Numerical Modeling of Expansive Soil Behavior

[hapsea]

Numerical Modeling of Expansive Soil Behavior

Author: Ayman Abed | Size: 11.7 MB | Format: PDF | Quality: Original preprint | Year: 2008 | pages: 216

Expansive soils contain clay minerals named montmorillonites or smectites. In this type
of soils, significant deformations are associated with changes in suction and degree of
saturation. As expansive soils are widespread in nature, they constitute an important
challenge for geotechnical engineering. In the unsaturated zone well above the phreatic
groundwater level the soil moisture content varies significantly over the seasons and the
study of expansive soil behaviour is thus based on unsaturated soil mechanics and unsaturated
groundwater flow. At present unsaturated flow is getting increasing attention
in literature and so is the mechanical behaviour of unsaturated soils. Although the title
of this study refers to expansive soils, most of the developments reported are applicable
to unsaturated soils in general.
Being from Syria, a land with large areas of expansive soils, Ayman Abed came to
Stuttgart to study the mechanical behaviour of such soils. Being not a specialist in this
field, I was very pleased to havemy colleague Professor Antonio Gens from Barcelona as
a co-advisor. No doubt, the Barcelona BasicModel represented the state-of-the-art in the
elastoplastic modelling of unsaturated soils in the year 2004 when Ayman Abed came to
Stuttgart, and a detailed description of this model is contained in the present study.
The main original contribution of this thesis to geomechanics is the extension or generalisation
of the Barcelona Basic Model from isotropic to anisotropic soil. Indeed unsaturated
clays are mostly anisotropic and should thus be modelled within the framework
of anisotropic plasticity as presently also done for saturated clays.
This study represents a significant contribution to the subject of unsaturated soil mechanics
that can be used as a spring board for further research in this challenging field
of geomechanics. To me it has been a great pleasure to work with Ayman Abed and I am
very happy to congratulate him with this achievement of the doctoral thesis.


