Determination of the critical rainfall of runoff-initiated debris flows by the perspective of physical mechanics and Shields stress

The critical rainfall of runoff-initiated debris flows is utmost importance for local early hazard forecasting. This paper presents research on the critical rainfall of runoff-initiated debris flows through comparisons between slope gradients and three key factors, including topographic contributing area, dimensionless discharge, and Shields stress. The rainfall amount was estimated by utilizing in-situ rainfall records and a slope-dependent Shields stress model was created. The created model can predict critical Shields stress more accurately than the other two models. Furthermore, a new dimensionless discharge equation was proposed based on the corresponding discharge-gradient datasets. The new equation, along with factors such as contributing area above bed failure sites, channel width, and mean diameter of debris flow deposits, predicts a smaller rainfall amount than the in-situ measured records. Although the slope-dependent Shields stress model performs well and the estimated rainfall amount is lower than the in-situ records, the sediment initiation in the experiments falls within sheet flow regime due to a large Shields stress. Therefore, further sediment initiation experiments at a steeper slope range are expected in the future to ensure that the sediment transport belongs to mass failure regime characterized by a low level of Shields stress. Finally, a more accurate hazard forecast on the runoff-initiated debris flow holds promise when the corresponding critical slope-dependent dimensionless discharge of no motion, fluvial sediment transport, mass flow regime, and sheet flow regime are considered.