Theoretical and numerical modeling of anisotropic damage in rock for energy geomechanics
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At present, most of the energy power consumed in the world is produced by fossil fuel combustion, which has raised increasing interest in renewable energy technologies, non-conventional oil and gas reservoirs, and nuclear power. Innovative nuclear fuels and reactors depend on the economical and environmental impacts of waste management. Disposals in mined geological formations are viewed as potential consolidated storage facilities before final disposition. Different stress paths during construction result in different kinds of failure mechanisms, which alter rock strength and induce anisotropy of rock elastic properties. Crack propagation in rock can be originated by these engineering activities (excavation, drilling, mining, building overburden), or by changes of the natural environment (tectonic processes, erosion or weathering). Damage is a mathematical variable that can represent a variety of microstructure changes, such as crack density, length, aspect ratio and orientation. The framework of Continuum Damage Mechanics allows modeling the resulting reduction in strength and stiffness, as well as the associated stress-induced anisotropy and irreversible deformation. This work presents a modeling framework for anisotropic crack propagation in rock, in conditions of stress typical of geological storage and oil and gas extraction. Emphasis is put on the prediction of the damage zone around cavities and ahead of pressurized fracture tips. An original model of anisotropic damage, the Differential Stress Induced Damage (DSID) model, is explained. The Drucker-Prager yield function is adapted to make the damage threshold depend on damage energy release rate and to distinguish between tension and compression strength. Flow rules are derived with the energy release rate conjugate to damage, which is thermodynamically consistent. The positivity of dissipation is ensured by using a non-associate flow rule for damage, while nonelastic deformation due to damage is computed by an associate flow rule. Stress paths simulated at the material point illustrate damaged stiffness and deformation variations in classical rock mechanics tests. The maximum likelihood method was employed to calibrate and verify the DSID model against stress-strain curves obtained during triaxial compression tests and uniaxial compression tests performed on clay rock and shale. Logarithmic transformation, normalization and forward deletion allowed optimizing the formulation of the DSID model, and reduce the number of damage constitutive parameters from seven to two for clay rock. The DSID model was implemented in ABAQUS Finite Element (FE) software. The iterative scheme was adapted in order to account for the non-linearities induce both by damage and damage-induced deformation. FE simulations of laboratory tests capture size an intrinsic anisotropy effects on the propagation of damage in rock. Smeared DSID zones representing shale delamination planes avoid some convergence problems encountered when modeling discontinuities with debonded contact surface elements. FE simulations of tunnel excavation, fracture propagation and borehole pressurization were performed to illustrate the evolution of the damage zone and the impact on energy dissipation, anisotropy of deformation, and loss of stiffness. Future work will focus on coupling the propagation of fractures with the evolution of the damage process zone, and on the transition from continuum damage to discrete fracture upon crack coalescence.