Probabilistic Modeling of Bed-Load Composition

This paper proposes that the changes which occur in composition of the bed load during the transport of mixed-grain-size sediments are largely controlled by the distributions of critical entrainment shear stress for the various size fractions. This hypothesis is examined for a unimodal sediment mixture by calculating these distributions with a discrete particle model and using them in a probabilistic calculation of bed-load composition. The estimates of bed-load composition compare favorably with observations of fractional transport rates made in a laboratory flume for the same sediment, suggesting that the hypothesis is reasonable. The analysis provides additional insight, in terms of grain mechanics, into the processes that determine bed-load composition. These insights strongly suggest that better prediction methods will result from taking account of the variation of threshold within size fractions, something that most previous studies have neglected.     

Approach to Separate Sand from Gravel for Bed-Load Transport Calculations in Streams with Bimodal Sediment

The bed material found in gravel-bed streams is nonuniform in terms of grain size and can typically be classified as unimodal or bimodal. The latter type of sediment distribution is usually represented by two modes, one of sand size and another of gravel. For this case, the movement of one mode becomes nonlinearly influenced by the other. As a result, the presence of the two modes in a bimodal material complicates the calculation of bed-load transport rates. The present study proposes an approach to separate the calculation of bed-load transport rates for bimodal materials into two independent fractions of sand and gravel, thereby rendering the bed sediment into two unimodal components. This approach is accomplished by decoupling the two fractions through scaling the reference Shields stresses of the sand and gravel modes to match the value of the mode of unimodal materials. Consequently, the contribution of each fraction to bed load can be estimated using a suitable relation derived for unimodal materials. Laboratory and field bed-load data available in the literature are used to examine the validity of the overall approach.     

Modeling Bed-Load Rates from Fine Grain-Size Patches during Small Floods in a Gravel-Bed River

This study investigates the applicability of five bed-load-transport formulas (the Meyer-Peter and Müller, Schoklitsch, Bagnold, Smart and Jaeggi, and Rickenmann equations) to predict bed-load transport rates of frequent, low-magnitude flood events (maximal bankfull discharge) for a mountainous, poorly sorted gravel-bed river characterized by a bimodal sediment-size distribution and spatially distributed patches. For model parametrization, special emphasis was placed on the spatial composition of the grain-size distribution (GSD) to evaluate the impact of preferential removal of sediments from patches with finer sediments on bed-load transport. Three parametrization approaches to the choice of an appropriate sediment size that considered the apparent bimodality of the GSD to varying degrees were tested. The modeling study demonstrated that the incorporation of spatial structure of GSD and its bimodal character has an important impact on model performance—a unimodal parametrization failed to reproduce measured bed-load rates for all tested bed-load formulas; a threshold parametrization approach that considered only finer sediments from the small patches as bed-load source material in combination with the Schoklitsch, Smart and Jaeggi, and Rickenmann equations yielded the best results, whereas the Meyer-Peter and Müller and the Bagnold equations failed to predict bed-load rates for all parametrization approaches. The modeling study thus showed that bed-load formulas are sensitive to the spatial structure of the GSD, which should not be treated as a continuum of sediment size fractions but rather as composition of finer sediment patches to enable an adequate reproduction of measured bed-load data from low-magnitude floods in gravel-bed rivers.     

Turbulence and Secondary Flow over Sediment Stripes in Weakly Bimodal Bed Material

Longitudinal stripes are a common bed form in heterogeneous alluvial sediments and consist of periodic, spanwise variations in bed texture and elevation that are aligned parallel to the mean flow direction. This paper quantifies mean and turbulent flow structures over self-formed sediment stripes in a weakly bimodal sand and gravel mixture. Turbulence anisotropy generates two secondary circulation cells across the channel half-width, which produce a cross-stream perturbation in boundary shear stress. The interaction between this flow structure and the selective transport of bed material generates spanwise sediment sorting that is symmetrical about the centerline. Finer sediments are entrained from regions of high shear stress, transported laterally by the secondary flow, and deposited in regions of lower shear stress. Lateral changes in bed texture further enhance the near-bed secondary flow, which provides a positive feedback mechanism for stripe growth. In bimodal sediments, at shear stresses just above the entrainment threshold, stripes may replace lower-stage plane beds. At higher shear stresses the coarser sediment becomes more mobile and the stripes are replaced by flow transverse bed forms.     

