Prediction of Critical Shields Number for Incipient Sediment Motion in Shallow Flows

Abstract

The Shields curve underestimates the critical shear stress for incipient sediment motion in shallow flow conditions. This study starts with a consideration of sediment transport based on Bagnold’s concept of stream power. Then it is shown that the critical Shields number is related to the dimensionless sediment transport rate and friction factor. Finally, by defining the threshold condition using the pickup probability, the critical Shields number is presented as a function of relative roughness height for incipient sediment motion in shallow flows. The proposed formula was calibrated with experimental data collected from 13 sources in the literature. Gravel-bed rivers usually are characterized by shallow water and steep slopes, e.g., in mountain rivers. Sediment motion in such a case long has been a subject of research interest. To evaluate incipient sediment motion over a gravel bed, we propose applying the critical sediment transport rate. With the concept of stream power and pickup probability, the critical Shields number is theoretically related to the dimensionless sediment transport rate and flow resistance. Consequently, a new formula was developed for calculating critical Shields number based on the relative roughness height. The formula was calibrated using previous experimental results.