Estimation of the Washout Depth of Fine Sediments from a Granular Bed

An exponential distribution of the bed-pressure fluctuations is used to estimate the depth within a porous gravel bed from which fine sediment of a given size can be removed. The coarsest grain size of the fine sediment that might be washed out is of O(10?1) in relation to both the gravel grain size and the equivalent grain roughness. A higher equivalent grain roughness results to a larger absolute cleaning depth, whereas the averaged gravel grain size is seen to be less important. The results are successfully tested for plausibility against the grain size distributions of an armored gravel bed and its underlaying bimodal layer as found in situ in the river Rhine. However, qualitative and quantitative experimental data for an in-depth validation remain to be performed.     

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. 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. 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.     

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.     

Method for Estimating Sediment Transport in Ice-Covered Channels

A method is proposed for estimating rates of sediment transport in ice-covered alluvial channels. The method extends existing, open-water procedures for estimating rates of sediment transport to conditions of ice-covered flow. A key aspect of the method is the assessment of flow resistance attributable to bed-surface drag. That assessment is used to estimate rates of bed load and suspended load, and thereby total bed-sediment transport rate. Estimation of ice-covered suspended load additionally entails an approximation whereby open-water suspended load is scaled in proportion to the ratio of a reference sediment concentration for ice-covered flow relative to that for open-water flow. The reference concentration is calculated in terms of bed-load rate and shear velocity attributed to bed-surface drag. Flume data are used to develop the method and tentatively verify it. Field verification of the method presently is hampered by the absence of field data on bed sediment transport in ice-covered channels.     

Modeling Sediment Transport Using Depth-Averaged and Moment Equations

A 1D mathematical model to calculate bed variations in alluvial channels is presented. The model is based on the depth-averaged and moment equations for unsteady flow and sediment transport in open channels. Particularly, the moment equation for suspended sediment transport is originally derived by the assumption of a simple vertical distribution for suspended sediment concentration. By introducing sediment-carrying capacity, suspended sediment concentration can be solved directly from sediment transport and its moment equations. Differential equations are then solved by using the control-volume formulation, which has been proven to have good convergence. Numerical experiments are performed to test the sensitivity of the calibrated coefficients α and k in the modeling of the bed deposition and erosion. Finally, the computed results are compared with available experimental data obtained in laboratory flumes. Comparisons of this model with HEC-6 and other numerical models are also presented. Good agreement is found in the comparisons.     

One-Dimensional Modeling of Dam-Break Flow over Movable Beds

A one-dimensional model has been established to simulate the fluvial processes under dam-break flow over movable beds. The hydrodynamic model adopts the generalized shallow water equations, which consider the effects of sediment transport and bed change on the flow. The sediment model computes the nonequilibrium transport of bed load and suspended load. The effects of sediment concentration on sediment settling and entrainment are considered in determining the sediment settling velocity and transport capacity. In particular, a correction factor is proposed to modify the Van Rijn formulas of equilibrium bed-load transport rate and near-bed suspended-load concentration for the simulation of sediment transport under high-shear flow conditions. The governing equations are solved by an explicit finite-volume method with the first-order upwind scheme for intercell fluxes. The model has been tested in two experimental cases, with fairly good agreement between simulations and measurements. The sensitivities of the model results to parameters such as the sediment nonequilibrium adaptation length, Manning’s roughness coefficient and the proposed correction factor have been verified. The proposed model has also been compared to an existing model and the results indicate the new model is more reliable.     

3D Numerical Simulation for Water Flows and Sediment Deposition in Dam Areas of the Three Gorges Project

This paper presents a three-dimensional (3D) mathematical model for suspended load transport in turbulent flows. Based on the stochastic theory of turbulent flow proposed by Dou, numerical schemes of Reynolds stresses for anisotropic turbulent flows are obtained. Instead of a logarithmic law, a specific wall function is used to describe the velocity profile close to wall boundaries. The equations for two-dimensional suspended load motion and sorting of bed material have been improved for a 3D case. Numerical results are in good agreement with the measured data of the Gezhouba Project. The present method has been employed to simulate sediment erosion and deposition in the vicinity of the Three Gorges Dam. The size distribution of the deposits and bed material, and flow and sediment concentration at different times and elevations, are predicted. The results agree well with the observations in physical experiments. Thus, a new method is established for 3D simulation of sediment motion in the vicinity of dams.     

