Pivoting analyses of the selective entrainment of sediments by shape and size with application to gravel threshold

Measured variations of pivoting angles with grain size, shape (‘reliability’ and angularity) and imbrication are employed in analyses of grain threshold to examine how these factors influence selective grain entrainment and sorting. With a bed of uniform grain sizes, as employed experimentally to establish the standard threshold curves such as that of Shields, the threshold condition depends on grain shape and fabric. The analysis demonstrates quantitatively that there should be a series of nearly-parallel threshold curves depending on grain pivoting angles. For a given grain size, the order of increasing flow strength required for entrainment is spheres, smooth ellipsoids (depending on their ‘reliability’), angular grains, and imbricated ellipsoids (depending on their imbrication angles). The relative threshold values for these different grain shapes and fabric are predicted according to their respective pivoting angles, but remain to be directly tested by actual threshold measurements. The pivoting angle of a grain also depends on the ratio of its size to those it rests upon. This dependence permits an evaluation of selective entrainment by size of grains from a bed of mixed sizes, the condition generally found in natural sediments. The pivoting model predicts systematic departures from the standard threshold curves for uniform grain sizes. Such departures have been found in recent studies of gravel threshold in rivers and offshore tidal currents. The pivoting model is compared with those threshold data with reasonable agreement. However, more controlled measurements are required for a satisfactory test of the model. It is concluded that variations in pivoting angles for grain entrainment are significant to the processes of selective sorting by grain size and shape.     

Laboratory measurements of pivoting angles for applications to selective entrainment of gravel in a current

Important to grain entrainment by a flowing fluid is the pivoting angle of the grain about its contact point with an underlying grain. A series of experiments has been undertaken to determine how this angle depends on grain shape (rollability and angularity), on the ratio of the size of the pivoting grain to those beneath, and on factors such as imbrication. The experiments involved gravel-sized spheres (ball-bearings and marbles), natural pebbles selected for their approximately triaxial ellipsoid shapes, and angular crushed basalt pebbles. The pivoting angles for these grains were measured on an apparatus consisting of a board which can be progressively inclined, the angle of the board being equal to the pivoting angle at the instant of grain movement. The pivoting angles of spheres showed reasonable agreement with a theoretically derived equation, showing much better agreement than in previous studies which utilized sand-sized spheres. A series of measurements with spheres ranging from sand to gravel sizes reveals that the pivoting angles decrease with increasing particle size. Our results are therefore consistent with the earlier studies limited to sand-size spheres. The cause of this size dependence is unknown since moisture and electrostatic binding can be ruled out. Similar size dependencies are also found for the ellipsoidal pebbles and angular gravel. The experiments with ellipsoidal pebbles demonstrated a strong shape dependence for the pivoting angle, being a function of the ratio of the pebble's smallest to intermediate axial diameters. This ratio controls the grain's ability to roll and pivot; with small ratios of these diameters the pebbles tended to slide out of position, whereas with ratios closer to unity (circular cross-section) true pivoting took place and the angles were smaller. Experiments with flat pebbles placed in an imbricated arrangement yielded much larger angles than when the pebbles lay in a horizontal position, the pivoting angle being increased approximately by the imbrication angle. The angular crushed gravel also required high pivoting angles, apparently due to interlocking of the grains resulting from their angularity. Other factors being equal, the measurements of pivoting angles demonstrate that the order of increasing difficulty of entrainment is spheres, ellipsoidal grains, angular grains, and imbricated grains. The results obtained here make possible the quantitative evaluation of these shape effects on grain threshold, as well as evaluation of the selective entrainment of grains from a bed of mixed sizes.     

