Abstract: Fully coupled governing equations are developed for hydro-mechanical analysis of deforming porous medium with fractures based on the stress balance equation, the seepage continuity equation and the modified Biot effective stress principle. The flow of the fluid within the medium, and fracture satisfies the Darcy law. The final nonlinear fully coupled equations reflect not only the coupling effect of the physical quantity within the porous medium, but also the coupling between the medium and the fracture. Since the extended finite element method (XFEM) has a unique advantage in dealing with fracture problems, both XFEM and the ordinary finite element method (FEM) are used to establish the numerical calculation system. During the spatial dispersion, the displacement and the pore pressure in the medium are discretized by FEM. To reflect the strong discontinuity of the fracture surface and the stress singularity at the crack tip, two kinds of additional displacement functions are introduced in the displacement model of the fracture area based on XFEM. The pore pressure enhancement function is also applied to represent the weakly discontinuous features of the normal pore pressure. Time discretization is performed using a backward difference scheme. Finally, numerical examples are provided to prove the correctness and effectiveness of the model and algorithm. Moreover, the delay of the fluid flow, the feature of the opening displacement and the pore pressure in the fracture are analyzed, and the effect of changes of the permeability and external flow on numerical results are discussed.

Key words: fracture, saturated porous medium, seepage, extended finite element method, full coupled