Appendix A Investigation of Suitable Soil Constitutive Models for 3-D Finite Element Studies of Live

155 Pages·2010·6.4 MB·English

Appendix A
Investigation of Suitable Soil Constitutive Models for 3-D
Finite Element Studies of Live Load Distribution Through
Fills Onto Culverts

National Cooperative Highway Research Program
Project 15-29

Limited Use Document

This Final Report is furnished only for review by

members of the NCHRP project panel and is

regarded as fully privileged. Dissemination of

information included herein must be approved by the

NCHRP.

CNA Consulting Engineers
Simpson, Gumpertz & Heger

April 2009
Table of Contents
1. INTRODUCTION 1
2. REVIEW OF AVAILABLE SOIL MODELS 1
2.1 Linear Elastic 2
2.2 Elasto-Plastic 3
2.3 Stress-Dependent Models 6
2.3.1 Duncan-Selig Model 6
2.3.2 Hardening Soil Model (Plaxis) 10
2.4 Findings from Soil Model Evaluation 22
3. TWO-DIMENSIONAL MODELING OF CULVERTS 22
3.1 Modeled Structures 22
3.2 Material Models 23
3.2.1 Linear-Elastic Model 23
3.2.2 Mohr-Coulomb Model with Perfect Plasticity in Plaxis 23
3.2.3 Hardening-Soil Model in Plaxis 24
3.2.4 In-Situ Soil Material 24
3.2.5 Other Materials 24
3.3 Live Load 24
3.4 Finite Element Model 26
3.5 Results of 2D Analysis 35
3.5.1 Concrete Box 35
3.5.2 Concrete Pipe 44
3.5.3 Metal Pipe 49
3.5.4 Thermoplastic Pipe 54
3.5.5 Concrete Arch 59
3.5.6 Metal Arch 64
3.5.7 Summary of Results from 2D Preliminary Analyses 69
3.6 Effect of Interface Strength 71
3.7 Conclusion 81
4. THREE DIMENSIONAL MODELING OF CULVERTS 82
4.1 Comparison of Responses to Factored and Unfactored Live Loads 82
4.1.1 Introduction 82
4.1.2 Method of Approach 82
4.1.3 Results 83
4.1.3.1 HDPE Pipe in ABAQUS 83
4.1.3.2 Three-Sided Arch Top Culvert in CANDE 85
4.1.4 Conclusion 86
4.2 Selected Field Tests for 3D Analysis 86
4.2.1 NCHRP Project 12-45 86
4.2.2 Minnesota DOT Study 90
4.3 Three-Dimensional Analysis 93
4.3.1 General Information 93
4.3.2 Long-Span Concrete Arch Culvert 94
4.3.2.1 Finite Element Model 94
4.3.2.2 Materials 95
4.3.2.3 Loading and Boundary Condition 96
4.3.2.4 Results 97
4.3.3 Long-Span Metal Arch Culvert 101
NCHRP 15-29 Appendix A i
4.3.3.1 Finite Element Model 101
4.3.3.2 Materials 102
4.3.3.3 Loading and Boundary Condition 102
4.3.3.4 Results 102
4.3.4 60-in. Diameter HDPE Pipe 108
4.3.4.1 Finite Element Model 108
4.3.4.2 Materials 109
4.3.4.3 Loading and Boundary Condition 109
4.3.4.4 Results 111
4.3.5 Discussion 126
4.4 Comparison between the Mohr-Coulomb and Hardening-Soil Models in Three-
Dimensional Analysis in PLAXIS 129
4.4.1 Method of Approach 130
4.4.2 Results 130
4.4.2.1 Metal Arch in Test 2 with 3 ft Cover 130
4.4.2.2 HDPE Pipe with A2 Backfill and 2.8 ft Cover 130
4.4.3 Conclusion 135
4.5 Three-Dimensional Analysis of Field Tests in ABAQUS 135
4.5.1 Introduction 135
4.5.2 Method of Approach 136
4.5.3 Validation of ABAQUS Model 139
4.5.4 Results 140
4.5.4.1 Metal Arch with 3 ft Cover 140
4.5.4.2 HDPE Pipe with A2 Backfill and 2.8 ft Cover 142
4.5.5 Conclusion 143
5. DISCUSSION 144
6. CONCLUSIONS AND RECOMMENDATIONS 145
7. REFERENCES 145
List of Tables
Table 1—Elastic soil properties for Backfill (Selig, 1990) ............................................................. 3
Table 2—Vertical Stresses and Estimated Horizontal Stresses under Gravity and Corresponding
Angle of Friction for SW85 ............................................................................................................ 6
Table 3—Parameters for Linear-Elastic and Mohr-Coulomb Models for SW85 ............................ 6
Table 4—Soil Properties of Backfill for Duncan-Selig Model (Selig, 1988) ................................... 9
Table 5—Input Parameters for Hardening-Soil Model for SW85, SW90, ML85, and CL85 ........ 15
Table 6—Structural Types and Cover Depths for 2D Analysis ................................................... 23
Table 7—Comparison of Bending Moments and Thrusts in Concrete Box Model ...................... 43
Table 8—Comparison of Bending Moments and Thrusts in Concrete Pipe Model ..................... 48
Table 9—Comparison of Bending Moments and Thrusts in Metal Pipe Model........................... 53
Table 10—Comparison of Bending Moments and Thrusts in Thermoplastic Pipe Model ........... 58
Table 11—Comparison of Bending Moments and Thrusts in Concrete Arch Model................... 63
