Poroelastic damage rheology: Dilation, compaction, and failure of rocks

We present three-dimensional numerical simulations for the behavior of porous rocks under loading based on the theoretical formulation recently developed by Y. Hamiel et al. This theoretical formulation combines the classic Biot poroelastic theory with a damage rheology model. The numerical simulations of triaxial compression tests reproduce the gradual transition from localized brittle failure to distributed cataclastic flow with increasing pressure at high-porosity rocks. Under relatively low confining pressures (approximately lower than 100 MPa for Berea sandstone samples), porous rocks fail in a brittle mode with sharp localization of damage in a narrow deformation zone and dilatancy preceding the total failure. At these pressures the yield stress increases with confining pressure (positive slope for yield curve). In simulations with higher confining pressures, instead of dilatancy, the deformation zone has a reduced porosity due to compaction. The porosity reduction plays an essential role in strengthening the deformation zone, and therefore continuous loading of the sample leads to the progressive development of a wide deformation zone. Under relatively high confining pressures (approximately higher than 300 MPa for Berea sandstone samples), damage is nonlocalized, and the macroscopic deformation of the model corresponds to experimentally observed cataclastic flow. At these pressures the yield stress decreases with confining pressure (negative slope for yield curve). We found good agreement between the measured and calculated yield curve for Berea sandstone.