How does the bed surface impact low-magnitude bedload transport rates over gravel-bed rivers?

Bedload transport is a complex phenomenon that is not well understood, especially for poorly sorted sediment and low transport rates, which is what is typically found in alpine gravel-bed rivers. In this paper, the interaction between bedload rate, bed stability and flow is investigated using flume experiments. Significant differences in bedload rates were observed for experiments conducted on beds formed with the same gravel material but presenting diverse arrangements and bedforms. Tests were performed under regimes of low transport rate, which are mainly controlled by gravel-bed roughness. Different scales of roughness were identified using the statistical characteristics of detailed bed elevation measurements: grain, structure and large bedform scales. The role played by these different roughness scales in bedload dynamics was examined. For quasi-flat beds, bed stability was quantified using a combination of bed surface criteria describing grain and structure scales. It was found that bed stability affects the bedload rate directly and not only through its influence on the flow or on the incipient motion. For beds with large bedforms, the analysis of bedload dynamics also showed the importance of accounting for effective bed shear stress distributions. An empirical bedload model for low transport regimes was suggested. Compared with previous formulae developed for alpine rivers, this model accounts for bed stability and distribution of effective bed shear stress. It significantly improves the understanding of gravel dynamics over complex beds such as arranged beds or those with large bedforms. However, further tests are needed to use the model outside the range of conditions of this study. © 2019 John Wiley & Sons, Ltd.     

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

The grain-size distributions of bedload gravels in Oak Creek, Oregon, follow the ideal Rosin distribution at flow stages which exceed that necessary to initiate breakup of the pavement in the bed material. The distributions systematically vary with flow discharge and bed stress, such that at higher flow stages the grain sizes are coarser while the spread of the distribution decreases. A differential bedload transport function for individual grain-size fractions is formulated utilizing the dependence of the two parameters in the Rosin distribution on the flow stress. The total transport rate, which is also a function of the flow stress, is apportioned within the Rosin grain-size distribution to yield the fractional transport rates. The derived bedload function has the advantage of yielding smooth, continuous frequency distributions of transport rates for the grain-size fractions, in contrast to the discrete transport functions which predict rates for specified sieve fractions. Successful reproduction of the measured fractional transport rates and bedload grain-size distributions in Oak Creek by this approach demonstrates its potential for evaluations of transport rates of size fractions in gravel-bed streams. The approach will be useful in investigations of downstream changes in bed material grain-size distributions.     

Effects on bedload transport of experimental removal of woody debris from a forest gravel-bed stream

Experimental removal of woody debris from a small, gravel-bed stream in a forested area resulted in a four-fold increase in bedload transport at bankfull discharge. This was caused by increased transportability of sediment previously stored upslope of debris buttresses or in low-energy hydraulic environments related to debris. Bank erosion delivered additional sediment to the channel, and transport energy was increased by an inferred increase in the component of total boundary shear stress affecting grains on the bed. Increased transport following debris removal in May 1987 continued throughout the entire autumn storm season through late November 1987, indicating persistent adjustment of the stream bed and banks despite marked response to earlier flows as large as bankfull. Stream bed adjustments included development of a semi-regular sequence of alternate bars and pools, many of which were spaced independently of former pool locations.     

Evolution of grain size distributions and bed mobility during hydrographs in gravel-bed braided rivers

Evolution of bed material mobility and bedload grain size distributions under a range of discharges is rarely observed in braiding gravel-bed rivers. Yet, the changing of bedload grain size distributions with discharge is expected to be different from laterally-stable, threshold, channels on which most gravel bedload theory and observation are based. Here, simultaneous observations of flow, bedload transport rate, and morphological change were made in a physical model of a gravel-bed braided river to document the evolution of grain size distributions and bed mobility over three experimental event hydrographs. Bedload transport rate and grain size distributions were measured from bedload samples collected in sediment baskets. Morphological change was mapped with high-resolution (~1 mm precision) digital elevation models generated from close-range digital photogrammetry. Bedload transport rates were extremely low below a discharge equivalent to ~50% of the channel-forming discharge (dimensionless stream power ~70). Fractional transport rates and plots of grain size distributions indicate that the bed experienced partial mobility at low discharge when the coarsest grains on the bed were immobile, weak selective mobility at higher discharge, and occasionally near-equal mobility at peak channel-forming discharge. The transition to selective mobility and increased bedload transport rates coincided with the lower threshold for morphological change measured by the morphological active depth and active width. Below this threshold discharge, active depths were of the order of D₉₀ and active widths were narrow (< 3% of wetted width). Above this discharge, both increased so that at channel-forming discharge, the active depth had a local maximum of 9D₉₀ while active width was up to 20% of wetted width. The modelled rivers approached equal mobility when rates of morphological change were greatest. Therefore, changes in the morphological active layer with discharge are directly connected to the conditions of bed mobility, and strongly correlated with bedload transport rate. © 2018 John Wiley & Sons, Ltd.     

