Theoretical Research on Diffusion Radius of Cement-Based Materials Considering the Pore Characteristics of Porous Media

In engineering, loose sandy (gravelly) strata are often filled with cement-based grout to form a mixed material with a certain strength and impermeability, so as to improve the mechanical properties of sandy (gravelly) strata. The tortuosity effect of sandy (gravelly) strata and the time-varying viscosity of slurry play a key role in penetration grouting projects. In order to better understand the influence of the above factors on the penetration and diffusion mechanism of power-law slurry, based on the capillary laminar flow model, this research obtained the seepage motion equation of power-law slurry, the time-varying constitutive equations of tortuosity and power-law fluid viscosity were introduced, and the spherical diffusion equation of penetration grouting considering both the tortuosity of porous media and time-varying slurry viscosity was established, which had already been verified by existing experiments. In addition, the time-varying factors of grouting pressure, the physical parameters of the injected soil layer, and slurry viscosity on penetration grouting diffusion law and the influencing factors were analyzed. The results show that considering the tortuosity of sandy (gravelly) strata and the time-varying of slurry viscosity at the same time, the error is smaller than the existing theoretical error, only 13~19%. The diffusion range of penetration grouting in the sandy (gravelly) strata is controlled by the tortuosity of sandy (gravelly) strata, the water–cement ratio of slurry, and grouting pressure. The tortuosity of sandy (gravelly) strata is inversely proportional to the diffusion radius of the slurry, and the water–cement ratio of slurry and grouting pressure are positively correlated with the diffusion radius. In sandy (gravelly) strata with a smaller particle size, the tortuosity effect of porous media dominates the slurry pressure attenuation. When the particle size is larger, the primary controlling factor of slurry pressure attenuation is the tortuosity effect of porous media in the initial stage and the time-varying viscosity of slurry in the later stage. The research results are of great significance to guide the penetration grouting of sandy (gravelly) strata.