer 8, at 1.6 m from the Base

182

00.20.40.60.8

11.21.41.6

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

) 200 kPa

400 kPa

600 kPa

800 kPa

Applied Pressure:

(i)

Figure 4.51 (continued): Reinforcement Strain Distribution of the Composite Mass in Test 2:

(i) Layer 9, at 1.8 m from the Base

183

Figure 4.52: Aerial View of the Reinforcement Sheets Exhumed from the Composite Mass after Test 2

(The numbers next to each sheet indicate the sheet number in Figure 4.53)

184

Rupture Lines

547.

637.

637.

637.

637.

637.

637.

637.

637.

637.

63

1

2

3

4

5

6

7

8

9

ReinforcementTest 2

(Note: All Dimensions in inches, Drawn to Scale)

Figure 4.53: Locations of Rupture Lines of Reinforcement in Test 2; Constructed based on Figure 4.52

185

186


Test 2

Test Conditions

Geosynthetic Reinforcement Geotex 4x4

Wide-Width Strength of Reinforcement 70 kN/m

Reinforcement Spacing 0.2 m


Test Results

Ultimate Applied Pressure 2700 kPa

Vertical Strain at Failure 6.5 %



Maximum strain in reinforcement at ruptured 12 %

Maximum measured strain in reinforcement 4.0 %

4.6.3 Test 3 – GSGC Test (2T, 2Sv)

In this test, the GSGC mass was reinforced by four double-sheet Geotex 4x4 at 0.4 m

spacing. The strength and stiffness of the double-sheet reinforcement were nearly

doubled compared to those of the single-sheet reinforcement used in Test 2. The

GSGC mass after testing is shown in Figure 4.54.

The measured data of Test 3 are highlighted below:

• Global stress-strain relationship (see Figure 4.55): The maximum applied

vertical pressure was about 1,750 kPa. The vertical displacement at the failure

pressure was 118 mm (6.1% global vertical strain).

• Lateral displacement: The average lateral displacement profiles on the open

faces of the composite under different vertical pressures shown in Figure 4.56.

The maximum lateral displacement under the failure pressure 1750 kPa was

54 mm.

• Internal displacements at selected points are shown in Figure 4.57. The trend

of the internal movements in Test 3 was nearly the same as that in Test 2. The

points 1, 3, 4, 5, 6, 7 and 9 near the open faces, the displacements move

downward and outward with angles from 49o to 71o to the horizontal. The

points 2, 5 and 8 along the center line, the displacements were almost vertical.

The maximum vertical displacement at the top of the specimen was 118 mm.



shown in Figure 4.59. Three reinforcement layers near the top of the

composite were ruptured after testing. The locations of the rupture lines can

be seen from the aerial view of the reinforcement sheets exhumed from the

composite after testing (see Figure 4.60). Based on the locations of the

187

rupture line, the rupture planes can be constructed as shown in Figure 4.61.

This rupture line agrees perfectly with the failure line in Figure 4.54. The

maximum strain in reinforcement measured was 4 % and located at near the

ruptured line as shown in Figure 4.61.


188

Figure 4.54: Composite Mass after Testing of Test 3

189

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00


App

lied

Verti

cal S

tress

(kPa

)

Figure 4.55: Global Stress-Strain Relationship of Test 3

190

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

0.0 10.0 20.0 30.0 40.0 50.0 60.0


Spe

cim

en H

eigh

t (m

)

260 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

1250 kPa

1500 kPa

1750 kPa

Applied Pressure:


191

76.3

5

Test 3

53.00

2.502.50

42.0

0

66.0

0

16.0

0

2x2'' Grid System

10.3

5

60.3

6

34.3

5

54.0

0

1 2

4

10 11

65

987


3

30.50

Before Loading

280 kPa

560 kPa

840 kPa

1120 kPa

1400 kPa

1680 kPa

1750 kPa

14.5

Legend:


Note:


192

Strain Gages

10.50 8.00 8.00 8.00 8.00 10.50

53.00

15.2

515

.25

15.2

515

.25

15.2

5

Sheet No 4

Sheet No 3

Sheet No 2

Sheet No 1

Reinforcement


Figure 4.58: Location of Strain Gauges on Geosynthetic Sheets in Test 3

193

00.5

11.5

22.5

33.5

44.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

)

260 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

1250 kPa

`

Applied Pressure:

(a)

00.5

11.5

22.5

33.5

44.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

) 260 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

Applied Pressure:

(b)



194

0.00.51.01.52.02.53.03.54.04.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

) 260 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

Applied Pressure:

(c)

0.00.51.01.52.02.53.03.54.04.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

) 260 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

Applied Pressure:

(d)

Figure 4.59 (continued): Reinforcement Strain Distribution in Test 3:

(c) Layer 3, at 1.2 m from the Base (d) Layer 4, at 1.6 m from the Base

195

Figure 4.60: Aerial View of the Reinforcement Sheets Exhumed from the Composite Mass after Test 3 (The numbers on each sheet indicate the sheet number in

Figure 4.61)

196

53

Test 3Rupture Lines

15.2

515

.25

15.2

515

.25

15.2

5

1

2

3

4

Reinforcement


Figure 4.61: Locations of Rupture Lines of Reinforcement in Test 3; Constructed based on Figure 4.60.

197


Test 3

Test Conditions





Test Results

Ultimate Applied Pressure 1,750 kPa






198

4.6.4 Test 4 – GSGC Test (T, 2 Sv)

The reinforcement used in this test was single-sheet of Geotex 4x4 at spacing of 0.4

m. The composite mass after testing is shown in Figure 4.62. The failure surfaces of

the composite mass after testing can be seen clearly in this Figure.

The measured data for of Test 4 are highlighted below:

• Global stress-strain relationship (see Figure 4.63): The maximum applied


pressure was 77 mm (4.0% global vertical strain).

• Lateral displacement: The average lateral displacements on the open faces of

the composite mass under different vertical pressures as shown in Figure 4.64.

The maximum lateral displacement under the failure pressure was 52 mm.

• Internal displacements at selected points are shown in Figure 4.65. The trends

of the internal movements in Tests 2, 3 and 4 were identical. The points 1, 3,

4, 5, 6, 7 and 9 near the open faces, the displacements move downward and

outward with angles from 30o to 63o to the horizontal. The points 2, 5 and 8

along the center line, the displacements were almost vertical. The maximum

vertical displacement at the top of the specimen was 77 mm.



shown in Figure 4.67. All reinforcement layers near the top of the composite

were ruptured after the test was completed. The locations of the rupture lines

can be seen from the aerial view of the reinforcement sheets exhumed from

the composite after testing (see Figure 4.68). Based on the locations of the



199

maximum strain in reinforcement at ruptured was about 12 % and located at

near the ruptured line as shown in Figure 4.69.


200

(a) (b)

Figure 4.62: Failure Planes of the Composite Mass after Testing in Test 4: (a) Front View at the South (b) Back View at the North.

201

0

200

400

600

800

1,000

1,200

1,400

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00


Appl

ied

Verti

cal S

tress

(kPa

)


202

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

0.0 10.0 20.0 30.0 40.0 50.0 60.0


Spec

imen

Hei

ght (

m)

200 kPa

400 kPa

600 kPa

800 kPa

1000 kPa

1250 kPa

1300 kPa

Applied Pressure:


203

76.3

0

Test 4

58.00

3.00

3.00

42.0

0

16.0

0

10.3

5

34.3

5

54.0

0

15.00

31.00

1 2

10

4 5

11

6

987


3

Before Loading

250 kPa

500 kPa

750 kPa

1000 kPa

1250 kPa

1300 kPa

Legend:

Note:



204

Strain Gages

13.35 8.00 8.00 8.00 8.00 13.35

58.75

15.2

515

.25

15.2

515

.25

15.2

5

Sheet No 4

Sheet No 3

Sheet No 2

Sheet No 1

Reinforcement



205

00.20.40.60.8

11.21.41.61.8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7


Stra

in (%

)

100 kPa200 kPa

300 kPa400 kPa500 kPa600 kPa

800 kPa

Applied Pressure:

(a)

00.20.40.60.8

11.21.41.61.8

2

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7


Stra

in (%

)

100 kPa

200 kPa

300 kPa

400 kPa

500 kPa

600 kPa

Applied Pressure:

(b)



206

0

0.2

0.4

0.6

0.8

1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7


Stra

in (%

) 100 kPa

200 kPa

300 kPa

400 kPa

Applied Pressure:

(c)

00.20.40.60.8

11.21.41.61.8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7


Stra

in (%

) 100 kPa

200 kPa

300 kPa

400 kPa

500 kPa

Applied Pressure:

(d)

Figure 4.67 (continued): Reinforcement Strain Distribution of the Composite Mass in

Test 4: (c) Layer 3, at 1.2 m from the Base (d) Layer 4, at 1.6 m from the Base

207

Figure 4.68: Aerial View of the Reinforcement Sheets Exhumed from the Composite Mass after Test 4 (The numbers on each sheet indicate the sheet number in

Figure 4.69)

208

Rupture Lines

58

15.2

515

.25

15.2

515

.25

15.2

5

1

2

3

4

ReinforcementTest 4



209


Test 4

Test Conditions





Test Results







210

4.6.5 Test 5 – GSGC Test (unconfined with T, Sv)

The configuration of this test was the same as Test 2. The reinforcement was the

single-sheet Geotex 4x4 at spacing of 0.2 m. The confining pressure was not applied

for this test. Without applying confining pressure, the soil on the open faces fell of

continuously with increasing applied pressure. The composite mass and failure

surfaces after testing are shown in Figures 4.70 and 4.71.

The measured data of Test 5 highlighted below:

• The global stress-strain relationship (see Figure 4.72): The maximum applied


pressure was 111 mm (6.0 % global vertical strain).

• Lateral displacement: The average lateral displacements on the open faces of

the composite mass under different vertical pressures as shown in Figure 4.73.

The maximum lateral displacement at the open faces under the failure

pressure could not been measured because the soil at these faces dropped

during testing under the high applied pressures.

• Internal displacements at selected points are shown in Figure 4.74. The trend

of the internal movements in Test 5 was nearly the same as that in the other

Tests 2, 3 and 4. The points 1, 3, 4, 5, 6, 7 and 9 near the open faces, the

displacements move downward and outward with angles from 35o to 63o to the

horizontal. The points 2, 5 and 8 along the center line, the displacements were

almost vertical. The maximum vertical displacement at the top of the

specimen was 111 mm.



shown in Figure 4.76. Eight reinforcement layers near the top of the

211

composite were ruptured after testing. The locations of the rupture lines can

be seen from the aerial view of the reinforcement sheets exhumed from the

composite after testing (see Figure 4.77). Based on the locations of the



maximum strain in reinforcement measured was 3.2 % and located at near the

ruptured line as shown in Figure 4.78.


212

Figure 4.70: Composite Mass at Failure of Test 5

213

(a) (b)

Figure 4.71: Failure Planes of the Composite Mass after Testing in Test 5: (a) Front View (South), (b) Back View (North)

214

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

2,200

0 1 2 3 4 5 6 7 8

Global Vetical Strain (%)

App

lied

Vert

ical

Str

ess

(kPa

)


215

0.000

0.250

0.500

0.750

1.000

1.250

1.500

1.750

2.000

0.0 10.0 20.0 30.0 40.0


Spec

imen

Hei

ght (

m)

200 kPa

400 kPa

600 kPa

1500 kPa

Applied Pressure:


216

76.3

5

Test 5

49.00

2.50

2.50

42.0

0

16.0

0

10.3

5

60.3

5

34.3

5

12.50

28.50

54.0

0

1

10

2 3

11

4 5 6

7 8 9


Before Loading

300 kPa

600 kPa

900 kPa

1200 kPa

1500 kPa

1800 kPa

Legend:


Note:


217

Strain Gages

8.50 8.00 8.00 8.00 8.00 8.50

49.0015

.25

15.2

515

.25

15.2

515

.25

Sheet No 9

Sheet No 8

Sheet No 7

Sheet No 6

Sheet No 5

Sheet No 4

Sheet No 3

Sheet No 2

Sheet No 1

Reinforcement



218

0

0.5

1

1.5

2

2.5

3

3.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6Distance from the Edge of the Composite Mass (m)

Stra

in (%

)

100 kPa

200 kPa

300 kPa

400 kPa500 kPa

600 kPa

750 kPa

Applied Pressure:

(a)

0

0.5

1

1.5

2

2.5

3

0.0 0.1 0.2 0.3 0.4 0.5 0.6Distance from the Edge of the Composite Mass (m)

Stra

in (%

)

100 kPa200 kPa

300 kPa400 kPa500 kPa600 kPa

750 kPa

Applied Pressure:

(b)



219

0

0.2

0.4

0.6

0.8

1

1.2

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

)

100 kPa

200 kPa

300 kPa

400 kPa

525 kPa

Applied Pressure:

(c)

Figure 4.76 (continued): Reinforcement Strain Distribution of the Composite Mass in

Test 5: (c) Layer 3, at 1.2 m from the Base

220

Figure 4.77: Aerial View of the Reinforcement Sheets Exhumed from the Composite Mass after Test 5 (The number on each sheet indicate the sheet number in

Figure 4.78)

221

Rupture Lines

497.

637.

637.

637.

637.

637.

637.

637.

637.

637.

63

1

2

3

4

5

6

7

8

9

Test 5Reinforcement



222


Test 5

Test Conditions




Confining Pressure 0

Test Results



Maximum Lateral Displacement of the Open Face at Failure Not Measured




223

4.7 Discussion of the Results

The results of the GSGC Tests are discussed in term of the following:

• Effects of geosynthetic inclusion (comparison between Tests 1 and 2).

