Investigating Composite Behavior of Geosynthetic reinforce soil mass - PhD Colorado US

INVESTIGATING COMPOSITE BEHAVIOR OF GEOSYNTHETICREINFORCED 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

viii

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

ix

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

6.3.2

Simulation of GSGC Test 2 ...........................................................................290

6.3.3

Simulation of GSGC Test 3 ...........................................................................295

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 Δσ h' ,vc , p against a Vertical Wall for a Single Drum Roller (Seed, 1983) ................................................................................................................50

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, γ b = 0 ......................................................95

3.12

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

3.13

Comparison of Lateral Displacement Calculated by Jewell-Milligan Method and the Analytical Model, γ b = 20 ....................................................97

3.14

Comparison of Lateral Displacement Calculated by Jewell-Milligan Method and the Analytical Model, γ b = 30 ....................................................98

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

4.48

Lateral Displacements on the Open Face of Test 2 .......................................174

4.49

Internal Displacements of Test 2 ...................................................................177

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

4.56

Lateral Displacements on the Open Face of Test 3 .......................................191

4.57

Internal Displacements of Test 3 ...................................................................192

4.58

Locations of Strain Gauges Geosynthetic Sheets in Test 3 ...........................193

4.59

Reinforcement Strain Distribution of the Composite Mass in Test 3 ............194

4.60

Aerial View of the Reinforcement Sheets Exhumed from the Composite Mass after Test 3 ............................................................................................196

4.61

Location of Rupture Lines of Reinforcement in Test 3 .................................197

4.62

Failure Planes of the Composite Mass after Testing in Test 4 ......................201

4.63

Global Stress-Strain Relationship of Test 4 ...................................................202

4.64

Lateral Displacements on the Open Face of Test 4 .......................................203

4.65

Internal Displacements of Test 4 ...................................................................204

4.66

Locations of Strain Gauges Geosynthetic Sheets in Test 4 ...........................205

4.67

Reinforcement Strain Distribution of the Composite Mass in Test 4 ............206

4.68

Aerial View of the Reinforcement Sheets Exhumed from the Composite Mass after Test 4 ............................................................................................208

4.69

Location of Rupture Lines of Reinforcement in Test 4 .................................209

4.70

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

4.71

Failure Planes of the Composite Mass after Testing in Test 5 ......................214

4.72

Global Stress-Strain Relationship of Test 5 ...................................................215

4.73

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

4.74

Internal Displacements of Test 5 ...................................................................217

4.75

Locations of Strain Gauges Geosynthetic Sheets in Test 5 ...........................218

4.76

Reinforcement Strain Distribution of the Composite Mass in Test 5 ............219

4.77

Aerial View of the Reinforcement Sheets Exhumed from the Composite Mass after Test 5 ............................................................................................221

4.78

Location of Rupture Lines of Reinforcement in Test 5 .................................222

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

6.5

Comparison of Lateral Displacement at Open Face of GSGC Test 2 ...........292

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

6.9

Comparison of Lateral Displacement at Open Face of GSGC Test 3 ...........297

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

4.8

Some Test Results for Test 2 .........................................................................186

4.9

Some Test Results for Test 3 .........................................................................198

4.10

Some Test Results for Test 4 .........................................................................210

4.11

Some Test Results for Test 5 .........................................................................223

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

4.14

Comparison between Test 2 and Test 4 .........................................................229

4.15

Comparison between Test 3 and Test 4 .........................................................230

4.16

Comparison between Test 2 and Test 5 .........................................................232

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

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

xx

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 lowpermeability 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.,

Trequired = σ h ∗ S v ∗ Fs

(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 compactioninduced 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 compactioninduced 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. Compactioninduced 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 soilgeosynthetic 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

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

8

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: Δσ 3 R =

Tf

(2.1)

Sv

(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,

σ 1R = σ 3C K P + 2cR ' K P

(2.2)

Referring to Figure 2.2,

σ 1R = σ 3 R K P

(2.3)

Knowing

σ 3 R = σ 3C + Δσ 3 R

(2.4)

Equation 2.3 can be written as:

σ 1R = σ 3 R K P = (σ 3C + Δσ 3 R )K P

(2.5)

Equating Equations 2.2 to Equation 2.5, we obtain c R '' =

(3)

Δσ 3 R K P

(2.6)

2

Substituting equation 2.1 into equation 2.6, c R '=

Tf

KP

(2.7)

2S v

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 Δσ 3 R =

Tf Sv

(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 Δσ 3 = RT / S v (see Figure 2.2) based on the explanation given by Schlosser and Long (1972) and Yang (1972); and it was Δσ 3 ≤ RT / S v in Hausmann’s study (1976), where RT ≡ T f .

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 AlRefeai, 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) Figure 2.5:

(b)

Unconfined Test Specimen (a) before and (b) after Testing (Elton and Patawaran, 2005)

17

Stress - Strain curves 300 TG500-12 (Spacing = 12 in.)

Stress (kPa)

250

TG500 (Spacing = 6 in.)

200 150 100 50 0 0

5

10

15

20

25

30

Vertical Strain εv (%)

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 loadcarrying 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 twodimensional 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:

⎛ h ⎞ ' K 0 = K 0 ⎜1 + 0 ⎟ h⎠ ⎝

(2.8)

where h0 is the surcharge head removed and h is the overburden head ( h = σ v / γ ). In any case, K 0 ≤ K P (KP = coefficient of passive earth pressure at limiting condition).

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:

⎛ h ⎞ ' K 0 = K 0 ⎜1 + 0 ⎟ h⎠ ⎝

α

(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 σ ' ho and σ ' vo . 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 σ ' h = K 0 σ ' v , 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 σ 'h = K1σ 'v . 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

K 0 ≤ K effective ≤ K 1 . 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.

σh =K0 σv

Effective overbunden pressure,

σv

C

B

σ'h0 /K0

σh =K1 σv

σ'v0

A E

Actual relationship

σ'h0 Effective lateral earth pressure,

Figure 2.16:

Assumed relationship

D

σh

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 σ ' h = K 0σ ' v . 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 σ 'h = K1σ 'v to point E’, resulting in a final condition

K 0 ' = K1 .

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 σ 'h = K1σ 'v 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 σ 'h = K1σ 'v . 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 σ 'h = K Aσ 'v instead of Broms’ σ 'h = K 0σ 'v . 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 indepth study on the subject of CIS. Seed’s study involved the following three areas:

•

Compaction induced stresses due to different stress paths, including the firstcycle 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 K ' 0 = K 0 (OCR ) to an arbitrary point B prior α

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:

σ *h ,r = σ 'h ,min + β ∗ Δ

(2.10)

40

σ * v ,r =

1 * σ h ,r K0

(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 K ' 0 = K 0 (OCR ) . The value α can be estimated by Equation 2.12 or by Figure 2.21: α

α = 0.018 + 0.974 sin φ '

Figure 2.20:

(2.12)

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: K 1 = K 1,φ +

2c' K 1,φ σ '3

(2.13)

φ' ⎞ ⎛ K 1, φ = tan 2 ⎜ 45 0 + ⎟ 2⎠ ⎝

(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 K 0 ' = K 0 (OCR ) , to point B; α

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 K 0 ' = K 0 (OCR ) , to point B; α

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 ( α * ≥ α ).

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 ( α * ≥ α ) 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 Method of Estimation Limits Based on φ’

α

Unloading coefficient

0 ≤α ≤1

β

Reloading coefficient

0 ≤ β ≤1

β ≅ 0.6

K0

Coefficient of at-rest lateral earth pressure for virgin loading

0 ≤ K0 ≤ 1

K 0 ≅ 1 − sin φ '

K1,φ

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

K 0 ≤ K1,φ ≤ K P

φ' ⎞ ⎛ K 1,φ ≅ tan 2 ⎜ 45 + ⎟ 2⎠ ⎝

c’

Effective stress strength envelope cohesion intercept

--

--

Note: K1 = Limiting coefficient of at-rest lateral pressure for unloading 2c' σ 'h,lim = K1σ 'v and K1 = K1,φ ' + B K1,φ ' σ '3 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 nondeflecting 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:

Figure 2.29:

Bi-Linear Approximation of Non-linear K0-unloading Model

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

K0

Coefficient of at-rest lateral earth pressure for virgin loading

K1,φ’,B

cB’

F or K2

K 2 = K 0 (1 − F )

K3

Recommended Limits

Frictional component of limiting coefficient of at-rest lateral earth pressure for unloading Effective stress strength envelope Cohesion Intercept - Fraction of peak lateral compaction stress retained as residual stress for virgin soil - Incremental coefficient of at-rest lateral earth pressure for reloading

Method of Estimation Based on φ’ Same as non-linear model

0 ≤ K0 ≤ 1

(Recommended K 0 ≅ 1 − sin φ ' )

K 1,φ ', B ≅

K 0 ≤ K1 ≤ K P

2 K1,ϕ ' 3

φ' ⎞ ⎛ K 1,φ ' ≅ tan 2 ⎜ 45 o + ⎟ 2⎠ ⎝ cB ' ≥ 0

c B ' ≅ 0.8c'

0 ≤ F ≤1

- 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:

(OCR − OCR ) F =1− α

K0 ≥ K2 ≥ 0

(OCR − 1)

Where a suitable OCR for “matching” the bi-linear and non-linear unloading curves is typical OCR ≅ 5 . Incremental coefficient of at-rest lateral earth pressure for reloading

Note: σ 'h,lim = K1σ 'v , K1 = K1,φ ',B +

2c' B σ '3

0 ≤ K3 ≤ K0

K 3 ≅ K 2 (= K 0 (1 − F ))

K1,φ ',B , K 1,φ ', B ≅

54

2 K 1,φ ' , and K1,φ ' = K P . 3

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 Δσ h ' = K 2 Δσ v ' until a K1type of limiting condition is reached, at which point further unloading follows a linear stress path according to σ h ' = K1Δσ v ' .

Reloading follows a linear stress path

according to Δσ h ' = K 3 Δσ v ' 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:

Δσ h ,r ' = F .Δσ h, p ' F = 1−

(2.15)

K2 (OCR − OCR α ) = 1− (OCR − 1) K0

(2.16)

55

K3 =

β3K2

(2.17)

K 1 − 2 (1 − β 3 ) K0

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 σ h ,r ' = K 0σ v ' + FΔσ h' ,vc , p . 4. Reduce the near-the-surface portion of the σ’h,r distribution with

σ h , r ' ≤ K1,φ ', Bσ v ' at all depths. 5. Increase the residual effective stress distribution such that σ h ,r ' ≥ K 0σ v ' 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

K0 = 1 - sinφ' = 0.43

φ'⎞ ⎛ K1,φ ' = tan 2 ⎜ 45o − ⎟ = 3.69 2⎠ ⎝

K1,φ ',B =

2 K1,φ ' = 2.46 3

F = 1−

5 − 5α = 0.44 5 −1

α = 0.63 (from Figure 2.20)

β = 0.6 (assumed)

K 3 = K 2 = 0.24

c' = 0

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

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 soilreinforcement interface friction tends to restrain lateral deformation of the soil mass and results in greater values of CIS. A review of previous studies on GRS masses including the effects of CIS is presented below.

2.4.1

Ehrlich and Mitchell (1994)

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 affecting the reinforcement tensions. The assumptions involved in the procedure are: •

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 compaction lift was subjected to only one cycle of loading, as shown in Figure 2.35.

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 stress-state condition at the end of construction. Ehrlich and Mitchell (1994) noted 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:

σ zc ' =

σ xp '

(2.18)

K0

where: K 0 = 1 − sin φ ' (Jaky, 1944)

(2.19)

63

σ xp ' = ν 0 (1 + K A ) and

0.5γ ' QN γ

(2.20)

L

Q = maximum vertical operating force of the roller drum L = length of the roller drum γ = effective soil unit weight.

