Bed-load Rate Research Articles

Quantification of bedload transport in the Hungarian Danube using multiple analysis methods

While bedload transport is crucial to river morphodynamics, quantifying it in large rivers, such as the Danube, poses significant challenges. The current study focuses on the gravel-dominated section of the Danube River in Hungary, where multiple methods have been concurrently applied to evaluate bedload transport. In a representative cross section of the river, the following methods were applied: (i) point-wise direct physical sampling using a BfG-type pressure difference sampler, quality controlled with a video camera mounted on the sampler; (ii) indirect acoustic-based analysis with an Acoustic Doppler Current Profiler (ADCP), evaluating the Bottom Tracking signal; and (iii) indirect acoustic and imaging-based method utilizing Acoustic Mapping Velocimetry (AMV). The ADCP method is calibrated using results from the physical sampling, while the AMV method relies on bedform tracking and is entirely independent from the two other techniques. The results from a series of measurement campaigns, covering a wide range of flow regimes, suggest a robust bedload rating curve for the study section, enabling the estimation of bedload yields and its relation to morphological changes. In addition, the applicability conditions of the implemented methods are discussed.

An improved formula for bed-load rate in open channel flows with emergent vegetation

There is an urgent need to predict the bed-load transport rate in vegetated river ecosystems to support restoration efforts. In response, we have developed a novel model for estimating the effective shear stress acting on the riverbed. This model is based on the energy equation and considers the intrinsic relationship between energy loss in the mean flow and turbulence generated by vegetation in open channel flows with emergent vegetation. Using this bed shear stress model, we assessed the performance of the Meyer-Peter–Müller (MPM) formula in predicting the bed-load transport rate in vegetated flows by comparing it with collected literature experimental data. The results revealed that the MPM formula does not provide accurate predictions. It tends to overestimate the bed-load transport rate when the dimensionless effective shear stress is approximately less than one and underestimate them when the dimensionless effective shear stress is approximately greater than one. This suggests that vegetation enhances and decreases the sediment transport rate when the dimensionless effective shear stress is approximately larger or lower than one, respectively. Consequently, we modified the coefficients of the MPM formula using extensive experimental data, leading to the development of a novel predictive formula for the bed-load transport rate in vegetated flows. This new formula outperforms existing literature equations and is effective for predicting the bedload transport rate, even for umbrella-like vegetation.

Quantitative definition of Shields criterion for incipient sediment motion

The Shields diagram has been widely used in the description of the threshold condition for incipient sediment motion. Because the current definition of the Shields criterion is generally subjective, the relevant data are subject to high uncertainty. To date, several efforts have been made to define the threshold condition quantitatively, but they are all based on certain low bedload rates that were empirically chosen. The current study aims to provide a theoretical framework to quantify the Shields criterion based on the concept of the pickup probability of sediment particles. The results show that the Shields criterion can be reasonably described with a low pickup probability (p = 1%), which can be further converted to a low dimensionless bedload rate (i.e., ϕ/θ1.5=0.13, where ϕ is the Einstein number and θ is the Shields number). The new approach is finally validated with experimental data of bedload rates published in the literature.

Flushing Efficiency of Run-of-River Hydropower Plants: Novel Approaches Based on Physical Laboratory Experiments

Periodic flushing operations during moderate flood events (≤annual flood flow HQ1) are an approach to counteract problems caused by disturbed sediment continuity in rivers, which is possibly an effect of run-of-river hydropower plants (RoR-HPPs). Considering ecology, flood risk, technical, and economical reasons, discharge values of 0.7 × HQ1 are a good reference point for the initiation of gate operations. This work aimed to investigate the role of different gate opening actions on the effectiveness of such flushing measures. Physical model tests were performed, to capture bed load rates, together with 2D velocity measurements in the vicinity of two movable radial gates above a fixed weir. The length scale of the idealized model arrangement was 1:20, and a conveyor-belt sediment feeder was used to supply a heterogeneous sediment mixture. Velocities were acquired using 2D laser doppler velocimetry (LDV). Based on the LDV measurements, mean velocity profiles and Reynolds stresses were derived. The full opening of both radial gates led to the highest bed load mobility. While the flushing efficiency drastically decreased, even for slightly submerged gates, an asymmetrical gate opening initially led to the formation of a flushing cone in the vicinity of the weir, accompanied by temporarily high flushing efficiency. In conclusion, our results stress the importance of full drawdowns in successfully routing incoming bed load downstream of the HPP. However, the combination of an asymmetric gate opening followed by a full drawdown could be a promising approach to further improve the flushing efficiency of RoR-HPPs.

