Abstract: The coupling analysis model of the surface runoff and water flow in fissures is established to study the effect of surface runoff and groundwater seepage on the stability of slope under heavy rainfall condition. The Navier–Stokes is used to describe the runoff and subsurface runoff, and the Brinkman-extended Darcy equation is used to describe the seepage in the soil and rock. Under the boundary conditions of the equal velocity and continuous shear stress at the interface of different media, we could inquire into the flow distribution of internal seepage and subsurface runoff. The drag force generated by water flow on the slope is obtained by applying the Newtonian friction law, and the drag force is embedded into the rigid body equilibrium theory to analyze the slope stability. The calculation results of the actual slope show that the safety coefficient of the slope is 1.164 when the effect of drag force is not considered. And the safety coefficient of the slope is 1.089 when the drag effect exerted by the water flow on the slope soil is taken into consideration, and the safety factor of the slope is decreased by 6.44%. It shows that the drag force effect has a great negative influence on the stability of the slope, and the drag force can play a decisive role in the critical steady state. Finally, the relationships between the safety coefficient of slope and runoff depth, soil thickness and slope inclination are discussed respectively considering drag force or not. The analysis shows that under similar conditions, the steeper the slope, the more obvious the decrease of the safety factor of the slope soil. The safety factor of the slope decreases with the increase of the slope inclination and the thickness of the soil layer.

Key words: drag force effect, stability of slope shallow soil, coupling of runoff and seepage, velocity distribution