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1.
Recent research has started to focus on how prolonged periods of sub‐threshold flows may be capable of imparting structural changes that contribute to increased bed stability. To date, this effect (termed ‘stress history’) has been found to be significant in acting to increase a bed's critical shear stress at entrainment threshold. However, it is supported by only limited, qualitative and often speculative information on the mechanisms of this stabilization process in grade‐specific studies. As such, this paper uses high resolution laser scanning to quantitatively ascertain the granular mechanics underpinning the relationship between stress history and entrainment threshold for beds of a range of grain size distributions. Employing a bed slope of 1/200, three grain size distributions with median grain sizes (D50) of 4·8 mm [uniform (σg = (D84/D16)0.5 = 1·13; bimodal (σg = 2·08); and, unimodal (σg = 1·63)] were exposed to antecedent stress histories of 60 and 960 minutes duration. Antecedent shear stress magnitude was set at 50% of the critical shear stress for the D50 when no stress history period was employed. Two laser displacement scans of the bed surface (approximate area 100 mm × 117 mm) were taken, one prior to the antecedent period and one after this period, so that changes to surface topography could be quantified (resolution of x = 0·10 mm, y = 0·13 mm and z = 0·24 mm). Rearrangement of bed surface structure is described using statistical analysis and two‐dimensional (2D) semi‐variograms to analyse scaling behaviour. Results reveal vertical settlement, changes to bed roughness and particle repositioning. However, the bed grain size distribution influences the relative importance of each mechanism in determining stress history induced bed stability; this is the focus of discussion in this paper. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
2.
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. 相似文献
3.
While clay and silt matrices of gravel‐bed rivers have received attention from ecologists concerned variously with the deteriorating environments of benthic and hyporheic organisms, their impact on sediment entrainment and transport has been explored less. A recent increase of such a matrix in the bed of Nahal Eshtemoa, an ephemeral river of the northern Negev, has more than doubled the boundary shear stress needed to initiate bedload, from 7 N m‐2 (τ* = 0.027) during the flash floods of 1991–2001 to 15 N m‐2 (τ* = 0.059) during those of 2008–2009. The relation between bedload flux and boundary shear stress continues to be well‐defined, but it is displaced. The matrix now contains a significant amount of silt and clay size material. The reasons for the increased entrainment threshold of bedload are explored. Large‐scale laser scanning of the dry bed reveals a reduction in grain‐scale morphological roughness, while artificial in situ tests of matrix integrity indicate considerable cohesion. The implications for adopting bed material sampling strategies that account for matrix development are assessed. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
4.
Bedload transport data from planebed and step‐pool reach types are used to determine grain size transport thresholds for selected upland streams in southeast Australia. Morphological differences between the reach types allow the effects of frictional losses from bedforms, microtopography and bed packing to be incorporated into the dimensionless critical shear stress value. Local sediment transport data are also included in a regime model and applied to mountain streams, to investigate whether empirical data improve the delineation of reach types on the basis of dimensionless discharge per unit width (q*) and dimensionless bedload transport (qb*). Instrumented planebed and step‐pool sites are not competent to transport surface median grains (D50s) at bankfull discharge (Qbf). Application of a locally parametrized entrainment equation to the full range of reach types in the study area indicates that the majority of cascades, cascade‐pools, step‐pools and planebeds are also not competent at Qbf and require a 10 year recurrence interval flood to mobilize their D50s. Consequently, the hydraulic parameters of the regime diagram, which assume equilibrium conditions at bankfull, are ill suited to these streams and provide a poor basis of channel delineation. Modifying the diagram to better reflect the dominant transported bedload size (equivalent to the D16 of surface sediment) made only slight improvements to reach delineation and had greatest effect on the morphologies with smaller surface grain sizes such as forced pool‐riffles and planebeds. Likewise, the Corey shape factor was incorporated into the regime diagram as an objective method for adjusting a base dimensionless critical shear stress (τ*c50b) to account for lithologically controlled grain shape on bed packing and entrainment. However, it too provided only minor adjustments to reach type delineation. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
5.
