Effects of Geosynthetic Reinforcement Spacing on The Behavior of Mechanically Stabilized Earth Walls

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TABLE OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

1. INTRODUCTION
2. BACKGROUND
   • 2.1 Review of Current Design Practice of MSEWs with Respect to Reinforcement Spacing
   • 2.2 Program FLAC: Theoretical Background and General Features
   • 2.3 Literature Review
3. NUMERICAL ANALYSIS
   • 3.1 Scope
   • 3.2 Numerical Model
     • 3.2.1 Modeling Methodology
     • 3.2.2 Model Description
     • 3.2.3 Material Properties
   • 3.3 Scope of Parametric Studies
4. RESULTS
   • 4.1 Failure Mechanisms of MSEWs
     • 4.1.1 Description of Identified Failure Mechanisms
       • 4.1.1.1 External Mode of Failure
       • 4.1.1.2 Deep-Seated Mode of Failure
       • 4.1.1.3 Compound Mode of Failure
       • 4.1.1.4 Connection Mode of Failure
       • 4.1.1.5 Mixed Modes of Failure
     • 4.1.2 Effects of Geosynthetic Spacing on Failure Mechanisms
     • 4.1.3 Effects of Soil Strength on Failure Mechanisms as Function of Geosynthetic Spacing
     • 4.1.4 Effects of Reinforcement Stiffness on Failure Mechanisms as Function of Geosynthetic Spacing
       • 4.1.4.1 High Strength Soil
       • 4.1.4.2 Medium Strength Soil
       • 4.1.4.3 Low Strength Soil
     • 4.1.5 Effects of Connection Strength on Failure Mechanisms as Function of Geosynthetic Spacing
       • 4.1.5.1 Cases with Small Reinforcement Spacing
       • 4.1.5.2 Cases with Large Reinforcement Spacing
     • 4.1.6 Effects of Foundation Stiffness on Failure Mechanisms as Function of Geosynthetic Spacing
   • 4.2 Effects of Reinforcement Length on Reinforcement Stresses and Wall Stability
   • 4.3 Effects of Secondary Reinforcement Layers on Connection Loads and Wall Stability
   • 4.4 Influence of Soil Dilatancy on Model Response
5. COMPARISON WITH EXISTING DESIGN PRACTICE
   • 5.1 Analysis of Baseline Cases using AASHTO
   • 5.2 Slope of Slip Planes
   • 5.3 Stresses
6. IMPLICATIONS TO DESIGN
7. CONCLUSIONS AND RECOMMENDATIONS

• APPENDIX: TYPICAL INPUT DATA FILE
• REFERENCES

LIST OF FIGURES

• 3.1 Numerical Model Components.
• 3.2 Schematic of Modeling of Construction Sequence of Wall with Reinforcement Spacing Equal to 0.4 m.
• 3.3 Definition of: (a) Failure State; (b) Critical State; (c) Stable State
• 3.4 Typical Numerical Grid.
• 3.5 Grid Definition: (a) Model Zones with Respect to Grid Generation; (b) Grid of Modular Blocks in the Current Model; (c) Grid of Modular Blocks in Early Versions of the Model.
• 3.6 Boundary Effects on Model Response: Horizontal Displacements along Vertical Section A Located 0.1 m behind the Facing.
• 3.7 Boundary Effects on Model Response: Stress Distributions along Vertical Section A Located 0.15 m behind the Facing.
• 3.8 Types of Interfaces at the Blocks.
• 3.9 Baseline Cases: (a) Number of Calculation Steps Necessary to Equilibrate Each Layer; (b) Maximum Cumulative Displacement during Wall Construction
• 3.10 Effects of FLAC Equilibrium Ratio Limit on Model Response of Case 1 (s=0.2 m, l=1.5 m): (a) Number of Calculation Steps; (b) Maximum Cumulative Displacement.
• 3.11 Effects of FLAC Step Limit on Model Response of Case 12 (s=0.2 m, l=1.5 m): (a) Number of Calculation Steps; (b) Maximum Cumulative Displacement.
• 3.12 Reinforcement Layout with Primary and Secondary Layers for Case 7 (s=0.6/0.2 m).
• 3.13 Some of the Executed Numerical Runs.
• 4.1 Critical Wall Height and Prevailing Mode of Failure: (a) Cases with Very Stiff Foundation; (b) Cases with Baseline Foundation.
