Coupled evolution of damage and porosity in poroelastic media: theory and applications to deformation of porous rocks

We address the gradual transition from brittle failure to cataclastic flow under increasing pressures by a new model, incorporating damage rheology with Biot's poroelasticity. Deformation of porous rocks is associated with growth of two classes of internal flaws, namely cracks and pores. Cracks act as stress concentrations promoting brittle failure, whereas pores dissipate stress concentrations leading to distributed deformation. The present analysis, based on thermodynamic principles, leads to a system of coupled kinetic equations for the evolution of damage along with porosity. Each kinetic equation represents competition between cracking and irreversible porosity change. In addition, the model correctly predicts the modes of strain localization such as dilating versus compacting shear bands. The model also reproduces shear dilatancy and the related change of fluid pressure under undrained conditions. For triaxial compression loading, when the evolution of porosity and damage is taken into consideration, fluid pressure first increases and then decreases, after the onset of damage. These predictions are in agreement with experimental observations on sandstones. The new development provides an internally consistent framework for simulating coupled evolution of fracturing and fluid flow in a variety of practical geological and engineering problems such as nucleation of deformation features in poroelastic media and fluid flow during the seismic cycle.