Propagation of cohesive crack in unsaturated porous media by use of XFEM method

Various damage models have been presented to model the cracks. These models don't simulate the discontinuity in displacement field; just see its effect on an upper level on stress field through damage parameter. Damage parameter is used to modify other fields like pressure. This paper tries to model crack itself through fracture mechanics. The opening of the crack is modeled and is connected to stress field by use of cohesive crack model that relates plasticity of crack tip to its opening. When crack opens, there exists discharge of water and gas through crack that are calculated by use of multiscale methods and incorporated in weak form of governing equations. Due to complexity of proposed model, it can't be solved analytically and extended finite element method (XFEM) is used to solve it. Xfem method which is based on partition of unity property of FEM adds some terms to conventional interpolation functions to model discontinuity of fields adjacent to the crack. This method simulates crack in ordinary mesh of FEM and doesn't need remeshing around the crack when it propagates.