Assessment of Methods Used in 1D Models for Computing Bed-Load Transport in a Large River: The Danube River in Slovakia

Comprehensive measurements of bed-load sediment transport through a section of the Danube River, located approximately 70?km downstream from Bratislava, Slovakia, are used to assess the accuracy of bed-load formulas implemented in 1D modeling. Depending on water discharge and water level, significant variations in the distribution of bed load across the section were observed. It appeared that, whatever the water discharge, the bed shear stress τ is always close to the estimated critical bed shear stress for the initiation of sediment transport τcr. The discussion focuses on the methods used in 1D models for estimating bed-load transport. Though usually done, the evaluation of bed-load transport using the mean cross-sectional bed shear stress yields unsatisfactory results. It is necessary to use an additional model to distribute the bed shear stress across the section and calculate bed load locally. Bed-load predictors also need to be accurate for τ close to τcr. From that point of view, bed-load formulas based on an exponential decrease of bed-load transport close to τcr appear to be more appropriate than models based on excess bed shear stress. A discussion on the bed-load formula capability to reproduce grain sorting is also provided.     

Measurements of Sediment Erosion and Transport with the Adjustable Shear Stress Erosion and Transport Flume

Soil and sediments play an important role in water management and water quality. Issues such as water turbidity, associated contaminants, reservoir sedimentation, undesirable erosion and scour, and aquatic habitat are all linked to sediment properties and behaviors. In situ analysis is necessary to develop an understanding of the erosion and transport of sediments. Sandia National Laboratories has recently patented the Adjustable Shear Stress Erosion and Transport (ASSET) Flume that quantifies in situ erosion of a sediment core with depth while affording simultaneous examination of transport modes (bedload versus suspended load) of the eroded material. Core erosion rates and ratios of bedload to suspended load transport of quartz sediments were studied with the ASSET Flume. The erosion and transport of a fine-grained natural cohesive sediment were also observed. Experiments using quartz sands revealed that the ratio of suspended load to bedload sediment transport is a function of grain diameter and shear stress at the sediment surface. Data collected from the ASSET Flume were used to formulate a novel empirical relation for predicting the ratio of bedload to suspended load as a function of shear stress and grain diameter for noncohesive sediments.     

Cohesive Sediment Characterization by Combined Sedimentation and Rheological Measurements

A laboratory characterization of cohesive sediment has been carried out in which data obtained from standard sedimentation and rheological measurements were combined in a determination of the critical solid concentration for the detection of elasticity in a weakly cohesive suspension. The corresponding storage modulus and shear stress are very critical in any in situ rheometry of sediments, especially in the study of mud-water surface erosion in a flume. Sedimentation results showed that particle size distribution rather than surface treatment controlled the rheological behavior of the suspension while the critical solid concentration for the appearance of three-dimensional space-filling network, showing some measurable elasticity in the suspension, occurred in the region of 0.015. This parallel between the consolidation behavior and shear rheology development for the flocculating system has been established. This technique could be an adjunct to the laboratory characterization of cohesive sediments for the estimation of critical shear stress for surface erosion, especially in a typical flume experiment under water wave pressure.     

Effect of Sediment pH on Resuspension of Kaolinite Sediments

The resuspension of contaminated cohesive sediments can impact water quality by mobilizing sediment particles and adsorbed contaminants. Changes in psysicochemical and electrochemical environments, around resuspended sediment particles, may cause some contaminants to desorb into the water column. The contribution of contaminated sediments to degradation of water quality depends on an estimate of sediment resuspension rates. In this study, the resuspension of Georgia kaolinite sediments under varying pH conditions was investigated in laboratory flume experiments. Because the edge charge of kaolinite particles is pH dependent, kaolinite particles exhibit different modes of particle associations under varying pH conditions. The paper characterizes these particle associations and relates them to the resuspension of kaolinite sediments for varying pH values. Variations in sediment water content, changes from a stratified to a uniform sediment bed, changes in rheological properties, and variations in the electrophoretic mobility of kaolinite particles were all indicative of the changes in particle associations that resulted from changes in sediment pH. The critical shear stress and the erosion rate coefficient were evaluated for varying pH values and explained by particle associations. A rheometer was used to measure rheological properties of the settled sediment bed; the measured yield stresses had a direct correlation with critical shear stresses.     

