Bed Load Transport Formula Research Articles

Formulation of bed shear stress for computing bed-load transport rate in vegetated flows

Difficulties are often encountered in estimating the bed shear stress in vegetated flows over a sediment bed due to complex interactions of the flow, sediment, and vegetation. Without involving any empirical partition of the bed friction and vegetation resistance, this study presents an analytical approach to evaluate the bed shear stress in the presence of vegetation in light of the phenomenological theory of turbulence. Then, the bed-load transport rate in vegetated flows is computed, with a result that agrees well with the bed-load transport formula developed for unvegetated flows. In addition, it is also shown that the present method is applicable not only to uniformly distributed vegetation but also to vegetation patches. However, further efforts are needed to extend the present model for flexible and submerged vegetation conditions.

Extending the Applicability of the Meyer–Peter and Müller Bed Load Transport Formula

The present paper deals with the applicability of the Meyer–Peter and Müller (MPM) bed load transport formula. The performance of the formula is examined on data collected in a particular location of Nestos River in Thrace, Greece, in comparison to a proposed Εnhanced MPM (EMPM) formula and to two typical machine learning methods, namely Random Forests (RF) and Gaussian Processes Regression (GPR). The EMPM contains new adjustment parameters allowing calibration. The EMPM clearly outperforms MPM and, also, it turns out to be quite competitive in comparison to the machine learning schemes. Calibrations are repeated with suitably smoothed measurement data and, in this case, EMPM outperforms MPM, RF and GPR. Data smoothing for the present problem is discussed in view of a special nearest neighbor smoothing process, which is introduced in combination with nonlinear regression.

Prediction of bed load sediments using different artificial neural network models

Modeling and prediction of bed loads is an important but difficult issue in river engineering. The introduced empirical equations due to restricted applicability even in similar conditions provide different accuracies with each other and measured data. In this paper, three different artificial neural networks (ANNs) including multilayer percepterons, radial based function (RBF), and generalized feed forward neural network using five dominant parameters of bed load transport formulas for the Main Fork Red River in Idaho-USA were developed. The optimum models were found through 102 data sets of flow discharge, flow velocity, water surface slopes, flow depth, and mean grain size. The deficiency of empirical equations for this river by conducted comparison between measured and predicted values was approved where the ANN models presented more consistence and closer estimation to observed data. The coefficient of determination between measured and predicted values for empirical equations varied from 0.10 to 0.21 against the 0.93 to 0.98 in ANN models. The accuracy performance of all models was evaluated and interpreted using different statistical error criteria, analytical graphs and confusion matrixes. Although the ANN models predicted compatible outputs but the RBF with 79% correct classification rate corresponding to 0.191 network error was outperform than others.

Numerical simulation of hydrodynamic characteristics and bedload transport in cross sections of two gravel-bed rivers based on one-dimensional lateral distribution method

Accurate evaluation and prediction of bedload transport are crucial in studies of fluvial hydrodynamic characteristics and river morphology. This paper presents a one-dimensional numerical model based on the one-dimensional lateral distribution method (1D-LDM) and six classic bedload transport formulae that can be used to simulate hydrodynamic characteristics and bedload transport discharge in cross sections. Two gravel-bed rivers, i.e. the Danube River located approximately 70 km downstream from Bratislava in Slovakia and the Toltén River in south of Chile are used as examples. In the 1D-LDM, gravity, bed shear stress, turbulent diffusion, and secondary flow are included to allow for accurate predictions of flow velocity and consequently bed shear stress in the cross sections. Six classic formulae were applied to evaluate the non-dimensional bedload transport rate, and the bedload transport discharge through a river cross section is obtained by integrating the bedload transport rate over the width of the cross section. The results show that the root mean square error (RMSE) and mean absolute error (MAE) of velocity and water discharge were less than 8% of the observed magnitude, while the correlation coefficient between model predictions and observations was close to unity. The formulae proposed by Ashida and Michiue (1972), in which particle collision with the bed is taken into account, and by Camenen and Larson (2005), which allows for yielding a non-zero bedload transport rate even when the bed shear stress is smaller than the critical bed shear stress value, appeared to be more appropriate for predicting the observed bedload transport rate in the studied cross sections of two gravel-bed rivers. If non-uniform sediment mixtures were considered, the bedload transport discharge through a cross-section could change considerably by up to 22.5% of the observed magnitude. The relations proposed by Ashida and Michiue (1972) and Egiazaroff (1965) for parameterizing the hiding factor yielded more realistic model predictions in comparison with observations for the measured data set collected for the Toltén River, while the one proposed by Wilcock and Crowe (2003) performs the best for the data set measured for the Danube River.