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. 相似文献
6.
Patterns of bedload entrainment and transport in forested headwater streams of the Columbia Mountains,Canada 
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下载免费PDF全文 We monitor bedload transport and water discharge at six stations in two forested headwater streams of the Columbia Mountains, Canada. The nested monitoring network is designed to examine the effects of channel bed texture, and the influence of alluvial (i.e. step pools and riffle pools) and semialluvial morphologies (i.e. boulder cascades and forced step pools) on bedload entrainment and transport. Results indicate that dynamics of bedload entrainment are influenced by differences in flow resistance attributable to morphology. Scaled fractional analysis shows that in reaches with high form resistance most bedload transport occurs in partial mobility fashion relative to the available bed material, while calibers finer than 16 mm attain full mobility during bankfull flows. Equal mobility transport for a wider range of grain sizes is achieved in reaches exhibiting reduced form resistance. Our findings confirm that the Shields value for mobilization of the median surface grain size depends on channel gradient and relative submergence; however, we also find that these relations vary considerably for cobble and gravel bed channels due to proportionality between dimensionless shear stress and grain size. Exponents of bedload rating curves across sites correlate most with the D90s of the mobile bed, however, where grain effects are controlled (i.e. along individual streams), differences in form resistance across morphologies exert a primary control on bedload transport dynamics. Application of empirical formulae developed for use in steep alpine channels present variable success in predicting transport rates in forested snowmelt streams. Formulae that explicitly account for reductions in mobile bed area and high morphological resistance associated with woody debris provide the best approximation to observed empirical data. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
7.
Transport of moderately sorted gravel at low bed shear stresses: The role of fine sediment infiltration 下载免费PDF全文
下载免费PDF全文 Emeline Perret Céline Berni Benoît Camenen Albert Herrero Kamal El Kadi Abderrezzak 《地球表面变化过程与地形》2018,43(7):1416-1430
A reliable estimation of sediment transport in gravel‐bed streams is important for various practical engineering and biological studies (e.g., channel stability design, bed degradation/aggradation, restoration of spawning habitat). In the present work, we report original laboratory experiments investigating the transport of gravel particles at low bed shear stresses. The laboratory tests were conducted under unsteady flow conditions inducing low bed shear stresses, with detailed monitoring of the bed topography using a laser scanner. Effects of bed surface arrangements were documented by testing loose and packed bed configurations. Effects of fine sediments were examined by testing beds with sand, artificial fine sand or cohesive silt infiltrated in the gravel matrix. Analysis of the experimental data revealed that the transport of gravel particles depends upon the bed arrangement, the bed material properties (e.g., size and shape, consolidation index, permeability) and the concentration of fine sediments within the surface layer of moving grains. This concentration is directly related to the distribution of fine particles within the gravel matrix (i.e., bottom‐up infiltration or bridging) and their transport mode (i.e., bedload or suspended load). Compared to loose beds, the mobility of gravel is reduced for packed beds and for beds clogged from the bottom up with cohesive fine sediments; in both cases, the bed shear stress for gravel entrainment increases by about 12%. On the other hand, the mobility of gravel increases significantly (bed shear stress for particle motion decreasing up to 40%) for beds clogged at the surface by non‐cohesive sand particles. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
8.
During bedload movement by saltation, streamwise momentum is transferred from the ?ow to the saltating grains. When the grains collide with other grains on the bed or in the ?ow, streamwise momentum is reduced, and there is a decrease in streamwise ?ow velocity and an increase in ?ow resistance, herein termed bedload transport resistance fbt. Based on experiments in two ?umes with ?xed and mobile plane beds and previously published data, an equation is developed that may be used to predict fbt for both capacity and non‐capacity ?ows. The variables in this equation are identi?ed by dimensional analysis and the coef?cients are determined by non‐linear regression. This equation applies to rough turbulent open‐channel ?ows, where the relative submergence is between 1 and 20 and the entire sediment load moves by saltation. An investigation of the relative magnitudes of fbt and grain resistance fc suggests that where dimensionless shear stress θ is less than 1 and saltation is the dominant mode of bedload transport, fbt/fc increases with θ but never exceeds 1. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
9.
