Test of Hack's slope to bed material relationship in the Southern Eifel Uplands,Germany

The local reach gradient of small gravel bed rivers (drainage area 0-8-110 km²) in the Eifel, West Germany, is adjusted to transport the river bed sediments. Transport of gravel becomes possible under high flow conditions (Shields entrainment factor ≈-03). Mean bed material size for riffle sections increases with distance downstream. For small drainage areas channel slope is a negative exponential function of drainage area, while for the larger region the additional influence of bedload size has to be considered. Good agreement with Hack's data (1957) for Virginia and Maryland, U.S.A., is achieved (S = 0.0066 (D₅₀/A)^{- 40.}, r = 0.67).     

Particle size distribution of bed materials in the sandy river bed of alluvial rivers

The particle size distribution of bed materials in the sandy river bed of alluvial rivers is important in the study of topics such as friction, river bed evolution, erosion, and siltation. It also can reflect the dependency relation between river bed sediment and flow intensity. In this paper, the critical pattern of sediment movement in the near-wall region of a sandy river bed was analyzed. According to the principle of momentum balance, the critical settling-rising condition of bed material in a sandy river bed was found to be instantaneous turbulent velocity equal to 2.7 times the sediment settling velocity in quiescent water. Based on a vertical instantaneous turbulent velocity with a Gaussian distribution, a theoretical relation for calculating the particle size distribution of bed materials in a sandy river bed without pre-known characteristic grain sizes was developed by solving a stochastic equation. The for-mula is verified using measured data, and the results show that the proposed formula was in accordance with the measured data. This study has theoretical significance and practical value for determining the bed material particle size distribution of the sandy bed of alluvial rivers.     

A probabilistic model for sediment entrainment:The role of bed irregularity

A generalized probabilistic model is developed in this study to predict sediment entrainment under the incipient motion, rolling, and pickup modes. A novelty of the proposed model is that it incorporates in its formulation the probability density function of the bed shear stress, instead of the near-bed velocity fluctuations, to account for the effects of both flow turbulence and bed surface irregularity on sediment entrainment. The proposed model incorporates in its formulation the collective effects of three para-meters describing bed surface irregularity, namely the relative roughness, the volumetric fraction and relative position of sediment particles within the active layer. Another key feature of the model is that it provides a criterion for estimating the lift and drag coefficients jointly based on the recognition that lift and drag forces acting on sediment particles are interdependent and vary with particle protrusion and packing density. The model was validated using laboratory data of both fine and coarse sediment and was compared with previously published models. The study results show that all the examined models perform adequately for the fine sediment data, where the sediment particles have more uniform gra-dation and relative roughness is not a factor. The proposed model was particularly suited for the coarse sediment data, where the increased bed irregularity was captured by the new parameters introduced in the model formulation. As a result, the proposed model yielded smaller prediction errors and physically acceptable values for the lift coefficient compared to the other models in case of the coarse sediment data.     

Sediment variability and bed material sampling in gravel-bed rivers

In a 350 m wide reach of the braided, gravel-bed Ashley River, the surface layer of the bed material was sampled in 141 areas of homogeneous graded sediment along seven cross-sections, and 30 kg bulk samples were collected at 86 randomly selected locations along the cross-sections. At one location, a single 854 kg sample composed of 28 subsamples was also collected. Analysis of the single large sample indicate that accurate determination of mean grain size D at that site requires, desirably, a sample of ～ 100 kg, but that samples in which the weight of the largest stone is less than 5 per cent of the total weight have unbiased estimates of D. Spatial variability of bulk material is such that 228 and 50 samples are needed to estimate D to ± 10 and ± 20 per cent respectively of the true value; requirements for estimating inclusive graphic standard duration are only 11 and 3 respectively. The grain-size distribution of the surface layer is only weakly related to the bulk material beneath. The results of ‘Wolman sampling’ along 12 cross-sections at two pace intervals (average 120 stones per cross-section) indicate that estimation of overall surface D to ±10 and ±20 per cent would require sampling along 64 and 14 cross-sections respectively. It is concluded that accurate characterization of bed sediment in gravel-bed rivers is very demanding of labour and resources, and that careful planning is needed to ensure efficiency and meaningful results.     