• 4.2 Change of Critical Wall Height with Respect to Soil Strength: (a) Cases with Very Stiff Foundation; (b) Cases with Baseline Foundation.
• 4.3 Slip Surface Types: (a) External Slip Surface; (b) Deep-Seated Slip Surface; (c) Compound Slip Surface; (d) Internal Slip Surface
• 4.4 Definition of Vertical Sections A, B, and C along which Stress and Displacement Distributions Were Investigated.
• 4.5 State of Soil for Case 1 (s=0.2 m, l=1.5 m): (a) Failure State (h=8.6 m, l/h=0.17); (b) Critical State (h=6.6 m, l/h=0.23).
• 4.6 Displacement Vectors for Case 1 (s=0.2 m, l=1.5 m): (a) Failure State (h=8.6 m, l/h=0.17); (b) Critical State (h=6.6 m, l/h=0.23).
• 4.7 Distorted Grid for Case 1 (s=0.2 m, l=1.5 m): (a) Failure State (h=8.6 m, l/h=0.17); (b) Critical State (h=6.6 m, l/h=0.23).
• 4.8 Cumulative Horizontal Displacements for Case 1 (s=0.2 m, l=1.5 m): (a) Failure State (h=8.6 m, l/h=0.17); (b) Critical State (h=6.6 m, l/h=0.23).
• 4.9 Axial Force Distribution in Reinforcement for Case 1 (s=0.2 m, l=1.5 m): (a) Failure State (h=8.6 m, l/h=0.17); (b) Critical State (h=6.6 m, l/h=0.23).
• 4.10 State of Soil for Case 1 (s=0.4 m, l=1.5 m): (a) Failure State (h=8.2 m, l/h=0.18); (b) Critical State (h=6.0 m, l/h=0.25).
• 4.11 State of Soil for Case 4 (s=0.2 m, l=1.5 m): (a) Failure State (h=7.0 m, l/h=0.21); (b) Critical State (h=5.6 m, l/h=0.27).
• 4.12 State of Soil for Case 9 (s=0.2 m, l=1.5 m): (a) Failure State (h=8.2 m, l/h=0.18); (b) Critical State (h=6.6 m, l/h=0.23).
• 4.13 State of Soil for Case 11 (s=0.2 m, l=1.5 m): (a) Failure State (h=7.2 m, l/h=0.21); (b) Critical State (h=6.0 m, l/h=0.25).
• 4.14 State of Soil for Case 12 (s=0.2 m, l=1.5 m): (a) Failure State (h=9.4 m, l/h=0.16); (b) Critical State (h=6.6 m, l/h=0.23).
• 4.15 State of Soil for Case 10 (s=0.2 m, l=1.5 m): (a) Failure State (h=4.4 m, l/h=0.34); (b) Critical State (h=3.2 m, l/h=0.47).
• 4.16 Displacement Vectors for Case 10 (s=0.2 m, l=1.5 m): (a) Failure State (h=4.4 m, l/h=0.34); (b) Critical State (h=3.2 m, l/h=0.47).
• 4.17 Distorted Grid for Case 10 (s=0.2 m, l=1.5 m): (a) Failure State (h=4.4 m, l/h=0.34); (b) Critical State (h=3.2 m, l/h=0.47).
• 4.18 Horizontal Displacements for Case 10 (s=0.2 m, l=1.5 m) at Failure State (h=4.4 m, l/h=0.34) and Critical State (h=3.2 m, l/h=0.47).
• 4.19 Axial Force Distribution in Reinforcement for Case 10 (s=0.2 m, l=1.5 m): (a) Failure State (h=4.4 m, l/h=0.34); (b) Critical State (h=3.2 m, l/h=0.47).
• 4.20 State of Soil for Case 5 (s=0.2 m, l=1.5 m): (a) Failure State (h=5.4 m, l/h=0.28); (b) Critical State (h=4.2 m, l/h=0.36).
• 4.21 State of Soil for Case 8–1 (s=0.4 m, l=1.5 m): (a) Failure State (h=8.0 m, l/h=0.19); (b) Critical State (h=5.0 m, l/h=0.30).
• 4.22 Displacement Vectors for Case 8–1 (s=0.4 m, l=1.5 m): (a) Failure State (h=8.0 m, l/h=0.19); (b) Critical State (h=5.0 m, l/h=0.30).
• 4.23 Distorted Grid for Case 8–1 (s=0.4 m, l=1.5 m): (a) Failure State (h=8.0 m, l/h=0.19); (b) Critical State (h=5.0 m, l/h=0.30).
