Fluid-driven transition from damage to fracture in anisotropic porous media: a multi-scale XFEM approach

In this paper, a numerical method is proposed to simulate multi-scale fracture propagation driven by fluid injection in transversely isotropic porous media. Intrinsic anisotropy is accounted for at the continuum scale, by using a damage model in which two equivalent strains are defined to distinguish mechanical behavior in the direction parallel and perpendicular to the layer. Nonlocal equivalent strains are calculated by integration and are directly introduced in the damage evolution law. When the weighted damage exceeds a certain threshold, the transition from continuum damage to cohesive fracture is performed by dynamically inserting cohesive segments. Diffusion equations are used to model fluid flow inside the porous matrix and within the macro-fracture, in which conductivity is obtained by Darcy's law and the cubic law, respectively. In the fractured elements, the displacement and pore pressure fields are discretized by using the XFEM technique. Interpolation on fracture elements is enriched with jump functions for displacements and with level set-based distance functions for fluid pressure, which ensures that displacements are discontinuous across the fracture, but that the pressure field remains continuous. After spatial and temporal discretization, the model is implemented in a Matlab code. Simulations are carried out in plane strain. The results validate the formulation and implementation of the proposed model and further demonstrate that it can account for material and stress anisotropy.