A forchheimer-based fluid-solid coupling model for nonlinear flow of power-law grouts in fractured rock grouting

Grouting in fractured rock masses is crucial in numerous engineering projects such as tunnel seepage prevention, foundation reinforcement, and energy storage. However, slurry flow within fractures involves complex nonlinear behavior and significant fluid-solid coupling effects, and its accurate modeling remains a challenge. This study aims to establish a more accurate coupled model for slurry flow in fractures and rock mass deformation. Innovatively extending the Forchheimer formula for porous media to fracture flow, a nonlinear Forchheimer flow model suitable for power-law fluids is proposed, and pore and fracture flow are uniformly described by introducing a shape factor. Furthermore, by incorporating the constitutive relationship between slurry pressure and fracture deformation, a new numerical model for fluid-solid coupling of slurry in fractures is developed. Validation shows: compared with COMSOL numerical simulations, the average relative error of the calculation results for the two-phase flow model is less than 2.5%, with a deviation of only 1.1% for power-law turbulent flow velocity. When this method is used to detect slurry flow within a fracture network, the computational time is only 1/10 to 1/100 of that required by numerical methods, thus it ensures high computational accuracy while reducing computation time. Field case data indicate a prediction error of 7.26% for slurry diffusion distance. This model provides an effective tool for accurately predicting slurry diffusion behavior and fracture dynamic response during high-pressure grouting.