Grouting diffusion of chemical fluid flow in soil with fractal characteristics

The chemical fluid property and the capillary structure of soil are important factors that affect grouting diffusion. Ignoring either factor will produce large errors in understanding the inherent laws of the diffusion process. Based on fractal geometry and the constitutive equation of Herschel-Bulkley fluid, an analytical model for Herschel-Bulkley fluid flowing in a porous geo-material with fractal characteristics is derived. The proposed model provides a theoretical basis for grouting design and helps to understand the chemical fluid flow in soil in real environments. The results indicate that the predictions from the proposed model show good consistency with the literature data and application results. Grouting pressure decreases with increasing diffusion distance. Under the condition that the chemical fluid flows the same distance, the grouting pressure undergoes almost no change at first and then decreases nonlinearly with increasing tortuosity dimension. With increasing rheological index, the pressure difference first decreases linearly, then presents a trend of nonlinear decrease, and then decreases linearly again. The pressure difference gradually increases with increasing viscosity and yield stress of the chemical fluid. The decreasing trend of the grouting pressure difference is non-linear and rapid for porosity Φ>0.4, while there is a linear and slow decrease in pressure difference for high porosity.