INVESTIGATING COMPOSITE BEHAVIOR OF GEOSYNTHETIC
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
REINFORCED SOIL (GRS) MASS
by
Thang Quyet Pham
2009
This thesis for the Doctor of Philosophy
degree by
Thang Quyet Pham
has been approved
by
Brian T. Brady
Date
Thang Quyet Pham (Ph.D., Civil Engineering)
Investigating Composite Behavior of GeosyntheticReinforced 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 largesize Generic SoilGeosynthetic Composite (GSGC) tests were
designed and conducted in the course of this study to examine the behavior of
GRS mass under wellcontrolled 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
soil mass, and the required tensile strength of reinforcement for a prescribed value
of spacing can be determined. The model was verified by using measured data
from the GSGC tests, measured data from largesize experiments by other
researchers, and results of the finite element method of analysis. Since GRS walls
with modular block facing are inherently flexible, an analytical procedure was
also developed to predict the lateral movement of the wall system. The procedure
also allows the required tensile strength of the reinforcement to be determined by
simple handcalculations. In addition, compactioninduced stresses which have
usually not been accounted for in design and analysis of GRS structures were
investigated. An analytical model for calculating compactioninduced stresses in
a GRS mass was proposed. Preliminary verification of the model was made by
using results from the GSGC tests and finite element analysis. The dilative
behavior of a GRS composite was also examined. The presence of geosynthetic
reinforcement has a tendency to suppress dilation of the surrounding soil, and
reduce the angle of dilation of the soil mass. The dilative behavior offers a new
explanation of the reinforcing mechanism, and the angle of dilation may be used
to reflect the degree of reinforcing of a GRS mass.
This abstract accurately represents the content of the candidates thesis. I
recommend its publication.
Signed
/
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 HonYim Ko, John McCartney, Brian Brady, and Ronald
Rorrer for their helpful comments.
A special thankyou 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 threemonth stay at the TumerFairbank
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
TurnerFairbank 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 CompactionInduced 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 CompactionInduced Stress Models by Seed (1983).....................40
2.4 CompactionInduced 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 CompactionInduced 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 JewellMilligan 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
3.2.4 Required Tensile Strength of Reinforcement of GRS Walls...............92
3.3 Verification of Analytical Model......................................93
3.3.1 Comparisons with the JewellMilligan Method for Lateral Wall Movement..93
3.3.2 Comparisons of with Measured Data of FullScale Experiment by Hatami and
Bathurst (2005 and 2006)..............................................99
3.4 Summary .............................................................103
4. The Generic SoilGeosynthetic 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 1Unreinforced Soil.............................................163
viii
4.6.2 Test 2GSGC Test (T, Sv).............................................169
4.6.3 Test 3GSGC Test (2T, 2SV)...........................................187
4.6.4 Test 4GSGC Test (T, 2SV)............................................199
4.6.5 Test 5GSGC 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 Patawarans Test
Data.................................................................261
5.3.3 Comparison of the Results between the Analytical Model and Finite Element
Results..............................................................266
IX
5.4 Required Reinforcement Strength in Design.........................268
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 CompactionInduced 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 SoilGeosynthetic Composites....................300
6.5 Verification of CompactionInduced 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 CrossSection 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 StressStrain Curves of Samples Reinforced at Spacing of 12 in. and 6 in.
in LargeSize Unconfined Compression Tests (Elton and Patawaran,
2005)...................................................................18
2.7 Mini Pier Experiments (Adams, 1997).....................................19
2.8 StressStrain Curve (Adams, et al., 2007)...............................20
2.9 Test Setup of Large Triaxial Tests with 1,100 mm High and 500 mm in
Diameter (Ziegler, et al., 2008)........................................21
2.10 LargeSize Triaxial Test Results (Ziegler, et al., 2008)................22
2.11 Vertical Stress Distribution at 6kN Vertical Load of the GRS Masses with
and without Reinforcement (Ketchart and Wu, 2001).......................24
2.12 Horizontal Stress Distribution at 6kN Vertical Load of the GRS Masses
with and without Reinforcement (Ketchart and Wu, 2001)..................25
2.13 Shear Stress Distribution at 6kN Vertical Load the GRS Masses with and
without Reinforcement (Ketchart and Wu, 2001)...........................26
2.14 Schematic Illustration of Rowes Theory (Rowe, 1954)....................29
2.15 Results of the TwoDirectional 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 FirstCycle KoReloading Model (Seed, 1983)......................41
2.21 Suggested Relationship between simj) and a (Seed, 1983).............42
2.22 Typical KoReloading Stress Paths (Seed, 1983).......................43
2.23 KoUnloading following Reloading (Seed, 1983)........................45
2.24 Unloading after Moderate Reloading (Seed, 1983)......................47
2.25 Basic Components of the NonLinear KoLoading/Unloading Model (Seed,
1983)................................................................49
2.26 Profile of kah 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 BiLinear Approximation of NonLinear KoUnloading Model (Seed,
1983)................................................................52
2.29 Relationship between K2 and F in the BiLinear Unloading Model (Seed,
1983)................................................................52
2.30 Relationship between K3 and Pi in the BiLinear Model (Seed, 1983)...53
2.31 Basic Components of the BiLinear Model (Seed, 1983).................55
2.32 Compaction Loading/Unloading Cycles in the BiLinear 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 BiLinear Model and NonLinear 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
Xll
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 Zj..........................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 JewellMilligan
Method and the Analytical Model, n = 0..................................95
3.12 Comparison of Lateral Displacement Calculated by JewellMilligan
Method and the Analytical Model, yh = 10 ...............................96
3.13 Comparison of Lateral Displacement Calculated by JewellMilligan
Method and the Analytical Model, n = 20.................................97
3.14 Comparison of Lateral Displacement Calculated by JewellMilligan