• Relationship between reinforcement spacing and reinforcement strength

(comparison between Tests 2 and 3).

• Effects of reinforcement spacing (comparison between Tests 2 and 4).

• Effects of reinforcement stiffness (comparison between Tests 3 and 4).

• Effects of confining pressure (comparison between Tests 2 and 5)

• Composite strength properties.

4.7.1 Effects of Geosynthetic Inclusion (Comparison between Tests 1 and 2)

Table 4.12 shows the result comparisons between an unreinforced soil mass (Test 1)

and a soil mass reinforced by Geotex 4x4 at 0.2 m spacing (Test 2). With the

presence of the reinforcement, the reinforced soil was much stronger than the

unreinforced soil. The ultimate applied pressure for the GSGC mass was about 3.5

times as large as the strength of the soil mass without reinforcement. The stiffness of

the unreinforced soil mass was 50 % of that for the reinforced soil mass. In addition,

the reinforced soil mass was much more ductile than the unreinforced soil mass. The

global vertical strain was 6.5 % at failure for Test 2; whereas it was only 3.0 % for

Test 1.

224

Table 4.12: Comparison between Test 1 and Test 2

Test 1 Test 2 (T, Sv)

Geosynthetic Reinforcement None Geotex 4x4

Wide-Width Strength of Reinforcement None Tf = 70 kN/m

Reinforcement Spacing No Reinforcement Sv = 0.2 m

Confining Pressure 34 kPa 34 kPa

Ultimate Applied Pressure 770 kPa 2,700 kPa

Vertical Strain at Failure 3 % 6.5 %

Maximum Lateral Displacement of the Open Face at Failure 47 mm 60 mm

Stiffness at 1% vertical strain (Eat 1%) 33,500 kPa 61,600 kPa

Stiffness for Unloading-Reloading (Eur) 87,100 kPa

Not Applied

225

4.7.2 Relationship between Reinforcement Spacing and Reinforcement

Strength (Comparison between Tests 2 and 3)

The relationship between reinforcement spacing and reinforcement strength can be

seen by comparing the results of Tests 2 and 3, as shown in Table 4.13. As noted in

Section 2.1, the current design methods are based on the concept that the

reinforcement spacing and reinforcement strength play an equal role on the

performance of a GRS mass. In other words, a GRS wall with reinforcement strength

of Tf at spacing Sv will behave the same as the one with reinforcement strength of

2*Tf at twice the spacing 2*Sv. The results of Tests 2 and 3 demonstrated that this

concept adopted in current design methods is not correct. With the same Tf / Sv ratio

(= 350 kN/m2) in Tests 2 and 3, the stiffness and strength of the Test 2 (with Tf and Sv

= 0.2 m) was much higher than that of the Test 3 (with 2Tf and Sv = 0.4 m). The

strength of the composite mass in Test 3 was only 65 % of the strength in Test 2 (see

Table 4.13). These results suggest that reinforcement spacing plays a much more

important role than strength of reinforcement in a reinforced soil mass.

226

Table 4.13: Comparison between Test 2 and Test 3 with the same Tf/Sv ratio

Test 2 (T, Sv) Test 3 (2 T, 2Sv)

Wide-Width Strength of Reinforcement Tf = 70 kN/m Tf = 140 kN/m

Reinforcement Spacing Sv = 0.2 m Sv = 0.4 m

Tf / Sv 350 kPa 350 kPa


Ultimate Applied Pressure 2,700 kPa 1,750 kPa


Vertical Strain at Failure 6.5 % 6.1 %


227

4.7.3 Effects of Reinforcement Spacing (Comparison between Tests 2 and 4)

The effects of reinforcement spacing can be seen by comparing the results of Tests 2

and 4, as shown in Table 4.13. All test conditions in the two tests are the same,

except the reinforcement spacing in Test 4 was 0.4 m, while it was 0.2 m in Test 2.

The results demonstrate the importance of reinforcement spacing on the behavior of a

GRS mass. With reinforcement spacing of 0.2 m, the strength of the GRS mass was

about twice as high as the one with 0.4 m spacing. The corresponding increase in

stiffness at 1 % strain was about 30 %. The GRS mass at 0.2 m spacing also

exhibited significantly higher ductility than at 0.4 m spacing.

228


Test 2 (T, Sv) Test 4 (T, 2Sv)









229

4.7.4 Effects of Reinforcement Strength (Comparison between Tests 3 and 4)

The effects of reinforcement strength can be seen by comparing the results of Tests 3

and 4, as shown in Table 4.15. All test conditions in the two tests are identical,

except that reinforcement strength in Test 3 was almost twice as high as that in Test

4. The results indicate that the increase in strength of the GRS mass due to doubling

the reinforcement strength was about 35%. The increase is much smaller than

doubling the reinforcement spacing (Section 4.7.3) where the increase in strength of

the GRS mass is over 100%. It is noted that the increase in stiffness at 1 % strain due

to doubling the reinforcement strength is only about 5%, compared to about 30%

increase due to doubling the reinforcement spacing.


Test 3 (2T, 2Sv) Test 4 (T, 2Sv)









230

4.7.5 Effects of Confining Pressure (Comparison between Tests 2 and 5)

The effects of confining pressure can be seen by comparing the test results of Tests 2

and 5, as shown in Table 4.16. All test conditions in the two tests are identical,

except that the confining pressure in Test 2 was 34 kPa, while Test 4 was conducted

without confinement. The results indicate that the increase in strength due to the

confining pressure was about 40 %. The increase in stiffness at 1 % strain due to the

confining pressure is about 15 %.

231


Test 2 (T, Sv) Test 5 (T, Sv)




Confining Pressure 34 kPa 0



Maximum Lateral Displacement of the Open Face at Failure 60 mm Not Measured

Stiffness at 1% vertical strain (Eat 1%)

61,600 kPa

52,900 kPa

232

4.7.6 Composite Strength Properties

Table 4.17 shows a comparison of the composite strength properties of five GSGC

tests as obtained from the measured data and calculated from Schlosser and Long’s

method (1972) by assuming the friction angle remains the same as unreinforced soil

(i.e., same φ value as in Test 1). The apparent cohesion, CR, from Schlosser and

Long’s method (1972) is calculated as cKS

TC p

v

fR +=

2, where c = the cohesion of

the backfill; Tf = the strength of reinforcement; Sv = reinforcement spacing; Kp =

coefficient of passive earth pressure. The values from Schlosser and Long’s method

were much higher than the measured by 20 % to 86 %.

233

234

Table 4.17: Comparison of strength properties of five GSGC Tests

Parameter Test 1

(un-reinforced)

Test 2

(T, Sv)

Test 3

(2 T, 2Sv)

Test 4

(T, 2Sv)

Test 5

(T, Sv)

Wide-Width Strength of Reinforcement, Tf (kN/m)

70 140 70 70

Reinforcement Spacing, Sv (m)

0.2 0.4 0.4 0.2

Tf / Sv (kPa) 350 350 175 350

Confining Pressure (kPa) 34 34 34 34 0

Apparent Cohesion, CR, (kPa) by Schlosser and

Long’s Method

550

550

310

550

Ultimate Applied Pressure (kPa) from

Measured Data 770 2,700 1,750 1,300 1,900

Ultimate Applied Pressure (kPa) by

Schlosser and Long’s Method

3,250 3,250 1,930 3030

Difference in Ultimate Pressure between

Measured Data and Schlosser and Long’s

Method

20 % 86 % 48 % 59 %

5. ANALYTICAL MODELS FOR EVALUATING COMPACTION-

INDUCED STRESSES (CIS), COMPOSITE STRENGTH PROPERTIES

OF A GRS COMPOSITE, AND REQUIRED REINFORCEMENT

STRENGTH

This Chapter described three analytical models. The models are for evaluating (1)

Compaction-Induced Stresses (CIS) in a GRS mass, (2) strength properties of a GRS

mass, and (3) required tensile strength of reinforcement in the design of GRS

structures. The first analytical model is a simple compaction model that is capable of

estimating the compaction-induced stresses, or the increase of the horizontal stresses,

in a GRS mass due to fill compaction. The model was developed by combining a

compaction model developed by Seed (1983) and the companion hand-calculation

procedure by Duncan and Seed (1986) for an unreinforced soil mass, and (b) the

theory of GRS composite behavior proposed by Ketchart and Wu (2001).

The second analytical model is for determination of the strength properties of a GRS

composite. With the analytical model, a new relationship between reinforcement

strength and reinforcement spacing is introduced to reflect an observation made in

actual construction and in controlled experiments regarding the relative effects of

reinforcement spacing and reinforcement strength on the performance of GRS

structures.

The third analytical model is for determination of reinforcement strength in design.

This model was also developed based on the new relationship between reinforcement

strength and reinforcement spacing.

235

5.1 Evaluating Compaction-Induced Stress in a GRS Mass

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

Based on previous studies regarding CIS for unreinforced soil masses, and very

limited study for reinforced soil masses, a conceptual stress path for loading-

unloading-reloading of a GRS mass is shown in Figure 5.1. An explanation of Figure

5.1 is given below:

- A GRS mass is loaded (due to application of compaction loads) from an initial

state (point A) following the Ki,c-line (with horizontal stress, vcih K '' , σσ = ,

where Ki,c = coefficient of lateral earth pressure of the GRS mass for initial

loading) up to point B. At point B, the GRS mass reaches a maximum stress

state with the vertical stress of max,,max, ''' cvvv σσσ Δ+= (σ'v = vertical stress at

the initial stress; Δσ'v,c,max = maximum increase in vertical stress due to

compaction loading).

- Upon unloading (i.e., upon removal of the compaction loads), the stresses in

the soil are reduced by following a non-linear path from point B to point C.

- In cases of “significant” unloading, i.e., during unloading, the unloading-path

reaches the limiting line (the “K1,c-line”) at point E, further unloading stress

path will follow line EF (with vch K '' ,1 σσ = ).

- Upon reloading due to the next cycle of compaction load application, the

stresses are to follow a K3,c-line (with vch K '' ,3 σσ = ) from either point C or

pint F until it meets the initial loading path (line AB).

- The subsequent cycles of unloading and reloading shall not deviate much

from the K3,c-line, as suggested by Broms (1971), Seed (1983), and Erlich and

Mitchell (1993). Therefore, the same K3-line can be used for all subsequent

cycles of reloading and unloading.

236

σ'h = Ki,c σ'v

σv

σhK1,c-line

K1,c

1B

σ'v + Δσ'v,c,max

G

Unloading-curve

E

F

A

D

C

σ'v

Ki,c-line

K3,c-line

K3,c-line Δσ'h,c,r

Figure 5.1: Conceptual Stress Path for Compaction of a GRS Mass

5.1.2 A Simplified Model to Simulate Fill Compaction of a GRS Mass

A simplified compaction simulation model, as depicted in Figure 5.2, is proposed for

simulation of fill compaction of a GRS mass. By using the proposed model, the

increase of the horizontal stresses in a GRS mass due to compaction can be estimated.

These stresses, namely CIS, are represented by the horizontal residual stresses,

Δσ'h,c,r, in Figure 5.2. The proposed model is based on the bi-linear compaction

model suggested by Seed (1983) for an unreinforced soil mass, and the companion

hand-calculation procedure suggested by Duncan and Seed (1986). The proposed

model considers the presence of geosynthetic inclusions.

The stress path for fill compaction of a GRS mass in the proposed model can be

considered as a simplified form of the conceptual model described in Section 5.1.

The differences between the simplified model and the conceptual model are:

237

- Upon the removal of the compaction loads, the stresses in the soil are

reduced by following the K2,c-line from point B to point C, of which the

vertical stress, σ’v, equals to that of point A. The horizontal residual stress

due to the compaction loading is Δσ'h,c,r.

- In case of an unreinforced soil mass (or the reinforcement stiffness is

negligible), the stress in the soil in response to removal of compaction

loads will reduce to point S (instead of point C). The horizontal residual

stress due to compaction loading will be Δσ'h,s,r with Δσ'h,s,r ≤ Δσ'h,c,r.

- Upon application of the next cycle of compaction loads or placement of

new fill layers, the reloading path will follow the K3,c-line

(with vch K '' ,3 σσ = , and cc KK ,2,3 ≤ ). The stress path is to follow K3,c-line

from point C or point F until it meets the initial loading path, then follow

Ki,c-line to a new stress state.

A Unreinforced soil

σ'h = Ki,c σ'vσ'h,c

σ'h,s

σ'v

Ki,c-line

σv

σh

1

KA1

KA-line

K2,c-line

S

C

Δσ'h,s,r

B

Δσ'h,c,max

Δσ'h,c,r

σ'v + Δσ'v,c,max

D

σ'h = K3,c σ'v

σ'h = K2,c σ'v

K3,c-line 1

K1,c

K1,c-line

E

F

K0

K0-line

Figure 5.2: Stress Path of the Proposed Simplified Model for Fill Compaction of a GRS Mass

238

5.1.3 Model Parameters of the Proposed Compaction Simulation Model

Four model parameters are needed for the proposed compaction simulation model,

including: Ki,c, K1,c, K2,c, and K3,c. These parameters can be estimated from soil and

reinforcement properties using correlations shown in Table 5.1, of which the

empirical coefficients (e.g., α and F) are to be calibrated by the measured data from

the Generic Soil-Geosynthetic Composite (GSGC) tests (to be described in Chapter

4). Recommended values of the empirical coefficients are to be given for routine

applications. Alternatively, the model parameters can be obtained directly from the

results of GSGC tests. Note that the term ⎟⎟⎠

⎞⎜⎜⎝

⎛− rvs

r

JSEE

7.07.0 , for the estimation of

K2, c, is to account for the presence of reinforcement. For hand calculations, the

maximum increase of "vertical" stress, max,,' cvσΔ as shown in Figure 5.2, due to

compaction can be estimated simply by using the Westergaard's solution (1938).