On the Capabilities of Emerging Nonintrusive Methods to Estimate Bedform Characteristics and Bedload Rates

AbstractA new measurement protocol, labeled Acoustic Mapping Velocimetry (AMV), has been successfully tested for in‐situ estimation of bedload transport features in sandy beds. The AMV has proven efficient in using the dune‐tracking method (DTM) for characterizing the bedform geometry and dynamics as well as for estimation of the rates of bedload transport. Given the novelty of the AMV protocol and its extensive reliance on multiple site‐specific assumptions and user‐defined parameters, a comparison of this emerging technique with other three non‐intrusive DTM‐based methods and analytical predictors is attempted in this paper. The comparison highlights that the AMV estimates are within 22% of the estimates with the other non‐intrusive protocols and up to 98% different from analytical predictions. The observed differences are related to the possible sources of uncertainty in the AMV workflows and to the means to reduce their impact on the targeted estimations.

Mapping 2‐D Bedload Rates Throughout a Sand‐Bed River Reach From High‐Resolution Acoustical Surveys of Migrating Bedforms

AbstractThis paper introduces a method for determining spatially‐distributed, 2‐D bedload rates using repeat, high‐resolution surveys of the bed topography. As opposed to existing methods, bedform parameters and bedload rates are computed from bed elevation profiles interpolated along the local bedform velocities. The bedform velocity fields are computed applying Large‐Scale Particle Image Velocimetry, initially developed for surface velocity measurements, to pairs of successive Digital Elevation Models (DEMs). The bathymetry data are interpolated along the direction of each bedform velocity and the mean height of the closest bedform is computed. The dune shape factor is also evaluated along each bedform direction of travel. The local bedload fluxes can be computed by multiplying the bedform velocity by its mean height averaged over the successive two DEMs, and they can be time‐averaged over a series of DEM pairs. This method is applied to a high‐resolution acoustical survey of an approximately 300 m long by 40 m wide reach of the Colorado River in Grand Canyon upstream from Diamond Creek, USA. The repeat period was about 6–10 min and bed elevation was interpolated every 0.25 m. The obtained results provide insight to the spatial and temporal variability of bedload rates, bedform parameters and bedload fluxes through cross‐sections. The method can be applied to other repeated acoustical surveys of river reaches provided that the space and time resolutions are high enough to capture the local movement of bedforms.

Bedload Fluxes in a Glacier‐Fed River at Multiple Temporal Scales

AbstractIn mountain rivers, long‐term observations of water and sediment fluxes are crucial for understanding the dynamics of bedload fluctuations. We analyze 7 years of continuous data gathered from eight geophone plates at a monitoring station in the glacier‐fed Sulden/Solda River (South Tyrol, Italy) to estimate the bedload flux at 1‐min scale. Sixty‐five bedload samples were used to derive the calibration equations adopted to quantify the transported bedload mass. The signal power is proposed as a more effective metric than threshold‐based impulses for calculating bedload masses. Results show (a) a remarkable variability of bedload rates for the same value of flow discharge, (b) the joint effect of storm‐driven flood events and seasonal changes in sediment supply on bedload rates, and (c) the strong impact of climatic factors (i.e., temperature and snow cover) on bedload fluxes. Moderate bedload rates occurring in late spring/early summer are likely related to the mobilization of riverbed sediments, while sustained bedload transport during melt flows in July–August—corresponding to the effective bedload discharge range—is associated with the activation of glacial and proglacial sediment sources. The data set shows a complex climatic control on bedload transport at the basin scale, where precipitation, air temperature, and snow cover determine flow and glacier melting dynamics. These findings suggest how the effects of climate change in the Alps likely will lead to an increase in peak bedload rates in a context of declining annual bedload yields as melt flows will progressively reduce in the next decades.