Method and the Analytical Model, n = 30.................................98
3.15 Configuration of a FullScale Experiment of a GRS Wall with Modular
Block Facing (Hatami and Bathurst, 2005 and 2006).......................100
3.16 Comparisons of Measured Lateral Displacement with JewellMilligan
Method and the Analytical Model........................................102
4.1 Typical Geometric and Loading Conditions of a GRS Composite.............107
4.2 Global StressStrain Curves for SoilGeosynthetic Composites of Different
Dimensions under a Confining Pressure of 0 kPa..........................109
4.3 Global Volume Change Curves for SoilGeosynthetic Composites of
Different Dimensions under a Confining Pressure of 0 kPa................110
xiii
4.4 Global StressStrain Curves for SoilGeosynthetic Composites of Different
Dimensions under a Confining Pressure of 30 kPa......................Ill
4.5 Global Volume Change Curves for SoilGeosynthetic Composites of
Different Dimensions under a Confining Pressure of 30 kPa............112
4.6 Global StressStrain 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 MohrCoulomb Failure Envelops of Backfill............................127
4.16 UniAxial Tension Test of Geotex 4x4.................................130
4.17 LoadDeformation 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 SingleSheet Geotex 4x4........................141
4.22 Calibration Curve for DoubleSheet 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 mmthick 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 1Unreinforced 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 Closeup 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 2Reinforced 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 StressStrain 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 StressStrain 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 StressStrain 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 II as Compaction Loads Moving toward Section
I1.................................................................243
5.4 Locations of Compaction Loads and Stress Paths during Compaction at
Depth a along Section II as Compaction Loads Moving away from Section
II.................................................................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 PlaneStrain 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 LargeSize Triaxial Tests
(Elton and Patawanran, 2005)........................................263
5.12 LargeSize 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 StressStrain 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 StressStrain 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 NoneLinear Koloading/unloading model parameters (Seed, 1983)........48
2.3 BiLinear Koloading/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 filldirection...........................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 Longs method and GSGC
tests..............................................................260
5.5 Comparison of the results between the analytical model and Elton and
Patawarans tests (2005)...........................................264
5.6 Comparison of the results between Schlosser and Longs method and Elton
and Patawarans 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, GeosyntheticReinforced Soil (GRS) structures, including
retaining walls, slopes, embankments, roadways, and loadbearing foundations, have
gained increasing popularity in the U.S. and abroad. In actual construction, GRS
structures have demonstrated a number of distinct advantages over their conventional
counterparts. GRS structures are generally more ductile, more flexible (hence more
tolerant to differential settlement and to seismic loading), more adaptable to low
permeability backfill, easier to construct, require less overexcavation, and more
economical than conventional earth structures (Wu, 1994; Holtz, et ah, 1997;
Bathurst, et ah, 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 geosyntheticreinforced 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 geosyntheticreinforced
soil mass, however, is always a compacted soil mass reinforced by layers of
geosynthetic reinforcement.
It is a wellknown 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 soilreinforcement 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
atrest pressure that is assumed to be unaffected by the configuration of the
reinforcement. Specifically, the design strength of the reinforcement, Trequired, has
been determined by multiplying an assumed lateral earth pressure at a given depth,
ah, by a prescribed value of reinforcement spacing, Sv, and a safety factor, Fs, i.e.,
Treared = 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 Oh (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 TurnerFairbank Highway Research Center have conducted a
series of fullscale 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 loadtested. The
former was found to be much stronger than the latter. An indepth 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 lockedin 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 lockedin lateral stresses are likely to become larger.
3
In numerical analysis of earth structures, the effects of CIS has either been overly
simplified (e.g., Katona, 1978; Hatami and Bathurst, 2005 and 2006; Morrison, et al.,
2006), or in most other studies, totally neglected. In the case of GRS walls, failure to
account for the CIS may be a critical culprit that has lead to the erroneous conclusion
by many numerical studies that Equation 1.1 is valid. Evaluation of compaction
induced stresses in GRS structures is considered a very important issue in the study of
GRS structures.
In addition, GRS walls with modular block facing is rather flexible, hence the
design of these structures should consider not only the stresses in the GRS mass, but
also the deformation. JewellMilligan 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 JewellMilligan method for calculating lateral wall movement is needed.
1.2 Research Objectives
The objectives of this study were fourfold. The first objective was to investigate the
composite behavior of GRS masses with different reinforcing configurations. The
second objective was to examine the relationship between reinforcement strength and
reinforcement spacing regarding their effects on the behavior of a GRS mass. The
third objective was to develop an analytical model for evaluation of compaction
induced stresses in a GRS mass. The fourth objective was to develop an analytical
model for predicting lateral movement of a GRS wall with modular block facing.
4
1.3 Tasks of Research
To achieve the research objectives outlined above, the following tasks were carried
out in this study:
Taskl: Reviewed previous studies on: (a) composite behavior of a GRS mass, (b)
compactioninduced stresses in a soil mass, and (c) reinforcing mechanism
of GRS structures.
Previous studies on composite behavior of a GRS mass were reviewed. The
review included theoretical analyses and experimental tests. Compaction
induced stresses in an unreinforced soil mass that have been undertaken by
different researchers were also reviewed, including simulation models for
fill compaction. In addition, a literature study on reinforcing mechanisms of
GRS structures was conducted.
