Micro-macro modeling of chemo-mechanical damage and healing in rocks

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Shen, Xianda
Arson, Chloé
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In rock mechanics, damage and healing respectively refer to the degradation and recovery of stiffness and strength induced by the evolution of microscopic defects. The gap between microscopic and macroscopic models makes it difficult to bridge the defects characterization at the microscopic scale to the development of deformation and stiffness at the macroscopic scale. Therefore, the goal of this doctoral research work is to understand and predict damage and healing processes in rock, by coupling microstructural and poromechanical models. In the first part of the thesis, we present micro-macro approaches to model the influence of micro-crack propagation on the accumulation of damage and irreversible deformation in salt rock. Consolidation tests and cyclic compression tests were conducted by our collaborators at Texas A&M University. Samples were taken out and sliced for microstructure observation at key stages of the loading paths. Based on statistical image analysis, the evolution of solidity, grain coordination, local solid volume fraction and crack volume exhibit the clearest trends. We use these fabric descriptors to relate microstructure evolution to macroscopic behavior. We found that deformation is dominated by grain rearrangement. In the consolidation tests, plastic deformation increases, grains are organized into horizontal layers, the size of the voids reduce and become more uniformly distributed, and salt rock becomes much denser laterally under compaction. In the cyclic compression tests, inter granular cracks mainly propagate in the axial direction, and grain-to-grain contact areas reduce. Large voids collapse into small and isolated voids, which, then, are connected by inter granular cracks and form large voids again. The evolution of the magnitude and orientation of the fabric descriptors correlates with the evolution of the Young's modulus and of the Poisson's ratio. During the cyclic compression tests, we also observed that macro-cracks form in two stages: (i) Wing cracks tensile opening; (ii) Main crack slipping, inducing additional wing crack opening. Larger confinement and higher friction at the crack faces leads to higher strength of salt rock. This model shows that salt rock develops damage-induced anisotropy. This observation contradicts the common assumption made in a large number of models of salt rock, in which damage and healing induce isotropic stiffness changes. We formulated, calibrated and validated a micro-mechanical model coupled with elasto-plastic model that captures these phenomena, called a discrete wing crack elastoplastic damage (DWCPD) model. We also formulated a chemo-mechanical homogenization framework to understand the rate dependent behavior of salt rock observed in cyclic compression tests. A higher rate of pressure solution and/or a larger volume fraction of sliding cracks lead to larger chemical deformation, stiffness degradation and larger hysteresis. When the chemical strain rate at sliding cracks is too large, the development of hysteresis is restrained due to the quasi-instantaneous stress redistribution. Models presented in this part of the thesis can be used to guide the design of geological energy storage (i.e. Compressed Air Energy Storage) and enhance the efficiency of energy geotechnologies. In the second part of the thesis, a micro-macro homogenization framework is established to understand the coevolution of chemical weathering of minerals and bedrock weakening. The proposed model quantifies the accumulation of damage in the matrix of bedrock driven by chemical weathering of minerals like biotite, which expand as they weather and create stresses sufficient to fracture rock. Our simulation results suggest that damage in the matrix of granite occurs earlier under higher biotite abundances and smaller biotite aspect ratios. Biotite orientation exerts a relatively weak effect on damage. The development of damage is also strongly influenced by the boundary conditions, and damage initiates earlier under laterally confined boundaries than under unconfined boundaries. This model shows that chemical weathering of minerals is the controlling mechanism of saprolite production. In the last part of the thesis, a novel multi-scale homogenization model is presented to simulate salt rock healing driven by pressure solution. Hollow sphere inclusions traversed by three inter-granular contact planes are modeled at the microscopic scale. Under sufficient normal stress, salt mineral is dissolved at grain contacts, diffuses along inter-granular crack planes, and precipitates on the pore walls. Pressure solution in the inclusions induces the accumulation of chemical strain and the recovery of stiffness of salt rock at the REV scale. The healing rate is faster in salt rock with uniformly distributed void sizes. The healing rate also increases with initial porosity, but the final porosity change is independent on the initial porosity of salt rock. We implemented the micro-macro model of healing in the Finite Element Method for simulating Carbon Dioxide storage in a salt cavern. Based on thermodynamic principles, a generalized thermodynamic thermo-hydro-chemo-mechanical framework is also proposed to model multiple processes of damage and healing. The research presented in this thesis sheds light on the processes that can control damage and healing in rocks and provides theoretical tools to guide the design of geological storage facilities.
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