Formula of bed-load transport based on the total threshold probability

The randomness of relative position of sediment particles and the flow conditions are the main influencing factors on incipient motion of sediment particles on the river bed surface, and the position of sediment particles is usually reflected by the relative exposure degree. In this study, the random effect of both flow conditions and relative location of sediment particles on the sediment incipient motion were investigated based on our previous study. The formula of sediment incipient motion based on the total probability was determined theoretically using the sliding mode. The total probability model of sediment incipient motion was then introduced into the study of bed-load sediment transport according to the Einstein assumption, and the dimensionless formula of bed-load sediment transport was finally proposed based on the definition of sediment transport rate per unit width. Through validation with experimental data and verification with other formulas in the literature, the formula developed in this study is proved to be reasonable and has higher calculation accuracy. This study contributes to enrich current knowledge regarding bed-load sediment transport on both the channel beds and riverbanks.