The paper presents a numerical method for the simulation of flow and mechanics in fractured rock. The governing equations which 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 non-penetration contact conditions prevent fractures from closing. 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 the MPGP algorithm. The capability of the numerical scheme is demonstrated on a benchmark problem for borehole excavation with hundreds of fractures in 3D. The paper's novelty consists in combination of three crucial ingredients: (i) application of discrete fracture matrix approach, (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 large number of fractures in mutual contact by means of own solvers with known rate of convergence implemented into in-house PERMON library.

翻译：本文提出了一种用于裂隙岩体中流动与力学行为模拟的数值方法。基于离散裂缝-基质方法，建立了耦合岩体与裂缝效应的控制方程：裂缝流动由立方定律驱动，非穿透接触条件防止裂缝闭合。针对位移-压力-流量公式，提出了稳定的有限元离散格式。通过稳健的迭代分裂将所得非线性代数方程组与不等式系统解耦为线性化流动子问题与力学二次规划子问题，其中非穿透条件采用MPGP算法求解。基于含数百条三维裂缝的钻孔开挖基准问题，验证了该数值方案的适用性。本文创新之处在于融合三项关键技术：（i）离散裂缝-基质方法的应用，（ii）适用于实际三维问题的非线性代数系统稳健迭代分裂策略，以及（iii）利用自主研发的PERMON库中具有已知收敛速度的求解器高效求解含大量相互接触裂缝的力学二次规划子问题。