Theoretical and probabilistic analyses of incipient motion of sediment particles

Initiation of sediment particles by the flow can be classified by three different modes: rolling, sliding, and lifting. In this paper, threshold conditions of each mode obtained from force and momentum balances are investigated. Theoretical analysis of these conditions leads to curves similar to Shields diagram, resulting that the rolling and lifting thresholds yield the minimum and the maximum values of dimensionless critical shear stresses, respectively. A probabilistic analysis of the same problem is carried out under the assumption that the velocity approaching the particle has a normal distribution. The results revealed that about 4% of the particles on the bed are lifted when the critical bed shear stress by Shields is applied. Entrainment probability and saltating probability are also estimated, and they are compared with existing results.