A Bed-load function based on kinetic theory

Bed-load transport plays a fundamental role in morphological processes of natural rivers and human-made channels.This paper presents bed-load function derived on the basis of kinetic theory. The bed-load function is obtained by integrating the pick-up rate of bed sediment with respect to its longitudinal travel distance,following the basic concept on bed-load put forward by Einstein.The pick-up rate is expressed as an upwards flux of bed sediment and determined by invoking the particle velocity distribution function derived by solving the Boltzmann equation of kinetic theory. Comparisons of the present formula with six other bed-load formulas and the experimental data are also made in this paper.The results show that the present bed-load formula agrees well with the experimental data.In addition,the influences due to collision between particles on bed-load is discussed which shows that an appreciable damping of the intensities of bed-load is observed only when the shear acting on particles is large enough to increase the concentration and intensity of random motion of bed load particles so that the collisions between sediment particles can occur.     

Bed-load transport rate based on the entrainment probabilities of sediment grains by rolling and lifting

A function for the bed-load sediment transport rate is derived. This function is obtained by using the entrainment probabilities of the rolling and lifted sediment grains, and by introducing two travel lengths, respectively. The predictions from the new bed-load function agree well with experimental results over the entire experimental range and show significant improvement over the commonly used formula for the bed-load transport rate. The new function shows that, in terms of contributing to the bed-load transport rate, the total entrainment probability of the sediment grains is a weighted summation of those for the lifted and rolling grains, rather than a simple addition of the two. The function is also used to predict the total entrainment probability, saltation length, and the bed layer thickness at a high bed-load transport rate. These predictions all agree well with the experimental results. It is found that, on average, the travel length for the rolling sand grains is about an order of magnitude less than that of the lifted grains.     

ON THE PHYSICS OF FLOW-DRIVEN SEDIMENTS (BED-LOAD)

l PROBLEMS AND AlMSSediments may be transported close to the bed, rolling and sliding, as we1l as susPended in the flow. Forvarious reasons the theoretical treatment of the bed-load problem has been exceptionally difficult. Noanalytical solution had been fOund uP to now, beginning with Du Buat (l786), Huebbe (l86l) and DuBoys (I 879). Since the aPProach of Du Boys numerous new attemPts have been catried out, mostly of anempirical nature. Consequently they are not generally valid an…     

Experimental study of bed-load transport using particle motion tracking

A series of experiments were conducted in a flume to study bed-load transport.The motion of bed-load particles was captured by a series of images taken by a high-speed camera.A novelparticle motion tracking method was developed to automatically detect all the moving particles and calculate the instantaneous particle velocities.The instantaneous bed load transport rate was calculated based on particle velocity and the volume of moving particles.To verify this method,bed load transport rate based on the image processing technique was compared to the manually measured ones as well as data from other experiments.Results showed that the new technique made it possible to quantify the spatial and temporal variations of bed load transport rate at the individual particle scale.     

Turbulence in mobile-bed streams

This study is devoted to quantify the near-bed turbulence parameters in mobile-bed flows with bed-load transport. A reduction in near-bed velocity fluctuations due to the decrease of flow velocity relative to particle velocity of the transporting particles results in an excessive near-bed damping in Reynolds shear stress (RSS) distributions. The bed particles are associated with the momentum provided from the flow to maintain their motion overcoming the bed resistance. It leads to a reduction in RSS magnitude over the entire flow depth. In the logarithmic law, the von Kármán coefficient decreases in presence of bed-load transport. The turbulent kinetic energy budget reveals that for the bed-load transport, the pressure energy diffusion rate near the bed changes sharply to a negative magnitude, implying a gain in turbulence production. According to the quadrant analysis, sweep events in mobile-bed flows are the principal mechanism of bed-load transport. The universal probability density functions for turbulence parameters given by Bose and Dey have been successfully applied in mobile-bed flows.     