Table 12—Comparison of Bending Moments and Thrusts in Metal Arch Model ........................ 68
Table 13—Ratios of Live Load Moments and Thrusts of Concrete Box ..................................... 69
Table 14—Ratios of Live Load Moments and Thrusts of Pipes with a Cover Depth of 2 ft ........ 70
Table 15—Ratios of Live Load Moments and Thrusts of Pipes with a Cover Depth of 6 ft ........ 70
Table 16—Ratios of Live Load Moments and Thrusts of Arches with a Cover Depth of 2 ft ...... 70
Table 17—Ratios of Live Load Moments and Thrusts of Arches with a Cover Depth of 6 ft ...... 70
NCHRP 15-29 Appendix A ii
Table 18—Comparison of Bending Moments and Thrusts between Concrete Pipe Models with
50% and 100% Interface Strength (Mohr-Coulomb Soil Model) ................................................. 76
Table 19—Comparison of Bending Moments and Thrusts Load between Thermoplastic Pipe
Models with 50% and 100% Interface Strength (Mohr-Coulomb Soil Model) ............................. 81
Table 20—Comparison of Structural Responses between Analyses with Factored and
Unfactored Live Loads (HDPE Pipe, A2 Backfill) ........................................................................ 85
Table 21—Comparison of Structural Responses between Analyses (Hanson Arch) ................. 86
Table 22—Properties of Reinforced Concrete Culvert ................................................................ 88
Table 23—Properties of Structural Steel Plate and Culvert ........................................................ 88
Table 24—Properties of Type S HDPE Pipe .............................................................................. 91
Table 25—Average Trench Measurements for Test Pipes in the MNDOT Study ....................... 92
Table 26—Soil Properties Used for the 3D Analyses of Long-Span Arches .............................. 96
Table 27—Concrete Properties Used for the 3D Analyses of Long-Span Arches ...................... 96
Table 28—Vertical Displacements at Crown of Concrete Arch due to Live Loads ..................... 99
Table 29—Chord Extension at Height of 88 in. of Concrete Arch Culvert due to Live Loads ..... 99
Table 30—Thrusts at Base of Concrete Arch Culvert due to Live Loads ................................... 99
Table 31—Axial and Bending Modulus of Metal Arch in Circumferential and Longitudinal
Directions (E=29,000 ksi) .......................................................................................................... 102
Table 32—Vertical Displacements at Crown of Metal Arch due to Live Loads ......................... 104
Table 33—Chord Extension at Height of 88 in. of Metal Arch Culvert due to Live Loads ......... 104
Table 34—Thrusts in Test 1 of Metal Arch Culvert due to Live Loads ...................................... 105
Table 35—Thrusts in Test 2 of Metal Arch Culvert due to Live Loads ...................................... 105
Table 36—Moments in Test 1 of Metal Arch Culvert due to Live Loads ................................... 106
Table 37—Moments in Test 2 of Metal Arch Culvert due to Live Loads ................................... 106
Table 38—Axial and Bending Modulus of HDPE Pipe in Circumferential and Longitudinal
Directions (E=100,000 psi) ........................................................................................................ 109
Table 39—Soil Properties Used for the 3D Analyses of HDPE Pipes ...................................... 110
Table 40—Comparison of Vertical Displacements at Crown of HDPE Pipes under Heavy Truck
.................................................................................................................................................. 125
Table 41—Comparison of Vertical Displacements at Crown of HDPE Pipes under Light Truck
.................................................................................................................................................. 125
Table 42—Comparison of Diametrical Changes at Springline of HDPE Pipes under Heavy Truck
.................................................................................................................................................. 125
Table 43—Comparison of Diametrical Changes at Springline of HDPE Pipes under Light Truck
.................................................................................................................................................. 125
