An NMM-based fluid-solid coupling model for simulating rock hydraulic fracturing process

•An NMM-based fluid-solid coupling model is proposed.•The closed loops are used to construct fracture flow network.•An unconditionally stable solution scheme for unsteady flow is established.•Arbitrary growth increment of crack is achieved in NMM.•The ability of proposed model in simulating rock hydraulic fracturing is verified. 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.