Hydrograph Shape Impact on Sand Infiltration and Sediment Transport Dynamics in Gravel‐Bed Rivers

AbstractSand (i.e., < 2 mm) infiltration into a gravel bed is recognized to affect sediment dynamics of coarser fractions (i.e., entrainment and transport rate), near‐bed velocities, bed morphology, and to pose significant engineering and ecological issues. Local hydraulics, sediment dynamics, and sand infiltration into the gravel matrix are related and mutually affect each other in gravel‐bed rivers. However, relatively little research has been done to explore sediment dynamics and sand infiltration in a mobile gravel‐bed under unsteady flow conditions. In the present study, we experimentally simulated three hydrographs of different durations of rising and falling limbs, and monitored sand infiltration over beds with a coarse and a fine grain size distribution. Results confirmed that the addition of sand enhances sediment dynamics. Moreover, the shape of the rising limb of the hydrograph was responsible for altering identified sand infiltration processes and bedload rate. Short time‐to‐peak floods (i.e., short time from the start to the peak of the hydrograph) experienced higher sediment transport rates during the falling limb than the rising limb of the hydrograph, favoring sand infiltration. In contrast, long time‐to‐peak floods (i.e., long time from the start to the peak of the hydrograph) experienced higher sediment transport rates during the rising limb than the falling limb of the hydrograph, resulting in reduced sand infiltration.

Viscous effects on bedload sediment transport rates

Viscous effects on bedload sediment transport rates have been seldom examined in previous studies. They may become significant in the low transport regime, as evidenced by experimental data. However, the problem cannot be resolved using classical bedload models that involve the shear excess, for example, Meyer-Peter–Müller formula. By applying the concept of the critical pickup probability for incipient sediment motion, this study derives a new bedload formula that takes the fluid viscosity into consideration. The results show that the relationship between the dimensionless bedload rate and the Shields number varies significantly with the viscosity-dependent parameter in the low transport regime, which partially accounts for the scattering of bedload data. In addition, the present study proposes a simple approach to the evaluation of the critical bedload transport rate that is associated with the Shields curve for incipient sediment motion.

Seasonal bedload pulses in a small alpine catchment

Natural fluctuations of bedload transport under steady hydraulic conditions have been often attributed to the propagation of sediment pulses in river channels, leading to hysteretic patterns in bedload rating curves at both the hydrograph and the seasonal timescales. However, direct field observations of the sediment pulse effect on bedload transport rates have been rarely reported. Two bedload datasets recorded in a small Mediterranean badland catchment of the Southern French Prealps (Moulin Ravine at Draix) are used here to investigate the effect of sediment pulses originating from hillslopes on the bedload response to flow conditions. The first dataset comes from a long-term erosion monitoring program providing time-integrated bedload yields since the late 1980s by means of a large sediment trap. The second dataset is based on a slot sampler providing bedload fluxes at a 1-min time resolution since autumn 2011. Sediment pulses have been tracked with regular scour chain surveys along the alluvial channel upstream of the bedload monitoring station. Both datasets revealed a seasonal counterclockwise bedload hysteresis which can be attributed to a yearly sediment pulse reaching the catchment outlet during autumn and early winter. We believe that these seasonal bedload pulses could be typical of small alpine catchments with active gully erosion on bedrock sensitive to frost-cracking processes.

Effect of Increasing Antecedent Flows on Equilibrium Bed-Load Transport Rates in a Laboratory Channel with a Sand and Gravel Bed Channel

Experiments were conducted in a laboratory flume in which gravel and total bed-load rates were measured continuously using independent methods that allowed evaluation of the effect of four antecedent flow conditions on the transport of bed load under standard flow. It was found that both mean total bed-load rate and gravel transport rates are related to the magnitude of antecedent flow. The changes in mean bed-load rates were attributed to changes in the stability of the coarsest fractions of the bed material, caused by the previous high-flow event. This work indicates that long-term mean bed-load transport rates for a sand and gravel bed are not just a function of grain size and flow rate but also vary with the magnitude of antecedent flow.