• 4.24 Horizontal Displacements for Case 8–1 (s=0.4 m, l=1.5 m) at Failure (h=8.0 m, l/h=0.19) and Critical State (h=5.0 m, l/h=0.30).
• 4.25 Axial Force Distribution in Reinforcement for Case 8–1 (s=0.4 m, l=1.5 m): (a) Failure State (h=8.0 m, l/h=0.19); (b) Critical State (h=5.0 m, l/h=0.30).
• 4.26 State of Soil for Case 2 (s=0.4 m, l=1.5 m): (a) Failure State (h=6.0 m, l/h=0.25); (b) Critical State (h=4.4 m, l/h=0.34).
• 4.27 State of Soil for Case 3 (s=0.2 m, l=1.5 m): (a) Failure State (h=4.2 m, l/h=0.36); (b) Critical State (h=4.0 m, l/h=0.38).
• 4.28 State of Soil for Case 7 (s=0.6/0.2 m, l=1.5 m): (a) Failure State (h=6.0 m, l/h=0.25); (b) Critical State (h=5.0 m, l/h=0.30).
• 4.29 State of Soil for Case 8–2 (s=0.4 m, l=1.5 m): (a) Failure State (h=5.4 m, l/h=0.28); (b) Critical State (h=3.2 m, l/h=0.47).
• 4.30 State of Soil for Case 8–3 (s=0.2 m, l=1.5 m): (a) Failure State (h=5.0 m, l/h=0.30); (b) Critical State (h=2.2 m, l/h=0.68).
• 4.31 State of Soil for Case 12 (s=0.6 m, l=1.5 m): (a) Failure State (h=6.0 m, l/h=0.25); (b) Critical State (h=4.6 m, l/h=0.33).
• 4.32 State of Soil for Case 2 (s=0.6 m, l=1.5 m): (a) Failure State (h=4.6 m, l/h=0.33); (b) Critical State (h=2.6 m, l/h=0.58).
• 4.33 Displacement Vectors for Case 2 (s=0.6 m, l=1.5 m): (a) Failure State (h=4.6 m, l/h=0.33); (b) Critical State (h=2.6 m, l/h=0.58).
• 4.34 Distorted Grid for Case 2 (s=0.6 m, l=1.5 m): (a) Failure State (h=4.6 m, l/h=0.33); (b) Critical State (h=2.6 m, l/h=0.58).
• 4.35 Horizontal Displacements for Case 2 (s=0.6 m, l=1.5 m) at Failure State (h=4.6 m, l/h=0.33) and Critical State (h=2.6 m, l/h=0.58).
• 4.36 Axial Force Distribution in Reinforcement for Case 2 (s=0.6 m, l=1.5 m): (a) Failure State (h=4.6 m, l/h=0.33); (b) Critical State (h=2.6 m, l/h=0.58).
• 4.37 State of Soil for Case 4 (s=0.6 m, l=1.5 m): (a) Failure State (h=5.4 m, l/h=0.28); (b) Critical State (h=3.8 m, l/h=0.39).
• 4.38 Case 1 (s=0.4 m, l=1.5 m, h=5.0 m): (a) State of Soil; (b) Axial Force Distribution in Reinforcement.
• 4.39 Connection Force and Maximum Force in Reinforcement for Case 1 (s=0.4 m, h=5.0 m, BR) and Case 8–1 (s=0.4 m, h=5.0 m, DR): Effects of Reinforcement Stiffness.
• 4.40 Horizontal Displacements along Section A: Comparison with Respect to Reinforcement Stiffness.
• 4.41 State of Soil for Cases 2 and 8–2 (s=0.4 m, h=3.2 m, l=1.5 m): (a) Case 2 (BR); (b) Case 8–2 (DR).
• 4.42 Axial Force Distributions in Reinforcement for Cases 2 and 8–2 (s=0.4 m, h=3.2 m, l=1.5 m): (a) Case 2 (BR); (b) Case 8–2 (DR).
• 4.43 Connection Force and Maximum Force in Reinforcement for Case 2 (s=0.4 m, h=3.2 m, BR) and Case 8–2 (s=0.4 m, h=3.2 m, DR): Effects of Reinforcement Stiffness.
• 4.44 State of Soil for Cases 3 and 8–3 (s=0.2 m, h=2.2 m, l=1.5 m): (a) Case 3 (BR); (b) Case 8–3 (DR).
