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.

翻译：本文提出了一种模拟裂隙岩体流动与力学行为的数值方法。采用离散裂隙-基质方法建立控制方程，该方程耦合了岩体与裂隙中的力学效应。裂隙流动遵循立方定律，接触条件防止裂隙发生自穿透。针对位移-压力-通量方程组提出了一种稳定的有限元离散格式。通过鲁棒性迭代分裂技术，将所得非线性代数方程组与不等式解耦为线性化流动子问题与力学部分的二次规划问题。利用对偶化方法及最优二次规划算法求解非穿透条件。通过三维含数百条裂隙的隧道开挖基准问题验证了该数值方案的可行性。本文的创新性体现在三个关键要素的结合：(i) 将离散裂隙-基质方法应用于孔隙弹性力学；(ii) 针对实际三维问题建立可解的鲁棒性非线性代数系统迭代分裂方法；(iii) 利用自主开发的软件库中实现的求解器，高效求解大量相互接触裂隙的力学二次规划部分。