Coupling mixed hybrid and extended finite element methods for the simulation of hydro-mechanical processes in fractured porous media

Simulation of coupled hydro-mechanical (HM) processes in fractured porous media requires specific numerical schemes to deal with nonlinearity, computational burden, and heterogeneity. The mixed hybrid finite element method (MHFEM) is superior to the standard finite element method in simulating flow in fractured domains. However, MHFEM formulation cannot be efficiently used for the discretization of solid mechanics equations. The extended finite element method (XFEM) has significant advantages in modeling mechanical processes in cracked domains. The main goal of this paper is to extend the application of the MHFEM to HM processes in fractured domains by combining it with XFEM. MHFEM and XFEM are applied to flow and mechanical equations, respectively. This coupling allows for an efficient extending of the hybrid dimensional approach to deal with coupled HM processes in fractured domains. The mass lumping technique is generalized to fractured domains and mechanical processes. We show how this technique can be implemented with the fixed-stress split scheme in order to improve the performance and stability of the numerical scheme. The new scheme (MHFEM-XFEM) is validated against analytical and numerical solutions. Comparison against the standard finite element method shows that the new scheme significantly reduces the computational overhead while providing a high accuracy.