Task 2: Developed a handcomputation analytical model for simulation of
compactioninduced stresses in a GRS mass.
An analytical model for simulation of CompactionInduced 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 compactioninduced stress in a GRS mass to be
evaluated by hand computations. The CIS was implemented into a finite
element computer code for investigating performance of GRS structures.
Task 3: Developed an analytical model for the relationship between reinforcement
strength and reinforcement spacing, and derived an equation for calculating
composite strength properties.
An analytical model for the relationship between reinforcement strength and
reinforcement spacing was developed. Based on the model and the average
5
stress concept for GRS mass (Ketchart and Wu, 2001), an equation for
calculating the composite strength properties of a GRS mass was derived.
The model represents a major improvement over the existing model that has
been used in current design methods, and more correctly reflects the role of
reinforcement spacing versus reinforcement strength on the behavior of a
GRS mass. The equation allows the strength properties of a GRS mass to be
evaluated by a simple method.
Task 4: Designed and conducted laboratory experiments on a generic soil
geosynthetic composite to investigate the performance of GRS masses with
different reinforcing conditions.
A generic soilgeosynthetic 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 stressstrain and volume
change behavior representative of a very large soilgeosynthetic 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 stressstrain 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 fullscale experiment of a GRS wall with modular block facing. The
analytical model can be used in design for determining the required design
strength of reinforcement for a prescribed value of maximum allowable
lateral wall movement.
7
Figure 11: Typical CrossSection 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 GeosyntheticReinforced Soil (GRS) mass, and CompactionInduced
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 Gi to ctir (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
value for unreinforced sand
and reinforced sand were about the same as long as slippage at the soilreinforcement
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 cti to 0ir
(with an increase of confining pressure Act3r), as shown in Figure 2.2, due to the
tensile inclusion. The value of A<73r can also be determined from a series of triaxial
tests, again by assuming that <)> 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 Aa3R is:
Aa}li = 4
(2) From Figure 2.1 and Figure 2.2 and using Rankines earth pressure
equate the principal stress at failure ctir
Referring to Figure 2.1,
cj\r= + yjKp
Referring to Figure 2.2,
a\r = ^irKp
Knowing
a3R = "3 C + A&ir
Equation 2.3 can be written as:
G\R = aiR^P ~ (^3C + ^*^3r)K~p
Equating Equations 2.2 to Equation 2.5, we obtain
r ^^iRyl^p
Cr 2
(3) Substituting equation 2.1 into equation 2.6,
, T,J^
(2.1)
theory to
(2.2)
(2.3)
(2.4)
(2.5)
(2.6)
Cr =
2 S
(2.7)
Equation 2.7 may be very useful for evaluating the stability of a reinforced soil mass.
Given a granular soil with strength parameters c (c = 0) and <)>, Equation 2.7 allows
the strength parameters of a reinforced soil mass (cr and ())r) 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
Tf
key assumption involved in the derivation the assumption of AcriR = (this
Sv
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 A
2.2) based on the explanation given by Schlosser and Long (1972) and Yang (1972);
and it was Acr3 < Rr / Sv in Hausmanns study (1976), where Rr = Tf.
13
(Ref. 13)
Schlosser and long
0972)
Rr Vkr
'STT
CRef. u)
Yang
(1972)
A cr _M_
3 Sv
(Ref. 15)
Hausmann
(1976)
, . 1+F,Ka
1F3+Ka
FS
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 soilgeosynthetic composites have been investigated through
different types of laboratory experiments, including: smallsize triaxial compression
tests with the specimen diameter no greater than 6 in. (Broms, 1977; Gray and Al
Refeai, 1986; Haeri et al., 2000; etc), largesize triaxial compression tests (Ziegler et
al., 2008), largesize unconfined compression tests (Elton and Patawaran, 2005),
unconfmed compression tests with cubical specimens (Adams, 1997 and Adams et
ah, 2007), and plane strain tests (Ketchart and Wu, 2001).
Figure 2.4 shows the effects of reinforcement layers on the stiffness and strength of
soilgeosynthetic 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 stressstrain 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 smallsize 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 compactioninduced stresses
are not simulated properly. For these reasons, a number of largersize 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 stressstrain curves of the specimens reinforced by TG500 at spacing of
12 in. and 6 in. It can be seen that the strength of the soilgeosynthetic composite was
much higher at 6 in. spacing than at 12 in. spacing.
(a) (b)
Figure 2.5: Unconfmed Test Specimen (a) before and (b) after Testing
(Elton and Patawaran, 2005)
17
Stress Strain curves
Vertical Strain eu (%)
Figure 2.6: Stress Strain Curves of Specimens Reinforced at Spacing of 12 in.