Comparison of Settling-Velocity-Based Formulas for Threshold of Sediment Motion

The critical condition for incipient sediment motion is formulated in this note based on the settling velocity. The formula obtained is simple, relating the ratio of critical shear velocity to settling velocity to the dimensionless sediment diameter. Comparisons are then made with other settling-velocity based formulas available in the literature. To facilitate the computation of the effective near-bed velocity at the threshold condition, a generalized law-of-the-wall function is proposed for predicting the velocity distribution under various boundary conditions. This study demonstrates that the settling velocity is equivalent to the critical near-bed velocity, which is experienced by a typical bed sediment particle under the threshold condition, but only for large sediment sizes such as sand and gravel. Comparison results show that Yang’s formula is suitable for flows with small flow depth relative to sediment size while Le Roux’s formula may overestimate the threshold condition for fine particles by up to 30%.     

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.     

Modeling Nonuniform Suspended Sediment Transport in Alluvial Rivers

Problems and difficulties in modeling sediment transport in alluvial rivers arise when one uses the theory of equilibrium transport of uniform sediment to simulate riverbed variation. A two-dimensional mathematical model for nonuniform suspended sediment transport is presented to simulate riverbed deformation. Through dividing sediment mixture into several size groups in which the sediment particles are thought to be uniform, the nonuniformity and the exchange between suspended sediment and bed material are considered. The change of concentration along the flow direction, size redistribution, and cross-sectional bed variation can then be described reasonably well by the model. In simulating the flow field with big dry-wet flats, moving boundary problems are solved very well by introducing a so-called finite-slot technique. Verification with laboratory data shows that the model has a good ability to simulate channel bed variations. Last, the model was applied to a real alluvial river system. Variables such as water level, sediment concentration, suspended sediment size distribution, and riverbed variation were obtained with encouraging results.     

Numerical Model of Turbidity Currents with a Deforming Bottom Boundary

A numerical model of turbidity currents with a deforming bottom boundary has been developed. The model predicts the vertical structure of the flow velocity and concentration as well as change in the bed level due to erosion and deposition of suspended sediment. The Reynolds-averaged Navier–Stokes equations for dilute suspension have been solved using a finite volume method. The bottom boundary and the grid system are allowed to adjust in response to sediment deposition and entrainment during the computation. The model has been applied to simulate the evolution of a conservative saline density current and turbidity currents along an 11.6?m long flume that includes a slope followed by a horizontal bed. The model successfully simulates the evolution of the currents. Model results have been compared with the experimental data. Good similarity profiles of velocity and excess density or suspended sediment concentration are obtained at both the upstream supercritical and the downstream subcritical flow regions. A turbulent Schmidt number larger than one has been found to be appropriate for providing a good match with the experimental data. Changes in bed level predicted by the model have also been found to be in agreement with the experiment data.     

Depth-Averaged Two-Dimensional Numerical Modeling of Unsteady Flow and Nonuniform Sediment Transport in Open Channels

A depth-averaged two-dimensional (2D) numerical model for unsteady flow and nonuniform sediment transport in open channels is established using the finite volume method on a nonstaggered, curvilinear grid. The 2D shallow water equations are solved by the SIMPLE(C) algorithms with the Rhie and Chow’s momentum interpolation technique. The proposed sediment transport model adopts a nonequilibrium approach for nonuniform total-load sediment transport. The bed load and suspended load are calculated separately or jointly according to sediment transport mode. The sediment transport capacity is determined by four formulas which are capable of accounting for the hiding and exposure effects among different size classes. An empirical formula is proposed to consider the effects of the gravity on the sediment transport capacity and the bed-load movement direction in channels with steep slopes. Flow and sediment transport are simulated in a decoupled manner, but the sediment module adopts a coupling procedure for the computations of sediment transport, bed change, and bed material sorting. The model has been tested against several experimental and field cases, showing good agreement between the simulated results and measured data.     

