A Phase-Field Method for Propagating Fluid-Filled Fractures Coupled to a Surrounding Porous Medium

The recently introduced phase-field approach for pressurized fractures in a porous medium offers various attractive computational features for numerical simulations of cracks such as joining, branching, and non-planar propagation in possibly heterogeneous media. In this study, the pressurized phase-field framework is extended to fluid-filled fractures in which the pressure is computed from a generalized parabolic diffraction problem. Here, the phase-field variable is used as indicator function to combine reservoir and fracture pressure. The resulting three-field framework (elasticity, phase-field, pressure) is a multiscale problem that is based on the Biot equations. The proposed numerical solution algorithm iteratively decouples the equations using a fixed-stress splitting. The framework is substantiated with several numerical benchmark tests in twoand three dimensions.