Abstract
The transverse deformation of a riverbed is a natural phenomenon of river channel evolution. Sediment transport is the vehicle for the interactions between the water flow and the banks of a river bend, and it affects the formation, disappearance, and evolution of the river bend. To further investigate the sediment incipient motion on the concave bank slope of a river bend, an equation representing the equilibrium of forces on a sediment particle at the critical incipient motion was established using mechanical analysis and probability theory. Based on this equation and the assumption of a sliding mode of the incipient motion, the effects of the circulation and water flow momentum variations in a river bend in addition to conventionally considered forces on the sediment incipient motion were considered. Illustrations and physical diagrams of the forces on a sediment particle and its motion initiation process were clearly described. A formula representing the sediment incipient velocity on the sloped concave bank of a river bend was derived theoretically. The derived formula predictions agreed well with available experimental data. The Pearson correlation coefficient was > 0.87. The overall mean absolute error was 17.6% < 30%, which corresponded to an improvement in accuracy of 7.17% compared with the predictions using the formula proposed by Li. The factors affecting the sediment incipient velocity were examined. For a given flow rate and sediment particle size, the sediment incipient velocity increases with the increase in the gradient coefficient of a concave bank slope of a river bend. For a given flow rate and gradient coefficient, the sediment incipient velocity increases with increasing particle size. The proposed formula meets the calculation accuracy requirement and provides a theoretical reference for sediment transport in river bends.