υ0 =

K0 (Poisson’s ratio under K0-condition) 1− K0

φ ' ⎞⎡ φ' ⎞ ⎤ ⎛ ⎛ N γ = tan⎜ 45 o + ⎟ ⎢ tan 4 ⎜ 45 o + ⎟ − 1⎥ (bearing capacity factor) 2 ⎠⎣ 2⎠ ⎦ ⎝ ⎝

(2.21)

(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:

2.4.2

Compaction and Reinforcement Stiffness Typical Influence (Ehrlich and Mitchell, 1994)

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 overconsolidation 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

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 nonlinear 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.

70

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.

q

Facing block

Reinforcement H

Sv

Soil

L.

Figure 3.1:

3.1

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

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 ≤

L ≤ 1.175 , H 4

3

2

⎛L⎞ ⎛L⎞ ⎛L⎞ ⎛L⎞ δ R = 11.81⎜ ⎟ − 42.25⎜ ⎟ + 57.16⎜ ⎟ − 35.45⎜ ⎟ + 9.471 ⎝H⎠ ⎝H⎠ ⎝H⎠ ⎝H⎠

(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):

⎛H⎞ ⎟ ⎝ 75 ⎠

δ max = δ R ⎜

(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:

δh =

εd L

(3.3)

2

where εd = strain limit (εmax), and L = reinforcement length.

εmax Strain Distribution

Rankine Surface Reinforcement

Φ/2

Figure 3.3:

3.1.3

Assumed Strain Distribution in the Geoservices Method

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: ⎛ H ⎞ ⎟ ⎝ 1.25 ⎠

δ max = ε d ⎜

(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 (45 0 + φ ps / 2 ) 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 (45 0 + ψ / 2) 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 (45 0 + ψ / 2) 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: ⎛ γH 2 ⎞ Prm = Pa = K a ⎜⎜ + q s H ⎟⎟ ⎝ 2 ⎠

(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: ψ ⎞ ⎛ tan⎜ 45 + − φds ⎟ 2 ⎝ ⎠ Ka = = ψ⎞ (1 + sin φ ps ) ⎛ tan ⎜ 45 + ⎟ 2⎠ ⎝ (1 − sin φ ps )

(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: tan(θ − φ ds ) Pr = Prm K a tan θ

(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,

δhK HPbase

then the horizontal displacement δh can be calculated from this factor.

, and The

reinforcement occurs at the base of the wall, Pbase, in the dimensionless factor above, can be calculated by Pbase = K a s v (γ H + q s )

(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 JewellMilligan 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.

45 + ψ/2

x

φds

Zone 1 zi

z

Zone 2

Pr m

Zone 3 H Lzone-1 (H - z i)

Figure 3.7:

Lzone-2

Li

Reinforcement

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: Δ h = Δ zone−1 + Δ zone−2 Δ zone −1 =

Lzone −1

∫ 0

(3.9)

Prm P dx = rm L zone −1 K re inf K re inf

85

(3.10)

Δ zone − 2 =

Lzone −1 + Lzone − 2

∫

Lzone −1

where Kreinf

Pr ⎛1⎞ P dx ≈ ⎜ ⎟ rm L zone − 2 K re inf ⎝ 2 ⎠ K re inf

(3.11)

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 Prm ⎛ 1 ⎞ ⎜ Lzone −1 + L zone − 2 ⎟ K re inf ⎝ 2 ⎠

(3.12)

ψ⎞ ⎛ L zone −1 = (H − z i ) tan⎜ 45 o − ⎟ 2⎠ ⎝

(3.13)

Δh =

Since

and ⎡ ψ ⎞⎤ ⎛ L zone −2 = (H − z i ) ⎢ tan 90 o − φ ds − tan⎜ 45 o − ⎟⎥ 2 ⎠⎦ ⎝ ⎣

(

)

(3.14)

Therefore, substituting Equation 3.13 and Equation 3.14 into Equation 3.12 leads to Δh =

Prm ⎧ ⎡ ⎛ o ψ⎞ 1 ⎛ o ψ ⎞⎤ ⎫ o ⎨(H − z i ) tan⎜ 45 − ⎟ + (H − z i ) ⎢ tan 90 − φ ds − tan⎜ 45 − ⎟⎥ ⎬ K re inf ⎩ 2⎠ 2 2 ⎠⎦ ⎭ ⎝ ⎝ ⎣

(

)

(3.15) Rearranging Equation 3.15, we have Δh =

⎧ ⎫ Prm (H − z i ) ⎨ tan⎛⎜ 45 o − ψ ⎞⎟ + 1 ⎡⎢ tan 90 o − φ ds − tan⎛⎜ 45 o − ψ ⎞⎟⎤⎥ ⎬ K re inf 2⎠ 2 ⎣ 2 ⎠⎦ ⎭ ⎝ ⎝ ⎩

(3.16)

⎧ Prm (H − z i ) ⎨ 1 ⎡⎢ tan⎛⎜ 45 o − ψ ⎞⎟ + tan 90 o − φ ds K re inf 2 ⎠ ⎩ 2 ⎣ ⎝

(3.17)

(

)

or Δh =

(

86

)⎤⎥ ⎫⎬ ⎦⎭

The value of Δh, lateral displacement of a GRS wall at depth zi, can be calculated directly from the following equation: ⎛1⎞⎛ P Δ h = ⎜ ⎟ ⎜⎜ rm ⎝ 2 ⎠ ⎝ K re inf

where Kreinf

⎞ ⎟⎟ (H − z i ) ⎠

⎡ ⎛ 0 ψ⎞ ⎤ 0 ⎢ tan⎜ 45 − 2 ⎟ + tan(90 − φ ds )⎥ ⎠ ⎣ ⎝ ⎦

(3.18)

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. Top of the wall

Ni-1

Zi

± Fi-1

Ffi reinforcement

Wi Sv

Ti Pi

±

Fi+1

Ni+1 b

Figure 3.8:

Forces Acting on Two Facing Blocks at Depth zi

The tensile connection force Ti in the reinforcement will be: Ti = Pi ± ( Fi +1 − Fi −1 )

(3.19)

where Pi = K h (γ s z i + q )S v

(3.20)

If Pi ± ( Fi +1 − Fi −1 ) < 0, Ti should be set equal to 0, as geosynthetic reinforcement can resist only tensile forces, i.e., Ti is always ≥ 0. From Figure 3.8, Ti = Pi ± ( N i +1 − N i −1 ) tan δ ; Ti = 0 if Ti ≤ 0

(3.21)

where Ni+1 and Ni-1 are normal forces on the top and the bottom of the two adjacent blocks. Ti = Pi ± (Wi + F fi ) tan δ

(3.22)

88

or, Ti = Pi ± (γ b bS v + pS v tan β ) tan δ

(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:

p=

F i +1− Fi −1 = γ bb tan δ Sv

(3.24)

Substituting Equation 3.24 into Equation 3.23, Ti , the connection force at depth zi, can be determined as: Ti = Pi ± (γ b bS v + γ b bS v tan δ tan β ) tan δ

(3.25)

Ti = K h (γ s z i + q )S v ± (γ b bS v + γ b bS v tan δ tan β ) tan δ

(3.26)

or,

Therefore, the tensile connection force in the reinforcement at depth zi can be expressed as: Ti = K h (γ s z i + q )S v ± γ b bS v tan δ (1 + tan δ tan β ) ; T = 0 if T ≤ 0

89

(3.27)

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: Ti = K h (γ s z i + q )S v ± (γ b bS v )(tan δ ) ; 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: Ti = K h (γ s z i + q ) S v − (γ b bS v )(tan δ )

(3.29)

The resistant connection force at depth zi at facing can be estimated by: Fr = 2γ b bz i (tan δ )

(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 Connection force (kN) 0

5

10

15

20

25

30

0 0.5

Proposed method

Depth (m)

1 1.5 2

Maximum friction capacity at facing

2.5 3 3.5 4

Connection Forces in Reinforcement (q = 0) Figure 3.9: (The Data of the Wall are from Section 3.3.1 with ψ = 150)

Connection force Connection force (kN) 0

5

10

15

20

25

30

35

40

0 0.5

Proposed method

Depth (m)

1 1.5 2

Maximum friction capacity at facing

2.5 3 3.5 4

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: ⎛ K (γ z + q )S v − γ b bS v tan δ (1 + tan δ tan β ) ⎞ ⎡ ⎤ ψ ⎟⎟ (H − z i ) ⎢ tan ⎛⎜ 45 0 − ⎞⎟ + tan(90 0 − φ ds )⎥ Δ i = 0.5 ⎜⎜ h s i K 2 ⎠ ⎣ ⎝ ⎦ re inf ⎠ ⎝

(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: ⎛ K (γ z + q )S v − (γ b bS v )(tan δ ) ⎞ ⎡ ⎤ ψ ⎟⎟ (H − z i ) ⎢ tan ⎛⎜ 45 0 − ⎞⎟ + tan(90 0 − φ ds )⎥ Δ i = 0.5 ⎜⎜ h s i 2⎠ K re inf ⎣ ⎝ ⎦ ⎝ ⎠

(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

Depth from the Top (m)

0

20

40

60

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Lateral Displacem ent (m m )

Analytical model Jew ell-Milligan method

q = 10 kN/m

Depth from the Top (m)

0

20

40

60

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Lateral Displacem ent (m m )

Analytical model Jew ell-Milligan method

q = 50 kN/m

Depth from the Top (m)

0

20

40

60

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Lateral Displacem ent (m m )

Analytical model Jew ell-Milligan method

Figure 3.11: Comparison of Lateral Displacement Calculated by the JewellMilligan Method and the Analytical Model, γb = 0 kN/m3

95

q=0

Depth from the Top (m)

0

20

40

60

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Lateral Displacem ent (m m )

Analytical model Jew ell-Milligan method

q = 10 kN/m

Depth from the Top (m)

0

20

40

60

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Lateral Displacem ent (m m )

Analytical model Jew ell-Milligan method

q = 50 kN/m

Depth from the Top (m)

0

20

40

60

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Lateral Displacem ent (m m )

Analytical model Jew ell-Milligan method

Figure 3.12: Comparison of Lateral Displacement Calculated by the JewellMilligan Method and the Analytical Model, γb = 10 kN/m3

96

q=0

Depth from the Top (m)

0

20

40

60

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Lateral Displacem ent (m m )

Analytical model Jew ell-Milligan method

q = 10 kN/m

Depth from the Top (m)

0

20

40

60

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Lateral Displacem ent (m m )

Analytical model Jew ell-Milligan method

q = 50 kN/m

Depth from the Top (m)

0

20

40

60

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Lateral Displacem ent (m m )

Analytical model Jew ell-Milligan method

Figure 3.13: Comparison of Lateral Displacement Calculated by the JewellMilligan Method and the Analytical Model, γb = 20 kN/m3

97

q=0

Depth from the Top (m)

0

20

40

60

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Lateral Displacem ent (m m )

Analytical model Jew ell-Milligan method

q = 10 kN/m

Depth from the Top (m)

0

20

40

60

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Lateral Displacem ent (m m )

Analytical model Jew ell-Milligan method

q = 50 kN/m

Depth from the Top (m)

0

20

40

60

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Lateral Displacem ent (m m )

Analytical model Jew ell-Milligan method

Figure 3.14: Comparison of Lateral Displacement Calculated by the JewellMilligan Method and the Analytical Model, γb = 30 kN/m3

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: tan φ ds =

sin φ ps cosψ 1 − sin φ ps sinψ

=

sin 44 o cos11o = 40 o 1 − sin 44 o sin 11o

99

(3.34)

(b) Empirical facing batter factor, Φfb, from Allen and Bathurst (2001), with facing batter of 8o:

Φ fb

⎛K = ⎜⎜ abh ⎝ K avh

d

⎞ ⎟⎟ = 0.88 ⎠

(3.35)

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 coefficient. 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 model, not unlike the Jewell-Milligan method, produced a displacement profile that had lower bending stiffness than the measured profile. However, considering that the analytical model is a simplified model, the simulation is considered adequate.