Adjustment of stream-channel shape to hydrologic regime

Bed-load channels tend to adjust their cross-sections so that given slope, roughness and sediment load, channel shape approaches the optimum for bed-load transport. The extent to which any one shape is the optimum varies with discharge, so four Cumberland Basin stream channels have been investigated to determine the discharges at which their present cross-sections represent the optimum for bed-load transport. These discharges have return periods ranging from 1.1 to 1.5 years on the annual series. The return periods closely correspond with return periods for the discharge at which, over a period of time, the most bed-load is transported. These return periods vary from 1.15 to 1.45 years when the same bed-load equation is used. The close correspondence between sets of return periods suggests that bed-load channels tend to adjust their cross-sections to become the optimum shape for bed-load transport at or close to the discharge at which the most bed-load transport is accomplished.     

A heuristic probabilistic approach to estimating size-dependent mobility of nonuniform sediment

This paper presents a heuristic probabilistic approach to estimating the size-dependent mobilities of nonuniform sediment based on the pre- and post-entrainment particle size distributions (PSDs), assuming that the PSDs are lognormally distributed. The approach fits a lognormal probability density function to the pre-entrainment PSD of bed sediment and uses the threshold particle size of incipient motion and the concept of sediment mixture to estimate the PSDs of the entrained sediment and post-entrainment bed sediment. The new approach is simple in physical sense and significantly reduces the complexity and computation time and resource required by detailed sediment mobility models. It is calibrated and validated with laboratory and field data by comparing to the size-dependent mobilities predicted with the existing empirical lognormal cumulative distribution function approach. The novel features of the current approach are: (1) separating the entrained and non-entrained sediments by a threshold particle size, which is a modified critical particle size of incipient motion by accounting for the mixed-size effects, and (2) using the mixture-based pre- and post-entrainment PSDs to provide a continuous estimate of the size-dependent sediment mobility.     

Effects of vegetation on flow conveyance and sediment transport capacity

In-stream and riparian vegetation may significantly affect flow and sediment transport in vegetated channels. A hydraulic model has been developed in this paper to compute the flow discharge in channels with rigid and flexible vegetation under emergent and submerged conditions. An empirical formula has also been presented to determine the bed-load discharge in vegetated channels. The model has been tested against experimental and field data available in the literature. The computed flow discharge and bed-load transport rate agree well with the measured data.     

The erosion of drainage ditches and its effect on bed-load yields in mid-Wales: Reconnaissance case studies

Open ditching is a common and relatively cheap way of providing drainage for wet upland soils prior to afforestation or improved agriculture; it is sometimes also used to channelize moorland runoff into water storage schemes. In contrast to piped under-drainage there is considerable danger of erosion in open ditches. Results are reported of investigations into the yield of bed-load from ditched catchments; compared with unditched catchments there is a considerable increase in yield and this causes costly local problems of sedimentation. However, the implications of the erosion for downstream channel changes and reservoir sedimentation in the uplands are harder to predict without further study of the storage processes affecting bed-load and of the influence of flood flows. The case studies are used to point to improvements in the design of open drainage networks.     

用于强震记录仿真地动位移的高精度累积数值积分方法研究

针对传统梯形积分方法的低精度缺陷,提出了一套高精度累积数值积分方法.首先对被积数据进行分段三次Hermite插值,之后采用积分区间四等分的Newton-Cotes积分公式进行积分.误差分析表明,本方法精度远高于梯形积分方法精度.在对构建信号进行方法验证的前提下,采用2013年4月20日雅安芦山地震和2008年5月12日汶川地震的真实强震动加速度记录对本方法进行测试,测试结果表明,本方法适用于将强震动加速度记录积分为位移记录.     

