为解决被注多孔介质的孔隙率和孔隙通道的多变性对现有注浆理论与试验结果误差的影响问题，引入分形理论相关知识，建立Bingham型浆液在分形多孔介质中柱形扩散的数学模型，并推导出分形渗透注浆扩散方程的解析解。通过室内注浆试验、传统注浆理论与本文理论对比验证该模型的有效性，并通过参数分析被注介质的体积分形维数和迂曲分形维数对多孔介质和浆液的影响。结果表明： 1）分形渗透率常数和分形孔隙率常数与体积分形维数呈正相关、与迂曲分形维数呈负相关关系； 2）随着孔隙最大直径的增加，分形渗透率常数和分形孔隙率常数也不断增加； 3）随着注浆时间的增加，浆液的扩散半径、扩散速度与注浆压力和浆液的水灰质量比呈正相关、与地下水头压力和迂曲分形维数呈负相关关系； 4）迂曲分形维数对浆液的扩散半径起重要作用，在直管极限条件下，浆液的扩散半径最大，随着迂曲分形维数的增加，浆液的扩散半径迅速减小。

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.