The Erosion Pattern and Hidden Momentum in Debris-Flow Surges Revealed by Simple Hydraulic Jump Equations

The erosion-deposition propagation of granular avalanches is prevalent and may increase their destructiveness. However, this process has rarely been reported for debris flows on gentle slopes, and the contribution of momentum hidden under the surge front to debris-flow destructiveness is ambiguous. Therefore, the momentum carried by the apparent surge front is often used to indicate debris-flow destructiveness. In this study, the erosion-deposition propagation is confirmed by surge-depth hydrographs measured at the Jiangjia Ravine (Yunnan Province, China). Based on simple hydraulic jump equations, the eroded deposition depth of surge flow is quantified, and the erosion pattern can be divided into two patterns (shallow and deep erosion). For surge flows with erosion-deposition propagation, significant downward erosion potential is confirmed, and debris-flow surge erosion is considered the deep erosion. The total momentum carried by surge flow is further quantified by two Froude numbers (surge-front and rearward Froude numbers) and verified through the field observation of surge flows. The total momentum of surge flow not only originates from the apparent surge front, but also includes the momentum within the eroded deposition layer. This study provides a theoretical approach for quantifying the upper limit of erosion depth and revealing the destructiveness of debris-flow surges. A perspective on the importance of substrate deposition for debris-flow erosion on gentle slopes is emphasized, as this approach can improve the reliability of debris-flow risk assessment.