On the Effect of the Froude Number and Hydromorphometric Parameters on Sediment Transport in Rivers

A number of requirements for sediment transport formulas are considered for using in mathematical and physical models of alluvial channels. Some formulas (Bagnold, Petrov, Kopaliani) are analyzed and compared. It is demonstrated that the universal bed load transport formula should implicitly contain the Froude number. At the same time, the dependence of bed load discharge on the hydraulic resistance coefficient and the non-moving flow velocity increases the calculation error. However, these parameters, must be taken into account in simulating bed deformations for non-uniform sediments.

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

ABSTRACTUnderstanding 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.

Quantifying bed‐related suspended load in gravel bed rivers through an analysis of the bedload‐suspended load relationship

AbstractSuspended load transport can strongly impact ecosystems, dam filling and water resources. However, contrary to bedload, the use of physically based predicting equations is very challenging because of the complexity of interactions between suspended load and the river system. Through the analysis of extensive data sets, we investigated extent to which one or several river bed or flow parameters could be used as a proxy for quantifying suspended fluxes in gravel bed rivers. For this purpose, we gathered in the literature nearly 2400 instantaneous field measurements collected in 56 gravel bed rivers. Among all standard dimensionless parameters tested, the strongest correlation was observed between the suspended sediment concentration and the dimensionless bedload rate. An empirical relation between these two parameters was calibrated. Used with a reach average bedload transport formula, the approach allowed to successfully reproduce suspended fluxes measured during major flood events in seven gravel bed alpine rivers, morphodynamically active and distant from hillslope sources. These results are discussed in light of the complexity of the processes potentially influencing suspended load in a mountainous context. The approach proposed in this paper will never replace direct field measurements, which can be considered the only confident method to assess sediment fluxes in alpine streams; however, it can increment existing panel tools that help river managers to estimate even rough but not unrealistic suspended fluxes when measurements are totally absent. © 2019 John Wiley & Sons, Ltd.

3D CFD Modeling of Local Scouring, Bed Armoring and Sediment Deposition

3D numerical models are increasingly used to simulate flow, sediment transport and morphological changes of rivers. For the simulation of bedload transport, the numerical flow model is generally coupled with an empirical sediment transport model. The application range of the most widely used empirical models is, however, often limited in terms of hydraulic and sedimentological features and therefore the numerical model can hardly be applied to complex situations where different kinds of morphological processes take place at the same time, such as local scouring, bed armoring and aggradation of finer particles. As a possible solution method for this issue, we present the combined application of two bedload transport formulas that widens the application range and thus gives more appropriate simulation results. An example of this technique is presented in the paper by combining two bedload transport formulas. For model validation, the results of a laboratory experiment, where bed armoring, local scouring and local sediment deposition processes occurred, were used. The results showed that the combined application method can improve the reliability of the numerical simulations.

Assessment of a numerical model to reproduce event-scale erosion and deposition distributions in a braided river.

Numerical morphological modeling of braided rivers, using a physics‐based approach, is increasingly used as a technique to explore controls on river pattern and, from an applied perspective, to simulate the impact of channel modifications. This paper assesses a depth‐averaged nonuniform sediment model (Delft3D) to predict the morphodynamics of a 2.5 km long reach of the braided Rees River, New Zealand, during a single high‐flow event. Evaluation of model performance primarily focused upon using high‐resolution Digital Elevation Models (DEMs) of Difference, derived from a fusion of terrestrial laser scanning and optical empirical bathymetric mapping, to compare observed and predicted patterns of erosion and deposition and reach‐scale sediment budgets. For the calibrated model, this was supplemented with planform metrics (e.g., braiding intensity). Extensive sensitivity analysis of model functions and parameters was executed, including consideration of numerical scheme for bed load component calculations, hydraulics, bed composition, bed load transport and bed slope effects, bank erosion, and frequency of calculations. Total predicted volumes of erosion and deposition corresponded well to those observed. The difference between predicted and observed volumes of erosion was less than the factor of two that characterizes the accuracy of the Gaeuman et al. bed load transport formula. Grain size distributions were best represented using two φ intervals. For unsteady flows, results were sensitive to the morphological time scale factor. The approach of comparing observed and predicted morphological sediment budgets shows the value of using natural experiment data sets for model testing. Sensitivity results are transferable to guide Delft3D applications to other rivers.