Relevance of acoustic methods to quantify bedload transport and bedform dynamics in a large sandy-gravel-bed river

Abstract. Despite the inherent difficulties in quantifying its value, bedload transport is essential for understanding fluvial systems. In this study, we assessed different indirect bedload measurement techniques with a reference direct bedload measurement in a reach of a large sandy-gravel-bed river. An acoustic Doppler current profiler (aDcp), the dune tracking method (DTM) and hydrophone measurement techniques were used to determine bedload transport rates by using calibration with the reference method or by using empirical formulas. This study is the first work which attempted to use a hydrophone to quantify bedload rates in a large sandy-gravel-bed river. Results show that the hydrophone is the most efficient and accurate method for determining bedload fluxes in the Loire River. Although further work is needed to identify the parameters controlling self-generated sediment noise, the calibration procedure adopted in this study allows a satisfactory estimation of bedload transport rates. Moreover, aDcp and hydrophone measurement techniques are accurate enough to quantify bedload variations associated with dune migration.

The intensity of siltation of a small reservoir in Poland and its relationship to environmental changes

Siltation of reservoirs is an indicator of the intensity of erosion processes and sediment yields of river catchments. An estimation of sediment yield is significant for hydroengineering practices, environmental prediction and modelling. It also reflects environmental changes in the form of climate and land use.The present study aimed to compare the amount of sediment deposited in a small reservoir in Poland, with the estimate of sediment yield from its catchment, using the Universal Soil Loss Equation coupled with a sediment delivery ratio (USLE-SDR) and an estimate of annual bed load transport, provided by a regional bed load formula. The estimate of the annual amount of bed load was based on the flow frequency graph and bed load rating curve of Skibinski. The dam of the reservoir was constructed in 1976. The first reservoir survey was carried out between 1979 and 1980, when the reservoir volume was estimated to be 252,000 m3. Subsequent surveys were carried out in 1991, 2003, 2009 and in the Spring of 2020. These surveys enabled the amount of sediment, deposited in the reservoir, to be measured across four different periods: 1980–1991, 1992–2003, 2004–2009 and 2010–2019. For the same periods, the USLE with a constant SDR (calculated using the approach provided by Vanoni) were used to estimate the quantity (mass) of suspended sediment yield from the contributing area of the catchment. The volume of suspended sediment, deposited in the reservoir, was obtained, taking into account the reservoir trap efficiency and assuming a density of suspended sediment deposits.Hydrological investigations of the Plachty gauging station on the Zagozdzonka River, the left tributary of the Vistula River, have been carried out by the Department of River Engineering at Warsaw University of Life Sciences since 1962. The catchment area at the Plachty gauging station, located just upstream of the reservoir, is 82.4 km2, whereas the catchment area above the dam of the Staw Górny reservoir, is 91.4 km2.The estimated annual sediment yields for the catchment, based on reservoir surveys across four periods between 1980 and 2020, suggest a general decrease over time. This study was also undertaken to examine long-term variability in sediment yield, both in suspended sediment and bed load, related to rainfall-runoff erosivity, river discharge and land use changes, which could influence changes in catchment sediment yield. An analysis of local temperature and catchment runoff revealed a long-term increase in the mean annual temperature and a corresponding decrease in annual discharge.The annual values of total sediment input to the reservoir (suspended and bed load), estimated using the USLE-SDR and a bed load formula with sediment trap efficiency, are very close to the measured amounts of deposits in the reservoir. Annual deposits in the reservoir are decreasing with time. This is presumably caused by the decrease in arable land in the catchment. From the mean annual deposits in the reservoir, around 35% is bed load and 65% is suspended load. The average annual specific suspended sediment yield in the catchment, is ca. 9 Mg/km2.

Extended Einstein's parameters to include vegetation in existing bedload predictors

Observations show that instream vegetation has a strong impact on bedload transport. However, there is a scarcity of sediment transport predictors that directly account for the effects of plants, and existing methods, based on re-calculation of roughness coefficients, may present some inconsistencies. The approach herein proposed extends Einstein's parameters to include the effects of vegetation on sediment transport for implementation in existing bedload predictors of the form Φ = f(Ψ). The new formulations are applicable in presence of submerged and emergent vegetation and reduce to the original Einstein's parameters if vegetation is absent. Calibration is based on laboratory data. For this purpose, an extensive experimental program was carried out on a tilting glass-walled flume with medium-sand bed and plants represented by aluminum cylinders. Validation is based on published bedload measurements from the literature. The results show a much better agreement between measurements and predictions when applying the extended parameters compared to using Einstein's original ones. Predicted bedload rates have, on average, the same order of magnitude of the measured ones, and quantitative agreement is substantially increased. Clear improvements were also observed when comparing the results with the bedload predictions of Baptist's (2005) method, which is based on the re-calculation of bed roughness in the presence of vegetation.

