Soutenance mémoire
Constitutive soil model
Various constitutive equations are used to reproduce rockfill material behavior (Costa et Alonso, 2009; Pramthawee, Jongpradist et Kongkitkul, 2011; Varadarajan et al., 2003; Xing et al., 2006). Some of them are listed below. The Barcelona basic model has been used by Costa and Alonso to simulate the mechanical behavior of the shoulder, filter, and core materials. This constitutive soil model was used to model the Lechago dam in Spain. The impacts of suction in soil strength and stiffness were considered in this model. A good agreement was achieved between laboratory results and model simulations (Costa et Alonso, 2009). An elastoplastic constitutive model (DSC) was applied by Varadarajan to reproduce the rockfill material characteristics. Large size triaxial tests were used to define the rockfill material parameters. As a result, it was shown that the model can provide a suitable prediction of the behavior of the rockfill materials (Varadarajan et al., 2003). An “evaluation of the HS model using numerical simulation of high rockfill dams” had been conducted by Pramthawee (Pramthawee, Jongpradist et Kongkitkul, 2011). To make a comparison with field data, the soil model was numerically implemented into a finite element program (ABAQUS).
The material parameters for the rockfill were obtained from laboratory triaxial testing data. Finally, it was shown that by using the HS constitutive model, the response of rockfills under dam construction conditions could be precisely simulated (Pramthawee, Jongpradist et Kongkitkul, 2011). The non-linear Hyperbolic model (Duncan and Chang, 1970) was used by Feng Xing to model a reliable approximation of soil behavior. The Hyperbolic model was implemented in two-dimensional finite element software. The study focused on the “physical, mechanical, and hydraulic properties of weak rockfill during placement and compaction in three dam projects in China”. The material parameters for the rockfill were estimated from laboratory tests. Numerical analysis was conducted to evaluate the settlements and slope stability of the dams and finally, the results were compared with field measurements. Slope stability and deformation analysis indicated a satisfactory performance of concrete-faced rockfill dams by using suitable rock materials (Xing et al., 2006). Another constitutive soil model that can be considered for further research on rockfill materials is the HSS model. This constitutive soil model can simulate the pre-failure nonlinear behavior of soil. Several applications of the HSS model in numerical modeling of geotechnical structures were reported by Obrzud (Obrzud et Eng, 2010).
Hardening soil model
In this section, the HS model is used to simulate the drained triaxial test. In contrast to the MC model, the soil stiffness in this model is defined more precisely by using three modulus stiffnesses, namely, the triaxial loading stiffness, triaxial unloading stiffness, and oedometer loading stiffness (Brinkgreve, 2007). A summary of the HS model parameters for Hostun sand is presented in table 2.5. The confining pressure, ?? is assumed as 300 kPa. The deviator stress values (?? − ??) for dense and loose sand, calculated theoretically using equation 2.2, are in good agreement with the results of Plaxis, Zsoil, and the results obtained from experimental tests. As shown in figure 2.12, for both experimental test data (dense Hostun sand) and numerical analysis conducted based on the HS constitutive model, a hyperbolic relationship can be observed between the deviatoric stress (principal stress difference) and the vertical strain. The stress–strain relationship of soil in the HS model before reaching failure is based on the hyperbolic model (Schanz, Vermeer et Bonnier, 1999). A good agreement is indicated in figure 2.12 between the first hyperbolic part of the simulation conducted using Plaxis and Zsoil and the experimental data. The HS model does not include any softening behavior (Obrzud et Eng, 2010); hence, the second part of the graph stays constant and cannot completely show the same experimental results. In figure 2.14, it can be observed that the triaxial test results (for loose Hostun sand) based on the HS constitutive model calculation are in good agreement with experimental test results. Finally, it is evident that the ultimate shear strength for dense sand is higher than loose sand; this can be observed in figures 2.12 and 2.14. A good agreement is observed between Plaxis and Zsoil test results.
Comparison between constitutive soil models
In this chapter, the data reported from earlier experiments (Brinkgreve, 2007; Schanz et Vermeer, 1996) were used to obtain the parameters for modeling and to compare the different constitutive models, i.e., Duncan–Chang, MC, HS, and HSS in Zsoil and Plaxis. The comparison was conducted by modeling a consolidated drained triaxial test. It can be observed from figures 2.24, 2.25, 2.28, and 2.29 that a simple linear function as in the MC model is not sufficient to describe the soil stress–strain relation completely. The hyperbolic relation implemented in the Duncan–Chang and HS models provide a better fit for the soil stress–strain relation as can be observed in figures 2.24, 2.25, 2.28, and 2.29. As sand soil is subjected to shear strains, it may expand or contract due to changes in granular interlocking. If the sand soil volume increases, the peak strength will be followed by a reduced shear strength due to reduced density. This lowering of shear strength is known as strain softening. A constant stress–strain relationship is obtained when the expansion or contraction of material ends, and when interparticle bonds are fragmented. When the soil reaches a state where its shear strength and density do not change, then it is said to have reached the critical state (Roscoe, Schofield et Wroth, 1958). “A loose soil will contract in volume on shearing, and may not develop any peak strength above the critical state” (Roscoe, Schofield et Wroth, 1958). From figures 2.28 and 2.29, it can be observed that the results using the Duncan–Chang, MC, HS, and HSS models correctly show the critical strength. In dense soil (figures 2.24 and 2.25), contraction is prevented once granular interlocks are formed. To overcome this, additional shear force is required to dilate the soil and peak shear strength can be observed. After reaching the peak strength, the shear strength of soil declines (softening) as the soil expands. Strain softening will continue until the critical state is reached and the volume becomes constant (Roscoe, Schofield et Wroth, 1958).
