Debris flow entrainment rates in non-uniform channels with convex and concave slopes

Channel topography plays an important role in debris flow entrainment processes. Field observations and flume experiments have demonstrated two notable erosion effects: abrasion on convex slopes resulting from layer-by-layer shearing and impact erosion on concave slopes. Most existing formulas for debris flow entrainment rates are derived from the uniform slope assumption and do not account for the two erosion effects. In order to take abrasion and impact erosion into consideration, this study incorporated two channel curvature functions into the entrainment formula that is based on equilibrium between flow frictional forces and basal resistance forces. The two functions control the effects of entrainment on different slope types and are based on empirical relationships with curvature obtained in flume experiments. The revised formula provides a unified procedure for debris flow entrainment rates in non-uniform channels.