Temporal variations in bedload transport rates: The effect of progressive bed armouring

The quantitative bedload transport data that are presently available confirm that the generalized bedload transport rate-stream power relationship is applicable to natural streams. However, the bedload transport rate is not solely dependent upon hydraulic parameters, but also upon the inter-relationship between bed material characteristics and flow properties. Segregation of the surficial bed material, as expressed through the development of an armour coat, limits the availability of transportable material. Under such circumstances observed bedload transport rates are less than the predicted values. The effect which the development of an armoured surface has upon the bedload transport rate is described with reference to bedload and bed material sampling in the Borgne d'Arolla, Valais, Switzerland. The data refer to two periods when the resumption of baseflow conditions following flood events which were of a sufficient magnitude to transport all but the coarsest (0·3–0·5 m) particles on the streambed, provided the opportunity for the bed to adjust to a comparatively stable flow regime. Observed and predicted bedload transport rate-stream power relationships are compared. The theoretical relationship does not adequately describe conditions in some gravel-bed channels, since it fails to take into account the effect which armouring may have upon the supply of transportable material.     

Channel morphology and bedload pulses in braided rivers: a laboratory study

Bedload pulses in gravel-bed rivers have been widely reported in recent years and attempts have been made to relate them to channel morphology. Bedload transport and channel morphology were measured in a small-scale generic model of braided gravel-bed streams. Two experiments are described in which braided channels developed in a 14 m × 3 m sand tray. Total bedload output from the tray was weighed every 15 minutes. Stream bed geometry was surveyed every four hours. Pulses were observed in the bedload output time series, and were qualitatively related to the channel morphology immediately upstream of the measuring section. The Bagnold (1980) bedload equation generally overpredicts measured bedload transport rates when applied to channels that were in equilibrium or aggrading. Underprediction occurred when applied to degrading channels. Aggradation was associated with channel multiplication and bar deposition. Channel pattern simplification occurred when degradation took place, and bars emerged from the water flow. Development of phases of aggradation and degradation is dependent upon the three-dimensional geometry of the stream beds. Spatial and temporal feedback loops can be identified, enabling links between channel morphology and bedload transport rate to be directly identified.     

Insights into bedload transport processes of a large regulated gravel‐bed river

A comprehensive monitoring programme focusing on bedload transport behaviour was conducted at a large gravel‐bed river. Innovative monitoring strategies were developed during five years of preconstruction observations accompanying a restoration project. A bedload basket sampler was used to perform 55 cross‐sectional measurements, which cover the entire water discharge spectrum from a 200‐year flood event in 2013 to a rare low flow event. The monitoring activities provide essential knowledge regarding bedload transport processes in large rivers. We have identified the initiation of motion under low flow conditions and a decrease in the rate of bedload discharge with increasing water discharge around bankfull conditions. Bedload flux strongly increases again during high flood events when the entire inundation area is flooded. No bedload hysteresis was observed. The effective discharge for bedload transport was determined to be near mean flow conditions, which is therefore at a lower flow discharge than expected. A numerical sediment transport model was able to reproduce the measured sediment transport patterns. The unique dataset enables the characterisation of bedload transport patterns in a large and regulated gravel‐bed river, evaluation of modern river engineering measures on the Danube, and, as a pilot project has recently been under construction, is able to address ongoing river bed incision, unsatisfactory ecological conditions for the adjacent national park and insufficient water depths for inland navigation. Copyright © 2017 John Wiley & Sons, Ltd.     

