On the Parallel Solution of Hydro-Mechanical Problems with Fracture Networks and Contact Conditions

The paper presents a numerical method for simulating flow and mechanics infractured rock. The governing equations that couple the effects in the rockmass and in the fractures are obtained using the discrete fracture-matrixapproach. The fracture flow is driven by the cubic law, and the contactconditions prevent fractures from self-penetration. A stable finite elementdiscretization is proposed for the displacement-pressure-flux formulation. Theresulting nonlinear algebraic system of equations and inequalities is decoupledusing a robust iterative splitting into the linearized flow subproblem, and thequadratic programming problem for the mechanical part. The non-penetrationconditions are solved by means of dualization and an optimal quadraticprogramming algorithm. The capability of the numerical scheme is demonstratedon a benchmark problem for tunnel excavation with hundreds of fractures in 3D.The paper's novelty consists in a combination of three crucial ingredients: (i)application of discrete fracture-matrix approach to poroelasticity, (ii) robustiterative splitting of resulting nonlinear algebraic system working forreal-world 3D problems, and (iii) efficient solution of its mechanicalquadratic programming part with a large number of fractures in mutual contactby means of own solvers implemented into an in-house software library.