Theoretical Investigation of Equilibrium Dynamics in Braided Gravel Beds for the Preservation of a Sustainable Fluvial Environment

Gravel bars have an important role in the exchange between surface and subsurface waters, in preventing and mitigating riverbank erosion, in allowing the recreational use of rivers, and in preserving fluvial or riparian habitats for species of fishes, invertebrates, plants, and birds. In many cases, gravel bars constitute an important substrate for the establishment and development of ground flora and woody vegetation and guarantee higher plant diversity. A sustainable management of braided rivers should, therefore, ensure their ecological potential and biodiversity by preserving a suitable braiding structure over time. In the present study, we propose an analytical–numerical model for predicting the evolution of gravel bars in conditions of dynamical equilibrium. The model is based on the combination of sediment balance equation and a regression formula relating dimensionless unit bedload rate and stream power. The results highlight the dependence of the evolving sediment particles’ pattern on the ratio of initial macro-bedforms longitudinal dimension to river width, which determines the gradual transition from advective and highly braiding to diffusive transport regime. Specifically, the tendency to maintain braiding and flow bifurcation is associated with equilibrium average bed profiles and, therefore, equilibrium average stream power characterized by the maximum period that does not exceed transverse channel dimension.

Influence of flow hydraulic characteristics on the ridge lower escarpment angle

In the riverbeds and canals that run on non-cohesive grounds, bedload sediments move in the ridges form. Ridge forms determine the flow rate of bedload sediments, hydraulic resistances, the types and rates of deformations in alluvial channels. The main elements of ridge formations are height, gentle and steep length with corresponding escarpments. The ridge's steep length and this corresponding escarpment change with changes in the flow hydraulic characteristics. With a change in the ridge's steep length and its steep escarpment, the hydraulic resistance of the channel, the flow rate of bedload sediments, the types, and the channel deformation rates change. In the laboratory, a series of experiments with different sediments compositions and diameters were carried out on the hydraulic tray to determine the main elements (total, gentle and steep length, and the ridge height) and the dynamic characteristics of the ridge formations and the flow hydraulic characteristics. Calculation formulas for determining the coefficient of the ridge lower escarpments with and without taking into account the angle of the natural ground escarpment under water and in the dry state, and the dependence of the steepness of the relative ridge on the relative flow velocity, are obtained. The obtained dependencies allow to accurately determine the geometric and dynamic characteristics of bedload ridges and the corresponding hydraulic characteristics that may define the view ridge formations, ridges resistance of the channel, and the flow rate of bedload sediments, and to design sustainable escarpments large channels.

Rational Evaluation Methods of Topographical Change and Building Destruction in the Inundation Area by a Huge Tsunami

In the case of huge tsunamis, such as the 2004 Great Indian Ocean Tsunami and 2011 Great East Japan Tsunami, the damage caused by ground scour is serious. Therefore, it is important to improve prediction models for the topographical change of huge tsunamis. For general models that predict topographical change, the flow velocity distribution of a flood region is calculated by a numerical model based on a nonlinear long wave theory, and the distribution of bed-load rates is calculated using this velocity distribution and an equation for evaluating bed-load rates. This bed-load rate equation usually has a coefficient that can be decided using verification simulations. For the purpose, Ribberink’s formula has high reproducibility within an oscillating flow and was chosen by the authors. Ribberink’s formula needs a bed-load transport coefficient that requires sufficient verification simulations, as it consumes plenty of time and money to decide its value. Therefore, the authors generated diagrams that can define the suitable bed-load coefficient simply using the data acquired from hydraulic experiments on a movable bed. Subsequently, for the verification purpose of the model, the authors performed reproduced simulations of topography changes caused by the 2011 Great East Japan Tsunami at some coasts in Northern Japan using suitable coefficients acquired from the generated diagrams. The results of the simulations were in an acceptable range. The authors presented the preliminary generated diagrams of the same methodology but with insubstantial experimental data at the time at the International Society of Offshore and Polar Engineers (ISOPE), (2018 and 2019). However, in this paper, an adequate amount of data was added to the developed diagrams based on many hydraulic experiments to further raise their reliability and their application extent. Furthermore, by reproducing the tsunami simulation on the Sendai Natori coast of Japan, the authors determined that the impact of total bed-load transport was much bigger than that of suspension loads. Besides, the simulation outputs revealed that the mitigation effect of the cemented sand and gravel (CSG) banks and artificial refuge hills reduced tsunami damage on Japan’s Hamamatsu coast. Since a lot of buildings and structures in the inundation area can be destroyed by tsunamis, building destruction design was presented in this paper through an economy and simplified state. Using the proposed tsunami simulation model, we acquired the inundation depth at any specific time and location within the inundated area. Because the inundation breadth due to a huge tsunami can extend kilometers toward the inland area, the evaluation of building destruction is an important measure to consider. Therefore, the authors in this paper presented useful threshold diagrams to evaluate building destruction with an easy and cost-efficient state. The threshold diagrams of “width of a pillar” for buildings or “width of concrete block walls” not breaking to each inundation height were developed using the data of damages due to the 2011 Great East Japan Tsunami.