101

q = 50 kN/m

0

30

60

90

0

Lateral Displacem ent (m m )

0.4

Depth from the Top (m)

0.8 1.2 1.6 Analytical model

2 2.4

Jew ell-Milligan method

2.8 Average measured

3.2 3.6

q = 70 kN/m

0

30

60

90

0

Lateral Displacem ent (m m )

0.4

Depth from the Top (m)

0.8 1.2 1.6 Analytical model

2 2.4

Jew ell-Milligan method

2.8 Average measured

3.2 3.6

Figure 3.16:

Comparisons of Measured Lateral Displacements with Jewell-Milligan Method and the Analytical Model

102

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.

103

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 loadtransfer 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 soilgeosynthetic 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:

⎛ ΔH ⎞ ⎟ 100% ⎝ H ⎠

εv = ⎜

(4.1)

where ΔH = 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.

σv

Reinforcement Soil

σc

σc H

Sv = 0.2 m

W = 0.7 H 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 A Dense sand: unit weight = 17 kN/m3; cohesion = 5 kPa; Soil

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

Constant confining pressures of 0 and 30 kPa.

Pressure

108

2000

1500

σ v -σ h (kPa)

Specimen Dimensio ns:

1000

7.0 m x 4.9 m

2.0 m x 1.4 m

500 1.0 m x 0.7 m

0.5 m x 0.35 m

0 0

5

10

15

20

25

Global Vertical Strain εv (%)

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

109

Global Volumetric Strain Δ V/V (%)

6

Specimen Dimensions:

5 7.0 m x 4.9 m

4 3

2.0 m x 1.4 m

2 1

1.0 m x 0.7 m

0 -1

0

2

4

6

8

10

12

14

16 0.5 m x 0.35 m

-2 Global Vertical Strain ε v (%)

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

110

2000

1500

σv -σ h (kPa)

Specimen Dimensions:

7.0 m x 4.9 m

1000

2.0 m x 1.4 m

1.0 m x 0.7 m

500

0.5 m x 0.35 m

0 0

5

10

15

20

25

Global Vertical Strain εv (%)

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

111

Global Volumetric Strain Δ V/V (%)

2.5 Specimen Dimensions: 2 7.0 m x 4.9 m

1.5 1

2.0 m x 1.4 m 0.5 0 0

2

4

6

8

10

12

14

16

1.0 m x 0.7 m

-0.5 0.5 m x 0.35 m

-1 -1.5

Global Vertical Strain ε v (%)

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

140.0

120.0

Specimen Dimensions:

σv-σh (kPa)

100.0

7.0 m x 4.9 m

80.0 2.0 m x 1.4 m 60.0

1.0 m x 0.7 m

40.0

20.0 0.5 m x 0.35 m 0.0 0

1

2

3

4

5

6

Global Vertical Strain εv (%)

Figure 4.6: Global Stress-Strain Curves of the Unreinforced Soil Under a Confining Pressure of 30 kPa

114

Global Volumetric Strain Δ V /V (%)

1 Specimen Dimensions

0.8

7m x 4.9m

0.6 0.4

2m x 1.4m

0.2 1m x 0.7m

0 0

1

2

3

4

-0.2

5

6 0.5m x 0.35m

-0.4 Global Vertical Strain εv (%)

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

H = 2.0 m

Sv = 0.2 m

1 L=

.2

m

W = 1.4 m

Figure 4.8:

Specimen Dimensions for the GSGC Tests

116

2.6

6.0

FRONT VIEW (Note: All Dimensions in Inches)

A

steel plate (43''x34''x2'') 160.00 34.00

6.00

2.00

D=1.125'' 30.75

26.00 2.625'' steel plate Load cell LC1 (1000 kip)

steel plate (26''x32.5''x2'')

16.93

jack 16.93

1.12

Load cell LC2 (300 kip) 2'' steel plate

1.94

51.98

steel plate (43''x34''x2'')

12.00

25.19

2.63 5.62

2.00

6.00

12.25

5.0

12.25

4.00

concrete pad (49''x41 3/8''x12'')

9.63 12.00

49.00

134.63

1.50

30.00 3.00

7.63

53.375 2.87 11.38

70.00 74.00

11.38

74.25 36.00

1

A

Figure 4.9:

108.00

36.00

2

3

Front View of the Test Setup

117

33.00

76.25

70.00

81.65

concrete block (7.625''x7.625''x15.625'')

PLAN

Anchor

(Note: All Dimensions in Inches) Specimen

Rigid frame

Open Face: Concrete blocks (7.625''x7.625''x15.625'') would be removed before testing

47.00

47.00

75.87

1.25

36.94

A

36.00 21.50

36.94

47.00

19.50

47.00

23.25 26.63 17.00

53.375 7.63

74.00

26.63 17.00

36.00

108.00

36.00

1

2

3

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

3.03

Solids

123

80 70

50 40 30 20

Percent finer (%)

60

10

100

10

1

0.1

Grain size (m m )

Figure 4.12:

Grain Size Distribution of Backfill

124

0 0.01

Test 1 Test 2

(a) Figure 4.13:

(b)

Typical Triaxial Test Specimen (a) before and (b) after Test

125

Deviatoric Stress versus Axial Strain Relationships 600 550 500 5 psi

Deviatoric Stress (psi)

450 400

15 psi

350 300

30 psi

250 70 psi

200 150

70 psi - Ketchart

100 50

110 psi - Ketchart

0 0

1

2

3

4

5

6

7

8

9

10

11

Axial Strain (%)

(a)

Volumetric Strain (%)

Volumetric Strain versus Axial Strain 0.6 0.4 0.2

5 psi

0 -0.2

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

30 psi

-0.4 Axial Strain (%)

(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

σ

Shear Streess (psi)

3

σ

3

σ

3

σ

3

σ

C2 = 35.1 psi

3

= 110 psi

= 70 psi

= 30 psi

= 15 psi

= 5 psi

C1 = 10.3 psi 0

30

98

172

265

433

Normal Stress (psi)

Figure 4.15:

Mohr-Coulomb Failure Envelops of Backfill

127

616

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: Property

Tensile Strength

Summary of Geotex 4x4 properties provided by the manufacture Test Method

Machine Direction

Cross-Direction

(Wrap Direction)

(Fill Direction)

2.67 kN

2.22 kN

(0.6 kips)

(0.5 kips)

70 kN/m

70 kN/m

(400 lb/in.)

(400 lb/in.)

21 kN/m

38 kN/m

(121 lb/in.)

(217 lb/in.)

10 %

10 %

ASTM D-4632

(Grab) Wide-Width

ASTM D-4595

Tensile Ultimate Strength Wide-Width

ASTM D-4595

Strength at 5% Strain Wide-Width

ASTM D-4595

Ultimate Elongation Puncture

ASTM D-4833

0.8 kN (170 lb)

Trapezoid

ASTM D-4533

1.11 kN (250 lb)

Tearing Strength

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

Single-Sheet

Stiffness (kN/m) at

Ultimate Strength (kN/m)

1% Strain

(% at break)

1,000

70 (12 %)

1,960

138 (12 %)

Geotex 4x4 Double-Sheet Geotex 4x4

131

160

Tensile Load (kN/m)

140 120 100 80 60 40 Single-Sheet

20

Double-Sheet

0 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

Axial Strain (%)

Figure 4.17:

4.3.3

Load-Deformation Curves of the Geosynthetics

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

Geosynthetic

Confining

Wide-Width

Reinforcement

Designation

Reinforcement

Pressure

Strength of

Spacing, Sv

Reinforcement 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

34 kPa

T = 140 kN/m

Sv = 0.4 m

Geotex 4x4 Test 4

Geotex 4x4

34 kPa

T = 70 kN/m

Sv = 0.4 m

Test 5

Geotex 4x4

0

T = 70 kN/m

Sv = 0.2 m

(unconfined)

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

Location of LVDTs and Dial Indicators SIDE VIEW FRONT VIEW 73.72 (1872.49) 72.25'' (1835.15)

47.37'' (1203.32) 1-1/4''

76.3'' (1938)

2''

55.12'' (1400) Center line

Cross Section A-A TOP VIEW

Dial Indicator

LVDTs on the open side

Jack

A

6''

76.3'' (1938)

2.34 (59.49) 13.0 13.0 11.0 13.0 304.8 (332.1) (332.1) (297.4) (332.1)

Figure 4.18:

LVDT on the top surface

81.65'' (2073.91)

2.34 (59.49)

GSGC MASS

Footing on the top of GRS specimen

Dial Indicator on the top surface

LVDT

6''

55.12'' (1400)

13.0 13.0 11.0 13.0 304.8 (332.1) (332.1) (297.4) (332.1)

Dial Indicator

5.35''

72.25'' (1835.15) LVDT

4'' 4''

Dial Indicator on the top surface

Dial Indicator on the open side

LVDT on the top surface (the location can be adjusted dependent on the size of the loading system)

Locations of LVDTs and Digital Dial Indicators

136

81.65'' (2073.91)

Dial Indicator

10.4 11.37 11.37 11.37 11.37 11.37 11.37 (264.16)(288.92)(288.92)(288.92)(288.92)(288.92)(288.92)

13.0 13.0 11.0 13.0 304.8 (332.1) (332.1) (297.4) (332.1)

76.3'' (1938)

81.65'' (2073.91)

2.34 (59.49)

LVDT

10.4 11.37 11.37 11.37 11.37 11.37 11.37 (264.16)(288.92)(288.92)(288.92)(288.92)(288.92)(288.92)

Dial Indicator

13.0 13.0 11.0 13.0 304.8 (332.1) (332.1) (297.4) (332.1)

13.0 13.0 11.0 13.0 304.8 (332.1) (332.1) (297.4) (332.1)

Dial Indicator

2.34 (59.49)

LVDT

2.34 (59.49)

LVDT

5.35''

Dial Indicator

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

Strain from Instron Machine (%)

6 5

y = 1.172x 2 R = 0.9913

4 3 2 1 0 0

1

2

3

4

Strain from Strain Gage (%)

Figure 4.21:

Calibration Curve for Single-Sheet Geotex 4x4

141

5

Strain from Instron Machine (%)

6

5 y = 1.078x R2 = 0.9986 4

3

2

1

0 0

1

2

3

4

Strain from Strain Gauge (%)

Figure 4.22:

Calibration Curve for Double-Sheet Geotex 4x4

142

5

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 predrawn 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

(a): Tests 1 and 2 10.25

2x2'' Grid System

2

3

4

5

6

7

8

9 16.00

42.00

66.00

60.25

Heigth = 76.25 in. (Test 1), 76.35 in. (Test 2)

34.25

1

2.50

32.50

24.50 2.50 Width

(b): Tests 3,4 and 5 10.35

2x2'' Grid System

1

2

10

3

11

5

6

7

8

9 16.00

42.00

54.00

4

Height = 76.30 in.

34.35

15.38

3.38 31.38

3.38 Width

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

2.00 1.80

Specimen Height (m)

1.60 1.40 Test 1

1.20

Test 2 1.00 Test 3 0.80

Test 4

0.60

Test 5

0.40 0.20 0.00 15

18

21

24

27

30

Dry Unit Weight (kN/m3)

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. unreinforced soil are summarized in Table 4.7.