Dynamics of bedload transport in Turkey brook,a coarse-grained alluvial channel

Automatic and continuously recording samplers are deployed in a Hertfordshire gravel-bed stream to show that bedload transport is related to stream power. The pattern is similar to that already established for North American channels but, because the record is so detailed, it is possible to identify the cause of the considerable scatter that is normal in such relationships. A major factor is the occurrence of rhythmic pulses in bedload discharge that are not matched by similar fluctuations in hydraulic variables. It is suggested that these pulses reflect downstream differences in the concentration of mobile particles in a slow-moving traction carpet, and that they may be likened to kinematic waves. The record also reveals that the threshold of sediment transport—always presumed hithero to be associated with incipient motion—is related to the cessation of bedload transport in a river flood. Indeed, the mean value of stream power at the finish of bedload transport is only 20 percent of that prevailing at the moment of incipient sediment motion. Because of this, there is an inevitably poor correlation between actual bedload transport rates and those predicted by bedload equations which rely upon a single traction threshold. These new data show that the general inverse relationship between bedload discharge and water-depth : grain-size ratio proposed by Bagnold (1977, 1980) is not universal. Transport efficiency for this gravel-bed stream is typically 0.05 per cent of available stream power, which compares with 1.6 per cent for a river moving both gravel and sand, and 5 per cent for another channel where bedload is composed predominantly of sand-sized particles. It is argued that coarse and fine-grained alluvial channels may need to be considered separately. By allowing for differences in traction threshold at the beginning and end of bedload events, and by averaging bedload discharge flood by flood in order to smooth out the effect of pulses, it is possible to achieve a reasonably good prediction of average bedload transport rate in terms of stream power.     

Listen to the sound of moving sediment in a small gravel-bed river

In order to assess the dynamics of rivers, a reliable characterization of bedload transport particularly during unsteady flow regimes is required. In contrast to highly energetic cases in hillslope areas, we aim to answer the question whether the usage of acoustic measurements can improve the characterization of bedload in small rivers draining low land mountains with comparatively low water discharge and bedload. In addition to the investigation of natural flood events, controlled floods were generated by releasing water from a reservoir into a small gravel-bed stream. The controlled releases allow for an evaluation of bedload solely from channel storage or bank erosion. For acoustical in-situ characterization of bedload transport, hydrophones were mounted onto the bottom side of steel plates, thus recording the impacts of sediments via the acoustic vibrations on the surface of the plates while at the same time minimizing the disturbing noise resulting from water turbulence. Corresponding bedload traps are removable boxes with open lids fixed in the riverbed so that bedload material registered by the hydrophone is trapped. The acoustic signals correlate well with the quantity of the transported material. During summer flood events the highest transport rates occur at the beginning of the rising limb fea-turing clockwise hysteresis. This is due to the rising transport energy of the flow and the presence of loose, unconsolidated material. During typical winter flood events bedload shows anticlockwise loops. The intensification of bedload conveyance after the runoff peak can be explained by a decreasing stability of the bed material from the beginning to the end of a transport event. Anticlockwise behavior also results from a combination of bedload exhaustion in the vicinity of the monitoring station with a delayed arrival of new material from distal sources later in the hydrograph.     

Bedload transport of small rivers in Malaysia

Numerous time-consuming equations, based on the relationship between the reliability and representativeness of the data utilized in defining variables and constants, require complex parameters to estimate bedload transport. In this study the easily accessible data including flow discharge, water depth, water surface slope, and surface grain diameter （ds0） from small rivers in Malaysia were used to estimate bedload transport. Genetic programming （GP） and artificial neural network （ANN） models are applied as complementary tools to estimate bed load transport based on a balance between simplicity and accuracy in small rivers. The developed models demonstrate higher performance with an overall accuracy of 97% and 93% for ANN and GP, respectively compared with other traditional methods and empirical equations.     