Table 44—Summary of Displacements under Wheel (Metal Arch, Test 2, 3 ft Cover) ............. 132
Table 45—Summary of Thrusts under Wheel (Metal Arch, Test 2, 3 ft Cover) ......................... 132
Table 46—Summary of Moments under Wheel (Metal Arch, Test 2, 3 ft Cover) ...................... 133
Table 47—Summary of Vertical Displacements under Wheel (HDPE Pipe, A2 Soil, 2.8 ft Cover)
.................................................................................................................................................. 134
Table 48—Summary of Horizontal Chord Extensions under Wheel (HDPE Pipe, A2 Soil, 2.8 ft
Cover) ....................................................................................................................................... 135
Table 49—Summary of Force Results (HDPE Pipe, A2 Soil, 2.8 ft Cover) .............................. 135
Table 50—Orthotropic Properties Used in ABAQUS Analyses ................................................ 137
Table 51—Orthotropic Stiffness Properties .............................................................................. 137
Table 52—Soil Porperties Used for Soft Haunch and Void Areas ............................................ 138
Table 53—Summary of Displacements from ABAQUS Analyses with Orthotropic Properties
(Metal Arch, 3 ft Cover) ............................................................................................................. 141
Table 54—Summary of Displacements from ABAQUS Analyses with Orthotropic Properties
(HDPE Pipe, A2 Backfill) ........................................................................................................... 143
List of Figures
NCHRP 15-29 Appendix A iii
Figure 1—Comparison of Plaxis Hardening-Soil Model and Duncan-Selig Model for SW85 in
Deviatoric Loading of Triaxial Test .............................................................................................. 16
Figure 2—Comparison of Plaxis Hardening-Soil Model and Duncan-Selig Model for SW90 in
Deviatoric Loading of Triaxial Test .............................................................................................. 17
Figure 3—Comparison of Plaxis Hardening-Soil Model and Duncan-Selig Model for ML85 in
Deviatoric Loading of Triaxial Test .............................................................................................. 18
Figure 4—Comparison of Plaxis Hardening-Soil Model and Duncan-Selig Model for CL85 in
Deviatoric Loading of Triaxial Test .............................................................................................. 19
Figure 5—Comparison of Plaxis Hardening-Soil Model and Duncan-Selig Model for SW85 in
Oedometer Loading .................................................................................................................... 20
Figure 6—Comparison of Plaxis Hardening-Soil Model and Duncan-Selig Model for SW90 in
Oedometer Loading .................................................................................................................... 20
Figure 7—Comparison of Plaxis Hardening-Soil Model and Duncan-Selig Model for ML85 in
Oedometer Loading .................................................................................................................... 21
Figure 8—Comparison of Plaxis Hardening-Soil Model and Duncan-Selig Model for CL85 in
Oedometer Loading .................................................................................................................... 21
Figure 9—Live Load per Unit Length of Culvert in 2D Analysis .................................................. 26
Figure 10—Conceptual Model for 2D Analysis of Pipes ............................................................. 27
Figure 11—Conceptual Model for 2D Analysis of Boxes ............................................................ 28
Figure 12—Conceptual Model for 2D Analysis of Arches ........................................................... 28
Figure 13—Finite Element Meshes of Concrete Box Model ....................................................... 29
Figure 14—Finite Element Meshes of Concrete Pipe Model ...................................................... 30
Figure 15—Finite Element Meshes of Metal Pipe Model ............................................................ 31