and 6 in. in LargeSize Unconfined Compression Tests
(Elton and Patawaran, 2005)
Five unconfined mini pier experiments were conducted by Adams and his
associates (Adams, 1997 and Adams et al., 2007). The dimensions of the specimen
were 2.0 m high, 1.0 m wide and 1.0 m deep. The test results showed that the load
carrying capacity is affected strongly by the spacing of the reinforcement, and not
significantly affected by the strength of the reinforcement. Figure 2.7 shows a photo
of the mini pier experiment and Table 2.1 shows the material properties and test
conditions for the tests. The stressstrain 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
Table 2.1: Properties of materials for the mini pier experiments (Adams et al., 2007)
Experiment Fill Avg. Density (kN/nr)
MP NR 22.4
MPA 23.0
MP B 22.7
MP C (Not Available)
MP D 22.8
Geotextile Reinforcement Schedule
Polypropylene type 1% Strength (kN/m) iLfi? Spacing (m)
none IB none iP none
A2044 w 70.0 0.40.6
A2044 w 70.0 0.4
A2000 Ty} 21.0 'V.* 0.2
A2044 70.0 0.2
19
Figure 2.8: StressStrain Curves of MiniPier Experiments (Adams et al., 2007)
Figure 2.9 shows the setup of the largesize 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
hydraulic plunger
(a) Schematic Diagram
(b) LargeSize Triaxial Load Cell
Figure 2.9: Test Setup of LargeSize 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 LargeSize Triaxial Test
21
LoadStrainCurves (o3 = 30kN/m2)
vertical strain of probe [%]
7 Layers
5 Layers
3 Layers
2 Layers
1 Layer
unreinforced
Figure 2.10: LargeSize Triaxial Test Results (Ziegler et al., 2008)
The behavior of soilgeosynthetic composites have also been investigated through
numerical analysis. Examples of these studies include Lee, 2000; Chen et al., 2000;
Holtz and Lee, 2002; Zhang et al., 2006; Ketchart and Wu, 2001; and Vulova and
Leshchinsky, 2003.
Vulova and Leshchinsky (2003) conducted a series of analyses using a two
dimensional finite difference program FLAC Version 3.40 (1998). From the analysis,
it was concluded that reinforcement spacing was a major factor controlling the
behavior of GRS walls. The analysis of GRS walls with reinforcement spacing varied
from 0.2 m to 1.0 m showed that the critical wall height (defined as a general
characteristic of wall stability) always increased when reinforcement spacing
22
decreased. Reinforcement spacing also controls the mode of failure of GRS walls. In
these analyses, compaction induced stresses in soil were not included.
Comparisons of the stress distribution in a soil mass with and without reinforcement
were made by Ketchart and Wu (2001). The reinforcement was a medium strength
woven geotextile (with widewidth 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
600
450
400
Â£
Â£
O'
X
c
Cl
C/3
20 GO 100
Distance from Center Line (mm)
i i i i i
20 60 100
Distance from Confer Line (mm)
(a) Vertical Stress at 6 kN (b) Vertical Stress at 6 kN
Of Test PMRB Of Test PM; RB+2044)
Figure 2.11: Vertical Stress Distribution at 6kN Vertical Load of the GRS Masses
(a) with and (b) without Reinforcement (Ketchart and Wu, 2001)
24
20 60 100 20 60 100
Distance from Center Line (mm) Distance from Center Line (mm)
(a) Horizontal Stress at 6 kN (b) Horizontal Stress at 6 kN
Of Test PMRB of Test PM(RB+2044)
Figure 2.12: Horizontal Stress Distribution at 6kN Vertical Load of the GRS
Masses (a) with and (b) without Reinforcement (Ketchart and Wu, 2001)
25
600f
550
500
450
400
 350
Â£
S>
'o
1 300
a
Â£
8 250
o.
in
200
150
100
50
~I l i l l
20 60 100
Distance from Center Line (mm)
20 60 100
Distance from Center Line (mm)
(a) Shear Stress(xy) at 6 kN (b) Shear Stress(xy) at 6 kN
Of Test PMRB Of Test PMfRB+2044)
Figure 2.13: Shear Stress Distribution at 6kN Vertical Load the GRS Masses (a)
with and (b) without Reinforcement (Ketchart and Wu, 2001)
26
2.3 CompactionInduced Stresses in an Unreinforced Soil Mass
Many studies have been conducted to address the compactioninduced 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 atrest and fully active and
fully passive states. Rowes work did not directly address CIS, but it contributed
strongly to the later study by Broms (1971) on compactioninduced earth pressures.
Seed (1983), and Seed and Duncan (1984) had developed a simulation model called
the "bilinear hysteretic loading/unloading model" to simulate the compaction effect
on vertical, nondeflecting 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 atrest and fully active and
fully passive states. Rowes stressstrain theory for calculations of lateral pressures
exerted on structures by cohesionless soils was based on the following hypotheses:
The degrees of mobilization of the soil friction angle <> and the soilwall
friction angle 8 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 <)> and 8 values.
The basic mechanics of Rowes 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
(a) Slip Strains of a Typical Sliding Wedge
(b) Example ForceEquilibriuta Analysis for a
Typical Sliding Wedge
1 Weight of soil.
2 w Force exerted on sliding wedge by underlying soil.
3 Force exerted on sliding wedge by wall.
Fractional friction angles developed as a result of
slipstralna.
Figure 2.14: Schematic Illustration of Rowes 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 yho (y = unit weight of soil, ho =
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 (Ko) could be
expressed as:
f h x
1 + ^
V
(2.8)
y
where ho is the surcharge head removed and h is the overburden head (h = crv I y). In
any case, K0 < KH (Kp = coefficient of passive earth pressure at limiting condition).
Figure 2.15: Results of the TwoDirectional Direct Shear Tests (Rowe, 1954)
30
It is interesting to note the similarity between Rowes early equation for residual,
compactioninduced 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 Kocondition). Schmidt's equation
which empirically allow for some degree of relaxation of lateral stresses following
surcharge removal, can be expressed as:
*0 = ^0
( h 'a
1+^
h
J
where: a 0.3 to 0.5 for most sands
a = 1.2 sincj)' for initially normally consolidated clays
(2.9)
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, nonyielding 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 a'ho and cr'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 Ko (denoted by point B in Figure 2.16) where Ko is the
coefficient of earth pressure at rest. Thereafter, increased vertical stress is
accompanied by an increased lateral stress according to
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
Ki (denoted by point D in Figure 2.16). Thereafter, continued decrease in vertical
pressure is accompanied by a decrease in lateral stress according to
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 Kiline, 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^cllve < . 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 Ki = Kp (the coefficient of passive earth pressure) reasoning that the
limiting condition reached is essentially a form of passive failure.
