Spherical Penetration Grouting Model for Bingham Fluids Considering Gravity and Time-Varying Slurry Viscosity

As an effective reinforcement technology for seepage prevention, penetration grouting has been widely used in geotechnical and underground engineering. Because grouting is a hidden project, the extent of slurry spread is often estimated theoretically and through experience. Therefore, it is important to understand the diffusion pattern and scope of penetration grouting in reinforcement engineering. Based on the generalized Darcy's law, a penetration grouting model considering the gravity and the time-varying nature of the slurry viscosity is proposed in this study. Its validity and effectiveness are verified through a comparison with existing penetration grouting tests. Based on the established penetration grouting model, the effects of the grouting pressure, permeability coefficient, water–cement ratio, and other factors on penetration grouting are analyzed. The penetration and diffusion process of a Bingham fluid considering gravity and time-variable slurry viscosity is computationally simulated using a finite-element software. The research results show that the proposed penetration grouting model is more accurate than the traditional one that does not consider the two aforementioned factors, and its results are more in line with the experimental ones. The rate of error calculated from the experimental value is about 11%. The diffusion radius of the slurry increases with increasing grouting pressure, permeability coefficient, and water–cement ratio, and decreases with increasing groundwater pressure. With the elapse of the grouting time, the increase rate of the diffusion radius exhibits a trend of increasing first and then decreasing and tending to level off. These research results can provide certain theoretical support for penetration grouting research in geotechnical and underground engineering.