Abstract Simulation of hydraulic fracturing process based on numerical manifold method (NMM) is a valuable research direction considering its advantages in dealing with continuous-discontinuous deformation problems. In this paper, an NMM-based fluid-solid coupling model is proposed, including numerical solution of unsteady fracture flow, hydraulic pressure-load conversion algorithm, rectification of hydraulic aperture and programming realization of arbitrary crack growth increment etc. In terms of the fluid phase, the fracture flow network is constructed based on the closed loops formed by cutting the mathematical mesh with fractures; in order to eliminate the sensitivity of explicit algorithm to time-step size, an unconditionally stable numerical solution scheme for unsteady flow is established. In terms of the solid phase, for the sake of realizing coupling process of hydraulic pressure to solid deformation, hydraulic pressure is converted into load vector by hydraulic pressure-load conversion algorithm to calculate the deformation of fractured surrounding rock; and Delaunay triangulation algorithm is introduced to subdivide manifold elements with multiple kinks, which effectively solves the problem that the crack tip cannot stop or kink in the same manifold element in the subsequent growth steps, realizes arbitrary crack growth increment. Several benchmark examples are utilized to demonstrate the accuracy of the proposed hydraulic fracturing model in simulating fracture fluid flow and solid deformation. Finally, the developed fluid-solid coupling model is used to simulate rock hydraulic fracturing processes under different conditions. The ability and reliability of the proposed model to describe the hydraulic fracture propagation laws are verified by comparing with previous experimental and numerical results.

中文翻译：

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基于NMM的流固耦合模拟岩石水力压裂过程

摘要 基于数值流形法（NMM）的水力压裂过程模拟是一个有价值的研究方向，因为它在处理连续-不连续变形问题方面具有优势。本文提出了一种基于NMM的流固耦合模型，包括非定常裂缝流的数值求解、水压-载荷转换算法、水力孔径的修正和任意裂纹扩展增量的编程实现等。阶段，基于通过裂缝切割数学网格形成的闭环构建裂缝流动网络；为了消除显式算法对时间步长的敏感性，建立了非定常流动的无条件稳定数值求解方案。在固相方面，为实现水压与固体变形的耦合过程，通过水压-载荷转换算法将水压转化为载荷矢量，计算裂隙围岩变形；并引入Delaunay三角剖分算法，对具有多个扭结的流形单元进行细分，有效解决了裂纹尖端在后续生长步骤中不能在同一流形单元内停止或扭结的问题，实现了任意的裂纹扩展增量。几个基准示例被用来证明所提出的水力压裂模型在模拟压裂流体流动和固体变形方面的准确性。最后，利用开发的流固耦合模型模拟不同条件下的岩石水力压裂过程。