Contents
1 Introduction 1
1.1 Unsaturated expansive soil . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Surface tension and suction . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Objectives and scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Layout of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Fundamental Principles 7
2.1 Sign convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Stresses and equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Displacements and strains . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Stresses in unsaturated soil . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5 Stress-strain relationship for unsaturated elastic soil . . . . . . . . . . . . . 16
2.6 Experimental determination of elastic soil parameters . . . . . . . . . . . . 19
2.6.1 Typical stress paths as used in triaxial tests on unsaturated soil . . 20
3 Elastoplastic Modeling of Soil 27
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Plastic behavior modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Yield function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.2 Flow rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.3 Hardening law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.4 The consistency condition . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 The stress-strain formulation in case of elastoplastic model . . . . . . . . . 34
3.4 Cam Clay model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4.1 Isotropic loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4.2 Yield surface and flow rule . . . . . . . . . . . . . . . . . . . . . . . 38
3.4.3 Modified Cam Clay hardening rule . . . . . . . . . . . . . . . . . . 40
3.4.4 Elastoplastic matrix for Cam Clay model . . . . . . . . . . . . . . . 40
3.4.5 On the failure criterion as used in Cam Clay . . . . . . . . . . . . . 41
3.5 On Modified Cam Clay parameters . . . . . . . . . . . . . . . . . . . . . . . 44
3.5.1 Stiffness parameters as used in Cam Clay model . . . . . . . . . . . 44
3.5.2 Strength parameter as used in Cam Clay model . . . . . . . . . . . 45
4 Elastoplastic Modeling of Unsaturated Soil 47
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Experimental evidences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.1 Effect of suction on soil stiffness . . . . . . . . . . . . . . . . . . . . 47
4.2.1.1 Loading-unloading under constant suction . . . . . . . . 48
4.2.1.2 Wetting under constant net stress . . . . . . . . . . . . . . 49
4.2.1.3 Drying under constant net stress . . . . . . . . . . . . . . . 51
4.2.1.4 Yielding of unsaturated soil . . . . . . . . . . . . . . . . . 52
4.2.2 Effect of suction on soil strength . . . . . . . . . . . . . . . . . . . . 52
4.2.3 Summary on the experimental observations . . . . . . . . . . . . . 54
4.3 Early attempts to model unsaturated soil behavior . . . . . . . . . . . . . . 55
4.3.1 Volumetric and shear strains . . . . . . . . . . . . . . . . . . . . . . 55
4.3.2 Shear strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 Barcelona Basic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.4.1 Isotropic loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.4.1.1 Net stress primary loading-unloading . . . . . . . . . . . 61
4.4.1.2 Suction primary loading-unloading . . . . . . . . . . . . . 62
4.4.1.3 General expression for isotropic stress state . . . . . . . . 63
4.4.1.4 Isotropic plastic compression upon wetting . . . . . . . . 64
4.4.2 More general states of stress . . . . . . . . . . . . . . . . . . . . . . . 66
4.4.2.1 Elastic behavior . . . . . . . . . . . . . . . . . . . . . . . . 66
4.4.2.2 Plastic behavior . . . . . . . . . . . . . . . . . . . . . . . . 67
4.4.2.3 LC and SI coupling . . . . . . . . . . . . . . . . . . . . . . 69
4.4.3 Elastoplastic matrix for Barcelona Basic Model . . . . . . . . . . . . 69
4.5 On the parameters of Barcelona Basic Model . . . . . . . . . . . . . . . . . 73
4.5.1 Parameters , 1 and pc . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.5.2 Suction stiffness parameters . . . . . . . . . . . . . . . . . . . . . . . 75
4.5.3 Capillary cohesion parameter . . . . . . . . . . . . . . . . . . . . . . 75
5 Finite Element Implementation 77
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2 Balance and kinematic equations . . . . . . . . . . . . . . . . . . . . . . . . 78
5.3 Virtual work principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.4 Finite element discretization in case of unsaturated soil . . . . . . . . . . . 80
5.5 Local integration of constitutive equation . . . . . . . . . . . . . . . . . . . 83
5.5.1 Explicit integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.5.2 Implicit integration . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.5.2.1 Elastic predictor . . . . . . . . . . . . . . . . . . . . . . . . 84
5.5.2.2 Plastic corrector with return mapping . . . . . . . . . . . . 84
5.5.3 Stress integration with LC is active . . . . . . . . . . . . . . . . . . . 87
5.5.4 Stress integration with SI is active . . . . . . . . . . . . . . . . . . . 87
5.5.5 Stress integration when both LC and SI are active . . . . . . . . . . 89
5.6 The global iterative procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.6.1 Global and element stiffness matrices . . . . . . . . . . . . . . . . . 91
5.6.2 Global Newton-Raphson iterations . . . . . . . . . . . . . . . . . . . 92
5.7 Validation of the BB-model implementation . . . . . . . . . . . . . . . . . . 94