• 4.45 Axial Force Distributions in Reinforcement for Cases 3 and 8–3 (s=0.2 m, h=2.2 m, l=1.5 m): (a) Case 3 (BR); (b) Case 8–3 (DR).
• 4.46 Connection Force and Maximum Force in Reinforcement for Case 3 (s=0.2 m, h=2.2 m, BR) and Case 8–3 (s=0.2 m, h=2.2 m, DR): Effects of Reinforcement Stiffness.
• 4.47 Effects of Connection Strength on Connection Force for Cases with Small Reinforcement Spacing (s=0.2 m).
• 4.48 Effects of Connection Strength on Maximum Force in Reinforcement for Cases with Small Reinforcement Spacing (s=0.2 m).
• 4.49 Effects of Connection Strength on Horizontal Displacements along Section A for Cases with Small Reinforcement Spacing (s=0.2 m).
• 4.50 Effects of Connection Strength on Connection Force and Maximum Force in Reinforcement for Cases with Large Reinforcement Spacing (s=0.6 m).
• 4.51 Axial Force Distribution in Reinforcement for Case 12 (l=1.5 m): (a) s=0.2 m, h=6.6 m; (b) s=0.6 m, h=2.6 m.
• 4.52 Effects of Connection Strength on Horizontal Displacements along Section A for Cases with Large Reinforcement Spacing (s=0.6 m).
• 4.53 Effects of Foundation Strength on Critical Wall Height.
• 4.54 Effects of Foundation Strength for Cases 1, 4, and 10 (s=0.2 m, l=1.5 m h=3.2 m) on: (a) Horizontal Displacements along Section A; (b) Connection Force and Maximum Axial Force in Reinforcement; (c) Stresses along Section A.
• 4.55 Stress Distributions along Section A for Critical and Stable States of Case 1 (s=0.2 m, h=6.6 m, l/h=0.23–0.5).
• 4.56 Stress Distributions along Section C for Critical and Stable States of Case 1 (s=0.2 m, h=6.6 m, l/h=0.23–0.5).
• 4.57 Horizontal Displacements along Sections A and B for Critical and Stable States of Case 1 (s=0.2 m, h=6.6 m, l/h=0.23–0.5).
• 4.58 Maximum Axial Force in Reinforcement for Critical and Stable States of Case 1 (s=0.2 m, h=6.6 m, l/h=0.23–0.5).
• 4.59 Connection Force for Critical and Stable States of Case 1 (s=0.2 m, h=6.6 m, l/h=0.23–0.5).
• 4.60 Stress Distributions along Section A for Critical and Stable States of Case 8–1 (s=0.4 m, h=5.0 m, l/h=0.3–0.5).
• 4.61 Stress Distributions along Section C for Critical and Stable States of Case 8–1 (s=0.4 m, h=5.0 m, l/h=0.3–0.5).
• 4.62 Horizontal Displacements along Sections A and B for Critical and Stable States of Case 8–1 (s=0.4 m, h=5.0 m, l/h=0.3–0.5).
• 4.63 Connection Force and Maximum Axial Force in Reinforcement for Critical and Stable States of Case 8–1 (s=0.4 m, h=5.0 m, l/h=0.3–0.5)
• 4.64 Stress Distributions along Section A for Critical and Stable States of Case 10 (s=0.2 m, h=3.2 m, l/h=0.47–0.7).
• 4.65 Stress Distributions along Section C for Critical and Stable States of Case 10 (s=0.2 m, h=3.2 m, l/h=0.47–0.7).
• 4.66 Horizontal Displacements along Sections A and B for Critical and Stable States of Case 10 (s=0.2 m, h=3.2 m, l/h=0.47–0.7).
• 4.67 Connection Force and Maximum Axial Force in Reinforcement for Critical and Stable States of Case 10 (s=0.2 m, h=3.2 m, l/h=0.47–.7).
• 4.68 Effects of Secondary Reinforcement: Axial Force Distribution in Reinforcement for Case 7 (s=0.6/0.2 m), (a) h=2.6 m; (b) h=5.0 m.
• 4.69 Effects of Secondary Reinforcement: State of Soil for Case 7 (h=2.6 m, s=0.6/0.2 m).
• 4.70 Effects of Secondary Reinforcement: Horizontal Displacements along Section A for Cases 2 and 7 (h=2.6 m).
• 4.71 Effects of Secondary Reinforcement: Connection Force and Maximum Axial Force in Reinforcement for Cases 2 and 7 (h=2.6 m).
