Exponential Formula for Bedload Transport

An exponential formula that does not involve the concept of the critical shear stress is derived in this study for computing bedload transport rates. The formula represents well various experimental data sets ranging from the weak transport to high shear conditions. Comparisons of the present study are also made with many previous bedload formulas commonly cited in the literature.     

Stochastic Prediction of Sediment Transport in Sand-Gravel Bed Rivers

Classical deterministic bedload transport predictors are applied to sand-gravel bed rivers. The turbulent bed shear stress is modeled according to a probability distribution to obtain realistic bedload transport rates at incipient motion. In extending the predictors to stochastic predictors for nonuniform sediment, many parameters that represent near-bed turbulence and the particle size distribution must be chosen. The parameters that give realistic results are chosen by analyzing the results of a new experimental flume dataset with relatively large water depths. Choosing other combinations of parameters may give equal total bedload transport rates, but at the cost of large errors in fractional transport rates. Attention is given to the hiding-exposure phenomenon and a hindrance effect related to nonuniform sediment. Validation based on two independent field datasets shows that successful predictions of particle sizes near the threshold for motion are feasible using the stochastic approach, while the deterministic approach gives successful predictions well above incipient motion.     

Influence of Turbulence on Bed Load Sediment Transport

This paper summarizes the results of an experimental study on the influence of an external turbulence field on the bed load sediment transport in an open channel. The external turbulence was generated by (1) a horizontal pipe placed halfway through the depth h; (2) a series of grids with a clearance of about one-third of the depth from the bed, and extending over a finite length of the flume; and (3) a series of grids with a clearance in the range (0.1–1.0)h from the bed, but extending over the entire length of the flume. Two kinds of experiments were conducted: plane-bed experiments and ripple-covered-bed experiments. In the former case, the flow in the presence of the turbulence generator was adjusted so that the mean bed shear stress was the same as in the case without the turbulence generator in order to single out the effect of the external turbulence on the sediment transport. In the ripple-covered-bed case, the mean and turbulence quantities of the streamwise component of the velocity were measured, and the Shields parameter, due to skin friction, was determined. The Shields parameter, together with the RMS value of the streamwise velocity fluctuations, was correlated with the sediment transport rate. The sediment transport increases markedly with increasing turbulence level.     

Bedload Transport in Gravel-Bed Streams with Unimodal Sediment

Bedload transport in many gravel-bed streams becomes highly complicated because of the nonuniformity of the grain size and the vertical stratification of channel bed material. A new relation for computing bedload transport rates in gravel-bed streams is proposed here. In an effort to account for the variation of the makeup of the surface material within a wide range of Shields stresses, the relation employs a two-parameter approach, one related to the material in the pavement and the other to that in the subpavement layers. The mode is used to represent the grain sizes of each layer. Available bedload transport data from gravel-bed streams with unimodal sediment are used to test the accuracy of the relation. A comparison with other bedload transport relations is also considered.     

Measurement of Coarse Gravel and Cobble Transport Using Portable Bedload Traps

Portable bedload traps (0.3 by 0.2 m opening) were developed for sampling coarse bedload transport in mountain gravel-bed rivers during wadable high flows. The 0.9 m long trailing net can capture about 20 kg of gravel and cobbles. Traps are positioned on ground plates anchored in the streambed to minimize disturbance of the streambed during sampling. This design permits sampling times of up to 1 h, overcoming short-term temporal variability issues. Bedload traps were tested in two streams and appear to collect representative samples of gravel bedload transport. Bedload rating and flow competence curves are well-defined and steeper than those obtained by a Helley–Smith sampler. Rating curves from both samplers differ most at low flow but approach each other near bankfull flow. Critical flow determined from bedload traps is similar using the largest grain and the small transport rate method, suggesting suitability of bedload trap data for incipient motion studies.     

