Estimating the mud depth of debris flow in a natural river channel: a theoretical approach and its engineering application

Mud depth of debris flow is an essential parameter for assessing the hazard magnitude in an event. However, direct prediction of mud depth in a natural river channel is a scientific challenge because current methods often treat the complex relief of bed surface as a rectangular one, which makes the prediction illogical. In this paper, we propose a new theoretical approach, the so-called numerical integral method-based approach for estimating the maximum mud depth of debris flow at a complex cross-section in a natural river channel. Given a predefined peak discharge of the debris-flow event, the numerical integral method-based iteration algorithm uses the Riemann method to search for an approximate mud depth. In contrast to the previous methods, the presented approach addresses an important issue, namely it takes into account the complex shape of the bed surface and superelevation at the bend for natural channels. Two cases are used to illustrate the performance and advantages of the presented approach: one is a well-documented event in the previous study, and the other is a debris-flow event after Ms. 8.0 Wenchuan earthquake. An engineering application regarding the rational design of a debris-flow canal is subsequently discussed. The canal was completely destroyed in a debris flow event in 2008. We used the proposed method to back-analyze the mud depth and velocity in the canal. It was found that the abrupt decrease of mud depth from the natural channel to the concrete canal significantly reduced the transportation capability, thereby causing blockage in the canal. The canal was modified and reconstructed in 2009 with suggested improvements from the proposed method, and successfully transported subsequent debris flow in 2011.