Theoretical model for slurry infiltration and particle dispersion in saturated sands based on non-Darcy flow

Revealing the seepage and diffusion behavior of slurry used in slurry shield tunneling within saturated sandy strata, along with its influencing factors, is critical for maintaining face stability during shield excavation. Considering that the slurry employed in shield tunneling is a non-Newtonian fluid exhibiting pronounced non-Darcy flow characteristics in high-permeability formations, a slurry infiltration-diffusion model was developed in this study based on mass conservation and non-Darcy flow theory. A system of governing equations was established incorporating multiple parameters, including seepage velocity, pore water pressure, and volume fraction of slurry suspension particles. Numerical solutions were obtained using the Lax finite difference scheme, implemented via MATLAB programing. The model's validity was verified through comparison with laboratory experimental results. The proposed model elucidates the spatiotemporal evolution patterns of pore water pressure and slurry particle volume fraction. Finally, relying on a large-diameter slurry shield tunneling project, the variation characteristics of parameters such as pore water pressure, seepage velocity, and slurry loss under specific conditions were analyzed. The results indicate that pore water pressure and suspended particle volume fraction decrease sharply with increasing infiltration distance. At t = 0.1 s, the decrease within 0.2 m exceeds 90% and approaches zero at 0.4 m. Between t = 0.4 s and t = 0.5 s, the values at 0.4 m show only a slight increase (approximately 10.8% and 7.7%), indicating that the spatial gradient weakens and approaches steady-state conditions. Additionally, the seepage velocity at the tunnel front continues to decrease, eventually approaching zero. These findings provide theoretical support and engineering guidance for predicting slurry filter cake formation time and optimizing slurry parameters.