在河流动力学研究中，泥沙推移质层的厚度(Bed-load thickness)是影 响明渠水流中输沙量的重要参数。已有一些关于确定泥沙推移质层厚度的理 论和实验研究工作。本研究采用基于 Tsallis 熵、Shannon 熵、Renyi 熵和 general index 熵的概率分析方法推导出泥沙推移质厚度的解析公式。该方法 假设推移质厚度是一个随机变量，构建此变量的不同形式的熵函数，并基于最 大熵原理推导出推移质厚度和无量纲水流剪切力之间的函数表达式。对比这 些基于熵的表达式以及已有的确定性方法和收集的实验数据，表明:四种基于 熵的方法有较低的误差，其中 Tsallis 熵能产生最小的误差。本研究表明基 于熵的方法能很好地估算明渠水流中的泥沙推移质层厚度，对现有的确定性 方法会是一个较好的补充。

In the context of river dynamics, the thickness of sediment bed load in open channels is an important parameter for determining the sediment discharge of open channel flows. There have been many researches to investigate the bed-load thickness in open channel hydraulics. This study attempts to derive the analytical expression for the thickness of sediment bed load in open channel, using the probability method based on four different entropy theories: Shannon, Renyi, Tsallis and General index entropy. By assuming the bed-load thickness be a random variable, four entropy-based expressions for it as a function of shear stress are derived by maximizing the entropy function. A comparison of the proposed entropy- based expressions, existing other methods and experimental data collected from literatures shows that the entropy-based method have a lower error for experimental data then other models. Especially, the Tsallis entropy-based expression leads to the least prediction error among all models. This study shows that the entropy-based methods could estimate the thickness of bed-load in open channel flows well and that they will be a good addition to existing determining methods for predicting the bed-load thickness in open channels.