A two-dimensional extended finite element method model of discrete fracture networks

This article presents the first effort to develop a two-dimensional model using the extended finite element method (XFEM) for the simulation of discrete fracture networks, in which the mesh does not conform to the natural fracture network. The model incorporates contact, cohesion, and friction between blocks of rock. Shear dilation is an important mechanism impacting the overall nonlinear response of naturally fractured rock masses and is also included in the model; physics previously not simulated within an XFEM context. Here, shear dilation is modeled by means of a linear dilation model, capped by a dilation limiting displacement. Highly nonlinear problems involving multiple joint sets are investigated within a quasi-static context. An explicit scheme is used in conjunction with the dynamic relaxation technique to obtain equilibrium solutions in the face of the nonlinear constitutive models from contact, cohesion, friction, and dilation. The numerical implementation is verified and its convergence is illustrated using a shear test and a biaxial test. The model is then applied to the practical problem of the stability of a slope of fractured rock.