5.7.1 Test Number 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.7.2 Test Number 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.7.3 Test Number 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.7.4 Test Number 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.7.5 Test Number 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.7.6 Test Number 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6 Unsaturated ground water flow 105
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2 Governing partial differential equation . . . . . . . . . . . . . . . . . . . . . 105
6.2.1 Steady-state water flow . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2.2 Transient saturated water flow . . . . . . . . . . . . . . . . . . . . . 106
6.2.3 Transient unsaturated water flow . . . . . . . . . . . . . . . . . . . . 109
6.2.4 Multiphase flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2.5 Fitting functions for soil degree of saturation . . . . . . . . . . . . . 112
6.2.6 Fitting functions for soil water permeability . . . . . . . . . . . . . 114
6.3 Finite element discretization in space . . . . . . . . . . . . . . . . . . . . . . 116
6.4 Finite differences discretization in time . . . . . . . . . . . . . . . . . . . . . 117
6.5 Picard iteration method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.6 Validation of the finite element code being used . . . . . . . . . . . . . . . 119
6.6.1 Validation in case of unsaturated stationary ground water flow . . 119
6.6.2 Validation in case of unsaturated transient ground water flow . . . 121
7 Anisotropic model for unsaturated soil 123
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.2 Origin of anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.3 Empirical observations and constitutive modeling of anisotropy . . . . . . 124
7.4 Models based on Cam Clay model . . . . . . . . . . . . . . . . . . . . . . . 125
7.4.1 SANICLAY model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.4.2 S-Clay1 model for anisotropic soil . . . . . . . . . . . . . . . . . . . 128
7.4.2.1 The initial value of  . . . . . . . . . . . . . . . . . . . . . 129
7.4.2.2 The constant  . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.4.2.3 The constant μ . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.4.2.4 S-Clay1 in the general state of stress . . . . . . . . . . . . . 130
7.5 Anisotropy in unsaturated soil . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.5.1 Anisotropic model for unsaturated soil . . . . . . . . . . . . . . . . 133
7.5.1.1 Flow and hardening rules . . . . . . . . . . . . . . . . . . 135
7.5.1.2 General states of stress . . . . . . . . . . . . . . . . . . . . 136
7.5.1.3 Numerical implementation of the new anisotropic model 137
7.6 Numerical validation of the implemented model . . . . . . . . . . . . . . . 138
7.6.1 Case 1: Isotropic fully saturated soil . . . . . . . . . . . . . . . . . . 140
7.6.2 Case 2: Isotropic unsaturated soil . . . . . . . . . . . . . . . . . . . . 142
7.6.3 Case 3: Anisotropic fully saturated soil . . . . . . . . . . . . . . . . 144
8 Boundary value problems 147
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
8.2 Problem 1: Shallow foundation exposed to a ground water table increase . 147
8.2.1 Geometry, boundary conditions and initial conditions . . . . . . . . 147
8.2.2 The interaction between the ground water flow finite element code
and the deformation code . . . . . . . . . . . . . . . . . . . . . . . . 148
8.2.3 Results of numerical analyses with isotropic BB-model . . . . . . . 149
8.2.4 Calculation with an anisotropic model . . . . . . . . . . . . . . . . . 152
8.3 Problem 2: Bearing capacity of unsaturated soil . . . . . . . . . . . . . . . . 153
8.4 Problem 3: Shallow foundation exposed to a rainfall event . . . . . . . . . 158
8.4.1 Phase 1: Deformation due to foundation loading . . . . . . . . . . . 159
8.4.2 Phase 2: Deformation due to infiltration . . . . . . . . . . . . . . . . 160
8.5 Problem 4: Trial wall on expansive soil in Sudan . . . . . . . . . . . . . . . 162
8.5.1 Soil properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
8.5.2 The test procedure and measurements . . . . . . . . . . . . . . . . . 165
8.5.3 Numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8.5.3.1 Geometry and boundary conditions . . . . . . . . . . . . 166
8.5.3.2 Parametric study . . . . . . . . . . . . . . . . . . . . . . . 167
8.5.3.3 Model predictions versus field data . . . . . . . . . . . . 170
9 Conclusions and recommendations 175
9.1 Conclusions on modeling and numerical implementation . . . . . . . . . . 175
9.2 Conclusions on the response of shallow foundation on unsaturated soil . . 176
9.2.1 Isotropic behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
9.2.2 Anisotropic behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
9.3 Recommendation for further research . . . . . . . . . . . . . . . . . . . . . 177
Bibliography 177

Code:

***************************************
Content of this section is hidden, You must be registered and activate your account to see this content. See this link to read how you can remove this limitation:

http://forum.civilea.com/thread-27464.html
***************************************

This post has been made by CivilEA Post-Generator ver 2.1.6

[mary]

direct link

Code:

***************************************
Content of this section is hidden, You must be registered and activate your account to see this content. See this link to read how you can remove this limitation:

http://forum.civilea.com/thread-27464.html
***************************************