239

Table 5.1 : Model parameters for the proposed compaction simulation model

Parameter Name Range of the Parameter

Values

Preliminary Estimation Based on Soil and Reinforcement Properties

Ki,c Coefficient of lateral earth pressure of a GRS mass for initial loading

0, KKK ciA ≤≤ Aci KK β≅,

1.0 1.5β≤ ≤

⎟⎠⎞

⎜⎝⎛ −≅

2'45tan 2 φ

AK

'sin10 φ−≅K

K1,c Limiting coefficient of lateral earth pressure for unloading

Pc KK ≅,1 ⎟⎠⎞

⎜⎝⎛ +≅≅

2'45tan 2

,1φ

Pc KK

K2,c Coefficient of lateral earth pressure for unloading

0,20 KK c ≤≤ ci

rvs

rc K

ESEEFK ,,2 7.0

7.011 ⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−≅

where: ( )( )1

1−

−−=

OCROCROCRF

α

(Seed,

1983); 'sin φα ≅

K3,c Coefficient of lateral earth pressure for reloading

0,30 KK c ≤≤ cc KK ,2,3 ≅

Note: K0 = coefficient of at-rest lateral earth pressure KA = coefficient of active lateral earth pressure KP = coefficient of passive lateral earth pressure OCR = over-consolidation ratio Es = soil stiffness (kPa) Er = reinforcement stiffness (kN/m) Sv = reinforcement spacing (m).

240

5.1.4 Simulation of Fill Compaction Operation

Fill compaction is a complex operation in term of change in stresses. This section

describes the maximum increase of vertical stress at depth z along a given section in a

soil mass due to typical compaction operation. Let us consider the change of vertical

stress at depth z in section I-I due to moving compaction loads, as shown in Figures

5.3 and 5.4. The directions of the moving compaction plant may be: (1) coming

toward section I-I, and (2) going away from section I-I. The compaction loads are

simulated by loading and unloading at different locations (locations 1, 2, and i), as

shown in Figures 5.3(a) and 5.4(a). Figure 5.3(b) and Figure 5.4(b) show the stress

path of the stresses at depth z along section I-I.

An explanation of Figure 5.3(b) is given below:

1. The initial stress condition at depth z along section I-I is denoted by

point A, with the initial vertical stress being σv;

2. With the compaction loads at location 1, the stresses are increased by

following the Ki,c-line to point B;

3. As the compaction loads are removed from location 1, the stresses will

reduce from point B to point C by following the K2,c-line;

4. When compaction loads move to a new location (location 2), the

stresses will increase from point C through point B to point D;

5. As the compaction loads are removed from location 2, the stresses will

reduce from point D to point E by following again the K2,c-line.

6. Steps 1 through 5 are repeated for all subsequent new locations as the

compaction plant moves toward section I-I. Note that as the

compaction plant moves closer to section I-I, the vertical stress at

depth z will become larger.

7. The maximum vertical stress condition will be reached when the

compaction plant is directly above section I-I. The corresponding

241

stress condition is represented by point F. Upon removal of the

compaction loads, the stress path will follow K2-line to point G.

In Figure 5.4, the compaction plant moves away from section I-I. Initially the

compaction is located directly above section I-I, which causes the stresses to increase

from point A to point F in Figure 5.4(b) due to the compaction loads. As the

compaction loads are removed from section I-I, the stresses are reduced from point F

to point G, following the K2,c-line. As the compaction plant moves away from

section I-I, the stress conditions will move to points D and B, along line FG. As the

compaction plant is finally removed, the stress condition will be at point G.

From Figures 5.3 and 5.4, it is noted that the residual stresses, as denoted by the

vertical distance AG, are the same for the two cases. It indicates that to determine the

compaction-induced stresses at a certain section due to a moving compaction plant,

one only need to determine the residual lateral stresses as the compaction loads are

directly above the section under consideration.

Figure 5.5 shows the conceptual stress path on the effect of the number of compaction

passes. For the first pass, the residual stress at point A is represented by point G.

With the subsequent pass of the compaction plant, the slope of the K2-line will

increase, and point G becomes point G'. As the number of compaction pass increases,

the final residual stresses will move from G’ to G’’, then to G'''.

242

A

σ'vσv

σh

GF

C

D

B

E

compaction load

location 1location 2location i

I

I

Δσ'vΖ

(a)

(b)

1

2i

changing K2,c-line due to passes of compaction

Ki,c-line

K2,c and K3,c-line(Assume: K2,c = K3,c)

Δσ'h,c,r

σ'v + Δσ'v,c,max

Figure 5.3: (a) Locations of Compaction Loads, and (b) Stress Paths during Compaction at Depth z along Section I-I, as Compaction Loads Moving toward

Section I-I.

243

A

σ'vσv

σh

GF

compaction load

location ilocation 2location 1

I

I

Δσ'vΖ

BD

(a)

(b)

1

2i

P

changing K2,c-line due to passes of compaction

Ki,c-line


Δσ'h,c,r

σ'v + Δσ'v,c,max

Figure 5.4: (a) Locations of Compaction Loads, and (b) Stress Paths during Compaction at Depth z along Section I-I, as Compaction Loads Moving away from

Section I-I.

244

A

σ'vσv

σh

G

FG'''

G'G''

Δσ'h,c,r

changing K2,c-line due to a number of compaction passes


Ki,c-line

σ'v + Δσ'v,c,max

Figure 5.5: Stress Path at Depth z when Subject to Multiple Compaction Passes

245

5.1.5 Estimation of K2,c

The estimation of the K2,c in the proposed model for determining the compaction-

induced stresses in a GRS mass is presented in this section. Two stress reduction

factors “F” and “A” (as shown in Figure 5.6) are introduced. Factor F represents the

compaction-induced stresses for unreinforced soil in Seed’s model (1983), while

factor A is considered the presence of the reinforcement in the GRS mass.

A

K2, s for soil

σ'v

Ki, c - line

σv

σh

K2, c for composite

S

C

B

Δσ

σ'v + Δσ'v, c, max

G*(Δσ)

F∗(Δσ)

Figure 5.6: Stress Path of the Proposed Model for Fill Compaction of a GRS Mass

(a) For Compacted Soil

For an unreinforced soil fill, the coefficient of lateral earth pressure for unloading in

Figure 5.2 can be estimated by using the expression suggested by Seed (1983):

( ) cis KFK ,,2 1−= (5.1)

246

where ( )1

1−

−−=

OCROCROCRF

α

; 'sinφα ≅ ; and 5≅OCR for typical

compacted sand (Seed, 1983).

(b) For GRS Composite

For a GRS mass, total residual strain in the soil can be determined as:

( ) ( )s

s EGF σε Δ+

= (5.2)

where F and G = stress reduction factors shown in figure 5.6; σΔ = increase in horizontal stress due to compaction; Es = soil stiffness.

From Equation 5.2, the reinforcement force, T, due to residual strain in the soil can be

determined as:

( )r

s

EEGFT ⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ+=

σ (5.3)

where Er = reinforcement stiffness.

The average residual stress in the soil due to compaction, )(* σΔG , is:

( )v

r

s SE

EGFG ⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ+=Δ

σσ 7.0* (5.4)

where Sv = reinforcement spacing.

or rrvs EGEFSEG 7.07.0 += (5.5)

Thus,

rvs

r

ESEEFG7.0

7.0−

= (5.6)

Since ( )[ cic KGFK ,,2 1 +−= ] (5.7)

Substituting (5.6) into (5.7), we have

247

cirvs

rc K

ESEE

FK ,,2 7.07.0

11 ⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−

+−≅ (5.8)

The Factor 0.7 in Equation 5.4 will be explained in the section 5.2.1. The increased

horizontal stress in a GRS mass due to compaction can be estimated as:

( ) ( )ccicvch KKFG ,2,max,,, ' −Δ=+Δ=Δ σσσ (5.9)

Substituting (5.8) into (5.9), we have

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−

++−Δ=Δrvs

rcicvch ESE

EFK7.0

7.0111' ,max,,, σσ (5.10)

or

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+Δ=Δrvs

rcicvch ESE

EFK7.0

7.01' ,max,,, σσ (5.11)

Equation 5.11 shows calculation of the residual lateral stress in a GRS mass due to

compaction. The effect of compaction-induced stress in a GRS mass can be also seen

from Equation 5.11.

Using Equation 5.11, the increase of lateral stress in a GRS mass can be estimated

and the increase in soil stiffness can be evaluated. For example, the stiffness of a soil

can be evaluated as:

( ) ( )( )

( )n

a

cha

ch

chf

PPK

cR

tE ⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ+

⎥⎥⎦

⎤

⎢⎢⎣

⎡

Δ++

Δ+−−−= ,3

2

,3

,31

sin2cos2sin1

1σσ

φσσφσσσφ

(5.12)

where

248

Et = tangent modulus

Rf = ratio of ultimate deviator stress to the failure deviator stress

c = cohesive strength

φ = angle of friction

Pa = the atmospheric pressure

K and n = material parameters.

249

5.2 Strength Properties of GRS Composite

Schlosser and Long (1972) proposed the concept of increase of apparent confining

pressure and concept of apparent cohesion of a GRS composite. The Mohr circles of

an unreinforced cohesive soil and a reinforced cohesive soil at failure are shown in

Figure 5.7.

Shea

r Stre

ess,

τ

σ

C

Normal Stress, σ

φ

φ

CR

3σ

3Rσ

1σ

1RΔσ3R

Unreinforced Soil

Reinforced Soil

Reinforced Soil

Figure 5.7: Concept of Apparent Confining Pressure and Apparent Cohesion of a GRS Composite

The apparent cohesion of a GRS composite can be determined as:

cK

c PRR +

Δ=

23σ

(5.13)

where = apparent cohesion of a GRS composite Rc

c = cohesion of soil

250

Kp = coefficient of passive earth pressure

R3σΔ = increase of confining pressure due to reinforcement

Schlosser and Long (1972) also proposed an equation to calculate increased confining

pressure as:

v

f

ST

=Δ 3σ (5.14)

This expression implies that an increase in reinforcement strength, Tf, has the same

effect as a proportional decrease in reinforcement spacing, Sv. Many experimental

test results have shown that Equation 5.14 is not correct. Reinforcement spacing

plays a far more important role than reinforcement strength (Adams, 1997 and 2007;

Elton and Patawaran, 2004 and 2005; Ziegler et al., 2008). This point is supported by

the experiments conducted as a part of this study, as presented in Chapter 4.

5.2.1 Increased Confining Pressure

A new method to estimate the increased confining pressure in soil due to the presence

of reinforcement is presented. The proposed equation for the increased confining

pressure can be expressed as:

⎟⎟⎠

⎞⎜⎜⎝

⎛=Δ

v

f

ST

W3σ (5.15)

where the factor, W, can be estimated as:

⎟⎟⎠

⎞⎜⎜⎝

⎛

= ref

v

SS

rW (5.16)

where Tf = extensile strength of reinforcement

r = a dimesionless factor (will be discussed later in this Section)

251

Sv = vertical spacing of reinforcement

Sref = the reference spacing (will be discussed further later)

To estimate the factor r in Equation 5.16, the concept of “average stresses” proposed

by Ketchart and Wu (2001) was employed. Instead of using average stresses,

however, average reinforcement forces were used.

a. Average Stress in GRS Mass by Ketchart and Wu (2001)

Ketchart and Wu (2001) developed a concept of “average stress” to determine the

behavior of a GRS composite based on a load-transfer analysis. From a simplified

preloading-reloading model for GRS mass, the equations to calculate stresses and

displacements of a GRS mass were developed using the idealized geometry of plain-

strain GRS mass and differential elements of the soil and reinforcement for

equilibrium equations (Hermann and Al-Yassin, 1978) as shown in Figures 5.8 and

5.9.

From the equilibrium equations and a number of assumptions, the stresses in soil and

the force in the reinforcement can be calculated as:

The force in the reinforcement:

( )( )⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛ −⎟

⎟⎠

⎞⎜⎜⎝

⎛ −⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

=Lx

EPPEAF

s

shv

s

srrx α

ααβυ

υυ

coshcosh11

11 2

2

(5.17)

The horizontal stress in the soil:

252

( )( ) ⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ −+⎟

⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

+⎟⎟⎠

⎞⎜⎜⎝

⎛−

−= 22 1coshcosh

11 αβ

αα

αβ

υυ

υυ

σLxPPP hv

s

sv

s

sx (5.18)

Based on a load-transfer analysis, the “average stresses” was determined.

