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On the parallel solution of hydro-mechanical problems with fracture networks and contact conditions

Published 22 Nov 2023 in math.NA and cs.NA | (2311.13310v2)

Abstract: The paper presents a numerical method for simulating flow and mechanics in fractured rock. The governing equations that couple the effects in the rock mass and in the fractures are obtained using the discrete fracture-matrix approach. The fracture flow is driven by the cubic law, and the contact conditions prevent fractures from self-penetration. A stable finite element discretization is proposed for the displacement-pressure-flux formulation. The resulting nonlinear algebraic system of equations and inequalities is decoupled using a robust iterative splitting into the linearized flow subproblem, and the quadratic programming problem for the mechanical part. The non-penetration conditions are solved by means of dualization and an optimal quadratic programming algorithm. The capability of the numerical scheme is demonstrated on 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) robust iterative splitting of resulting nonlinear algebraic system working for real-world 3D problems, and (iii) efficient solution of its mechanical quadratic programming part with a large number of fractures in mutual contact by means of own solvers implemented into an in-house software library.

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