163

The test results of Test 1 for

Figure 4.40: Soil Mass at Failure of Test 1

164

900

Applied Vertical Stress (kPa)

800 700 600 500 400 300 200 100 0 0

1

2

3 4 Global Vertical Strain (%)

5

6

(a) 1.2

Volumetric Strain (%)

1 0.8 0.6 0.4 0.2 0 0

0.5

1

1.5

2

2.5

-0.2 -0.4 Global Vertical Strain (%)

(b) Figure 4.41: Test 1-Unreinforced Soil Mass: (a) Global Vertical Stress-Vertical Strain Relationship (b) Global Volume Change Strain Relationship

165

3

3.5

2.00

1.75

Specimen Height (m)

1.50

1.25

Applied Pressure:

1.00

200 kPa 400 kPa

0.75

600 kPa

0.50

770 kPa

0.25 700 kPa

0.00 0

10

20

30

40

50

Lateral Displacement (mm)

Figure 4.42: Lateral Displacements on the Open Face of Test 1

166

10.25

Test 1

1

2

3

5

6

8

9

34.25

2'' x 2'' Grid System

76.25

4

66.00

Legend: Before Loading 190 kPa (75 kips) 310 kPa (120 kips) 620 kPa (240 kips) 42.00

770 kPa (300 kips)

16.00

7

Note: (All Displacements in inches, Drawn to Scale of the Soil Mass) 2.50 32.50

2.50 57.00

Figure 4.43: Internal Displacements of Test 1

167

Table 4.7: Some test results of Test 1 Test 1

Test Conditions

Test Results

Geosynthetic Reinforcement

None

Wide-Width Strength of Reinforcement

None

Reinforcement Spacing

No Reinforcement

Confining Pressure

34 kPa

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

Applied Vertical Stress (kPa)

3,000

2,500

2,000

1,500

1,000

500

0 0

1

2

3

4

5

6

7

8

9

Global Vertical Strain (% )

(a)

0

Volumetric Strain (%)

-0.2

0

1

2

3

4

5

-0.4 -0.6 -0.8 -1 -1.2 -1.4 -1.6 -1.8

Global Vertical Strain (%)

(b) Figure 4.47: Test 2-Reinforced Soil Mass: (a) Global Vertical Stress-Vertical Strain Relationship (b) Global Volume Change Strain Relationship

173

6

7

2 Applied Pressure:

1.75 200 kPa 400 kPa

Specimen Height (m)

1.5

600 kPa

1.25

770 kPa 1000 kPa

1

1250 kPa 1500 kPa

0.75

1750 kPa 2000 kPa

0.5

2250 kPa

0.25

2500 kPa 2700 kPa

0 0

10

20

30

40

50

60

70

Lateral Displacement (mm)

Figure 4.48: Lateral Displacements on the Open Face of Test 2

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

10.35

Test 2

1

2

3

5

6

8

9

4

76.35

38.35

2'' x 2'' Grid System

66.00

Legend: Before Loading 270 kPa 540 kPa

...

16.00

7

38.00

2,700 kPa

Note:

(All Displacements in inches, Drawn to Scale of the Composite Mass) 3.00 31.00

3.00 54.00

Figure 4.49: Internal Displacements of Test 2

177

Reinforcement

7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63

Strain Gages

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

11.00

8.00 8.00 8.00 8.00

11.00

54 (Note: All Dimensions in inches)

Figure 4.50:

Locations of Strain Gauges on Geosynthetic sheets in Test 2

178

2.5

Applied Pressure: 200 kPa

Strain (%)

2

400 kPa 1.5

600 kPa 800 kPa

1

1000 kPa 0.5

1250 kPa 1500 kPa

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(a)

Applied Pressure:

3.00

200 kPa

Strain (%)

2.50

400 kPa

2.00

600 kPa

1.50

800 kPa

1.00

1000 kPa

0.50

1250 kPa 1500 kPa

0.00 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(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

Strain (%)

Applied Pressure:

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

200 kPa 400 kPa 600 kPa 800 kPa 1000 kPa 1250 kPa 1500 kPa 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(c)

3.5 Applied Pressure:

Strain (%)

3 2.5

200 kPa

2

400 kPa

1.5

600 kPa

1

800 kPa

0.5

1000 kPa

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(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

3 Applied Pressure:

Strain (%)

2.5

200 kPa

2

400 kPa

1.5

600 kPa 1 800 kPa 0.5 1000 kPa 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(e)

3

Applied Pressure:

Strain (%)

2.5 200 kPa

2

400 kPa

1.5

600 kPa 1 800 kPa 0.5 1000 kPa 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(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

4

Applied Pressure:

Strain (%)

3.5 3

200 kPa

2.5

400 kPa

2

600 kPa

1.5

800 kPa

1

1000 kPa

0.5

1250 kPa

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(g)

Strain (%)

3

Applied Pressure:

2.5

200 kPa

2

400 kPa

1.5

600 kPa

1

800 kPa 1000 kPa

0.5

1250 kPa 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(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

1.6 1.4

Applied Pressure:

Strain (%)

1.2 200 kPa

1 0.8

400 kPa

0.6 600 kPa

0.4 0.2

800 kPa

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(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 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63

Test 2 Reinforcement

1 2 3 4 5 6 7 8 9

54 (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

Table 4.8: Some test results of Test 2 Test 2

Test Conditions

Test Results

Geosynthetic Reinforcement

Geotex 4x4

Wide-Width Strength of Reinforcement

70 kN/m

Reinforcement Spacing

0.2 m

Confining Pressure

34 kPa

Ultimate Applied Pressure

2700 kPa

Vertical Strain at Failure

6.5 %

Maximum Lateral Displacement of the Open Face at Failure

60 mm

Stiffness at 1% vertical strain (Eat 1%)

61,600 kPa

Maximum strain in reinforcement at ruptured

12 %

Maximum measured strain in reinforcement

4.0 %

186

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.

•

Reinforcement strain: Figure 4.58 shows the locations of the strain gauges on the geosynthetic sheets. The strain in the reinforcement of the GSGC mass is shown in Figure 4.59.

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).

187

Based on the locations of the

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. •

The test results of Test 3 are summarized in Table 4.9.

188

Figure 4.54:

Composite Mass after Testing of Test 3

189

2,000 1,800

Applied Vertical Stress (kPa)

1,600 1,400 1,200

1,000 800 600 400 200 0 0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

Global Vertical Strain (% )

Figure 4.55:

Global Stress-Strain Relationship of Test 3

190

8.00

2

Specimen Height (m)

1.75

Applied Pressure:

1.5 260 kPa

1.25

400 kPa 600 kPa

1

800 kPa

0.75

1000 kPa

0.5

1250 kPa 1500 kPa

0.25

1750 kPa

0 0.0

10.0

20.0

30.0

40.0

50.0

60.0

Lateral Displacement (mm)

Figure 4.56:

Lateral Displacements on the Open Face of Test 3

191

Test 3 10.35

2x2'' Grid System

2

3

34.35

1

14.5

11

60.36

10

5

6 Legend:

2'' x 2'' Grid System

76.35

4

Before Loading 66.00

280 kPa 560 kPa

54.00

840 kPa 1120 kPa

42.00

1400 kPa 1680 kPa 1750 kPa 8

9

16.00

7

Note:

(All Displacements in inches, Drawn to Scale of the Composite Mass) 2.50 2.50

30.50 53.00

Figure 4.57:

Internal Displacements of Test 3

192

Strain Gages

15.25

Reinforcement

15.25

Sheet No 4

15.25

Sheet No 3

15.25

Sheet No 2

15.25

Sheet No 1

10.50

8.00 8.00 8.00 8.00

10.50

53.00 (Note: All Dimensions in inches)

Figure 4.58:

Location of Strain Gauges on Geosynthetic Sheets in Test 3

193

Strain (%)

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

Applied Pressure: 260 kPa 400 kPa 600 kPa `

800 kPa 1000 kPa 1250 kPa

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

Strain (%)

(a)

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

Applied Pressure: 260 kPa 400 kPa 600 kPa 800 kPa 1000 kPa 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(b) Figure 4.59:

Reinforcement Strain Distribution of the Composite Mass in Test 3: (a) Layer 1, at 0.4 m from the Base (b) Layer 2, at 0.8 m from the Base

194

Strain (%)

4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

Applied Pressure: 260 kPa 400 kPa 600 kPa 800 kPa 1000 kPa 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

Strain (%)

(c)

4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

Applied Pressure: 260 kPa 400 kPa 600 kPa 800 kPa 1000 kPa 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(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

Rupture Lines 15.25

Test 3 Reinforcement

15.25

1

15.25

2

15.25

3

15.25

4

53 (Note: All Dimensions in inches, Drawn to Scale)

Figure 4.61:

Locations of Rupture Lines of Reinforcement in Test 3; Constructed based on Figure 4.60.

197

Table 4.9: Some test results of Test 3 Test 3

Test Conditions

Test Results

Geosynthetic Reinforcement

Geotex 4x4

Wide-Width Strength of Reinforcement

140 kN/m

Reinforcement Spacing

0.4 m

Confining Pressure

34 kPa

Ultimate Applied Pressure

1,750 kPa

Vertical Strain at Failure

6.1 %

Maximum Lateral Displacement of the Open Face at Failure

54 mm

Stiffness at 1% vertical strain (Eat 1%)

48,900 kPa

Maximum strain in reinforcement at ruptured

12 %

Maximum measured strain in reinforcement

4.0 %

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 vertical pressure was about 1,300 kPa. The vertical displacement at the failure 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.

•

Reinforcement strain: Figure 4.66 shows the locations of the strain gauges on the geosynthetic sheets. The strain in the reinforcement of the GSGC mass is shown in Figure 4.67. 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

rupture line, the rupture planes can be constructed as shown in Figure 4.69. This rupture line agrees perfectly with the failure line in Figure 4.62. The

199

maximum strain in reinforcement at ruptured was about 12 % and located at near the ruptured line as shown in Figure 4.69. •

The test results of Test 4 are summarized in Table 4.10.

200

(a) Figure 4.62:

(b)

Failure Planes of the Composite Mass after Testing in Test 4: (a) Front View at the South (b) Back View at the North.

201

1,400

Applied Vertical Stress (kPa)

1,200

1,000

800

600

400

200

0 0.00

1.00

2.00

3.00

4.00

5.00

6.00

Global Vertical Strain (%)

Figure 4.63:

Global Stress-Strain Relationship of Test 4

202

7.00

2 1.75

Specimen Height (m)

1.5

Applied Pressure: 200 kPa

1.25

400 kPa 1 600 kPa 0.75

800 kPa

0.5

1000 kPa 1250 kPa

0.25

1300 kPa 0 0.0

10.0

20.0

30.0

40.0

50.0

60.0

Lateral Displacement (mm)

Figure 4.64:

Lateral Displacements on the Open Face of Test 4

203

15.00

10.35

Test 4

1

2

3

11 34.35

10

4

5

6 76.30

2'' x 2'' Grid System Legend: Before Loading 250 kPa 54.00

500 kPa 750 kPa

42.00

1000 kPa 1250 kPa 1300 kPa 7

9

16.00

8

Note:

(All Displacements in inches, Drawn to Scale of the Composite Mass) 3.00 31.00

3.00 58.00

Figure 4.65:

Internal Displacements of Test 4

204

Strain Gages

15.25

Reinforcement

15.25

Sheet No 4

15.25

Sheet No 3

15.25

Sheet No 2

15.25

Sheet No 1

13.35

8.00 8.00 8.00 8.00

13.35

58.75 (Note: All Dimensions in inches)

Figure 4.66:

Location of Strain Gauges on Geosynthetic Sheets in Test 4

205

1.8

Applied Pressure:

Strain (%)

1.6 1.4

100 kPa

1.2

200 kPa

1

300 kPa

0.8

400 kPa

0.6

500 kPa

0.4

600 kPa

0.2

800 kPa

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Distance from the Edge of the Composite M ass (m)

Strain (%)

(a)

2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

Applied Pressure: 100 kPa 200 kPa 300 kPa 400 kPa 500 kPa 600 kPa 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Distance from the Edge of the Composite M ass (m)

(b) Figure 4.67:

Reinforcement Strain Distribution of the Composite Mass in Test 4: (a) Layer 1, at 0.4 m from the Base (b) Layer 2, at 0.8 m from the Base

206

1 Applied Pressure:

Strain (%)

0.8

100 kPa

0.6

200 kPa

0.4

300 kPa 0.2 400 kPa 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Distance from the Edge of the Composite M ass (m)

Strain (%)

(c)

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

Applied Pressure: 100 kPa 200 kPa 300 kPa 400 kPa 500 kPa 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Distance from the Edge of the Composite Mass (m)

(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 15.25

Test 4 Reinforcement

15.25

1

15.25

2

15.25

3

15.25

4

58 (Note: All Dimensions in inches, Drawn to Scale)

Figure 4.69:

Locations of Rupture Lines of Reinforcement in Test 4; Constructed based on Figure 4.68.

