Title: Capturing Evolving Size-Dependent Anisotropy from Brittle Fracture to Plasticity for Geological Materials
Description: We present a computational framework for modeling geomaterials undergoing failure in the brittle and ductile regimes. This computational framework introduces anisotropic gradient regularization to replicate a wide spectrum of size-dependent anisotropic constitutive responses exhibited in layered and sedimentary rock. Relevant subsurface applications include oil/gas wellbore completions, caprock evaluation for carbon sequestration in saline aquifers, and geothermal energy recovery. Considered failure modes are mixed-mode fracture, shear band formation due to plastic strain localization, and rate-dependent frictional slip along the propagated fracture's rock surface, subsequent to fracture closure. Our nonlocal modeling framework extends the state-of-the-art gradient-enhanced plasticity and damage mechanics for frictional materials with a special treatment that injects bias for the regularization for different orientations. A novel contribution is that the formulations not only contains a regularization, but that the regularization also provides a method to introduce size-dependent anisotropies.

Consequently, this treatment provides a new means to create non-associative flow via a variational framework while introducing different anisotropic responses for specimens of different sizes (introduced in Chapter 1). These anisotropic regularization modeling techniques are then applied to three classes of common geomechanics problems: critical state plasticity of clay and shale rock (Chapter 2), brittle fracture of rock (Chapter 3), and the plastic slip of interfaces and cracks (Chapter 4). This combination, of established rock physics, local anisotropy, and size-dependent anisotropy enfranchised with diffusive regularization, is investigated. For instance, experimentation on uniaxially compressed specimens failing in the brittle regime reveals a repeatable typology of wing- and coalescent-crack patterns, broadly taken to indicate a mixed-mode fracture phenomenon particular to rock-like materials. In the ductile regime, biaxially compressed shale rock displays orientation-dependence of the plastic deformation difficult to capture merely by attributing anisotropy to the elastic response, with localization at or near the critical state.

We numerically capture both these phenomena. Verification and/or validation is provided for proposed constitutive relations.