Non-local formulation for transport and damage in porous media

We present a novel damage-poroelastic model for analyzing the failure response of porous media in geomechanics applications. In this new approach, a gradient non-local permeability that leads to non-local transport and consequently non local damage, is introduced. Damage evolution is a function of an equivalent strain measure that is computed from non-local permeability using an inverse permeability–strain constitutive relation. A monolithic, mixed finite element method is proposed to solve the coupled system with a displacement–pressure–regularized permeability (u−p−κ̃) element formulation. The system is linearized and solved using Newton's method and a backward Euler scheme is used to evolve the system in time. A consistent Jacobian matrix and residual vector are derived analytically and a bilinear damage model is used to evolve the damage. Numerical examples considering hydraulic fracture problems in 1-d and 2-d and damage enhanced consolidation are presented and discussed. The proposed non-local model results are compared with local damage–permeability models. While the local models are shown to suffer from mesh dependence and non-physical spurious oscillations in strain, permeability and fluid pressure evolution, the proposed model is reliable and seems to overcome all these limitations.