The average vertical stress, vσ , is assumed to be equal to the boundary vertical

pressure, i.e.,

vv P=σ (5.19)

The average horizontal stress, hσ , is:

L

dxxL

x

h

∫= 0

)(σσ (5.20)

or

( )⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛ −+⎟

⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

−⎟⎟⎠

⎞⎜⎜⎝

⎛−

= 1.

tanh111 2 L

LPPP hvs

sv

s

sh α

ααβ

υυ

υυ

σ (5.21)

253

Figure 5.8: An Idealized Plane-Strain GRS Mass for the SPR Model

Figure 5.9: Equilibrium of Differential Soil and Reinforcement Elements (Reproduced from Hermann and Al-Yassin, 1978)

254

b. Average Reinforcement Forces in a GRS Mass

The equations of the forces in the reinforcement and the maximum force in the

reinforcement could be expresses as:

( )( )⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛ −⎟

⎟⎠

⎞⎜⎜⎝

⎛ −⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

=Lx

EPPEAF

s

shv

s

srrx α

ααβυ

υυ

coshcosh11

11 2

2

(5.22)

and

( )⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛ −⎟

⎟⎠

⎞⎜⎜⎝

⎛ −⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

=LE

PPEAFs

shv

s

srr αα

βυυ

υcosh

1111

1 2

2

max (5.23)

The average force in the reinforcement may be calculated as:

L

dxFF

L

x∫= 0 (5.24)

Substituting Equation (5.22) into Equation (5.24), we have:

( )( )∫ ⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛ −⎟

⎟⎠

⎞⎜⎜⎝

⎛ −⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

=L

s

shv

s

srr dxLx

EPP

LEAF

02

2

coshcosh11

11 α

ααβυ

υυ

(5.25)

or

( )( )∫ ⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛ −⎟

⎟⎠

⎞⎜⎜⎝

⎛ −⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

=L

s

shv

s

srr dxLx

EPP

LEA

F0

2

2

coshcosh11

11

.αα

αβυ

υυ

(5.26)

Thus,

( )( )⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟

⎠⎞

⎜⎝⎛ −⎟

⎟⎠

⎞⎜⎜⎝

⎛ −⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

=L

xLE

PPLEA

Fs

shv

s

srr

ααα

αβυ

υυ

coshsinh1

11

.2

2

(5.27)

255

Introducing a factor maxFFr = , and from Equations (5.23) and (5.27), r can be

determined as:

( ) ( )( )( )1cosh

sinhcosh−

−=

LLLLLr

ααααα (5.28)

Using the data from the calculation example in the SPR model (Ketchart and Wu,

2001), the values of factor r for different applied pressures and reinforcement lengths

are presented in Table 5.2.

Table 5.2: Values of factor r under different applied pressure and reinforcement lengths

Increment of

Vertical Pressure

Reinforcement

Length, L (m)

α r

(maxFFr = )

Pv = 9.0 kPa 0.127 13.875 0.698

Pv = 18.0 kPa 0.127 14.616 0.701

Pv = 9.0 kPa 0.225 6.851 0.691

Pv = 18.0 kPa 0.225 6.966 0.692

It can be seen from Table 5.2, the average reinforcement forces are about 70% of the

maximum reinforcement force. The highest value of the maximum reinforcement

force, Fmax, can not exceed the tensile strength of reinforcement, Tf.

256

(5.29) fTF =max

and the average reinforcement force favg TT 7.0= .

Equation 5.16 becomes:

⎟⎟⎠

⎞⎜⎜⎝

⎛

= ref

v

SS

W 7.0 (5.30)

5.2.2 Apparent Cohesion and Ultimate Pressure Carrying Capacity of a GRS

Mass

Substituting Equation 5.30 into Equation 5.15, the increased confining pressure in a

GRS mass becomes:

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=⎟⎟

⎠

⎞⎜⎜⎝

⎛=Δ

⎟⎟⎠

⎞⎜⎜⎝

⎛

v

fSS

v

f

ST

ST

W ref

v

7.03σ (5.31)

Therefore, the apparent cohesion, CR, of a GRS composite can be evaluated as:

cKS

TcKC p

v

fSS

pRref

v

+⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=+

Δ=

⎟⎟⎠

⎞⎜⎜⎝

⎛

27.0

23σ

(5.32)

where c = cohesion of soil Kp = coefficient of passive earth pressure Tf = extension strength of reinforcement Sv = vertical spacing of reinforcement Sref = the reference spacing and can be calculated by: (5.33) max6 dSref = (dmax = the maximum particle/grain size of soil)

Therefore, the ultimate pressure carrying capacity, R1σ , of a soil-geosynthetic

composite mass is:

257

1 3 2fR p

v

TW K c K

Sσ σ

⎛ ⎞= + +⎜ ⎟⎝ ⎠

p (5.34)

where 3σ = confining pressure.

5.1 Verification of the Analytical Model with Measurement Data

Verification of the proposed analytical model for GRS composite strength properties

is made by comparing the model calculation results with the measured data from

GSGC tests (as presented in Chapter 4), and with the measured data by Elton and

Patawaran (2005).

5.1.1 Comparison between the Analytical Model and GSGC Test Results

The results of the GSGC tests have been reported in section 4.6. The dimensions of

the GSGC tests are 2 m high and 1.4 m wide in a plane strain condition. The soil

mass in the tests were reinforced with Geotext 4x4 geotextile at 0.2 m and 0.4 m

spacing. For the Diabase soil used in GSGC Tests, the maximum particle size was

about 1.3 in.; therefore, .8.76 max indSref == (or 0.2 m). Comparisons of the results

between the analytical model and the GSGC tests are presented in Table 5.3. The

deviatoric stresses at failure calculated from the analytical model are in good

agreement with those of the GSGC tests. The differences between them are less than

10 %.

For reference purposes, comparisons of the results between Schlosser and Long’s

method and the GSGC tests are also presented (see Table 5.4). The deviatoric

stresses at failure calculated from the Schlosser and Long’s method are about 20 % to

86 % larger than the measured values.

258

Table 5.3: Comparison of the results between the analytical model and the GSGC tests

Parameter Test 2 (T, S) Test 3 (2T, 2S) Test 4 (T, 2S)

Tf (kN/m) 70 140 70

Sv (m) 0.2 0.4 0.4

3σΔ (kN/m2)

by the Analytical Model

245

172

86

CR (kN/m2)


407

305

188

( 31 )σσ −R (kN/m2)

from Measured Data

2,700 1,750 1,300

( 31 )σσ −R (kN/m2)


2,460

1,900

1,250

Difference between

the Analytical Model and

Measured Data

- 9 %

+ 8 %

- 4 %

Note: Internal friction angle of soil, φ = 50o; cohesion of soil, c = 70 kPa.

259

Table 5.4: Comparison of the results between Schlosser and Long’s method and the GSGC tests

Parameter Test 2 (T, S) Test 3 (2T, 2S) Test 4 (T, 2S)

Tf (kN/m) 70 140 70

Sv (m) 0.2 0.4 0.4

3σΔ (kN/m2)

by Schlosser & Long’s Method

350 350 175

CR (kN/m2)


550 550 310

( 31 )σσ −R (kN/m2)

from Measured Data

2,700 1,750 1,300

( 31 )σσ −R (kN/m2)


3,250 3,250 1,930

Difference between

Schlosser & Long’s Method

and Measured Data

+ 20 % + 86 % + 48 %

Note: Internal friction angle of soil, φ = 50o; cohesion of soil, c = 70 kPa.

260

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

Test Results

Elton and Patawaran (2005) conducted seven large-size triaxial tests for reinforced

soil with the dimensions of 5 ft in height and 2.5 ft in diameter (see Figure 5.10). All

the tests were conducted under an unconfined condition. The properties of the tests

are summarized as follows:

• Backfill: The soil used in the test was a poorly graded sand with the gradation

test results shown in Figure 5.11; maximum dry unit weight γdry = 121 pcf;

optimum moisture content wopt = 9.3%; internal friction φ = 40o; and cohesion

c = 4 psi.

• Reinforcement: Six types of reinforcement (TG500, TG600, TG 700, TG800,

TG1000 and TG028) were used for the tests with the reinforcement spacing of

6 in. and 12 in. The strength, Tf, of the reinforcement and reinforcement

spacing, Sv, are shown in Table 5.5.

The maximum particle size (from gradation tests, Figure 5.11) of the backfill in the

large-size triaxial tests was .5.0max ind = (or 12.7 mm); therefore,

(or 0.08 m). The measured results are shown in Figure 5.12.

The comparisons of Elton and Patawaran’s tests results with the analytical model and

with Schlosser and Long’s Method are presented in Tables 5.5 and 5.6, respectively.

.36 max indSref ==

The differences in the deviatoric stresses at failure calculated from the analytical

model and Elton and Patawaran’s measured data are less than 18 %. Whereas, the

results calculated from Schlosser and Long’s method are 69 % to 97 % larger than the

measured values.

261

Figure 5.10: Reinforced Soil Test Specimen before Testing (Elton and Patawaran, 2005)

262

Figure 5.11: Backfill Grain Size Distribution before and after Large-Size Triaxial

Tests (Elton and Patawaran, 2005)

Figure 5.12: Large-Size Triaxial Test Results (Elton and Patawaran, 2005)

263

Table 5.5: Comparison of the results between the analytical model and Elton and Patawaran’s tests (2005)

Reinforcement

Type

TG

500

TG

500

TG

600

TG

700

TG

800

TG

1000

TG

028

Tf (kN/m) 9 9 14 15 19 20 25

Sv (m) 0.15 0.30 0.15 0.15 0.15 0.15 0.15

3σΔ (kN/m2) by the Analytical

Model

30 8 47 48 62 67 83

CR (kN/m2)


60 36 78 79 94 99 116

( 31 )σσ −R (kN/m2) from Measured

Data

230 129 306 292 402 397 459

( 31 )σσ −R (kN/m2)


256 153 333 341 402 426 498

Difference between the Analytical

Model and Measured Data

11 % 18 % 9 % 17 % 0 % 7 % 8 %

Note: Internal friction angle of soil, φ = 40o; cohesion of soil, c = 27.6 kPa.

264

Table 5.6: Comparison of the results between Schlosser and Long’s method and Elton and Patawaran’s tests (2005)

Reinforcement Type

TG

500

TG

500

TG

600

TG

700

TG

800

TG

1000

TG

028

Tf (kN/m) 9 9 14 15 19 20 25

Sv (m) 0.15 0.30 0.15 0.15 0.15 0.15 0.15

3σΔ (kN/m2) by Schlosser & Long’s Method

59 30 92 95 122 132 163

CR (kN/m2)


91 59 126 130 158 169 202

( 31 )σσ −R (kN/m2)

From Measured Data

230 129 306 292 402 397 459

( 31 )σσ −R (kN/m2)


390 254 541 557 678 726 868

Difference between Schlosser & Long’s

Method and Measured Data

70 % 97 % 77 % 91 % 69 % 83 % 89 %

Note: Internal friction angle of soil, φ = 40o; cohesion of soil, c = 27.6 kPa.

265

5.3.3 Comparison of the Results between the Analytical Model and Finite

Element Results

Finite element analyses were conducted to provide additional data for verifying the

analytical model. The test conditions and material properties used for the finite

element analyses were the same as those used in GSGC Test 2, but with confining

pressures of 34 kPa, 70 kPa, 100 kPa and 200 kPa. The confining pressure used in

GSGC Test 2 was 34 kPa. The comparison indicates that the results of the analytical

model are in good agreement with those obtained from the finite element analyses at

the different confining pressures. The largest difference in terms of the deviatoric

stress at failure is 9%.

266

Table 5.7: Comparison of the results between the analytical model and results for GSGC Test 2 with different confining pressures from FE analyses

Parameter S3 = 34 kPa

S3 = 70 kPa

S3 = 100 kPa

S3 = 200 kPa

3σΔ (kN/m2)

by the Analytical Model 245 245 245 245

CR (kN/m2)

by the Analytical Model 407 407 407 407

( 31 )σσ −R (kN/m2)

from FE Analysis 2,700 2,970 3,190 3,860

( 31 )σσ −R (kN/m2)

by the Analytical Model 2,490 2,760 2,990 3,740

Difference between

the Analytical Model and FE analyses

- 8 %

- 7 %

- 6 % - 3 %

Note: Internal friction angle of soil, φ = 50o; cohesion of soil, c = 70 kPa; reinforcement strength, Tf = 70 kN/m; reinforcement spacing, Sv = 0.2 m.

267

5.4 Required Reinforcement Strength in Design

In this Section, an analytical model for determining required tensile strength in

reinforcement is developed, a comparison of the analytical model with current design

equation is made, and verification of the analytical model is presented.

5.4.1 Proposed Model for Determining Reinforcement Force

In current design methods the following equation is used to determine the required

reinforcement strength, Trequired, for the design of GRS structures:

svhrequired FST ∗∗= σ (5.35)

where

Trequired = required strength for reinforcement at depth z

hσ = horizontal stress in a GRS mass at depth z

Fs = safety factor

Assuming Fs = 1, we have frequired TT = (ultimate strength of reinforcement) and

Equation 5.35 becomes

hv

f

ST

σ= (5.36)

Note that when the horizontal stress, hσ , is a constant, the ratio f

v

TS

becomes a

constant; i.e., Tf is linearly proportional to Sv. Using Equation 5.15 a new expression

for the increase of confining pressure due to tensile inclusion, a modified equation for

determination of required reinforcement strength can be obtained. The derivation of

268

the modified equation is described as follows. The horizontal stress, hσ , in a GRS

structure at depth z is:

33 σσσ Δ+=h (5.37)

or 33 σσσ −=Δ h (5.38)

Since,

v

f

ST

W=Δ 3σ (see Section 5.2.1) (5.39)

Substituting Equation 5.39 into Equation 5.36 leads to

v

fh S

TW=− 3σσ (5.40)

or ( )

WST h

v

f 3σσ −= (5.41)

Since,

⎟⎟⎠

⎞⎜⎜⎝

⎛

= max67.0 dSv

W (5.42)

Therefore,

( )

⎟⎟⎠

⎞⎜⎜⎝

⎛

−=

max6

3

7.0 dS

h

v

f

vST σσ

(5.43)

where

Tf = ultimate strength of reinforcement at depth z

hσ = horizontal stress in a GRS mass at depth z

3σ = lateral constraint pressure at depth z, lateral earth pressure exerted by

external constraint. For a GRS wall with modular block facing, 3σ

can be estimated as:

δγσ tan3 bb= (5.44)

269

where

γb = unit weight of facing block

b = width of facing block

δ = friction angle between modular block facing elements (δ can be

the friction angle between facing blocks if there is no

reinforcement between the blocks, or it can be the friction

angle between facing block and geosynthetic if there is

reinforcement sandwiched between blocks)

Sv = reinforcement spacing

dmax = maximum grain size of the backfill

The required tensile strength of the reinforcement in design can be expressed as:

sv

dS

hrequired FST

v**

7.0 max6

3

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−

=⎟⎟⎠

⎞⎜⎜⎝

⎛

σσ (5.45)

Note that Trequired is always equal or greater than zero. For a GRS mass without

lateral constraint (e.g., a wrapped wall), 3σ = 0, and Equation 5.45 becomes

sv

dS

hrequired FST

v**

7.0 max6 ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎟⎟⎠

⎞⎜⎜⎝

⎛

σ (5.46)

5.4.2 Comparison of Reinforcement Strength between the Analytical Model

and Current Design Equation

A comparison of reinforcement forces is made between the proposed model

(Equation 5.45) and the current design equation (Equation 5.35). The reinforcement

270

forces in a 6.0 m high GRS wall, as determined by the two equations, are shown in

Table 5.8. Note that the facing stiffness is ignored in the current design method;

while the facing rigidity, as denoted by the lateral constraint pressure, σ3, can be

accounted for in the proposed model.