Selective gravel entrainment and the empirical evaluation of flow competence

The concept of flow competence is generally employed to evaluate velocities and bed stresses of river floods from the sizes of the largest sediment particles transported. For the most part, this evaluation has been empirical, combining data from a number of separate flood events in different river systems. Those data are re-examined and compared with empirical equations for the selective entrainment of gravel from deposits of mixed sizes. It is found that the competence relationships trend counter to those obtained for selective entrainment, indicating that the competence evaluations are affected by varying degrees of selective size entrainment. Individual data sets which have been employed to establish the flow-competence relationships either show no trend on their own or yield a trend which runs counter to the competence equation, instead being more compatible with the selective-entrainment relationships. In most instances, the empirical competence equations greatly overestimate the hydraulics of flood flows, and it is suggested that the better established selective entrainment equations be used for competence evaluations as well. Empirical equations are available for this purpose, relating the dimensionless Shields entrainment function or the bed shear stress to the diameter of the largest grain moved and to the median diameter of the deposit as a whole.     

Initial motion and pivoting characteristics of sand particles in uniform and heterogeneous beds: experiments and modelling

Experiments are described in which the threshold conditions for sediment entrainment are measured for uniform and mixed sand beds beneath both steady and combined steady/oscillatory flows. Derived critical shear stresses are compared with the mixed bed entrainment model of Wiberg & Smith (1987). As predicted by the model, coarser grains within a sand mixture are entrained at lower bed shear stresses than progressively finer grains. Entrainment occurs generally at lower shear stresses than predicted by the model, especially under unidirectional flows. This may be the result of grains resting in unusually unstable positions during the experiments because the beds are ‘unworked’ at the start of the experiments. The model of Wiberg and Smith predicts threshold conditions more accurately for the mixed beds if the bed pivoting angle is correctly defined. The pivoting angles of the beds used here are measured using a new technique designed specifically for comparison with the threshold data. The measured angles repeat the finding that the coarse grains are more mobile than the finer fractions of a mixture. The results are poorly described by the pivoting angle model presented by Wiberg & Smith (1987) and are better represented by a model of the form Φ = αD^γ(D_i/D₅₀)^β (after 21 ), where α, γ and β are empirical constants. The threshold model is found to be more effective using the improved pivoting relationship. The entrainment of grains is found to be easier beneath unidirectional flows than combined flows, in accordance with previous authors’ findings. A suggestion that this result is caused by a change in the erosion mechanism beneath wave flows is made. Wave boundary layers may act as an extended laminar sublayer over bed grains and reduce the erosive efficiency of the overlying current flow. The results of the experiment have implications for the natural sorting mechanisms of sediment beds being deposited in near-threshold flows.     

Hydraulic controls of grain-size distributions of bedload gravels in Oak Creek, Oregon, USA

Grain-size distributions of gravels transported as bedload in Oak Creek, Oregon, show systematic variations with changing flow discharges. At low discharges the gravel distributions are nearly symmetrical and Gaussian. As discharges increase, the distributions become more skewed and follow the ideal Rosin distribution. The patterns of variations are established by goodness-of-fit comparisons between the measured and theoretical distributions, and by Q-mode factor analysis. Two end members are obtained in the factor analysis, having (respectively) almost perfect Gaussian and Rosin distributions, and the percentages of the two end members within individual samples vary systematically with discharge. Transformation from Gaussian to Rosin distribution with increasing discharge may be explained by processes of selective entrainment of grains from a bed of mixed sizes. Samples of bed material in Oak Creek follow the Rosin distribution. At high discharges, the transported bedload approaches the grain sizes of that bed-material source and mimics its Rosin distribution. Random-selection processes must be more important to grain entrainment at lower discharges, so that the resulting Gaussian distributions of transported bedload reflect similar distributions of bed stresses exerted by the stream flow. The results from Oak Creek demonstrate that the competence of the flow is reflected in the entire distribution of transported gravel sizes. A sequence of layers of fluvial gravels, modern or ancient, might show systematic variations between coarse Rosin and finer-grained Gaussian distributions, and these could be used to infer frequencies of various discharges and to establish a relationship to the source sediment. With further study, analyses of changing bedload grain-size distributions and their transport rates will lead to a better understanding of downstream variations in grain sizes of bed sediments and how their distributions reflect the progressive development of textural maturity.     

