Study on the downcutting rate of a debris flow dam based on grain-size distribution

Though widespread in disaster-prone areas, debris flow dams have unique characteristics in their formation and failure. An accurate description of their failure is the prerequisite to predict the dam-break floods, although little has been done in this research area. This paper describes the longitudinal evolution processes of a debris flow dam with 15 different grain-size distributions through flume tests, and put forward the formula of the downcutting rate for the whole process of overtopping failure. Results have shown that, according to the longitudinal evolution characteristics of the debris flow dam failure, the breach process can be divided into three stages: the formation of a retrogressive scarp, the erosion of the retrogressive scarp, and its decline stage. When the dam overtops and breaches, the downcutting rate for the whole evolution process can be expressed as E = k v sin(0.85 + θ)3, where E is the erosion rate, v and θ are the flow velocity and the longitudinal slope of the breach respectively, and k is the erosion rate coefficient. The larger the value of the erosion rate coefficient k is, the faster the erosion rate E is. The minimum correlation coefficient R2 between the calculated and the measured erosion rates is 0.73. In addition, the relationship among erosion rate coefficient k, grain-size distribution parameters μ, and Dc is also proposed, and the correlation coefficient R2 reaches 0.965. The results provide an important theoretical basis for the prediction of debris flow dam-break floods, which can facilitate evidence-based decision-making in disaster prevention and mitigation.