Effect of incoming sediment on the transport rate of bed load in mountain streams

Field experiments were conducted on bed load transport in the Diaoga River, a mountain stream in southwest China, to study the variation of bed load transport with varying sediment supply. The rate of bed load transport is greatly affected by incoming sediment （load and size）. Under the same flow conditions, bed load transport rates may differ by three orders of magnitude depending on whether measurements were taken before or after the first flood of the year. The relation of the ＂bed load transport rate versus flow intensity＂ appears to have similar characteristics as a clockwise looped-rating curve. Experiments also were conducted during the non-flood season to study bed load transport processes with different incoming load from an upstream section. Bed load with different sizes can be grouped into two types： traveling bed load and structural bed load. Traveling bed load is composed of sediment finer than a critical size, De, and its transport rate depends mainly on the incoming sediment rate. The incoming sediment rate can alter the rate of bed load transport by three orders of magnitude. Structural bed load is composed of coarser sediment and its transport rate closely relies on the flow intensity.     

Distribution and species composition of macroinvertebrates in the hyporheic zone of bed sediment

The hyporheic zone is a layer of substrate on a river bed where benthic animals normally live,grow,feed,reproduce,and exist for any portion of their life cycle.The hyporheic zone was studied by samplin...     

长江中游沙质河段床沙级配调整过程计算

三峡工程运用后,长江中游荆江河段持续冲刷,床沙与推移质、悬移质泥沙不断交换,从而造成该河段床沙发生不同程度的调整,对长江中下游河床演变及非平衡输沙机理的研究具有重要影响.在新水沙条件下,总结分析了沙波运动特性及床沙交换方式,引入Markov三态转移概率及非均匀沙隐暴系数,得到基于状态转移概率的沙质河段床沙级配调整的计算模型.研究结果表明:(1)20092014年,沙市站年内床沙中值粒径有先增大后减小的趋势,而监利站年内床沙中值粒径则先减小后增大,且荆江河段年际床沙中值粒径总体呈上升趋势,粗化程度约为6.9%~9.3%;(2)20092014年,沙市站床沙组成中粒径d<0.062 mm的泥沙所占比重不变,0.062 mm≤d<0.25 mm的泥沙所占比重逐年减少(累计减少11.4%),d≥0.25 mm的泥沙所占比重逐年增加(累计增加11.4%),而监利站床沙组成均存在波动性变化;(3)荆江河段床沙转换为推移质的概率随着泥沙粒径的增大而增大,床沙转换为悬移质的概率随着泥沙粒径的增大而减小,而推移质和悬移质转换为床沙的概率均随着泥沙粒径的增大而增大,河床发生冲刷粗化时泥沙输移的主要形式为悬移质(概率为81%~87%),而淤积细化时床沙补给主要来源于推移质(概率为8%~12%).通过验证,本文概率模型的计算结果与实测资料符合较好,能够应用于长江中游沙质河段年际床沙粗化及年内床沙级配调整过程预报,为进一步开展三峡工程下游非均匀悬移质泥沙沿程恢复机理的研究提供理论基础.     

