Quantifying the sheet-rill erosion process along a saturated soil slope

•Erosion masses in sheet and rill erosion states are quantified on saturated soil slopes.•FSM&ARM can precisely estimate the erosion masses in sheet and rill erosion states.•Effects of the rainfall intensity & slope gradient in sheet and rill erosion states are evaluated. The sheet and rill erosion process on a saturated soil slope is different from that on an unsaturated soil, resulting in different erosion masses. Nevertheless, few studies have investigated sheet erosion and rill erosion along a saturated soil slope. Quantifying and comparing erosion masses of sheet and rill erosion along a saturated soil slope are important to understanding soil erosion mechanisms and control soil loss. Based on indoor soil flume simulated rainfall experiments, the erosion process characteristics from sheet erosion to rill erosion were studied, and the erosion masses were measured under combined conditions of different rainfall intensities (30, 60, and 90 mm/h) and slope gradients (2°, 5°, 10°, 15°, and 20°). The fitting method of sheet erosion (FSM) and an analytical method of rill erosion (ARM) were utilized to determine the erosion mass in different erosion stages from sheet to rill erosion. The results showed that the FSM and ARM methods were applicable to estimate erosion masses during the erosion process from sheet to rill erosion. The relationship among the rainfall intensity, slope gradient and erosion mass in the sheet erosion and rill erosion states could be expressed by a power function. The erosion masses in the sheet and rill erosion states were more sensitive to the rainfall intensity than to the slope gradient. Furthermore, the erosion masses in the rill erosion state were approximately 2.31–5.42 times higher than those in the sheet erosion state under the combined conditions of three rainfall intensities (30, 60, 90 mm/h) and five slope gradients (2°, 5°, 10°, 15°, and 20°). Relatively higher slope gradients and rainfall intensities corresponded to greater amplitudes of the variation in erosion masses in the sheet and rill erosion states than those under relatively lower slope gradients and rainfall intensities. The results provide simplified and accurate experiments and methods for quantifying erosion masses in different erosion stages between sheet and rill erosion and clarifying the erosion process from sheet to rill erosion.