On the poromechanics of anisotropic elastoplastic geomaterials with compressible grains

In the recent few decades, a more frequent and drastic change in climate resulting from global warming has raised up increasing concern in our society. Shale, a typical anisotropic sedimentary rock, is playing a critical role in engineering practices that tackle global warming and greenhouse gas emission. In carbon geological sequestration, shale serves as a seal rock thanks to its low permeability and high ductility. In the extraction of shale gas, a cleaner alternative energy source, the shale rock is the energy-bearing matrix. The physical processes that take place in both cases involve a coupled hydro-mechanical response, and material anisotropy will influence both the mechanical behavior and transport properties of shale. This thesis is aimed to develop constitutive models and poromechanical frameworks for geomaterials with inherent anisotropy like shale, in the hope to provide a theoretical tool for the long-term performance analysis of these engineering practices. In nature, the most common type of material anisotropy in geomaterials is transverse isotropy induced by a laminated structure, which can be characterized by planes of transverse isotropy (i.e., the bedding planes) and the axis of cross-anisotropy (i.e., the norm to the bedding planes). In the first part of the thesis, a general method to extend isotropic yield criteria for anisotropic materials is introduced through mapping the Cauchy stress tensor to an alternative stress state. Following this scheme, the isotropic modified Cam-Clay model is extended for transversely isotropic rocks. A return mapping algorithm with two nested Newton iteration loops is adopted for the numerical solution of the constitutive equations. This constitutive model is then cast into a finite element framework, with which simulations of compression tests on Tournemire shale in both 2D and 3D are conducted to investigate factors that influence the failure modes of transversely isotropic rocks. In the second part of the thesis, we extended the discussion to poromechanical modeling of coupled solid deformation and fluid flow in anisotropic elastoplastic media. What's new in the proposed formulation is that two distinct effective stress measures are identified for elastic and plastic response respectively from continuum thermodynamics. The effective stress for elasticity modeling is in the form of Biot's effective stress, where pore pressure p is scaled with a second-rank tensor b. The effective stress for plasticity modeling is in the form of Terzaghi's effective stress where pore pressure is scaled with Kronecker delta. The anisotropic modified Cam-Clay model introduced in the first part of the thesis is adopted in constitutive modeling of the solid skeleton, extended for cases where the interstitial pore pressure is nonzero consistent with the two-effective-stress formulation. Darcy's law with an anisotropic permeability tensor is employed to model pore fluid flow. This framework is then implemented in a stabilized finite element formulation, which is later validated by simulating a 2D consolidation problem of an elastic halfspace under a strip load. Finally, simulations of a 2D consolidation problem of a rectangular domain made up of transversely isotropic rocks under a strip load are conducted, where how different factors such as material anisotropy, stress history and the Biot tensor b would influence the overall system's response is investigated. In the last part of the thesis, the proposed poromechanical framework is extended for double-porosity media, where two independent pore networks at different scales with distinct fluid flow mechanisms and permeabilities have been considered. As in nature, the pore size distribution in aggregated soils and fissured rocks usually follows a bimodal distribution. In this work, two effective stresses are still identified for elasticity and plasticity modeling respectively, expressed now in terms of the mean pore pressure at two pore scales. This framework is then discretized with finite element method with a stabilization scheme in the undrained limit for the double-porosity formulation. The unique characteristic of the double-porosity formulation has been demonstrated through reproducing the 1D consolidation process of Opalinus shale, as the proposed model can capture both the primary and secondary consolidation processes, represented by the dissipation of pore fluid in macropores and micropores respectively. Finally, the simulation of a 2D consolidation process of a rectangular domain made up of transversely isotropic rocks under a strip load introduced in earlier in the single-porosity formulation has been repeated for double-porosity media, exhibiting the efficacy of the proposed stabilization scheme as well as how different factors, including stress history, material anisotropy, and different porosity systems (either single-porosity or double-porosity), will influence the overall system's response

Advisor: Borja Ronaldo I. (Ronaldo Israel)
Linder Christian (Engineering professor)
Vanorio Tiziana