Fractional Bed Load Research Articles

Characteristics and selective mobility of bedload sheets

Bedform-driven flux is a fundamental component of bedload transport along riverbeds, resulting in unsteady transport rates. For bedload sheets, these fluctuations emerge through the preferential sorting of coarser grains in the leading front of the bedform. This study establishes key characteristics of bedload sheets formed in a sand-dominated unimodal sediment and, using fractional transport rates, determines the state of grain mobility to evaluate a proposed bedform regime (Venditti et al., 2017). A series of 10 flume experiments were executed using a water-worked sediment bed, with Shields numbers ranging from 0.037 to 0.15. Sediment supply was set by operating the flume in sediment recirculation mode. For each run bedform dimensions and migration rate were measured as well as hydraulic conditions. Sampling and analysis of bedload and bed sediment were used to derive fractional transport rates and grain size distributions to determine scaled transport rates and transport-supply ratios. Bedload sampling partitioned transport into bedload sheets and the load between sheets. Bedload sheets initially formed at a Shields number equal to 0.056 and persisted to a value of 0.13. Over this range, sheets grew in size and frequency, migrated faster, and produced elevated bedload transport rates that were consistently coarser than the flux between sheets. Scaled transport rates indicate selective mobility when sheets existed but this state of grain mobility does not uniquely define bedload sheets. Nonetheless, the mobility of larger grains relative to those in the surface sediment and the sediment supply conditions during runs fall within the bounds that define bedload sheets in the bedform regime diagram evaluated. Incorporating these conditions for bedload sheets into fractional bedload transport rates could improve predictions of bedload fluxes.

Toward a general calibration of the Swiss plate geophone system for fractional bedload transport

Abstract. Substantial uncertainties in bedload transport predictions in steep streams have encouraged intensive efforts towards the development of surrogate monitoring technologies. One such system, the Swiss plate geophone (SPG), has been deployed and calibrated in numerous steep channels, mainly in the Alps. Calibration relationships linking the signal recorded by the SPG system to the intensity and characteristics of transported bedload can vary substantially between different monitoring stations, likely due to site-specific factors such as flow velocity and bed roughness. Furthermore, recent flume experiments on the SPG system have shown that site-specific calibration relationships can be biased by elastic waves resulting from impacts occurring outside the plate boundaries. Motivated by these findings, we present a hybrid calibration procedure derived from flume experiments and an extensive dataset of 308 direct field measurements at four different SPG monitoring stations. Our main goal is to investigate the feasibility of a general, site-independent calibration procedure for inferring fractional bedload transport from the SPG signal. First, we use flume experiments to show that sediment size classes can be distinguished more accurately using a combination of vibrational frequency and amplitude information than by using amplitude information alone. Second, we apply this amplitude–frequency method to field measurements to derive general calibration coefficients for 10 different grain-size fractions. The amplitude–frequency method results in more homogeneous signal responses across all sites and significantly improves the accuracy of fractional sediment flux and grain-size estimates. We attribute the remaining site-to-site discrepancies to large differences in flow velocity and discuss further factors that may influence the accuracy of these bedload estimates.

Hysteretic Implications for Graded Bed Load Sediment Transport in Symmetrical Hydrograph Flows