对若干地震动包线函数的比较分析

对已经提出的四种经常使用的包线函数模型进行了评价,认为对于评价单峰点包线函数,除了要求形式简单以外,其优劣可以用函数对峰点位置和高峰隆起程度的控制能力作为标准。借助结构动力试验中阻尼比的确定方法,提出用平稳度指数来评价单峰点包线函数平缓程度。据此对四种包线函数的平稳度进行了分析,还对某些包线函数提出了一些改进。通过分析指出如果把“金井清谱”和“Penzien谱”等模型,看作是时间域中包线,这两个模型的调节能力都很强,而且比较方便,其中“Penzien谱”模型可以用来表示具有两个峰点的包线。文中的比较分析结果可以用于地震动包线函数选择和模拟。     

The 1982 eruptions of El Chichon volcano,Mexico (3): Physical properties of pyroclastic surges

Two major pyroclastic surges generated during the 4 April 1982 eruption of El Chichon devastated an area of 153 km² with a quasi-radial distribution around the volcano. The hot surge clouds carbonized wood throughout their extent and were too hot to allow accretionary lapilli formation by vapor condensation. Field evidence indicates voidage fraction of 0.99 in the surge cloud with extensive entrainment of air. Thermal calculations indicate that heat content of pyroclasts can heat entrained air and maintain high temperatures in the surge cloud. The dominant bed form of the surge deposits are sand waves shaped in dune forms with vertical form index of 10–20, characterized by stoss-side erosion and lee-side deposition of 1–10 cm reversely graded laminae. A systematic decrease in maximum lithic diameter with distance from source is accompanied by decrease in wavelength and amplitude. Modal analysis indicates fractionation of glass and pumice from the surge cloud relative to crystals, resulting in loss of at least 10%–25% of the cloud mass due to winnowing out of fines during surge emplacement. Greatest fractionation from the –1.0–0.0– grain sizes reflects relatively lower pumice particle density in this range and segregation in the formative stages of the surge cloud. Extensive pumice rounding indicates abrasion during bed-load transport. Flow of pyroclastic debris in the turbulent surge cloud was by combination of bed-load and suspended-load transport. The surges are viewed as expanding pyroclastic gravity flows, which entrain and mix with air during transport. The balance between sedimentation at the base of the surge cloud and expansion due to entrainment of air contributed to low cloud density and internal turbulence, which persisted to the distal edge of the surge zone.     

Non-uniform sediment incipient velocity

Based on the mechanism of non-uniform sediment incipient motion, the dragging force and uplift force coefficient expressions are put forward for the non-uniform bed material exposure and close alignment state. The incipient velocity formula of the non-uniform sediment is then established. It is shown that the formula structure is reasonable, and fine particles of the non-uniform sediment are more difficult to set into motion than the same sized uniform particles, whereas coarser particles are easier to set into motion than their uniform equivalents. The validity of the formula is verified by field and experiment data.     

Numerical analysis of synthetic granulate deposition in a physical model study

The current study focuses on the application of a three-dimensional numerical model for the prediction of morphological bed changes. The sediment deposition in a reservoir during a 10-year-flood was investigated and the results of the simulation were validated with data derived from a physical model study. Because of the small grain sizes in the prototype, synthetic granulate was used in the physical model. The numerical computation domain was a reproduction of the physical model, including the grain sizes and the density of the particles, in order to ensure comparability. The CFD code SSIIM, which solves the RANS-equations in three-dimensions, was used for the simulations. The sediment transport in SSIIM is divided into suspended sediment transport, computed by solving the convection-diffusion equation, and bed-load transport, calculated by an empirical formula. The results of the numerical simulation correspond well to the results of the physical model study. The simulated location and the pattern of the sediment deposition in the reservoir are an accurate representation of the observed distribution in the physical model.     

INCIPIENT MOTION OF COARSE PARTICLES IN HIGH GRADIENT RIVERS

1 INTRODUCTION To data, there are about 100 formulae for the incipient motion of sediment, among which, only about ten are convenient and practical. In 1936, using nondimensional drag force and the sediment’s Reynolds number, Shields (1936) presented the…     

EXPERIMENTAL STUDY ON SALTATION OF SOLID GRAINS IN FLOWING WATER

This paper deals with the saltation of bed-load solid grains in flowing water. Experiments have been carried out by means of high-speed photographing and advanced data processing techniques while the analysis is made by combined method of mechani- cal and statistical theories. Experiments reveal that saltation is the main form of the bed-load transport under ordinary flow conditions. Taking successive saltation as the model of bed-load transport, systematic analysis has been made with regard to the forces acting on grains and the variation of their magnitudes along the saltation trajec- tories to obtain the kinematic and dynamic properties of these grains. The statistical analysis shows that the probability density functions of the relative height and length of saltation are in conformity with distribution, while the probability density functions of the relative velocities of saltation are in conformity with the Gaussian distribution.     