There is growing acknowledgement of the interaction between animals and the river bed on which they live and the implications of biological activity for geomorphic processes. It has been observed that signal crayfish (Pacifastacus leniusculus) disturb gravel substrates, potentially promoting sediment transport and impacting ecological communities. However, the mechanisms involved and the extent of their impact remain poorly understood, especially in relation to other processes that affect grain mobility in gravel‐bed rivers. A series of flume experiments, using loose and water‐worked gravel beds of narrowly graded grain sizes that were exposed to 6 h of crayfish activity under low‐velocity flows, showed a substantial increase in the number of grains entrained by subsequent higher‐velocity flows when compared with control runs in which crayfish were never introduced. Crayfish alter the topography of their substrate by constructing pits and mounds, which affect grain protrusion. When walking and foraging, they also alter gravel fabric by reorienting and changing the friction angle of surface grains. In water‐worked surfaces, this fabric rearrangement is shown to lead to a statistically significant, partial reversal of the structuring that had been achieved by antecedent flow. For these previously water‐worked surfaces, the increase in entrainment arising from disturbance by crayfish was statistically significant, with grain transport nearly twice as great. This suggests that signal crayfish, an increasingly widespread invasive species in temperate latitudes beyond their native NW North America, have the potential to enhance coarse‐grained bedload flux by altering the surface structure of gravel river beds and reducing the stability of surface grains. This study illustrates further the importance of acknowledging the impact of mobile organisms in conditioning the river bed when assessing sediment entrainment mechanics in the context of predicting bedload flux. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
10.
The incidence and nature of bedload transport during flood flows in coarse-grained alluvial channels
A continuous record reveals that the incidence of bedload in a coarse-grained river channel changes from flood to flood. Long periods of inactivity encourage the channel bed to consolidate sufficiently so that bedload is largely confined to the recession limb of the next flood-wave. But when floods follow each other closely, the bed material is comparatively loose and offers less resistance to entrainment. In this case, substantial amounts of bedload are generated on the rising limb. This is confirmed by values of bed shear stress or stream power at the threshold of initial motion which can be up to five times the overall mean in the case of isolated floods or those which are the first of the season. This produces a complicated relationship between flow parameters and bedload and explains some of the difficulties in establishing bedload rating curves for coarse-grained channels. Besides this, the threshold of initial motion is shown to occur at levels of bed shear stress three times those at the thresholds of final motion. This adds further confusion to attempts at developing predictive bedload equations and clearly indicates at least one reason why equations currently in use are unsatisfactory. Bedload is shown to be characterized by a series of pulses with a mean periodicity of 1.7 hours. In the absence of migrating bedforms, it is speculated that this well-documented pattern reflects the passage of kinematic waves of particles in a slow-moving traction carpet. The general pattern of bedload, including pulsations, is shown to occur more or less synchronously at different points across the stream channel. 相似文献
11.
In the literature it has been suggested that on permeable, granular beds, both the threshold and rate of aerodynamic entrainment may be affected significantly by seepage flows into and out of the bed induced by fluctuating pressures in the overlying turbulent boundary layer. Using a range of grain sizes and flow conditions, the series of laboratory experiments reported here compares directly the aerodynamic entrainment of loose grains overlying fixed permeable sediment beds with that occuring over fixed impervious beds. For a given granular material, no significant differences in entrainment dynamics on the two types of bed were observed and in the range of flow conditions examined both the threshold shear velocity (U *T) and the aerodynamic entrainment coefficient (k) were found to be independent of bed permeability. 相似文献
12.
