Erosion and Cross Section on the Cohesive Stream Bed

Abstract

Usually some cohesive materials are contained in bare slopes, where the rill-like streams are formed in the process of surface water erosion. For the prediction of the sediment run-off from such a slope, it is important to know the arrangement and scale of streams and soil property against erosion. In this study a new theoretical model is offered to obtain the shear distribution along the channel perimeter with an arbitrary corss section, and the erosion process of the cohesive material bed is investigated. The theory is examined by flume experiments using bentonite. Main results are as follows. The rate of erosion is related to the local shear. Shear distribution in a uniform flow is obtained by differentiating the area between the normals to the wall with the wetted perimeter. Bed unevenness in the lateral direction may be amplified or reduced according to the shape of the unevenness and the flow conditions. The criterion is obtained in the domain of a/H and L/H, where a and L are the wave height and length respectively and H is the water depth. A stream has an equilibrium cross section corresponding to the hydraulic conditions. When the rate of erosion is proportional to the shear velocity, the ratio of the water surface width to the maximum water depth is about 4 in the equilibrium state.