5.4.3 Verification of the Analytical Model for Determining Reinforcement

Strength

Verification of the analytical model for determination of reinforcement strength is

made by comparing the results with the forces in reinforcement at failure from the

GSGC tests (see Chapter 4), with the measured data by Elton and Patawaran (2005),

and with a typical GRS wall.

Table 5.9 shows a comparison of the results from the proposed model and measured

data from the GSGC tests. The largest difference in reinforcement forces between the

two is 16 %, whereas there is 47 % between the current design methods and the test

data.

A comparison of the reinforcement forces between the proposed model and the

measured data from Elton and Patawaran’s tests (2005) is shown in Table 5.10. The

largest difference in reinforcement forces between the two is 13 %, whereas it was as

high as 74 % between the current design method (Equation 5.35) and the test results.

The proposed model clearly gives a much improved value for estimating

reinforcement strength compared to the current design methods.

271

272

Table 5.8: Comparison of reinforcement forces between proposed model and current design equation for a GRS wall

z (m)

Trequired (kN/m), for Fs = 1

Current Design Equation

Proposed Model

No Facing Modular Block Facing with

bb = 35o

Modular Block Facing with

bb = 54o

0.4 0.3 1.1 0 0

0.8 0.6 1.5 0.1 0

1.2 1.0 2.0 0.5 0

1.6 1.3 2.4 1.0 0

2.0 1.6 2.9 1.4 0

2.4 1.9 3.3 1.9 0.1

2.8 2.3 3.7 2.3 0.6

3.2 2.6 4.2 2.8 1.0

3.6 2.9 4.6 3.2 1.5

4.0 3.2 5.1 3.6 1.9

4.4 3.6 5.5 4.1 2.4

4.8 3.9 6.0 4.5 2.8

5.2 4.2 6.4 5.0 3.2

5.6 4.5 6.8 5.4 3.7

6.0 4.9 7.3 5.8 4.1 Note: Internal friction angle of soil, = 38o; cohesion of soil, c = 0; reinforcement spacing, Sv = 0.2 m; maximum grain size of soil, mmd 38max ; unit weight of soil,

backfill 17 kN/m3; unit weight of facing block, block 25 kN/m3; bb = friction angle between facing blocks; width of blocks, b = 0.3 m.

Table 5.9: Comparison of reinforcement forces between proposed model and the GSGC tests

Parameter Test 2 (T, S)

Test 3 (2T, 2S)

Test 4 (T, 2S)

Test 5 (T, S)

Reinforcement Force at Failure Tf (kN/m) 70 140 70 70

Reinforcement Spacing Sv (m) 0.2 0.4 0.4 0.2

Measured Failure Pressure (kPa) 2,700 1,750 1,300 1,900

Lateral Constraint Pressure 3σ (kPa) 34 34 34 0

Maximum Reinforcement Force from Current Design

Equation, Equation 5.35 (kN/m)

62.4 74.4 50.5 41.2

Difference between Current Design Equation (Equation 5.35) and Tf

- 11 % - 47 % - 28 % - 41 %

Maximum Reinforcement Force from Proposed Model, Equation 5.45

(kN/m)

79.4 124.1 75.4 58.8

Difference between Proposed Model (Equation

5.45) and Tf

+ 13 % - 11 % + 8 % -16 %

Note: Internal friction angle of soil, φ = 50o; cohesion of soil, c = 70 kPa; unit weight of soil, =backfillγ 24 kM/m3; maximum grain size of soil, mmd 33max = .

273

274

Table 5.10: Comparison of reinforcement forces between proposed model and test data from Elton and Patawaran (2005)

Parameter TG 500

TG 500

TG 600

TG 700

TG 800

TG 1000

TG 028

Reinforcement Force at Failure Tf (kN/m) 9 9 14 15 19 20 25

Reinforcement Spacing Sv (m) 0.15 0.30 0.15 0.15 0.15 0.15 0.15

Measured Failure Pressure (kPa) 230 129 306 292 402 397 459

Maximum Reinforcement Force from Current Design Equation, Equation

5.35 (kN/m)

4.47 2.35 6.95 6.49 10.08 9.91 11.94

Difference between Current Design

Equation (Equation 5.35) and Tf

- 50 %

- 74 %

- 50 %

- 57 %

- 47 %

- 50 %

- 52 %

Maximum Reinforcement Force

from Proposed Model, Equation 5.45 (kN/m)

9.02 9.56 14.02 13.10 20.34 20.01 24.09

Difference between Proposed Model

(Equation 5.45) and Tf

0 %

+ 6 %

0 %

-13 %

+ 7 %

0 %

- 4 %

Note: Internal friction angle of soil, φ = 40o; cohesion of soil, c = 27.6 kPa; unit weight of soil, =backfillγ 18.8 kM/m3; lateral constraint pressure, 3σ = 0 kPa; maximum grain size of soil, mmd 12max 7.= .

6. FINITE ELEMENT ANALYSES

In this chapter, the GSGC tests described in Chapter 4 were simulated using the Finite

Element (FE) method of analysis. The behavior of the reinforced soil mass in GSGC

Test 2 under different confining pressures, which was not part of the experimental

program, was investigated by using FE model. The angle of dilatation of a GRS

composite was investigated. In addition, the analytical model developed for

evaluation of compaction-induced stresses in a GRS mass was verified by comparing

the results with those obtained from the FE analysis.

Many finite element codes are readily available for the analysis of soil-structure

interaction problems, including Abacus, FLAC, LS-Dyna, Plaxis, Sage Crisp, Sigma

(Geoslope). In this study, Plaxis 8.2 code was selected for the analysis, due primarily

to the author’s familiarity with the code. This code has been used successfully for the

analysis of various earth structures, including GRS structures (e.g., Bueno, et al.,

2005), Christopher, et al., 2005, and Morison, et al., 2007).

6.1 Brief Description of Plaxis 8.2

Version 8.2 of Plaxis is a finite element code intended for two-dimensional analysis

of deformation and stability problems in geotechnical engineering. The details of

Plaxis 8.2 program can be found in the Plaxis manual (Plaxis, 2002). A brief

description of some key features of the program is presented bellow:

Graphical input of geometry models: The input of layers, structures, construction

stages, loads and boundary conditions is based on CAD drawing procedures, which

275

allows for a detailed modeling of the geometry. From the geometry model, a 2-

dimensional finite element mesh is easily generated.

Automatic mesh generation: Plaxis allows for automatic generation of 2-dimensional

finite element meshes with options for global and local mesh refinement.

High-order elements: Quadratic 6-node and 4th order 15-node triangle elements are

available to describe the stress-deformation behavior of the soil.

Plates/Beams: Special beam elements can be used to model the bending of retaining

walls, tunnel linings, shells, and other slender structures. The behavior of these

elements is defined using a flexural rigidity, a normal stiffness and an ultimate

bending moment. Plates with interfaces can also be used to model the behavior of

structures.

Interfaces: Joint elements are available to model soil-structure interface behavior.

For example, joint elements can be used to simulate the thin zone of intensely

shearing material at the contact between a retaining wall and the surrounding soil, a

tunnel lining and the soil, or between reinforcement and surrounding soil. Values of

the interface friction angle and adhesion are generally not the same as the friction

angle and cohesion of the surrounding soil.

Anchors: Elastoplastic spring elements can be used to model anchors and struts. The

behavior of these elements is defined using a normal stiffness and a maximum force.

A special option exists for the analyses of prestressed ground anchors and excavation

supports.

Geogrids/geotextiles: Geogrids or geotextiles in GRS structures can be simulated in

Plaxis by special tension elements. It is often convenient to combine these elements

with joint elements to model the interaction between geosynthetic reinforcement and

the surrounding soil.

Tunnels: The Plaxis program offers a convenient option to create circular and non-

circular tunnels using arcs and lines. Plates and interfaces may be used to model the

tunnel lining and the interaction with the surrounding soil. Fully isoparametric

276

elements can be used to model the curved boundaries within the mesh. Various

methods are available for the analysis of the deformation caused by various methods

of tunnel construction.

Mohr-Coulomb model: This non-linear model is based on soil parameters that are

well-known in geotechnical engineering practice. Not all non-linear features of soil

behavior are included in this model; however, the Mohr-Coulomb model can be used

to compute realistic support pressures for tunnel faces, ultimate loads for footings,

etc. It can also be used to calculate a safety factors using a “phi-c reduction’

approach.

Advanced soil models: In addition to the Mohr-Coulomb model, Plaxis offers a

variety of advanced soil model. A general second-order model, an elastoplastic type

of hyperbolic model, called the Hardening Soil model, is available. To model

accurately the time-dependent and logarithmic compression behavior of normally

consolidated soft soils, a creep model is also available, which is referred to as the Soft

Soil Creep model. In addition, a special model is available for the analysis of

anisotropic behavior of jointed rock.

User-defined soil models: A special feature in Plaxis 8.2 is that it has a user-defined

soil model option. This feature enables users to include self-programmed soil models

for the analysis.

Staged construction: This feature enables realistic simulation of construction of earth

structures by activating and deactivating compaction loads, and simulation of

excavation processes by activating and deactivating clusters of elements, application

of loads, changing of water tables, etc. The procedure allows for a realistic

assessment of stresses and displacements caused, for example, by compaction loads

or soil excavation during underground construction.

277

6.2 Compaction-Induced Stress in a GRS Mass

The residual lateral stresses in a GRS mass due to compaction can be evaluated by the

following equation (see Section 5.15 for details):

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+Δ=Δrvs

rcicv ESE

EFK

7.07.0

1,max,,3 σσ (6.1)

where max,,cvσΔ is the maximum vertical stress due to compaction loading;

( )1

1sin

−−

OCROCR

−=OCRF

φ

; Es and Er are soil and reinforcement stiffness,

respectively; and Sv is reinforcement spacing.

To illustrate how to compute the residual lateral stresses, or compaction-induced

stresses (CIS), in a GRS mass, a 6-m high GRS mass was chosen as an example. The

parameters used for the calculation of CIS are:

• Soil: A dense sand with unit weight γ = 17 kN/m3; angle of internal friction φ

= 45o; soil modulus, =sE 30,000 kPa; compaction lift S = 0.2 m.

• Geosynthetics: =rE 2,000 kPa; Sv = 0.2 m.

The vertical maximum pressures of 44 kPa, 100 kPa, 200 kPa, 300 kPa and 500 kPa

due to compaction were used for the calculation of the residual stresses. Note that the

maximum vertical compaction stress of 44 kPa was the contact pressure used in the

GSGC Tests described in Chapter 4.

Figure 6.1 shows the distribution of the lateral residual stresses with depth due to the

different maximum compaction pressures. The values of the lateral residual stresses

in this figure were calculated based on Equation 6.1 with the assumption that the

compaction lift of 0.2 m is small compared to the dimensions of the compaction plant.

As a result, the distribution of the lateral residual stress within the 0.2 m-thick lift due

278

to compaction is constant. Near the surface, the lateral residual stresses will follow

the limiting lateral earth pressure for unloading condition, i.e., the K1,c-line, as shown

in Figure 5.2 and Table 5.1.

-6

-5

-4

-3

-2

-1

00 25 50 75 100

Residual Lateral Stress (kPa)D

epth

(m)

44 kPa

100 kPa

200 kPa

300 kPa

500 kPa

Maximum Vertical Pressure due to Compaction:

Figure 6.1: Distribution of Residual Lateral Stresses of a GRS mass with Depth due to fill compaction

279

6.3 Finite Element Simulation of the GSGC Tests

The Finite Element (FE) program Plaxis 8.2 was used for the simulation of GSGC

Tests 1, 2 and 3, as described in Chapter 4. The backfill of all GSGC test specimens

was compacted at 0.2 m lifts using a plate compactor MBW-GP1200 with a contact

pressure of 44 kPa. The soil stiffness, , can be estimated from triaxial tests using

Janbu’s equation (1963). The Poisson’s ratio of the backfill can be estimated as:

refE50

• ( )EV

V zzyx

σνεεε 21−=++=

Δ (for uniaxial tests)

• ( ) ( )( )ν

σννεεε

−−+

=++=Δ

1211

EVV z

zyx (for triaxial Tests)

For GSGC Test 1-unreinforced soil, the soil model and parameters used in the

analysis are as bellows:

• Soil model: Hardening model

• Dry unit weight γ = 24 kN/m3, wet unit weight γ = 25 kN/m3

• Angle of internal friction, φ = 50o; angle of dilation, ψ = 17.5o, cohesion c =

70 kPa (for confining pressure < 30 psi)

• Soil modulus: =refE50 62,000 kPa, =refurE 124,000 kPa, Poisson’s ratio ν =

0.37

• Power m = 0.5.

