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.     

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.     

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 Modeling of Flow and Sediment Transport in Open Channels

A 3D numerical model for calculating flow and sediment transport in open channels is presented. The flow is calculated by solving the full Reynolds-averaged Navier-Stokes equations with the k ? ε turbulence model. Special free-surface and roughness treatments are introduced for open-channel flow; in particular the water level is determined from a 2D Poisson equation derived from 2D depth-averaged momentum equations. Suspended-load transport is simulated through the general convection-diffusion equation with an empirical settling-velocity term. This equation and the flow equations are solved numerically with a finite-volume method on an adaptive, nonstaggered grid. Bed-load transport is simulated with a nonequilibrium method and the bed deformation is obtained from an overall mass-balance equation. The suspended-load model is tested for channel flow situations with net entrainment from a loose bed and with net deposition, and the full 3D total-load model is validated by calculating the flow and sediment transport in a 180° channel bend with movable bed. In all cases, the agreement with measurements is generally good.     

Effects of Lifting Force on Bed Topography and Bed-Surface Sediment Size in Channel Bend

In bed-load sediment transport, the lifting force plays an important role in reducing the friction between sediment particles and the bed surface, and it makes particle transportation by the shear force easier. Because the lifting force is related to vorticity, a three-dimensional (3D) numerical model incorporating large eddy simulations was applied to simulate the vorticity field in a channel bend. The results show that the distribution of vorticity is highly nonuniform, and it can lead to significant variations in lifting force and bed-load sediment transport per unit width in a channel bend. Relevant theories are modified on the basis of physical reasoning and then incorporated into numerical models to investigate the lifting-force effects on the bed topography and bed-surface sediment size gradation in a channel bend. With the lifting-force effects considered, it is shown that the errors in simulated bed topography can be reduced by approximately 40% and in bed-surface sediment size by 50%.     

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.     

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.     

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.     

Prediction of Concerted Sediment Flushing

A proprietary one-dimensional numerical model was developed for predicting the amounts of sediment flushed and deposited in the reservoirs in series, the bed evolutions, and variations of the suspended solids concentrations along a river during the concerted sediment flushing events. The model consists of a flow movement module and sediment transport module in which the bed material load is taken as sediment mixture. The nonuniform property of the bed material load is modeled by the introduction of a mixing layer, transition layer, and deposition strata. The model was calibrated on the basis of the field data at Dashidaira and Unazuki reservoirs on the Kurobe River in Japan. The calculated results are in good agreement with the measurements. For the reservoirs out of Japan, the Ashida and Michiue bed load formula used in the model should be verified or replaced by other formulas.     

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.     

Aspect Ratio to Maximize Sediment Transport in Rigid Bank Channels

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

3D Numerical Modeling of Flow and Sediment Transport in Laboratory Channel Bends

The development of a fully three-dimensional finite volume morphodynamic model, for simulating fluid and sediment transport in curved open channels with rigid walls, is described. For flow field simulation, the Reynolds-averaged Navier–Stokes equations are solved numerically, without reliance on the assumption of hydrostatic pressure distribution, in a curvilinear nonorthogonal coordinate system. Turbulence closure is provided by either a low-Reynolds number k?ω turbulence model or the standard k?ε turbulence model, both of which apply a Boussinesq eddy viscosity. The sediment concentration distribution is obtained using the convection-diffusion equation and the sediment continuity equation is applied to calculate channel bed evolution, based on consideration of both bed load and suspended sediment load. The governing equations are solved in a collocated grid system. Experimental data obtained from a laboratory study of flow in an S-shaped channel are utilized to check the accuracy of the model’s hydrodynamic computations. Also, data from a different laboratory study, of equilibrium bed morphology associated with flow through 90° and 135° channel bends, are used to validate the model’s simulated bed evolution. The numerically-modeled fluid and sediment transportation show generally good agreement with the measured data. The calculated results with both turbulence models show that the low-Reynolds k?ω model better predicts flow and sediment transport through channel bends than the standard k?ε model.     

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.     