Differential parametric values associated with bed load sediment transport, that result at the same discharge levels on the rising and falling limbs of a flood hydrograph, are usually defined as bed load hysteresis. This hysteresis in bed load sediment transport rates is of considerable interest in the field of fluvial hydraulics. Within this study, a series of well-defined, symmetrical hydrograph flows are generated over a graded, mobile sediment bed to fully examine the hysteresis of the resulting bed load sediment transport in terms of the threshold of motion, and differential bed load transport rates and bed load yields during the hydrographs. The experiments are conducted in a titling flume without sediment supply specified at the upstream inlet, thereby representing typical river reach conditions immediately downstream of a dam that are exclusively subject to net in-channel bed degradation from sediment transport initiated during flood events. Our results show that the fractional bed load transport of defined fine, medium and coarse size classes within the graded sediment bed generally display clockwise, no/mixed and counter-clockwise hysteresis patterns, respectively, with clockwise hysteresis most commonly found for the coarse size class mobilised by hydrographs with long durations. By contrast, counter-clockwise hysteresis is usually observed for fine size class transported by hydrographs with short durations. Accordingly, the corresponding reference stresses for each size class vary between different hydrographs and are primarily controlled by the hydrograph flashiness (i.e. unsteadiness) and magnitude (i.e. total water work). Moreover, it is shown that the hysteresis effect, particularly for those size classes and hydrograph combinations that result in clockwise and counter-clockwise behaviour, should be fully accounted for when reproducing bed load transport rates using separate-limb based method. Finally, we investigate the relative fractions of the overall bed load yields generated during the rising and falling limbs of all symmetrical hydrographs (i.e. the bed load yield ratio), which are found to be primarily dependent on bed load transport hysteresis. Finally, the relationship between the bed load yield ratio and the ratio of reference stresses for the fractional sediment motion of each size class on both limbs is found to follow a power law.

Graded bed load transport in sediment supply limited channels under unsteady flow hydrographs

Natural river channels that are sediment supply limited due to upstream water management practices and/or flow regulation are often subject to in-channel bed degradation and bed surface restructuring during natural flood hydrographs or controlled flow releases from upstream dams. The heterogeneity of sediment sizes present in these channels means that different size classes are transported more actively during different parts of the hydrograph. A series of laboratory experiments is conducted to investigate the in-channel response of a graded sediment bed to a range of design flow hydrographs when no sediment is supplied at the upstream boundary. The results show varying temporal lag and bed load transport hysteresis for different transported fractions, defined by fine, medium and coarse size classes in the graded sediment mixture. The coarse size class typically exhibits clockwise hysteresis, indicating more active transport during the rising hydrograph limb, whereas the fine size class demonstrates either no/mixed or counterclockwise hysteresis, as it becomes more active during the falling limb. On this separate limb basis, predictions of fractional bed load transport rates are improved by calculating unique reference threshold shear stresses for each size class at the initiation and cessation of fractional grain motions on the rising and falling limbs, respectively. Corresponding temporal variations in the bed load median grain size vary depending on the hydrograph total water work and unsteadiness, with peak values generally attained during the rising limb and overall bed load fining observed during the falling limb. Analysis of the three size classes also indicates that the medium-coarse and fine fractions are transported in larger relative proportions during smaller magnitude, more flashy hydrographs and larger magnitude, flatter hydrographs, respectively. The resulting armouring of the post-hydrograph bed surface layer is most significant at the upstream end of the channel and decreases exponentially in the downstream direction. Two empirical models, based on combined hydrograph and bed sediment descriptors, are also shown to predict reasonably well the overall bed load yields generated under different flow hydrographs from the satisfactory collapse of the current experimental data and previous datasets for both uniform and graded bed sediments. These bed load yields provide an empirical means to describe the extent of upstream bed armouring and the downstream fining of the bed surface layer after the passage of individual hydrographs.

Toward the Prediction of Bed Load Rating Curve Parameter Values: The Influence of Scale, Particle Size, and Entrainment Threshold

AbstractThree‐parameter bed load rating curves for fractional and total bed load transport rates are presented for 15 bed load data sets, and the relationships between the parameter values and physical attributes of the transport process are investigated. The coefficients in these rating curves represent the product of the bed load particle size raised to a power near 1.5 and the active channel width divided by the threshold for bed load entrainment raised to the power of the bed load rating curve exponent. Because bed load entrainment thresholds for different streams typically increase with stream scale faster than do mean bed load particle sizes, total bed load rating curves coefficients for different streams decrease with increasing stream size. In the case of fractional bed load, however, differences between the entrainment thresholds for different particle size fractions are relatively small, so coefficients in fractional bed load rating curves for a given stream usually increase with the particle size class considered. Much of the variability in bed load rating curve exponents appears to be due to estimation errors rather than physical conditions in the stream. The exponents can be overestimated when the sample data used to estimate them are confined to discharges near the sediment entrainment threshold, and the mathematical consequences of summing multiple fractional rating curves can inflate the exponents for mixed size sediments. We recognize channel geometry as another important factor determining the value of rating curve exponents, but the detailed topographic data needed to assess the role of channel form is unavailable for the most of the sampling locations analyzed in this study.