Effective lateral earth pressure, Oh
Figure 2.16: Hypothetical Stress Path during Compaction (Broms, 1971)
32
By employing this theory to estimate the lateral pressure exerted on a vertical, rigid,
nonyielding 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 asc'^ = K0cr\ 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,
* ((< fitI
'***'?
(a) Single layer compacted
with 10.2 metric ton roller.
(b) Fill compacted in 0.5 m. (c) Generalized residual lateral
lifts with 10.2 metric ton earth pressure distribution,
roller.
'O
o
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
K0'=K,.
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
is greater than that at point D.
**ftt #rw*,d*4
a) Shallow Soil Element:
2 < 2
C
b) Deep Soil Element:
Z > 2
Figure 2.18: hypothetical Stress Paths of Shallow and Deep Soil Elements
(Broms, 1971)
35
Following the process above and knowing values of Ko and Ki, 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
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 compactioninduced lateral
pressure for each new layer will be surpassed in magnitude by the atrest 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
failure controlled the other limiting condition, therefore Ki = Kp.
2.3.3 Finite Element Analysis by Aggour and Brown (1974)
Aggour and Brown (1974) were the first to model compactioninduced lateral earth
pressure by twodimensional 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 Ei.
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 Ei 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
righthand boundary of the finite element mesh. The fill materials were placed in five
4ft 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 scalemodel 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 compactioninduced earth
pressures on yielding structures.
38
(b) Problem Analysed
Concrete:
Soil:
c
Vs
da
E
E
1
U
2
432 x 106 psf
150 psf
0.2
125 psf
0.3
36 x 103 psf
(c) Results of First Sample Problem
*<**! Hfcrl *( tmmim f pum (Ifl Hffl')
(d) Results of Second Sample Problem
Figure 2.19: A Sample Problem Analyzed by Aggour and Brown (1974)
39
2.3.4 CompactionInduced Stress Models by Seed (1983)
Seed (1983) proposed a method to estimate the effects of CIS and associated
deflections. Seed's study will be summarized in detail as it represents the most in
depth study on the subject of CIS. Seeds study involved the following three areas:
Compaction induced stresses due to different stress paths, including the first
cycle Koreloading stress path, typical Koreloading stress path, multicycle
Kounloading/reloading stress path, and Kounloading following reloading
stress path.
The nonlinear and bilinear hysteretic loading/unloading compaction models
for simulation of fill compaction behind vertical, nondeflecting structures.
Finite element analysis of fill compaction using the nonlinear and bilinear
models.
a) FirstCycle KoReloading Stress Path and Typical Kounloading/Reloading
Stress Path
Seed (1983) proposed what is termed firstcycle Koreloading 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 Koline to point A (see Figure 2.20), after which
the unloading stress path is followed by K\ = K0(OCR)a to an arbitrary point B prior
to reloading. Reloading is then assumed to follow a linear path to point R, the
intersection of the reloading path with the Koline, and again to follow the Koline
thereafter. Point R, the intersecting point of the reloading path with the virgin loading
path is determined as:
& h,r /i.min
+ P* A
(2.10)
40
(2.11)
. 1 .
O v,r O h,r
*o
In which A is the decrease in horizontal effective stress from the maximum loading at
point A to the minimum unloading at point B, P is assumed constant regardless of the
degree of unloading which precedes reloading (Figure 2.20), CT\mm is minimum
horizontal stress, a*v,r crYrare 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 = K0(OCR)a. The value a can be estimated by Equation 2.12 or by Figure 2.21:
a = 0.018 + 0.974 sin ' n\T\
41
13 20 25 30 35 40 45 50
o'
O Coheslonless Solis
A Cohesive Soils
Figure 2.21: Suggested Relationship between sin<)), and a (Seed, 1983)
42
Some typical results of using the model are illustrated in Figure 2.22. In this figure, p
remains constant but A varies with magnitude of unloading.
/
cr
h
Figure 2.22: Typical KoReloading Stress Paths (Seed, 1983)
In Figures 2.21 and 2.22, Kiline is at the limiting condition and defined as:
+
K, =tan"
2c' Jk ,,
45 +')
V 2)
(2.13)
(2.14)
where Ki, <(, = coefficient of passive lateral earth pressure, and
friction angle of soil.
43
b) MultiCycle KoUnloading/Reloading Stress Path and KoUnloading
Following Reloading Stress Path.
Seed (1983) proposed another model for multicycle Kounloading/reloading
conditions. The values a and p are assumed to remain constant regardless of the
number of loadingreloading 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 Koline to point A;
2. Unloading by following the Koline, with K0'= K0 (OCR.)a, to point B;
3. Reloading through point R then to point C, passing through previous
maximum loading point A;
4. Subsequent loadingunloading path is assumed to follow an atype path CD.
44
Figure 2.23: Kounloading 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 Koline to point A;
2. Unloading by following the Koline, with K0'= K0(OCR)a, to point B;
3. Reloading through point R to point C on the virgin Koline, but at a stress less
than the maximum previous loading point A;
4. Subsequent loadingunloading path is assumed to follow an a*type path CD
(a >a).