Erosion of the Upper Layer of Cohesive Sediments: Characterization of Some Properties

A recent companion paper reported an experimental protocol used to analyze sediment properties. This protocol identified for both freshwater and marine sediments a surface layer with specific dynamic properties (critical erosion shear stresses in the range 0.025–0.05?N?m?2) and a second layer with critical erosion shear stresses about ten times larger. The present study compares these former results with recent work which extended the applicability domain of the Shields diagram to very fine particles. The surface layer is shown to consist in fine and unconsolidated sediments that behave like noncohesive material whereas the second layer is characterized as being cohesive. The surface layer is mainly representative of recent deposits of suspended particles. This points out the existence of a fluffy layer of fine sized particles resting near the bed, with specific erosion characteristics, which has to be considered separately when studying sediment properties.     

Equilibrium Near-Bed Concentration of Suspended Sediment

A new approach is presented for calculating the equilibrium near-bed concentration of suspended sediment in an alluvial channel flow. It is formulated from the balance between bed sediment entrainment and suspended sediment deposition across the near-bed boundary. The entrainment flux is determined making use of a turbulent bursting outer-scale-based function and the flux of deposition by the product of near-bed concentration and hindered settling velocity of sediment. A number of flume data records in the literature are analyzed to calibrate and verify the present approach. The observed near-bed concentrations for the data records are obtained by first isolating the suspended load transport rate from the observed total load transport rate using Engelund and Fredsoe's bed-load formula and then equating the suspended load transport rate to the shape integration of Dyer and Soulsby. The present approach is shown to perform satisfactorily compared to the results of data analysis. It is found that the near-bed concentration is evidently dependent on sediment particle size in addition to the Shields parameter due to skin friction. This finding seems to challenge previous relationships that simply represent the near-bed concentration as empirical functions of the purely skin-friction-related Shields parameter.     

Effect of Sand Supply on Transport Rates in a Gravel-Bed Channel

In a series of flume experiments using constant discharge, flow depth, and gravel feed rate, sand feed rates were varied from 0.16 to 6.1 times that of gravel. The bed slope decreased with increasing sand supply, indicating that the gravel could be transported at the same rate, along with increasing amounts of sand, at smaller shear stresses. Prediction of river response to an increase in sediment supply requires prediction of mutual changes in bed composition and transport, and therefore a transport model defined in terms of the grain size of the bed surface. A recent model provides satisfactory prediction of the experimental observations and indicates the general response of gravel beds to increased sand supply. An increase in sand supply may increase the sand content of the river bed and the mobility of gravel fractions, which can lead to bed degradation and preferential evacuation of these sediments from the river.     

Modeling the Effect of Flow and Sediment Transport on White Sturgeon Spawning Habitat in the Kootenai River, Idaho

Kootenai River white sturgeon spawn in an 18-km reach of the Kootenai River, Id. Since completion of Libby Dam upstream from the spawning reach in 1972, 1974 is the only year with documented significant recruitment of juvenile fish. Where successful in other rivers, white sturgeon spawn over clean coarse material of gravel size or larger. The channel substrate in the current (2008) 18-km spawning reach is composed primarily of sand and some buried gravel; within a few kilometers upstream there is an extended reach of clean gravel, cobble, and bedrock. We used a quasi-three-dimensional flow and sediment-transport model along with the locations of collected sturgeon eggs as a proxy for spawning location from 1994 to 2002 to gain insight into spawning-habitat selection in a reach which is currently unsuitable due to the lack of coarse substrate. Spatial correlations between spawning locations and simulated velocity and depth indicate fish select regions of higher velocity and greater depth within any river cross section to spawn. These regions of high velocity and depth occur in the same locations regardless of the discharge magnitude as modeled over a range of pre- and postdam flow conditions. A flow and sediment-transport simulation shows high discharge, and relatively long-duration flow associated with predam flow events is sufficient to scour the fine sediment overburden, periodically exposing existing lenses of gravel and cobble as lag deposits in the current spawning reach. This is corroborated by video observations of bed surface material following a significant flood event in 2006, which show gravel and cobble present in many locations in the current spawning reach. Thus, both modeling and observations suggest that the relative rarity of extremely high flows in the current regulated flow regime is at least partly responsible for the lack of successful spawning; in the predam flow regime, frequent high flows removed the fine sediment overburden, unveiling coarse material and providing suitable substrate in the current spawning reach.     

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.