Aerodynamic entrainment threshold: effects of boundary layer flow conditions

Experimental data are presented demonstrating the influence of boundary layer flow conditions on aerodynamic entrainment of grains in the absence of intersaltation collisions. New methods are proposed for (1) the unambiguous determination of aerodynamic threshold for any grain population and (2) approximation of the probability density function (PDF) distributions of threshold shear velocity for aerodynamic entrainment. In wind tunnel experiments, the orderly spatial development of flow conditions within a developing boundary layer over the roughened surface of a flat plate constrains the aerodynamic threshold condition in terms of both mean and fluctuating values. Initial grain dislodgements and subsequent erosion from narrow strips of loose, finely fractionated ballotini were recorded photographically as wind speed was increased. Boundary layer parameters, including average threshold shear velocity (U_*t), were calculated using the momentum integral method. Direct observations show that sporadic oscillation of grains preceded dislodgement. At slightly higher velocities most grains rolled over their neighbours before entering saltation. Initial entrainment in spatially semi-organized flurries of 50 or more grains was followed by quiescent periods at airflow velocities close to threshold. These observations provide strong circumstantial evidence linking both the nature and spatial pattern of initial grain motions to sweep events during the fluid bursting process. For each grain fraction, values of U_*t were found to span an unexpectedly wide range and to decrease downwind from the leading edge of the plate as turbulence intensity increased. A probabilistic entrainment model is applied to the aerodynamic threshold condition so as to incorporate the effects of changing turbulent flow regimes over the plate. Analysis of strip erosion curves gives both an objective definition of the threshold condition and usable approximations of the PDF for U_*t required by the model and for future stochastic treatment of the threshold condition.     

The variability of critical shear stress, friction angle, and grain protrusion in water-worked sediments

The erodibility of a grain on a rough bed is controlled by, among other factors, its relative projection above the mean bed, its exposure relative to upstream grains, and its friction angle. Here we report direct measurements of friction angles, grain projection and exposure, and small-scale topographic structure on a variety of water-worked mixed-grain sediment surfaces. Using a simple analytical model of the force balance on individual grains, we calculate the distribution of critical shear stress for idealized spherical grains on the measured bed topography. The friction angle, projection, and exposure of single grain sizes vary widely from point to point within a given bed surface; the variability within a single surface often exceeds the difference between the mean values of disparate surfaces. As a result, the critical shear stress for a given grain size on a sediment surface is characterized by a probability distribution, rather than a single value. On a given bed, the crtitical shear stress distributions of different grain sizes have similar lower bounds, but above their lower tails they diverge rapidly, with smaller grains having substantially higher median critical shear stresses. Large numbers of fines, trapp.ed within pockets on the bed or shielded by upstream grains, are effectively lost to the flow. Our calculations suggest that critical shear stress, as conventionally measured, is defined by the most erodible grains, entrained during transient shear stress excursions associated with the turbulent flow; this implies a physical basis for the indeterminacy of initial motion. These observations suggest that transport rate/shear stress relationships may be controlled, in part, by the increasing numbers of grains that become available for entrainment as mean shear stress increases. They also suggest that bed textures and grain size distributions may be controlled, within the constraints of an imposed shear stress and sediment supply regime, by the influence of each size fraction on the erodibility of other grain sizes present on the bed.     