209

Table 4.10: Some test results of Test 4 Test 4

Test Conditions

Test Results

Geosynthetic Reinforcement

Geotex 4x4

Wide-Width Strength of Reinforcement

70 kN/m

Reinforcement Spacing

0.4 m

Confining Pressure

34 kPa

Ultimate Applied Pressure

1,300 kPa

Vertical Strain at Failure

4.0 %

Maximum Lateral Displacement of the Open Face at Failure

53 mm

Stiffness at 1% vertical strain (Eat 1%)

46,600 kPa

Maximum strain in reinforcement at ruptured

12 %

Maximum measured strain in reinforcement

2.0 %

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 vertical pressure was about 1,900 kPa. The vertical displacement at the failure 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. •

Reinforcement strain: Figure 4.75 shows the locations of the strain gauges on the geosynthetic sheets. The strain in the reinforcement of the GSGC mass is shown in Figure 4.76.

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

rupture line, the rupture planes can be constructed as shown in Figure 4.78. This rupture line agrees perfectly with the failure line in Figure 4.70. The maximum strain in reinforcement measured was 3.2 % and located at near the ruptured line as shown in Figure 4.78. •

The test results of Test 5 are summarized in Table 4.11.

212

Figure 4.70:

Composite Mass at Failure of Test 5

213

(a) Figure 4.71:

(b)

Failure Planes of the Composite Mass after Testing in Test 5: (a) Front View (South), (b) Back View (North)

214

2,200 2,000

Applied Vertical Stress (kPa)

1,800 1,600 1,400 1,200 1,000 800 600 400 200 0 0

1

2

3

4

5

6

7

Global Vetical Strain (%)

Figure 4.72:

Global Stress-Strain Relationship of Test 5

215

8

2.000 1.750

Specimen Height (m)

1.500 Applied Pressure: 1.250 200 kPa 1.000 400 kPa 0.750

600 kPa

0.500

1500 kPa

0.250 0.000 0.0

10.0

20.0

30.0

40.0

Lateral Displacement (mm)

Figure 4.73:

Lateral Displacements on the Open Face of Test 5

216

12.50

10.35

Test 5

2

3

34.35

1

11

60.35

10

5

6

2'' x 2'' Grid System

Legend:

76.35

4

Before Loading 300 kPa 600 kPa 54.00

900 kPa 1200 kPa 42.00

1500 kPa 1800 kPa 8

9

16.00

7

Note:

(All Displacements in inches, Drawn to Scale of the Composite Mass) 2.50 28.50

2.50 49.00

Figure 4.74:

Internal Displacements of Test 5

217

Strain Gages

15.25

Reinforcement

Sheet No 9

15.25

Sheet No 8 Sheet No 7

15.25

Sheet No 6 Sheet No 5

15.25

Sheet No 4 Sheet No 3

15.25

Sheet No 2 Sheet No 1

8.50

8.00 8.00 8.00 8.00

8.50

49.00 (Note: All Dimensions in inches)

Figure 4.75:

Location of Strain Gauges on Geosynthetic Sheets in Test 5

218

Strain (%)

3.5

Applied Pressure:

3

100 kPa

2.5

200 kPa

2

300 kPa

1.5

400 kPa

1

500 kPa 600 kPa

0.5

750 kPa

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(a)

Strain (%)

3

Applied Pressure:

2.5

100 kPa

2

200 kPa 300 kPa

1.5

400 kPa

1

500 kPa

0.5

600 kPa 750 kPa

0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(b) Figure 4.76:

Reinforcement Strain Distribution of the Composite Mass in Test 5: (a) Layer 1, at 0.4 m from the Base (b) Layer 2, at 0.8 m from the Base

219

1.2 Applied Pressure:

Strain (%)

1

100 kPa

0.8

200 kPa 0.6 300 kPa 0.4 400 kPa 0.2

525 kPa

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(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 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63 7.63

Test 5 Reinforcement

1 2 3 4 5 6 7 8 9

49 (Note: All Dimensions in inches, Drawn to Scale)

Figure 4.78:

Locations of Rupture Lines of Reinforcement in Test 5; Constructed based on Figure 4.77.

222

Table 4.11: Some test results of Test 5 Test 5

Test Conditions

Test Results

Geosynthetic Reinforcement

Geotex 4x4

Wide-Width Strength of Reinforcement

70 kN/m

Reinforcement Spacing

0.2 m

Confining Pressure

0

Ultimate Applied Pressure

1,900 kPa

Vertical Strain at Failure

6.0 %

Maximum Lateral Displacement of the Open Face at Failure

Not Measured

Stiffness at 1% vertical strain (Eat 1%)

52,900 kPa

Maximum strain in reinforcement at ruptured

12 %

Maximum measured strain in reinforcement

3.2 %

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

Confining Pressure

34 kPa

34 kPa

Ultimate Applied Pressure

2,700 kPa

1,750 kPa

Stiffness at 1% vertical strain (Eat 1%)

61,600 kPa

48,900 kPa

Vertical Strain at Failure

6.5 %

6.1 %

Maximum Lateral Displacement of the Open Face at Failure

60 mm

54 mm

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

Table 4.14: Comparison between Test 2 and Test 4 Test 2 (T, Sv)

Test 4 (T, 2Sv)

Wide-Width Strength of Reinforcement

Tf = 70 kN/m

Tf = 70 kN/m

Reinforcement Spacing

Sv = 0.2 m

Sv = 0.4 m

Tf / Sv

350 kPa

175 kPa

Confining Pressure

34 kPa

34 kPa

Ultimate Applied Pressure

2,700 kPa

1,300 kPa

Vertical Strain at Failure

6.5 %

4.0 %

Maximum Lateral Displacement of the Open Face at Failure

60 mm

53 mm

Stiffness at 1% vertical strain (Eat 1%)

61,600 kPa

46,600 kPa

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. Table 4.15: Comparison between Test 3 and Test 4 Test 3 (2T, 2Sv)

Test 4 (T, 2Sv)

Wide-Width Strength of Reinforcement

Tf = 140 kN/m

Tf = 70 kN/m

Reinforcement Spacing

Sv = 0.4 m

Sv = 0.4 m

Tf / Sv

350 kPa

175 kPa

Confining Pressure

34 kPa

34 kPa

Ultimate Applied Pressure

1,750 kPa

1,300 kPa

Vertical Strain at Failure

6.1 %

4.0 %

Maximum Lateral Displacement of the Open Face at Failure

54 mm

53 mm

Stiffness at 1% vertical strain (Eat 1%)

48,900 kPa

46,600 kPa

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

Table 4.16: Comparison between Test 2 and Test 5 Test 2 (T, Sv)

Test 5 (T, Sv)

Wide-Width Strength of Reinforcement

Tf = 70 kN/m

Tf = 70 kN/m

Reinforcement Spacing

Sv = 0.2 m

Sv = 0.2 m

Tf / Sv

350 kPa

350 kPa

Confining Pressure

34 kPa

0

Ultimate Applied Pressure

2,700 kPa

1,900 kPa

Vertical Strain at Failure

6.5 %

6.0 %

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 C R =

Tf 2 Sv

K p + c , 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

Table 4.17: Comparison of strength properties of five GSGC Tests Test 1

Test 2

Test 3

Test 4

Test 5

(unreinforced)

(T, Sv)

(2 T, 2Sv)

(T, 2Sv)

(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

34

34

34

0

550

550

310

550

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 %

Parameter

Confining Pressure (kPa)

34

Apparent Cohesion, CR, (kPa) by Schlosser and Long’s Method Ultimate Applied Pressure (kPa) from Measured Data

770

234

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 loadingunloading-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, σ ' h = K i , c σ ' v ,

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 σ 'v , max = σ 'v + Δσ 'v , c , max (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 σ 'h = K1, c σ 'v ). - Upon reloading due to the next cycle of compaction load application, the stresses are to follow a K3,c-line (with σ ' h = K 3, c σ ' v ) 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

K1,c-line

σh

K1,c Ki,c-line

Unloading-curve

1

B D

K3,c-line C

Δσ'h,c,r

G

K3,c-line

E

σ'h = Ki,c σ'v

F A

σ'v

Figure 5.1:

5.1.2

σ'v + Δσ'v,c,max

σv

Conceptual Stress Path for Compaction of a GRS Mass

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 σ ' h = K 3, c σ ' v , and K3, c ≤ K 2, c ). 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.

K1,c-line

σh

K2,c-line

σ'h = K2,c σ'v

K1,c

σ'h,s Δσ'h,c,r Δσ'h,s,r

K0

K3,c-line σ'h = K3,c σ'v

1

σ'h,c

K0-line

1 B

D

C

Δσ'h,c,max

σ'h = Ki,c σ'v

E

KA-line KA

S F

1 A

Unreinforced soil Ki,c-line

σ'v

Figure 5.2:

σ'v + Δσ'v,c,max

σv

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 ⎛ Er results of GSGC tests. Note that the term ⎜⎜ 0.7 E s S v − 0.7 J r ⎝

⎞ ⎟⎟ , for the estimation of ⎠

K2, c, is to account for the presence of reinforcement. For hand calculations, the maximum increase of "vertical" stress, Δσ 'v , c , max as shown in Figure 5.2, due to compaction can be estimated simply by using the Westergaard's solution (1938).

239

Table 5.1 : Parameter

Ki,c

Model parameters for the proposed compaction simulation model Name

Range of the Parameter Values

Preliminary Estimation Based on Soil and Reinforcement Properties K i ,c ≅ β K A

Coefficient of K A ≤ K i ,c ≤ K 0 lateral earth pressure of a GRS mass for initial loading

1.0 ≤ β ≤ 1.5

φ' ⎞ ⎛ K A ≅ tan 2 ⎜ 45 − ⎟ 2⎠ ⎝ K 0 ≅ 1 − sin φ '

K1,c

Limiting coefficient of lateral earth pressure for unloading

K 1,c ≅ K P

K2,c

Coefficient of lateral earth pressure for unloading

0 ≤ K 2 ,c ≤ K 0

φ' ⎞ ⎛ K 1,c ≅ K P ≅ tan 2 ⎜ 45 + ⎟ 2⎠ ⎝

⎡ ⎛ Er K 2, c ≅ ⎢1 − F ⎜⎜1 + 0.7 E s S v − 0.7 E r ⎝ ⎣

where: F = 1 −

(OCR − OCR ) (Seed,

1983); α ≅ sin φ ' K3,c

Coefficient of lateral earth pressure for reloading

0 ≤ K 3, c ≤ K 0

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

⎞⎤ ⎟⎟⎥ K i , c ⎠⎦

α

(OCR − 1)

K 3, c ≅ K 2 , c

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

compaction load

I

(a)

location i

Ζ

location 2

location 1

Δσ'v

I

changing K2,c-line due to passes of compaction

σh

(b)

F G

Δσ'h,c,r

Ki,c-line

i 2

E

D

1

C

B

K2,c and K3,c-line (Assume: K2,c = K3,c)

A

σ'v

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

σv

compaction load

I

(a)

location 1

Ζ

location 2

location i

Δσ'v P

I

changing K2,c-line due to passes of compaction

σh (b)

1 F G i

B

2

D Ki,c-line

Δσ'h,c,r K2,c and K3,c-line (Assume: K2,c = K3,c) A

σ'v

σ'v + Δσ'v,c,max

σv

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

σh

changing K2,c-line due to a number of compaction passes

G'' G'

G'''

F Ki,c-line

G

Δσ'h,c,r K2,c and K3,c-line (Assume: K2,c = K3,c) A

σ'v

Figure 5.5:

σ'v + Δσ'v,c,max

σv

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 compactioninduced 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.

