Unified View of Sediment Transport by Currents and Waves. III: Graded Beds

The problem of suspended load and bed load transport in river and coastal flows over graded beds is addressed. Two effects are important: the degree of exposure of the sediment particles of unequal size within a mixture (hiding of smaller particles resting or moving between the larger particles) and the nonlinear dependence of transport on particle diameter. The former effect can be modeled by modifying the critical bed-shear stress through a correction factor and by modifying the effective grain roughness through another correction factor. The modeling of the effective bed-shear stress parameter is studied by using various alternative methods. Based on comparison with suspended load and bed load transport data for graded beds in steady and oscillatory flow, the most promising method is selected. The proposed prediction method is found to work well for the fine sand bed range as well as the coarse sand-gravel bed range.     

Unified View of Sediment Transport by Currents and Waves. II: Suspended Transport

The problem of suspended sediment transport in river and coastal flows is addressed. High-quality field data of river and coastal flows have been selected and clustered into four particle size classes (60–100, 100–200, 200–400, and 400–600?μm). The suspended sand transport is found to be strongly dependent on particle size and on current velocity. The suspended sand transport in the coastal zone is found to be strongly dependent on the relative wave height (Hs/h), particularly for current velocities in the range 0.2–0.5?m/s. The time-averaged (over the wave period) advection–diffusion equation is applied to compute the time-averaged sand concentration profile for combined current and wave conditions. Flocculation, hindered settling, and stratification effects are included by fairly simple expressions. The bed-shear stress is based on a new bed roughness predictor. The reference concentration function has been recalibrated using laboratory and field data for combined steady and oscillatory flow. The computed transport rates show reasonably good agreement (within a factor of 2) with measured values for velocities in the range of 0.6–1.8?m/s and sediments in the range of 60–600?μm. The proposed method underpredicts in the low-velocity range (<0.6?m/s). A new simplified transport formula is presented, which can be used to obtain a quick estimate of suspended transport. The modeling of wash load transport in river flow based on the energy concept of Bagnold shows that an extremely large amount of very fine sediment (clay and very fine silt) can be transported by the flow.     

Unified View of Sediment Transport by Currents and Waves. IV: Application of Morphodynamic Model

The TR2004 transport formulations for clay, silt, and sand as proposed in Parts 1 and 2 have been implemented in morphodynamic models to predict bed level changes. These models have been verified using various laboratory and field data cases concerning coastal flow in offshore and near-shore zones. Furthermore, the model has been applied to two complicated sediment environments concerning the flow around a spurdike in a river and the tidal flow of cohesive sediments in the Yangtze Estuary in China. Overall, it is concluded that the morphodynamic models using default settings performs reasonably well. The applied scaling factors of the sediment transport model are in the generally accepted range of 0.5–2.     

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.     

Effect of Seepage-Induced Nonhydrostatic Pressure Distribution on Bed-Load Transport and Bed Morphodynamics

Bed-load transport is commonly evaluated in the condition of a hydrostatic pressure distribution of the flow field; while this condition is reasonable for quasi-steady, quasi-uniform rectilinear flows, it cannot be satisfied in a large variety of flow conditions, i.e., near an obstacle as in the case of a bridge pier. The dimensionless Shields number, which contains the assumption of a hydrostatic pressure distribution in its denominator, therefore cannot be strictly applied to evaluate bed-load transport in all the configurations where nonhydrostatic pressure distributions are observed. In the present work, a generalization of the Shields number is proposed for the case of nonhydrostatic pressure distribution produced by groundwater flow. Experiments showing the effects of vertical groundwater flow on the bed morphodynamics are presented. The comparison between the experimental observations and numerical results, obtained by means of a morphodynamic model which employs the new formulation of the Shields number, suggests that the proposed generalization of the Shields number is able to account the effect of the nonhydrostatic pressure distribution on the bed-load transport.     

Simulation of Bed-Load Dispersion Process

Two general dispersion models suitable for nonequilibrium bed-load transport were constructed. The first one, called the P model, is based on the probability of migration for specific groups of sediment particles. The second one, called the D model, is derived from the advection equation discretized in finite-difference form, which is equivalent to the general dispersion equation. By comparing these models, it is found that the D model can be treated like the P model in some respects. The Courant number, Cr, in the D model has the same physical meaning as the probability of migration, P, in the P model. Although the D model and P model were based on different concepts, the simulated bed-load transport rates, which result from their application, are the same. Therefore, the dispersion equation was replaced by the numerical algorithm of the advection equation (D model) to examine several dispersion phenomena of bed-load transport. To explore further the nonequilibrium dispersion process, a series of flume experiments was conducted by using color-painted fine gravels. Having compared model simulation results and experimental data, it is shown that the models derived in this study have a reasonably good agreement with the experimental results. In summary, this study has indirectly proven that the D model, which is equivalent to the dispersion equation, is capable of simulating the nonequilibrium bed-load transport.     

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.     

