Analytical and Numerical Analysis of Bingham Fluid Grouting in Rough Fracture

Accurately describing slurry diffusion in fracture remains challenging due to the complexity of fracture roughness and the non‐linear rheological properties of slurry. This study presents an analytical solution for the single‐hole grouting in rough fractures considering the time‐dependent viscosity of Bingham fluid. Fracture roughness is described by introducing two parameters, the fractal dimension D and the characteristic scale parameter G . The accuracy of the analytical solution is validated by comparing the slurry flow and diffusion radius from experimental results with predicted results. The corresponding slurry flow Q calculated from the analytical solution is used to delineate different areas. Variations in D and G shift the slurry flow resistance from rough ( Q < 0.1 L) to transitional (0.1–0.8 L) and smooth ( Q > 0.8 L) areas under constant other parameter conditions. Variations in yield stress and viscosity shift the slurry flow areas among low, medium, and high sensitivity areas. Additionally, numerical analysis of two‐hole grouting in rough fractures is performed to determine optimal grouting hole spacing based on the percentage of the area covered by the slurry relative to the total fracture area. During two‐hole grouting, mutual squeezing effect between slurry alternately promotes and impedes flow. The optimal grouting hole spacing of Bingham fluids with varying water‐to‐cement ratios decreases with fracture roughness and increases with grouting pressure. Bingham fluids with water‐to‐cement ratios of 1.0–2.0 exhibit greater sensitivity to grouting pressure in wide fractures due to complex flow characteristics, providing a reference for simplifying grouting process across varying geological conditions.