Particle-scale kinematic model for the surface erosion of granular beds

The surface erosion of a granular bed can be quantitatively assessed by the erosion rate. Most of the existing methods for predicting erosion rates rely on empirical formulas, which do not take into account the motion of particles during the erosion process. This paper introduces a particle-scale kinematic model to determine the erosion rate of the granular bed. The model accounts for the interactions between water flow and the particles, and considers the arrangement of particles within the bed by incorporating a probability density function for the contact angle of the particle assembly. The proposed model has been validated through experimental measurements, demonstrating high accuracy. Using this model, it is possible to predict the distinct motion modes of granular particles under surface water flow, including stationary, rolling and suspension. We discovered that while the water flow may initiate the movement of particles on the granular bed, the particles might stay within the bed if the drag forces are too weak or if the initial contact angle of the particles is close to 90º, without influencing the erosion rate. For particles in different motion modes, typically over 60% of exposed particles in the granular bed contribute little to erosion, while typically no more than 30% are actively contributing to the surface erosion across varying shear stresses and particle sizes. This model provides an effective method for predicting the surface erosion rate and also sheds light on the mechanisms of particle motion during surface erosion.