Exploring the velocity distribution of debris flows: An iteration algorithm based approach for complex cross-sections

The estimation of debris-flow velocity in a cross-section is of primary importance due to its correlation to impact force, run up and superelevation. However, previous methods sometimes neglect the observed asymmetric velocity distribution, and consequently underestimate the debris-flow velocity. This paper presents a new approach for exploring the debris-flow velocity distribution in a cross-section. The presented approach uses an iteration algorithm based on the Riemann integral method to search an approximate solution to the unknown flow surface. The established laws for vertical velocity profile are compared and subsequently integrated to analyze the velocity distribution in the cross-section. The major benefit of the presented approach is that natural channels typically with irregular beds and superelevations can be taken into account, and the resulting approximation by the approach well replicates the direct integral solution. The approach is programmed in MATLAB environment, and the code is open to the public. A well-documented debris-flow event in Sichuan Province, China, is used to demonstrate the presented approach. Results show that the solutions of the flow surface and the mean velocity well reproduce the investigated results. Discussion regarding the model sensitivity and the source of errors concludes the paper.