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.     

Accuracy of Global Microirrigation Distribution Uniformity Estimates

Emitter pressures and flow rates were systematically and extensively sampled in one drip and one microspray field. The data distributions are presented. The accuracy of rapid (limited samples) evaluation pressure sampling procedures was found to be quite good if the pressure distribution was systematic, but erroneous if the pressure distribution throughout a field was random. A simple mathematical combination of two nonuniformity components (due to pressure differences, and other causes of flow variation) provided a better estimate of overall system distribution uniformity than more complex mathematics.     

Modeling In-Sewer Deposit Erosion to Predict Sewer Flow Quality

High levels of suspended solids are typically observed during the initial part of storms. Field evidence suggests that these suspended solids derive from the erosion of in-sewer sediment beds accumulated during dry and previous wet weather periods. Suspended sediment transport rate models within existing sewer network modeling tools have utilized inappropriate transport rate relationships developed mainly in fluvial environments. A process model that can account for the erosion of fine-grained highly organic in-sewer sediment deposits has been formulated. Values of parameters describing the increase in deposit strength with depth are required. These values are obtained using a genetic algorithm based calibration routine that ensures model simulations of suspended sediment concentrations that correspond to field data collected in a discrete length of sewer in Paris under known hydraulic event conditions. These results demonstrate the applicability of this modeling approach in simulating the magnitude and temporal distribution of suspended in-sewer sediment eroded by time varying flow. Further work is developing techniques to enable the application of this type of model at the network level.     

Simulating Sediment Transport in a Flume with Forced Pool-Riffle Morphology: Examinations of Two One-Dimensional Numerical Models

One-dimensional numerical sediment transport models (DREAM-1 and DREAM-2) are used to simulate seven experimental runs designed to examine sediment pulse dynamics in a physical model of forced pool-riffle morphology. Comparisons with measured data indicate that DREAM-1 and -2 closely reproduce the sediment transport flux and channel bed adjustments following the introduction of fine and coarse sediment pulses, respectively. The cumulative sediment transport at the flume exit in a DREAM-1 simulation is within 10% of the measured values, and cumulative sediment transport at flume exit in a DREAM-2 simulation is within a factor of 2 of the measured values. Comparison of simulated and measured reach-averaged aggradation and degradation indicates that 84% of DREAM-1 simulation results have errors less than 3.3?mm, which is approximately 77% of the bed material geometric mean grain size or 3.7% of the average water depth. A similar reach-averaged comparison indicates that 84% of DREAM-2 simulation results have errors less than 7.0?mm, which is approximately 1.7 times the bed material geometric mean grain size or 11% of the average water depth. Simulations using measured thalweg profiles as the input for the initial model profile produced results with larger errors and unrealistic aggradation and degradation patterns, demonstrating that one-dimensional numerical sediment transport models need to be applied on a reach-averaged basis.     

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

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

Sediment Transport on Arbitrary Slopes: Simplified Model

The paper presents a study on the influence of gravity on the incipient motion and the bed-load transport of sediment. The computation of critical bed-shear stress is revisited considering the balance of forces (hydrodynamic forces and submerged self-weight) acting on a solitary sediment particle lying on an arbitrary sloping bed. Modified effective bed-shear stress and the corresponding critical bed-shear stress, which are defined to assess the incipient motion of sediment in the direction of resultant force, are applied for the estimation of bed-load transport rate in the direction of resultant force. The sediment transport induced by the gravitational force, which is oblique to the direction of the drag force induced by flow, is incorporated into the bed-load transport equation. This modified model provides a reasonable prediction of the critical bed-shear stress and the bed-load transport rate. The model is validated by experimental data. It can be applied to steep slopes and can also avoid the problem of singularity that arises in numerically calculation of sediment transport rate. Additionally, the vectorial transport rate obtained in the model calculation can be implemented in a numerical simulation of channel bed evolution.     

Initiation of Motion of Calcareous Sand

This paper examines the initiation of motion of four natural and five sieved calcareous sand samples in unidirectional flow. Flume experiments yield the sediment transport rate as a function of bed shear stress up to bed-form development. Reference-based criteria are supplemented by visual observations to determine the critical shear stress. The results are compared with published data for rounded and irregular particles in terms of the median sieve size and the corresponding nominal and equivalent diameters as functions of particle Reynolds number. The comparison shows that the critical shear stresses of the irregular particles are higher than the Shields curve in the hydraulically smooth flow regime and lower in the rough turbulent flow regime.     

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.     

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.     

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.     

