Analytical method for determining rill detachment rate of purple soil as compared with that of loess soil

Abstract

Rill detachment is an important process in rill erosion. The rill detachment rate is the fundamental basis for determination of the parameters of a rill erosion model. In this paper, an analytical method was proposed to estimate the rill detachment rate. The method is based on the exact analytical solution of rill erosion to the differential equation of rill detachment. The rill sediment concentration distribution as a function of rill length was identified through laboratory experiments under different slope gradients and flow rates. The sediment concentration processes from experiments on loess and purple rills were considered to estimate the rill detachment rates of both soils analytically. They were respectively used as a function of rill length and sediment concentration. The analytical detachment rates were compared with the numerically determined values to verify the analytical methods. The rill detachment rates of the two soils under different flow rates and slope gradients estimated by the analytical method were further compared on the basis of detachment-sediment function and detachment-rill length function. Results indicated that the analytically estimated values were very close to the numerically estimated values. Numerical and analytical methods were equally useful for rill detachment rate estimation. Therefore, the analytical method was verified to be rational and applicable for the rapid determination of the rill detachment rates based on either sediment concentration or rill length. The analytical detachment values of purple and loess soils suggested that the detachment rates of loess soil were significantly and considerably higher than those of purple soil. The erosion potentials of loess soil were also significant higher than those of purple soil. The differences in the erosion of the two soils decreased as the slope gradient and flow rate increased. These observations implied that the degree of loess soil erosion was greater than that of purple soil erosion at low slope gradients and flow rates. The factors causing these differences may be determined in terms of the properties of the two soils. Therefore, the proposed analytical method, in addition to the concepts and direct relationship to erosion process, could be applied to obtain the rill detachment rate for the determination of rill erosion model parameters.