Probabilities of sediment entrainment and estimation of bedload flux

We explore the probabilities of sediment entrainment in turbulent flow over a loosely packed bed of particles in tetrahedral and square-pyramid configurations. The rolling and lifting probabilities of a target particle are derived by considering the normal, lognormal and Gram–Charlier distributions to characterize either the area-averaged instantaneous streamwise velocity or the area-averaged velocity fluctuation. For each distribution, the mean rolling and lifting probabilities are obtained by incorporating the effects of particle exposure and entrainment angle. The mean rolling probability increases with the Shields parameter attaining a maximum value and then decreases. Conversely, the mean lifting probability increases with the Shields parameter. This study successfully captures experimental data for both rolling and lifting probabilities and effectively differentiates between the rolling and lifting modes. The effects of flow regime and sediment non-uniformity on the mean rolling and lifting probabilities are examined. The mean rolling probability corresponding to the threshold of sediment entrainment is obtained as a function of the particle parameter. Finally, using the mean lifting probability, the model developed at the particle scale is extended to the continuum scale to estimate the bedload flux. The predicted bedload flux shows excellent agreement with the experimental data.