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

• Published in: Entropy (Basel, Switzerland) Vol. 21; no. 2; p. 123
• Main Authors: Zhu, Zhongfan, Yu, Jingshan
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 29.01.2019; MDPI
• Subjects: Bed load; Datasets; Diameters; Distribution functions; Entropy; Entropy (Information theory); Hydraulics; Hypotheses; Investigations; Laboratories; Measurement techniques; Model accuracy; Open channels; Particle size; probability distribution; Random variables; Sediment transport; Shear stress; Thickness; Tsallis entropy; bed-load; probability distribution; Tsallis entropy; open channels; thickness
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e21020123

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.