Quantifying the Morphological Print of Bedload Transport

Bedload and river morphology interact in a strong feedback manner. Bedload conditions the development of river morphology along different space and time scales; however, by concentrating the flow in preferential paths, a given morphology controls bedload for a given discharge. As bedload is a non‐linear response of shear stress, local morphology is likely to have a strong impact on bedload prediction when the shear stress is averaged over the section, as is usually done. This was investigated by comparing bedload measured in different bed morphologies (step‐pool, plane bed, riffle‐pool, braiding, and sand beds), with bedload measured in narrow flumes in the absence of any bed form, used here as a reference. The initial methodology consisted of fitting a bedload equation to the flume data. Secondly, the morphological signature of each river was studied as the distance to this referent equation. It was concluded that each morphology affects bedload in a different way. For a given average grain shear stress, the larger the river, the larger the deviation from the flume transport. Narrow streams are those morphologies that behave more like flumes; this is particularly true with flat beds, whereas results deviate from flumes to a greater extent in step‐pools. The riffle‐pool's morphology impacts bedload at different levels depending on the degree of bar development, considered here through the ratio D₈₄/D₅₀ which is used as a proxy for the local bed patchiness and morphology. In braiding rivers morphological effects are important but difficult to assess because width is dependent on transport rate. Bed morphology was found to have negligible effects in sand bed rivers where the Shields stress is usually sufficiently high to minimize the non‐linearity effects when hydraulics is averaged over the section. Copyright © 2015 John Wiley & Sons, Ltd.     

Bedload transport from analytical and turbulence phenomenological perspectives

In this paper, we present the dynamics of bedload transport from two different perspectives. They are the analytical perspective and the turbulence phenomenological perspective. In bedload transport from the analytical perspective, we highlight the systematic advances in the analytical modelling of bedload transport over the decades. These advances are principally classified into three broad foundations, namely, the deterministic foundation, that includes the bed shear stress concept, stream power concept, force balance concept and bedform concept, and the probabilistic foundation and the turbulence phenomenological foundation of bedload transport. The bedload transport from the turbulence phenomenological perspective brings into focus the bedload-induced turbulence phenomenology, including the hydrodynamics of mobile-bed and water-worked bed flows. We also discuss the recent advances in the biofilm-coated bedload transport. Finally, conclusion is drawn, highlighting the major research challenges.     

Testing bedload transport formulae using morphologic transport estimates and field data: lower Fraser River,British Columbia

Morphologic transport estimates available for a 65‐km stretch of Fraser River over the period 1952–1999 provide a unique opportunity to evaluate the performance of bedload transport formulae for a large river over decadal time scales. Formulae tested in this paper include the original and rational versions of the Bagnold formula, the Meyer‐Peter and Muller formula and a stream power correlation. The generalized approach adopted herein does not account for spatial variability in flow, bed structure and channel morphology. However, river managers and engineers, as well as those studying rivers within the context of long‐term landscape change, may find this approach satisfactory as it has minimal data requirements and provides a level of process specification that may be commensurable with longer time scales. Hydraulic geometry equations for width and depth are defined using morphologic maps based on aerial photography and bathymetric survey data. Comparison of transport predictions with bedload transport measurements completed at Mission indicates that the original Bagnold formula most closely approximates the main trends in the field data. Sensitivity analyses are conducted to evaluate the impact of inaccuracies in input variables width, depth, slope and grain size on transport predictions. The formulae differ in their sensitivity to input variables and between reaches. Average annual bedload transport predictions for the four formulae show that they vary between each other as well as from the morphologic transport estimates. The original Bagnold and Meyer‐Peter and Muller formulae provide the best transport predictions, although the former underestimates while the latter overestimates transport rates. Based on our findings, an error margin of up to an order of magnitude can be expected when adopting generalized approaches for the prediction of bedload transport. Copyright © 2005 John Wiley & Sons, Ltd.     

Bedload transport processes in a braided gravel-bed river model

A 1:50 scale hydraulic model was designed, based on Froude number similarity and using hydrological and sediment data from a small braided gravel-bed river (the North Branch of the Ashburton River, Canterbury, New Zealand). Eighteen experiments were conducted; seven using steady flows, and eleven using unsteady flows. The experiments were carried out in a 20 m × 3 m tilting flume equipped with a continuous sediment feed and an automated data acquisition and control system. In all experiments water at 30°C was used to reduce viscosity-related scale effects. Analyses of the experimental data revealed that bedload transport rates in braided channels are highly variable, with relative variability being inversely related to mean bedload transport rate. Variability was also found to be cyclic with short-term variations being caused by the migration of bedforms. Bedload transport was found to be more efficient under steady flow than under unsteady flow, and it was postulated that this is caused by a tendency for channel form to evolve towards a condition which maximizes bedload transport for the occurring flow. Average bedload transport rate was found to vary with channel form, although insufficient measurements were made to define a relationship.     

