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.     

Numerical Model of Sediment Pulses and Sediment-Supply Disturbances in Mountain Rivers

Sediment pulses in rivers can result from many mechanisms including landslides entering from side slopes and debris flows entering from tributaries. Artificial sediment pulses can be caused by the removal of a dam. This paper presents a numerical model for the simulation of gravel bedload transport and sediment pulse evolution in mountain rivers. A combination of the backwater and quasi-normal flow formulations is used to calculate flow parameters. Gravel bedload transport is calculated with the surface-based bedload equation of Parker in 1990. The Exner equation of sediment continuity is used to express the mass balance at different grain size groups and lithologies, as well as the abrasion of gravel. The river is assumed to have no geological controls such as bedrock outcrops and immobile boulder pavements. The results of nine numerical experiments designed to study various key parameters relevant to the evolution of sediment pulses are reported here. Results of the numerical runs indicate that the evolution of sediment pulses in mountain rivers is dominated by dispersion rather than translation. Here dispersion is an expression for the observation that a sediment pulse aggrades both upstream and downstream of its apex whereas its amplitude decreases in time. The results also indicate that grain abrasion is an important and yet often neglected mechanism in removing the excess sediment associated with pulse inputs from some mountain rivers.     

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.     

Bedload Transport in Gravel-Bed Streams with Unimodal Sediment

Bedload transport in many gravel-bed streams becomes highly complicated because of the nonuniformity of the grain size and the vertical stratification of channel bed material. A new relation for computing bedload transport rates in gravel-bed streams is proposed here. In an effort to account for the variation of the makeup of the surface material within a wide range of Shields stresses, the relation employs a two-parameter approach, one related to the material in the pavement and the other to that in the subpavement layers. The mode is used to represent the grain sizes of each layer. Available bedload transport data from gravel-bed streams with unimodal sediment are used to test the accuracy of the relation. A comparison with other bedload transport relations is also considered.     

Multiple Linear Regression Model for Total Bed Material Load Prediction

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

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.     

Hans Albert Einstein: Innovation and Compromise in Formulating Sediment Transport by Rivers

This paper is written to mark the hundredth anniversary of the birth of Hans Albert Einstein (1904–1973). It casts his career as that of the archetypal researcher protagonist determined to master intellectually the way water flows and conveys alluvial sediment in rivers. In that effort, Einstein personified the mix of success and frustration experienced by many researchers who have attempted to formulate the complicated behavior of alluvial rivers in terms of mechanically based equations. His formulation of the relationship between rates of bed-sediment transport (especially bedload transport) and water flow comprised an innovative departure from the largely empirical approach that prevailed at the time. He introduced into that relationship the emerging fluid-mechanic concepts of turbulence and boundary layers, and concepts of probability theory. Inevitably the numerous complexities attending sediment transport mire formulation and prompt his use of several approximating compromises in order to make estimating bed-sediment transport practicable. His formulation nonetheless is a milestone in river engineering.     

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.     

Bedload Transport in Alluvial Channels

Hydraulic, sediment, land-use, and rock-erosivity data of 22 alluvial streams were used to evaluate conditions of bedload transport and the performance of selected bedload-transport equations. Transport categories of transport-limited (TL), partially transport-limited (PTL), and supply-limited (SL) were identified by a semiquantitative approach that considers hydraulic constraints on sediment movement and the processes that control sediment availability at the basin scale. Equations by Parker et al. in 1982, Schoklitsch in 1962, and Meyer-Peter and Muller in 1948 adequately predicted sediment transport in channels with TL condition, whereas the equations of Bagnold in 1980, and Schoklitsch, in 1962, performed well for PTL and SL conditions. Overall, the equation of Schoklitsch predicted well the measured bedload data for eight of 22 streams, and the Bagnold equation predicted the measured data in seven streams.     

Role of Resistance Coefficient in Seasonal Adjustments in Alluvial Rivers

Using the river, canal, and flume data, it is found that the role played by the seasonal variation in the Manning rugosity coefficient, n, equalizes the sediment transporting capacity with sediment supply in the dune bed-form regime. Aggradation/degradation in a sand-bed river is thus avoided on a seasonal basis. A relation between the dimensionless rugosity coefficient and the dimensionless ratio of stream power to sediment concentration exists in sand-bed rivers for any specific gauge height. Once field measurements of the sediment transport rate are made and such a relationship is worked out, thereafter, it may be possible to estimate the sediment concentration for each observed flow discharge merely by applying this relationship adopting the data of velocity, depth, slope, and bed material size which are routinely observed at a stream-gauging site.     

Calculation of Bed Changes in Mountain Streams

Simulation of flow and sediment transport in mountain streams is complicated by the presence of high gradients, abrupt changes in geometry, variations in regime of flow, and large roughness elements. Most of the numerical models to predict aggradation and degradation in alluvial channels have been developed for low-gradient rivers. This paper is devoted to the development of a numerical model to calculate bed elevation and grain size distribution changes in mountain streams where the maximum bed material size is in the range of boulders. An attempt is made to validate the model by using observed field data collected upstream from a small retention dam in a Venezuelan stream. After calibration of the sediment transport equation, reasonable agreement is obtained for the variations in the grain size distribution of the bed-surface material. An additional application is presented in the Cocorotico River, a small mountain stream located in the northwest region of Venezuela, which illustrates the adaptability of the model to handle a case of coarsest-bed-material removal from the active channel and to simulate the armoring process.     

