Abstract: The variability in porosity and pore channels within porous media significantly impacts existing grouting theories and experimental outcomes. To address this, fractal theory is introduced to establish a mathematical model for the cylindrical diffusion of Bingham grout in fractal porous media, from which an analytical solution for the fractal infiltration grouting diffusion equation is derived. The effectiveness of the model is validated through indoor grouting experiments, traditional grouting theory, and the proposed theory. Further parameter analysis examines the influence of the volume fractal dimension and tortuosity fractal dimension on porous media and grout. The results reveal the following: (1) The fractal permeability constant and fractal porosity constant are positively and negatively correlated with the volume fractal dimension and the tortuosity fractal dimension, respectively. (2) As the maximum pore diameter increases, the fractal permeability constant and porosity constant increase. (3) As grouting time increases, the diffusion radius and velocity of the grout positively correlate with the grouting pressure and water-cement ratio, and negatively correlate with the groundwater head pressure and tortuosity fractal dimension. (4) The tortuosity fractal dimension significantly affects the grout diffusion radius; under the limit condition of a straight pipe, the grout diffusion radius is maximized. As the tortuosity fractal dimension increases, the grout diffusion radius rapidly decreases.

Key words: Bingham grout, porous medium, volume integral dimension, tortuous fractal dimension