Fractional Bedload Transport Rates 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.

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.

Experimental investigations of graded sediment transport under unsteady flow hydrographs

Natural fluvial channels can experience significant variations in sediment transport rates under unsteady flow conditions, especially during flood hydrograph events. At present, however, there is a distinct lack of understanding of the interaction between unsteady hydrograph flow properties and temporal variability in graded sediment transport rates. In the current study, a series of parametric experiments were conducted to investigate the response of two-graded sediment beds to a range of different unsteady hydrograph flow conditions. Investigations of the total and fractional bed-load sediment transport rates revealed strong temporal variations in transport over the hydrographs, with size-dependent temporal lag effects observed between peak flow conditions and peak bed-load transport rates. Specifically, coarse gravels had increased mobility during the rising limb of the hydrographs, attaining their peak bed-load transport rate either prior to, or near, peak flow conditions. By contrast, the finer grades tended to have enhanced mobility during the receding limb of the hydrographs, with peak transport rates measured after peak flow conditions had passed. Grain size distributions measured from the collected bed-load samples also indicated material coarsening over the rising limb and fining during the receding limb, while corresponding image analysis measurements of bed surface composition showed only marginal variation over the hydrographs. Computation of total and fractional sediment yields revealed that the bimodal sediment mixture tested was transported at significantly higher rates than the uni-modal mixture over all hydrograph conditions tested. This finding indicated that the uni-modal sediment bed was inherently more stable than the bimodal bed due to the increased abundance of medium-sized gravels present in the uni-modal sediment grade. The parametric dependences established in the study have clear implications for improved understanding of fractional inter-granular effects at the bed surface and their influence on graded sediment transport processes within natural fluvial channels under flood flow hydrographs.

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.

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.

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.

Nonuniform sediment transport in alluvial rivers

A correction factor has been developed in this paper to account for the hiding and exposure mechanism of nonuniform sediment transport. This factor is assumed to be a function of the hidden and exposed probabilities, which are stochastically related to the size and gradation of bed materials. Based on this concept, the formulas to calculate the critical shear stress of incipient motion and the fractional bed-load and suspended load transport rates of nonuniform sediment have been established. These formulas have been tested against a wide range of laboratory and field data and compared with several other existing empirical methods. The predictions by these newly proposed formulas are very good.

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.

Fractionwise calculation of bed load transport

Extensive experiments conducted by the writers on fractional bed load transport rates are reported. These data as well as those available from other sources, covering wide range of flow conditions and sediment nonuniformity, have been analysed. Firstly, the semi-theoretical model proposed by Misri et al. (1984) is modified to evolve a method of bed load calculation and finally an empirical relationship is proposed incorporating the several parameters influencing the bed load transport of nonuniform sediments.

An experimental study of flow, bedload transport and bed topography under conditions of erosion and deposition and comparison with theoretical models

ABSTRACTThe nature of flow, sediment transport and bed texture and topography was studied in a laboratory flume using a mixed size‐density sediment under equilibrium and non‐equilibrium (aggradational, degradational) conditions and compared with theoretical models. During each experiment, water depth, bed and water surface elevation, flow velocity, bed shear stress, bedload transport and bed state were continuously monitored. Equilibrium, uniform flow was established with a discharge of about 0.05 m3 s−1, a flow depth of about 0.01 m, a flow velocity of about 0.81–0.88 m s−1, a spatially averaged bed shear stress of about 1.7–2.2 Pa and a sediment transport rate of about 0.005–0.013 kg m−1 s−1 (i.e. close to the threshold of sediment transport). Such equilibrium flow conditions were established prior to and at the end of each aggradation or degradation experiment. Pebble clusters, bedload sheets and low‐lying bars were ubiquitous in the experiments. Heavy minerals were relatively immobile and occurred locally in high concentrations on the bed surface as lag deposits.Aggradation was induced by (1) increasing the downstream flow depth (flume tilting) and (2) sediment overloading. Tilt‐induced aggradation resulted in rapid deposition in the downstream half of the flume of a cross‐stratified deposit with downstream dipping pebbles (pseudo‐imbricated). and caused a slight decrease in the equilibrium mean water surface slope and total bedload transport rate. These differences between pre‐ and post‐aggradation equilibrium flow conditions are due to a decrease in the local grain roughness of the bed. Sediment overloading produced a downstream fining and thinning wedge of sediment with upstream dipping pebbles (imbricated), whereas the equilibrium flow and sediment transport conditions remained relatively unchanged. Degradation was induced by (1) decreasing the downstream flow depth (flume tilting) and (2) cutting off the sediment feed. Tilt‐induced degradation produced rapid downstream erosion and upstream deposition due to flow convergence with little change to the equilibrium flow and sediment transport conditions. The cessation of sediment feed produced degradation and armour development, a reduction in the mean water surface slope and flow velocity, an increase in flow depth, and an exponential decrease in bedload transport rate as erosion proceeded. A bedload transport model predicted total and fractional transport rates extremely well when the coarse‐grained (or bedform trough) areas of the bed are used to define the sediment available to be transported. A sediment routing model, MIDAS, also reproduced the equilibrium and non‐equilibrium flow conditions, total and fractional bedload transport rates and changes in bed topography and texture very well.

Differential bedload transport rates in a gravel‐bed stream: A grain‐size distribution approach

AbstractTwo methods that were recently proposed for calculating fractional bedload transport rates in gravel‐bed streams are examined closely. Both of them employ the Oak Creek bedload data. The Diplas (PD) method is guided by dimensional analysis and, therefore, can be used to predict bedload transport in different gravel rivers. The only requirement for using this method is the knowledge of the subsurface material size distribution of the stream of interest. The expression for the fractional bedload transport obtained by the Shih and Komar (SK) method for Oak Creek cannot be used for other streams. Its use for a given stream requires information that is rarely available. For the Oak Creek case both methods demonstrate similar predictive ability.