Generalized Bed-Load Function Based on Empirical Data
Publication: Journal of Hydraulic Engineering
Volume 147, Issue 8
Abstract
There exist many bed-load functions in the literature to calculate bed-load transport rates, but none of them fit data from low to high shear stress conditions. This research presents a generalized bed-load function based on empirical data. Specifically, the classic power law in high shear stress conditions is extended to low shear stress conditions by applying a complimentary error function (or logistic function) and using Coles’ mathematical idea for the wake law in turbulent boundary layer velocity distribution. The resulting generalized bed-load function agrees well with the classic data sets; it reduces to Huang’s power law in the very low and the high shear stress conditions, and it is numerically close to Paintal’s 16th power law in the transitional regime. It is found that the maximum turbulence-induced lift force and the minimum critical shear stress in the Shields diagram correspond to the inflection point (in terms of logarithmic scale) in the Einstein bed-load diagram, resulting in the most efficient bed-load transport rate. After that, this paper discusses the effects of turbulence-induced lift force, critical shear stress, viscosity, nonlinearity, and uncertainty on bed-load transport. Finally, an example with uncertainty analysis is illustrated for applications.
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Data Availability Statement
All data, models, or code generated or used during the study are available from the author by request.
Acknowledgments
The author thanks Professor Nian-Sheng Cheng in Ocean College at Zhejiang University for providing the data sets used in this research, Professor He Qing Huang in the Institute of Geographic Sciences and Natural Resources Research at the Chinese Academy of Sciences for assistance on Huang’s power law, and Professor Pierre Y. Julien at Colorado State University for his suggestion to use the complementary error function for the correction function in this paper. The author also appreciates the constructive comments offered by the three anonymous reviewers, the Associate Editor, and the Chief Editor, which have significantly improved this paper during its preparation.
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Published In
Journal of Hydraulic Engineering
Volume 147 • Issue 8 • August 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jan 22, 2021
Accepted: Mar 25, 2021
Published online: Jun 14, 2021
Published in print: Aug 1, 2021
Discussion open until: Nov 14, 2021
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