• 5.1 Maximum Force in Reinforcement: Comparison of FLAC and AASHTO Results for Case 1 (s=0.4 m) and Case 2 (s=0.6 m).
• 5.2 Maximum Force in Reinforcement: Comparison of FLAC and AASHTO Results for Case 8–1 (s=0.4 m) and Case 10 (s=0.2 m).
• 5.3 Comparison of FLAC and AASHTO Results for Case 8–1 (s=0.4 m, h=5.0 m, l=1.5 m): (a) MSEW 1.1 Analysis: Critical Slip Surface from Compound Stability Analysis; (b) FLAC Analysis: Failure Zones Distribution at the Critical State.
• 5.4 Comparison of FLAC and AASHTO Results for Case 10 (s=0.2 m, h=3.2 m, l=1.5 m): (a) MSEW 1.1 Analysis: Critical Slip Surface from Deep-Seated Stability Analysis; (b) FLAC Analysis: Failure Zones Distribution at the Critical State.
• 5.5 Stress Distributions along Sections A and C for Failure State of Case 1 (s=0.2 m, h=8.6 m, l/h=0.17).
• 5.6 Stress Distributions along Sections A and C for Critical State of Case 1 (s=0.2 m, h=8.6 m, l/h=0.17).
• 5.7 Stress Distributions along Sections A and C for Failure State of Case 2 (s=0.6 m, h=4.6 m, l/h=0.33).
• 5.8 Stress Distributions along Sections A and C for Critical State of Case 2 (s=0.6 m, h=4.6 m, l/h=0.33).
• 5.9 Stress Distributions along Sections A and C for Failure State of Case 8–1 (s=0.4 m, h=8.0 m, l/h=0.19).
• 5.10 Stress Distributions along Sections A and C for Critical State of Case 8–1 (s=0.4 m, h=8.0 m, l/h=0.19).
• 5.11 Stress Distributions along Sections A and C for Failure State of Case 10 (s=0.2 m, h=4.4 m, l/h=0.34).
• 5.12 Stress Distributions along Sections A and C for Critical State of Case 10 (s=0.2 m, h=4.4 m, l/h=0.34).

LIST OF TABLES

• 3.1 List of Model Variables.
• 3.2 Major Results for Case 1 (s=0.2 m, h=6.6 m, l=1.5 m) for Different FLAC Equilibrium Ratio Limits.
• 3.3 Properties of Modeled Soil: Strength and Elastic Values.
• 3.4 Properties of Modeled Soil Stiffness.
• 3.5 Model Parameters and Properties of Facing.
• 3.6 Modeling of Reinforcement Stiffness.
• 3.7 Modeling of Block-Block and Block-Reinforcement Interfaces.
• 3.8 Parametric Study Cases.
• 3.9 General Information for Runs Corresponding to Failure States.
• 3.10 General Information for Runs Corresponding to Critical States.
• 4.1 Summary of Results Identifying Failure Modes.
• 4.2 Critical Wall Height and Prevailing Mode of Failure.
• 4.3 Maximum Axial Force in Reinforcement.
• 4.4 Maximum Connection Force.
• 4.5 Effects of Reinforcement Stiffness on Model Response: Comparison of Case 1 (s=0.4 m) and Case 8–1 (s=0.4 m).
• 4.6 Effects of Reinforcement Stiffness of Model Response: Comparison of Case 2 (s=0.4 m) and Case 8–2 (s=0.4 m).
• 4.7 Effects of Reinforcement Stiffness on Model Response: Comparison of Case 3 (s=0.2 m) and Case 8–3 (s=0.2 m).
• 4.8 Effects of Connection Strength on Model Response: Cases with Small Reinforcement Spacing (s=0.2 m).
• 4.9 Effects of Connection Strength on Model Response: Cases with Large Reinforcement Spacing (s=0.6 m).
• 4.10 Effects of Foundation Stiffness on Model Response: Comparison of Cases 1, 4, and 10 (s=0.2 m).
• 4.11 Effects of Secondary Reinforcement on Model Response.
• 4.12 Effects of Soil Dilatancy on Model Response: Comparison of Case 1 (s=0.2 m) and Case 11 (s=0.2 m).
• 5.1 Input Data for AASHTO Analysis Using MSEW 1.1 Program.
• 5.2 Results from AASHTO Analysis Using MSEW 1.1 Program.
• 5.3 Slope of Slip Planes.