Stress History Effects on Graded Bed Stability

This paper presents the first detailed examination of the dependence of graded bed stability on antecedent flow conditions (stress history). Thirty-three experiments, including repetitions, were undertaken where a bimodal sediment bed (D50 = 4.8?mm, σg = 2.1) was conditioned for between 30 and 5,760?min. The antecedent shear stress ranged from 53 to 91% of the critical shear stress for the D50 of the sediment bed. Data indicate that higher antecedent shear stresses reduce bed stability due to selective entrainment of the fine matrix; conversely, extending the duration of the antecedent conditioning phase increases bed stability due to local particle rearrangement. Analysis of the competitive effects indicates that particle rearrangement may be of greater relative importance than compositional change. Overall, the paper demonstrates the significance of antecedent flow conditions for hydraulic engineering and research, including the modeling of bed-load transport during flood events and the need for standardizing the flume-based experimental procedure.     

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

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

Three-Dimensional Modeling of Sediment Transport in a Narrow 90° Channel Bend

A three-dimensional numerical model was used for calculating the velocity and bed level changes over time in a 90° bended channel. The numerical model solved the Reynolds-averaged Navier-Stokes equations in three dimensions to compute the water flow and used the finite-volume method as the discretization scheme. The k-ε model predicted the turbulence, and the SIMPLE method computed the pressure. The suspended sediment transport was calculated by solving the convection diffusion equation and the bed load transport quantity was determined with an empirical formula. The model was enhanced with relations for the movement of sediment particles on steep side slopes in river bends. Located on a transversally sloping bed, a sediment particle has a lower critical shear stress than on a flat bed. Also, the direction of its movement deviates from the direction of the shear stress near the bed. These phenomenona are considered to play an important role in the morphodynamic process in sharp channel bends. The calculated velocities as well as the bed changes over time were compared with data from a physical model study and good agreement was found.     

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.     

Bed Shear Stress Boundary Condition for Storage Tank Sedimentation

Computational fluid dynamics-based (CFD) software tools enable engineers to simulate flow patterns and sediment transport in ancillary structures of sewer systems. Lagrangian particle tracking represents a computationally efficient technique for modeling sediment transport. In order to represent the process of sedimentation in storage tanks, careful consideration must be given to the boundary condition at the bottom of the tanks. None of the boundary conditions currently available in the FLUENT CFD software appears to represent the observed behavior of sediment particles, which may become resuspended after first contact with the bed if the local flow velocity is sufficiently high. In this study, a boundary condition based on bed shear stress has been implemented in FLUENT and evaluated against laboratory data. A particle is trapped if the local bed shear stress is below the critical bed shear stress; otherwise, the particle is resuspended. The approach gives satisfactory agreement with measured sedimentation efficiency data, and the simulated spatial distribution is very similar to the sediment distribution observed in a laboratory tank.     

Discrete Particle Modeling of Entrainment from Flat Uniformly Sized Sediment Beds

The stability of randomly deposited sediment beds is examined using a discrete particle model in which individual grains are represented by spheres. The results indicate that the threshold shear stress for flat beds consisting of cohesionless uniformly sized grains cannot be adequately described by a single-valued parameter; rather, it is best represented by a distribution of values. Physically, this result stems from the localized heterogeneity in the arrangement of surface grains. For uniformly sized beds, geometric similarity exists such that the critical entrainment shear stress distributions scale directly with grain size. A Shields parameter of 0.06 is commonly used to define “threshold conditions,” and it was found that this corresponds to a point on the distributions where approximately 1.4% by weight of the surface is mobile. Furthermore the analysis includes a comparison of the contributions of sheltering to variation in critical entrainment shear stress. It was found that remote sheltering, induced by prominent upstream grains, has a significant effect in increasing the apparent critical entrainment shear stress of exposed surface grains.     

