Formula of bed-load transport based on the total threshold probability
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The randomness of relative position of sediment particles and the flow conditions are the main influencing factors on incipient motion of sediment particles on the river bed surface, and the position of sediment particles is usually reflected by the relative exposure degree. In this study, the random effect of both flow conditions and relative location of sediment particles on the sediment incipient motion were investigated based on our previous study. The formula of sediment incipient motion based on the total probability was determined theoretically using the sliding mode. The total probability model of sediment incipient motion was then introduced into the study of bed-load sediment transport according to the Einstein assumption, and the dimensionless formula of bed-load sediment transport was finally proposed based on the definition of sediment transport rate per unit width. Through validation with experimental data and verification with other formulas in the literature, the formula developed in this study is proved to be reasonable and has higher calculation accuracy. This study contributes to enrich current knowledge regarding bed-load sediment transport on both the channel beds and riverbanks.
KeywordsTotal threshold probability Relative exposure degree The Einstein formula Bed-load transport
This research is supported by the National Natural Science Foundation of China (Grant No. 51279170).
- 2.Bagnold RA (1966) An approach to the sediment transport problem from general physics. US Geol Surv Prof Pap 422(1):231–291Google Scholar
- 4.Cheng NS (2002) Exponential formula for bed-load transport. J Hydraul Eng 128(10):942–946. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:10(942) CrossRefGoogle Scholar
- 7.Einstein HA (1950) The bed-load function for sediment transportation in open channel flows. US Department of Agriculture, WashingtonGoogle Scholar
- 9.Gregoretti C (2008) Inception sediment transport relationships at high slopes. J Hydraul Eng 134(11):1620–1629. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:11(1620) CrossRefGoogle Scholar
- 10.Han QW, He MM (1984) Statistics theory of sediment motion. Science Press, BeijingGoogle Scholar
- 11.Han QW, He MM (1999) The incipient disciplinarian and incipient velocity of sediment. Science Press, BeijingGoogle Scholar
- 13.Li LL, Zhang GG, Zhang JJ, Liu JQ (2017) Incipient motion velocity of sediment particles on the positive and negative slope. Taiwan Water Conserv 65(2):72–81Google Scholar
- 17.Meyer-Peter E, Müller R (1948) Formulas for bed-load transport. In: Proceedings of the 2nd meeting of the international association for hydraulic structures research, pp 39–64Google Scholar
- 25.Wang SQ (1985) A modification of Einstein’s bed-load function for uniform particles. J Sediment Res 1:44–53. https://doi.org/10.16239/j.cnki.0468-155x.1985.01.005 CrossRefGoogle Scholar
- 26.Wang XK, Zheng J, Li DX (2008) Modification of the Einstein bed-load formula. J Hydraul Eng 134(9):1363–1369. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:9(1363) CrossRefGoogle Scholar
- 30.Zhou S, Zhang GG, Wang XL (2015) Study on relative exposure degree of uniform sediment. J Sediment Res 40(6):40–45. https://doi.org/10.16239/j.cnki.0468-155x.2015.06.0 CrossRefGoogle Scholar