Unsteady bedload transport was measured in two c. 5 m wide anabranches of a gravel‐bed braided stream draining the Haut Glacier d'Arolla, Switzerland, during the 1998 and 1999 melt seasons. Bedload was directly sampled using 152 mm square Helley–Smith type samplers deployed from a portable measuring bridge, and independent transport rate estimates for the coarser size fractions were obtained from the dispersion of magnetically tagged tracer pebbles. Bedload transport time series show pulsing behaviour under both marginal (1998) and partial (1999) transport regimes. There are generally weak correlations between transport rates and shear stresses determined from velocity data recorded at the measuring bridge. Characteristic parameters of the bedload grain‐size distributions (D50, D84) are weakly correlated with transport rates. Analysis of full bedload grain‐size distributions reveals greater structure, with a tendency for transport to become less size selective at higher transport rates. The bedload time series show autoregressive behaviour but are dif?cult to distinguish by this method. State–space plots, and associated measures of time‐series separation, reveal the structure of the time series more clearly. The measured pulses have distinctly different time‐series characteristics from those modelled using a one‐dimensional sediment routing model in which bed shear stress and grain size are varied randomly. These results suggest a mechanism of pulse generation based on irregular low‐amplitude bedforms, that may be generated in‐channel or may represent the advection of material supplied by bank erosion events. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
13.
The mobility conditions of bedload transport in an alpine high‐gradient step–pool stream (Rio Cordon) are analysed. Since 1986, a device system at the downstream end section of the stream has been operating in order to monitor the water discharge, suspended sediment and bedload transport. Sediment distribution of bedload transported by various floods has been analysed, and equal‐mobility evidence is recognized only for the high‐magnitude flows ever recorded (RI > 50 years). The thresholds for size‐selective and equal‐mobility transport conditions are identified and quantified by using both data provided by the fractional transport rate and by length displacements of marked particles. Size‐selective bedload transport seems to dominate when the critical shear stress of the size fractions τci considered is exceeded, whereas the equal‐mobility condition is approached as levels of excess shear stress become higher (τeqi = 1·45τci). Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
14.
Michael R. Leeder 《地球表面变化过程与地形》1977,2(1):1-12
Bagnold's theory of bedload stresses and bedforms requires that the tangential stress exerted at the base of a moving bedload dispersion in high stage plane beds is carried entirely by the grain stress T. Derivation of T from experimental data in flow channnels shows, however, that the fluid contribution τ′ is still dominant (≈ 1 to 2 × T). Particle concentrations in the experimental bedload dispersions approached 10 per cent and it is inferred that no appreciable concentration gradient exists. Grain collisions are thought to be most probable whenever more than 1 former stationary grain layer is in forward motion. High stage plane beds may be unstable when grain collisions cease. Current ripples evolve from the amplification and migration of chance defects due to unsteady fluid impulses generated by injection, or burst, phenomena in the viscous sublayer and not through any inherent static shear resistance deficit exerted by stationary bed grains. 相似文献
15.
Heather Haynes Anne-Marie Ockelford Elisa Vignaga William M. Holmes 《Acta Geophysica》2012,60(6):1589-1606
The vertical structure of river beds varies temporally and spatially in response to hydraulic regime, sediment mobility, grain size distribution and faunal interaction. Implicit are changes to the active layer depth and bed porosity, both critical in describing processes such as armour layer development, surface-subsurface exchange processes and siltation/ sealing. Whilst measurements of the bed surface are increasingly informed by quantitative and spatial measurement techniques (e.g., laser displacement scanning), material opacity has precluded the full 3D bed structure analysis required to accurately define the surface-subsurface transition. To overcome this problem, this paper provides magnetic resonance imaging (MRI) data of vertical bed porosity profiles. Uniform and bimodal (?? g = 2.1) sand-gravel beds are considered following restructuring under sub-threshold flow durations of 60 and 960 minutes. MRI data are compared to traditional 2.5D laser displacement scans and six robust definitions of the surface-subsurface transition are provided; these form the focus of discussion. 相似文献
16.
