Abstract
In this study, the distribution of sediment concentration and the mean sediment concentration in debris flow were investigated using deterministic and probabilistic approaches. Tsallis entropy and Shannon entropy have recently been employed to estimate these parameters. However, other entropy theories, such as the general index entropy and Renyi entropy theories, which are generalizations of the Shannon entropy, have not been used to derive the sediment concentration in debris flow. Furthermore, no comprehensive and rigorous analysis has been conducted to compare the goodness of fit of existing conventional deterministic methods and different entropy-based methods using experimental data collected from the literature. Therefore, this study derived the analytical expressions for the distribution of sediment concentration and the mean sediment concentration in debris flow based on the general index entropy and Renyi entropy theories together with the principle of maximum entropy and tested the validity of existing conventional deterministic methods as well as four different entropy-based expressions for the limited collected observational data. This study shows the potential of using the Tsallis entropy theory together with the principle of maximum entropy to predict sediment concentration in debris flow over an erodible channel bed.
Highlights
Debris flow is one of the disastrous geohazards in mountainous areas around the world
This study shows the potential of using the Tsallis entropy theory together with the principle of maximum entropy to model the distribution of sediment concentration and the mean sediment concentration in debris flow
The entropy-based expressions were based on the general index entropy, Renyi entropy, Tsallis entropy, and Shannon entropy theories
Summary
Debris flow is one of the disastrous geohazards in mountainous areas around the world. It is usually triggered by rainfall, earthquakes, and human activities and often has a destructive nature, greatly influencing human life and valuable property [1,2,3]. Many debris flows have occurred, resulting in large losses. On 7 August 2010, two large-scale debris flows occurred in both the Sanyanyu and Luojiayu valleys in the northern part of the city of Zhouqu, Northwest China, due to heavy rainfall in this area [4]. 1557 people living in this area were killed, and more than 5500 houses along the path of the debris flow were damaged. A 550-m-long and 70-m-wide debris dam was formed, and one-third of the city was inundated for five days [5,6]
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