Assessment of Methods Used in 1D Models for Computing Bed-Load Transport in a Large River: The Danube River in Slovakia

Comprehensive measurements of bedload sediment transport through a section of the Danube River, located approximately 70km downstream from Bratislava, Slovakia, are used to assess the accuracy of bedload formulae implemented in 1D modelling. Depending on water discharge and water level, significant variations in the distribution of bedload across the section were observed. It appeared that, whatever the water discharge, the bed shear stress tau is always close to the estimated critical bed shear stress for the initiation of sediment transport . The discussion focusses on the methods used in 1D models for estimating bedload transport. Though usually done, the evaluation of bedload transport using the mean cross-sectional bed shear stress yields unsatisfactory results. It is necessary to use an additional model to distribute the bed shear stress across the section and calculate bedload locally. Bedload predictors also need to be accurate for tau close to tau. From that point of view, bedload formulae based on an exponential decrease of bedload transport close to tau appear to be more appropriate than models based on excess bed shear stress. A discussion on the bedload formula capability to reproduce grain sorting is also provided

The concept of transport capacity in geomorphology

The notion of sediment-transport capacity has been engrained in geomorphological and related literature for over 50 years, although its earliest roots date back explicitly to Gilbert in fluvial geomorphology in the 1870s and implicitly to eighteenth to nineteenth century developments in engineering. Despite cross fertilization between different process domains, there seem to have been independent inventions of the idea in aeolian geomorphology by Bagnold in the 1930s and in hillslope studies by Ellison in the 1940s. Here we review the invention and development of the idea of transport capacity in the fluvial, aeolian, coastal, hillslope, débris flow, and glacial process domains. As these various developments have occurred, different definitions have been used, which makes it both a difficult concept to test, and one that may lead to poor communications between those working in different domains of geomorphology. We argue that the original relation between the power of a flow and its ability to transport sediment can be challenged for three reasons. First, as sediment becomes entrained in a flow, the nature of the flow changes and so it is unreasonable to link the capacity of the water or wind only to the ability of the fluid to move sediment. Secondly, environmental sediment transport is complicated, and the range of processes involved in most movements means that simple relationships are unlikely to hold, not least because the movement of sediment often changes the substrate, which in turn affects the flow conditions. Thirdly, the inherently stochastic nature of sediment transport means that any capacity relationships do not scale either in time or in space. Consequently, new theories of sediment transport are needed to improve understanding and prediction and to guide measurement and management of all geomorphic systems

An analysis of nonlinearity effects on bedload transport prediction

Because bedload equations are nonlinear and because parameters describing the flow and the bed can have large variance, different results are expected when integrating bedload over a cross section with respect to spatially variable local data (2D), or when computing bedload from cross-section averaged data, which reduces the problem to uniform conditions (1D). I have shown evidence of these effects by comparing 1D (flume-derived) equations to 2D field measurements, and by comparing a 2D (field-derived) equation to 1D flume measurements, concluding that different equations should be used depending on whether local or averaged data are used. However, whereas nonlinearity effects are considerable for low-transport stages, they tend to disappear for higher flow conditions. I propose probability distribution functions describing the variance in flow and bed grain size distribution (GSD) and I used the width-integrated bedload data (implicitly containing the natural variance in bed and flow parameters) to calibrate these functions. The method consisted of using a Monte Carlo approach to match the measured 2D bedload transport rates with 1D computations artificially reproducing the natural variance associated with the mean input parameters. The Wilcock and Crowe equation was used for the 1D computations because it was considered representative of 1D transport. The results suggest that nonlinearity effects are mostly sensitive to the variance in shear stress, modelled here with a gamma function, whose shape coefficient alpha was shown to increase linearly with the transport stage. This variance in shear stress suggests that even for very low flow conditions, shear stress can locally exceed the critical shear stress for the bed armour, generating local armour break-up. This could explain why the bedload GSD is usually very similar to subsurface GSD, even in the presence of complete armour

(trad auto)Transport de la charge de lit dans les rivières : du canal au champ.