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.     

Measurement of Coarse Gravel and Cobble Transport Using Portable Bedload Traps

Portable bedload traps (0.3 by 0.2 m opening) were developed for sampling coarse bedload transport in mountain gravel-bed rivers during wadable high flows. The 0.9 m long trailing net can capture about 20 kg of gravel and cobbles. Traps are positioned on ground plates anchored in the streambed to minimize disturbance of the streambed during sampling. This design permits sampling times of up to 1 h, overcoming short-term temporal variability issues. Bedload traps were tested in two streams and appear to collect representative samples of gravel bedload transport. Bedload rating and flow competence curves are well-defined and steeper than those obtained by a Helley–Smith sampler. Rating curves from both samplers differ most at low flow but approach each other near bankfull flow. Critical flow determined from bedload traps is similar using the largest grain and the small transport rate method, suggesting suitability of bedload trap data for incipient motion studies.     

Effect of Flow Pulses on Degradation Downstream of Hapcheon Dam, South Korea

The changes in channel geometry downstream of Hapcheon Dam, South Korea, are closely examined. Daily pulses of water from peak hydropower generation and from sudden sluice gate operations affect the 45-km reach of the Hwang River between the Hapcheon Reregulation Dam and the Nakdong River. From 1983 to 2003, the median bed-material size, d50, increased from 1.0 to 5.7 mm, and the bed slope of the reach decreased from 94 to 85 cm/km. The vertical riverbed degradation averaged 2.6 m for a distance of 20 km below the reregulation dam. A simple analytical model is developed to predict the increase in sediment transport and the river bed adjustments from flow pulses in comparison with steady flow discharges. Numerical model simulations confirm the theoretical prediction that sediment transport rates from daily pulses are 21% higher than for steady flow discharges. Unsteady sediment transport simulations indicate that the channel bed degradation should extend mostly 20–25 km below the reregulation dam and should not change much after 2013.     

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.     

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.     

Three-Dimensional Modeling of Nonuniform Sediment Transport in an S-Shaped Channel

A three-dimensional numerical model was applied to compute uniform and nonuniform sediment transport and bed deformation in an S-shaped laboratory channel located at the University of Innsbruck, where detailed measurements of the velocity field and bed elevation changes were made. The channel had two bends, a trapezoidal cross section, and a slope of S = 0.005. Gravel with a mean diameter of 4.2?mm was used as movable bed material and for sediment feeding. Wu’s formula for multiple grain sizes was compared with van Rijn’s formula using one grain size. Fairly good agreement was found between the computed and measured bed elevations for both approaches, whereas Wu’s formula could further improve the numerical results. Looking at the physics of the erosion pattern, the computed scour areas were located slightly more downstream than what was observed in the physical model. The current study also includes several parameter tests: grid distribution in vertical, lateral, and longitudinal direction; time step; number of inner iterations/time step; active sediment layer thickness; and the Shields coefficient. The variation of those parameters gave some differences in the results, but the overall pattern of bed elevation changes remained the same.     

Physical Basis for Quasi-Universal Relationships Describing Bankfull Hydraulic Geometry of Sand-Bed Rivers

Empirical data indicate that hydraulic geometry relationships for single-thread sand-bed rivers (i.e., rivers with median bed-material size between 0.062 and 0.50?mm) can be delineated such that bankfull width, bankfull depth, and channel slope are related in consistent ways to bankfull discharge. Such relationships ought to be the external expression of physical relationships intrinsic to sand-bed river dynamics. In this study, a back-calculation is performed to identify parameters (exponents and coefficients) for three relationships taken to be intrinsic to sand-bed rivers: (1)?a generalized Manning-Strickler resistance relationship; (2)?a relationship for channel-forming Shields number; and (3)?a relationship for sand yield at bankfull flow. To back-calculate parameters for the physical relationships, first the hydraulic geometry relationships are expressed in suitable dimensionless form. Second, the physical relationships are expressed with coefficients and exponents that are analytically related to parameters in the hydraulic geometry relationships. Third, parameters from the hydraulic geometry relationships are used to calculate parameters for the physical relationships. The analysis yields the following results for the sand-bed rivers: (1)?no physical basis exists for using an exponent of 1/6 in the resistance relationship; (2)?channel-forming Shields number decreases with particle Reynolds number, and thus grain size, in a consistent way; and (3)?sand concentration at bankfull flow must decline with increasing bankfull discharge. Although each of these relationships could have been established independently on its own, in this study they have been obtained as the only conclusions consistent with the observed hydraulic geometry relationships and the proposed physical framework. The analysis also yields a useful, dimensionally homogeneous predictive relationship for bankfull discharge as a function of bankfull width, bankfull depth, bed slope, and bed-material median grain size.     

Modeling Bed Changes in Meandering Rivers Using Triangular Finite Elements

A two-dimensional depth-averaged model was used for the simulation of scour and deposition in sand-bed meandering channels with fixed banks. The model employs unstructured meshes based on triangular elements and incorporates the effects of curvature-induced helical flow and transverse bed slope in the direction of bed-load sediment transport. The model was tested using experimental data from a well-known laboratory curved channel and a full scale meandering river. The numerical results agreed well with observed data, demonstrating that the model can reproduce the main features of bed profiles along meandering rivers, such as the formation of point bars and pools.