A Coupled Darcy-Forchheimer Flow Model in Fractured Porous Media

Abstract

Aiming at nonlinear flow in fractured porous media, based on the finite volume method, the discrete equations of Darcy flow in porous and Forchheimer flow in fracture were derived, and a solution method for coupling flow is proposed. The flow solution by the proposed method for single fracture and intersecting fracture is verified against Frih’s solution. Based on this method, nonlinear flow behavior for fractured rock deep-buried tunnels under high water heads was discussed. The results show that the hydraulic gradient of surrounding rock is characterized by “large at the bottom and small at the top”, with a maximum difference of 2.5 times. Therefore, the flow rate at the bottom of the tunnel is greater than that at the top. The fracture flow rate along the flow direction is also greater than that in the vertical flow direction, with a maximum difference of 60 times. The distribution homogeneity and density of fracture are the most important factors that affect the hydraulic behavior of fractured rock tunnels. The more fractures concentrated in the direction of water pressure and the greater the density, the greater the surrounding rock conductivity and the greater the flow rate of the tunnel. Under this condition, the water-inflow accident of the tunnel would be prone to occur. The research results provide a reference for the waterproof design and engineering practice of fractured rock tunnels.