Multigene genetic programming for sediment transport modeling in sewers for conditions of non-deposition with a bed deposit

It is known that construction of large sewers based on consideration of flow with non-deposition without a bed deposit is not economical. Sewer design based on consideration of flow with non-deposition with a bed deposit reduces channel bed slope and construction cost in which the presence of a small depth of sediment deposition on the bed increases the sediment transport capacity of the flow. This paper suggests a new Pareto-optimal model developed by the multigene genetic programming (MGGP) technique to estimate particle Froude number (Fr_p) in large sewers with conditions of sediment deposition on the bed. To this end, four data sets including wide ranges of sediment size and concentration, deposit thickness, and pipe size are used. On the basis of different statistical performance indices, the efficiency of the proposed Pareto-optimal MGGP model is compared to those of the best MGGP model developed in the current study as well as the conventional regression models available in the literature. The results indicate the higher efficiency of the MGGP-based models for Fr_p estimation in the case of no additional deposition onto a bed with a sediment deposit. Inasmuch as the Pareto-optimal MGGP model utilizes a lower number of input parameters to yield comparatively higher performance than the conventional regression models, it can be used as a parsimonious model for self-cleansing design of large sewers in practice.     

A comparison between different methods for determining grain distribution in coarse channel beds

The determination of grain size distribution in alluvial channels plays a crucial role in understanding fluvial dynamics and processes (e.g., hydraulic resistance, sediment transport and erosion, and habitat suitability). However, to determine an accurate distribution, tremendous field efforts are often required. Traditionally, the grain size distribution of channel beds have been obtained by manually counting a set of randomly selected stones (the“pebble count”). Based on this elementary principle, many authors have proposed different adaptations to overcome weaknesses and problems with the original method; with the development of digital technology, photographic methods have been developed in order to sig-nificantly reduce the time spent in the field. Two of these“image-assisted”methods include Automated Grain Sizing, AGS, and Manual Photo Sieving, MPS. In this study, AGS and MPS were applied under ideal laboratory conditions, to be used as reference, and in two field conditions with different degrees of difficulty in terms of visual determination of the grain size distribution; these included an artificial unlined channel and two natural mountainous streams. The results were compared with those obtained with the pebble-count method. In general, strong agreement between the methods was found when they were applied under favorable conditions (”the laboratory”), and the differences between the image-assisted and pebble count methods were similar to those found in previous studies. Despite being more time consuming, MPS was deemed preferable to AGS when conditions are not optimal;in these cases, the time spent on image elaboration significantly increased in the AGS method (approximately three-fold), but the estimation error of the median grain size decreased by approximately 37%. The use of image-assisted analysis has proven to be robust for characterizing sediment in watercourse beds and reducing fieldwork time, but because field conditions can significantly affect the accuracy of results, the method choice must be carefully considered.     

A 2D weakly-coupled and efficient numerical model for transient shallow flow and movable bed

Recent advances in the simulation of free surface flows over mobile bed have shown that accurate and stable results in realistic problems can be provided if an appropriate coupling between the shallow water equations (SWE) and the Exner equation is performed. This coupling can be done if using a suitable Jacobian matrix. As a result, faithful numerical predictions are available for a wide range of flow conditions and empirical bed load discharge formulations, allowing to investigate the best option in each case study, which is mandatory in these type of environmental problems. When coupling the equations, the SWE are considered but including an extra conservation law for the sediment dynamics. In this way the computational cost may become unrealistic in situations where the application of the SWE over rigid bed can be used involving large time and space scales without giving up to the adequate level of mesh refinement. Therefore, for restoring the numerical efficiency, the coupling technique is simplified, not decreasing the number of waves involved in the Riemann problem but simplifying their definitions. The effects of the approximations made are tested against experimental data which include transient problems over erodible bed. The simplified model is formulated under a general framework able to insert any desirable discharge solid load formula.     

Comparison of fractional bed‐material load ­computation methods in sand‐bed channels

This paper presents a comparison of different fractional bed‐material load computation methods in sand‐bed channels. These methods include the direct computation by size fraction approach of Einstein, Laursen and Toffaleti; the bed material fraction (BMF) approach using equations of Engelund and Hansen, Ackers and White, Yang, and Karim's modified BMF method; and the transport capacity fraction (TCF) approach using the transport capacity distribution functions of Karim and Kennedy, Li, and Wu and Molinas. Over 150 sets of flume and field data in the sand size range containing a total of 1007 data points are used to evaluate and compare the accuracy of these methods. Statistical analysis and graphical comparison are utilized to demonstrate the performance and variations in different methods. Overall, the Einstein method underpredicts the transport rate for finer sizes and overpredicts for the coarser sizes, while the other methods overestimate the finer fractions and underestimate the coarser fractions. The Wu and Molinas method, which was developed to account for these deficiencies, is shown to significantly improve fractional bed‐material load computations. The Karim and Kennedy method is also found to be applicable. Copyright © 2000 John Wiley & Sons, Ltd.     