Effect of Coarse Surface Layer on Bed-Load Transport

Existing bed-load transport formulas may overestimate the transport rate in mountain rivers by two orders of magnitude or more. Recently published field data sets provide an opportunity to take a fresh look at the bed-load transport relationship and it is hypothesized that the overestimate is due to a failure to account for the effect of a coarse surface layer of bed material inhibiting the release of fine subsurface material. Bed-load transport is determined as gs = aρ(q?qc) where q=water discharge per unit width; qc=critical value for initiation of bed material movement; ρ=water density; and a=coefficient. The gs/q relationship is typically piecewise linear, characterized by two transport phases with, respectively, low and high rates of change. Twenty-one flume and 25 field data sets were used to quantify the relationship for Phase 2. The flume data confirm the dependence of a on S1.5, where S=channel slope, in agreement with earlier studies. The field data additionally show that a varies inversely with the degree of bed armoring, given by the ratio of surface to subsurface bed material size. The finding is consistent with the hypothesis and suggests the need to account for the bed material supply limitation in the bed-load transport formula. However, the available data are not entirely sufficient to rule out an alternative dependency, or codependency, on flow resistance. The critical conditions for initiation of Phase 2 transport are also quantified as a function of bed material size and channel slope. The resulting set of equations allows a more accurate estimation of Phase 2 bed-load transport rates. However, the equations are empirical and should be restricted for use within the range of conditions used in their development, to determine mean rather than instantaneous transport rates and to determine bulk transport rates, not transport by size fraction.     

Field Assessment of Alternative Bed-Load Transport Estimators

Measurement of near-bed sediment velocities with acoustic Doppler current profilers (ADCPs) is an emerging approach for quantifying bed-load sediment fluxes in rivers. Previous investigations of the technique have relied on conventional physical bed-load sampling to provide reference transport information with which to validate the ADCP measurements. However, physical samples are subject to substantial errors, especially under field conditions in which surrogate methods are most needed. Comparisons between ADCP bed velocity measurements with bed-load transport rates estimated from bed-form migration rates in the lower Missouri River show a strong correlation between the two surrogate measures over a wide range of mild to moderately intense sediment transporting conditions. The correlation between the ADCP measurements and physical bed-load samples is comparatively poor, suggesting that physical bed-load sampling is ineffective for ground-truthing alternative techniques in large sand-bed rivers. Bed velocities measured in this study became more variable with increasing bed-form wavelength at higher shear stresses. Under these conditions, bed-form dimensions greatly exceed the region of the bed ensonified by the ADCP, and the magnitude of the acoustic measurements depends on instrument location with respect to bed-form crests and troughs. Alternative algorithms for estimating bed-load transport from paired longitudinal profiles of bed topography were evaluated. An algorithm based on the routing of local erosion and deposition volumes that eliminates the need to identify individual bed forms was found to give results similar to those of more conventional dune-tracking methods. This method is particularly useful in cases where complex bed-form morphology makes delineation of individual bed forms difficult.     

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.     

Bed-Load Sediment Transport on Large Slopes: Model Formulation and Implementation within a RANS Solver

Standard bed-load sediment-transport formulas are extended using basic mechanical principles to include gravitational influence on large slopes of arbitrary orientation. The resulting sediment fluxes are then incorporated into a morphodynamics model in a general-purpose, three-dimensional, finite-volume, Reynolds-averaged Navier–Stokes (RANS) code. Major features are: (1) the downslope component of weight is combined with the fluid stress to form an effective bed stress (similar to the work of Wu in 2004); (2) the critical effective stress is reduced in proportion to the component of gravity normal to the slope; (3) a simple flux-based model for avalanching is implemented as a numerical means of preventing the local slope from exceeding the angle of repose; (4) an entirely vectorial formulation of bed-load transport is developed to account for arbitrary surface orientation; and (5) methods for reducing numerical instability in the morphodynamics equation are described. Sample computations are shown for scour and accretion in a channel bend and for the movement of sand mounds on erodible and nonerodible bases.     

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.     

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.     

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.     

Microforms in Gravel Bed Rivers: Formation, Disintegration, and Effects on Bedload Transport

This research aims to advance current knowledge on cluster formation and evolution by tackling some of the aspects associated with cluster microtopography and the effects of clusters on bedload transport. The specific objectives of the study are (1) to identify the bed shear stress range in which clusters form and disintegrate, (2) to quantitatively describe the spacing characteristics and orientation of clusters with respect to flow characteristics, (3) to quantify the effects clusters have on the mean bedload rate, and (4) to assess the effects of clusters on the pulsating nature of bedload. In order to meet the objectives of this study, two main experimental scenarios, namely, Test Series A and B (20 experiments overall) are considered in a laboratory flume under well-controlled conditions. Series A tests are performed to address objectives (1) and (2) while Series B is designed to meet objectives (3) and (4). Results show that cluster microforms develop in uniform sediment at 1.25 to 2 times the Shields parameter of an individual particle and start disintegrating at about 2.25 times the Shields parameter. It is found that during an unsteady flow event, effects of clusters on bedload transport rate can be classified in three different phases: a sink phase where clusters absorb incoming sediment, a neutral phase where clusters do not affect bedload, and a source phase where clusters release particles. Clusters also increase the magnitude of the fluctuations in bedload transport rate, showing that clusters amplify the unsteady nature of bedload transport. A fourth-order autoregressive, autoregressive integrated moving average model is employed to describe the time series of bedload and provide a predictive formula for predicting bedload at different periods. Finally, a change-point analysis enhanced with a binary segmentation procedure is performed to identify the abrupt changes in the bedload statistic characteristics due to the effects of clusters and detect the different phases in bedload time series using probability theory. The analysis verifies the experimental findings that three phases are detected in the bedload rate time series structure, namely, sink, neutral, and source.     

