A Mathematical Method for Estimating the Critical Slope Angle of Sheet Erosion

Abstract

Estimating the critical slope angle (CSA) for sheet erosion is important for the precision estimation of sheet erosion and the development of erosion control practices. This study developed mathematical equations considering rainfall intensity and soil infiltration to efficiently estimate both instantaneous (at a given instant during rainfall) and cumulative CSAs, while also providing a valuable explanation for the change in CSA. The mathematical equations were consistent with observations from runoff plots (NSE = −1.01) of loess soils from Zhangjiakou (China) and simulation results (NSE = 0.96) from the Water Erosion Prediction Project model for a loam soil in Montana (USA). Estimated instantaneous CSA determined by the mathematical equations increased as the ratio of rainfall intensity to soil infiltration (I/f) increased, resulting in higher observed cumulative CSA after heavy versus normal rainfall events. Heavy rainfall, compacted soil, and varying rainfall duration affected the CSA by changing the I/f ratio. Maximum instantaneous CSA provided a better prediction of changes in soil erosion dynamics than that obtained from CSAs determined by field observations or experimental simulations. The mathematical equations illustrate the underlying physical mechanisms by which rainfall intensity and soil infiltration affect the CSA through changing the shear stress of overland flow. The results of this study provide critical information for guiding the development of effective soil erosion control strategies.

Keywords

• sheet erosion
• rainfall–infiltration dynamics
• critical slope angle
• shear stress analysis
• soil erosion control