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 Koline. Subsequent loading is then modeled
as follows:
1. Point C is projected vertically down to point C on the Koline, 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 a*type (a > a) 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) NonLinear, MultiCycle KoUnloading/Reloading Compaction Model
The nonlinear, multicycle Kounloading/reloading model was developed based on
the stress paths described in Sections (a) and (b) above. The model requires five
material parameters: a, p, Ko, and c. The name of each model parameter,
recommended limits of each parameter, and the correlations with (j) are given in
Table 2.2.
47
Table 2.2: Nonlinear Koloading/unloading model parameters (Seed, 1983)
Parameter Name Recommended Limits Method of Estimation Based on
a Unloading coefficient 0 < a < 1
P Reloading coefficient fi = 0.6
Ko Coefficient of atrest lateral earth pressure for virgin loading 0'
K.,+ Frictional component of limiting coefficient of atrest lateral earth pressure for unloading K0 < K < Kp ( d)'^ Ku= tan2 45+ v 2J
c Effective stress strength envelope cohesion intercept
Note: K/ = Limiting coefficient of atrest lateral pressure for unloading
= K,&, ami K, K, ,. + ^ fiN
cr 3 v
Kp = Coefficient of passive lateral earth pressure
Basic component of the nonlinear Koloading/unloading model is described in Figure
2.25. In the figure, the Ki line is the stress path at limiting condition; Ko 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 NonLinear KoLoading/Unloading Model
(Seed, 1983)
The term Aa'h,vc,p (same as A 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 Aa'h,vc,p
resulted from surficial loading can be obtained from simple elastic solution, such as
Boussinesqs 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.
Boussinesqs solution is for a semiinfinite mass. For any point along a vertical non
deflecting wall, the change in lateral stress will be twice as much as the values
obtained from Boussinesqs solution.
49
Figure 2.26 (a) shows the distribution of Act'^vc.p for loads applied at different
distances under the condition that the soil is not underlain by a rigid base. The
distribution of Aa'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 Aa'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, AaV!o is remained because of the
soil weight of this layer). After compaction, Aa\r is residual horizontal stress in soil
at this layer.
Figure 2.26: Profiles of Aa'h.vc.p against a Vertical Wall for a Single Drum Roller
(Vlp/ft2)
6 ft.
50
CTh'
Figure 2.27: Stress Path associated with Placement and Compaction of a Typical
Layer of Fill (Seed, 1983)
d) Simplified BiLinear Approximation to the NonLinear Model
In this model, the atype nonlinear unloading model for the firstcycle unloading
is approximated by a bilinear 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 bilinear
unloading model is shown in Figure 2.29. Figure 2.30 shows the relationship
between K3 (slope of reloading path) and P3 (as defined in Figure 2.30) of the model.
The bilinear Koloading/unloading model parameters are described in Table 2.3.
51
Figure 2.28: BiLinear Approximation of Nonlinear Kounloading Model
Figure 2.29: Relationship between K2 and F in the BiLinear Unloading Model
(Seed, 1983)
52
Figure 2.30: Relationship between K3 and P3 in the BiLinear Model (Seed, 1983)
53
Table 2.3: Bilinear Koloading/unloading model parameters (Seed, 1983)
Parameter Name Recommended Limits Method of Estimation Based on f
K0 Coefficient of atrest lateral earth pressure for virgin loading 0 < K0 < 1 Same as nonlinear model (Recommended K0 = 1 sin^')
Ki,*,b Frictional component of limiting coefficient of atrest lateral earth pressure for unloading K0
cb Effective stress strength envelope Cohesion Intercept IV o cB'= 0.8c'
F or k2 k2 = k0(if)  Fraction of peak lateral compaction stress retained as residual stress for virgin soil  Incremental coefficient of atrest lateral earth pressure for reloading 0 < F < 1 K0>K2> 0  F (or K2) should be chosen such that the bilinear unloading stress path intersects the atype nonlinear unloading stress path at a suitable OCR. Recommended: (
k3 Incremental coefficient of atrest lateral earth pressure for reloading 0 < K3 < K0 K,sK2(=K,{\F))
2^i ^
Note: <7 hXXm = Kx
54
Figure 2.31 shows the basic components of the bilinear model. Virgin loading is
assumed to follow the Koline in the same manner as in the nonlinear model.
Unloading initially follows a linear stress path according Aah'~ K2Acrv' until a Ki
type of limiting condition is reached, at which point further unloading follows a linear
stress path according tocrh'= KxA
according to Acrh'= K3Acrr' until the virgin K0loading stress path is regained, after
that further reloading follows the virgin stress path.
Figure 2.31: Basic Components of the Bilinear Model (Seed, 1983)
From Figure 2.31, the parameters of bilinear model can be calculated as:
T
A
(2.15)
F = li
K2 t (OCR OCR")
K0 ~ (OCR1)
55
(2.16)
y
(vi)4~i
(Z.17)
a) Compaction Loading/Unloading Cycle Resulting in a
Positive Residual Increase in Horizontal Effective
Stress.
b) Compaction Loading/Unloading Cycle Resulting in No
Residual Change in Horizontal Effective Stress.
Figure 2.32: Compaction Loading/Unloading Cycles in the BiLinear 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., Acj'h,vc,p vs. depth
relationship) by the method described in Section c, as shown in Figure
2.32(b).
2. Multiply the Aa'h.vc.p values with the bilinear model parameter F.
3. Calculate the lateral residual stress as
4. Reduce the nearthesurface portion of the a\r distribution with
5. Increase the residual effective stress distribution such that K0crv'at all
depths.