Prediction of bed level variations in nonuniform sediment bed channel

In the present study, a numerical model, based on one-dimensional de Saint-Venant equations along with sediment continuity equation, is developed for prediction of bed levels in non-cohesive sediments in aggrading alluvial channels. One-dimensional, unsteady flow equations and sediment continuity equations are solved using ‘shock-capturing’, second order accurate, explicit MacCormack finite difference scheme while considering upstream and downstream boundary conditions in the channel. Series of experimental investigations have been undertaken for measurements of bed and water levels in an aggrading channel due to overloading of nonuniform sediments, extracted from the bed of Tapi River at Surat City, in a flume installed in Advanced Hydraulics Laboratory of SVNIT, Surat, India. A satisfactory coupling between the water flow and sediment flow has been achieved. The sediment continuity equation is used for the each size class to compute the volume of each size class after each time step at any computational node in the computational grid. The fractional bed and suspended load transport capacities for different size fractions have been computed using fractional transport laws for nonuniform sediments. The active bed layer concept has been implemented in finite difference scheme to consider the interaction and exchange of sediment and water flow near the mixing layer. The performance of developed numerical model has been satisfactorily verified with independent experimental data of nonuniform sediment bed. Also, consideration of sediment nonuniformity in computation of bed level variation has been demonstrated by comparing the results based on sediment transport functions of uniform and nonuniform sediments.

The Impact of Urbanization on Temporal Changes in Sediment Transport in a Gravel Bed Channel in Southern Ontario, Canada

AbstractA field investigation has been undertaken to characterize the event‐based bed load transport dynamics of a highly urbanized gravel bed stream. A combination of direct bed load and tracer particle measurements were taken over a 3 year period during which time approximately 30 sediment mobilizing events occurred. Sediment transport measurements were used to calibrate a fractional bed load transport model and combined with hydrometric data which represent four different land use conditions (ranging from rural to highly urbanized) to analyze the differences in discharge magnitude and frequency and its impact on sediment transport. Fractional transport analysis of the bed load measurements indicates that frequent intermediate discharge events can mobilize sand and fine gravel to an approximate equally mobile condition, however, the transport rates at these discharges exhibit greater variability than at discharges above the bankfull discharge. Path lengths of the coarse fraction, measured using tracer clasts, are insensitive to peak discharge, and instead transport at distances less than those reported in other gravel bed channels, which is attributed to the shorter duration discharge events common to urban streams. The magnitude‐frequency analysis reveals that the frequency, time, and volume of competent sediment mobilizing events are increasing with urbanization. Variability in effective discharges suggests that a range of discharges, spanning between frequent, low magnitude events to less frequent, high magnitude events are geomorphically significant. However, trends in the different land use scenarios suggest that urbanization is shifting the geomorphic significance toward more frequent, lower magnitude events.

Bed load transport in a very steep mountain stream (Riedbach, Switzerland): Measurement and prediction

AbstractCompared to lower‐gradient channels, steep mountain streams typically have rougher beds and shallower flow depths, making macro‐scale flow resistance (due to, e.g., immobile boulders and irregular bedforms) more important as controls on sediment transport. The marked differences in hydraulics, flow resistance, and grain mobility between steep and lower‐gradient streams raise the question of whether the same equations can predict bed load transport rates across wide ranges of channel gradients. We studied a steep, glacier‐fed mountain stream (Riedbach, Ct. Valais, Switzerland) that provides a natural experiment for exploring how stream gradients affect bed load transport rates. The streambed gradient increases over a 1 km stream reach by roughly one order of magnitude (from 3% to 38%), while flow discharge and width remain approximately constant. Sediment transport rates were determined in the 3% reach using Bunte bed load traps and in the 38% reach using the Swiss plate geophone system. Despite a ten‐fold increase in bed gradient, bed load transport rates did not increase substantially. Observed transport rates for these two very different bed gradients could be predicted reasonably well by using a flow resistance partitioning approach to account for increasing bed roughness (D84 changes from 0.17 m to 0.91 m) within a fractional bed load transport equation. This suggests that sediment transport behavior across this large range of steep slopes agrees with patterns established in previous studies for both lower‐gradient and steep reaches, and confirms the applicability of the flow resistance and bed load transport equations at very steep slopes.

