One-Dimensional Numerical Model for Nonuniform Sediment Transport under Unsteady Flows in Channel Networks

In this study, the proposed one-dimensional model simulates the nonequilibrium transport of nonuniform total load under unsteady flow conditions in dendritic channel networks with hydraulic structures. The equations of sediment transport, bed changes, and bed-material sorting are solved in a coupling procedure with a direct solution technique, while still decoupled from the flow model. This coupled model for sediment calculation is more stable and less likely to produce negative values for bed-material gradation than the traditional fully decoupled model. The sediment transport capacity is calculated by one of four formulas, which have taken into consideration the hiding and exposure mechanism of nonuniform sediment transport. The fluvial erosion at bank toes and the mass failure of banks are simulated to complement the modeling of bed morphological changes in channels. The tests in several cases show that the present model is capable of predicting sediment transport, bed changes, and bed-material sorting in various situations, with reasonable accuracy and reliability.     

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.     

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.     

Numerical Modeling of Bed Deformation in Laboratory Channels

A depth-average model using a finite-volume method with boundary-fitted grids has been developed to calculate bed deformation in alluvial channels. The model system consists of an unsteady hydrodynamic module, a sediment transport module and a bed-deformation module. The hydrodynamic module is based on the two-dimensional shallow water equations. The sediment transport module is comprised of semiempirical models of suspended load and nonequilibrium bedload. The bed-deformation module is based on the mass balance for sediment. The secondary flow transport effects are taken into account by adjusting the dimensionless diffusivity coefficient in the depth-average version of the k–ε turbulence model. A quasi-three-dimensional flow approach is used to simulate the effect of secondary flows due to channel curvature on bed-load transport. The effects of bed slope on the rate and direction of bed-load transport are also taken into account. The developed model has been validated by computing the scour hole and the deposition dune produced by a jet discharged into a shallow pool with movable bed. Two further applications of the model are presented in which the bed deformation is calculated in curved alluvial channels under steady- and unsteady-flow conditions. The predictions are compared with data from laboratory measurements. Generally good agreement is obtained.     

Numerical Model for Channel Flow and Morphological Change Studies

In this paper a depth-integrated 2D hydrodynamic and sediment transport model, CCHE2D, is presented. It can be used to study steady and unsteady free surface flow, sediment transport, and morphological processes in natural rivers. The efficient element method is applied to discretize the governing equations, and the time marching technique is used for temporal variations. The moving boundaries were treated by locating the wet and dry nodes automatically in the cases of simulating unsteady flows with changing free surface elevation in channels with irregular bed and bank topography. Two eddy viscosity models, a depth-averaged parabolic model and a depth-averaged mixing length model, are used as turbulent closures. Channel morphological changes are computed with considerations of the effects of bed slope and the secondary flow in curved channels. Physical model data have been used to verify this model with satisfactory results. The feasibility studies of simulating morphological formation in meandering channels and flows in natural streams with in-stream structures have been conducted to demonstrate its applicability to hydraulic engineering research∕design studies of stream stabilization and ecological quality among other problems.     

Two-Dimensional Nonequilibrium Noncohesive and Cohesive Sediment Transport Model

The purpose of this paper is to develop an unsteady 2D depth-averaged model for nonuniform sediment transport in alluvial channels. In this model, the orthogonal curvilinear coordinate system is adopted; the transport mechanisms of cohesive and noncohesive sediment are both embedded; the suspended load and bed load are treated separately. In addition, the processes of hydraulic sorting, armoring, and bed consolidation are also included in the model. The implicit two-step split-operator approach is used to solve the flow governing equations and the coupling approach with iterative method are used to solve the mass-conservation equation of suspended sediment, mass-conservation equation of active-layer sediment, and global mass-conservation equation for bed sediment simultaneously. Three sets of data, including suspension transport, degradation and aggradation cases for noncohesive sediment, and aggradation, degradation, and consolidation cases for cohesive sediment, have been demonstrated to show the rationality and accuracy of the model. Finally, the model is applied to evaluate the desilting efficiency for Ah Gong Diann Reservoir located in Taiwan to show its applicability.     

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.     

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.     

Monitoring River Channel and Flume Surfaces with Digital Photogrammetry

This paper describes and illustrates a technique for high resolution monitoring of the surface morphology of water-worked sediments. The monitoring uses close-range digital photogrammetry. While photogrammetry is a long-established technique, more recent developments in digital photogrammetry allow application in fluvial research to be highly cost effective in both flume and natural river channel studies. Results are presented that involve two scales of laboratory flume: a smaller-scale application associated with sediment sorting processes in a straight channel; and a larger-scale application involving sediment transport and bed material feedbacks in a meandering channel subject to overbank flows. A preliminary assessment of data quality is undertaken with encouraging results. The precision of elevation estimates corresponds to the scale of the imagery acquired and hence may be controlled by design of the image acquisition process.     

Numerical Model for Sediment Transport and Bed Degradation in the Yangtze River Channel Downstream of Three Gorges Reservoir

This paper presents a two-dimensional morphological model for unsteady flow and both suspended-load and bed-load transport of multiple grain size to simulate transport of graded sediments downstream from the Three Gorges Reservoir. The model system includes a hydrodynamic module and a sediment module. The hydrodynamic module is based on the depth-averaged shallow water equations in orthogonal curvilinear coordinates. The sediment module describing nonuniform sediment transport is developed to include nonequilibrium transport processes, bed deformation, and bed material sorting. The model was calibrated using field observations through application to a 63-km-long alluvial river channel on the middle Yangtze River in China. A total of 16 size groups and a loose layer method of three sublayers were considered for the transport of the nonuniform bed materials in a long-term simulation. Predictions are compared with preliminary results of field observations and factors affecting the reliability of the simulated results are discussed. The results may be helpful to the development of more accurate simulation models in the future.     

