Superelevation and runup height of debris flows in bends based on typical rectangular cross-sections and gravity center offset

Owing to the superelevation in the bend, debris flow rushed out of the channel and destroyed the engineering facilities near the bend, which brings challenges to the design of disaster prevention and mitigation projects. Under the assumption of a continuous homogeneous medium and rectangular channel section, the debris flow velocity in the bend is decomposed into a tangential velocity that causes superelevation and a normal velocity that generates runup. The calculation equations of superelevation, runup, and total superelevation of debris flow in the bend are derived based on the gravity center offset of the flow section in the debris flow movement. The proposed equation can determine and depict the evolution of total superelevation value along the bend, which is useful for engineers to carry out the targeted design in debris flow prevention and control engineering. Meanwhile, using the equation in this paper and two other representative equations, the total superelevation, superelevation, and runup height of debris flow in 37 groups of test data and bends in the case study are computed to compare with the test and measured results. The test findings showed that the runup height accounts for about 40% of the total superelevation, and the runup height of the five bend points in the case accounts for 43-48%, indicating that the runup is an essential part of the total superelevation and needs to be calculated in the design of the bend of the debris flow prevention and control project.

Automated summary

Due to the superelevation in the bend, debris flow rushed out and caused damage to nearby engineering facilities, posing challenges to disaster prevention and mitigation project designs. This study derives calculation equations for superelevation, runup, and total superelevation of debris flow in the bend, based on the gravity center offset of the flow section. The proposed equation allows engineers to determine and visualize the evolution of total superelevation, aiding targeted design in debris flow prevention and control engineering.