Applicability of bed load transport models for mixed‐size sediments in steep streams considering macro‐roughness

AbstractIn steep mountain streams, macro‐roughness elements typically increase both flow energy dissipation and the threshold of motion compared to lower‐gradient channels, reducing the part of the flow energy available for bed load transport. Bed load transport models typically take account of these effects either by reducing the acting bed shear stress or by increasing the critical parameters for particle entrainment. Here we evaluate bed load transport models for mixed‐size sediments and models based on a median grain size using a large field data set of fractional bed load transport rates. We derive reference shear stresses and bed load transport relations based on both the total boundary shear stress and a reduced (or “effective”) shear stress that accounts for flow resistance due to macro‐roughness. When reference shear stresses are derived from the total boundary shear stress, they are closely related to channel slope, but when they are derived from the effective shear stress, they are almost invariant with channel slope. The performance of bed load transport models is generally comparable when using the total shear stress and a channel slope‐related reference shear stress, or when using the effective shear stress and a constant reference shear stress. However, dimensionless bed load transport relations are significantly steeper for the total stress approach, whereas they are similar to the commonly used fractional Wilcock and Crowe (WC) transport model for the effective stress approach. This similarity in the relations allows the WC model, developed for lower‐gradient streams, to be used in combination with an effective shear stress approach, in steep mountain streams.

Downstream lightening and upward heavying: Experiments with sediments differing in density

AbstractSorting and selective transport of particles by material density is important for understanding a wide range of processes, including the formation of mineral placers, deposition of mine tailings and routing of tracers and contaminants. This article describes an experimental study of the transport of mixtures of particles of differing density in a sediment‐feed flume. During the runs, a downstream prograding wedge‐shaped deposit was formed. Results show two sorting processes: (i) longitudinal sorting characterized by preferential deposition of heavy particles in the upstream part of the deposit – downstream lightening; and (ii) vertical sorting with less dense particles preferentially deposited in the lowermost portion of the migrating front – upward heavying. Downstream lightening is the analogue of the well‐known downstream fining observed in the more studied case of mixtures of heterogeneous size with the same density. In both cases, the lighter particles are carried further downstream than the heavier particles. Upward heavying is unexpected when compared with deposits of heterogeneous size and same‐density particles, where the heaviest (i.e. coarsest) particles are deposited in the lowermost part of the front. The physical mechanism underlying this upward heavying might be related to the physics of gravity‐driven granular flows; the front of the deposit acts like a dense granular flow down an inclined plane. In this case, the denser particles settle away from the free surface and at the top of the heap, while the lighter particles flow to the bottom. As the front of the deposit advances, this progressively gives rise to an upward heavying pattern. The application of classical surface‐based fractional bedload transport models suggests that equal mobility is not approached in the case of mixtures of particles with uniform size and different densities. This study hypothesizes that other mechanics related to the physics of the segregation processes in these systems contribute to these results.

SedFlow – a tool for simulating fractional bedload transport and longitudinal profile evolution in mountain streams

