| This dissertation is an attempt for a comprehensive study of poroelasticity with application to rock mechanics. The research covers anisotropic and non-linear constitutive relations, Finite Element Method (FEM) in three-dimensional and generalized plane strain geometries, analytical and semi-analytical solutions to anisotropic and nonlinear problems, and stress and stability analyses of borehole problems.; The anisotropic constitutive relations presented by Thompson and Willis are reformulated in terms of engineering notations and parameters. Based on the micromechanics approach, poroelastic constants are explicitly linked to the mechanical properties of the individual constituents of the saturated porous media. Their relations to measurable engineering constants are also demonstrated.; For an isotropic poroelastic material, the effects of stress-dependent poroelastic properties, such as the permeability, Biot's effective stress coefficient, Biot's modulus, Skempton's pore pressure coefficient, as well as elastic properties are explored. Using Mackenzie's model of spherical pores, an explicit expression of the stress dependent porosity is derived. Based on the assumption of microhomogeneity, all material properties required in the constitutive relations are explicitly expressed in terms of Terzaghi's effective stresses, leading to a stress-dependent constitutive model.; A three-dimensional FEM based on the full version of poroelasticity is developed in the present work. It includes general anisotropy and nonlinearity of poroelastic materials. A generalized plane strain element is developed for the purpose of the efficient analysis of generalized plane strain problems. The FEM code is extensively validated, particularly for its anisotropic and nonlinear capabilities, using analytical solutions derived in this thesis.; Analytical solutions involving material anisotropy are derived for several basic poroelasticity problems in one-dimensional, axisymmetric, and generalized plane strain geometries. Among them, solutions of 1-D consolidation and Mandel's problem are developed for orthotropic materials. Solutions of the axisymmetric problem and borehole problem are limited to a transversely isotropic material. The effect of material anisotropy is investigated. In particular, it is demonstrated that for an anisotropic Biot's effective coefficient tensor there does not exist a good scalar approximation. A significant error may result, if an average value of the directional Biot's effective stress coefficients is taken.; The effect of nonlinearity is investigated in the form of a stress-dependent permeability. A one-dimensional consolidation and an axisymmetric borehole problem are examined. The similarity transform is employed to reduce governing equations to ordinary differential equations. The solutions are obtained by combining the Runge-Kutta method with a shooting method.; An analytical solution of an inclined borehole in an isotropic poroelastic medium is derived. This solution is extended to the case of a transversely isotropic material. Using both analytical and finite element solutions, more complicated borehole problems involving anisotropy are investigated. Aiming at petroleum engineering applications, a borehole stability analysis is carried out. For an isotropic poroelastic medium, several failure criteria are applied to reveal different types of failures, including compressive, shear, and tensile failures. In each of the failure mode, the time factor plays an important role, as the failure is often not instantaneous. For an anisotropic material, FEM analysis shows that the material anisotropy exerts a significant impact on the effective stress magnitude and distribution, especially at large borehole inclination. |
