Newtonian Fluid Diffusion Mechanism Considering Time-Dependent Grout Viscosity and Tortuosity Effect

Grouting operations are inherently concealed and unobservable, making the estimation of grout diffusion range often reliant on empirical and theoretical methods. In practical engineering, Newtonian fluid grouts frequently exhibit a columnar–hemispherical diffusion pattern. To achieve a more accurate prediction of this diffusion morphology, this study develops a two-stage columnar–hemispherical penetration grouting model for Newtonian fluids based on Darcy's law. The model comprehensively accounts for the time-dependent viscosity of the grout and the tortuosity effect. This research analyzes the factors influencing the grout diffusion radius and utilizes the COMSOL (version 6.2) Multiphysics platform to simulate the grout's penetration and diffusion process in porous media. The results demonstrate that, compared to the traditional columnar–hemispherical model, the proposed model more accurately describes the diffusion behavior of grout in porous media. The grout diffusion radius shows a positive correlation with the grouting pressure and a negative correlation with porosity. Furthermore, as the grouting time increases, the radius initially grows rapidly and then gradually levels off. The new model's prediction for the diffusion radius is 19.4% smaller than that of the traditional model, aligning more closely with practical engineering observations. The findings of this study can serve as a technical reference for grouting construction in underground engineering.