Molecular weights and molecular-weight distributions from ultracentrifugation of nonideal solutions

Ultracentrifugation, membrane osmometry and capillary viscometry experiments have been performed on two dextran samples, which have molecular-weight distributions (MWDs) similar to those of dextrans used as blood plasma extenders. The manufacturer reported values of Mn and MW, determined by end group analysis and by light scattering, respectively. Our values of Mn, determined by osmometry, and MW, calculated from ultracentrifugal and viscometry experiments, agreed quite well with the manufacturer's results. Good agreement was obtained with values of MW and BLS (the light scattering second virial coefficient) obtained from sedimentation equilibrium experiments at different speeds using sector or nonsector-shaped centerpieces. Several ways of obtaining MW, MZ and BLS from sedimentation equilibrium experiments are presented. We have also shown how to obtain the speed-dependent term of the sedimentation equilibrium second virial coefficient. Both BLS and the speed-dependent nonideal terms could be used to correct the sedimentation equilibrium data, so that ideal values of d in c/d(r2) or dc/d(r2) could be estimated and used to obtain the MWDs of the dextran samples. Both Donnelly's and Scholte's methods were used with the sedimentation equilibrium data. With both methods, unimodal MWDs were encountered, which gave good agreement with the manufacturer's MWDs, obtained by a combination of analytical gel chromatography and light scattering. Uncorrected sedimentation equilibrium data gave MWDs quite different from the manufacturer's results. The MWD calculated from the differential distribution of sedimentation coefficients also gave a unimodal MWD, but this MWD did not give a good agreement with the sedimentation equilibrium results or with the manufacturer's results.     

Density Functions for Entrainment and Deposition Rates of Uniform Sediment

A model has been developed for the prediction of the density functions of bed-elevation and entrainment and deposition rates of sediment in sand bed streams within the lower regime flow condition. The model incorporates both statistical and deterministic parameters in its form. A total of 46 experimental runs have been carried out in a recirculating tilting flume under the equilibrium flow condition using three grain sizes of uniform gradation to validate the model and estimate its parameters. The model parameters are related to the hydraulic conditions of flow and fluid and sediment properties through dimensional and regression analyses. The study has shown that the density functions of bed elevation and entrainment and deposition rates can be approximated quite satisfactorily with the normal distribution curve. Transformation of the density functions into the standardized normal distribution curve provides a unique pattern for all the experimental runs regardless of the sediment grain size, flow condition, and shapes and dimensions of the bed forms. The developed density functions have been utilized to provide a closure for the probabilistic Exner equation for uniform sediment.     

溶样方法对化探样品中砷锑测定的影响

在地球化学样品分析中,采用传统的王水分解样品一原子荧光法测得的国家标准物质的砷、锑结果往往比标准值低,因此建立了一种采用HF-HNO3-H2SO4混合酸分解样品一原子荧光仪测定地球化学样品中砷、锑的方法。经水系沉积物、土壤和岩石等国家一级标准物质验证,并与传统的王水分解样品一原子荧光法测定结果相比较,发现该方法测定结果与标准值符合得更好,更接近被测元素的全量。     

Bed-Material Load Computations for Nonuniform Sediments

The nonuniformity of bed material affects the bed-material load calculations. A size gradation correction factor Kd is developed to account for the lognormal distribution of bed material. The use of Kd in conjunction with bed-material load equations originally developed for single particle sizes improves the accuracy of transport calculations for sediment mixtures. This method is applicable to laboratory flumes and natural rivers with median diameter d50 of bed material in the sand size ranges. The improvement on transport rate by Kd factor is significant for data with standard deviation σg of bed material greater than 2, while the correction is negligible for data with σg less than 1.5. Sediment in transport also follows a lognormal distribution with a median diameter d50t generally finer than the corresponding d50. As the size gradation increases, d50t becomes much finer than the corresponding value of d50. The relationship between d50t and d50 is defined as a function of σg and agrees well with field data. The previously recommended use of d35 as representative size of the bed material is found not to be generally applicable.     

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.     

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.     

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.     

Movement of Finite Amplitude Sediment Accumulations

The movement of finite amplitude sediment accumulations is studied using a simple advection-diffusion relation derived from the sediment continuity equation and using some heuristic reasoning. The movement of a finite amplitude sediment accumulation is found to be strongly diffusive with a small advection component due to the increase in transport rate of the sediment accumulation relative to the transport rate of the original bed material. A semianalytical solution to the advection-diffusion equation is found and the equation is applied to two laboratory experiments. The equation is found to predict the general movement of finite amplitude sediment accumulations with a minimal number of parameters.     

Sand Transport on Steeply Sloping Plane and Rippled Beds

Experiments on sand transport have been carried out in the Sloping Sediment Duct at HR Wallingford. The aim of the experiments was to investigate sediment transport mechanisms, for sand of varying degree of grading, on sloping beds. The Sloping Sediment Duct is a steady flow, recirculating duct, capable of generating mean flow speeds of up to 1 m/s and tilting to +/?30°. Twenty-two tests with two different sediments were conducted. Both sediments had a median grain size of about 0.23 mm but different standard deviations. Bed slopes up to +/?20° were used in the experiments. The results show that bedforms have a significant effect on the transport rate. Since the bedforms, in turn, are affected significantly by the slope, the relation between transport rate and slope is not a monotonic function. Maximum suspended transport rates were attained for downslope flows at angles of about 10°. The transport rate for widely graded sediment was significantly larger than that for well-sorted sediment for almost all flows and slopes.     

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.