σh

K2, s for soil

B

K2, c for composite C

Δσ

G*(Δσ) S

Ki, c - line

F∗(Δσ) A

σ'v

Figure 5.6:

σ'v + Δσ'v, c, max

σv

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): K 2, s = (1 − F ) K i ,c

(5.1)

246

(OCR − OCR ) ; α ≅ sin φ ' ; and OCR ≅ 5 for typical where F = 1 − α

OCR − 1

compacted sand (Seed, 1983).

(b) For GRS Composite

For a GRS mass, total residual strain in the soil can be determined as:

εs =

(F + G ) (Δσ )

(5.2)

Es

where F and G = stress reduction factors shown in figure 5.6; Δσ = 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: ⎛ (F + G ) Δσ T = ⎜⎜ Es ⎝

⎞ ⎟⎟ E r ⎠

(5.3)

where Er = reinforcement stiffness. The average residual stress in the soil due to compaction, G * (Δσ ) , is: ⎛ (F + G ) Δσ G * Δσ = 0.7 ⎜⎜ Es ⎝

⎞ Er ⎟⎟ ⎠ Sv

(5.4)

where Sv = reinforcement spacing. or

G E s S v = 0.7 F E r + 0.7 G E r

(5.5)

Thus, 0.7 F E r E s S v − 0.7 E r

(5.6)

K 2 ,c = [ 1 − (F + G ) ] K i ,c

(5.7)

G=

Since

Substituting (5.6) into (5.7), we have

247

⎡ K 2, c ≅ ⎢1 − F ⎣

⎛ 0.7 E r ⎜⎜1 + ⎝ E s S v − 0.7 E r

⎞⎤ ⎟⎟⎥ K i , c ⎠⎦

(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: Δσ h , c = Δσ (G + F ) = Δσ ' v , c , max (K i , c − K 2, c )

(5.9)

Substituting (5.8) into (5.9), we have ⎧⎪ ⎡ Δσ h , c = Δσ ' v , c , max ⎨ K i , c ⎢ 1 − 1 + F ⎪⎩ ⎣

⎛ 0.7 E r ⎜⎜ 1 + E s S v − 0.7 E r ⎝

⎞⎤ ⎫⎪ ⎟⎟⎥ ⎬ ⎠⎦ ⎪⎭

(5.10)

or ⎛ ⎞ 0.7 E r ⎟⎟ Δσ h , c = Δσ ' v , c , max K i , c F ⎜⎜ 1 + − E S 0 . 7 E s v r ⎠ ⎝

(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: ⎡ R f (1 − sin φ ) (σ 1 − (σ 3 + Δσ h ,c ))⎤ ⎛ σ 3 + Δσ h ,c E = ⎢1 − K Pa ⎜⎜ ⎥ t ⎢ 2 c cos φ + 2 (σ 3 + Δσ h ,c ) sin φ ⎦⎥ Pa ⎝ ⎣ 2

where

248

⎞ ⎟⎟ ⎠

n

(5.12)

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.

Shear Streess, τ

φ

φ

Reinforced Soil Reinforced Soil

CR

C

Unreinforced Soil

σ3

Figure 5.7:

Δσ3R

σ3R σ1

Normal Stress, σ

σ1R

Concept of Apparent Confining Pressure and Apparent Cohesion of a GRS Composite

The apparent cohesion of a GRS composite can be determined as: cR =

Δσ 3 R K P 2

+c

(5.13)

where c R = apparent cohesion of a GRS composite c = cohesion of soil

250

Kp = coefficient of passive earth pressure Δσ 3 R = increase of confining pressure due to reinforcement

Schlosser and Long (1972) also proposed an equation to calculate increased confining pressure as: Δσ 3 =

Tf

(5.14)

Sv

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: ⎛ Tf ⎞ Δσ 3 = W ⎜⎜ ⎟⎟ ⎝ Sv ⎠

(5.15)

where the factor, W, can be estimated as: W = r

where

⎛ Sv ⎜ ⎜ S ref ⎝

⎞ ⎟ ⎟ ⎠

(5.16)

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 plainstrain 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: ⎡⎛ υ Fx = Ar E r ⎢⎜⎜ s ⎣⎝ 1 − υ s

⎤ ⎛1 −υs2 ⎞ ⎟⎟ Pv − Ph ⎥ ⎜ ⎜ ⎠ ⎦ ⎝ Es

⎞⎛ ⎟ ⎜1 − β ⎟⎝ α2 ⎠

The horizontal stress in the soil:

252

⎞ ⎛ cosh (α x ) ⎞ ⎟⎟ ⎟ ⎜⎜1 − ⎠ ⎝ cosh (α L ) ⎠

(5.17)

⎛ υ σ x = − ⎜⎜ s ⎝1 −υs

⎛⎛ υ ⎞ ⎟⎟ Pv + ⎜ ⎜⎜ s ⎜ 1−υ s ⎠ ⎝⎝

⎞ ⎛ β cosh (α x ) ⎛ ⎞ β ⎟⎟ Pv − Ph ⎟ ⎜⎜ 2 1 + − ⎜ ⎟ α cosh (α L ) ⎝ α 2 ⎠ ⎠⎝

⎞⎞ ⎟ ⎟⎟ ⎠⎠

(5.18)

Based on a load-transfer analysis, the “average stresses” was determined. The average vertical stress, σ v , is assumed to be equal to the boundary vertical pressure, i.e.,

σ v = Pv

(5.19)

The average horizontal stress, σ h , is: L

σh =

∫σ

x

( x)dx

0

(5.20)

L

or

⎛ υ σ h = ⎜⎜ s ⎝1 −υs

⎛⎛ υ ⎞ ⎟⎟ Pv − ⎜ ⎜⎜ s ⎜ 1−υ s ⎠ ⎝⎝

⎞⎛ ⎞ β ⎛ tanh (α L ) ⎞ ⎞ ⎟⎟ Pv − Ph ⎟ ⎜⎜1 + 2 ⎜ − 1⎟ ⎟⎟ ⎟ α L . α ⎝ ⎠⎠ ⎠ ⎠⎝

253

(5.21)

Figure 5.8:

Figure 5.9:

An Idealized Plane-Strain GRS Mass for the SPR Model

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: ⎡⎛ υ Fx = Ar E r ⎢⎜⎜ s ⎣⎝ 1 − υ s

⎤ ⎛1 −υs2 ⎞ ⎟⎟ Pv − Ph ⎥ ⎜ ⎜ ⎠ ⎦ ⎝ Es

⎞⎛ ⎟ ⎜1 − β ⎟⎝ α2 ⎠

⎞ ⎛ cosh (α x ) ⎞ ⎟⎟ ⎟ ⎜⎜1 − ⎠ ⎝ cosh (α L ) ⎠

(5.22)

and Fmax

⎡⎛ υ = Ar E r ⎢⎜⎜ s ⎣⎝ 1 − υ s

⎤ ⎛1 −υs 2 ⎞ ⎟⎟ Pv − Ph ⎥ ⎜ ⎜ ⎠ ⎦ ⎝ Es

⎞⎛ ⎟ ⎜1 − β ⎟⎝ α2 ⎠

⎞ 1 ⎞⎛ ⎟⎟ ⎟ ⎜⎜1 − ⎠ ⎝ cosh (α L ) ⎠

(5.23)

The average force in the reinforcement may be calculated as: L

∫ F dx x

F=

0

(5.24)

L

Substituting Equation (5.22) into Equation (5.24), we have: Ar E r L ⎡⎛ υ s F = ⎢⎜ L ∫0 ⎣⎜⎝ 1 − υ s

⎤ ⎛1 −υs 2 ⎞ ⎟⎟ Pv − Ph ⎥ ⎜ ⎜ ⎠ ⎦ ⎝ Es

⎞⎛ ⎟ ⎜1 − β ⎟⎝ α2 ⎠

⎞ ⎛ cosh (α x ) ⎞ ⎟⎟ dx ⎟ ⎜⎜1 − ⎠ ⎝ cosh (α L ) ⎠

(5.25)

(5.26)

or A .E F = r r L

⎡⎛ υ s ⎢⎜⎜ ⎣⎝ 1 − υ s

⎤ ⎛1 −υs 2 ⎞ ⎟⎟ Pv − Ph ⎥ ⎜ ⎜ ⎠ ⎦ ⎝ Es

L ⎞⎛ ⎛ ⎞ ⎟ ⎜1 − β ⎞⎟ ⎜1 − cosh (α x ) ⎟ dx ⎟ ⎝ α 2 ⎠ ∫ ⎜ cosh (α L ) ⎟ ⎠ 0⎝ ⎠

⎡⎛ υ s ⎢⎜⎜ ⎣⎝ 1 − υ s

⎤ ⎛1 −υs 2 ⎞ ⎟⎟ Pv − Ph ⎥ ⎜ ⎜ ⎠ ⎦ ⎝ Es

⎞⎛ ⎟ ⎜1 − β ⎟⎝ α2 ⎠

Thus, A .E F = r r L

255

sinh (α x ) ⎞ ⎞⎛ ⎟ ⎟ ⎜⎜ L − α cosh (α L ) ⎟⎠ ⎠⎝

(5.27)

Introducing a factor

r=

F , and from Equations (5.23) and (5.27), r can be Fmax

determined as: r=

α L cosh (α L ) − sinh (α L ) α L (cosh (α L ) − 1)

(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

Reinforcement

Vertical Pressure

Length, L (m)

α

r (r =

F ) Fmax

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

Fmax = T f

(5.29)

and the average reinforcement force Tavg = 0.7 T f . Equation 5.16 becomes: W = 0.7

5.2.2

⎛ Sv ⎜ ⎜ S ref ⎝

⎞ ⎟ ⎟ ⎠

(5.30)

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: ⎛ Tf Δσ 3 = W ⎜⎜ ⎝ Sv

⎡ ⎛ Sv ⎞ ⎤ ⎞ ⎢ ⎜⎜⎝ S ref ⎟⎟⎠ ⎥ ⎛ T f ⎟⎟ = 0.7 ⎜ ⎥ ⎜⎝ S v ⎠ ⎢⎢ ⎥⎦ ⎣

⎞ ⎟⎟ ⎠

(5.31)

Therefore, the apparent cohesion, CR, of a GRS composite can be evaluated as: Δσ 3 CR = 2

where

⎡ ⎛⎜ Sv ⎞⎟ ⎤ T ⎜S ⎟ f K p + c = ⎢0.7 ⎝ ref ⎠ ⎥ ⎢ ⎥ 2 Sv ⎢⎣ ⎥⎦

Kp + c

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: S ref = 6 d max (dmax = the maximum particle/grain size of soil)

(5.32)

(5.33)

Therefore, the ultimate pressure carrying capacity, σ 1R , of a soil-geosynthetic composite mass is:

257

⎛

σ 1R = ⎜ σ 3 + W ⎝

where 5.1

Tf ⎞ ⎟ Kp + 2 c Kp Sv ⎠

(5.34)

σ 3 = confining pressure. 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, S ref = 6 d max = 7.8 in. (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

Δσ 3 (kN/m2)

245

172

86

407

305

188

2,700

1,750

1,300

2,460

1,900

1,250

-9%

+8%

-4%

by the Analytical Model CR (kN/m2) by the Analytical Model

(σ 1R − σ 3 ) (kN/m2) from Measured Data

(σ 1R − σ 3 ) (kN/m2) by the Analytical Model Difference between the Analytical Model and Measured Data

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

Δσ 3 (kN/m2)

350

350

175

550

550

310

2,700

1,750

1,300

3,250

3,250

1,930

+ 20 %

+ 86 %

+ 48 %

by Schlosser & Long’s Method CR (kN/m2) by Schlosser & Long’s Method

(σ 1R − σ 3 ) (kN/m2) from Measured Data

(σ 1R − σ 3 ) (kN/m2) by Schlosser & Long’s Method Difference between Schlosser & Long’s Method and Measured Data

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

d max = 0.5 in.

(or

12.7

mm);

therefore,

S ref = 6 d max = 3 in. (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.