SGC Tests, the backfill stiffness was increased due to CIS as described

e first lift of facing blocks and soil. The compaction lift thickness was

0.2 m.

For the G

below:

1. Place th

280

2. Apply a uniform vertical stress of 44 kPa over the entire surface of each newly

placed soil layer before analysis, and remove it afterwards (see Table 6.2).

This step was employed to simulate the compaction operation.

3. Place a sheet of reinforcement at pre-selected reinforcement spacing to cover

the entire backfill surface plus the facing blocks.

4. Place another lift of facing blocks and soil.

5. Repeat Steps 2 to 4 until the fill reached the total height of the specimen.

6. Remove facing blocks

7. Apply a prescribed confining pressure.

8. Apply vertical stresses on the top of the specimen at equal increments until

failure.

The properties of the backfill were modified due to compaction effects. The

Poisson’s ratio under plane strain condition was reduced to minν , as suggested by

Hatami and Bathurst (2006). Soil modulus was calculated using the increase in

confining pressure due to compaction. The value of can be estimated by using

Equation 5.12 with

refE50

refE50

333 '' σσσ Δ+= S , where 3σΔ is the average residual lateral stress,

and can be estimated by Equation 6.1. Note that the elastic modulus was increased by

factor of 2.25 for walls 1 and 2 in Hatami and Bathurst’s numerical analyses (2006)

and by factor of 10 in the FE analyses by Morrison, et al. (2006).

The conditions and properties of the backfill and reinforcement of GSGC Tests 2 and

3 used in FE analyses are shown in Table 6.1.

281

Table 6.1: Parameters and properties of the GSGC Tests used in analyses

Description

Soil

Material: Diabase; Soil model: Hardening soil model; dry unit

weight, γd = 24 kN/m3; wet unit weight, γw = 25 kN/m3;

cohesion, c = 70 kPa; angle of internal friction, φ = 50o; angle

of dilation, ψ = 17o; soil modulus, 63,400 kPa,

126,800 kPa; Poisson’s ratio

=refE50

=refurE ν = 0.2; power, m = 0.5.

Reinforcement

GSGC

Test 2

Single-sheet Geotex 4x4: axial stiffness, EA = 1,000

kN/m; ultimate strength, Tult = 70 kN/m;

reinforcement spacing, Sv = 0.2 m;

GSGC

Test 3

Double-sheet Geotex 4x4: axial stiffness, EA = 2,000

kN/m; ultimate strength, Tult = 140 kN/m;

reinforcement spacing, Sv = 0.4 m

Facing Block FE Model: linear elastic model; modulus, E = 3*107 kPa; unit

weight, γ = 12.5 kN/m3 (hollow blocks); Poisson’s ratio, ν = 0.

Block-Block

Interface

FE Model: Mohr-Coulomb model; modulus, E = 3*106 kPa;

unit weight, γ = 0 kN/m3; cohesion, c = 2 kPa; angle of internal

friction, φ = 33o; Poisson’s ratio, ν = 0.45.

Confining

Pressure

Constant confining pressures of 34 kPa for the GSGC Tests 1 to

3.

Note: Soil-reinforcement interface was assumed to be fully bonded in the analyses.

282

Table 6.2 shows the steps in the finite element analyses. The first 20 steps were used

for modeling the preparation of the specimen. The loading began from step 21.

283

Table 6.2: The steps of analysis for the GSGC Tests

Step Configuration

1

2

3

4

284

Table 6.2 (continued): The steps of analysis for the GSGC Tests Step Configuration

20

Note: The full height of the GSGC mass was reached at the last step of the

specimen preparation

285

Table 6.2 (continued): The steps of analysis for the GSGC Tests

Step Configuration

21

Note: The facing blocks were removed, a confining pressure and vertical

pressures were applied (during loading)

286

6.3.1 Simulation of GSGC Test 1

The global stress-strain relationship and volume change relationship as obtained from

FE analysis and the GSGC tests are shown in Figure 6.2. The analysis results are in

good agreement with the measured data. The maximum differences of the results

between the FE analysis and the tests were about 5 %. Figure 6.3 shows the lateral

movements on the open faces of the specimen at 200 kPa, 400 kPa, 600 kPa and 770

kPa. The results from FE analyses and the tests are also in good agreement.

287

0

100

200

300

400

500

600

700

800

900

0 1 2 3 4 5 6 7


Appl

ied

Vet

ical

Stre

ss (k

Pa)

FE Analysis

Measured Data

(a)

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5 3 3.5


Vol

umet

ric

Stra

in (%

)

Mearsued Data

FE Analysis

(b)

Figure 6.2: Comparison of Results for GSGC Test 1:

(a) Global Vertical Stress-Strain Relationship, and (b) Volume Change Relationship

288

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

0 10 20 30 40 50


Spec

imen

Hei

ght (

m)

200 kPa(Measured)

400 kPa(Measured)

600 kPa(Measured)

770 kPa(Measured)

200 kPa (FE)

400 kPa (FE)

600 kPa (FE)

770 kPa (FE)

Applied Pressure

Figure 6.3: Comparison of Lateral Displacements on Open Face of GSGC Test 1

289

6.3.2 Simulation of GSGC Test 2

The global stress-strain relationships, as obtained from FE analysis and the GSGC

tests, are shown in Figure 6.4. The results of FE analysis with and without

consideration of CIS are included in Figure 6.4. It is seen that the results with

consideration of CIS gives slightly better simulation of stress-strain curve. It should

be noted that the compaction energy used in the GSGC tests was very low. As a

result, the magnitude of CIS was very small, and the effect of CIS on the global

stress-strain relationship was not significant.

Figure 6.5 shows the lateral displacements on the open faces of the specimen at

applied pressures of 400 kPa, 1,000 kPa, 2,000 kPa and 2,500 kPa. The simulated

lateral displacements are no more than 5% greater than the measured values.

Figure 6.6 shows the simulated and measured displacements of the GSGC mass at

selected points in Figure 4.49. It is seen that the simulated displacements are in

agreement with the measured values.

A comparison of the distribution of strains in the reinforcement in GSGC Test 2

between the FE analyses and measured data are shown in Figure 6.7. It is seen that

the simulated strains are in good agreement with the measured values.

290

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10


Dev

iato

ric

Stre

ss (k

Pa)

Measured Data

FE Analysis-w ithout CIS

FE Analysis-w ith CIS

Figure 6.4: Comparison of Global Stress-Strain Relationship of GSGC Test 2

291

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

0 20 40 60


Spec

imen

Hei

ght (

m)

2500 kPa(Measured)

2000 kPa(Measured)

1000 kPa(Measured)

400 kPa(measured)

2500 kPa (FE)

2000 kPa (FE)

1000 kPa (FE)

400 kPa (FE)

Applied Pressure:

Figure 6.5: Comparison of Lateral Displacement at Open Face of GSGC Test 2

292

-160

-140

-120

-100

-80

-60

-40

-20

0-80 -60 -40 -20 0 20 40 60 80

x (mm)

y (m

m)

Point 1 (Measured)

Point 2 (Measured)

Point 3 (Measured)

Point 4 (Measured)

Point 6 (Measured)

Point 7 (Measured)

Point 8 (Measured)

Point 9 (Measured)

Point 1 (FE)

Point 4 (FE)

Point 7 (FE)

Point 3 (FE)

Point 6 (FE)

Point 9 (FE)

Note: Locations of Points are show n in Figure 4.49

Figure 6.6: Comparison of Internal Displacements of GSGC Test 2

293

0

0.5

1

1.5

2

2.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

)200 kPa(Measured)600 kPa(Measured)800 kPa(Measured)1000 kPa (Measured)200 kPa (FE)

600 kPa (FE)

800 kPa (FE)

1000 kPa (FE)

Applied Pressure

(a)

0

0.5

1

1.5

2

2.5

3

3.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

)

200 kPa(Measured)600 kPa(Measured)800 kPa(Measured)1000 kPa(Measured)200 kPa (FE)

600 kPa (FE)

800 kPa (FE)

1000 kPa (FE)

Applied Pressure:

(b)

Figure 6.7: Comparison of Reinforcement Strains of GSGC Test 2:

(a) At reinforcement Layer 1.6 m from the Base, and (b) At reinforcement Layer 0.8 m from the Base

294

6.3.3 Simulations of GSGC Test 3

A comparison of the global stress-strain relationships of GSGC Test 3, as obtained

from FE analysis and measured data of GSGC Test 3, are shown in Figure 6.8. The

FE results are in good agreement with the measured data. The lateral displacements

on the open faces at applied pressures of 400 kPa, 600 kPa, 800 kPa, 1000 kPa and

1250 kPa are shown in Figure 6.9. Figure 6.10 shows a comparison of simulated and

measured internal displacements of the GSGC Test 3 specimen at selected points in

Figure 4.57. Once again, the results from FE analyses are in very good agreement

with the measured values.

The comparisons of the distribution of strains in the reinforcement in GSGC Test 3

between FE analyses and measured data are shown in Figure 6.11. It is seen that the

simulated strains are in agreement with the measured values.

295

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

0 1 2 3 4 5 6 7 8Global Vertical Strain (%)

Dev

iato

ric S

tres

s (k

Pa)

Measured Data

FE Analyses

Figure 6.8: Comparison of Global Stress-Strain Relationship of GSGC Test 3

296

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

0.0 10.0 20.0 30.0

Lateral Movement (mm)

Spe

cim

en H

eigh

t (m

)

400 kPa (Measured)

600 kPa (Measured)

800 kPa (Measured)

1,000 kPa (Measured)

1,250 kPa (Measured)

400 kPa (FE)

600 kPa (FE)

800 kPa (FE)

1,000 kPa (FE)

1,250 kPa (FE)

Applied Pressure:

Figure 6.9: Comparison of Lateral Displacement at Open Face of GSGC Test 3

297

-140

-120

-100

-80

-60

-40

-20

0-80 -60 -40 -20 0 20 40 60 80

x (mm)

y (m

m)

Point 1 (Measured)

Point 2 (Measured)

Point 3 (Measured)

Point 4 (Measured)

Point 6 (Measured)

Point 1 (FE)

Point 3 (FE)

Point 4 (FE)

Point 6 (FE)

Note: Locations of Points are show n in Figure 4.57

Figure 6.10: Comparison of Internal Displacements of GSGC Test 3

298

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

)260 kPa(Measured)600 kPa(Measured)1000 kPa(Measured)260 kPa (FE)

600 kPa (FE)

1000 kPa (FE)

Applied Pressure

(a)

0

0.5

1

1.5

2

2.5

3

3.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6


Stra

in (%

)

260 kPa(Measured)600 kPa(Measured)1000 kPa(Measured)200 kPa (FE)

600 kPa (FE)

1000 kPa (FE)

`

Applied Pressure

(b)

Figure 6.11: Comparison of Reinforcement Strains of GSGC Test 3:

(a) At reinforcement Layer 1.2 m from the Base, and (b) At reinforcement Layer 0.4 m from the Base

299

6.4 FE Analysis of GSGC Test 2 under Different Confining Pressures and

Dilation Angle of Soil-Geosynthetic Composites

Figure 6.12 shows a comparison of the global stress-strain and volume change

relationships of GSGC Test 2 as obtained from FE analysis and the measured data.

GSGC Test 2 was conducted under a confining pressure of 34 kPa. It is seen that the

global stress-strain and volume change relationships under the confining pressure of

34 kPa as obtained from FE analysis are in good agreement with the measured data.

To provide additional data under different confining pressures, the FE model was

used to generate data under confining pressures of 100 kPa and 200 kPa, as shown in

Figure 6.12.

It is interesting to note that the reinforcing mechanism of GRS mass can be viewed in

terms of the angle of dilation. The angle of dilation of a geosynthetic-reinforced soil

mass is smaller than the angle of dilation of an unreinforced soil mass. Using the data

in Figure 6.12 as an example, the angles of dilation of the soil-geosynthetic

composites were approximately -8o, -11o and -12o (a negative dilation angle means no

dilation, the greater the absolute value the less likely the material will dilate) under

confining pressures of 34 kPa, 100 kPa and 200 kPa, respectively; whereas the angle

of dilation of the reinforced soil was +17o under a confining pressure up to 200 kPa.

This suggests that the presence of geosynthetic reinforcement has a tendency to

“suppress” dilation the surrounding soil. A soil having less tendency to dilate will

become stronger. The dilation behavior offers a new explanation of the reinforcing

mechanism, and the angle of dilation provides a quantitative measure of the degree of

reinforcing effect of a GRS mass.

