[1] A data set of 2890 field measurements was used to test the ability of several conventional flow resistance equations to predict mean flow velocity in gravel bed rivers when used with no calibration. The tests were performed using both flow depth and discharge as input since discharge may be a more reliable measure of flow conditions in shallow flows. Generally better predictions are obtained when using flow discharge as input

[1] Several decades of flume and field measurements have indicated that in rough turbulent flows the critical Shields stress increases with increasing slope and associated decreasing relative depth. This result contradicts the usual consideration of a decreased critical Shields value on very steep slopes because of increased gravitational effects. However, recent studies have demonstrated that these experimental results could be reproduced with a force balance model if the classical logarithmic velocity profile was replaced with a velocity profile that was more compatible with available velocity measurements over gravel beds. These measurements indicate the existence of a roughness layer that is a zone of almost constant velocity close to the bed, whose properties (mean velocity and turbulence) depended on the flow's relative depth. Unfortunately, velocity profile measurements for low relative depth associated with steep slopes are scarce, and it is still difficult to include such flow properties in a force balance model. Flow resistance data (on the basis of depth average velocity measurements) are very common and cover a wide range of slopes and relative depths. In this paper these data are used to fit a velocity profile including a roughness layer. When used in a force balance model for incipient motion, it adequately reproduced a data set composed of 270 critical Shields values measured in a flume with near-uniform sediments. The relevance of this research to field problems is discussed using a data set composed of 92 critical Shields stresses obtained from field measurements. Finally, a model is proposed for field applications taking into account the slope effect.

[1] To calculate bed load, engineers often use flow resistance equations that provide estimates of bed shear stress. In these equations, on the basis of the estimate of the appropriate hydraulic radius associated with the bed only, the bed roughness k s is commonly set as a constant, whatever the bed load intensity. However, several studies have confirmed the existence of feedback mechanisms between flow resistance and bed load, suggesting that a flow-dependent bed roughness should be used. Therefore, using a data set composed of 2282 flume and field experimental values, this study investigated the importance of these feedback effects. New flow resistance equations were proposed for three flow domains: domain 1 corresponds to no bed load and a constant bed roughness k s = D (where D is a representative grain diameter), whereas domain 3 corresponds to a high bed load transport rate over a flat bed with a constant bed roughness k s = 2.6D. Between these two domains, a transitional domain 2 was identified, for which the bed roughness evolved from D to 2.6D with increasing flow conditions. In this domain, the Darcy-Weisbach resistance coefficient f can be approximated using a constant for a given slope. The results using this new flow resistance equation proved to be more accurate than those using equations obtained from simple fittings of logarithmic laws to mean values. The data set indicates that distinguishing domains 2 and 3 is still relevant for bed load. In particular, the data indicate a slope dependence in domain 2 but not in domain 3. A bed load model, based on the tractive force concept, is proposed. Finally, flow resistance and bed load equations were used together to calculate both shear stress and bed load from the flow discharge, the slope, and the grain diameter for each run of the data set. Efficiency tests indicate that new equations (implicitly taking a feedback mechanism into account) can reduce the error by a factor of 2 when compared to other equations currently in use, showing that feedback between flow resistance and bed load can improve field bed load modeling.Citation: Recking, A., P. Frey, A. Paquier, P. Belleudy, and J. Y. Champagne (2008), Feedback between bed load transport and flow resistance in gravel and cobble bed rivers, Water Resour. Res., 44, W05412,

The ability of simple equations to predict bed load transport with limited knowledge of the bed surface material was investigated. This was done using a data set consisting of 7,636 bed load transport values from the flume (1,317 data) and from 84 river reaches (6,319 field data). It was possible to collapse field and flume data by correcting the ratio between the Shields number and its critical value with a very simple hiding function proposed as a power law of the D84/D50 ratio. In so doing, a surface‐based bed load transport formula was proposed. It was successfully tested on an independent data set (comprising sand and gravel bed rivers with slope in the range 0.0002–0.08), with 86% of the values predicted within a precision of 1 order of magnitude. Moreover, the formula reproduced the low transport rates well, contrary to the usual surface‐based formulas also tested, and is particularly well suited for estimating low transport rates associated with near‐bankfull flow discharge. This new formula is neither time consuming (no fractionwise calculation) nor data consuming (the required parameters are the flow discharge, the active width, the slope, and the surface grain diameters D50 and D84).

[1] Field measurements indicate that, in gravel bed rivers, bed load may not be a one-toone response to shear stress but may instead fluctuate a great deal over time for a given flow condition. Both in flume and field experiments, these fluctuations were often associated with migration of low-relief bed forms called bed load sheets. Whereas several studies have described bed load sheets as a consequence of grain sorting, little is known about the mechanisms responsible for their production and migration. These were investigated in flume experiments. A set of 20 experiments was conducted under constant feeding rate conditions, with mixtures of different uniform sediments and for slopes varying from 0.8 to 9%. Except for runs performed in high flow conditions, we observed periodic bed load sheet production and migration associated with fluctuations of bed slope, bed state (bed fining and paving), and bed load. Observations allowed us to conclude that bed load sheets resulted from very efficient vertical and longitudinal grain sorting that produced periodic local bed aggradation and erosion clearly observed in the upstream section of the flume. Fractional transport rates were measured in one run. Combined with the results of experiments previously conducted by authors with uniform sediments, this experiment showed that the highest (peak) solid discharges were essentially caused by the much greater mobility of the coarser gravels when transported within bed load sheets. A scenario is proposed for the mechanisms involved in bed load sheet production and migration.Citation: Recking, A., P. Frey, A. Paquier, and P. Belleudy (2009), An experimental investigation of mechanisms involved in bed load sheet production and migration,

Bedload transport is known to be a highly fluctuating temporal phenomenon, even under constant (mean) flow conditions, as a consequence of stochasticity, bedform migration, grain sorting, hysteresis, or sediment supply limitation. Because bedload transport formulas usually refer to a single mean transport value for a given flow condition, one can expect that prediction accuracy (when compared to measurements) will depend on the amplitude and duration of fluctuations, which in turn depend on the time scale used for observations. This paper aims to identify how the time scale considered can affect bedload prediction. This was done by testing 16 common bedload transport formulas with four data sets corresponding to different measurement period durations: (i) highly fluctuating (quasi‐)instantaneous field measurements; (ii) volumes accumulated at the event scale on two small alpine gravel‐bed rivers, potentially affected by seasonal fluctuations; (iii) volumes accumulated at the interannual scale in a meandering gravel bed river, thought to be weakly subject to fluctuations; (iv) time‐integrated flume measurements with nearly uniform sediments. The tests confirmed that the longer the measurement period, the better the precision of the formula's prediction interval. They also demonstrate several consequential limitations. Most threshold formulas are no longer valid when the flow condition is below two times the threshold condition for the largest elements' motion on the bed surface (considering D84). In such conditions, equations either predict zero transport, or largely overestimate the real transport, especially when D84 is high. There is a need for new sediment data collected with highly reliable techniques such as recording slot bedload samplers to further investigate this topic. Copyright © 2012 John Wiley & Sons, Ltd.

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