Because it is difficult to measure bedload sediment transport in rivers during flooding, flume experiments have been widely used for studying the mechanisms involved and for constructing bedload transport equations. However, flume experiments usually involve several simplifications concerning the sediment material (usually a uniform grain size distribution is used) and the flow conditions (usually maintained high for one-dimensional transport and no bed meandering), which can have strong consequences when the flume-derived equations are used in the field. This manuscript presents the results of my research on this topic and aims to fill the gap between the flume and the field. The three parts of the manuscript concern the hydraulics, the threshold conditions for bedload transport, and bedload transport rates. It is shown that large diameters such as D84 are recommended for matching the results obtained in the flume and in the field, both for flow resistance and threshold dimensional shear stress. The comparison is less trivial for bedload transport as (i) most flume bedload transport were measured for high shear stress and almost full mobility of the bed sediments, whereas in the field, measurements usually correspond to partial transport (the finer fractions are transported whereas the coarsest fractions are maintained at rest) and (ii) because of nonlinearity, 1D flume derived equations tend to underestimate bedload transport when they are used with width averaged data.En raison de la difficulté à mesurer le charriage dans les rivières en crue, l'expérimentation en canal a très largement été utilisée pour étudier les mécanismes impliqués et pour élaborer des équations. Cependant, les expériences en canal impliquent généralement plusieurs simplifications concernant les sédiments (généralement une distribution uniforme est utilisée) et les conditions d'écoulement (généralement maintenues élevées pour un transport unidimensionnel), ce qui peut avoir des conséquences fortes lorsque les équations qui en sont issues sont utilisées sur le terrain. Ce manuscrit présente les résultats de ma recherche sur ce sujet et vise à faire le lien entre le laboratoire et le terrain. Les trois parties du manuscrit concernent l'hydraulique, les conditions de début de mouvement, et la modélisation du charriage. Il est montré que les grands diamètres tels que le D84 sont recommandés pour comparer les résultats obtenus au laboratoire et sur le terrain, à la fois pour la résistance à l'écoulement et pour la contrainte adimensionnel de mise en mouvement. La comparaison est moins triviale pour charriage car (i) le charriage au laboratoire a souvent été mesuré pour des contraintes de cisaillement fortes et une mobilité quasi totale des sédiments du lit alors que sur le terrain, les mesures correspondent habituellement à un transport partiel (les fractions les plus fines sont transportées alors que le fractions plus grossières sont maintenus au repos) et (ii) en raison de la non-linéarité du phénomène, les équations 1D issues du canal ont tendance à sous-estimer le charriage lorsqu'elles sont utilisées sur le terrain avec grandeurs moyennées sur la section

Une méthode simple pour le calcul du charriage en rivière

International audienceA simple and robust method is proposed for calculating reach-averaged bedload transport in sand and gravel bed rivers, with no calibration. The data required are the bed surface D50 and D84 measured with the non-truncated pebble count technique, the slope, the width and the flow depth or discharge. The method is illustrated by comparison with bedload samples measured in 15 river reaches

Etude expérimentale de l'influence du tri granulométrique sur le transport solide par charriage

