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Modeling of discontinuities (fractures and fault surfaces) is of major importance to assess the geomechanical behavior of oil and gas reservoirs, especially for tight and unconventional reservoirs. Numerical analysis of discrete discontinuities traditionally has been studied using interface element concepts, however more recently there are attempts to use extended finite element method (XFEM). The development of an XFEM tool for geo-mechanical fractures/faults modeling has significant industrial potential; particularly within the hydrocarbon industry where it could lead to improved predictions for porosity/permeability changes in coupled geomechanical reservoirs. In this paper, we present a novel methodology based on the extended finite element method (XFEM) to analyze the behavior of pre-existing multiple strong discontinuities (faults and/or fractures) in reservoir rock. Detailed mathematical framework leveraging XFEM for multiple discontinuities in rock masses has been derived. This XFEM based framework is robust enough to represent strong discontinuities independently of the mesh. The approximation of discontinuities is constructed in terms of Heaviside/junction functions which lead to additional unknowns to capture the displacement jump across and at intersections of joints. Our framework and algorithm are general in nature and can handle complex geo-mechanical problems with different loading conditions. For validation of the implemented mathematical framework using XFEM, we analyze the behavior of a rock sample with multiple discontinuities and compare displacement and stress with known theoretical solution. Triaxial3D loading examples involving multiple discontinuities are also presented to demonstrate the accuracy and robustness of the proposed methodology., Postprint (published version)

Modeling of big faults or weak planes of strong and weak discontinuities is of major importance to assess the Geomechanical behaviour of mining/civil tunnel, reservoirs etc. For modelling fractures in Geomechanics, prior art has been limited to Interface Elements which suffer from numerical instability and where faults are required to be aligned with element edges. In this paper, we consider comparative study on finite elements for capturing strong discontinuities by means of elemental (EFEM) and nodal enrichments (XFEM) for Geomechanical applications. For general fracture scenarios, Oliver et al. (2008) have demonstrated advantages of EFEM over XFEM for including: (a) ease of modeling in any standard finite element code due to the possibility of static condensation, (b) higher accuracy in some cases for coarse meshes, and, (c) a reduced computational cost. However, there has been no work that considers cohesive fractures in Geomechanics. We present a numerical analysis based on a linear constitutive model and linear triangular elements for the bulk and a linear constitutive behaviour for the fault for a representative set of fault planes in a circular tunnel made in rock mass. In the numerical examples we consider both well-traced and bad-traced meshes. We focus on traction profile analysis for both EFEM and XFEM, since that is crucial to understand the cohesive fracture behaviour specially rock joint. Therefore in each case, shear, normal and stress ratio are compared across the two methods along the fault plane. This is the first such work that compares XFEM and EFEM behaviour for Geomechanics problems. For the considered class of problems and the sharp penalization approach without regularizations adopted, it can be observed that accuracy and robustness of EFEM may strongly depend on the fault orientation with respect to the element edges, while, XFEM is independent of fault alignment with element edges. It has been also observed that, with mesh refinement model, Postprint (published version)