Closed-Conduit Bed-Form Initiation and Development

Nonintrusive measurement of closed-conduit erodible-bed development was undertaken for 12 experiments of ranges of flow strengths and sediment (solids) sizes. Analogous to open-channel flows, wavelets on the sediment bed of a closed-conduit are instigated by discontinuities in the bed, with wavelet lengths λ for laminar and turbulent open-channel and closed-conduit flows given by λ = 175d0.75, where λ and sediment size d are in millimeters. For closed-conduit flows, ripples, and dunes grow from these wavelets (at rates increasing with increasing flow strength, and utilizing the mechanisms of bed-form coalescence and throughpassing) to limiting lengths, heights, steepnesses, and bed friction factors that are approximately maintained or possibly decrease thereafter. Limitation of free-surface deformation results in increased rates of bed-wave development for closed-conduit flows in comparison to open-channel flows. Measured results indicate that equilibrium closed-conduit ripple and dune magnitudes can be predicted using relations derived for equivalent open-channel flows. The present findings are of particular relevance for understanding and modeling engineering activities ranging from dredging to transport of solids in stormwater and sewer systems, bed-form transport of solids in closed conduits influencing (potentially markedly) conduit conveyance, rate of solids transport, and system head losses for such flows.     

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.     

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.     

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.     

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.     

Numerical Modeling of Breach Erosion of River Embankments

The process of breach erosion of river embankments depends on the interaction among flow, sediment transport, and the corresponding morphological changes. Levees often consist of noncohesive material with a wide range of grain sizes. The dam material is mainly eroded due to the transport capacity of the overtopping water. Both bed load and suspended load are of importance. For breach formation, the lateral erosion due to slope instabilities has a significant impact. A depth averaged, two-dimensional numerical model was developed to account for these processes. The sensitivity of the discharge through the breach related to different processes and material parameters was investigated and compared to experimental and field data. The results show that the most sensitive parameter of an erosion-based dike-breach simulation is the breach side-slope angle which determines the lateral erosion. The application of the described Model 2dMb to different embankment failures at the Elbe River illustrates its capability in simulating overtopping breaching.     

Numerical Morphological Modeling of Open-Check Dams

Open-check dams are built in mountain streams to control sediment transport during a flood. Sediment passes through them at the lowest discharges, whereas deposition occurs during the highest discharges. Open-check dams are currently designed based mainly on construction experience. Modeling of hydraulics and bed morphology in check dams involves mixed flows (supercritical and subcritical) as well as discontinuities such as hydraulic jumps. In this paper an unsteady coupled numerical mobile-bed model that can tackle rapid varying flows and discontinuities is applied. The numerical technique is based on the classical staggered grids and implicit integration schemes, together with a proper mass and momentum balance. The 1D numerical model is successfully verified with experimental data of slit-check dams. The applicability of the model in the design of open-check dams is also illustrated.     

Formula for Sediment Transport in Rivers, Estuaries, and Coastal Waters

The aim of the present study is to develop a formula for the relationship between flow strength and sediment discharge. The appropriate definition of energy dissipation rate E in the theorem of Bagnold in 1966 is discussed and it is found that the sediment transport rate gt in unidirectional flows can be well predicted when E is defined as the product of bed shear stress τ0 and near bed velocity u*′. Then the linear relationship between u*′E and the sediment transport rate is examined using measured data. The good agreement between measured and predicted values indicates that the phenomena of sediment transport can be reasonably described by the near bed flow characteristics. As the hydrodynamic modelers are able to calculate the bed shear stress and near bed velocity in various cases now, thus the new relationship may provide numerical modelers a tool to calculate the sediment transport in rivers, estuaries and coastal waters. To prove this, the simplified analytical expressions of E and u*′ in wave-current flows and coastal waters are derived, the results are checked with the available data over a wide range of flow conditions; and good agreements are achieved, indicating that the presumption is valid in the cases investigated.     

Predicting Boundary Shear Stress and Sediment Transport over Bed Forms

To estimate bed-load sediment transport rates in flows over bed forms such as ripples and dunes, spatially averaged velocity profiles are frequently used to predict mean boundary shear stress. However, such averaging obscures the complex, nonlinear interaction of wake decay, boundary-layer development, and topographically induced acceleration downstream of flow separation and often leads to inaccurate estimates of boundary stress, particularly skin friction, which is critically important in predicting bed-load transport rates. This paper presents an alternative methodology for predicting skin friction over 2D bed forms. The approach is based on combining the equations describing the mechanics of the internal boundary layer with semiempirical structure functions to predict the velocity at the crest of a bedform, where the flow is most similar to a uniform boundary layer. Significantly, the methodology is directed toward making specific predictions only at the bed-form crest, and as a result it avoids the difficulty and questionable validity of spatial averaging. The model provides an accurate estimate of the skin friction at the crest where transport rates are highest. Simple geometric constraints can be used to derive the mean transport rates as long as bed load is dominant.