Abstract. Especially in mountainous environments, the prediction of sediment dynamics is important for managing natural hazards, assessing in-stream habitats and understanding geomorphic evolution. We present the new modelling tool {sedFlow} for simulating fractional bedload transport dynamics in mountain streams. sedFlow is a one-dimensional model that aims to realistically reproduce the total transport volumes and overall morphodynamic changes resulting from sediment transport events such as major floods. The model is intended for temporal scales from the individual event (several hours to few days) up to longer-term evolution of stream channels (several years). The envisaged spatial scale covers complete catchments at a spatial discretisation of several tens of metres to a few hundreds of metres. sedFlow can deal with the effects of streambeds that slope uphill in a downstream direction and uses recently proposed and tested approaches for quantifying macro-roughness effects in steep channels. sedFlow offers different options for bedload transport equations, flow-resistance relationships and other elements which can be selected to fit the current application in a particular catchment. Local grain-size distributions are dynamically adjusted according to the transport dynamics of each grain-size fraction. sedFlow features fast calculations and straightforward pre- and postprocessing of simulation data. The high simulation speed allows for simulations of several years, which can be used, e.g., to assess the long-term impact of river engineering works or climate change effects. In combination with the straightforward pre- and postprocessing, the fast calculations facilitate efficient workflows for the simulation of individual flood events, because the modeller gets the immediate results as direct feedback to the selected parameter inputs. The model is provided together with its complete source code free of charge under the terms of the GNU General Public License (GPL) (www.wsl.ch/sedFlow). Examples of the application of sedFlow are given in a companion article by Heimann et al. (2015).

Maximum likelihood parameter estimation for fitting bedload rating curves

Fluvial sediment loads are frequently calculated with rating curves fit to measured sediment transport rates. Rating curves are often treated as statistical representations in which the fitted parameters have little or no physical meaning. Such models, however, may produce large errors when extrapolation is needed, and they provide no insight into the sediment transport process. It is shown that log-linear least squares, the usual method for fitting rating curves, does not generally produce physically meaningful parameter values. In addition, it cannot accommodate data that include zero-transport samples. Alternative fitting methods based nonlinear least squares and on maximum likelihood parameter estimation are described and evaluated. The maximum likelihood approach is shown to fit synthetic data better than linear or nonlinear least squares, and to perform well with data that include zero-transport samples. In contrast, nonlinear least squares methods produce large errors in the parameter estimates when zero-transport samples are present or when the variance structure of the data is incorrectly specified. Analyses with fractional bedload data from a mountain stream suggest that bedload transport rates are gamma distributed, that the arrivals of bedload particles in a sampler conform to a Poisson distribution, and that the variance of nonzero samples can be expressed as a power function of the mean. Preliminary physical interpretations of variations in the rating curve parameters fit to fractional bedload data with the maximum likelihood method are proposed, and their relation to some previous interpretations of rating curve parameters are briefly discussed.

Fractional bed load transport model for nonuniform unimodal and bimodal sediments

Experimental programme for collection of flume data on bed load transport of unimodal and bimodal sediments is reported. Existing relationships for fractional bed load transport of nonuniform sediments are assessed for their applicability to bimodal sediments using data collected in the present study and those available from past investigations. Keeping in view the inadequate performance of existing relationships for bimodal sediments, parameters for computation of fractional bed load transport rates of unimodal and bimodal sediments are identified; and a new relationship is proposed based on recent developments on critical shear stress of such sediments. The performance of proposed relationship is verified with independent data on flume and field studies.

Nonuniform sediment transport under non-breaking waves and currents

Empirical formulas have been developed to calculate the fractional bed-load and suspended-load transport rates and near-bed suspended-load concentration under non-breaking waves and currents for coastal applications. The formulas relate the bed-load transport rate to the grain shear stress, the suspended-load transport rate to the energy of the flow system, and the near-bed suspended-load concentration to the bed-load transport rate, velocity and layer thickness. Adequate methods are adopted to determine the bed shear stress due to coexisted waves and currents. The hiding and exposure mechanism in nonuniform bed material is considered through a correction factor that is related to the hiding and exposure probabilities and in turn the size composition of bed material. The developed formulas have been tested using a large database of single-sized sediment transport and several sets of multiple-sized sediment transport data collected from literature, and compared with several existing formulas. The developed formulas can provide reasonably good predictions for the test cases.

Estimation of fractional critical tractive stress from fractional bed load transport measurements of unimodal and bimodal sediments

Experimental investigation on estimation of fractional critical tractive stress of nonuniform unimodal and bimodal sediment mixtures is reported. The observed data on fractional bed load transport rates for different flow strength, under equilibrium condition, have been used to estimate critical tractive stress (CTS) of each size fraction in sediment mixture from reference transport method (RTM). Further, the accuracy of these estimated CTS values are assessed by comparing the same with CTS values estimated using largest grain method (LGM). The estimated CTS values of individual size fractions for different sediment mixtures have been used to assess the performance of CTS relationship recently proposed by Patel et al. [12].