The purpose of this research was to investigate the effects of grain sorting on bedload. The main procedure consisted first of analysing flow properties over uniform materials (Part 1), and then comparing this with the results obtained with mixtures of uniform materials (Part 2). The experimental setup is presented. One hundred and fourty-four friction factor values were measured under bedload equilibrium flow conditions, over uniform gravel bed materials and on slopes varying from 1% to 9%. Newly produced values indicate that bedload contributes to a not insignificant increase in the friction factor when compared to clear water flow. The data set was extended to 1551 values (with historical data) and the Darcy-Weisbach flow resistance equation was reviewed for a wide range of flow conditions. Three regimes were identified: no sediment transport, low sediment transport and high sediment transport. Each regime was characterized by a different friction law associated with differences in particle motion. The new flow resistance model was used to analyse the bedload data set. The analysis revealed a good correspondence between the identified regimes and the transport rate efficiency, calculated from the flow power concept. A new bedload model is proposed, in the form of a modified Meyer-Peter and Muller (1948) equation for the low regime and a power law for the high regime, the transition between both regimes being slope-dependent. Twenty-six experiments were conducted under constant feeding rate conditions, with mixtures of different uniform sediments and for slopes varying from 0.8% to 9%. No equilibrium slope was obtained whatever the run and experiment duration (up to more than 60 h). Instead a periodic fluctuation pattern was observed, affecting the bed slope, the bed state (varying from armour to fine bed) and the bedload discharge. Two types of fluctuations were observed: short fluctuations associated with bedload sheets (local bed slope changes) and large fluctuations associated with strong overall changes in bed morphology. Bedload sheets appeared to be the keystone of the fluctuating process and a hypothesis was formulated for its formation, based on steep slope observations. Based on the experimental observations, a compartment model is proposed for modelling the evolution of the long-term gravel bed profile. This model provides a relationship between the different time scale periods and the grain-sorting phenomenon. It also explains how the flume length can control periodicities. Lastly, the concept of transport rate efficiency was used to demonstrate that grain sorting may control the fluctuation periods and amplitudes by controlling the sand content of the bedload mixture. This hypothesis, plus advances in transport rate efficiency established from the study of flows over uniform materials, was used to reproduce the amplitude of the mean bed slope fluctuations observed with the long-term experiments for different slopes and sediment mixtures. This led to the conclusion that both slope and the periodic fluctuations in solid discharge may be a natural phenomenon in gravel-bed rivers.Le but de cette thèse est l'étude expérimentale de l'influence du tri granulométrique sur le transport solide par charriage. Dans un premier temps, les résultats des mesures en canal, complétés par les données de la bibliographie, ont permis de constituer un jeu de données de 1551 valeurs pour des écoulements sur matériaux uniformes. Ce jeu de données a servi à valider des lois de frottement et de transport. Dans un second temps, des expériences d'écoulements sur matériaux à granulométrie étendue ont permis de remettre en question la notion d'équilibre. Des fluctuations périodiques du débit solide, de la pente et de l'état de pavage du lit ont en effet été observées à différentes échelles de temps et d'espace. Des formes particulières du lit, appelées nappe de charriage, semblent être une manifestation directe du phénomène de tri granulométrique. En faisant varier l'efficacité du transport sédimentaire, par un contrôle de la teneur en sable de la couche charriée, ces structures pourraient être à l'origine du phénomène de fluctuation. Des modèles ont été proposés et semblent confirmer la justesse de ces hypothèses

Influence des sources sédimentaires sur le transport solide en torrent

International audienceSediment transport and storage in mountain streams channels are closely dependent on hillslope activities and bank erosion. This paper analyses bedload measured in 13 mountain streams (989 values with slope higher than 5%) in an attempt to investigate how much the sediment supply condition impacts bedload transport rates. First, the sediment supply condition of each stream was evaluated qualitatively using information available in the original studies. In the second step, the data set was analysed by comparing bedload transport rates considering a Shields stress ratio and by comparing transport rate efficiency with consideration of a dimensionless stream power. The two analyses indicate higher sediment transport rates for the streams identified as “connected” to an active source. The consequences for bedload transport prediction are discussed with a nonthreshold bedload equation. Even though predicting the exact sediment supply condition and the associated transport rate is not yet possible, this study suggests that defining an envelope delimiting minimum and maximum transport for a given river reach should be possible

Le concept du Travelling bedload et ses conséquences sur le calcul du transport par charriage dans les torrents de montagne

International audienceIn bedload transport modelling, it is usually presumed that transported material is fed by the bed itself. This may not be true in some mountain streams where the bed can be very coarse and immobile for the majority of common floods, whereas a finer material, supplied by bed-external sources, is efficiently transported during floods, with marginal morphological activities. This transport mode was introduced in an earlier paper as ‘travelling bedload’. It could be considered an extension of the washload concept of suspension, applied to bedload transport in high-energy, heavily armoured streams. Since this fine material is poorly represented in the bed surface, standard surface-based approaches are likely to strongly underestimate the true transport in such streams. This paper proposes a simple method to account for travelling bedload in bedload transport estimations. The method is tested on published datasets and on a typical Alpine stream, the Roize (Voreppe, France). The results, particularly on active streams that experience greater transport than expected from the grain sizes of their bed material, reinforce the necessity of accounting for the ‘travelling bedload concept’ in bedload computation. The method relevance is discussed regarding varying flood magnitudes, geomorphic responses and eventual anthropic origin of the ‘travelling bedload’ phenomena. To conclude, this paper considers how to compute bedload transport for a wide range of situations, ranging from sediment-starved cases to the general mobile bed alluvial case, including the intermediate situation of external source supply on armoured bed