The study of the slurry reinforcement mechanism is mainly focused on the interaction between slurry and soil. The seepage effect of the slurry always exists no matter what way the slurry interacts with the soil around the pile. In the process of slurry diffusion, the porosity of the soil, the permeability of the slurry, and the slurry pressure vary due to some cement particles being blocked by the soil particle skeleton. Therefore, the study of the slurry filtration effect is of great significance for predicting the permeation and diffusion law of slurry. In this paper, a macroscopic linear filtration model was introduced and the changes of slurry properties in the permeation diffusion process were considered. Firstly, a spherical (cylindrical) permeation diffusion model, which takes the linear filtration effect and the variation of slurry viscosity into account, was derived based on the conservation of mass. Furthermore, in order to more accurately reflect the influence of the filtration effect on the slurry permeation diffusion model, a polynomial nonlinear filtration model was proposed, and the numerical solution for the permeation diffusion model was derived using finite difference and finite element methods. Finally, the numerically simulated values, the measured values, and the values from the spherical permeation diffusion model that does not consider slurry viscosity variations were compared. The results indicate that the grout pressure is inconsistent with the measured value without considering the effect of the filtration. The initial grouting pressure calculated by the model in this paper is slightly larger, and the required grouting pressure over time is greater than that without considering the filtration effect, regardless of whether the grout diffuses in a spherical or cylindrical manner. The results of this study can contribute to a better understanding of grouting engineering and provide some theoretical guidance for actual grouting.
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