Brittle deformation and damage-induced seismic wave anisotropy in rocks

We study the relations between rock fracturing, non-linear deformation and damage- and stress-induced anisotropy of seismic waves by comparing theoretical predictions of a damage rheology model to results of laboratory experiments with granite samples. The employed damage model provides a generalization of Hookean elasticity to a non-linear continuum mechanics framework of cracked media incorporating degradation and recovery of the effective elastic properties, along with gradual accumulation of irreversible deformation beyond the elastic regime. The model assumes isotropic distribution of local microcracks expressed in terms of a scalar damage variable, but the non-linear elastic response caused by the opening, closure and evolution of the internal cracks is predicted to lead to seismic wave anisotropy. We develop relations between the seismic wave anisotropy, internal rock damage and stress field, and test the viscoelastic damage rheology against sets of laboratory experiments with cylindrical granite samples. The observed data include measurements of stress and strain in three loading cycles culminating in a final macroscopic failure, together with measured wave velocities along and perpendicular to the axis of the cylinder. Using a single set of parameters, the model fits well the overall evolution of the axial and transversal stress-strain relations, as well as the anisotropic elastic wave velocities, during all cycles from the onset of fracturing in the first cycle until the macroscopic failure in the final cycle.