Mathematical model on grain-size distribution in suspension over sand-gravel bed

•Modeling on grain-size distribution in suspension over sand-gravel bed has been done.•Stratification and hindered settling effect have been included.•Effect of particle-particle interaction is included in the computed reference level.•Effect of different probability is considered in the computed reference concentration.•The proposed model is verified with existing experimental data.

SummaryIn this study, the grain-size distribution in suspension over a sand-gravel bed in an open channel turbulent flow is investigated from theoretical point of view. On the basis of diffusion equation, a model on grain-size distribution is developed incorporating the effect of stratification and hindered settling due to increased suspension concentration. The hydrodynamic diffusion related to particle-particle interaction is considered in the computation of reference level and the influence of incipient motion probability, non-ceasing probability and pick-up probability of the sediment particles are considered in the computation of reference concentration. Due to inclusion of several factors, the proposed model predicts well the grain-size distribution of suspended load when compared with the experimental data and also shows its prediction superiority with respect to other existing models.