Figure 16—Finite Element Meshes of Plastic Pipe Model .......................................................... 32
Figure 17—Finite Element Meshes of Concrete Arch Model ...................................................... 33
Figure 18—Finite Element Meshes of Metal Arch Model ............................................................ 34
Figure 19—Deformation of Concrete Box due to Live Load ....................................................... 36
Figure 20—Bending Moments and Thrusts due to Live Load in Top Slab of Concrete Box Model
(0 ft Cover) .................................................................................................................................. 37
Figure 21—Bending Moments and Thrusts due to Live Load in Right Wall of Concrete Box
Model (0 ft Cover) ....................................................................................................................... 38
Figure 22—Bending Moments and Thrusts due to Live Load in Top Slab of Concrete Box Model
(2 ft Cover) .................................................................................................................................. 39
Figure 23—Bending Moments and Thrusts due to Live Load in Right Wall of Concrete Box
Model (2 ft Cover) ....................................................................................................................... 40
Figure 24—Bending Moments and Thrusts due to Live Load in Top Slab of Concrete Box Model
(6 ft Cover) .................................................................................................................................. 41
Figure 25—Bending Moments and Thrusts due to Live Load in Right Wall of Concrete Box
Model (6 ft Cover) ....................................................................................................................... 42
Figure 26—Deformation of Concrete Pipe due to Live Load ...................................................... 45
Figure 27—Bending Moments and Thrusts due to Live Load in Concrete Pipe Model (2 ft Cover)
.................................................................................................................................................... 46
Figure 28—Bending Moments and Thrusts due to Live Load in Concrete Pipe Model (6 ft Cover)
.................................................................................................................................................... 47
Figure 29—Deformation of Metal Pipe due to Live Load ............................................................ 50
Figure 30—Bending Moments and Thrusts due to Live Load in Metal Pipe Model (2 ft Cover) . 51
Figure 31—Bending Moments and Thrusts due to Live Load in Metal Pipe Model (6 ft Cover) . 52
Figure 32—Deformation of Thermoplastic Pipe due to Live Load .............................................. 55
Figure 33—Bending Moments and Thrusts due to Live Load in Thermoplastic Pipe Model (2 ft
Cover) ......................................................................................................................................... 56
Figure 34—Bending Moments and Thrusts due to Live Load in Thermoplastic Pipe Model (6 ft
Cover) ......................................................................................................................................... 57
NCHRP 15-29 Appendix A iv
Figure 35—Deformation of Concrete Arch due to Live Load ...................................................... 60
Figure 36—Bending Moments and Thrusts due to Live Load in Concrete Arch Model (2 ft Cover)
.................................................................................................................................................... 61
Figure 37—Bending Moments and Thrusts due to Live Load in Concrete Arch Model (6 ft Cover)
.................................................................................................................................................... 62
Figure 38—Deformation of Metal Arch due to Live Load ............................................................ 65
Figure 39—Bending Moments and Thrusts due to Live Load in Metal Arch Model (2 ft Cover) . 66
Figure 40—Bending Moments and Thrusts due to Live Load in Metal Arch Model (6 ft Cover) . 67
Figure 41—Plastic Points in Soil Elements of Concrete Pipe Models with 50% and 100%
