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A constitutive model based on rate-independent elastoplasticity concepts is developed to simulate the behavior of geologic materials under arbitrary three-dimensional stress paths, stress reversals and cyclic loading. The model accounts for the various factors such as friction, stress path, stress history, induced anisotropy and initial anisotropy that influence the behavior of geologic materials. A hierarchical approach is adapted whereby models of progressively increasing sophistication are developed from a basic isotropic-hardening associative model. The influence of the above factors is captured by modifying the basic model for anisotropic (kinematic) hardening and deviation from normality (nonassociativeness). Both anisotropic hardening and deviation from normality are incorporated by introducing into the formulation a second order tensor whose evolution is governed by the level of induced anisotropy in the material. In the stress-space this formulation may be interpreted as a translating potential surface Q that moves in a fixed field of isotropic yield surfaces. The location of the translating surface in the stress-space, at any stage of the deformation, is given by the 'induced anisotropy' tensor. A measure to represent the level of induced anisotropy in the material is defined. The validity of this representation is investigated based on a series of special stress path tests in the cubical triaxial device on samples of Leighton Buzzard sand. The significant parameters of the models are defined and determined for three sands based on results of conventional laboratory test results. The model is verified with respect to laboratory multiaxial test data under various paths of loading, unloading, reloading and cyclic loading.

This PhD thesis consists of five complementary chapters. Chapters 2 through 4 constitute the basis of research papers to be published subsequently. These three chapters summarize the state of a single crystal undergoing elastoplastic deformation. The studies presented in this thesis primarily deal with experimental and computational concepts that enable the calculation, measurement and extraction of the spatially resolved net Burgers density vector and the geometrically necessary dislocation densities (GNDs), which reveal the small scale continuum characteristics of a single crystal in the elastoplastic state. The calculation methodology of a new validation parameter, β, which is the orientation of the net Burgers density vector, is given in chapter 2. This new parameter, β, enables us to validate the elastic-plastic constitutive relations. Since the existing methods used for validation cannot give direct information about the state of the material, the β-variable is introduced for elastic- plastic constitutive models. β-fields, which are essentially contour maps of β-variables on two dimensional spatial coordinates, are used to monitor the activity regions of effective slip systems. Chapters 2 through 4 present a comprehensive analysis of the spatially resolved net Burgers density vector, along with the length scale characterization of dislocation structures and validation of constitutive relations. The studies presented in this work are the outcome of experimental and computational research. The experimental work consists of the indentation of a nickel single crystal deformed through a quasi-statically applied line load parallel to the [110] crystallographic orientation. The line load was applied onto (001) surface of the single crystal by a tungsten carbide wedge indenter with a 90◦ included angle. A two-dimensional deformation field on an indented single crystal, in which the only non-zero lattice rotation occurs in the plane of deformation and only three effective in-plane slip systems are activated, was investigated. The mid-section of the deformed single crystal was exposed by EDM and polished electrochemically. The in-plane lattice rotations were measured by high-resolution electron backscattered diffraction (HR-EBSD). The Nye's dislocation density components, lattice curvatures, GNDs and net Burgers density vectors were calculated. Therefore, the β- variable and the β-fields are calculated both experimentally, analytically and numerically in Chapter 2. A qualitative comparison of the three methods showed that the β-field obtained from experimental measurements agrees with those obtained from analytical and numerical methods. The directions of the net Burgers density vector, which are used to determine the boundaries of the slip activity regions, are also given in Chapter 2. Chapter 3 mainly deals with the hardening parameters associated with strain hardening rules utilized in finite element simulations, and investigates the sensitivity of the β-variable to parameters such as latent hardening ratio, initial hardening modulus and saturation strength. The study revealed that a change in the saturation strength has a significant effect on both magnitude of the β-variable and the boundary of the slip activity regions. Chapter 4 presents a length scale analysis associated with dislocation structures such as cell size and cell wall width. The methods presented in this chapter employ the SEM- based continuum method and Fourier Analysis. As-measured GNDs are extracted along the local crystallographic traces, and a quasi-periodic arrangement of dislocation structures is obtained. The extracted GND functions are truncated, interpolated, and filtered. Finally, Fourier Transform is applied to obtain a relationship between cell size and cell wall width of the dislocation structures. The results are compared with those obtained by TEM micrographs. Whereas TEM micrographs characterize the dislocation structures in small scale, the method that is presented in this chapter provides multi scale characterization, which is an order of magnitude larger. Concluding remarks and recommendations for future studies are given in Chapter 5.

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In the true triaxial test procedure used for testing laboratory-prepared kaolinite clay samples, undrained (with constant mean stress) strength tests were conducted to study the yield and failure of the clays. The principle concern focussed around the influence of orientation of particle bedding plane on the development of yield and failure characteristics of the clay. As the true triaxial cell permits variations of the three principal stresses, it was possible to study the soil response in any chosen quadrant of the principal space. / As a consequence to what is mentioned above, two types of consolidated undrained true triaxial tests were conducted in this study. In the first type, specimens were trimmed from the block sample with 90, 60, 30 and 0 degree orientation angles of particle's bedding planes; these angles were measured with respect to the direction of the major principal stress axis. For each degree of inclination, specimens were tested with three confining pressures 207, 276 and 345 kPa, and for each value of confining pressure, the loading path was varied from compression to tension. / The degree of dissociation between the stress and strain increment vectors was seen to depend on both initial and stress induced anisotropy. / Most important of all, a constitutive relationship for anisotropic kaolinite clay was derived on the basis of the observed experimental behaviour of soil samples under loading. / Additionally, anisotropy is characterized by a double transformation technique. The first transformation accounts for the directional dependency whilst the second transformation concerns itself with anisotropy of the base vectors. The relative joint invariant principle is used to calculate the degree of dissociation during the loading process. The variation of the dissociation angle during the loading process can be considered as a measure of the evolution of the resultant anisotropy. The model has shown to provide viable predictions of the stress-strain relationships obtained from true triaxial tests on an anisotropic kaolinite clay for: (a) different inclinations of particle's bedding planes, (b) different stress paths in one sector, (c) different stress paths in other sectors, and (d) the failure surfaces for different inclinations of particle's bedding planes in the octahedral plane. (Abstract shortened with permission of author.)

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