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.     

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.     

Simulating Bed-Load Transport in a Complex Gravel-Bed River

An existing two-dimensional mobile-bed hydrodynamic model has been modified to simulate bed-load transport in a complex gravel-bed river. We investigated the sensitivity of predicted bed load to control parameters, and compared model predictions of flow depth, shear stress, and gravel transport with field measurements made from the river. The predictions are based on concurrent field data of flow discharge, water level, and sediment for model input. The model takes into account multiple-fraction transport rates, and continuously updates the river bed and surface grain-size distribution. The model predictions are in reasonable agreement with field measurements.     

Application of Incomplete Self-Similarity Argument for Predicting Bed-Material Load Discharge

By applying the incomplete self-similarity argument, this study presents a structural analysis of models for predicting bed-material load discharge, which can be formulated consistently according to the number of independent variables considered. The coefficients involved in the proposed models are calibrated with published laboratory and field data (comprising almost 6,600 records). In comparison with the six bed-material formulas that are recommended in the recently updated ASCE manual on sedimentation engineering, the proposed models show significant improvements on the prediction of bed-material load discharge. This study also implies that the model developed, based on regular regression analysis, can be enhanced by considering interaction terms of independent variables.     

Suspended Wash Load Transport of Nonuniform Sediments

The results of an experimental study on transport of suspended wash load through a coarse-bed stream are presented. The experiments were conducted under different concentrations of fine suspended sediment (wash load of uniform size, 0.064 mm diameter) and with three different coarse-bed sediments: two having uniform sizes and one with nonuniform size distribution. For any equilibrium concentration of wash load in suspension, a definite proportion of the wash material was observed to be present within the bed material. No difference is found in this regard between wash load and suspended load transport. Therefore, the relationship, as stated by Samaga et al., for the parameter representing sheltering—exposure and interference effects in the suspended load transport of nonuniform sediments was applied in a modified form by using the present data and the data collected from the literature.     

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.     

Measurement of Bed Load Velocity using an Acoustic Doppler Current Profiler

A new technique has been developed to measure the apparent velocity of bed load (va) using an acoustic Doppler current profiler. The technique involves estimating the bias in bottom tracking due to a moving bottom. Mean va measured at sampling stations in the gravel-bed Fraser River correlated well (r2 = 0.93,?n = 9) with mean bed load transport rates measured using conventional samplers. Mean va was also correlated (r2 = 0.44,?n = 19) with boundary shear stress estimated by a log-law fit to the mean velocity profile. Estimates of va from individual 5 s ensemble averages were extremely variable: the coefficient of variation for a sampling station ranged from 1.0 to 6.4, and 25 min of sampling were required to achieve stable estimates of the mean and coefficient of variation (within 5% error). Variance was due to both real temporal variability of transport and measurement error. The mechanisms that produce this variability are discussed and preliminarily quantified.     

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.     

Particle Densimetric Froude Number for Estimating Sediment Transport

It has been established that for ratios of flow depth to bed particle diameter less than ten (flow on very rough boundaries) neither the Reynolds number of the solid loose particles at a stream bed nor the Shields parameter are adequate variables to predict critical flow conditions for the initiation of motion. A particle densimetric Froude number F? = U/[(s?1)gD]1/2 (where U=mean velocity, s=ratio of sediment and fluid densities, g=acceleration due to gravity, and D=characteristic diameter of bed particle) is here proposed as an alternative criterion to predict hydraulic conditions for the initiation of motion. Values of critical F? were computed after calibration with available experimental data sets. After the critical conditions for the initiation of particle motion were exceeded, transport of bed particles was established. In order to evaluate the performance of a transport equation that contains F? in sediment transport, a set of the most employed formulations to estimate bed material transport in steep slope macrorough flows were tested. The comparison of the results shows that F? can be used to accurately predict sediment discharge.     

Multiple Linear Regression Model for Total Bed Material Load Prediction

A new total bed material load equation that is applicable for rivers in Malaysia was developed using multiple linear regression analyses. A total of 346 hydraulic and sediment data were collected from nine natural and channelized rivers having diverse catchment characteristics in Malaysia. The governing parameters were carefully selected based on literature survey and field experiments, examined and grouped into five categories namely mobility, transport, sediment, shape, and flow resistance parameters. The most influential parameters from each group were selected by using all possible regression model method. The suitable model selection criteria namely the R-square, adjusted R-square, mean square error, and Mallow’s Cp statistics were employed. The accuracy of the derived model is determined using the discrepancy ratio, which is a ratio of the calculated values to the measured values. The best performing models that give the highest percentage of prediction from the validation data were chosen. In general, the newly derived model is best suited for rivers with uniform sediment size distribution with a d50 value within the range of 0.37–4.0 mm and performs better than the commonly used Graf, Yang, and Ackers–White total bed material load equations.     

