Incomplete Self-similarity Analysis of Bed Resistance in Mountainous Gravel-cobble Channels

Xiao-yang XU , Ping WANG , Guang-ming ZHANG , Ting LI , Yan GUO , Xu GENG

Science Technology and Engineering ›› 2026, Vol. 26 ›› Issue (21) : 9235 -9244.

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Science Technology and Engineering ›› 2026, Vol. 26 ›› Issue (21) : 9235-9244 DOI: 10.12404/j.issn.1671-1815.2506763
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Incomplete Self-similarity Analysis of Bed Resistance in Mountainous Gravel-cobble Channels
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Abstract

The bed resistance characteristics of gravel-cobble rivers in mountainous areas are of great significance to the theoretical development of sediment transport mechanics and the practical application of water conservancy projects. Compared with the condition of small roughness in deep water, the law of bed resistance in shallow water with large roughness is more complex, and the classical Manning-Strickler formula is difficult to apply directly. In consideration of the aforementioned points, the functional relationship of the flow resistance coefficient in conditions of shallow water with substantial roughness was determined through dimensional analysis. Moreover, an analysis method for the flow resistance coefficient was proposed on the basis of the principle of incomplete self-similarity. This calculation model was established for the flow resistance coefficient in conditions of shallow water with substantial roughness. Based on the measured data of flume and field, the parameters of the model proposed and the classical model in the literature were calibrated, and the final expressions of the calculation models were determined. This process culminates in the determination of the final expressions for the calculation models. The findings indicate that the flow resistance coefficient can be expressed as an exponential function of the relative smoothness, the energy slope and the Froude number. Furthermore, it is demonstrated that the relative smoothness can be replaced by the Reynolds number without compromising the model’s precision. In comparison with the Ferro model which has the highest accuracy in the literature, the goodness of fit of the proposed model is improved by 0.403%~0.413%, and the calculation error is reduced by 61.2%~63.7% (MER) and 35.2%~36.5% (RMSE). The research results can provide reference for practical engineering application.

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Keywords

open-channel flow / shallow flow / large-scale roughness / flow resistance / dimensional analysis / non-complete self-similarity

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Xiao-yang XU, Ping WANG, Guang-ming ZHANG, Ting LI, Yan GUO, Xu GENG. Incomplete Self-similarity Analysis of Bed Resistance in Mountainous Gravel-cobble Channels. Science Technology and Engineering, 2026, 26(21): 9235-9244 DOI:10.12404/j.issn.1671-1815.2506763

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