Analysis and classification of bedload transport events with variable process characteristics

Knowledge about the magnitude of bedload fluxes at given hydraulic conditions in natural streams is essential for improved process understanding, for the application, calibration and validation of bedload transport formulas, and for numerical sediment transport models. Nonetheless, extensive field measurements of bedload transport are challenging and therefore data from such efforts are rare.Bedload transport has been measured comprehensively at the downstream section of the Urslau torrent in Salzburg, Austria, since 2011. We used an integrative monitoring system that combines direct (mobile basket sampler, slot sampler) and indirect measuring devices (geophone plates). Continuous information about the intensity and distribution of bedload transport within the channel cross-section is available in high spatial and temporal resolution. Seven geophone plates at a stream width of 8m are part of a measurement system that delivers data in 1-min intervals. These geophone data are calibrated using results of direct bedload measurements, providing an opportunity to calculate bedload rates and bedload yields in selected time periods.Continuous data on the bedload transport process over three years enabled assessing several bedload transport events. The investigation of bedload transport rate/discharge relationships reveals order-of-magnitude changes. For individual events, we observed shifts in the data, reflecting different bedload rates at comparable hydraulic conditions. This study reveals that variable sediment supply conditions affect the prevailing bedload transport rates at the Urslau stream. Calculating the bedload transport efficiency enables comparing bedload transport events that exhibit similar process characteristics. Finally, we provide a conceptual model of bedload transport process types as a function of bedload transport efficiency and dimensionless stream power.

Intra-swash hydrodynamics and sediment flux for dambreak swash on coarse-grained beaches

The paper reports on dambreak-type swash experiments in which intra-swash hydrodynamics and sediment flux are measured for swash on a coarse sand beach and a gravel beach. Flow velocity and depth are measured using PIV and LIF respectively; the intra-swash sediment flux is measured using sediment traps. Comparison of measured hydrodynamics with the immobile, permeable bed experiments of Kikkert et al. (2013) indicates that bed mobility impacts on the swash hydrodynamics, reducing the maximum run-up by approximately 8% for both beaches, compared to the maximum run-up on the corresponding immobile beach. The measured intra swash sediment flux at a given location is characterised by high flux at the moment of bore arrival, followed by rapid decay during uprush, becoming zero at some time before flow reversal. For the gravel beach, the backwash sediment flux is negligibly small, while for the sand beach the backwash flux increases slowly as the flow accelerates down the beach, and peaks at about the time of maximum backwash velocity. Intra-swash sediment flux calculated using the Meyer-Peter and Müller bed load transport formula, with measured hydrodynamics as input and bed shear stress estimated using both the Swart and Colebrook formulae, is within a factor 2 of the measured intra-swash flux. The agreement between the calculated and measured flux is better for the sand beach than for the gravel beach, and better for uprush than for backwash. For the sand beach there is good agreement between calculated and measured total uprush and total backwash sediment volumes. The agreement is less good for the gravel beach, for which calculated and measured uprush volumes show a similar trend but the calculated backwash volumes over-estimate the (negligible) volumes observed in the experiments.

Numerical Simulation of Bed Level Variation in Open Channels Under Steady Flow Conditions

Bed load transport is an important process in maintaining balance and stabilising channel geometry for restoring the form and function of river ecosystems. The amount and spatial distribution of bed load sediment particles contribute significantly to riverbed level changes. The prediction of bed load sediment transport evolution is an important aspect of catchment planning. This work can be effectively supported through numerical simulation by detailed analyses of flow components and sediment transport inside watersheds. The purpose of this research is to develop a twodimensional depth-averaged numerical model for flow and sediment transport using eight bed load transport equations to predict the time variation of bed deformation in steep slope, torrents and mountain river areas. The two-dimensional depth-averaged shallow water equations, along with the sediment continuity equation, are solved by using the Marker and Cell explicit scheme. Applying the eight bed load transport formulas to both ADM and MLSHM experimental flumes. After we will choice to the most appropriate formula to simulate the bed load transport rate and bed elevation change in the Yang yang mountains river in South Korea. The differences found between the measured experimental data and the numerical simulation for both flow and the time variations of bed deformation showed that the numerical model used in this research is useful for the analysis and prediction of riverbed level variations.