Validation of Existing Bed Load Transport Formulas Using In-Sewer Sediment

Granular sediment in pipe inverts has been reported in a number of sewer systems in Europe. Given the range of flow conditions and particle characteristics of inorganic sewer sediments the mode of transport may normally be considered as bed load. Current commercial software for modeling the erosion and transport of sediments in sewer pipes still utilizes well-known, or modified versions of transport equations that were derived for transport of noncohesive sediment in alluvial streams. In this paper the performances of the equations of Ackers and White (originally developed for the transport of river sediments) and of May (derived from laboratory pipe experiments) are examined against two separate data sets. One set is from laboratory erosion experiments on sewer sediment obtained in Paris. A second data set has bed load transport rate measurements recorded in a sewer inlet pipe. The formulas were selected because of their widespread use in the prediction of in-sewer sediment transport both in commercial software and in the latest United Kingdom design guidance for new sewers. The results indicated that both the relationships performed poorly, even in such well-controlled conditions. These formulas have significant difficulties in predicting the erosion thresholds and fractional transport rates for non-uniformly sized in-sewer sediments. An empirical formula to adjust the threshold of motion for individual grain size fractions was developed which significantly improved predictions. Although such techniques have been used in gravel bed rivers, the threshold adjustment function for in-sewer deposits was significantly different from these previously published for fluvial gravels, indicating that a direct transfer of fluvial relationships to sewers may be inappropriate without further research.     

Response of Velocity and Turbulence to Sudden Change of Bed Roughness in Open-Channel Flow

The experimental study shows how an open-channel flow would respond to a sudden change (from smooth to rough) in bed roughness. Using a two-dimensional acoustic Doppler velocimeter and a laser Doppler velocimeter, the velocity, turbulent intensities, and Reynolds stress profiles at different locations along a laboratory flume were measured. Additionally, the water surface profile was also measured using a capacitance-type wave height meter. The experimental data show the formation of an internal boundary layer as a result of the step change in bed roughness. The data show that this boundary layer grows much more rapidly than that formed in close-conduit flows. The results also show that the equivalent bed roughness, bed-shear stress, turbulent intensities, and Reynolds stress change gradually over a transitional region, although the bed roughness changes abruptly. The behavior is different from that observed in close-conduit flows, where an overshooting property—which describes the ability of the bed-shear stress to attain a high-peak value over the section with the larger roughness, was reported. A possible reason for the difference is the variation of the water surface profile when an open-channel flow is subjected to a sudden change in bed roughness.     

Experimental and Numerical Investigation of Bed-Load Transport under Unsteady Flows

The dynamic behavior of bed-load sediment transport under unsteady flow conditions is experimentally and numerically investigated. A series of experiments are conducted in a rectangular flume (18?m in length, 0.80?m in width) with various triangular and trapezoidal shaped hydrographs. The flume bed of 8?cm in height consists of scraped uniform small gravel of D50 = 4.8??mm. Analysis of the experimental results showed that bed-load transport rates followed the temporal variation of the triangular and trapezoidal hydrographs with a time lag on the average of 11 and 30?s, respectively. The experimental data were also qualitatively investigated employing the unsteady-flow parameter and total flow work index. The analysis results revealed that total yield increased exponentially with the total flow work. An original expression which is based on the net acceleration concept was proposed for the unsteadiness parameter. Analysis of the results then revealed that the total yield increased exponentially with the increase in the value of the proposed unsteadiness parameter. Further analysis of the experimental results revealed that total flow work has an inverse exponential variation relation with the lag time. A one-dimensional numerical model that employs the governing equations for the conservation of mass for water and sediment and the momentum was also developed to simulate the experimental results. The momentum equation was approximated by the diffusion wave approach, and the kinematic wave theory approach was employed to relate the bed sediment flux to the sediment concentration. The model successfully simulated measured sedimentographs. It predicted sediment yield, on the average, with errors of 7% and 15% of peak loads for the triangular and trapezoidal hydrograph experiments, respectively.     

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.     

Maximum Level and Time to Peak of Dam-Break Waves on Mobile Horizontal Bed

This experimental study focuses the influence of bed material mobility and initial downstream water level on maximum water level and time to peak of dam-break waves. It covers horizontal bed conditions on fixed bed, sand bed, and pumice bed. Results include water surface level time evolution, maxima wave levels and time to peak. The influence of bed material mobility and downstream water level was identified and characterized, stressing the importance of using mathematical models with appropriate sediment transport formulations instead of purely hydrodynamic models to simulate dam-break waves on mobile bed channels.