Comparison of settling-velocity-based formulas for threshold of sediment motion

The critical condition for incipient sediment motion is formulated in this note based on the settling velocity. The formula obtained is simple, relating the ratio of critical shear velocity to settling velocity to the dimensionless sediment diameter. Comparisons are then made with other settling-velocity based formulas available in the literature. To facilitate the computation of the effective near-bed velocity at the threshold condition, a generalized law-of-the-wall function is proposed for predicting the velocity distribution under various boundary conditions. This study demonstrates that the settling velocity is equivalent to the critical near-bed velocity, which is experienced by a typical bed sediment particle under the threshold condition, but only for large sediment sizes such as sand and gravel. Comparison results show that Yang's formula is suitable for flows with small flow depth relative to sediment size while Le Roux's formula may overestimate the threshold condition for fine particles by up to 30%.Accepted versio