Assessment of hydro-morphodynamic modelling and geomorphological impacts of a sediment-charged jökulhlaup, at Sólheimajökull, Iceland

Understanding of complex flood-riverbed interaction processes in large-scale (field) outburst floods remains incomplete, not least due to a lack of well-constrained field data on hydraulics and sediment transport, but also because consensus on an appropriate model framework has yet to be agreed. This study presents a novel full 2D hydro-morphodynamic model containing both bedload and suspended load capability. Firstly, the model design is presented with an emphasis on its design to simulate rapidly-varied sediment-laden outburst floods and also the associated geomorphological impacts. Secondly, the model is applied to a large-scale (field) glacier outburst flood or ‘jokulhlaup’ at Solheimajokull, Iceland. For this real-world event, model scenarios with only water and with inclusion of sediment with different parameter setups were performed. Results indicated that grain size specifications affected resultant geomorphological changes, but that the sensitivity of the simulated riverbed changes to the empirical bedload transport formulae were insignificant. Notably, a positive feedback occurred whereby the jokulhlaup led to significant net erosion of the riverbed, producing an increase in flow conveyance capacity of the river channel. Furthermore, bulking effects of sediment entrainment raised the peak discharge progressively downstream, as well as the flood volume. Effects of geomorphological changes on flood water level and flow velocity were significant. Overall, despite the increased computational effort required with inclusion of sediment transport processes, this study shows that river morphological changes cannot be ignored for events with significant in-channel erosion and deposition, such as during outburst floods.

A well‐balanced FV scheme for compound channels with complex geometry and movable bed

AbstractThis work focuses on the implementation of a Shallow Water‐Exner model for compound natural channels with complex geometry and movable bed within the finite volume framework. The model is devised for compound channels modeling: cross‐section overbanks are treated with fixed bed conditions, while the main channel is left free to modify its morphology. A capacitive approach is used for bed load transport modeling, in which the solid flow rates are estimated with bed load transport formulas. The model equations pose some numerical issues in the case of natural channels, where bed load transport may occur for both subcritical and supercritical flows and geometry varies in space. An explicit path‐conservative scheme, designed to overcome all these issues, is presented in the paper. The scheme solves liquid and solid phases dynamics in a coupled manner, in order to correctly model near critical currents/channel interactions and is well‐balanced, that is able to properly reproduce steady states. The Roe and Osher Riemann solvers are implemented, so as to take into account the spatial geometry variations of natural channels. The scheme reaches up to second‐order accuracy. Validation is performed with fixed and movable bed test cases whose analytical solution is known, and with flume experimental data. An application of the model to a real case study is also shown.

Study on threshold motion of sediment and bedload transport by tsunami waves

Tsunami wave produces high bed shear stresses and can mobilize a mount of sediment movements over large areas. In this study, laboratory experiments were performed in a wave flume to investigate sediment transport by tsunami wave attacking sand beaches. The flow field of tsunami wave was calculated by the numerical model OpenFOAM®. The numerical results showed that flow characteristic of simulated tsunami wave uprush and backwash belongs to the rapid unsteady flow. The drag force and its duration are necessary and sufficient to trigger particle entrainment. It is recommended that time-mean near bottom velocity averaging over the force duration rather than the maximum velocity is relevant to better description of the incipient motion phenomenon in rapid unsteady tsunami flow. The experimental results show that some of the commonly used or recent bedload formulas for steady flow or wave are not suitable for the rapid unsteady or non-uniform tsunami flow. According to the experimental data presented in this paper, the bedload transport formulas for the tsunami uprush and backwash processes are proposed. An appropriate criterion of “sediment transport impulse”, which is the product of magnitude and duration, is conjectured and could well explain the sandy beach deposition and erosion caused by tsunami wave.