Interface Strength (Mohr-Coulomb Soil Model, 2 ft Cover) ......................................................... 72
Figure 42—Plastic Points in Soil Elements of Concrete Pipe Models with 50% and 100%
Interface Strength (Mohr-Coulomb Soil Model, 6 ft Cover) ......................................................... 73
Figure 43—Comparison of Bending Moments and Thrusts due to Live Load between Concrete
Pipe Models with 50% and 100% Interface Strength (2 ft Cover) ............................................... 74
Figure 44—Comparison of Bending Moments and Thrusts due to Live Load between Concrete
Pipe Models with 50% and 100% Interface Strength (6 ft Cover) ............................................... 75
Figure 45—Plastic Points in Soil Elements of Thermoplastic Pipe Models with 50% and 100%
Interface Strength (Mohr-Coulomb Soil Model, 2 ft Cover) ......................................................... 77
Figure 46—Plastic Points in Soil Elements of Thermoplastic Pipe Models with 50% and 100%
Interface Strength (Mohr-Coulomb Soil Model, 6 ft Cover) ......................................................... 78
Figure 47—Comparison of Bending Moments and Thrusts due to Live Load between
Thermoplastic Pipe Models with 50% and 100% Interface Strength (2 ft Cover) ....................... 79
Figure 48—Comparison of Bending Moments and Thrusts due to Live Load between
Thermoplastic Pipe Models with 50% and 100% Interface Strength (6 ft Cover) ....................... 80
Figure 49—Finite Element Model of Three-Sided Arch Top Culvert with 3 ft Cover ................... 83
Figure 50—Comparison of Vertical and Horizontal Displacements from Factored Live Load with
1.75 times those from Unfactored Live Load (HDPE Pipe, A2 Backfill) ...................................... 84
Figure 51—Comparison of Thrusts and Moments from Factored Live Load with 1.75 times those
from Unfactored Live Load (HDPE Pipe, A2 Backfill) ................................................................. 84
Figure 52—Comparison of Thrusts and Moments from Factored Live Load with 1.75 times those
from Unfactored Live Load (Hanson Arch) ................................................................................. 85
Figure 53—Test Setup of NCHRP Project 12-45 ........................................................................ 87
Figure 54—Instrumentation for Deformation in Concrete Culvert ............................................... 89
Figure 55—Instrumentation for Deformation in Metal Culvert ..................................................... 89
Figure 56—Cross Sections of HDPE Pipes: Type D and Type S ............................................... 91
Figure 57—Typical Installation of PE Pipe .................................................................................. 91
Figure 58—Live Load Vehicle in the MNDOT Study ................................................................... 92
Figure 59—Typical Test Pipe Instrumentation in the MNDOT Study .......................................... 93
Figure 60—Typical Dimensions of Finite Element Models of Long-Span Arch and HDPE Pipe 94
Figure 61—Finite Element Model of Concrete Arch Culvert with a Cover Depth of 3 ft.............. 95
Figure 62—Live Load Position in the 3D Analysis of Long-Span Arches ................................... 97
Figure 63—Deformed Shapes of Concrete Arch in the Plane of Wheel Loads (Effects of Live
Loads only) ................................................................................................................................. 98
Figure 64—Displacements Due to Live Loads from the 3D Analyses of Concrete Arch Culvert 98
Figure 65—Thrusts and Moments due to Live Loads in the Plane of Wheel Loads from the 3D
Analyses of Concrete Arch Culvert ............................................................................................. 99
Figure 66—Plastic Points in Soil Elements in the Plane of Wheel Loads in Concrete Arch
Analysis ..................................................................................................................................... 100
Figure 67—Finite Element Model of Metal Arch Culvert with a Cover Depth of 3 ft ................. 101
Figure 68—Soft Element to Match Longitudinal Stiffness of Metal Arch .................................. 102