Figure 2.33 shows an example problem given by Seed (1983) to show how to
determine the compactioninduced lateral pressure on a vertical nondeflecting
structure using bilinear model and nonlinear model. The material parameters of the
models based on the given angle of friction (
Table 2.4: Material parameters for nonlinear and bilinear models
Nonlinear model parameters Bilinear model parameters
K<>= 1 sin^'= 0.43 ( A<\ Kif= tan2 45 =3.69 V 2 a = 0.63 (from Figure 2.20) (5 = 0.6 (assumed) c' = 0 Ko= 1 sincf)' = 0.43 K,, =!*,> =246 55 F = 1 =0.44 51 K^=K2= 0.24 c'B= 0
58
Figure 2.34 shows the residual lateral stresses as a result of unloading due to fill
compaction and the atrest earth pressure. The results of the bilinear model (the solid
line) and the nonlinear model (the bold dots) are approximately the same.
59
0 IOC 200 300
Figure 2.33: An Example Problem for Hand Calculation of Peak Vertical
Compaction Profile (Seed, 1983)
60
0
100
200
500
0.0
2.5
5.0
Depth
(ft.)
7.5
10.0
300
A 00
Figure 2.34: Solution Results from the BiLinear Model and the Nonlinear Model
(Seed, 1983)
The compaction models developed by Seed (1983) has been used to determine the
CIS for fullscale 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 bilinear model) or the nonlinear 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 CompactionInduced 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 compactioninduced stresses (CIS) in the fills
have been ignored completely. The CIS in a GRS mass is likely to be more
pronounced than those induced in an unreinforced soil mass because soil
reinforcement interface friction tends to restrain lateral deformation of the soil mass
and results in greater values of CIS. A review 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 multicycle operations of soil placement and compaction during
construction, the soil surrounding the reinforcement maximum tension point
in each compaction lift was subjected to only one cycle of loading, as shown
in Figure 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
stressstate 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 az and ctzc 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 (azc), can be estimated using a new procedure, based on the method
given by Duncan and Seed (1986) for conventional retaining walls.
In Figure 2.35, the value of azc can be estimated as the following:
where:
K0 = 1 sin (Jaky, 1944)
(2.18)
(2.19)
63
(2.20)
05 y'QNy
L
and
Q = maximum vertical operating force of the roller drum
L = length of the roller drum
y = effective soil unit weight.
K
O
\K
o
(Poissons ratio under Kocondition)
tan f45" + ) 1 B ( 45" + 1
2 ) l 2 J
(bearing capacity factor)
(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 soilreinforcements stiffness index, Si, and compaction are the
major factors determining reinforcement tensions (typical Si for metallic
reinforcement: 0.5003.200; plastic reinforcement: 0.0300.120 and
geotextile reinforcement: 0.0030.012);
Increasing Si, usually means increased lateral earth pressure and
reinforcement tension, but at shallow depths the opposite effect can occur
depending on compaction conditions;
 The coefficient of horizontal earth pressure, K, can be greater than Ko at
the top of the wall and be greater than Ka to depths of more than 6.1 m (20
ft) depending on the relative soilreinforcements stiffness index, and the
compaction load; and
Ko is the upper limit for the coefficient of horizontal earth pressure, K, if
there is no compaction of the backfill.
64
Figure 2.36: Compaction and Reinforcement Stiffness Typical Influence
(Ehrlich and Mitchell, 1994)
2.4.2 Hatami and Bathurst (2006)
Hatami and Bathurst (2006) noted that fill compaction has two effects on the soil: (1)
increase the lateral earth pressure, (2) reduce the effective Poissons 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 Poissons ratio, Hatami and
Bathurst used the numerical simulation to find vmjn 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 fieldscale test. They considered that the inward maintained
pressures are "lockingin" stresses in soil due to compaction.
The stiffness of soil was increased by the factor of ten (10) to consider the
compactioninduced 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.
"Plate element to
model 1m by 2.5m by
0 .5m concrete footing 
Point load to model
applied loading
Free
Geognd" element to
model unconnected
Tensar UX1500 geogrid
Sand modeled using
HardeningSoil model
with hyperbolic stressstrain
& stressdependent
stiffness formulations
boundary
UfM3
V':
LifMO
.V,V,, VUTf
. ..iift9;7g>
\
r4l
"Anchor element
applied at top of each
face unit to model
diagonal component of
face unit (only one
anchor shown for
clarity)
"Plate element
to model vertical
component of
face unit
Legend
Primary nodes
A z Pressure
tracking point A
'l
.LiftS
Lift 7.
a c
8
^......1a
ISMSf'
>: .LW.5 7D
ilf
Lift3
Surcharge loading
applied to each lift to
simulate compaction
Lift 2
 C/
 Lft'1
A, '
...I
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 CompactionInduced Earth Pressures in the Literature
A number of important highlights regarding compactioninduced lateral earth
pressures in the literature are summarized below:
1. Compaction of soil against a rigid, vertical, nonyielding structure appears to
result in the following residual lateral pressure distribution: (a) the lateral
pressures near the surface increase rapidly with depth, exceeding the atrest
value, but limited a passive failure, (b) at intermediate depths, the lateral
pressures exceed the atrest 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 atrest pressures, showing no affects of compaction
(Broms, 1971, Seed, 1983).
2. Compaction of soil against deflecting structures appears to increase near
surface.
