基於全概率的斜坡上推移質輸沙率公式

Formula of Bed-load Sediment Transport Based on Full Threshold Probability of Slopes

10.6937/TWC.201906_67(2).0009

許曉陽(XIAO-YANG XU)；張根廣(GEN-GUANG ZHANG)；王愉樂(YU-LE WANG)

全概率 ； 斜坡床面 ； 可動層厚度 ； 起動條件 ； 推移質平均運動速度 ； 推移質輸沙 ； Full threshold probability ； Bed slopes ； Movable layer thickness ； Incipient motion ； The mean velocity of bed-load sediment transport ； Bed-load sediment transport

台灣水利

67卷2期（2019 / 06 / 01）

75 - 82

繁體中文

為了獲得物理概念更加清晰、精度更高和適用範圍更廣的斜坡上推移質輸沙率公式，基於水流隨機特性和泥沙顆粒位置隨機特性對泥沙起動概率的影響，採用滾動模型，推導了斜坡泥沙起動的全概率公式，以多層運動模型替換單層運動模型，修正了單位床面上可運動的泥沙顆粒數，從理論上推導了斜坡上泥沙臨界起動條件和推移質平均運動速度，結合Engelund的推移質輸沙率公式的基本概念，得到了斜坡上的單寬推移質輸沙率公式，通過與不同坡度實測輸沙率資料及其它經典輸沙率公式對比，分析了平坡時計算誤差較大的主要原因，證明了本文公式在不同坡度下均具有較高的計算精度。

This paper commits to the formula of slope load transport rate with clearer physical concept, higher precision and wider application range. Based on the random characteristics of water flow and the random characteristics of sediment particle position on the probability of sediment initiation, the rolling model was used to derive the full threshold probability formula of slope sediment initiation; the single-layer motion model was replaced by a multi-layer motion model, and the number of movable sediment particles per unit bed surface was corrected; based on the theory, the sediment starting conditions and the average moving speed of the bed were derived. Combined with Engelund's basic concept of the load-transporting rate formula, the formula for the single-wide bed-load sediment transport rate and the sediment transport intensity calculation formula on the slope were obtained. The formulas of the sediment transport rate with different slopes are compared and verified. The results show that the physical concept of the formula is clearer and has higher calculation accuracy under different slopes.

1. Bagnold, R.A.(1966).An approach to the sediment transport problem from general physics.U.S. Geol. Surv. Prof. Pap,422,231-291.
2. Cheng, N.S.(2002).Exponential formula for bed-load transport.Journal of Hydraulic Engineering,128,942-946.
3. Cheng, N.S.,Chen. X.(2014).Slope correction for calculation of bed-load sediment transport rates in steep channels.Journal of Hydraulic Engineering,140,298-307.
4. Cheng, N.S.,Chiew, Y.M.(1998).Pickup probability for sediment entrainment.Journal of Hydraulic Engineering,124,232-235.
5. Cheng, N.S.,Law, A.W.K.,Lim, S.Y.(2003).Probability distribution of bed particle in stability.Advances in Water Resources,26,427-433.
6. Damgaard, J.S.,Whitehouse, R.J.S.,Soulsby, R. L.(1997).Bed-load sediment transport on steep longitudinal slopes.Journal of Hydraulic Engineering,123,1130-1138.
7. Dey, S.,Debnath, K.(2001).Sediment pickup on streamwise sloping beds.Journal of Irrigation and Drainage Engineering,127,39-43.
8. Einstein, H.A., 1949, “Hydrodynamic forces on a rough wall,” Reviews of Modern Physics, Vol. 21, 520-524.
9. Einstein, H.A.(1950).,US Department of Agriculture.
10. Engelund, F.,Fredsøe, J.(1976).A sediment transport model for straight alluvial channels.Nordic Hydrology,7,293-306.
11. Han, Q.W.(1982).Sediment start law and starting flow rate.Journal of Sediment Research,7,11-26.
12. Han, Q.W.,He, M.M.(1984).Statistical theory of sediment movement.Beijing:Science Press.
13. Han, Q.W.,He, M.M.(1999).Incipient principies and cipient velocity of sedment.Beijing:Science Press.
14. Ll, L.L.(2018).College of Water Resources and Architectural Engineering.
15. Meng, Z.,Chen, H.,Li, D.X.(2015).Study of bedload transport formulas.Journal of Hydraulic Engineering,46,1080-1088.
16. Meyer-Peter, E., Müller, R., 1948, “Formulas for bed-load transport,” Proceedings of the 2nd Meeting of the International Association for Hydraulic Structures Research.
17. Nielsen, P.(1992).Coastal Bottom Boundary Layers and Sediment Transport.World Scientific.
18. Qian, N.,Wan, Z.H.(1983).Mechanics of Sediment Transport.Beijing:Science Press.
19. Recking, A.,Frey, P.,Paquier, A.(2008).Bed-load transport flume experiments on steep slopes.Journal of Hydraulic Engineering,134,1302-1310.
20. Smart, G.M.(1984).Sediment transport formula for steep channels.Journal of Hydraulic Engineering,110,267-276.
21. Sun, Z.L.,Donahue, J.(2000).Statistically derived bed-load formula for any fraction of nonuniform sediment.Journal of Hydraulic Engineering,126,105-111.
22. Wang, X.K.,Zheng, J.,Li, D.X.(2008).Modification of the Einstein bed-load formula.Journal of Hydraulic Engineering,134,1363-1369.
23. Wang, Y.L,Zhang, G.G.,Zhou, S.(2018).Formula of bed load sediment transport rate on bed slopes.Journal of Hydroelectric Engineering,37,100-106.
24. Wu, F.C.,Lin, Y.C.(2002).Pick up probability of sediment under log-normal velocity distribution.Journal of Hydraulic Engineering,124,438-442.
25. Yalin, M.S.(1977).Mechanics of sediment transport.Oxford, UK:Pergamon Press.
26. Yang, F.G.,Liu, X.N.,Huang, E.(2009).Study of sediment incipient velocity in the lower reaches of Tang Yan Lake.Advanced Engineering Sciences,41,84-89.
27. Yang, S.F.,Zhou, H.J.,Wang, X.K.(2006).The experm ental study on the bed-load rate of the high gradient gravel river.JOURNAL OF HYDRODYNAMICS,21,672-678.
28. Yang, W.J.,Meng, Z.(2011).Theoretical Analysis on Sediment Relative Hidden Degree.Journal of Yangtze River Scientific Research Institute,28,17-25.
29. Zhou, S.,Zhang, G.G.,Wang, X.L.(2015).Study on relative exposure degree of uniform sediment.Journal of Sediment Research,40,40-45.

1. 龔仁能,賀承明,許曉陽,張根廣,李青芝(2023)。推移質泥沙的隨機起動規律研究。台灣水利，71(1)，51-66。
2. 許曉陽,張根廣,周雙(2022)。基於床沙位置分佈特性的推移質輸移規律研究。中國土木水利工程學刊，34(2)，129-136。