Verification of the detachment–transport coupling relationship of rill erosion using colluvium material in steep nonerodible slopes

The detachment–transport coupling equation by Foster and Meyer is a classical equation that describes the relationship between detachment and transport. The equation quantifies the relationship between sediment loads and soil detachment rates, deepens the understanding of soil erosion and provides a reliable basis for the establishment of an erosion model. However, the applicability of this equation to slopes with gradients greater than 47% is limited. In this work, the detachment–transport coupling relationship is investigated using the colluvium material of Benggang. A nonerodible rill flume 4 m long and 0.12 m wide was adopted. The slope gradient ranged from 27% to 70%, the unit flow discharge ranged from 0.56 × 10(−3) to 3.33 × 10(−3) m(2) s(−1), and the sediment transport capacity (T(c)) was measured under each slope and discharge combination. The sediment was inputted into the flume according to the predetermined sediment addition rate (from 0% to 100% of T(c)), and the detachment rate (D(r)) under each combination of the slope and discharge was measured. D(r) linearly decreased with increasing sediment loads, which is consistent with the detachment–transport coupling equation by Foster and Meyer. The linear equations can predict the detachment capacity (D(c)) and T(c) well (Nash–Sutcliffe efficiency coefficient (NSE) = 0.98 for D(c), and NSE = 0.99 for T(c)). The detachment–transport coupling equation can adequately predict the D(r) (NSE = 0.89). However, its applicability to slopes of <47% (NSE: 0.92–0.96) was greater than that to slopes of ≥47% (NSE: 0.81–0.89), and the predicted D(r) under T(c) levels of 20% and 40% were higher than the measured values, while the predicted value under a T(c) level of 80% was lower than the measured value. In summary, the detachment–transport coupling equation by Foster and Meyer can accurately reflect the negative feedback relationship between detachments and transports along steep-slope fixed beds and is suitable for colluvial deposit research. The results provide a basis for the construction of steep-slope colluvial deposit erosion models. In the future, the study of the hydrodynamic characteristics of sediment transport processes should be strengthened to clarify the detachment–transport effect of flows through hydrodynamics.