300

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

0 1 2 3 4 5 6 7 8 9


Dev

iato

ric S

tres

s (k

Pa)

34 kPa (Measured)

34 kPa (FE)

100 kPa (FE)

200 kPa (FE)

Confining Pressure:

(a)

-4

-3

-2

-1

0

1

2

0 2 4 6 8 10


Vol

umet

ric

Stra

in (%

)

34 kPa (T2)

34 kPa (FE)

100 kPa (FE)

200 kPa (FE)

34 kPa (Soil - T1)

Confining Pressure:

(b)

Figure 6.12: FE Analyses of GSGC Test 2 under Different Confining Pressures:

(a) Global Stress-Strain Relationship, and (b) Volume Change Curves

301

6.5 Verification of Compaction-Induced Stress Model

The analytical model for evaluating compaction-induced stresses (CIS), as described

in Section 3.2, was verified using the finite element (FE) method of analysis. The FE

analysis was carried out by using Version 8.2 of Plaxis code (2002). To verify CIS

model, a 6 m-high GRS mass was chosen as an example. The parameters used for the

calculation of CIS in the analytical model and the FE analysis are:

• Soil: a dense sand with mass unit weight γ = 17 kN/m3; angle of internal

friction φ = 45o; loading modulus, =sE 30,000 kPa; unloading modulus,

=urE 90,000 kPa; Poisson ratio, ν = 0.2; compaction lift S = 0.2 m (Note:

The behavior of soil was simulated in FE analysis by using the Hardening Soil

model in plane strain condition.)

• Geosynthetics: tensile modulus =rE 2,000 kPa; reinforcement spacing, Sv =

0.2 m.

• Interface: the interface between the soil and geosynthetic reinforcement is

fully bonded.

The very fine mesh of a FE analyses to simulate CIS in a GRS mass is shown in

Figure 6.13. Figure 6.14 shows the lateral stress distributions at the center line of the

GRS mass without considering CIS and with CIS under the maximum compaction

pressures of 200 kPa and 500 kPa. The compaction operation was simulated by

loading and unloading at different locations on the surface area of each lift. The

“residual lateral stresses” were the differences between the lateral stresses with

simulating CIS and those without CIS at the same location as shown in Figure 6.14.

Comparisons of residual lateral stresses distribution resulting from compaction

pressures of 200 kPa and 500 kPa between the CIS model and the FE analysis are

302

shown in Figures 6.15. It is seen that the compaction-induced stresses calculated

from the CIS hand-computation model are in very good agreement with the values

obtained from the FE analysis. Note that the residual lateral stresses in a GRS mass

are higher under a higher vertical compaction pressure. In actual construction, the

maximum vertical pressure of compaction is in the range of 200 kPa to 500 kPa. As

seen from Figure 6.15, the effects of CIS can be rather significant in actual

construction. The zigzag lines in FE analyses in Figure 6.15 were caused by the

thickness of compaction lift of 0.2 m. With the larger compaction lift, the amplitude

of the zigzag is larger and the effect of CIS is smaller.

The analyses form FE show more accurately with the finer meshes. But to get the

results for only one curve from the FE analysis as shown in Figure 6.14, it took more

than 20 hours for inputting data and running program with a strong PC configuration

e.g. Dual Core 1.86 GHz, 3 GB RAM, whereas, the analytical model is simple and

can use hand calculation for several minutes. To reduce the time consuming, a coarse

mesh can be used with somewhat tolerated error. Figure 6.16 shows the comparison

between FE results with the coarse mesh and the analytical model. The EF results in

Figure 6.16 obtained from simulating the compaction operation by applying the

compaction pressure over the entire surface area of the GRS mass at each compaction

lift. From Figures 6.15 and 6.16, it can be seen that the fine mesh should be used

when analyzing GRS structures.

303

Figure 6.13: FE Mesh to Simulate CIS in a Reinforced Soil Mass

304

-6

-5

-4

-3

-2

-1

00 25 50 75

Residual Lateral Stress (kPa)

Dep

th (m

)

Lateral StressDistributionw ithoutConsidering CIS

Lateral StressDistribution w ithConsidering CIS(200 kPa)

Residual LateralStress (due toMaximum VerticalCompactionPressure of 200kPa)

-6

-5

-4

-3

-2

-1

00 25 50 75 100 125


Dep

th (m

)

Lateral StressDistributionw ithoutConsidering CIS

Lateral StressDistribution w ithConsidering CIS(500 kPa)

Residual LateralStress (due toMaximum VerticalCompactionPressure of 500kPa)

(a) (b)

Figure 6.14: Lateral Stress Distribution of a GRS Mass from FE Analyses with:

(a) Maximum Vertical Compaction Pressures of 200 kPa (b) Maximum Vertical Compaction Pressures of 500 kPa

305

-6

-5

-4

-3

-2

-1

00 25 50 75 100


Dep

th (m

)

Maximum verticalpressure due tocompaction:

200 kPa (Model)

500 kPa (Model)

200 kPa (FE)

500 kPa (FE)

Figure 6.15: Comparison of Residual Lateral Stresses of a GRS Mass due to Fill Compaction between FE Analysis with Very Fine Mesh and the Analytical Model

306

307

-6

-5

-4

-3

-2

-1

00 25 50 75 100


Dep

th (m

)

Maximum verticalpressure due tocompaction:

200 kPa (Model)

300 kPa (Model)

500 kPa (Model)

200 kPa (FE)

300 kPa (FE)

500 kPa (FE)

Figure 6.16: Comparison of Residual Lateral Stresses of a GRS Mass due to Fill Compaction between FE Analysis with Coarse Mesh and the Analytical Model

7. SUMMARY AND CONCLUSIONS

7.1 Summary

A study was taken to investigate the composite behavior of a geosynthetic-reinforced

soil (GRS) mass. The study focused on the strength of a GRS mass, the compaction-

induced stresses in a GRS mass, and the lateral deformation of a GRS wall with

modular block facing.

The following tasks were carried out:

1. Reviewed previous studies on: (1) composite behavior of a GRS mass and (2)

CIS in an unreinforced soil mass and in a GRS mass.

2. Designed a generic soil-geosynthetic composite (GSGC) test for investigating

the composite behavior of GRS mass, and conducted five GSGC tests with

well-controlled condition with extensive instrumentation to monitor the

behavior under different reinforcement spacing, reinforcement strength, and

confining pressure.

3. Developed an analytical model for the relationship between reinforcement

strength and reinforcement spacing, and derived an equation for calculating

composite strength properties.

4. Developed a hand-computation analytical model for simulation of

compaction-induced stresses in a GRS mass.

5. Performed finite element analyses to simulate the GSGC tests, generate

additional data (with different confining pressures) for verifying the analytical

models in this study, and investigate the behavior of GRS composites.

308

6. Verify the analytical models using measured data from the GSGC tests,

relevant test data available in the literature, and FE analyses.

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

with modular block facing.

7.2 Findings and Conclusions

The findings and conclusions of this study can be summarized as follows:

1. The results of the GSGC tests are consistent and appear very reliable. The

tests provide direct observation on the behavior of a GRS mass as related to

reinforcement strength and spacing. The tests also provide better

understanding of the composite behavior of GRS mass and can be used for

validation of analytical models in this study and other models of GRS

structures in the future.

2. An equation describing the relative effects of reinforcement spacing and

reinforcement strength was developed and verified. Based on the equation,

the required reinforcement strength in a GRS wall can be determined, and so

as the composite strength properties and ultimate pressure carrying capacity of

a GRS mass.

3. An analytical model for calculating lateral deformation of a GRS wall with

modular block facing was developed and verified.

4. An analytical model for simulating compaction operation of a GRS mass was

developed. The model allows the compaction-induced stresses in the fill to be

determined.

5. The presence of geosynthetic reinforcement has a tendency to suppress

dilation the surrounding soil, and reduce the angle of dilation of the soil mass.

The dilation behavior offers a new explanation of the reinforcing mechanism,

309

310

and the angle of dilation provides a quantitative measure of the degree of

reinforcing effect of a GRS mass.

APPENDIX A

MATERIAL TESTS

A.1 Backfill

A.1.1 Specific Gravity and Absorption of Coarse Aggregate (per AASHTO T85

and ASTM C127)

• Test Date: April 26 and 27, 2008.

The results of the tests are shown in Table A1 – 1.

311

Table A.1 Specific Gravity determination

A = mass of oven-dry test sample in air, g 184.7

B = mass of saturated-surface-dry test sample in air, g 185.5

C = mass of saturated test sample in water, g 123.4

1. Bulk Specific Gravity = A/(B-C) 2.974

2. Bulk Specific Gravity (Saturated-Surface-Dry) = B/(B-C) 2.987

3. Apparent Specific Gravity = A/(A-C) 3.013

Average Specific Gravity:

3.03

G1 = specific gravity for size fraction passing sieve # 4: 3.038

G2 = apparent specific gravity for size fraction retained on sieve # 4: 3.013

P1 = mass percentage of size faction passing sieve # 4: 58.0

P2 = mass percentage of size faction retained on sieve # 4: 42.0

4. Absorption = [(B – A) / A] x 100, (%) 0.433

2

2

1

1

100100

1

GP

GP

G+

=

312

A.1.2 Moisture-Density (Compaction) Tests (per AASHTO T99 and ASTM

698, Method A)

• Test Date: from May 1st to May 3rd, 2008

A.1.2.1 Density

• Volume of mold = 944 cm3;

• Mass of mold = 4191.5 g.

Table A.2 Unit weight determination for size fraction passing sieve # 4

Compacted Soil number 1 2 3 4 5 6

Actual average water content, % 6.06 7.63 8.57 9.63 11.24 11.92

Mass of compacted soil and mold (g) 6396.9 6466.1 6543.9 6538.9 6521.6 6501.0

Wet mass of soil in mold (g) 2205.4 2274.6 2352.4 2347.4 2330.1 2309.5

Wet density, (g/cm3) 2.34 2.41 2.49 2.49 2.47 2.45

Dry density, (g/cm3) 2.20 2.24 2.30 2.27 2.22 2.19

Dry density, (pcf) 151.05 153.52 157.39 155.54 152.16 149.9

313

2.15

2.20

2.25

2.30

2.35

2.40

2 3 4 5 6 7 8 9 10 11 12 13

Water Content (%)

Dry

Den

sity

(g/c

m3 )

Wopt = 8.57 %

γ d (max) = 2.3 (g/cm3)

Figure A.1: Moisture-Density Curve for Size Fractions Passing Sieve # 4

314

A.1.2.2 Rock Correction Calculations

• Bulk Specific Gravity: 2.974

• Absorption: 0.433 %

• Optimum Moisture Content of - #4 Materials: 8.57 %

• Percent Retained on Sieve #4 by Weight: 42 %

The rock correction calculations for this material are follows:

• Corrected Maximum Dry Density = 153.7 pcf = 24.1 kN/m3; and

• Optimum Moisture Content = 5.2% (see Table A.3).

315

Table A.3 Rock correction calculations

Percent Retained on Sieve

# 4

Water Content

(%) Dry

Density

Percent Retained on Sieve

# 4

Water Content

(%) Dry

Density 0 8.57 144 24 6.6 149.5 1 8.5 144.2 25 6.5 149.8 2 8.4 144.5 26 6.5 150.0 3 8.3 144.7 27 6.4 150.2 4 8.2 144.9 28 6.3 150.4 5 8.2 145.2 29 6.2 150.7 6 8.1 145.4 30 6.1 150.9 7 8.0 145.6 31 6.0 151.1 8 7.9 145.8 32 6.0 151.4 9 7.8 146.1 33 5.9 151.6 10 7.8 146.3 34 5.8 151.8 11 7.7 146.5 35 5.7 152.1 12 7.6 146.8 36 5.6 152.3 13 7.5 147.0 37 5.6 152.5 14 7.4 147.2 38 5.5 152.7 15 7.3 147.5 39 5.4 153.0 16 7.3 147.7 40 5.3 153.2 17 7.2 147.9 41 5.2 153.4 18 7.1 148.1 42 5.2 153.7 19 7.0 148.4 43 5.1 153.9 20 6.9 148.6 44 5.0 154.1 21 6.9 148.8 45 4.9 154.4 22 6.8 149.1 46 4.8 154.6 23 6.7 149.3 47 4.7 154.8

316

A.1.3 Gradation (per ASTM D422)

• Test Date: April 20, 2008

• Weight of container: 171.3 g (Sample # 1); 171.2 g (Sample # 2)

• Weight container and dry soil: 920.0 g (Sample # 1); 853.8 g (Sample # 2)

• Weight of dry soil: 748.7 g (Sample # 1); 682.6 g (Sample # 2)

The results of these tests are presented in Table A.4 and Figure A.2.

317

Table A.4 Grain size analysis for Sample 1 and (Sample 2)

Sieve Number

Diameter

(mm)

Mass of Container +

Soil Retained

(g) Soil

Retained (g)

Percent Retained

(%)

Percent Passing

(%)

3/8'' 9.5

389.2

(361.9)

217.9

(190.7)

29.1

(27.9)

70.9

(72.1)

4 4.75

490.5

(451.6)

101.3

(89.7)

13.5

(13.1)

57.4

(58.9)

10 2

598.4

(548.6)

107.9

(97.0)

14.4

(14.2)

43.0

(44.7)

40 0.425

724.7

(668.1)

126.3

(119.5)

16.9

(17.5)

26.1

(27.2)

60 0.25

756.8

(699.5)

32.1

(31.4)

4.3

(4.6)

21.8

(22.6)

100 0.106

786.8

(725.9)

30.0

(26.4)

4.0

(3.9)

17.8

(18.7)

200 0.075

810.6

(754.2)

23.8

(28.3)

3.2

(4.2)

14.6

(14.6)

<200

14.6

(14.6)

0

(0)

318

0

10

20

30

40

50

60

70

80

0.010.1110100

Grain size (mm)

Perc

ent f

iner

(%)

Test 1

Test 2

Figure A.2: Grain Size Distribution for Samples 1 and 2

319

A.1.4 Triaxial Compression Test

A.1.4.1 Test Material

A series of large-size triaxial tests were conducted on specimens of the backfill

material. The backfill was a crushed Diabase rock from a local source near

Washington D.C. The material was classified as a well graded gravel A-1a per

AASHTO M-15 or GW-GM per ASTM D2487. It has 14.6 % of fines passing sieve

#200. The triaxial tests were conducted in a consolidated drained condition. The

maximum dry density of the diabase was 24.1 kN/m3 (153.7 lb/ft3) and the specific

gravity was 3.03. The optimum moisture content was 5.2 %.

