Previous studies focused on the bed load transport rate for the condition of turbulent flow,while the knowledge of sediment transport in laminar flow is very limited.As an extreme case to reflect the viscous effect on sediment transport,sediment transport in laminar flow is considered in this paper.There are at least two factors affecting the transport rate of sediment under laminar flow conditions: (1) fluid forces;(2) particle to particle interactions.Together,these two factors represent the physical transport system.First,an exposure degree Probability Density Function (PDF) is developed to explore how the transport rate can be associated with characteristics of laminar flow and this factor reflects the particle to particle interactions,and the pickup probability equation in the absence of turbulence is developed based on the stochastic approach which reflects the exposure degree influence.Then,the formulas to calculate the critical shear stress of incipient motion and the bed load transport rate of fine uniform sediment are established.The derivation is made mainly based on Einstein’s bed load theory;we choose Einstein’s equation to model this system because we believe that the probabilistic approach taken is an appropriate way to account for the spatial and temporal variations in the forces causing sediment transport.These formulas have been tested against a wide range of existing laboratory data and compared with other existing empirical or semiempirical methods.The predictions by these newly proposed formulas are very good.
YANG FengGuang,LIU XingNian,CAO ShuYou,YANG KeJun & HUANG Er State Key Laboratory of Hydraulics and Mountain River Engineering,Sichuan University,Chengdu 610065,China
A conception of exposure degree is used in this article to account for the hiding and exposure mechanism of nonuniform sediment transport. The force arms of particles on the bed slope are assumed to be a function of the exposure degree, which is stochastically related to the size and gradation of bed materials. Based on this conception, the formula for the angle of repose of nonuniform sediment is developed. The angle of repose of nonuniform sediment is experimentally investigated in rotation drum at the rolling motion of sediment particles. The nonuniform sediment is gotten from the mixture of two kinds of uniform sediment with different weight ratios and two experimental plans that one for changing the weight ratio of two kinds of uniform sediment from 1：9 to 9：1 and the other changing the uniform sediment size and weight ratio are used. The effect of the rotation speed and the filling degree on the angle of repose is investigated, too. Finally, the formula has been tested against a wide range of laboratory data, the prediction by the newly proposed formulas is very good.
YANG Feng-guang LIU Xing-nian YANG Ke-jun CAO Shu-you
Dambreak-induced bed scouring may undermine the foundation of bridge piers and other structures,and that destruction can pose a serious threat.Consequently,this paper aims at exploring the mechanisms of scouring and armoring.Firstly,the incipient velocity for nonuniform sediment particles was studied,and a formula was derived based on the angle of repose of nonuniform sediment.The results showed that the mechanism of incipient motion for sand and fine gravel differed from that for coarse gravel and cobbles.Also,comparison between experimental and field data shows that the results from the proposed formula agree well with those observed for all conditions.Secondly,a birth-death,immigration-emigration Markov process was developed to describe the bed load transport rate associated with scouring and armoring.The comparison between experimental data and computed results shows that our model can predict the bed load transport rate,although there may be some limitations,the chief of which is that there are many variables in the model to be determined through experiment.This makes its application in river engineering inconvenient.
