Sec. Title |
Page |
Chapter 1: Research background, importance of the problem, research statement and questions |
1 |
1. Introduction |
2 |
1. 1. Background |
2 |
1.1.1. Unsaturated soil mechanics: its importance and engineering applications |
2 |
1.1. 2. The Constitutive modeling of unsaturated soils: the role of effective stress concept |
3 |
1.2. Motivation for this research |
4 |
1.3. Statement of the research problem and the research objectives |
5 |
1.4 Research Methodology |
8 |
1.5. Outline of the thesis |
9 |
Chapter 2: A general literature review: overview of different approaches to formulation of the effective stress |
11 |
2.1. Stress state variables for unsaturated soils |
13 |
2.2.Do we need a second stress state variable? |
14 |
2.3.The current challenges in unsaturated soil mechanics |
15 |
2.4.The role of effective stress parameter in unsaturated soil mechanics |
15 |
2.4.1.Factors affecting effective stress parameter |
15 |
2.4.2.Different categories for formulating effective stress parameter |
16 |
2.4.3. Simple geometrical considerations and force equilibrium |
16 |
2.4.4. Emprical formulae for effective stress parameter |
19 |
2.4.5. Determination of effective stress parameter using artificial neural networks (ANNs) |
19 |
2.4.6. Determination of effective stress and effective stress parameter using pore network modeling |
22 |
2.4.6.1. Historical and theoretical backgrounds |
22 |
2.4.7. Mirco-mechanical approaches to effective stress and effective stress parameter |
25 |
2.4.8.Thermodynamic approaches to effective stress parameter |
26 |
2.5. Interfacial areas and their role in the study of unsaturated soils |
25 |
2.5.1. From Microscopic scale to macroscopic scale |
26 |
2.5.2. Mechanics and hydraulics of unsaturated soils: interfacial areas as missing state variables |
28 |
Chapter 3: Review of the major thermodynamic approaches, their procedure, and their assumptions |
30 |
3.1.1 Houlsby (1997): Effective stress as work conjugate of the strain rate |
31 |
3.1.2 Gray and Schrefler (2002) and Gray et al. (2009): a rational thermodynamic approach and variational method |
33 |
3.1.3 Coussy and Dangla (2002): Unsaturated thermoporoelasticity |
38 |
3.1.4. Hassanizadeh and Gray (1990): A combination of averaging theories and mixture theories |
39 |
3.2. Concluding remarks |
40 |
Chapter 4: The importance of hydraulic hysteresis: Insights into variation of the effective stress in drying and wetting from pore network modeling |
41 |
4.1. Pore network modeling |
42 |
4.1.1 Proposed algorithm and the conceptual model |
43 |
4.2. Results and discussion |
44 |
4.2.1 Determination of the effective stress parameter from available data in the literature |
44 |
4.2.2 Simulation results and discussion of results |
45 |
4.3. Conclusion |
47 |
Chapter 5: When a thermodynamic framework confirms findings of micro-mechanics |
48 |
5.1Theory |
50 |
5.1.1 Balance laws for phases and interfaces |
50 |
5.1.1.1 Conservation of mass |
50 |
5.1.1.2 Conservation of momentum |
51 |
5.1.1.3. Conservation of energy |
51 |
5.1.1.4 Balance of entropy |
52 |
5.1.2 Second law of thermodynamics |
53 |
5.1.3. Constitutive assumptions |
53 |
5.2. Result and discussion |
54 |
Chapter 6: The role of fluid-fluid interfacial areas in hydro-mechanical coupling |
56 |
6.1 Effective stress approach: Is a bishop type equation able to interpret variation of the effective stress? |
57 |
6.2. Review of the recent experimental evidences: Roles of different physical phenomena |
58 |
6.2.1 Role of hydraulic history |
58 |
6.2.2 Role of capillary forces (Bonding phenomenon) |
58 |
6.2.3 Hydro-mechanical coupling |
59 |
6.3. Requirements for a proper thermodynamic approach for unsaturated soils |
60 |
6.4. Theory |
61 |
6.4.1 Outline of the method |
61 |
6.4.2. Hydro-mechanical coupling and its influence on constitutive assumptions for free energies |
62 |
6.4.3 Exploitation of entropy inequality |
63 |