Consolidated sediment budget of Lake Tana, Ethiopia (2012–2016)

Lake sediment budgeting is a vital tool to better understand catchment sediment fluxes. It allows assessing lake lifetime and can be used to design improved catchment management plans. Over the past few years, we collected sediment and runoff discharge data at fine spatial-temporal resolutions for the Lake Tana Basin (LTB), Ethiopia. Based on these data, this study presents a consolidated sediment budget of Lake Tana, following the proof of concept by Lemma et al. (2018). Sediment yield (SY) was quantified for 15 rivers and 2 lake outlets based on 12,671 suspended sediment concentration (SSC) samples, making this the most complete dataset for Lake Tana. In particular, we investigated seasonal and temporal patterns of sediment dynamics and the role of lakeshore floodplains. The latter was done by comparing the SSC measurements at upper and lower borders of the floodplains. Sediment rating curves were prepared that account for land cover conditions and rainfall seasonality. SY calculations for the main contributing rivers take bedload fluxes into account by means of a bedload rating curve. As a result, the gross annual sediment mass mobilized on the hillslopes of LTB was 33.30 Mt (9.93 Mt from ungauged rivers), dominantly from large river catchments in the southern and eastern parts of LTB. SSC and SY are generally larger at the beginning of the rainfed cropping calendar (May–June). By the end of rainfed cropping calendar (September–October), SY decreases. Floodplains store 2.28 Mt suspended sediment whereas annually an average SY of 31.02 Mt entered the lake. From this, 96.6% is suspended load and 3.4% is bedload. With ca. 30 Mt sediment deposited in the lake, its mean trapping efficiency equals 97%. Only 1.14 Mt of sediment leaves the lake through the two outlets. The rate of lake sedimentation (9.8 kg m−2 yr−1) is in line with the sedimentation rates of large lakes in the world. However, because Lake Tana is shallow, its expected lifetime is only 918 years. Moreover, this study is useful for managing freshwater ecosystems that requires understanding of sedimentation rate and associated reduction in storage capacity of lakes, especially lakes that are shallow and have experienced extensive catchment degradation.

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

AbstractBedload 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.

Einstein conjecture and resting-time statistics in the bed-load transport of monodispersed particles

Sediment transport in rivers consists, at moderate discharge stage, of individual grains that undergo a series of step movements and rest periods (bed-load). Following a large number of grain trajectories in time and space is difficult and the results are affected by bias due to censorship of the time-spatial window. Therefore, the data sets available for the description of the statistics of resting-times, travel-time and lengths of the steps, are still insufficient. In this paper, an innovative experimental methodology has been designed and applied to get data representing the evolution of a bed surface and to support a robust statistical analysis of sediment transport. The methodology is based on image sequences taken of a flat bed made of well-sorted (mono-dispersed) particles. The acquired data are interpreted analytically through equations that describe the effects of grain entrainment and deposition. We show that grains’ displacement have a mean value independent of bed-load rate under low to moderate transport intensity for a given sediment type and bed-slope. Hence, we provide a strong validation of the seminal conjecture of Einstein in his theoretical statistical description of sediment transport. Finally, we describe the probability density functions of the resting-time for a few values of the sediment discharge.