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

TG

TG

TG

TG

TG

TG

TG

Type

500

500

600

700

800

1000

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

Δσ 3 (kN/m2) by the Analytical Model

30

8

47

48

62

67

83

60

36

78

79

94

99

116

230

129

306

292

402

397

459

256

153

333

341

402

426

498

11 %

18 %

9%

17 %

0%

7%

8%

CR (kN/m2) by the Analytical Model

(σ 1R − σ 3 ) (kN/m2) from Measured Data

(σ 1R − σ 3 ) (kN/m2) by the Analytical Model Difference between the Analytical Model and Measured Data

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

TG

TG

TG

TG

TG

TG

500

500

600

700

800

1000

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

Δσ 3 (kN/m2) by Schlosser & Long’s Method

59

30

92

95

122

132

163

91

59

126

130

158

169

202

230

129

306

292

402

397

459

390

254

541

557

678

726

868

70 %

97 %

77 %

91 %

69 %

83 %

89 %

CR (kN/m2) by Schlosser & Long’s Method

(σ 1R − σ 3 ) (kN/m2) From Measured Data

(σ 1R − σ 3 ) (kN/m2) by Schlosser & Long’s Method Difference between Schlosser & Long’s Method and Measured Data

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 Δσ 3 (kN/m2)

S3 = 34 kPa

S3 = 70 kPa

S3 = 100 kPa

S3 = 200 kPa

245

245

245

245

407

407

407

407

2,700

2,970

3,190

3,860

2,490

2,760

2,990

3,740

-8%

-7%

-6%

-3%

by the Analytical Model CR (kN/m2) by the Analytical Model

(σ 1R − σ 3 ) (kN/m2) from FE Analysis

(σ 1R − σ 3 ) (kN/m2) by the Analytical Model Difference between the Analytical Model and FE analyses

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: Trequired = σ h ∗ S v ∗ Fs

(5.35)

where Trequired =

required strength for reinforcement at depth z

σh =

horizontal stress in a GRS mass at depth z

Fs =

safety factor

Assuming Fs = 1, we have Trequired = T f (ultimate strength of reinforcement) and Equation 5.35 becomes Tf Sv

=σh

(5.36)

Note that when the horizontal stress, σ h , is a constant, the ratio

Tf Sv

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, σ h , in a GRS

structure at depth z is:

or

σ h = σ 3 + Δσ 3

(5.37)

Δσ 3 = σ h − σ 3

(5.38)

Since, Δσ 3 = W

Tf

(see Section 5.2.1)

Sv

(5.39)

Substituting Equation 5.39 into Equation 5.36 leads to

σh − σ3 =W or

Tf Sv

=

Tf

(5.40)

Sv

(σ h − σ 3 )

(5.41)

W

Since,

W = 0.7

⎛ Sv ⎜ ⎜6d max ⎝

⎞ ⎟ ⎟ ⎠

(5.42)

Therefore, Tf Sv

=

(σ h − σ 3 ) 0.7

⎛ Sv ⎜ ⎜6d max ⎝

(5.43)

⎞ ⎟ ⎟ ⎠

where Tf =

ultimate strength of reinforcement at depth z

σ h = horizontal stress in a GRS mass at depth z σ 3 = lateral constraint pressure at depth z, lateral earth pressure exerted by external constraint. For a GRS wall with modular block facing, σ 3 can be estimated as:

σ 3 = γ b b tan δ

(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:

Trequired

⎡ ⎤ ⎢ σh −σ3 ⎥ = ⎢ ⎛ S ⎞ ⎥ * S v * Fs v ⎜ ⎟ ⎢ 0.7 ⎜⎝ 6 d max ⎟⎠ ⎥ ⎣ ⎦

(5.45)

Note that Trequired is always equal or greater than zero. For a GRS mass without lateral constraint (e.g., a wrapped wall), σ 3 = 0, and Equation 5.45 becomes

Trequired

5.4.2

⎡ ⎤ ⎢ σh ⎥ = ⎢ ⎛ S ⎞ ⎥ * S v * Fs v ⎜ ⎟ ⎢ 0.7 ⎜⎝ 6 d max ⎟⎠ ⎥ ⎣ ⎦

(5.46)

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

Table 5.8: Comparison of reinforcement forces between proposed model and current design equation for a GRS wall Trequired (kN/m), for Fs = 1 z (m)

Current Design Equation

Proposed Model No Facing

Modular Block Facing with  bb = 35o

Modular Block Facing with  bb = 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, d max  38 mm ; unit weight of soil,

 backfill  17 kN/m3; unit weight of facing block,  block  25 kN/m3;  b b = friction angle between facing blocks; width of blocks, b = 0.3 m.

272

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 σ 3 (kPa)

34

34

34

0

62.4

74.4

50.5

41.2

- 11 %

- 47 %

- 28 %

- 41 %

79.4

124.1

75.4

58.8

+ 13 %

- 11 %

+8%

-16 %

Maximum Reinforcement Force from Current Design Equation, Equation 5.35 (kN/m) Difference between Current Design Equation (Equation 5.35) and Tf Maximum Reinforcement Force from Proposed Model, Equation 5.45 (kN/m) Difference between Proposed Model (Equation 5.45) and Tf

Note: Internal friction angle of soil, φ = 50o; cohesion of soil, c = 70 kPa; unit weight of soil, γ backfill = 24 kM/m3; maximum grain size of soil, d max = 33 mm .

273

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

4.47

2.35

6.95

6.49

10.08

9.91

11.94

- 50 %

- 74 %

- 50 %

- 57 %

- 47 %

- 50 %

- 52 %

9.02

9.56

14.02

13.10

20.34

20.01

24.09

0 %

+6 %

0 %

-13 %

+7 %

0 %

-4 %

Maximum Reinforcement Force from Current Design Equation, Equation 5.35 (kN/m) Difference between Current Design Equation (Equation 5.35) and Tf Maximum Reinforcement Force from Proposed Model, Equation 5.45 (kN/m) Difference between Proposed Model (Equation 5.45) and Tf

Note: Internal friction angle of soil, φ = 40o; cohesion of soil, c = 27.6 kPa; unit weight of soil, γ backfill = 18.8 kM/m3; lateral constraint pressure, σ 3 = 0 kPa; maximum grain size of soil, d max = 12.7 mm .

274

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 2dimensional 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 noncircular tunnels using arcs and lines. Plates and interfaces may be used to model the tunnel lining and the interaction with the surrounding soil.

276

Fully isoparametric

elements can be used to model the curved boundaries within the mesh. Various methods are available for the analysis of the deformation caused by various methods of tunnel construction. Mohr-Coulomb model: This non-linear model is based on soil parameters that are 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): ⎛ 0.7 E r Δσ 3 = Δσ v , c , max K i , c F ⎜⎜ 1 + E s S v − 0.7 E r ⎝

⎞ ⎟⎟ ⎠

(6.1)

where Δσ v ,c ,max is the maximum vertical stress due to compaction loading; F =1−

(OCR − OCR ) ; sin φ

OCR − 1

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, E s = 30,000 kPa; compaction lift S = 0.2 m.

•

Geosynthetics: E r = 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.

Residual Lateral Stress (kPa) 0 0

25

50

75

100

-1

Maximum Vertical Pressure due to Compaction:

Depth (m)

-2

44 kPa

-3

100 kPa

200 kPa

-4

300 kPa

-5

500 kPa

-6

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, E50ref , can be estimated from triaxial tests using Janbu’s equation (1963). The Poisson’s ratio of the backfill can be estimated as: •

σ ΔV = ε x + ε y + ε z = (1 − 2ν ) z V E

(for uniaxial tests)

•

(1 + ν ) (1 − 2ν ) σ z ΔV = εx +εy +εz = V E (1 − ν )

(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: E50ref = 62,000 kPa, Eurref = 124,000 kPa, Poisson’s ratio ν = 0.37

•

Power m = 0.5.

For the GSGC Tests, the backfill stiffness was increased due to CIS as described below: 1. Place the first lift of facing blocks and soil. The compaction lift thickness was 0.2 m.

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 ν min , as suggested by Hatami and Bathurst (2006). Soil modulus E50ref was calculated using the increase in confining pressure due to compaction. The value of E50ref can be estimated by using Equation 5.12 with σ '3 = σ '3 S + Δσ 3 , where Δσ 3 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 Material: Diabase; Soil model: Hardening soil model; dry unit Soil

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, E50ref = 63,400 kPa,

Eurref = 126,800 kPa; Poisson’s ratio ν = 0.2; power, m = 0.5. GSGC

Single-sheet Geotex 4x4: axial stiffness, EA = 1,000

Test 2

kN/m; ultimate strength, Tult = 70 kN/m; reinforcement spacing, Sv = 0.2 m;

Reinforcement

GSGC

Double-sheet Geotex 4x4: axial stiffness, EA = 2,000

Test 3

kN/m; ultimate strength, Tult = 140 kN/m; reinforcement spacing, Sv = 0.4 m

FE Model: linear elastic model; modulus, E = 3*107 kPa; unit Facing Block

weight, γ = 12.5 kN/m3 (hollow blocks); Poisson’s ratio, ν = 0.

Block-Block

FE Model: Mohr-Coulomb model; modulus, E = 3*106 kPa;

Interface

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

900

Applied Vetical Stress (kPa)

800 700 600 500 400 300 200

FE Analysis

100

Measured Data

0 0

1

2

3

4

5

6

7

Global Vertical Strain (%)

(a) 1.4 1.2

Volumetric Strain (%)

1 0.8 0.6 0.4

Mearsued Data

0.2

FE Analysis

0 -0.2

0

0.5

1

1.5

2

2.5

3

3.5

-0.4 -0.6

Global Vertical Strain (%)

(b) Figure 6.2: Comparison of Results for GSGC Test 1: (a) Global Vertical Stress-Strain Relationship, and (b) Volume Change Relationship

288

2

1.75

Applied Pressure

1.5

Specimen Height (m)

200 kPa (Measured) 1.25

400 kPa (Measured) 600 kPa (Measured)

1

770 kPa (Measured) 0.75 200 kPa (FE)

0.5

400 kPa (FE)

600 kPa (FE) 0.25 770 kPa (FE) 0 0

10

20

30

40

50

Lateral Displacement (mm)

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

3500

3000

Deviatoric Stress (kPa)

2500

2000

1500

1000

Measured Data 500 FE Analysis-w ithout CIS FE Analysis-w ith CIS 0 0

2

4

6

8

10

Global Vertical Strain (%)

Figure 6.4:

Comparison of Global Stress-Strain Relationship of GSGC Test 2

291

2

1.75

Applied Pressure: 2500 kPa (Measured)

Specimen Height (m)

1.5

2000 kPa (Measured)

1.25

1000 kPa (Measured) 1

400 kPa (measured) 2500 kPa (FE)

0.75

2000 kPa (FE)

0.5

1000 kPa (FE) 0.25 400 kPa (FE) 0 0

20

40

60

Lateral Displacement (mm)

Figure 6.5:

Comparison of Lateral Displacement at Open Face of GSGC Test 2

292

0 -80

-60

-40

-20

0

20

40

60

80 Point 1 (Measured) Point 2 (Measured)

-20

Point 3 (Measured) Point 4 (Measured)

-40

Point 6 (Measured)

y (mm)

-60

Point 7 (Measured) Point 8 (Measured)

-80 Point 9 (Measured) Point 1 (FE)

-100

Point 4 (FE) Point 7 (FE)

-120

Point 3 (FE) -140

Point 6 (FE) Point 9 (FE)

-160 Note: Locations of Points are show n in Figure 4.49

x (mm)

Figure 6.6:

Comparison of Internal Displacements of GSGC Test 2

293

Applied Pressure 2.5

200 kPa (Measured) 600 kPa (Measured) 800 kPa (Measured) 1000 kPa (Measured)

Strain (%)

2 1.5 1

200 kPa (FE) 0.5 600 kPa (FE) 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

800 kPa (FE) 1000 kPa (FE)

(a)

Applied Pressure: 3.5

1

200 kPa (Measured) 600 kPa (Measured) 800 kPa (Measured) 1000 kPa (Measured) 200 kPa (FE)

0.5

600 kPa (FE)