Figure 69—Deformed Shapes of Metal Arch in the Plane of Wheel Loads (Effects of Live Loads
only) .......................................................................................................................................... 103
NCHRP 15-29 Appendix A v
Figure 70—Displacements due to Live Loads from the 3D Analyses of Metal Arch Culvert .... 104
Figure 71—Thrusts and Moments due to Live Loads in the Plane of Wheel Loads from the 3D
Analyses of Metal Arch Culvert ................................................................................................. 104
Figure 72—Plastic Points in Soil Elements in the Plane of Wheel Loads in Metal Arch Analysis
.................................................................................................................................................. 107
Figure 73—Finite Element Model of HDPE Pipe Culvert for Pipe Run 9 .................................. 108
Figure 74—Soft Element to Match Longitudinal Stiffness of HDPE Pipe ................................. 109
Figure 75—Positions of Live Load Vehicle Axles in the 3D Analyses of HDPE Pipes.............. 111
Figure 76—Deformed Shapes of Pipe Run 1 due to Live Loads in the Plane of Wheel Loads (A-
1, 1.4 ft Cover) .......................................................................................................................... 113
Figure 77—Vertical Crown Displacements of Pipe Run 1 due to Live Loads ........................... 113
Figure 78—Horizontal Displacements of Pipe Run 1 due to Live Loads (A-1, 1.4 ft Cover) ..... 114
Figure 79—Thrusts of Pipe Run 1 due to Live Loads in the Plane of Wheel Loads ................. 114
Figure 80—Moments of Pipe Run 1 due to Live Loads in Plane of Wheel Loads .................... 114
Figure 81—Plastic Points in Soil Elements of Pipe Run 1 in the Plane of Wheel Loads .......... 115
Figure 82—Deformed Shapes of Pipe Run 9 due to Live Loads in the Plane of Wheel Loads (A-
1, 2.5 ft Cover) .......................................................................................................................... 116
Figure 83—Vertical Crown Displacements of Pipe Run 9 due to Live Loads ........................... 116
Figure 84—Horizontal Displacements of Pipe Run 9 Due to Live Loads .................................. 117
Figure 85—Thrusts of Pipe Run 9 Due to Live Loads in the Plane of Wheel Loads ................ 117
Figure 86—Moments of Pipe Run 9 Due to Live Loads in Plane of Wheel Loads .................... 117
Figure 87—Plastic Points in Soil Elements of Pipe Run 9 in the Plane of Wheel Loads .......... 118
Figure 88—Deformed Shapes of Pipe Run 3 due to Live Loads in the Plane of Wheel Loads (A-
2, 1.6 ft Cover) .......................................................................................................................... 119
Figure 89—Vertical Crown Displacements of Pipe Run 3 due to Live Loads ........................... 119
Figure 90—Horizontal Displacements of Pipe Run 3 due to Live Loads (A-2, 1.6 ft Cover) ..... 120
Figure 91—Thrusts of Pipe Run 3 due to Live Loads in the Plane of Wheel Loads (A-2, 1.6 ft
Cover) ....................................................................................................................................... 120
Figure 92—Moments of Pipe Run 3 due to Live Loads in Plane of Wheel Loads .................... 120
Figure 93—Plastic Points in Soil Elements of Pipe Run 3 in the Plane of Wheel Loads .......... 121
Figure 94—Deformed Shapes of Pipe Run 7 due to Live Loads in the Plane of Wheel Loads (A-
2, 2.8 ft Cover) .......................................................................................................................... 122
Figure 95—Vertical Crown Displacements of Pipe Run 7 due to Live Loads (A-2, 2.8 ft Cover)
.................................................................................................................................................. 122
Figure 96—Horizontal Displacements of Pipe Run 7 due to Live Loads (A-2, 2.8 ft Cover) ..... 123
Figure 97—Thrusts of Pipe Run 7 due to Live Loads in the Plane of Wheel Loads (A-2, 2.8 ft
Cover) ....................................................................................................................................... 123
Figure 98—Moments of Pipe Run 7 due to Live Loads in Plane of Wheel Loads (A-2, 2.8 ft