Two Stochastic Fraction Bedload Transport Rate Models for Nonuniform Sediment

Based on a method stochastic processes, two new bedload transport models for the ith size fraction nonuniform sediment are theoretically developed by using a stochastic model of sediment exchange and the probabilistic distribution of fractional bedload transport rates. The relations, proposed recently by Yang, for the probability of fractional incipient motion and for the average velocity of particle motion are introduced to bedload formulas. Plenty of experimental data for the bedload transport rate of uniform sediment are used to determine parameters. Finally, the two models are 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 shows that the proposed formula still applies to uniform sediment transportation condition as long as the relevant parameters for uniform sediment are taken into account.

A one-dimensional bedload transport model for steep slopes

A sediment routing model called SETRAC has been developed to simulate bedload transport in torrents and mountain streams. SETRAC is the acronym for Sediment Transport in Alpine Catchments. Flow resistance is modelled using an approach proposed by Smart and Jäggi, and bedload transport is predicted with an equation by Rickenmann. Form roughness losses are accounted for by an empirical approach which is based on flow resistance observations in mountain streams. It is possible to compute fractional bedload transport taking grain sorting effects into account. Flow hydrographs are routed through the channel network by using the kinematic wave approach. An application of the model is discussed for an extreme flood event of August 2005 in the Chiene catchment, Switzerland, which mobilized 120,000 m3 of bedload along the mountain stream. The simulation results underline the importance of form resistance when modelling bedload transport in steep and rough channels.

Predicting fractional bed load transport rates: Application of the Wilcock‐Crowe equations to a regulated gravel bed river

Bed load samples from four locations in the Trinity River of northern California are analyzed to evaluate the performance of the Wilcock‐Crowe bed load transport equations for predicting fractional bed load transport rates. Bed surface particles become smaller and the fraction of sand on the bed increases with distance downstream from Lewiston Dam. The dimensionless reference shear stress for the mean bed particle size (τ*rm) is largest near the dam, but varies relatively little between the more downstream locations. The relation between τ*rm and the reference shear stresses for other size fractions is constant across all locations. Total bed load transport rates predicted with the Wilcock‐Crowe equations are within a factor of 2 of sampled transport rates for 68% of all samples. The Wilcock‐Crowe equations nonetheless consistently under‐predict the transport of particles larger than 128 mm, frequently by more than an order of magnitude. Accurate prediction of the transport rates of the largest particles is important for models in which the evolution of the surface grain size distribution determines subsequent bed load transport rates. Values of τ*rm estimated from bed load samples are up to 50% larger than those predicted with the Wilcock‐Crowe equations, and sampled bed load transport approximates equal mobility across a wider range of grain sizes than is implied by the equations. Modifications to the Wilcock‐Crowe equation for determining τ*rm and the hiding function used to scale τ*rm to other grain size fractions are proposed to achieve the best fit to observed bed load transport in the Trinity River.

Quantifying the role of bed surface topography in controlling sediment stability in water‐worked gravel deposits

This study uses measured bed topography scans and fractional bed load transport rate data obtained from previous laboratory studies of gravel transport to examine the influence of the local grain‐scale topography on grain entrainment and fractional transport rates. A simple steady state fluid model is developed to impose fluid forces onto the exposed areas of the bed surface. Image analysis is used to identify the surface grains and simple physically based algorithms are used to include the effects of sheltering. Comparisons of modeled and experimental fractional transport rates show that remote sheltering has a very strong influence on grain entrainment. With the effects of remote sheltering included, the model was found to be able to predict fractional transport rates well for a range of bed topographies and feed conditions. Further studies using a wider range of bed shear stresses would allow the effects of turbulence and bed re‐arrangement to be included in the model.

Fractional bedload transport during small floods in a regulated gravel-bed river

Vericat, D., Batalla, R. J. (2007). Fractional bedload transport during small floods in a regulated gravel-bed river. Zeitschrift fur Geomorphologie, 51 (2), 227-240.