A probabilistic damage model of stress-induced permeability anisotropy during cataclastic flow

A fundamental understanding of the effect of stress on permeability evolution is important for many fault mechanics and reservoir engineering problems. Recent laboratory measurements demonstrate that in the cataclastic flow regime, the stress-induced anisotropic reduction of permeability in porous rocks can be separated into 3 different stages. In the elastic regime (stage I), permeability and porosity reduction are solely controlled by the effective mean stress, with negligible permeability anisotropy. Stage II starts at the onset of shear-enhanced compaction, when a critical yield stress is attained. In stage II, the deviatoric stress exerts primary control over permeability and porosity evolution. The increase in deviatoric stress results in drastic permeability and porosity reduction and considerable permeability anisotropy. The transition from stage II to stage III takes place progressively during the development of pervasive cataclastic flow. In stage III, permeability and porosity reduction becomes gradual again, and permeability anisotropy diminishes. Microstructural observations on deformed samples using laser confocal microscopy reveal that stress-induced microcracking and pore collapse are the primary forms of damage during cataclastic flow. A probabilistic damage model is formulated to characterize the effects of stress on permeability and its anisotropy. In our model, the effects of both effective mean stress and differential stress on permeability evolution are calculated. By introducing stress sensitivity coefficients, we propose a first-order description of the dependence of permeability evolution on different loading paths. Built upon the micromechanisms of deformation in porous rocks, this unified model provides new insight into the coupling of stress and permeability.