Cover) ....................................................................................................................................... 123
Figure 99—Plastic Points in Soil Elements of Pipe Run 7 in the Plane of Wheel Loads (A-2, 2.8
ft Cover) .................................................................................................................................... 124
Figure 100—Ratios of 3D Analysis Results to Field Test Data for Displacements of Concrete
Arch ........................................................................................................................................... 128
Figure 101—Ratios of 3D Analysis Results to Field Test Data for Displacements of Metal Arch
.................................................................................................................................................. 128
Figure 102—Ratios of 3D Analysis Results to Field Test Data for Displacements of HDPE Pipes
.................................................................................................................................................. 129
Figure 15—Comparison of Displacements between Cases with Mohr-Coulomb and Hardening-
Soil Models (Metal Arch, Test 2, 3 ft Cover) ............................................................................. 131
Figure 16—Comparison of Thrusts and Moments under Wheel between Cases with Mohr-
Coulomb and Hardening-Soil Models (Metal Arch, Test 2, 3 ft Cover) ..................................... 132
NCHRP 15-29 Appendix A vi
Figure 17—Comparison of Crown Vertical Displacements between Cases with Mohr-Coulomb
and Hardening-Soil Models (HDPE Pipe, A2 Soil, 2.8 ft Cover) ............................................... 133
Figure 18—Comparison of Horizontal Diameter Changes between Cases with Mohr-Coulomb
and Hardening-Soil Models (HDPE Pipe, A2 Soil, 2.8 ft Cover) ............................................... 134
Figure 19—Comparison of Thrusts between Cases with Mohr-Coulomb and Hardening-Soil
Models (HDPE Pipe, A2 Soil, 2.8 ft Cover) ............................................................................... 134
Figure 20—Comparison of Moments between Cases with Mohr-Coulomb and Hardening-Soil
Models (HDPE Pipe, A2 Soil, 2.8 ft Cover) ............................................................................... 134
Figure 21—Cross Section of Finite Element Model for HDPE Pipe in ABAQUS ...................... 138
Figure 22—ABAQUS Metal Arch Model with 3 ft Cover ........................................................... 139
Figure 23—ABAQUS HDPE Pipe Model with 3 ft Cover .......................................................... 139
Figure 24—Comparison of Vertical and Horizontal Displacements between PLAXIS 3D and
ABAQUS Analyses (Metal Arch, Test 2, 3 ft Cover) ................................................................. 140
Figure 25—Comparison of Thrusts and Moments under Wheel between PLAXIS 3D and
ABAQUS Analyses (Metal Arch, Test 2, 3 ft Cover) ................................................................. 140
Figure 26—Vertical and Horizontal Displacements from ABAQUS Analyses with Orthotropic
Properties (Metal Arch, 3 ft Cover) ........................................................................................... 141
Figure 27 –Thrusts and Moments under Wheel from ABAQUS Analyses with Orthotropic
Properties (Metal Arch, 3 ft Cover) ........................................................................................... 141
Figure 28—Vertical and Horizontal Displacements from ABAQUS Analyses with Orthotropic
Properties (HDPE Pipe, A2 Backfill, 2.8 ft Cover) ..................................................................... 142
Figure 29—Vertical and Horizontal Displacements from ABAQUS Analyses with Orthotropic
Properties (HDPE Pipe, A2 Backfill, 1.6 ft Cover) ..................................................................... 143

NCHRP 15-29 Appendix A vii
1. INTRODUCTION
NCHRP Project 15-29 was funded to investigate the distribution of live loads through fills and
onto culverts. The project is intended to improve AASHTO Specifications for design of buried
structures and to investigate differences between the AASHTO Standard Specifications for
Highway Bridges, 17th Edition (AASHTO, 2002) and the AASHTO LRFD Bridge Design
Specifications, 3th Edition (AASHTO, 2004).
