SUMMARYIn this paper, an enriched finite element technique is presented to simulate the mechanism of interaction between the hydraulic fracturing and frictional natural fault in impermeable media. The technique allows modeling the discontinuities independent of the finite element mesh by introducing additional DOFs. The coupled equilibrium and flow continuity equations are solved using a staggered Newton solution strategy, and an algorithm is proposed on the basis of fixed-point iteration concept to impose the flow condition at the hydro-fracture mouth. The cohesive crack model is employed to introduce the nonlinear fracturing process occurring ahead of the hydro-fracture tip. Frictional contact is modeled along the natural fault using the penalty method within the framework of plasticity theory of friction. Moreover, an experimental investigation is carried out to perform the hydraulic fracturing experimental test in fractured media under plane strain condition. The results of several numerical and experimental simulations are presented to verify the accuracy and robustness of the proposed computational algorithm as well as to investigate the mechanisms of interaction between the hydraulically driven fracture and frictional natural fault. Copyright

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An energy minimization formulation of initially rigid cohesive fracture is introduced within a discontinuous Galerkin finite element setting with Nitsche flux.The finite element discretization is directly applied to an energy functional, whose term representing the energy stored in the interfaces is nondifferentiable at the origin. Unlike finite element implementations of extrinsic cohesive models that do not operate directly on the energy potential, activation of interfaces happens automatically when a certain level of stress encoded in the interface potential is reached. Thus, numerical issues associated with an external activation criterion observed in the previous literature are effectively avoided. Use of the Nitsche flux avoids the introduction of Lagrange multipliers as additional unknowns. Implicit time stepping is performed using the Newmark scheme, for which a dynamic potential is developed to properly incorporate momentum. A continuation strategy is employed for the treatment of nondifferentiability and the resulting sequence of smooth nonconvex problems is solved using the trust region minimization algorithm. Robustness of the proposed method and its capabilities in modeling quasistatic and dynamic problems are shown through several numerical examples. KEYWORDScohesive fracture, continuation method, discontinuous Galerkin method, initially rigid, nondifferentiable energy minimization, trust region method Int J Numer Methods Eng. 2018;115:627-650.wileyonlinelibrary.com/journal/nme

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