Analysis of Grout Diffusion Law in 3D Rough Fractures Based on Fractal Characteristics of JRC Curves

Understanding grout diffusion behavior in rough-walled rock fractures is essential for optimizing grouting design in mining and geotechnical engineering. This study couples fractal surface reconstruction with three-dimensional volume-of-fluid (VOF) simulation to systematically investigate grout diffusion in fractures characterized by the Weierstrass–Mandelbrot fractal function. Twelve simulation cases, comprising four JRC profiles and three grout viscosities, are analyzed to elucidate the spatiotemporal evolution of grout filling. The results reveal a consistent three-stage diffusion pattern—initial filling, rapid diffusion, and stable equilibrium—across all conditions. Fracture fractal dimension emerges as the dominant factor controlling seepage velocity and diffusion zoning, while grout viscosity plays a secondary, roughness-modulated regulatory role. The equivalent hydraulic aperture is identified as the core parameter governing zone proportions. Engineering guidelines for viscosity selection and injection strategy under different roughness conditions are proposed.