The scope of project 15-29 is to conduct studies through three-dimensional (3-D) finite element
(FE) modeling of live loads on buried culverts and to develop new AASHTO Specifications
based on the findings. Results and proposed design methods will be evaluated against test
data available in the literature, but no new tests will be conducted as a part of this project.
This report presents an investigation of the available constitutive models for soils that could be
used in the 3-D analyses. Information presented includes initial review of available soil models
and important model features, preliminary two-dimensional FE studies of live load distribution,
and full 3-D FE studies.
2. REVIEW OF AVAILABLE SOIL MODELS
Numerous soil constitutive models have been developed to date and are available for finite
element analysis. Lade (2005) prepared a summary of widely available soil constitutive models.
Each model has different capabilities and requires different experimental data for calibration.
Predicting the response of buried structures to surface live loads in a finite element analysis
requires a soil constitutive model that accurately captures culvert-soil interaction. Research has
been conducted with linear-elastic soil models (for example, Moore and Brachman (1994) and
Fernando and Carter (1998)); with nonlinear models including nonlinear elastic models,
perfectly plastic models, and plastic models with hardening (for example, Pang (1999)). For
typical culvert analysis, which has been historically conducted in 2-D, stress-dependent stiffness
and shear failure have been found to be important characteristics of suitable soil models. The
Duncan-Selig hyperbolic model (Duncan et al., 1980; Selig, 1988) has such features, and has
been implemented in the finite element programs CANDE (Musser, 1989) and SPIDA (Heger et
al., 1985) to analyze soil-structure interaction problems for culverts. Soil properties based on
these models have been used in the development of current AASHTO specifications for
reinforced concrete and thermoplastic pipe. The Duncan-Selig model, consists of the hyperbolic
Young's modulus model developed by Duncan (1980), and the hyperbolic bulk modulus
NCHRP 15-29 Appendix A 1
developed by Selig (1988). As discussed below, the soil properties used with this model were
developed by Selig (1988).
CANDE was developed by the FHWA, and has been widely used to design culverts, but
operates only in two dimensions. For ease of computation and to allow comparison with
CANDE we conducted preliminary analyses in 2-D and then extended these models to 3-D for a
complete investigation of actual live load distribution.
3-D modeling is computationally intensive. Because of this, it is important to select the
computationally simplest soil model that can accurately capture culvert/soil interaction as
resulting from live load. We selected three levels of soil model with varying levels of
sophistication for use on the project:
• linear-elastic (representing the simplest possible model),
• Mohr-Coulomb (linear elastic model with post-failure plasticity), and
• Plaxis 3D hardening-soil (stress dependence plus plasticity, similar to Duncan-Selig).

Features of the linear-elastic model, Mohr-Coulomb model, Hardening-Soil model, and Duncan-
Selig model are briefly discussed below. Compressive stresses are positive throughout this
report.
2.1 Linear Elastic
Modeling soil as linear elastic provides the most basic soil behavior, with no consideration of
non linear stress-strain behavior or plasticity at failure. Linear elastic soil behavior is described
by isotropic linear elasticity. Four elastic constants are used in analysis, but given any two of
the four, the other two can be calculated. The four parameters are: modulus of elasticity, E,
Poisson’s ratio, ν, bulk modulus, B, and shear modulus, G. In actual soil these elastic
constants vary with soil stress level, and some analysts use elastic properties that vary with
depth. One set of such properties, proposed by Selig (1990) are shown in Table 1. Selig
estimated Young's modulus of elasticity from the hyperbolic model for increasing values of
maximum principal stress, (σ , typically vertical stress), with the minimum principal stress, (σ ,
1 3
typically horizontal stress), equal to one-half to one- times the maximum principal stress. Elastic
constants can be selected by evaluating the soil vertical stress level, usually calculated as the
depth of fill times the soil density, ignoring the presence of a culvert. Procedures to select
elastic constants are described in detail in the following section on the Mohr-Coulomb model.
McGrath (1998) found that the proposed soil properties produced soil stiffnesses higher than
NCHRP 15-29 Appendix A 2