3

Strain (%)

2.5 2 1.5

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

800 kPa (FE) 1000 kPa (FE)

(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

2,000

1,800

1,600

Deviatoric Stress (kPa)

1,400

1,200

1,000

800

600

400 Measured Data 200 FE Analyses 0 0

Figure 6.8:

1

2

3 4 Global Vertical Strain (%)

5

6

7

8

Comparison of Global Stress-Strain Relationship of GSGC Test 3

296

2

1.75

Applied Pressure: 400 kPa (Measured)

1.5

Specimen Height (m)

600 kPa (Measured) 1.25

800 kPa (Measured) 1,000 kPa (Measured)

1 1,250 kPa (Measured) 0.75

400 kPa (FE) 600 kPa (FE)

0.5 800 kPa (FE) 1,000 kPa (FE)

0.25

1,250 kPa (FE) 0 0.0

10.0

20.0

30.0

Lateral Movement (mm)

Figure 6.9:

Comparison of Lateral Displacement at Open Face of GSGC Test 3

297

0 -80

-60

-40

-20

0

20

-20

40

60

80

Point 1 (Measured)

Point 2 (Measured)

Point 3 (Measured)

-40

Point 4 (Measured)

y (mm)

-60 Point 6 (Measured) -80 Point 1 (FE)

-100

Point 3 (FE)

Point 4 (FE)

-120

Point 6 (FE) -140 Note: Locations of Points are show n in Figure 4.57

x (mm)

Figure 6.10:

Comparison of Internal Displacements of GSGC Test 3

298

Applied Pressure 4.5

2.0

260 kPa (Measured) 600 kPa (Measured) 1000 kPa (Measured) 260 kPa (FE)

1.5

600 kPa (FE)

4.0

Strain (%)

3.5 3.0 2.5

1.0 1000 kPa (FE)

0.5 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(a)

Applied Pressure 3.5

260 kPa (Measured) 600 kPa (Measured) 1000 kPa (Measured) 200 kPa (FE)

3

Strain (%)

2.5 2

`

1.5

600 kPa (FE)

1 0.5

1000 kPa (FE)

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

Distance from the Edge of the Composite Mass (m)

(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

4,500 4,000

Deviatoric Stress (kPa)

3,500 3,000 2,500 Confining Pressure: 2,000 34 kPa (Measured) 1,500 34 kPa (FE) 1,000 100 kPa (FE) 500 200 kPa (FE) 0 0

1

2

3

4

5

6

7

8

9

Global Vertical Strain (%)

(a)

Confining Pressure: 2

Volumetric Strain (%)

34 kPa (T2) 1 34 kPa (FE)

0 0

2

4

6

-1

8

10 100 kPa (FE)

-2

200 kPa (FE)

-3 34 kPa (Soil - T1) -4

Global Vertical Strain (%)

(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, E s = 30,000 kPa; unloading modulus,

Eur = 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 E r = 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

Residual Lateral Stress (kPa)

Residual Lateral Stress (kPa)

0

0

0

25

50

75

-1

0

75

100

125

Lateral Stress Distribution w ithout Considering CIS

-2

Lateral Stress Distribution w ith Considering CIS (200 kPa) -3 Residual Lateral Stress (due to Maximum Vertical Compaction Pressure of 200 kPa)

-4

Depth (m)

Depth (m)

50

-1

Lateral Stress Distribution w ithout Considering CIS

-2

Lateral Stress Distribution w ith Considering CIS (500 kPa) -3

-5

-6

-6

(a)

Residual Lateral Stress (due to Maximum Vertical Compaction Pressure of 500 kPa)

-4

-5

Figure 6.14:

25

(b)

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

Residual Lateral Stress (kPa) 0 0

25

50

75

100

-1

Maximum vertical pressure due to compaction:

-2

Depth (m)

200 kPa (Model)

-3

500 kPa (Model)

200 kPa (FE) -4 500 kPa (FE)

-5

-6

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

Residual Lateral Stress (kPa) 0 0

25

50

75

100

-1

Maximum vertical pressure due to compaction:

-2

Depth (m)

200 kPa (Model)

300 kPa (Model)

-3

500 kPa (Model)

-4

200 kPa (FE)

300 kPa (FE) -5 500 kPa (FE)

-6

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

307

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 compactioninduced 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

and the angle of dilation provides a quantitative measure of the degree of reinforcing effect of a GRS mass.

310

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:

G =

1 P1 P2 + 100 G 1 100 G

3.03 2

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, (%)

312

0.433

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 Actual average water content, %

1

2

3

4

6.06

7.63

8.57

9.63

5

6

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

151.05

153.52

157.39

155.54

152.16

149.9

Dry density, (pcf)

313

3

Dry Density (g/cm )

2.40

2.35 3 γ d (max) = 2.3 (g/cm )

2.30

2.25

2.20 Wopt = 8.57 % 2.15 2

3

4

5

6

7

8

9

10

11

12

Water Content (%)

Figure A.1:

Moisture-Density Curve for Size Fractions Passing Sieve # 4

314

13

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 Water on Sieve Content #4 (%) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

8.57 8.5 8.4 8.3 8.2 8.2 8.1 8.0 7.9 7.8 7.8 7.7 7.6 7.5 7.4 7.3 7.3 7.2 7.1 7.0 6.9 6.9 6.8 6.7

Percent Retained Water on Sieve Content #4 (%)

Dry Density 144 144.2 144.5 144.7 144.9 145.2 145.4 145.6 145.8 146.1 146.3 146.5 146.8 147.0 147.2 147.5 147.7 147.9 148.1 148.4 148.6 148.8 149.1 149.3

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

316

6.6 6.5 6.5 6.4 6.3 6.2 6.1 6.0 6.0 5.9 5.8 5.7 5.6 5.6 5.5 5.4 5.3 5.2 5.2 5.1 5.0 4.9 4.8 4.7

Dry Density 149.5 149.8 150.0 150.2 150.4 150.7 150.9 151.1 151.4 151.6 151.8 152.1 152.3 152.5 152.7 153.0 153.2 153.4 153.7 153.9 154.1 154.4 154.6 154.8

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

3/8''

4

10

40

60

100

200

Diameter (mm)

9.5

4.75

2

0.425

0.25

0.106

0.075

Mass of Container + Soil Retained

Percent Retained

Percent Passing

(%)

(%)

(g)

Soil Retained (g)

389.2

217.9

29.1

70.9

(361.9)

(190.7)

(27.9)

(72.1)

490.5

101.3

13.5

57.4

(451.6)

(89.7)

(13.1)

(58.9)

598.4

107.9

14.4

43.0

(548.6)

(97.0)

(14.2)

(44.7)

724.7

126.3

16.9

26.1

(668.1)

(119.5)

(17.5)

(27.2)

756.8

32.1

4.3

21.8

(699.5)

(31.4)

(4.6)

(22.6)

786.8

30.0

4.0

17.8

(725.9)

(26.4)

(3.9)

(18.7)

810.6

23.8

3.2

14.6

(754.2)

(28.3)

(4.2)

(14.6)

14.6

0

(14.6)

(0)

<200

318

80 70

50 40 30 20

Percent finer (%)

60

10

100

10

1

0.1

0 0.01

Grain size (m m )

Figure A.2:

Grain Size Distribution for Samples 1 and 2

319

Test 1 Test 2

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

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

5.2

5.2

5.2

5.2

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

Confining Pressure

C1 = 10.3 psi,

from 0 to 30 psi

φ1 = 50o, ψ = 12.1o

Confining Pressure

C2 = 35.1 psi, φ2 = 38o

Confining Pressure (psi)

Water Content (%) Failure Condition

Strength Parameters

from 30 psi to 70 psi

332

Deviatoric Stress versus Axial Strain Relationships 600 550 500 5 psi

Deviatoric Stress (psi)

450 400

15 psi

350 300

30 psi

250 70 psi

200 150

70 psi - Ketchart

100 50

110 psi - Ketchart

0 0

1

2

3

4

5

6

7

8

9

10

11

Axial Strain (%)

(a)

Volumetric Strain (%)

Volumetric Strain versus Axial Strain 0.6 0.4 0.2

5 psi

0 -0.2

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-0.4 Axial Strain (%)

(b) Figure A.13: Triaxial Test Results: (a) Stress-Strain Curves (b) Volume Change Curves

333

3.5

4.0

30 psi

σ

Shear Streess (psi)

3

σ

3

σ

3

σ

3

σ

C2 = 35.1 psi

3

= 110 psi

= 70 psi

= 30 psi

= 15 psi

= 5 psi

C1 = 10.3 psi 0

30

98

172

265

433

Normal Stress (psi)

Figure A.14: Mohr Circles of the Stress at Failure

334

616

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 Wide-Width Tensile Strength Geosynthetic Type

ASTM D 4595 Stiffness at

Ultimate

Strain at Break

1% Strain

Strength

(%)

(kN/m)

(kN/m)

Single-sheet Geotex 4x4

1,000

70

12 %

Double-sheet Geotex 4x4

1,960

138

12 %

338

160

Tensile Load (kN/m)

140 120 100 80 60

Single sheet

40

Double Sheets

20 0 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

Axial Strain (%)

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-08250BG-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 doublesheet specimens, respectively.

342

Strain from Instron Machine (%)

6 5

y = 1.172x 2 R = 0.9913

4 3 2 1 0 0

1

2

3

4

Strain from Strain Gage (%)

Figure A.18: Calibration Curve for Single-Sheet Geotex 4x4

343

5

Strain from Instron Machine (%)

6

5 y = 1.078x R2 = 0.9986 4

3

2

1

0 0

1

2

3

4

Strain from Strain Gauge (%)

Figure A.19: Calibration Curve for Double-Sheet Geotex 4x4

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5

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:

q = 500 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:

⎛ q l2 M req = ⎜⎜ ⎝ 8

⎞ ⎛ (500 kPa ) * (2.074 / 7 ) * (1.835 m )2 ⎟⎟ = ⎜ ⎜ 8 ⎠ ⎝

⎞ ⎟ = 62.4 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:

M allow = M top and bottom + M 2 sides

in which,

(

)(

)[

)(

]

Mtop and bottom = A* h *[σ steel] = 6.35*10−3 * 50.8*10−3 * (304.8 − 6.35) *10−3 * 3.17*105 = 30.5 kN.m

M 2 sides = S x

(2 * 6.35 *10 )* ((304.8 − 2 * 6.35) *10 ) * [3.17 *10 ] = 57.2 * [σ ] = 6 −3 2

−3

5

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: ⎛ (500 kPa) * (2.074/ 7) * (1.835 m) ⎞ ⎛ql⎞ −6 ⎟ / (50.8 + 304.8) * 2 * 6.35*10 = 30,097 ⎟ /( A) = ⎜ 2 2 ⎠ ⎝ ⎝ ⎠

(

σ req = ⎜

)

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:

(

⎛ (500 kPa ) * 11.4' '*25.4 * 10 −3 m ⎛ql⎞ Qreq = ⎜ ⎟ / (2 bolts ) = ⎜⎜ 2 ⎝ 2 ⎠ ⎝

) ⎞⎟ / 2 = 36.2 kN ⎟ ⎠

The required shear stress will be:

σ req =

Q 36.2 = A π * 7 / 8' '*2.54 * 10 −3

(

)

2

= 93,311 kPa = 13,436 psi = 13.4 kpsi

/4

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:

M req

⎛ q l2 = ⎜⎜ ⎝ 12

⎞ ⎛ (500 kPa ) * (2.074 / 7m )2 ⎟⎟ = ⎜ ⎜ 12 ⎠ ⎝

⎞ ⎟ = 3.66 kN.m ⎟ ⎠

The maximum required stress is: ⎛ M req

σ req = ⎜⎜ ⎝ Sx

⎛ ⎜ ⎞ ⎜ 3.66 ⎟⎟ = 2 ⎠ ⎜⎜ (1m ) * (1.25' '*25.4 / 1000 ) 6 ⎝

⎞ ⎟ ⎟ = 21,784 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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