Reduced bed material stability and increased bedload transport caused by foraging fish: a flume study with juvenile Barbel (Barbus barbus) 下载免费PDF全文
下载免费PDF全文 The plants and animals that inhabit river channels may act as zoogeomorphic agents affecting the nature and rates of sediment recruitment, transport and deposition. The impact of benthic‐feeding fish, which disturb bed material sediments during their search for food, has received very little attention, even though benthic feeding species are widespread in rivers and may collectively expend significant amounts of energy foraging across the bed. An ex situ experiment was conducted to investigate the impact of a benthic feeding fish (Barbel Barbus barbus) on particle displacements, bed sediment structures, gravel entrainment and transport fluxes. In a laboratory flume changes in bed surface topography were measured and grain displacements examined when an imbricated, water‐worked bed of 5.6 to 16 mm gravels was exposed to feeding juvenile Barbel (on average, 0.195 m in length). Grain entrainment rates and bedload fluxes were measured under a moderate transport regime for substrates that had been exposed to feeding fish and control substrates which had not. On average, approximately 37% of the substrate, by area, was modified by foraging fish during a four‐hour treatment period, resulting in increased microtopographic roughness and reduced particle imbrication. Structural changes by fish corresponded with an average increase in bedload flux of 60% under entrainment flows, whilst on average the total number of grains transported during the entrainment phase was 82% higher from substrates that had been disturbed by Barbel. Together, these results indicate that by increasing surface microtopography and undoing the naturally stable structures produced by water working, foraging can increase the mobility of gravel‐bed materials. An interesting implication of this result is that by increasing the quantity of available, transportable sediment and lowering entrainment thresholds, benthic feeding might affect bedload fluxes in gravel‐bed rivers. The evidence presented here is sufficient to suggest that further investigation of this possibility is warranted. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
17.
Rolf Schruder 《地球表面变化过程与地形》1991,16(8):731-736
The local reach gradient of small gravel bed rivers (drainage area 0-8-110 km2) in the Eifel, West Germany, is adjusted to transport the river bed sediments. Transport of gravel becomes possible under high flow conditions (Shields entrainment factor ≈-03). Mean bed material size for riffle sections increases with distance downstream. For small drainage areas channel slope is a negative exponential function of drainage area, while for the larger region the additional influence of bedload size has to be considered. Good agreement with Hack's data (1957) for Virginia and Maryland, U.S.A., is achieved (S = 0.0066 (D50/A)- 40., r = 0.67). 相似文献
18.
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. 相似文献
19.
Michael R. Leeder 《地球表面变化过程与地形》1979,4(3):291-295
A test is proposed for Bagnold's postulate that the normal weight stress due to moving ‘bedload’ is balanced by a solid transmitted stress due to the rate of change of momentum produced by grain impacts on unit area of the stationary bed. The test involves derivation of an expression for normal momentum transfer due to saltating grains at moderate transport stages when grain-to-grain collisions and partial suspension during saltation may be ignored. A dimensionless number, Φ, (a grain Froude Number) is derived, given by ū2/g where ū is the mean grain forward velocity, g is the gravitational acceleration and L? is the length of a single saltation ‘jump’. Equilibrium demands that Φ be unity during bedload transport involving saltating grains if Bagnold's postulate is correct. Experimental data shows Φ < 1, the discrepancy between theory and experiment being due to the existence of lift forces acting upon bedload grains. Bagnold's postulate is correct for concentrated dispersions of grains, as in grain flows, when fluid lift forces may be neglected due to high particle concentration. 相似文献
20.
《国际泥沙研究》2020,35(2):203-216
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(1 D-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 Tolten River in south of Chile are used as examples.In the 1 D-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 Tolten River,while the one proposed by Wilcock and Crowe(2003) performs the best for the data set measured for the Danube River. 相似文献