Extended Finite Element Method for Analyzing Hydraulic Fracturing of Rock Cracks Under Compression

This paper presents a numerical model based on the extended finite element method (XFEM) to tackle the problems of hydraulic fracturing and frictional contact in rock cracks. By considering the water pressure distribution on the crack surfaces and the virtual work principle of frictional contact on the crack surfaces, the governing equations for analyzing hydraulic fracturing and frictional contact problems using the XFEM are derived, and the implementation method of the XFEM with frictional contact and water pressure distribution on the crack surfaces is presented. Taking a single-edge-cracked flat plate as an example, the interaction integral method is employed to compute the stress intensity factor in the case of water pressure distribution on the crack surface. Subsequently, a comparative analysis is carried out between the obtained results and the exact solutions. It is demonstrated that this method can yield highly accurate calculation results. Taking a flat plate with a through crack as an example, the nonlinear complementary method is adopted to solve the frictional contact problem. This contact algorithm can effectively prevent the crack surfaces from interpenetrating, and its results are consistent with those calculated by the finite-element penalty function method. Based on the XFEM, the hydraulic fracturing analysis of a flat plate with a central crack under uniaxial compression is carried out. The critical water pressure decreases as the crack length increases, and the critical water pressure increases as the external axial pressure increases. Taking a gravity dam with an initial crack as an example, the calculation results show that hydraulic fracturing will increase the mode I stress-intensity factor at the crack’s tip and reduce the stability of the crack located in the dam foundation of the gravity dam.