一种新的三维大地电磁积分方程正演方法

采用规则六面体单元和并矢Green函数奇异积分等效积分技术,已有的大地电磁积分正演方法具有不能有效模拟地下复杂地质体和计算精度偏低的缺点.本文提出了一种新的三维大地电磁积分方程正演技术,即采用四面体单元、解析的并矢Green函数奇异积分表达式,达到既能模拟地下复杂异常体,又能有效提高已有积分方程法计算精度的目的.首先,采用四面体网格技术离散地下复杂异常体,获得四面体单元上的大地电磁积分方程.然后,利用针对四面体单元开发的新的奇异值积分的解析表达式,准确计算线性方程中的并矢Green函数的奇异积分,从而获得精确的线性方程.借助于PARDISO高性能并行直接求解器,实现了三维大地电磁问题的高精度求解.最后,基于国际标准3D-1模型和六棱柱模型,通过与其他方法结果的对比分析,验证了本文方法的正确性、处理高电导率对比度的能力（1000：1）和处理复杂模型的能力.

     

Channel geometry,bed material,and inferred flow conditions in ephemeral stream systems,barrier range,western N.S.W. Australia

Streams draining the Barrier Range uplands in arid western N.S.W. are ephemeral and undergo rapid channel contraction away from the uplands as a consequence of transmission loss. These processes are documented on the basis of surveys of channel form and bed material at sequential sites located along the contracting lowland reaches of two representative streams. Channel width and depth display considerable fluctuation downstream, but cross-sectional area and maximum bed surface grain size decline in a very regular manner. Flood discharge, estimated from the channel capacity and predicted critical and mean flow velocities, also declines regularly. the trends are well fitted by log-linear models, and are reported in terms of a half-distance, the channel length in km over which the value of a morphometric parameter declines by 50 per cent. Rates of channel contraction and transmission loss are inferred to be inversely proportional to the volume of flow delivered from the upland section of the drainage basin. Unusual channel characteristics, including extensive tree growth in the bed, make application of ordinary flow equations difficult, because friction factors cannot be estimated with confidence. Systematic changes in the nature of the bed surface in contracting streams such as those studied here also have implications for the application of critical velocity equations, and highlight a need for further study of desert channels.     

A new sampler for extracting bed material sediment from sand and gravel beds in navigable rivers

Grain‐size distributions of bed material sediment in large alluvial rivers are required in various scientific and management applications, but characterizing gravel beds in navigable rivers is hampered by difficulties in sediment extraction. The newly developed and preliminarily tested sampler reported here can extract sediment from a range of riverbeds. The 36 × 23 × 28 cm stainless steel toothed sampler is deployed from and dragged downstream by the weight of a jet boat, and it improves upon previous samplers that are unable to penetrate gravel bed surfaces, have small apertures, and/or cannot retain fine sediment. The presented sampler was used to extract 167 bed material sediment samples of up to 16 kg (dry weight) with an average sample size of ～6 kg from 67 cross‐sections spanning 160 river kilometres along the Sacramento River. It was also tested at three sites on a subaerial bar to compare surface, subsurface, and sampler distributions. Sampler penetration is ～5 cm. The device collects individual samples that satisfy the criterion for bed material sediment whereby the largest particle comprises no more than 5% of the total sample mass in gravel and sand beds, except where the degree of surface armouring is large (e.g. armor ratios >> 2) and where more than 10% of bed material sediment is composed of grains larger than 64 mm. When aggregated samples exceed 15 kg, all satisfy the criterion whereby the largest particle comprises no more than 1% of the total sample mass. Samples closely resemble surface size distributions, except where armouring is strong. The sampler should be subject to more rigorous field testing, but many of its current limitations are expected to become negligible with the advent a larger, heavier version of the sampling device. Copyright © 2008 John Wiley & Sons, Ltd.     

