Critical runoff depth estimation for incipient motion of non-cohesive sediment on loose soil slope under heavy rainfall

Abstract

Incipient motion of non-cohesive sediment, as a branch of water erosion, has been studied for decades, and criteria proposed in predicting incipient motion mainly focus on dimensionless shear stress and shear velocity. The two parameters could provide runoff erosive power, however, are invisible and not easy-measured in experiment. In this paper, critical runoff depth was recognized as another parameter, which is visible, measurable, and closely connected with shear velocity. To get it, a mathematical model coupling surface flow and subsurface flow was established, and they are governed by Navier-Stokes equation and Brinkman-extended Darcy equation, respectively. Velocity derived from the model could be indirectly applied in particle force analysis and finally a new criterion about critical runoff depth was obtained. Accuracy of the criterion was verified by comparison of experimental and theoretical values, e.g. theoretical critical runoff depth ranges from 2.71 $ 1.14 mm with a slope angle range of 20 $ 28 and mean particle diameter of 2.5 mm while the corresponding experiment values ranges from 3 $ 1 mm and the absolute errors are less than 0.3 mm. Compared with Yang's formula, this criterion could also be applied in predicting incipient motion of non-cohesive sediment for its significant advantages of high accuracy and concise formulation.

Estimating the critical shear stress for incipient particle motion of a cohesive soil slope

“…Herein, we modeled a simplified soil slope (Fig. 2 a) and considered runoff-seepage coupling 18 . The soil slope has a slope gradient of θ , and the soil properties include porosity n and permeability K .…”

“…Yuan et al 18 derived the velocity distribution in the y direction, which is expressed as Eq. ( 18 ), and the velocity distribution is shown in Fig.…”

“…These achievements have made great progress when the soil layer is approximately horizontal, but they cannot be directly applied to slope soil particles. In fact, slope runoff is driven by gravity, and the runoff depth is closely connected to the shear velocity 18 . Based on the force analysis of slope soil particles, the formula for incipient sediment motion of shallow soil slopes can be obtained.…”