工程科学与技术2025，Vol.57Issue(6)：62-69,8.DOI:10.12454/j.jsuese.202300968
均匀沙起动概率计算模型比较研究
Comparison of Pickup Probability Formulas for Uniform Sediment
摘要
Abstract
Objective The incipient motion of sediment constitutes an integral component in the study of sediment transportation.It plays a significant role in the design of stable channels,sediment transport analysis,and hazard assessment related to channel degradation.Due to the stochastic nature of sediment movement in natural rivers,defining the incipient motion criteria precisely is challenging.Therefore,accurately assessing the pickup probability of natural sediments remains essential.The objective of the present study is to develop a theoretical pickup probability formula for uni-form sediment by employing a force balance mechanism in conjunction with a stochastic method. Methods The forces acting on a sediment particle that are considered to influence the incipient motion included the drag force,lift force,sub-merged weight,and resistance force.Based on the rolling motion,a critical relation for the incipient motion is derived.Under the condition of in-cipient motion,the tangential and normal forces are related to the angle of repose of sediment particles.The incipient motion of a sediment par-ticle occurs when the tangential drag force exceeds the tangential resistance forces.Hence,a theoretical pickup probability formula was devel-oped based on the force balance model.Experimental results showed that the time-averaged velocity increases with increasing flow depth.It reached the maximum value at the water surface for wide open-channel flow.The time-averaged velocity was distributed based on a logarithmic law.The near-bed time-averaged velocity in the present pickup probability equation was derived by assuming the drag force acted at a position of 0.35 d distance from the theoretical bed level.For uniform flow,previous results showed that the turbulence intensity followed the exponential law.Also,the turbulence intensity in the water flow direction decreased with increasing water depth.With reference to the experimental data for a rough open-channel flow bed conducted by Kironoto,the parameter of near-bed turbulence intensity in the present pickup probability equation was obtained.The angle of repose is a fundamental property of sediment particles.Under static conditions,the angle of repose is the steepest in-cline beyond which the slope of the sediment particles collapses.This property is important in sediment transportation.Previous results showed that it increases with sediment size d.With reference to the experimental data conducted by Yang,the present study derived a theoretical formula to calculate the angle of repose in a water medium.Unlike previous studies,the angle of repose equation developed in this study is a function of dimensionless sediment size d*.The parameter of the tan value of the angle of repose was determined based on the angle of repose equation devel-oped in this study.The drag and lift force coefficients were usually considered as unknown functions of the particle Reynolds number.Different values of both coefficients were reported in the literature.This study combined the two coefficients with an unknown function.The unknown function in the pickup probability equation was determined by comparison to the measured data. Results and Discussions There are five parameters:the angle of repose of sediment,near-bed average velocity,near-bed turbulence intensity,drag force coefficient,and lift force coefficient.Once they are determined,the present pickup probability equation can be used in engineering ap-plications.This study obtained all the parameters with reference to the experimental data in rough open-channel flow.The measured pickup prob-ability data were utilized to test the proposed model.Also,the present pickup probability model was compared to the Einstein formula,Engelund and Fredsoe formula,and Cheng and Chiew formula.The pickup probability was computed using the present study formula,Einstein formula,En-gelund and Fredsoe formula,and Cheng and Chiew formula with the measured input data to test the accuracy of the pickup probability equation developed in the present study.The pickup probability predictions by the four equations were listed in an error table to explain the results.The pickup probability formula developed in this study has an average relative error of 22.8%for Luque data,66.9%for Guy ripple data,and 28.2%for Guy dune data.The results showed that the equation developed in this study provides the best representation of experimental measurements.Einstein's formula has an average relative error of 772.9%for Luque data,2 666.4%for Guy ripple data,and 418.4%for Guy dune data.Ein-stein's pickup probability formula produces the highest errors,probably because his formula was not verified with experimental data in his origi-nal papers.For a given pickup probability,the pickup probability equation can be utilized to calculate the critical shear velocity of uniform sedi-ments.Under threshold conditions,the present pickup probability P=0.000 045 98,Einstein pickup probability P=0.02,Engelund and Fredsoe formula P=0.018 7,and Cheng and Chiew formula P=0.013.The threshold value P of this study fell into the"weak movement"criterion,whereas the other three equations fell into the"middle movement"criterion.In addition,the present pickup probability model fitted the classic Shields diagram quite well under the incipient motion condition. Conclusions The integral expression of sediment particle pickup probability is derived.This expression fully reveals the force mechanism acting on sediment particles and compensates for the limitation of previous pickup probability formulas that ignored the drag force of water.The pickup probability formula developed in this study demonstrates the highest calculation accuracy.In addition,for sediment particles in the critical state,the pickup probability derived in this study tends to align with the weak moving pickup criteria,whereas other formulas correspond to the moder-ate moving pickup criteria.Finally,when compared to the classical Shields curve,the pickup probability formula proposed in this study shows good agreement,while other formulas yield a straight line that can only determine the incipient shear stress of large particles.关键词
均匀沙/平均流速/水流上举力/水流推移力/泥沙起动Key words
uniform sediment/average flow velocity/flow lift force/flow drag force/incipient motion of sediment分类
水利科学引用本文复制引用
钟臣勇,杨奉广,聂锐华,黄尔,刘兴年..均匀沙起动概率计算模型比较研究[J].工程科学与技术,2025,57(6):62-69,8.基金项目
国家自然科学基金项目(51979180) （51979180）
四川省科技计划项目(2023NSFSC1989) （2023NSFSC1989）
