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SummaryA methodology is developed in SPH framework to analyze the behavior of preexisting multiple intersecting discontinuities or joints in rock material. The procedure does not require any additional unknowns to represent discontinuities and to capture velocity jump across them. Instead, a discontinuity is represented by a set of joint particles placed along the discontinuity plane, in which relative velocity and traction vector is evaluated, obeying the Mohr–Coulomb friction law with zero tension constrain. For failure of continuous rock material, the Drucker–Prager yield criterion with tensile cracking is employed in the elastic‐plastic constitutive model. Free‐sip, no‐slip, and symmetric boundary conditions are also implemented in SPH framework for proper representation of physical system.The paper analyzes behavior of a rock sample having a discontinuity plane under uniaxial loading and compares velocity and stress with a theoretical solution derived considering effective vertical stiffness of the joint planes. The efficacy of the proposed method is successfully demonstrated by solving another two problems of jointed rock mass under uniaxial and gravitational loading conditions.Copyright © 2014 John Wiley & Sons, Ltd.

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A better understanding of failure in heterogeneous rock materials can benefit a wide range of areas, from earthquake engineering to petroleum engineering. Study of such failure is of particular interest in the field of hydraulic fracturing. The prediction of this breakage phenomenon is a big challenge for the scientific community. Traditional continuum modeling techniques have the advantage of using classical nonlinear material models, however they often fail to accurately capture the complexity of the fractured geometry and path of multiple intersecting fractures. In particular, mesh dependence of the fracture path, 3D representation of natural fractures and their intersections, closing of an opened fracture, or shear in fractures, are difficult to accurately capture using these techniques. The use of the smoothed particle hydrodynamics (SPH) method for simulation of fracture in solids is relatively recent, where mesh free methods like SPH have the potential to overcome the previously mentioned limitations of mesh based methods. Simulation of the initiation and propagation of pressuredriven fractures in brittle rocks is presented in this study. By exploiting techniques commonly used in traditional continuum methods, we have implemented an elasto-plastic SPH model, which is based on the Drucker-Prager yield criterion, and the Grady-Kipp damage model. Results show that SPH is able to correctly predict the evolution of fracture in brittle rocks. The SPH method has been applied to the solution of crack propagation in a variety of test cases, including a pressurized borehole, 2D line crack, and 3D penny shaped crack. The influence of initial in-situ stresses was also accounted for. Comparison of SPH results for these cases to analytical solutions shows that SPH may be applied to accurately simulate the evolution of fluid-driven fractures in brittle rocks. Such model is a vital tool in correctly predicting fracture propagation in highly heterogeneous formations, for instance, shale formations.

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