Incipient Motion Criteria of Wide-Grading Particles on Loose Soil Slopes under Coupling of Runoff and Seepage

Wide-grading particles on loose soil slopes will experience scouring erosion under the coupling of runoff and seepage. In this paper, the particle critical incipient velocity was calculated based on an analysis of the rolling dynamics, and a runoff-seepage coupled nonlinear mathematical model was established. In the model, the Navier–Stokes equation and the Brinkman–Darcy equation were used to describe runoff and seepage motion, respectively. The expressions for the interface velocity and safety factor of the incipient particle motion were obtained by introducing a stress-jumping boundary condition where the velocity is continuous and the stress is jumping, with an incipient motion probability distribution. An indoor flume-scouring experiment on the wide-grading gravel particles was conducted, and the absolute errors of the particle incipient probabilities between the theoretical and experimental results were found to be less than 0.14. Furthermore, the existing theoretical model is a special case of the present model when the jumping coefficient is equal to 0. The parameter analysis results show that increasing the runoff depth, jumping coefficient, slope angle, porosity, and permeability aggravates the erosion of wide-grading particles, while increasing the equivalent diameter, unit weight, and exposure angle has the opposite effect. This study can provide guidance on wide-grading soil erosion due to runoff and seepage.