Observations of bedload movement,bar development and sediment supply in the braided Ohau river

Relative bedload transport rate and hydraulic parameters were measured on two occasions in a reach of the braided, gravel-bedded Ohau River. Each reach contained a deep, fast-flowing chute leading to an area of diverging, shallow flow which contained a middle bar. The measurements are self-consistent, and indicate that, where flow is concentrated in a deep chute, shear stress is high, but where flow diverges, depth, slope and shear stress decrease. In the first survey, the bed was scoured in the chute and sediment transport rates were high, but where flow diverged sediment transport rate decreased. It appears that deposition leads to bar growth, bar growth in turn reduces slope and depth, deposition is encouraged, and the bar continues to grow vertically, laterally and upstream. In the second survey no sediment transport was observed, despite hydraulic conditions very similar to the first survey. The absence of sediment transport is attributed to the cessation of sediment supply to the river channel.     

‘Bedload’ dynamics: Grain-grain interactions in water flows

Owing to experimental difficulties, the transport stage at which collisions between moving ‘bedload’ grains might become significant has never been investigated, yet the existence or otherwise of such collisions is of some importance in the understanding of the mechanics of sediment transport, in particular the theory developed by Bagnold. Application of the basic principles of gaseous kinetic theory to ‘bedload’ grains moving in saltant trajectories and the adoption of a ‘characteristic’ saltation path leads to the prediction that grain-grain collisions should dominate in the transport of coarse sands over plane beds in water flows above a transport stage of about 2, i.e. when the mean boundary fluid shear stress exceeds the critical boundary shear stress for grain motion by about 4 times. Above this stage interrupted saltations should always occur, with the ‘bedload’ grains held above the stationary bed by a combination of fluid and solid momentum transfer mechanisms. A classification of the types of grain motions is given and evidence is presented for the existence of an upward decrease in grain collision frequency and of grain concentration at the top of the ‘bedload’ zone.     

Bedload transport and temporal variation of non-uniform sediment in a seepage-affected alluvial channel

Understanding bedload transport fluctuations in rivers is crucial for complementing the existing knowledge on sediment transport theory. In this contribution, we use a natural-scale laboratory flume to analyse bedload transport fluctuations in non-uniform sand under normal flow conditions. Based on the significance of downward seepage, we incorporate the seepage effect on bedload transport over a non-uniform sand bed channel. The weight of the dry material was measured, and the volumetric transport rate per unit width (bedload transport rate) was estimated. An important observation is that the bedload transport rate initially rapidly increases with time and reaches a maximum value. Based on experimental data, we propose an empirical expression to estimate temporal bedload transport. In addition, an empirical model for bedload transport is proposed by incorporating downward seepage among other variables. The performance of several existing bedload transport formulae was also taken into account by the experimental datasets.     

Formation of stationary alternate bars in a steep channel with mixed-size sediment: A flume experiment

Alternate bars were formed by sediment transport in a flume with Froude-modelled flow and relative roughness characteristic of gravel-boulder channels with steep slopes. The flume (0.3 m wide × 7.5 m long) was filled with a sand-gravel mixture, which was also fed into the top of the flume at a constant rate under constant discharge. Channel slope was set at 0.03. Initially, coarse particles accumulated on incipient bar heads near one side of the flume and diverted flow and bedload transport across the flume toward a pool scoured against the opposite flume wall downstream. Sorting in the pool directed coarse particles onto the next bar head downstream. Alternate sequences of pools and coarse bar heads were thereby linked down the entire flume by interactions of sediment sorting, flow, and channel morphology. During episodes of bar construction, unsorted bedload invaded interior bar surfaces and was deposited. Persistent deposition of coarse particles on bar heads prevented downstream migration of bars by inhibiting bar-head erosion and bedload transport over bars. Likely factors leading to bar-head stabilization in modelled gravel-bed channels are coarse mixed-size sediment, steep channel gradients, and shallow depths.     

The nahal yatir bedload database: Sediment dynamics in a gravel-bed ephemeral stream

The Nahal Yatir Bedload Transport Database arises from the Northern Negev River Sediment Monitoring Programme and represents the first body of bedload information to be collected during flash floods in desert gravel-bed streams. Bedload flux was established automatically with three slot-samplers of the Birkbeck type. This was complemented by hydraulic measurements that allow sediment transport to be rated against channel average shear stress and specific stream power. Bed material and bedload grain-size distributions are also provided. The database is given in both printed and electronic tabular format.