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

Abstract

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. KEYWORDSextended finite element method, discrete fracture network, shear dilation Int

A contact algorithm for cohesive cracks in the extended finite element method

“…On the other hand, due to geometric complexity, there are not as many studies of the contact problem in three‐dimensional (3D) compared with two‐dimensional (2D) XFEM. To the authors' knowledge, most studies are limited to 2D or simple 3D problems, even in recent years …”

A virtual interface‐coupled extended finite element method for three‐dimensional contact problems

“…In the XFEM, the contact constraints are usually achieved with the formulation based on the penalty or Lagrange multiplier method. [12][13][14][15][16][17] The former requires a large penalty parameter to obtain accurate contact traction, which results in an ill-conditioned system matrix. The latter needs to discretize the Lagrange multiplier space independently because the discontinuous interfaces are allowed to pass through the finite element mesh.…”

“…To the authors' knowledge, most of the research is limited to 2D or simple 3D problems, even in the past decade. 12,13,[35][36][37][38] In this article, we present a novel numerical algorithm to model the contact behavior of discontinuous interfaces with nonconforming mesh. By enriching nodes in independent subdomains, we reformulate the XFEM to model 3D contact problems of arbitrary discontinuities.…”

“…The second challenging aspect of XFEM is the implementation of contact constraints. In the XFEM, the contact constraints are usually achieved with the formulation based on the penalty or Lagrange multiplier method 12‐17 . The former requires a large penalty parameter to obtain accurate contact traction, which results in an ill‐conditioned system matrix.…”

“…On the other hand, due to the complexity of geometry, 3D XFEM contact problems have not been studied as much as 2D problems. To the authors' knowledge, most of the research is limited to 2D or simple 3D problems, even in the past decade 12,13,35‐38 …”