Superposition-based concurrent multiscale approaches for poromechanical problems aimed at resolving localized fluid flow and deformation of a solid skeleton including its possible fracture are developed. The main departure of the proposed formulation is that the primary unknowns in the coupling zone, the solid displacement u and pore pressure p, are discretized by possibly different numerical models. Two discretization schemes are studied: (i) superposition of two or more finite element (FE) discretizations of the Biot's u-p model of a porous medium, and (ii) superposition of the peridynamics (PD) discretization of the fractured solid phase on the FE discretization of the Biot's u-p model of a porous medium. In the latter case, the total stress of the fluid–solid mixture in the coupling domain is derived from the effective stress obtained from the combined PD and finite element method solutions while the pore pressure is obtained from the FE solution. The accuracy of the superposition-based concurrent multiscale method is studied on several benchmark problems including the classical Terzaghi's one-dimensional consolidation problem, the two-dimensional strip footing problem, and the pressure- and fluid-driven fracture propagation problem in saturated porous media. The main hydraulic fracture characteristics, including complex crack paths and fluid flow patterns, have been found to be reasonably well reproduced by the proposed method.

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基于叠加的多孔力学并发多尺度方法

开发了基于叠加的并发多尺度多孔力学问题方法，旨在解决固体骨架的局部流体流动和变形，包括其可能的断裂。所提出的公式的主要偏离是耦合区中的主要未知量，固体位移u和孔隙压力p，可能由不同的数值模型离散化。研究了两种离散化方案：(i)多孔介质Biot u -p模型的两个或多个有限元 (FE) 离散化的叠加，以及 (ii) 裂隙固相的近场动力学 (PD) 离散化的叠加Biot 的u -p的有限元离散化多孔介质模型。在后一种情况下，耦合域中流固混合物的总应力来自有效应力，而有效应力是从有限元法解中获得的，而孔隙压力是从有限元法中获得的。基于叠加的并发多尺度方法的准确性在几个基准问题上进行了研究，包括经典的 Terzaghi 一维固结问题、二维条形基础问题以及饱和多孔介质中压力和流体驱动的裂缝扩展问题。主要的水力压裂特征，包括复杂的裂缝路径和流体流动模式，已被发现可以通过所提出的方法很好地再现。