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.     

Comparisons of Sidewall Correction of Bed Shear Stress in Open-Channel Flows

When investigating sediment transport in laboratory open-channel flows, it is often necessary to remove sidewall effects for computing effective bed shear stress. Previous sidewall correction methods are subject to some assumptions that have not been completely verified, and different values of the bed shear stress may be obtained depending on the approach used in making sidewall corrections. This study provides a quantitative assessment of the existing correction procedures by comparing them to a new sidewall correction model proposed in this study. The latter was derived based on the shear stress function and equivalent roughness size for both rigid and mobile bed conditions, which were obtained directly from experimental measurements. The comparisons show that the Einstein correction formula and the Vanoni and Brooks method generally predict relatively lower and higher bed shear stresses, respectively, while the Williams’ empirical function leads to more scatter. This study also demonstrates that the widely used Vanoni and Brooks approach can be well approximated by a simple formula derived based on the Blasius resistance function. The sidewall effects, when removed in the different ways, would consequently affect the presentation of the bedload function. Experimental results of bedload transport, when plotted as the dimensionless transport rate against the dimensionless shear stress with the latter being corrected using the present model, exhibit less scatter than those associated with the previous procedures.     

Numerical Simulation of Longitudinal and Lateral Channel Deformations in the Braided Reach of the Lower Yellow River

Bank erosion frequently occurs in the Lower Yellow River (LYR), playing an important role in the evolution of this braided river. A two-dimensional (2D) composite model is developed herein that consists of a depth-averaged 2D flow and sediment transport submodel and a bank-erosion submodel. The model incorporates a new technique for updating bank geometry during either degradational or aggradational bed evolution, allowing the two submodels to be closely combined. Using the model, the fluvial processes in the braided reach of the LYR between Huayuankou and Laitongzhai are simulated, and the calculated results generally agree with the field measurements, including the water-surface elevation, variation of water-surface width, and variations of cross-sectional profiles. The calculated average water-surface elevation in the study reach was 0.09?m greater than the observed initial value, and the calculated mean bed elevation for six cross sections was 0.11?m lower than the observed value after 24 days. These errors are attributed to the large variability of flow and sediment transport processes. Sensitivity tests of three groups of parameters are conducted, and these groups of parameters are related to flow and sediment transport, bank erosion, and model application, respectively. Analysis results of parameter sensitivity tests indicate that bank erodibility coefficient and critical shear stress for bank material are sensitive to the simulated bank erosion process. The lateral erosion distance at Huayuankou will increase by 19% as the value of bank erodibility coefficient changes from 0.1 to 0.3, and it will decrease by 57% as the value of critical shear stress for bank increases from 0.6 to 1.2?N/m2. Limited changes of other parameters have relatively small effects on the simulated results for this reach, and the maximum change extent of calculated results is less than 5%. Because the process of sediment transport and bank erosion in the braided reach of the LYR is very complicated, further study is needed to verify the model.     

Analysis of Suspended Sediment Transport in Open-Channel Flows: Kinetic-Model-Based Simulation

This paper presents a comprehensive analysis of suspended sediment transport in open channels under various flow conditions through a kinetic-model-based simulation. The kinetic model, accounting for both sediment-turbulence and sediment-sediment interactions, successfully represents experimentally observed diffusion and transport characteristics of suspended sediments with different densities and sizes. Without tuning any model coefficients, the nonmonotonic concentration distribution and the noticeable lag velocity with a negative value close to the wall are reasonably reproduced. Examination of flow conditions typical of suspension dominated rivers shows that the conventional method may overestimate or underestimate unit suspended-sediment discharge, depending on the Rouse number, sediment size, as well as shear velocity. The error may be less than 20% for dp<0.5?mm and might exceed 60% for dp>1.0?mm under typical flow conditions where shear velocity ranges from 1.0?to?12.5?cm/s and flow depth ranges from 1.0?to?5.0?m.     

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.     

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

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