Sediment transport and shear stress partitioning in a vegetated flow

AbstractVegetation is a common feature in natural coastal and riverine water ways, interacting with both the water flow and sediment transport. However, the physical processes governing these interactions are still poorly understood, which makes it difficult to predict sediment transport and morphodynamics in a vegetated environment. We performed a simple experiment to study how sediment transport responds to the presence of flexible, single‐blade vegetation, and how this response is influenced by the vegetation density. We found that the skin friction and sediment transport are reduced in a plant patch, and that this effect is larger for denser vegetation. We then evaluated several methods to calculate the skin friction in a vegetated flow, which is the key to sediment transport prediction. Among these, the inversion of bed load transport formulas and the Einstein and Banks (1950) methods appeared to produce the most reasonable values of the skin friction. Finally, we suggest using the parameter α, which is the ratio of the skin friction computed by these methods to the total bed shear stress, to make more realistic sediment transport predictions in morphodynamic models.

NUMERICAL STUDY ON FLUSHING CHANNEL EVOLUTION, CASE STUDY OF DASHIDAIRA RESERVOIR, KUROBE RIVER

Due to the high sedimentation rate in reservoirs located along the Kurobe River (e.g. Dashidaira reservoir), sediment flushing with water level drawdown is employed to preserve the effective storage capacity. During a flushing operation with full drawdown, the incoming flood erodes a flushing channel into the deposited sediment. The flushing channel evolution procedure is a complex phenomenon especially in steep reservoirs owing to the dynamic interaction between the unsteady flow field and bed variations. The flushing channel formation and evolution procedure were investigated in meandering channel of Dashidaira reservoir utilizing field measurements and numerical simulations. A 3D numerical model which applies the Finite Volume Method (FVM) in combination with a wetting/drying algorithm was used together with different bed load transport formulas . Numerical outcomes disclosed a reasonable agreement with the field measurements. In addition, a further insight in the correlation between the flushed out sediment discharge and the water discharge as well as the water level was found.

A nested grid based computational fluid dynamics model to predict bridge pier scour

A three-dimensional numerical model that computes hydrodynamics and morphodynamics is applied to the problem of calculating local scour around cylinders. A nested grid approach is implemented in the numerical scheme in order to decrease the overall computational demand but at the same time allow for high spatial resolution around the cylinder to increase numerical accuracy there. The computational grid consists of two structured blocks – a coarse block that discretises the entire domain and a fine block that only discretises the area around the cylinders. A novel interpolation technique accomplishes communication between the two blocks. Sediment transport in the morphodynamic model is calculated with a bed load transport formula combined with the sediment continuity equation to reproduce the unsteady scour hole development while the flow field is recalculated at each time step. Experimental data of flow and the local clear-water scour around single and multiple circular cylinders in a laboratory channel with a movable bed are obtained and compared with the results of the model. Flow, the maximum scour hole depth and the general scour hole geometry are reproduced well in all cases. The time evolution of the scouring is also captured reasonably well.

Evaluation of bed load transport formulae in a large regulated gravel bed river: The lower Ebro (NE Iberian Peninsula)

This paper tests the predictive power of 10 bed load formulae against bed load rates obtained for a large regulated river (River Ebro) the armor layer of which is subject to repeated cycles of break-up and reestablishment. The theoretical principles of two of the 10 formulae explicitly include the effects of river bed armoring. The results obtained showed substantial differences in equation performance but no evident relationship between predictive power and theoretical approach (e.g., discharge, stream power and probability) was found. Overall, the predictive power of the tested formulae was relatively low. The average percentages of predicted bed load discharge that did not exceed factors of 2 (0.5 < r < 2) and 10 (0.1 < r < 10) in relation to the observed discharge were 19% and 57%, respectively (where r is the discrepancy ratio between the predicted and observed values). In particular, the formulae of Yang (1984) and Parker et al. (1982) presented the better levels of agreement with the observed bed load discharges. The bed load rating curve for the lower Ebro showed a similar degree of agreement to the best-performing formulae. However, its predictive power was limited because only flow discharge acts as an independent variable and river bed dynamics, such as armoring cycles, are not contemplated.

On the influence of the thickness of the sediment moving layer in the definition of the bedload transport formula in Exner systems

In this paper we study Exner system and introduce a modified general definition for bedload transport flux. The new formulation has the advantage of taking into account the thickness of the sediment layer which avoids mass conservation problems in certain situations. Moreover, it reduces to a classical solid transport discharge formula in the case of quasi-uniform regime. We also present several numerical tests where we compare the proposed sediment transport formula with the classical formulation and we show the behavior of the new model in different configurations.