A new approach for analyzing the velocity distribution of debris flows at typical cross-sections

The asymmetrical distribution of debris-flow velocity in a cross-section has long been observed and is currently regarded as one of the most essential issues in debrisflow research. Due to a lack of quantitative models for the velocity distributions of debris flows, most studies consider only the mean velocity. However, to optimize countermeasure structures, to estimate the erosion rate, or to evaluate the constitutive equations for shear behavior, it is beneficial to know the velocity profile in a cross-section. In this paper, a generalized model of typical channel geometries (e.g., rectangular, trapezoid, or V-shape) is proposed. A description of the velocity distribution that optimizes the Manning–Strickler velocity equation for transverse distribution and Egashira’s velocity equation for vertical distribution is presented; thus, the debris-flow velocity at any point in the cross-section can be calculated and the distribution profile therefore obtained. A well-documented debrisflow reference case and the Jiasikou debris flow in the high-seismic-intensity zone of the Wenchuan earthquake are selected as case studies to demonstrate the model. Analyses of both cases confirm the asymmetrical distribution of debris-flow velocity in cross-section, as originally expected. This shows that the velocity at the top surface in the middle of the channel is much larger than that at each sidewall and than the mean value calculated by former equations. The obtained velocity distribution profile is a better approximation of the observed field profiles.