6.4.3.1. Effective stress formula for rigid grains |
63 |
6.4.3.2 The concept of suction stress characteristic surface (SSCS) |
64 |
6.4.3.3 Bishop’s Effective stress parameter |
67 |
6.5. Results and discussion |
69 |
6.6. Concluding remarks |
76 |
Chapter 7: Beyond equilibrium condition (formulation of effective stress in transient unsteady flow) |
78 |
7.1. Short literature survey on dynamic effects in matric suction |
80 |
7.2. Importance of non-equilibrium conditions and their types |
83 |
7.3. Formulation of the effective stress in non-equilibrium condition |
84 |
7.4. How to measure required parameters |
85 |
7.5. Future perspectives and possible advances in experimental techniques |
86 |
Chapter 8: Summary of the results and directions for future research |
87 |
8.1. Summary of the major contributions of the current study |
88 |
8.2. Further research works and possible research directions |
89 |
Appendices |
90 |
Appendix A: Exploitation of entropy inequality for a granular porous medium with rigid grains |
91 |
Appendix B: Exploitation of entropy inequality for deformable solid |
94 |
Appendix C: on the relationship connecting effective stress parameter to the area between soil water retention curve and saturation axis |
96 |
References |
98 |
List of Figures
Sec. Title |
Page |
Fig. 1.1 Major topics (questions) to address in this thesis |
7 |
Fig. 2.2 Wavy section of general unsaturated soil (Karube and Kawai, 2001) |
19 |
Fig. 2.3 Variation of the effective stress parameter with degree of saturation (Zerhouni, 1991) |
21 |
Fig. 2.4 Evolution of the pore network models (Berkowitz and Ewing, 1998) |
23 |
Fig. 2.5 A schematic illustration of a regular pore network model |
24 |
Fig. 2.6 Conceptual sketch for unsaturated soils, (Jahanandish et al., 2010) |
25 |
Fig. 4.1 Conceptual sketch for unsaturated soils, (Xu, 2004) |
44 |
Fig. 4.2 Modeling hydraulic hysteresis using pore network |
45 |
Fig. 4.3 Simulation of the effective stress parameter in drying and wetting paths as compared to the experimental data |
46 |
Fig. 6.1 A 2D schematic sketch of suction stress trajectories |
67 |
Fig. 6.2 a 2D plot (drying and wetting trajectories) and b 3Dplot (surface) of suction stress for Buffalo dam clay (Exp. data from Khalili and Zargarbashi (2010)) |
73 |
Fig. 6.3 a 2D plot (drying and wetting trajectories) and b 3Dplot (surface) of suction stress for Bourke silt (Exp. data from Khalili and Zargarbashi (2010)) |
74 |
Fig.6.4 a 2D plot (drying and wetting trajectories) and b 3Dplot (surface) of suction stress for mixture of Sydney sand (75%) and kaolin (25%) (Exp. data from Khalili and Zargarbashi (2010)) |
74 |
Fig. 6.5 a 2D plot (drying and wetting trajectories) and b 3Dplot (surface) of suction stress for mixture of Sydney sand (70%) and Buffalo dam clay (30%) (Exp. data from Khalili and Zargarbashi (2010)) |
74 |
Fig. 6.6 a 2D plot (drying and wetting trajectories) and b 3Dplot (surface) of suction stress for compacted kaolin samples (Exp. data from Uchaipichat (2010 b)) |
75 |
Fig. 6.7 Plots of effective stress parameter a Buffalo dam clay and b Bourke silt |
75 |
Fig. 6.8 Plots of effective stress parameter a mixture of Sydney sand (75%) and kaolin (25%) b Mixture of Sydney sand (70%) and Buffalo dam clay (30%) |
75 |
Fig. 6.9 Plot of effective stress parameter for compacted kaolin samples |
76 |
Fig. 7.1 Results of Top et al. (1967): Dynamic versus equilibrium retention curves |
81 |
Fig. 7.2 Results of Vachaud et al. (1972): Dynamic versus equilibrium retention curves at three different depths |
82 |
Fig. 8.1 Formulation of suction stress in transient condition |
88 |
List of Tables
Sec. Title |
Page |
Table 1.1. Research statement and research questions |
7 |
Table 6.1 Different relationships for effective stress parameter, c |
68 |
Table 6.2 Coefficients of SWRC for different soil samples used in this study |
72 |
Table 6.3 Coefficients of Suction Stress Characteristic Surface (SSCS) |
73 |