Statistically Derived Bedload Formula for Any Fraction of Nonuniform Sediment

Based on a method of combining stochastic processes with mechanics, a new bedload formula for the arbitrary kth size fraction of nonuniform sediment is theoretically developed by using a stochastic model of sediment exchange and the probabilistic distribution of fractional bedload transport rates. The relations, proposed recently by Sun, for the probability of fractional incipient motion and for the average velocity of particle motion are introduced to bedload formula. Plenty of experimental data for the bedload transport rate of uniform sediment are used to determine two constants. The theoretical bedload formula for any fraction of nonuniform sediment possesses several advantages, including a clear physical concept, a strict mathematical derivation, and a self-adaptability to uniform sediment. The formula is verified with natural data expressing the transport of nonuniform sediment under full motion in laboratory flume. The result shows that the experimental observations agree well with the predicted fractional bedload transport rates. Comparison of the theory with field data finds that the proposed formula still applies to partial transport of bedload in gravel-bed streams as long as the immobile percentage of bed material is taken into account.     

Multiple Time Scales of Fluvial Processes with Bed Load Sediment and Implications for Mathematical Modeling

Fluvial bed load transport is often considered to assume a capacity regime exclusively determined by local flow conditions, but its applicability in naturally occurring unsteady flows remains to be theoretically justified. In addition, mathematical river models are often decoupled, being based on simplified conservation equations and ignoring the feedback impacts of bed deformation to a certain extent. So far whether the decoupling could have considerable impacts on the fluvial processes with bed load transport remains poorly understood. This paper presents a theoretical investigation of both issues. The multiple time scales of fluvial processes with bed load sediment are evaluated to examine the applicability of bed load transport capacity and decoupled models. Numerical case studies involving active bed load transport by highly unsteady flows complement the analysis of the time scales. It is found that bed load transport can sufficiently rapidly adapt to capacity in line with local flow because sediment exchange with the bed overwhelms the advection of bed load sediment by the mean flow. The present work provides theoretical justification of the concept of bed load transport capacity in most circumstances, which is underpinned by existing observations of bed load transport by flash floods. For fluvial processes with bed load transport, the feedback impacts of bed deformation are limited; therefore, decoupled modeling is, in this sense, appropriate.     

Temporal Variation of Scour Depth at Nonuniform Cylindrical Piers

The paper proposes a semiempirical model to estimate the temporal development of scour depth at cylindrical piers with unexposed foundations. A cylindrical pier with a foundation is considered as nonuniform pier. The concept of primary vortex and the principle of volumetric rate of sediment transport are used to develop a methodology to characterize the rate of evolution of the scour hole at nonuniform cylindrical piers. The model also simulates the entire scouring process at nonuniform cylindrical piers having the discontinuous surface located below the initial bed level. The scouring process includes three zones; viz Zone 1 having the scouring phenomenon similar to that of a uniform pier, Zone 2 in which the scour depth remains unchanged with its value equal to the depth of the top level of foundation below the initial bed level while the dimensions of the scour hole increase, and in Zone 3 the geometry pier foundation influences the scouring process. A concept of superposition using an effective pier diameter is proposed to simulate the scouring process in Zone 3. In addition, the laboratory experiments were conducted to utilize the laboratory results for the validation of the model. The simulated results obtained from the proposed model are in good agreement with the present experimental results and also other experimental data. Also, the effect of unsteadiness of flow is incorporated in the model and the results of the model are compared with the experimental data. The model agrees satisfactorily with the experimental data.     

Applicability of Sediment Transport Capacity Formulas to Dam-Break Flows over Movable Beds

In this paper, we investigate the extent to which well-known sediment transport capacity formulas can be used in one-dimensional (1D) numerical modeling of dam-break waves over movable beds. The 1D model considered here is a one-layer model based on the shallow-water equations, a bed update (Exner) equation, a space-lag equation for the nonequilibrium sediment transport and an empirical formula calculating the sediment transport capacity of the flow. The model incorporates a variety of sediment transport capacity formulas proposed by Meyer-Peter and Müller, Bagnold, Engelund and Hansen, Ackers and White, Smart and Jaeggi, van Rijn, Rickenmann, Cheng, Abrahams and Camenen, and Larson. We examine the performance of each formula by simulating four idealized laboratory cases on dam-break waves over sandy beds. Comparisons between numerical results and measurements show that for each case better predictions are obtained using a particular formula, but overall, formulas proposed by Meyer-Peter and Müller (with the factor 8 being replaced by 12), Smart and J?ggi, Cheng, Abrahams and Camenen, and Larson rank as the best predictors for the entire range of conditions studied here. Moreover, results show that in the cases where a bed step exists, implementing a mass failure mechanism in the numerical modeling plays an important role in reproducing the bed and water profiles.     

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.     

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.