An explicit analytical expression for bed-load layer thickness based on maximum entropy principle

The present study aims to derive an analytical model on bed-load layer thickness in an open channel turbulent flow carrying sediments. Determination of the thickness of the bed-load layer is of utmost importance in the study of bed-load transport as it is required to determine the bed-load transport rate, as well as in the study of suspended load transport as it acts as reference level for the particles in suspension. Apart from the several deterministic approaches available in the literature, the work adopts probabilistic approach based on entropy theory to determine the bed-load layer thickness. The concept of entropy theory developed by Shannon is used and the method of Lagrange multipliers is employed for the maximization of entropy function to find the least biased probability distribution. To calculate the Lagrange multipliers, present in the probabilistic model of dimensionless bed-load layer thickness, two different methodologies are presented. The model of bed-load layer thickness is a function of dimensionless shear stress and also depends on three other parameters which are found to be functions of specific gravity of sediment particle and dimensionless particle diameter from a non-linear regression analysis. The proposed model is validated with wide sets of experimental data available in literature and a good agreement is achieved. Apart from comparison with data, the model is also compared with existing deterministic model and computation of relative percentage error proves the better efficiency of the present model.