Two-stage column–hemispherical penetration diffusion model considering porosity tortuosity and time-dependent viscosity behavior.

The diffusion of chemical grouts in porous media is important for soil reinforcement and stabilization. Slurry diffusion radius and pressure change are important parameters to measure the grouting effect. Using flower tube grouting to make Newtonian fluid slurries diffuse in a column–hemispherical shape is common in engineering, but its diffusion law is still unclear. In terms of the diffusion process, the grout adjacent to the grouting hole first spherically diffuses; with the continuous grouting, it will gradually intersect and overlap and then enter the second diffusion stage, at which the grout will continue to diffuse in a spheroidicity and the slurry in the middle does not spread out vertically anymore. If the stages during grouting are not considered, there will be some errors between the slurry diffusion and the actual situation. Meanwhile, in the traditional study of slurry diffusion law, the tortuous effect of the pore channels and viscosity time denaturation of grout is not considered, resulting in an obvious deviation between the calculated grouting diffusion diameter and the actual value. Therefore, based on the fractal theory, a two-stage column–hemispherical diffusion model of Newtonian fluid was derived considering the tortuosity of porous media and the time-dependent viscosity behavior of slurry. The influences of grouting flow rate, slurry viscosity and pore tortuosity on grouting pressure and diffusion radius under constant flow grouting mode were analyzed. The results show that the grouting flow rate had a positive effect on both of the diffusion radius and the grouting pressure, while the slurry viscosity and porosity tortuosity had a positive effect on the grouting pressure but a negative effect on the diffusion radius. Under the same condition, compared with the traditional column–hemispherical grouting diffusion model, the column–hemispherical grouting diffusion model with two-stage diffusion considering porosity zigzag had a larger diffusion radius and required a lower grouting pressure. The numerical simulation and model test also proved that the calculated diffusion radius and injection pressure from the theoretical model developed in this study were closer to the measured results, with an error of less than 10% in the diffusion radius and less than 20% in the grouting pressure. Therefore, the model may provide a certain reference for grouting design, construction and theoretical research. [ABSTRACT FROM AUTHOR]