3. The compactioninduced residual earth pressures are significant affected by
the compaction equipments. For compaction by small handoperated 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. Compactioninduced residual lateral earth pressures in cohesive soils appear
to dissipate with time, even against nondeflecting structures, and eventually
approach atrest values.
6. There is some evidence suggesting that the direction of rolling with the
compactor can have a significant effect in compactioninduced earth pressures
(Erhlich and Mitchell, 1993).
7. Field observations indicate that available overburden pressures are sufficient
that possible passive failure does not limit residual lateral earth pressure, a
high percentage of the peak lateral earth pressures induced during compaction
may be retained as residual pressures. In previously compacted soil, however,
additional compaction can result in only small increases in peak pressures, and
a negligible fraction of this (Aggour and Brown, 1974).
8. A number of simulation models have been proposed to explain and to evaluate
the residual lateral earth pressures induced by compaction. Common to all of
these theories is the idea that compaction represents a form of over
consolidation wherein stresses resulting from a temporary or transient loading
condition are retained to some extent following removal of this peak load.
9. Many researchers, including Rowe (1954), Broms (1971), Gotteland et al.
(1997), and Hatami and Bathurst (2006), have simulated fill compaction by
application and removal of a surficial surcharge pressure.
10. Broms (1971) proposed a theory to calculate compactioninduced residual
lateral earth pressures against a rigid, vertical, frictionless, nonyielding 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 failuretype condition is
reached, and (b) reloading results in no increase in lateral stress until the
virgin Koloading 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 non
linear model and a bilinear 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 bilinear model is easy to apply by
using hand calculation. Both models, bilinear and nonlinear models, are
based on the Ko condition. These are very useful to estimate CIS for soil only.
To use it for GRS structures, indepth 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, GeosyntheticReinforced 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
lowpermeability backfill, easier to construct, require less overexcavation, and
significantly more economical than conventional earth structures (Wu, 1994; Holtz
et al., 1997; Bathurst et ah, 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 castinplace 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 fullscale 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 ah, 1996; Bathurst et
ah, 2006).
The prevailing methods for estimating the maximum lateral displacement of GRS
walls include: the FHWA method (Christopher, et ah, 1989), the Geoservices method
(Giroud, 1989), the CTI method (Wu, 1994), and the JewellMilligan method (1989).
Among these methods, the JewellMilligan method has been found to give the closest
agreement with finite element analysis (Macklin, 1994). The JewellMilligan
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
wrappedfaced 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 JewellMilligan method (1989) to include the rigidity of facing element.
The analytical model can be used in routine design by determining the required
reinforcement strength for a limiting value of maximum allowable wall movement.
To verify the analytical model, the lateral wall displacements calculated by the
analytical model were compared with the results of the JewellMilligan 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
72
data of a fullscale experiment of GRS wall with modular block facing (Hatami and
Bathurst, 2005 & 2006).
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.
Figure 3.1: Basic Components of a GRS Wall with a Modular Block Facing.
3.1 Review of Existing Methods for Estimating Maximum Wall Movement
The most prevalent methods for estimating the maximum lateral displacement of
GRS walls are the FHWA method (Christopher, et al., 1989), the Geoservices method
73
(Giroud, 1989), the CTI method (Wu, 1994), and the JewellMilligan method (1989).
A summary of each method is presented below.
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 5r, the empirically derived relative
displacement coefficient. Based on 6 m high walls, the 8r 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 fourthorder polynomial
as:
For extensible reinforcement, the maximum lateral wall displacement, Smax, can be
calculated from by the following equation (8max is in units of H):
For 0.3 < <1.175,
H
=11.81 42.25 +57.16 35.45 +9.471
UJ UJ UJ UJ
f 1 \
(3.1)
f1
,75,
(3.2)
74
RELATIVE DISPLACEMENT &
3
cc
0
^max =
<^max= *&R H /75
WHERE' SmQX =
(INEXTENSIBLE)
(EXTENSIBLE)
MAXIMUM DISPLACEMENT
IN UNITS OF H
H = HEIGHT OF WALL IN Ft.
6r = EMPI RICALLY DERIVED
RELATIVE DISPLACEMENT
COEFFICIENT.
0
0.5
1.0
1.5
L/H
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, 8r, 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 limitequilibrium 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. Nonwoven 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, 8h, then becomes:
where Sd = strain limit (emax), and L = reinforcement length.
Figure 3.3: Assumed Strain Distribution in the Geoservices Method
3.1.3 The CTI Method (Wu, 1994)
Differing from all other design methods based on ultimatestrength of the
geosynthetic reinforcement, the CTI method is a serviceload 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, 8max, can be estimated
by the following empirical equation:
f H '
8 = Â£
1.25
(3.4)
where Sd = 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 wrappedfaced walls.
Walls with significant facing rigidity will have smaller maximum lateral
displacement. For example, a modular block GRS walls will have 8max about 15%
smaller than that calculated Equation 3.4.
3.1.4 The JewellMilligan 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 planestrain plastic
deformation of soil: the plane strain angle of friction,
78
The planes on which the maximum shearing resistance ps is mobilized are called the
stress characteristics and are inclined at (45 + 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 +^/2) to the direction of major principal stress, as shown in Figure
3.4(b).
Stress characteristics Velocity characteristics
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 +if/12) to the horizontal, and
between zone 2 and 3 at an angle (j>dS. Large reinforcement forces are required in zone
1 to maintain stability across a series of critically inclined planes. In zone 2, the
required reinforcement forces reduce progressively.
79
The assumptions of the JewellMilligan 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 dS 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
