Estimating the Bed-Load Layer Thickness in Open Channels by Tsallis Entropy

Abstract

In the research field of river dynamics, the thickness of bed-load is an important parameter in determining sediment discharge in open channels. Some studies have estimated the bed-load thickness from theoretical and/or experimental perspectives. This study attempts to propose the mathematical formula for the bed-load thickness by using the Tsallis entropy theory. Assuming the bed-load thickness is a random variable and using the method for the maximization of the entropy function, the present study derives an explicit expression for the thickness of the bed-load layer as a function with non-dimensional shear stress, by adopting a hypothesis regarding the cumulative distribution function of the bed-load thickness. This expression is verified against six experimental datasets and are also compared with existing deterministic models and the Shannon entropy-based expression. It has been found that there is good agreement between the derived expression and the experimental data, and the derived expression has a better fitting accuracy than some existing deterministic models. It has been also found that the derived Tsallis entropy-based expression has a comparable prediction ability for experimental data to the Shannon entropy-based expression. Finally, the impacts of the mass density of the particle and particle diameter on the bed-load thickness in open channels are also discussed based on this derived expression.

An Expression for Velocity Lag in Sediment-Laden Open-Channel Flows Based on Tsallis Entropy Together with the Principle of Maximum Entropy

“…The fitting accuracy improves as R decreases. Relative error analysis has been frequently adopted and confirmed to be a good statistical method to compare the prediction accuracy of the developed models by some researchers [15,[17][18][19][20]24,25,[27][28][29].…”

“…As Singh et al [16] have reviewed, the Tsallis entropy theory together with the principle of maximum entropy have been widely applied to solve certain typical water and environmental engineering problems. For example, the Tsallis entropy theory has been adopted by many researchers to estimate the one-dimensional and two-dimensional velocity distributions of open channels [17][18][19][20], the potential rate of infiltration in unsaturated soils [21][22][23], the vertical distribution of suspended sediment concentration [24,25], the flow-duration curve [26], the sediment concentration distribution in debris flow [27,28], and the thickness of the bed-load layer in an open channel [29]. In these studies, the Tsallis entropy-based model has showed a high prediction accuracy with experimental data, suggesting that the probability method based on the Tsallis entropy theory could be a good addition to some existing deterministic models for approaching certain water and environmental engineering problems [16].…”

MIMR Criterion Application: Entropy Approach to Select the Optimal Quality Parameter Set Responsible for River Pollution

“…This theory, built on the mathematical concept of entropy, represents the quantitative measure of the information content associated with a signal. It has been widely used in different sectors of hydraulics and hydrology to derive models of rainfall-runoff, infiltration, and soil moisture [22][23][24][25][26][27] as well as distribution of velocity, sediment concentration, and shear stress in open-channel flows [28][29][30][31][32][33][34][35][36][37][38][39]. Among the different applications, information theory has also been employed for the optimization, design, and management of several gauge stations including networks of water quality and groundwater [40,41], rainfall [42,43], streamflow, and water level [44][45][46][47][48][49][50][51].…”

Modeling Bed Shear Stress Distribution in Rectangular Channels Using the Entropic Parameter

“…Knowledge of the bed shear stress distribution in rivers helps with the evaluation of sediments and pollutants transport, the prediction of erosion and deposition phenomena, the estimation of morphological and geometrical changes, and the calculation of resistance coefficients [1][2][3][4][5][6][7][8][9][10][11]. It can also be useful in planning and designing stable open channels.…”