A prediction method for the size distribution of saltating particles above a mixed-size bed

In aeolian saltation, the sand bed is a mixture of sand particle with a wide range of particle sizes. Generally, the particle size distribution (PSD) of saltating particles is ignored by previous aeolian transport models, which will result in differences between predictions and observations. To better understand the saltation process, a prediction method of the PSD of saltating particles was proposed in this article. The probability of contact between incident sand and bed sand was introduced into the particle-bed collision process. An artificial PSD of the incident saltating particles was set as the initial condition. A stochastic particle-bed collision model considering contact probability was then used in each iteration step to calculate a new PSD of saltating particles. Finally, the PSD of saltating particles can be determined when aeolian saltation reaches a steady state (saltation is in a steady state when its primary characteristics, such as horizontal mass flux and the concentration of saltating particles, remain approximately constant over time and distance). Meanwhile, according to the experimental results, a calculation formula for the contact parameter n is given, which characterizes the shielding effect of particles on each other. That is, if soil PSD and friction velocity were given, the PSD of saltating particles can be determined. Our results do not depend on the initial conditions, and the predicted results are consistent with the experimental results. It indicated that our method can be used to determine the PSD of saltating particles. © 2020 John Wiley & Sons, Ltd.     

A master equation for reactive solute transport in porous media

The mean value of a density of a cloud of points described by a generalized Liouville equation associated with a convection dispersion equation governing adsorbing solute transport yields a joint concentration probability density. The general technique can be applied for either linear or nonlinear adsorption; here the application is restricted to linear adsorption in one-dimensional transport. The equation generated for the joint concentration probability density is in the general form of a Fokker-Planck equation, but with a suitable coordinate transformation, it is possible to represent it as a diffusion equation with variable coefficients.     

A new ultrasonic interferometer for the determination of equation of state parameters of sub-millimeter single crystals

A new giga-Hertz ultrasonic interferometer has been developed, based on ultrasonic microscopy technology. The interferometer operates from 0.3 GHz to 1.5 GHz. The high frequency and associated small wavelengths together with the large bandwidth make it possible to measure travel times in samples with thicknesses of several microns and allow for unprecedented accuracy in bond corrections. An absolute accuracy of 1 part in 10⁵ in travel time measurements is achievable in single crystals (thickness of 200 microns) or glasses of interest to the earth sciences. The high precision travel time data, combining with sample length measurements using a laser interferometer built in our laboratory, yield very high precision ultrasonic velocities.The interferometer is intended for use in conjunction with a newly developed 4 GPa gas piston cylinder apparatus (Getting andSpetzler, 1993) for equation of state measurements under simultaneous pressure and temperature. A separate correction for the bond will be made for each datum at every point in temperature pressure space.     

Evaluation of the Ross fast solution of Richards’ equation in unfavourable conditions for standard finite element methods

Ross [Ross PJ. Modeling soil water and solute transport – fast, simplified numerical solutions. Agron J 2003;95:1352–61] developed a fast, simplified method for solving Richards’ equation. This non-iterative 1D approach, using Brooks and Corey [Brooks RH, Corey AT. Hydraulic properties of porous media. Hydrol. papers, Colorado St. Univ., Fort Collins; 1964] hydraulic functions, allows a significant reduction in computing time while maintaining the accuracy of the results. The first aim of this work is to confirm these results in a more extensive set of problems, including those that would lead to serious numerical difficulties for the standard numerical method. The second aim is to validate a generalisation of the Ross method to other mathematical representations of hydraulic functions.