The initiation of particle movement by wind

When air blows across the surface of dry, loose sand, a critical shear velocity (fluid threshold, ut), must be achieved to initiate motion. However, since most natural sediments consist of a range of grain sizes, fluid threshold for any sediment cannot be defined by a finite value but should be viewed as a threshold range which is a function of the size, shape, sorting and packing of the surface sediment. In order to investigate the initiation of particle movement by wind a series of wind-tunnel tests was carried out on a range of pre-screened fluvial sands and commercially available glass beads with differing mean sizes and sorting characteristics. A sensitive laser-monitoring system was used in conjunction with a high speed counter to detect initial grain motion and to count individual grain movements. Test results indicate that when velocity is slowly increased over the sediment surface the smaller or more exposed grains are first entrained by the fluid drag and lift forces either in surface creep (rolling) or in saltation (bouncing or hopping downwind). As velocity continues to rise, larger or less exposed grains may also be moved by fluid drag. On striking the surface saltating grains impart momentum to stationary grains. This impact may result in the rebound of the original grain as well as the ejection of one or more stationary grains into the air stream at shear velocities lower than that required to entrain a stationary particle by direct fluid pressure. As a result, there is a cascade effect with a few grains of varying size initially moving over a range of shear velocities (the fluid threshold range) and setting in motion a rapidly increasing number of grains. Results of the tests showed that the progression from fluid to dynamic threshold, based on grain movement, can be characterized by a power function, the coefficients of which are directly related to the mean size and sorting characteristics of the sediment.     

Formation and preservation of open-framework gravel strata in unidirectional flows

Open‐framework gravel (OFG) in river deposits is important because of its exceptionally high permeability, resulting from the lack of sediment in the pore spaces between the gravel grains. Fluvial OFG occurs as planar strata and cross strata of varying scale, and is interbedded with sand and sandy gravel. The origin of OFG has been related to: (1) proportion of sand available relative to gravel; (2) separation of sand from gravel during a specific flow stage and sediment transport rate (either high, falling or low); (3) separation of sand from gravel in bedforms superimposed on the backs of larger bedforms; (4) flow separation in the lee of dunes or unit bars. Laboratory flume experiments were undertaken to test and develop these theories for the origin of OFG. Bed sediment size distribution (sandy gravel with a mean diameter of 1·5 mm) was kept constant, but flow depth, flow velocity and aggradation rate were varied. Bedforms produced under these flow conditions were bedload sheets, dunes and unit bars. The fundamental cause of OFG is the sorting of sand from gravel associated with flow separation at the crest of bedforms, and further segregation of grain sizes during avalanching on the steep lee side. Sand in transport near the bed is deposited in the trough of the bedform, whereas bed‐load gravel avalanches down the leeside and overruns the sand in the trough. The effectiveness of this sorting mechanism increases as the height of the bedform increases. Infiltration of sand into the gravel framework is of minor importance in these experiments, and occurs mainly in bedform troughs. The geometry and proportion of OFG in fluvial deposits are influenced by variation in height of bedforms as they migrate, superposition of small bedforms on the backs of larger bedforms, aggradation rate, and changes in sediment supply. If the height of a bedform increases as it migrates downstream, so does the amount of OFG. Changes in the character of OFG on the lee‐side of unit bars depend on grain‐size sorting in the superimposed bedforms (dunes and bedload sheets). Thick deposits of cross‐stratified OFG require high bedforms (dunes, unit bars) and large amounts of aggradation. These conditions might be expected to occur during high falling stages in the deeper parts of river channels adjacent to compound‐bar tails and downstream of confluence scours. Increase in the amount of sand supplied relative to gravel reduces the development of OFG. Such increases in sand supply may be related to falling flow stage and/or upstream erosion of sandy deposits.     

Rates of aerodynamic entrainment in a developing boundary layer

Despite its significance for inception of grain transport by wind, the initial dislodgement of grains from a static surface by aerodynamic forces of drag and lift in the absence of grain collision has received little attention. This paper describes a series of wind-tunnel experiments in which the erosion of narrow strips of loose grains from the roughened surface of a flat plate exposed to a range of wind speeds was examined. The progressive downwind development of the boundary layer over the plate provided a range of airflow conditions which permitted systematic evaluation of grain entrainment rates arising from purely aerodynamic forces. Use of closely graded size fractions in flat, single grain layers resting on identical, fixed grain support eliminated the effects of surface irregularities and impacts from saltation. Results show that erosion of strips of loose grains develops with time according to an inverse exponential function in which the entrainment rate time constant relates to Shields dimensionless shear stress function. An empirical expression defining aerodynamic entrainment rate in terms of rate of strip erosion is derived and comparisons are made between present and published data. The need for additional data to resolve several questions raised by the present investigation is stressed. In addition, a simple, objective technique for accurate determination of the aerodynamic entrainment threshold of any loose, granular sediment is proposed.     