A.1.4.2 Test Procedure

Four large-size triaxial tests were conducted at different confining pressures, and the

results were compared with existing results by Ketchart et al. The soil specimen was

approximately 6 in. in diameter and 12 in. in height. The test procedure is described

as follows:

1. Use o-ring to attach a 0.35 – mm thick latex membrane to the base platen;

2. Place a filter paper and a copper porous stone at the base of the platen;

3. Measure the total height of 2 copper porous stone plates, 2 filter paper sheets

and a base plate (see Figure A.3);

4. Attach the fist latex membrane sheet to the base plate (see Figure A.4);

5. Place a metallic mold (a split-barrel type) around the latex membrane and fold

the top portion of the latex membrane down and over the mold;

6. Use vacuum pump to suck air between the latex membrane and the mold (see

Figure A.5);

7. Compact the soil inside the mold, in five layers at the prescribed density of

24.1 kN/m3, with 54 blows/layer as shown in Figure A.6;

320

8. Check the height of the specimen at the fifth (last) layer after 10 first blows,

and adjust (add/remove soil) to get approximately the specimen height of 12

in. if necessary (see Figure A.7);

9. Place a filter paper and a copper porous stone on the top of the specimen;

10. Place the top platen on the porous stone and roll the latex membrane over the

top platen;

11. Use vacuum pump to apply low confining pressure on the specimen to keep

the large-size specimen stable;

12. Remove the metallic mold and attach the second layer of latex membrane to

the specimen with o-rings on the top and base platens (see Figure A.8);

13. Obtain the average height in three different locations of the specimen by using

a stand ruler (see Figure A.9);

14. Obtain the average diameter at two ends and the middle of the specimen by

using a π-type;

15. Place the lucid cylinder on the cell base and fill water up in the cylinder

chamber;

16. Apply a predetermined confining pressure in the chamber using compressed

air, disconnect the specimen with the vacuum pump, and open the back

pressure valve connected to the base of the specimen (see Figure A.10);

17. After 24 hours of consolidation with the confining pressure, place the cell in a

loading frame and start to apply shear stress at a constant strain of 0.1 % per

minute (see Figure A.11);

18. Record the testing load versus strain at every increment and measure the

volume change of the specimen during testing;

19. After failure, remove the test chamber out of the loading machine, remove the

lucid cylinder covering the test specimen and clean up all devices.

Figures A.12 shows the specimen before and after failure.

321

Figure A.3: Measure the Total Height of a Top Plate, 2 Copper Porous Stone Plates, 2 Filter Paper Sheets, and a Base Plate

322

Figure A.4: Attach the First Latex Membrane Sheet to the Base Plate

323

Figure A.5: Place a Metallic Mold and Apply Vacuum to Remove Air between the Mold and the Membrane

324

Figure A.6: Compact the Soil in Five Layers

325

Figure A.7: Check the Height of the Specimen at the Last Layer

326

Figure A.8: Roll the Latex Membrane over the Top Plate and Attach the Second Latex Membrane

327

Figure A.9: Measure the Height and the Diameter of a Specimen Using a Stand Ruler and a π-Tape

328

Figure A.10: Apply Confining Pressure

329

Figure A.11: Test Cell in the Instron - 5569 Machine During Loading

330

` (a) (b)

Figure A.12: Specimen # 3 before (a) and after (b) Failure

331

A.1.4.3 Test results

The results of the test are shown in Table A.5. Figure A.14 shows the stress-strain

curves and the volume change curves. The stress-strain curves obtained by Ketchart

et al. are also included for comparison and for a more complete set of data. The Mohr

circles at failure are shown in Figure A.14.

Table A.5 Triaxial test results

Specimen Designation Test # 1 Test # 2 Test # 3 Test # 4

Date Test 05/08/08 05/06/08 05/09/08 05/13/08

Confining Pressure (psi) 5 15 30 70

Strain Rate (%/min) 0.1 0.1 0.1 0.1

Diameter (in.) 6.06 6.033 6.05 6.06

Height (in.) 12.08 11.95 12.01 12.11

Water Content (%) 5.2 5.2 5.2 5.2

Failure Condition

Peak Deviatoric Stress (psi) 93.4 157.1 235.5 363.8

Axial Strain at Failure (%) 2.3 2.9 3.7 5.0

Mohr-Coulomb Shear

Strength Parameters

Confining Pressure

from 0 to 30 psi

C1 = 10.3 psi,

φ1 = 50o, ψ = 12.1o

Confining Pressure

from 30 psi to 70 psi

C2 = 35.1 psi, φ2 = 38o

332

Deviatoric Stress versus Axial Strain Relationships

0

50

100

150

200

250

300

350

400

450

500

550

600

0 1 2 3 4 5 6 7 8 9 10 11

Axial Strain (%)

Dev

iato

ric

Stre

ss (p

si)

5 psi

15 psi

30 psi

70 psi

70 psi - Ketchart

110 psi - Ketchart

(a)

Volumetric Strain versus Axial Strain

-0.4

-0.2

0

0.2

0.4

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Axial Strain (%)

Volu

met

ric S

trai

n (%

)

5 psi

30 psi

(b)

Figure A.13: Triaxial Test Results:

(a) Stress-Strain Curves (b) Volume Change Curves

333

σ3 = 15 psi

σ3 = 30 psi

Shea

r St

rees

s (ps

i)

Normal Stress (psi)

σ3 = 5 psi

σ3 = 70 psi

σ3 = 110 psi

433265172 61698300

C2 = 35.1 psi

C1 = 10.3 psi

Figure A.14: Mohr Circles of the Stress at Failure

334

A.2 Geotextile

A.2.1 Uniaxial Load-Deformation Test (per ASTM D 4595)

• Material: In this study, geosynthetic used for the tests was Geotex 4x4, a

woven polypropylene geotextile (formally known as Amoco2044).

• Specimen dimensions: The dimensions of the geotextile specimen

accordance with ASTM D 4595 are: Width = 200 mm (8 in.) and Length =

100 mm (4 in.). For non-woven geotextiles, the aspect ration of the

reinforcement specimen (i.e., the ratio of width to length) should be

sufficiently large (say, greater than 4) to alleviate significant “necking” (i.e.

Poisson) effect. There is little “necking” effect for woven geotextiles,

regardless of the aspect ratio. Besides measuring stress-strain relationships,

the calibration curves (between actual geotextile strain and strain gages) were

also obtained from these tests. The length of the geotextile should be long

enough for a strain gage to be attached. The selected specimen dimensions

for these tests, therefore, were: Width = 305 mm (12 in.) and the Length =

152 mm (6 in.).

• Clamps: The grip portion at two ends of the Geotex 4x4 specimen was

treated with high-strength epoxy and two steel plates. The specimen then

was clamped tightly at two ends of the specimen by screwing total number

of 16 bolts in to stiff steel jaws (see Figure A.15) to prevent the specimen

slipping in the jaws.

• Strain Rate: The constant strain rate of 10 %/min was used.

A uni-axial load-deformation test of geotextile is shown in Figure A.15. A series of

tests were conducted using two types of geosynthetic: (1) single-sheet Geotex 4x4

and (2) double-sheet Geotex 4x4. The double-sheet was manufactured by gluing two

335

sheets of Geotex 4x4 geotextile together using spray glue “3M Super 77 Adhesive”.

Some index properties of the geotextile reinforcement are shown in Table A.6 and

stress-strain relationships are shown in Figure A.16.

336

Figure A.15: Uniaxial Load-Deformation Test of Geotex 4x4

337

Table A.6 Index properties of the reinforcement for fill direction

Geosynthetic

Type

Wide-Width Tensile Strength

ASTM D 4595

Stiffness at

1% Strain

(kN/m)

Ultimate

Strength

(kN/m)

Strain at Break

(%)

Single-sheet Geotex 4x4 1,000 70 12 %

Double-sheet Geotex 4x4 1,960 138 12 %

338

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Axial Strain (%)

Tens

ile L

oad

(kN

/m)

Single sheet

Double Sheets

Figure A.16: Load-Strain Curves for Single-Sheet and Double-Sheet Geotex 4x4

339

A.2.2 Instrumentation for Measuring Strain Gage in Geotextile

To measure the strain in the geotextile, a high elongation strain gage (type EP-08-

250BG-120), manufactured by Measurements Group, Inc., was used. Each strain

gage was glued to the geotextile only at two ends to avoid inconsistent local stiffening

of geotextile due to the adhesive. The strain gage attachment technique was

developed at the University of Colorado Denver. The gage was first mounted on a 25

mm by 76 mm patch of a lightweight nonwoven geotextile (see Figure A.17). A

Microcystalline wax and a rubber coating (M-Coat B, Nitrile Rubber coating) were

used to cover strain gages to protect the gages from moisture. To check the effects of

the moisture-protection materials, the geotextile specimens with the strain gages were

tested after immersing in water for 24 hours. The rubber coating was selected to use

for the experiments. Before installing the reinforcement sheet in the composite mass,

the M-Coat FB-2, 6694, Butyl Rubber Tape was applied over the gages to protect

them during compaction as shown in Figure A.17.

340

(a) (b)

Figure A.17: Strain Gage on Geotex 4x4 Geotextile: (a) Before Applying Protection Tape; (b) After Applying Protection Tape (M-Coat FB-2, 6694, Butyl Rubber Tape) in the Experiment.

341

A.2.3 Calibration of Strain Gages for Measuring Deformation Geotextile

Due to the presence of the light-weight geotextile patch, calibration is needed. The

calibration tests were performed to relate the strain obtained from the strain gage to

the actual strain of the reinforcement. Figures A.18 and A.19 show the calibration

curves along the fill direction of Geotex 4x4 geotextile for single-sheet and double-

sheet specimens, respectively.

342

y = 1.172xR2 = 0.9913

0

1

2

3

4

5

6

0 1 2 3 4 5Strain from Strain Gage (%)

Stra

in fr

om In

stro

n M

achi

ne (%

)

Figure A.18: Calibration Curve for Single-Sheet Geotex 4x4

343

y = 1.078xR2 = 0.9986

0

1

2

3

4

5

6

0 1 2 3 4 5

Strain from Strain Gauge (%)

Stra

in fr

om In

stro

n M

achi

ne (%

)

Figure A.19: Calibration Curve for Double-Sheet Geotex 4x4

344

APPENDIX B

REVIEW DESIGN OF THE GSGC TEST FRAME

B.1 Pressure on Plexiglass (in the plane strain direction of GSGC Test)

The pressure on the plexiglass is calculated from the maximum vertical pressure on

the top of the specimen. The maximum lateral pressure on the plexiglass is:

500=q kPa (72psi).

Figure B.1: Dimensions of the Test Frame

345

B.2 Checking the Capacity of the Horizontal Tubings

B.2.1 Checking Bending Moment

The maximum required moment of horizontal tubing (like a beam with the simple

supports) is:

( ) ( ) ( ) 4.628

835.1*7/074.2*5008

22

=⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

mkPalqM req kN.m

The tensile strength of the tubings is 400,000 kN/m2 (58,000 psi) and yield strength is

317,000 kN/m2 (46,000 psi). For the 2” x 12” x ¼” steel tubings used in the design,

the maximum allowable moment is:

sidesbottomandtopallow MMM 2+=

in which,

[ ] ( ) ( ) ( )( ) [ ] 5.3010*17.3*10*35.68.304*10*8.50*10*35.6** 5333 =−== −−−steelbottomandtop hAM σ

kN.m

[ ] ( ) ( )( ) [ ] 2.5710*17.3*6

10*35.6*28.304*10*35.6*2* 5233

2 =−

==−−

σxsides SM

kN.m

Therefore,

Mallow = 30.5 + 57.2 = 87.7 kN.m. > Mreq = 62.4 kN.m. It is acceptable.

346

B.2.2 Checking Shear Stress

The maximum required shear stress of a horizontal tubing is:

( ) ( ) ( ) ( ) ( )( ) 097,3010*35.6*2*8.3048.50/2

835.1*7/074.2*500/2

6 =+⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛= −mkPaAlq

reqσ

kN.m = 4,334 psi.

Therefore, shear capacity of the tubings is acceptable.

B.2.3 Checking the Bolts

The maximum required shear force of one bolt is:

( ) ( ) ( ) 2.362/2

10*4.25'*'4.11*5002/2

3

=⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎠⎞

⎜⎝⎛=

− mkPaboltslqQreq kN

The required shear stress will be:

( )311,93

4/10*54.2'*'8/7*2.36

23===

−πσ

AQ

req kPa = 13,436 psi = 13.4 kpsi

The shear capacity of 7/8 A325 bolt is: 0.4 * Fy = 0.4 * 36 = 14.4 kpsi.

Therefore, the bolt capacity is acceptable.

347

B.2.4 Checking the Capacity of the Plexiglass

The maximum required moment acting on Plexiglass is:

( ) ( ) 66.312

7/074.2*50012

22

=⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

mkPalqM req kN.m

The maximum required stress is:

( ) ( )784,21

61000/4.25'*'25.1*1

66.32 =

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

=⎟⎟⎠

⎞⎜⎜⎝

⎛=

mSM

x

reqreqσ kPa = 3,137 psi

With the tensile strength of the Plexiglass acrylic sheet of 10,500 psi, the moment

capacity of the plexiglass is acceptable.

348

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Pham Thang Investigating Composite Behavior of Geosynthetic Reinforced Soil Mass Thesis

Documents

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