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.     

Evaluation and Improvement of Bed Load Discharge Formulas based on Helley–Smith Sampling in an Alpine Gravel Bed River

Bed load discharge formulas have been evaluated by analyzing them in relation to measured Helley–Smith data for the gravel-bedded armored Drau River, Austria. Comparison of calculations with measurements leads to ranking of the formulas that depends on the evaluation parameters. The choice of formula is made with respect to our specific aims: the investigation of individual floods requires a different approach from that of long-term budgets. Formula performance is consistently improved when conditions for the threshold of motion are modified according to data measured up on the initiation of motion. Formulas such as those reported by Parker in 1990, Zanke in 1999, and Sun and Donahue in 2000 are capable of coping with partial transport, which is commonly found in Alpine rivers. These formulas therefore provide encouraging results, particularly after the introduction of modifications. The augmentation of field measurements, even if limited in scope, considerably improves the performance of bed load discharge formulas.     

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.     

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.     

Sand Transport in Nile River, Egypt

Measurements of bed-load and suspended-load transport rates were carried out successfully at four cross sections of the Nile River, in Egypt, along the entire length from Aswan to Cairo using a mechanical sampler called the Delft Nile Sampler. The measured transport rates were compared to similar data sets from two other large scale rivers: the Rhine-Waal River in the Netherlands and the Mississippi River in the USA. The bed-load transport rates in the Nile River and in the Rhine-Waal River are in very good agreement. Comparison of suspended transport rates in the Nile River and in the Mississippi River shows that both data sets are complementary, revealing a very consistent trend of suspended transport against current velocity; suspended transport is roughly proportional to (Vav)3?to?4. Three formulas for the prediction of bed-load transport were tested using the Nile data: Meyer-Peter–Muller, Bagnold, and Van Rijn. The prediction formula of Van Rijn produced significantly better results than the other two formulas; the average relative error was about 60%. The formula of Van Rijn was modified to extend it to conditions with slightly nonuniform sediment mixtures by introducing a correction factor for the bed shear parameter. Based on a limited number of flume experiments, the correction factor was found to be dependent on the characteristics of the sediment mixture (d10, d50, d90, and σg). Comparison of bed-load transport measured in the Nile River with computed transport rates of the modified formula showed improved results; the average relative error decreased to about 30%. The formulas of Bagnold and Van Rijn were also used to compute the suspended transport rates in the Nile River. The computed transport rates were found to be within a factor of 2 of measured values; the formula of Bagnold performed slightly better. The total load transport formula of Engelund–Hansen was also successfully used (computed values within a factor of about 2 of measured values).     

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.     

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.     

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.     

Sediment Transport in River Models with Overbank Flows

Some laboratory sediment-transport experiments are described in which a compound channel with a mobile-bed composed of uniform sand with a d50 of 0.88?mm was subjected to overbank flows. The main river channel was monitored to determine the effect of floodplain roughness on conveyance capacity, bed-form geometry, resistance, bed-load transport, and dune migration rate. The floodplain roughness was varied to simulate a wide range of conditions, commensurate with conditions that can occur in a natural river. For a given discharge, the main river channel bed was found to adjust itself to a quasi-equilibrium condition governed by the lateral momentum transfer between the floodplain and main channel flows and the local alluvial resistance relationship appropriate for the proportion of total flow in the main river channel. The sediment transport rate was found to reflect all these influences. The data are summarized in equation form for comparison with other experimental studies and for checking numerical river simulation models.     

Transition between Two Bed-Load Transport Regimes: Saltation and Sheet Flow

In the saltation regime where bed-shear stress is low, bed load moves by sliding, rolling, and saltating along the bed, while in the sheet-flow regime where bed-shear stress is high, it travels by a combination of saltation and sheet flow. In this paper a theoretical model is developed for predicting the onset of the sheet-flow regime as shear stress increases. This model is based on a new variable Pb representing the proportion of grains on the bed that are entrained as bed load. The model yields the equation Pb = 2.56θG3 in which G = 1?θc/θ, θ = dimensionless bed-shear stress; and θc = critical value of θ at which grains begin to move. The equation shows that θt, which is the value of θ at the onset of the sheet-flow regime and is assumed to occur when Pb = 1, is around 0.5 with the exact value controlled by θc. For example, when θc = 0.045, θt = 0.52. The theoretical model is verified by performing a nonlinear regression analysis on data from 285 flume experiments. Additional flume experiments with a high-speed video (HSV) system result in consistent values of θ for the onset of the sheet-flow regime, which support the theoretical model. The HSV images further reveal that: (1) the sheet-flow regime is characterized by granular sheets or laminations; and (2) a zone of mixed saltation and rolling grains exists not only in the saltation regime but also in the sheet-flow regime.