Coupled mechanical and fluid flow analysis in fractured saturated porous media using the XFEM

In this paper, we study the fluid flow in a deformable porous linear elastic media with a single crack Γ. Fluid exchange between the crack and the surrounding porous media is taken into account through the definition of appropriate boundary conditions on Γ obtained by applying an averaging process of the Darcy flow within the crack. Two models are considered and compared: a semianalytical one which solves the general potential solution of the singular integral equation modelling the steady state flow in an infinite porous media with one linear crack, obtained by applying the complex potential method, and a numerical one based on the Extended Finite Element Method (XFEM) of the governing equations. The XFEM we apply employs the standard enriched basis functions represented by the Heaviside function on Γ to describe the discontinuity jump of the displacement field across the crack, the distance function to Γ to describe the non differentiability of the pressure field across Γ and the singular functions describing the r-singularity at the crack tip of the stress and pressure field, where r is the distance to the crack tip. The semianalytical model is used to verify the application of the XFEM. We include then the coupling with the mechanical response of the body, which is analyzed by using only the XFEM. Several numerical experiments are then carried out which illustrate the variation of the hydro-mechanical quantities around the crack and within the crack.