One-dimensional morphodynamic model for retrogressive erosion based on a sediment entrainment theory at high flow velocity

Retrogressive erosion is a high-speed erosion process that usually occurs during the rapid release of stored water in reservoirs built on sandy rivers. Retrogressive erosion has been utilized in the practice of reservoir sedimentation control, but accurate prediction of the bed deformation process by numerical models has rarely been reported. The current study presents a one-dimensional morphodynamic model for simulating the evolution process of retrogressive erosion induced by high-velocity flows on steep slopes. The governing equations apply a Cartesian coordinate system with a vertically oriented z axis. The bed surface gradient and friction terms in the flow equations include correction factors to take account of the effects of high slope on flow movement. The net vertical sediment flux term in the sediment transport and bed deformation equations is calculated using an equation of erosion velocity. Particularly, this equation is based on an empirical relation between the sediment entrainment rate and the Shields parameter in contrast to the traditional sediment transport capacity, and the critical Shields parameter is modified by taking into account the permeability of the sediment layer and the stability of particles on a slope. The feedback of scoured sediment on the flow movement is considered by additional terms in the governing equations. Flume experiments of retrogressive erosion in literature were simulated to validate the model. The temporal variations of the longitudinal profiles of the free surface and channel bed and the sediment transport rate were well predicted. The algorithm calculating sediment entrainment in the proposed model also was validated for an experiment measuring entrainment rate from the literature. More importantly, it was found that the morphodynamic model using the sediment transport capacity equation predicts the trend of cumulative erosion contrary to the measurements, while results of the proposed model can follow a similar trend with the observed data in the retrogressive erosion process.