Effect of drag force on stability of residual soil slopes under surface runoff

Abstract

ABSTRACTTo investigate the effect of drag force on stability of residual soil slopes, a modified approach based on the limit equilibrium method is proposed by establishing a nonlinear coupled mathematical model to calculate the seepage velocities in soils and the runoff velocities at a fluid–solid interface. In this mathematical model, the Navier–Stokes equation and Brinkman-extended Darcy equation are used to describe the incompressible surface runoff and seepage in soils, respectively. Then, the drag force can be derived by adopting Newton's law of internal friction, and the factor of safety (FOS) of residual soil slopes considering drag force can be calculated based on the limit equilibrium method. The modified approach was applied to analyse the stability of rainfall-induced landslides in residual soils in Nanjiang, Sichuan, China, 2011. We found that the runoff depth can significantly control the FOS of the residual soil slopes and cause slope failures. The results of sensitivity analysis highlight the significance for considering drag force due to surface runoff when calculating the FOS of the residual soil slope. The FOS obtained from the modified approach is more reasonable, and this modified approach also can be used for evaluating or predicting rainfall-induced slope instability in residual soils.