Bedload Model for Nonuniform Sediment

In this study, a bedload model for nonuniform sediment is developed considering the density function of sediment entrainment with no active layer. The model is formulated based on physical considerations, dimensional reasoning, regression analysis, and laboratory data. Four parameters are incorporated in the model formulation, namely the Shields stress ${\tau }_{*g}^{\prime }$, the critical Shields stress ${\tau }_{*cg}$, the Kramer coefficient of uniformity $c_u$, and the relative grain size (size of the $j$th grain fraction to the geometric mean size, $d_j/d_g$). The model collectively accounts for the hiding effects and the variation of the transported bedload material fractions from the surface and subsurface material. The findings of the study show that at low values of ${\tau }_{*g}^{\prime }/{\tau }_{*cg}$ fractions within the range of $0.3<d_j/d_g<3.0$ are present with larger amounts in the transported bedload material than in the substrate, whereas fractions finer or coarser than that range are present with larger amounts in the surface layer than in the substrate. The study shows also that only fractions of $d_j/d_g>3.0$ could contribute to the formation of the armor layer, whereas fractions close to the geometric mean value would contribute the most to the bedload transport rate at low values of ${\tau }_{*g}^{\prime }/{\tau }_{*cg}$. The armor layer would completely obliterate at high values of ${\tau }_{*g}^{\prime }/{\tau }_{*cg}>3.5$. Further, the model provides more insight in the expected errors in the predictions of both the substrate-based and surface-based models. Model results show that errors in the predictions of some fractions in the sediment mixture can be as large as 100% and 350% for the substrate-based and surface-based models, respectively. For both types of models, the errors were obvious at low shear stresses and decline with the increase of ${\tau }_{*g}^{\prime }/{\tau }_{*cg}$. By comparing the predictions of selected models with measured bedload data, it has been found that the proposed bedload model provides better predictions over the other models examined herein, highlighting the importance of considering the interaction between the surface and subsurface material when estimating the bedload rate material.