Viscous Resistance of Pore Water to Soil Particle Detachment by Overland Flow.

Studies of soil erosion by overland water flow indicate that, once particle detachment has initiated,  detachment rate increases more or less linearly with increasing shear stress exerted by the flowing water at the soil surface.  For relatively small particles, the rate of particle detachment at a given shear stress decreases with reduction in particle size.  Current soil constitutive models do not provide a clear explanation for these phenomena. Here a simple constitutive model, based on familiar soil physics concepts, is presented which predicts the above behavior. The underlying principle is that in a saturated bed of soil particles subject to overland flow, detachment of a particle into the external flow field requires that water must flow into the soil to compensate for the volume vacated by the particle. During initial stages of particle movement, when the particle is still closely confined by neighboring particles, water flow into the vacated volume must occur through narrow inter-particle channels, causing a viscous fluid reaction to particle extraction. Assuming non - cohesive soils, and neglecting gravitational and inertial forces, the fluid reaction suction is equal in magnitude to the hydraulic lift stress pulling particles out of the bed. For Newtonian inter-particle fluid flow and Miller scaling relations, one obtains additionally that the viscous reaction suction is directly proportional to fluid viscosity and particle extraction velocity, and inversely proportional to the square of particle diameter.  Combining these results yields that particle detachment velocity is proportional to the product of hydraulic lift stress (approximately proportional to shear stress) and the square of particle size, divided by fluid viscosity. A laboratory scale model  experiment indicates significant viscous reaction to particle detachment in soil water systems, which should be considered in soil erosion modeling.