Finite element method-based numerical modeling to investigate the role of heterogeneity and damage during brittle deformation

In the present study, I investigate the aspects of brittle deformations such as faulting and fracturing that are related to structural heterogeneities or damage, with a particular focus on the concentration of stress produced around voids and inclusions. In my PhD research, I made use of the powerful tool of the Finite Element Method (FEM) to develop numerical models designed to simulate different types of rock deformation. In particular, the FEM-based numerical models that I coded and used are designed to deal with two classes of physical problems: I) Linear elastic problems II) Nonlinear viscous problems The first type of numerical models, specifically designed for solving elastostatic problems, was applied to study the dependence of differential stress on the geometry and configuration of collinear elliptic cracks intercepting a rock experiencing elastic deformation. The code allowed the computation of the stress field in this system, evaluating the magnitude and limits of stress concentration produced by the presence of structural voids. The reason to consider this type of system is that it aims to simulate the geometry of a rough fault or fracture. The code was also applied to a second research problem, the evaluation of displacement, stress and strain fields during the deformation of a syn-sedimentary carbonate platform. The second class of numerical models aims to study the apparent viscosity of a two-phase system composed of power-law fluids. I start from the evaluation of analytical solutions for the viscosity of a bilaminate to discuss the anisotropy arising from the interaction of materials with a high viscosity contrast. The purpose of this part of the research is to apply these results to study the viscous frictional behavior of subduction mélanges. These are block-in-matrix systems that consist in competent clasts embedded in a fine-grained matrix. The slow viscous creep of the matrix can be obstructed by a the formation of a load-bearing network of clasts, which may fracture when a yield stress is reached at their boundaries. The model of nonlinear viscosity of heterogeneous systems may also be applied to the study of the deformation of phyllosilicate-rich fault gouges. The work of defining, building, and implementing numerical models functional for the study of rock deformation was complemented by a structural investigation of a large fault system in the Ligurian Alps. With the help of the team of structural geologist with which I collaborate, I performed a complex geological-structural study of fault and fracture systems with the plan of collecting data for a future implementation of the FEM codes. This part of the research project represents the first description of a large NE-SW-striking fault network, that was performed integrating field and Digital Outcrop Model (DOM) data. This part of the thesis will serve as a preliminary case study to apply the numerical models to the description of natural rough faults.