Measurements of Sediment Erosion and Transport with the Adjustable Shear Stress Erosion and Transport Flume

Soil and sediments play an important role in water management and water quality. Issues such as water turbidity, associated contaminants, reservoir sedimentation, undesirable erosion and scour, and aquatic habitat are all linked to sediment properties and behaviors. In situ analysis is necessary to develop an understanding of the erosion and transport of sediments. Sandia National Laboratories has recently patented the Adjustable Shear Stress Erosion and Transport (ASSET) Flume that quantifies in situ erosion of a sediment core with depth while affording simultaneous examination of transport modes (bedload versus suspended load) of the eroded material. Core erosion rates and ratios of bedload to suspended load transport of quartz sediments were studied with the ASSET Flume. The erosion and transport of a fine-grained natural cohesive sediment were also observed. Experiments using quartz sands revealed that the ratio of suspended load to bedload sediment transport is a function of grain diameter and shear stress at the sediment surface. Data collected from the ASSET Flume were used to formulate a novel empirical relation for predicting the ratio of bedload to suspended load as a function of shear stress and grain diameter for noncohesive sediments.     

Wash Load and Bed-Material Load Transport in the Yellow River

It has been the conventional assumption that wash load is supply limited and is only indirectly related to the hydraulics of a river. Hydraulic engineers also assumed that bed-material load concentration is independent of wash load concentration. This paper provides a detailed analysis of the Yellow River sediment transport data to determine whether the above assumptions are true and whether wash load concentration can be computed from the original unit stream power formula and the modified unit stream power formula for sediment-laden flows. A systematic and thorough analysis of 1,160 sets of data collected from 9 gauging stations along the Middle and Lower Yellow River confirmed that the method suggested by the conjunctive use of the two formulas can be used to compute wash load, bed-material load, and total load in the Yellow River with accuracy.     

Bed-Load Transport Equation for Sheet Flow

When open-channel flows become sufficiently powerful, the mode of bed-load transport changes from saltation to sheet flow. Where there is no suspended sediment, sheet flow consists of a layer of colliding grains whose basal concentration approaches that of the stationary bed. These collisions give rise to a dispersive stress that acts normal to the bed and supports the bed load. An equation for predicting the rate of bed-load transport in sheet flow is developed from an analysis of 55 flume and closed conduit experiments. The equation is ib = ω where ib = immersed bed-load transport rate; and ω = flow power. That ib = ω implies that eb = tan?α = ub/u, where eb = Bagnold’s bed-load transport efficiency; ub = mean grain velocity in the sheet-flow layer; and tan?α = dynamic internal friction coefficient. Given that tan?α ≈ 0.6 for natural sand, ub ≈ 0.6u, and eb ≈ 0.6. This finding is confirmed by an independent analysis of the experimental data. The value of 0.60 for eb is much larger than the value of 0.12 calculated by Bagnold, indicating that sheet flow is a much more efficient mode of bed-load transport than previously thought.     

Unified View of Sediment Transport by Currents and Waves. I: Initiation of Motion, Bed Roughness, and Bed-Load Transport

Attention is given to the properties of sediment beds over the full range of conditions (silts to gravel), in particular the effect of fine silt on the bed composition and on initiation of motion (critical conditions) is discussed. High-quality bed-load transport data sets are identified and analyzed, showing that the bed-load transport in the sand range is related to velocity to power 2.5. The bed-load transport is not much affected by particle size. The prediction of bed roughness is addressed and the prediction of bed-load transport in steady river flow is extended to coastal flow applying an intrawave approach. Simplified bed-load transport formulas are presented, which can be used to obtain a quick estimate of bed-load transport in river and coastal flows. It is shown that the sediment transport of fine silts to coarse sand can be described in a unified model framework using fairly simple expressions. The proposed model is fully predictive in the sense that only the basic hydrodynamic parameters (depth, current velocity, wave height, wave period, etc.) and the basic sediment characteristics (d10, d50, d90, water temperature, and salinity) need to be known. The prediction of the effective bed roughness is an integral part of the model.     

Bed-Material Load Computations for Nonuniform Sediments

The nonuniformity of bed material affects the bed-material load calculations. A size gradation correction factor Kd is developed to account for the lognormal distribution of bed material. The use of Kd in conjunction with bed-material load equations originally developed for single particle sizes improves the accuracy of transport calculations for sediment mixtures. This method is applicable to laboratory flumes and natural rivers with median diameter d50 of bed material in the sand size ranges. The improvement on transport rate by Kd factor is significant for data with standard deviation σg of bed material greater than 2, while the correction is negligible for data with σg less than 1.5. Sediment in transport also follows a lognormal distribution with a median diameter d50t generally finer than the corresponding d50. As the size gradation increases, d50t becomes much finer than the corresponding value of d50. The relationship between d50t and d50 is defined as a function of σg and agrees well with field data. The previously recommended use of d35 as representative size of the bed material is found not to be generally applicable.     

