Channel longitudinal profile plays an important role in debris flow entrainment processes. According to whether the bed slope is fixed or not, we consider three types of geomorphic channel condition: uniform, concave and convex bed slope. Most existing models for calculating basal entrainment are based on the simple assumption that the underlying erodible bed is sufficiently long and has a uniform slope. However, longitudinal profiles of natural channels in mountain regions are not ideally uniformed and thereby affect the processes of debris flow entrainment. For example, field investigations of a debris flow event in the Wenjia catchment in southwestern China after the 2008 Wenchuan earthquake indicate that the entrainment depth in debris flow channels is much greater at concave sites than at those with uniform slope.

On the basis of these considerations,supported by the National Natural Science Foundation of China [grant number 41371039], the Key Research Program of the Chinese Academy of Sciences (Grant No. KZZD-EW-05-01) and the National Basic Research Program of China (973 Program) [grant number 2015CB452704], Kaiheng Hu research group from Institute of Mountain Hazards and Environment, Chinese Academy of Sciences (IMHE, CAS), achieved new progress in the research of debris flow entrainment and proposed a revised erosion rate formula in non-uniform, slope-discontinuous channels, with convex and concave slopes.

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,featuring head-on collisions. Then a formula for calculating the erosion rate of debris flow in non-uniform channels was derived  below.

This study introduced two channel curvature functions into the entrainment formula to represent the effects of entrainment on different slope types and a specific term that account for impact erosion was incorporated.

The research achievements have been published in Journal of Mountain Science (DOI:org/1.1007/s11629-015-3749-6) and Journal of Hydraulic Research (DOI:org/10.1080/00221686.2017.1313321).