Flow field analysis and particle erosion of tunnel-slope systems under coupling between runoff and fast (slow) seepage

The presence of particles on the surface of a tunnel slope renders it susceptible to erosion by water flow, which is a major cause of soil and water loss. In this study, a nonlinear mathematical model and a mechanical equilibrium model are developed to investigate the distribution of flow fields and particle motion characteristics of tunnel slopes, respectively. The mathematical model of flow fields comprises three parts: a runoff region, a highly permeable soil layer, and a weakly permeable soil layer. The NavierStokes equation controls fluid motion in the runoff region, while the Brinkman-extended Darcy equation governs fast and slow seepage in the highly and weakly permeable soil layers, respectively. Analytical solutions are derived for the velocity profile and shear stress expression of the model flow field under the boundary condition of continuous transition of velocity and stress at the fluidsolid interface. The shear stress distribution shows that the shear stress at the tunnel-slope surface is the largest, followed by the shear stress of the soil interface, indicating that particles in these two locations are most vulnerable to erosion. A mechanical equilibrium model of sliding and rolling of single particles is established at the fluidsolid interface, and the safety factor of particle motion (sliding and rolling) is derived. Sensitivity analysis shows that by increasing the runoff depth, slope angle, and soil permeability, the erosion of soil particles will be aggravated on the tunnel-slope surface, but by increasing the particle diameter, particle-specific gravity, and particle stacking angle, the erosion resistance ability of the tunnel-slope surface particles will be enhanced. This study can serve as a reference for the analysis of surface soil and water loss in tunnel-slope systems.