Bedload Transport in Alluvial Channels

Hydraulic, sediment, land-use, and rock-erosivity data of 22 alluvial streams were used to evaluate conditions of bedload transport and the performance of selected bedload-transport equations. Transport categories of transport-limited (TL), partially transport-limited (PTL), and supply-limited (SL) were identified by a semiquantitative approach that considers hydraulic constraints on sediment movement and the processes that control sediment availability at the basin scale. Equations by Parker et al. in 1982, Schoklitsch in 1962, and Meyer-Peter and Muller in 1948 adequately predicted sediment transport in channels with TL condition, whereas the equations of Bagnold in 1980, and Schoklitsch, in 1962, performed well for PTL and SL conditions. Overall, the equation of Schoklitsch predicted well the measured bedload data for eight of 22 streams, and the Bagnold equation predicted the measured data in seven streams.     

One-Dimensional Model for Transient Flows Involving Bed-Load Sediment Transport and Changes in Flow Regimes

This study presents a novel, simple, but rather accurate approximation of the eigenvalues of the system formed by the Saint-Venant–Exner equations, based on the comparison between eigenvalues for the complete system and eigenvalues for the water phase only. Moreover, a strategy is proposed to compute efficiently the intercell fluxes by properly adapting a Harten, Lax, and van Leer scheme for each equation. Two examples of transient transcritical flows are developed: the erosive migration of a knickpoint induced by an increase in the bed slope, and the evolution of a hydraulic jump over a mobile bed.     

Use of the Lorenz Curve to Quantify Statistical Nonuniformity of Sediment Transport Rate

The Lorenz curve and the Gini index are statistical tools that have been widely used to quantify nonuniformity in economics, ecology, and medicine, but have apparently not been previously applied in hydraulic engineering. In this work, the Lorenz curve was applied to the analysis of sediment transport data from several experiments with natural and lightweight solid particles. The distributions of instantaneous sediment transport rate data have been analyzed, leading to some interesting observations: (1) the values are quite nonuniformly distributed, with a significant proportion of zero values at the lowest sediment transport rates; and (2) the distributions of the values considering only samples with nonzero values are still quite nonuniform; yet the variability of the Gini index with the average sediment transport rate is much smaller than that obtained for the complete data samples, indicating a major role of intermittency in determining the nonuniformity of sediment transport.     

Two-Dimensional Total Sediment Load Model Equations

An unsteady total load equation is derived for use in depth-averaged sediment transport models. The equation does not require the load to be segregated a priori into bed and suspended but rather automatically switches to suspended load, bed load, or mixed load depending on a transport mode parameter consisting of local flow hydraulics. Further, the sediment transport velocity, developed from available data, is explicitly tracked, and makes the equation suitable for unsteady events of sediment movement. The equation can be applied to multiple size fractions and ensures smooth transition of sediment variables between bed load and suspended load for each size fraction. The new contributions of the current work are the consistent treatment of sediment concentration in the model equation and the empirical definition of parameters that ensure smooth transitions of sediment variables between suspended load and bed load.     

Experimental Study of Bed Load Transport through Emergent Vegetation

Vegetation is an important agent in fluvial geomorphology and sedimentary processes, through its influence on the local hydraulics that determine sediment transport. Within stands of emergent vegetation, bed shear is substantially reduced through the absorption of momentum by drag on the stems. This stimulates deposition of sediment and reduces capacity for bed load transport. The effect of emergent vegetation on hydraulic parameters (including equilibrium bed gradient, flow depth, and velocity) and on bed load transport rate has been investigated experimentally for one sediment size, stem diameter, and stem spacing. Bed load transport rate was found to be closely related to bed-shear stress, which must be estimated by partitioning total flow resistance between stem drag and bed shear.     