As can be observed from figures 2.24 and 2.25, the graphs of HS and HSS overlap with each other and provide a better fit when compared with that of MC. For all the models, the peak and critical state coincide and reach the same peak stress. None of the models is able to display the softening phenomenon. From figures 2.26, 2.27, 2.30, and 2.31, it can be observed that MC, HS, and HSS accurately show the dilatant behavior of soil (Roscoe, Schofield et Wroth, 1958). HS and HSS provide better results as compared with MC for both types of soils. HS and HSS have identical plots in case of dense sand (figures 2.26 and 2.27), whereas in case of loose soil, the plot using HS model is closer to the experimental results by a narrow margin (figures 2.30 and 2.31). Additionally, the Duncan–Chang soil model does not consider dilatancy; hence, a large difference can be observed between the simulation and experimental data for dense sand (figure 2.26). Overall, the Duncan–Chang, HS, and HSS provide a better fitting stress–strain curve in comparison with MC; however, they fail to account for softening in case of dense sand. For the volumetric strain versus axial strain, both HS and HSS results have acceptable accuracy, which are better than those of MC and Duncan–Chang.
Duncan–Chang Model
Numerical analyses implemented using the Duncan–Chang model are shown in figures 2.38 and 2.39. The Duncan–Chang model is a non-linear elastic model based on a hyperbolic relationship between stress and strain (Duncan, Wong et Mabry, 1980). This type of constitutive model was formulated in order to depict an appropriate and fit result on the data from different laboratory experiments (e.g., triaxial or oedometer tests) (Duncan, Wong et Mabry, 1980). However, as mentioned in chapter 1, some limitations and restrictions, such as plasticity and dilatancy can be observed in this model (Seed, Duncan et Idriss, 1975). Two different material sets (dense Hostun sand and loose Hostun sand) were used. The properties of these materials are listed in table 2.7. The results shown in figures 2.38 and 2.39 do not indicate a good agreement between the experimental test and simulation. The experimental results exhibit a permanent strain after each loading and unloading (deformation results in irreversible plastic strain), whereas the Duncan–Chang simulation displays elastic behavior. For the simulation conducted using the Duncan–Chang model, unloading and reloading curves coincide with the loading curve during different loading steps. From figures 2.38 and 2.39, it can be observed that the simulation and experimental results for loose and dense sand are not compatible. The Duncan–Chang model cannot provide a satisfactory prediction behavior of the stress–strain relationship (??? − ???) under loading and unloading cycles.
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Table des matières
INTRODUCTION
CHAPTER 1 A REVIEW OF CONSTITUTIVE SOIL MODELS
1.1 Introduction
1.2 Constitutive soil model
1.2.1 Hyperbolic model
1.2.2 Hardening soil model
1.2.3 Hardening soil-small strain model
CHAPTER 2 COMPARISON AMONG DIFFERENT CONSTITUTIVE SOIL MODELS THROUGH TRIAXIAL AND OEDOMETER TESTS
2.1 Introduction
2.2 Triaxial test
2.3 Finite element modeling
2.3.1 Geometry of model and boundary conditions in Plaxis
2.3.2 Geometry of model and boundary condition in Zsoil
2.4 Experimental data
2.5 Application of constitutive soil models
2.5.1 Mohr–Coulomb model
2.5.2 Hardening soil model
2.5.3 Hardening small strain soil model
2.5.4 Duncan–Chang soil model
2.6 Comparison between constitutive soil models
2.7 Oedometer test
2.8 Finite element modeling
2.8.1 Geometry of model and boundary conditions in Plaxis
2.8.2 Model geometry and boundary conditions in Zsoil
2.9 Experimental data
2.10 Application of constitutive soil models
2.10.1 Duncan–Chang Model
2.10.2 Hardening soil model
2.10.3 Hardening small strain constitutive soil model
2.11 Comparison between constitutive soil models
2.12 Updated mesh results for triaxial test
CHAPTER 3 NUMERICAL SIMULATIONS FOR DAM-X
3.1 Introduction
3.2 Asphalt core dam
3.3 Dam-X
3.4 Typical cross section
3.5 Soil parameters
3.6 Instrumentation
3.7 Finite element modeling
3.8 Displacement contours at the end of construction
3.9 Comparison between measured data and numerical simulations after construction
3.9.1 Comparison between measured and computed displacements after construction (inclinometer INV-01)
3.9.2 Comparison between measured and computed displacements after construction ( inclinometer INV-02)
3.9.3 Comparison between measured and computed displacements after construction ( inclinometer INV-03)
3.9.4 Comparison between measured and computed displacements after construction (INH-01 and INH-02)
3.10 Comparison between Plaxis and Zsoil
3.11 Numerical simulation procedure for wetting
3.11.1 Justo approach
3.11.2 Nobari–Duncan approach
3.11.3 Escuder Procedure
3.11.4 Plaxis Procedure
3.12 Results after impoundment
3.12.1 Comparison between measured and computed displacements after impoundment (inclinometer INV-01)
3.12.2 Comparison between measured and computed displacements after impoundment (inclinometer INV-02)
3.12.3 Comparison between measured and computed displacements after impoundment (inclinometer INV-03)
3.12.4 Comparison between measured and computed displacements after impoundment (inclinometer INH-01)
3.13 Shear wave velocity measurement
3.13.1 Material properties for zone 3O and 3P
3.13.2 Comparison between measured and computed displacements
3.14 Concluding remarks
CONCLUSION
RECOMMENDATIONS
APPENDIX I
APPENDIX II
BIBLIOGRAPHY
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