DEPTH-AVERAGED 2-D CALCULATION OF FLOW AND SEDIMENT TRANSPORT IN CURVED CHANNELS

The helical flow significantly affects the flow, sediment transport and morphological evolution in curved channels. A semi-empirical formula is proposed to determine the cross-stream distribution of the helical flow intensity in the developed regions of a channel bend. It is then used to evaluate the dispersion terms in the depth-averaged 2-D momentum equations and suspended-load transport equation as well as the bed-load transport angle, thus enhancing the depth-averaged 2-D model to account for the effect of helical flow. The tests in several experimental and field cases show that the enhanced depth-averaged 2-D model can much more reasonably predict the shifting of main flow from inner bank to outer bank, the erosion along outer bank and deposition along inner bank than the depth-averaged 2-D model without considering this effect.     

Numerical modelling of riverbed grain size stratigraphic evolution

For several decades,quantification of riverbed grain size stratigraphic evolution has been based upon the active layer formulation（ALF）,which unfortunately involves considerable uncertainty.While it is the sediment exchange across the bed surface that directly affects the riverbed stratigraphy,it has been assumed in the ALF that the sediment fraction at the lower interface of the active layer is a linear function of the sediment fraction in the flow.Here it is proposed that the sediment fraction of the sediment exchange flux is used directly in estimating the sediment fraction at the lower surface of the active layer.Together with the size-specific mass conservation for riverbed sediment,the modified approach is referred to as the surface-based formulation（SBF）.When incorporated into a coupled non-capacity modelling framework for fluvial processes,the SBF leads to results that agree as well or better than those using ALF with laboratory and field observations.This is illustrated for typical cases featuring bed aggradation and degradation due to graded bed-load sediment transport.Systematic experiments on graded sediment transport by unsteady flows are warranted for further testing the modified formulation.     

透射边界高频耦合失稳机理及稳定实现——SH波动

就大型近场波动的高效数值模拟而言,稳定实现高阶人工边界是一个尚未圆满解决的问题.本文针对使用多次透射公式的SH波动集中质量有限元模拟,依据GKS定理的群速度解释,进一步阐明了人工边界与内域离散格式耦合所导致高频失稳的机理,即两者支持群速度指向内域的外行高频平面谐波,波动能量自发地从人工边界进入內域,从而导致失稳,而这类谐波是由集中质量有限元离散引入的.本文提出了消除此种耦合失稳的一种方法:通过修改有限元刚度阵来改变内域离散格式,并保证修改格式的精度不低于原有格式的精度.理论分析和数值实验表明此法能稳定实现透射边界.本文研究结果具有推广应用前景.     

3D numerical simulation of particle-particle collisions in saltation mode near stream beds

The importance of particle-particle collisions in sediment saltation in the bed-load layer is analyzed herein by means of numerical simulation. The particle saltation theoretical/numerical model follows a Lagrangian approach, and addresses the motion of sediment particles in an open channel flow described by a logarithmic velocity profile. The model is validated with experimental data obtained from the literature. In order to evaluate the importance of the phenomenon, simulations with and without particle-particle collisions were carried out. Results for two different sediment concentrations are presented, namely 0.13% and 2.33%. For each concentration of particles, three different flow intensities were considered, and trajectories of two different particle sizes, within the sand range were computed. Changes in particle rotation, particle velocity, and angle of trajectory before and after particle-particle collisions appear to be relatively important at lower shear stresses, whereas they decrease in significance with increasing flow intensities. Analyses of the evolution in time of the second order moment of particle location suggest that inter-particle collisions introduce transverse diffusion in saltating particles in the span-wise direction.