Aspect Ratio to Maximize Sediment Transport in Rigid Bank Channels

The continuity equation, Manning’s equation, Einstein’s wall correction procedure and sediment transport equations are combined to indicate channel aspect ratios which maximize sediment transport for a given water discharge in rigid-bank trapezoidal and rectangular channels with fixed slope. Higher aspect ratios are required to maximize sediment transport for channels conveying bed load than for those with a dominant suspended load. A total load equation predicts optimum aspect ratios lying in between those for bed load and suspended load channels. The equations imply that the optimum aspect ratio increases markedly as the channel bank to channel bed roughness ratio increases. The resulting optimum ratios are smaller than the aspect ratios of many natural rivers.     

Machine Learning Approach to Modeling Sediment Transport

Inaccuracies of sediment transport models largely originate from our limitation to describe the process in precise mathematical terms. Machine learning (ML) is an alternative approach to reduce the inaccuracies of sedimentation models. It utilizes available domain knowledge for selecting the input and output variables for the ML models and uses modern regression techniques to fit the measured data. Two ML methods, artificial neural networks and model trees, are adopted to model bed-load and total-load transport using the measured data. The bed-load transport models are compared with the models due to Bagnold, Einstein, Parker et al., and van Rijn. The total-load transport models are compared with the models due to Ackers and White, Bagnold, Engelund and Hansen, and van Rijn. With the chosen data sets on bed-load and total-load transport the ML models provided better accuracy than the existing ones.     

Fluctuations of Suspended Sediment Concentration and Turbulent Sediment Fluxes in an Open-Channel Flow

A complex problem of turbulent-sediment interactions in an open-channel flow is approached experimentally, using specially designed field experiments in an irrigation canal. The experimental design included synchronous measurements of instantaneous three-dimensional (3D) velocities and suspended sediment concentration using acoustic Doppler velocimeters (ADV) and a water sampling system. Various statistical measures of sediment concentration fluctuations, turbulent sediment fluxes, and diffusion coefficients for fluid momentum and sediment are considered. Statistics, fractal behavior, and contributions of bursting events to vertical fluxes of fluid momentum and sediment are evaluated using quadrant analysis. It has been found that both turbulence and sediment events are organized in fractal clusters which introduce additional characteristic time and spatial scales into the problem and should be further explored. It is also shown that Barenblatt’s theory of sediment-laden flows appears to be a good approximation of experimental data.     

Near-Bed Sediment Concentration Distribution and Basic Probability of Sediment Movement

Sediment concentration distribution and the basic probability of sediment movement near the channel bed are two of the most important and fundamental issues in the study of sediments. Based on statistical analysis and considering the transport mechanisms, the rules of sediment concentration distribution near a channel bed are studied. Analytical expressions for the near-bed sediment concentration distribution and mean sediment concentration are derived, and the expression for the mean sediment concentration near the bed is verified by measured data, which were obtained from previous experiments. With the help of statistical theory, the expressions of basic probabilities, i.e., rolling, saltating, and suspending probabilities, for sediment movement near the bed are also derived. The expression for starting probability is verified by the measured data. The verification shows that the results from the proposed expression agree well with the measured data. This research has both theoretical and practical significance for further investigation concerning rules of bed load and suspended sediment transport.     

Approach to Separate Sand from Gravel for Bed-Load Transport Calculations in Streams with Bimodal Sediment

The bed material found in gravel-bed streams is nonuniform in terms of grain size and can typically be classified as unimodal or bimodal. The latter type of sediment distribution is usually represented by two modes, one of sand size and another of gravel. For this case, the movement of one mode becomes nonlinearly influenced by the other. As a result, the presence of the two modes in a bimodal material complicates the calculation of bed-load transport rates. The present study proposes an approach to separate the calculation of bed-load transport rates for bimodal materials into two independent fractions of sand and gravel, thereby rendering the bed sediment into two unimodal components. This approach is accomplished by decoupling the two fractions through scaling the reference Shields stresses of the sand and gravel modes to match the value of the mode of unimodal materials. Consequently, the contribution of each fraction to bed load can be estimated using a suitable relation derived for unimodal materials. Laboratory and field bed-load data available in the literature are used to examine the validity of the overall approach.