Abstract:Abstract: In order to study the scouring effect on particles in a loose granular slope with surface runoff，an analytical model was set up on the basis of the characteristics of slope runoff and seepage. A generalized equation known as the Brinkman-extended Darcy equation is solved inside the seepage zone

along with the incompressible Navier–Stokes equation in the upper runoff zone. We also use the continuity equation for both regions and a Neal–Nader boundary condition on the interface of the two regions. Combining Navier–Stokes equation and Brinkman-extended Darcy equation with the continuity equation can derive the flow velocity distributions of fluid in both regions

respectively. And the flow velocity is increase by the growing effecting factors. According to the flow velocity expressions

it is noted that the velocity mainly depends on slope gradient

runoff depth

porosity and permeability of the slope earth. In order to investigate the starting mechanism of particles on slope under the condition of runoff

Newton’s law of friction is introduced

and the shear stress at the interface of the two regions is obtained. The two cases of particle sliding and rolling are analyzed respectively

and the corresponding instability criterion of particle in sliding and rolling are presented in the two motion modes. Based on the analysis of the two criterions

it can be concluded that: (1) For the sliding case

the anti-sliding stability coefficient is mainly affected by the slope gradient

friction angle

particle radius

runoff depth and the porosity and permeability of the slope earth

and it increases with the rising of the internal friction angle

particle radius

porosity and permeability of the slope earth

and decreases with the drop of the slope gradient and runoff depth; (2) Whether the particle rolls or not depends mainly on the slope gradient

runoff depth

particle radius

and the porosity and permeability of the slope earth

and the larger the value

the easier the instability of the particles.