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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 τ'*g, the critical Shields stress τ*cg, the Kramer coefficient of uniformity cu, and the relative grain size (size of the jth grain fraction to the geometric mean size, dj/dg). 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 τ'*g/τ*cg fractions within the range of 0.3 < dj/dg < 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 dj/dg > 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 τ'*g/τ*cg. The armor layer would completely obliterate at high values of τ'*g/τ*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 τ'*g/τ*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. [ABSTRACT FROM AUTHOR]

A model has been developed for the prediction of the density functions of bed-elevation and entrainment and deposition rates of sediment in sand bed streams within the lower regime flow condition. The model incorporates both statistical and deterministic parameters in its form. A total of 46 experimental runs have been carried out in a recirculating tilting flume under the equilibrium flow condition using three grain sizes of uniform gradation to validate the model and estimate its parameters. The model parameters are related to the hydraulic conditions of flow and fluid and sediment properties through dimensional and regression analyses. The study has shown that the density functions of bed elevation and entrainment and deposition rates can be approximated quite satisfactorily with the normal distribution curve. Transformation of the density functions into the standardized normal distribution curve provides a unique pattern for all the experimental runs regardless of the sediment grain size, flow condition, and shapes and dimensions of the bed forms. The developed density functions have been utilized to provide a closure for the probabilistic Exner equation for uniform sediment. [ABSTRACT FROM AUTHOR]