Settling velocities and entrainment thresholds of biogenic sands (shell fragments) under unidirectional flow

Settling velocities and entrainment thresholds of biogenic sedimentary particles, under unidirectional flow conditions, are derived on the basis of settling tower and laboratory flume experiments. Material consisting predominantly of equant blocks (shell fragments of Cerastoderma edule , density, ρ _s=2800 kg m⁻³) or of mica-like flakes and elongate rods ( Mytilus edulis fragments, ρ _s=2720 kg m⁻³) are used in separate series of experiments. Differences in the measured settling and threshold properties are related primarily to particle shape. The selection of a characteristic length scale for non-spherical grains is investigated by comparing two approaches used to define the grain size ( D ) of the sediment samples: grain settling and sieve analysis that are used to derive data for the threshold criteria, in terms of the Shields and Movability diagrams. The empirical curves effectively predict the threshold conditions for any grain shape, provided that grain size is defined in terms of grain settling velocity. However, a functional distinction is made between the characteristic `hydraulic' grain size, defined by grain settling for grain transport applications, and the actual (physical) grain size defined by sieve analysis.     

Stream-driven, high-density gravelly traction carpets: possible deposits in the Trabeg Conglomerate Formation, SW Ireland and some theoretical considerations of their origin

Within high-density flood flows a prominent mechanism of gravel transport and deposition is by stream-driven, high-density traction carpet (with a rheology similar to grain flow). These gravel carpets are envisaged to form the basal portion of a bipartite high-density flood flow, decoupled from an overlying sand- and silt-laden turbulent flow. Several examples already documented in the literature are reviewed and an additional case from the Lower Old Red Sandstone of southwest Ireland is presented. Two mechanisms of traction carpet initiation are discussed: by rapid entrainment of gravel into suspension on rising stage, followed by settling into the gravel traction carpet at peak and falling stage; and by overconcentration of a ‘normal’, low-density bedload. Gravel entrainment, suspension and traction carpet development are significantly easier if the flood water already carries a high concentration of sand and silt in suspension. Theoretical consideration further shows that gravelly traction carpets can be maintained in channels of relatively low gradient by the shear stress exerted by the high-density, sand-bearing turbulent flood flow above. This tangential shear stress is converted to dispersive pressure, which aids buoyancy and quasi-static grain-to-grain contacts in the support of the clasts within the gravel carpet. The carpet is thought to have a quasi-plastic rheology but behave much like a viscous fluid at high shear rates. Stream-driven gravelly traction carpets are expected to produce sheet-like units of clast- to matrix-supported conglomerate, characterized by a parallel or an a(p)a(i) clast fabric. These units may be ungraded, normally or inversely graded, depending on the rate of shear, the viscosity of the flow and the celerity of deposition.     

Experiments on the entrainment threshold of well-sorted and poorly sorted carbonate sands

Few studies have examined the hydrodynamic behaviour of carbonate sediments. The data presented here are the result of preliminary research on entrainment in well- and poorly sorted carbonate sands. Experiments were performed using naturally occurring sediments in a tilting, recirculating freshwater flume. Results indicate that when of similar size, shape and density, the transport threshold of carbonate sands is similar to that of quartz. However, owing to their lower density and often platy or irregular shape, skeletal sands require a lower shear stress to initiate transport. Because the density of carbonate particles may increasingly vary with grain size, the threshold of motion in coarse carbonate grains may differ more markedly from that of quartz. In poorly sorted samples, results show that the coarse-grained constituents move before the finer-grained components. Grain properties and boundary-layer dynamics are believed to explain this phenomenon. Rollability of the larger grains combined with physical trapping and immersion within a low velocity sublayer are believed to prevent finer particles from moving. Given the appropriate sediments and flow conditions, it may therefore be possible to deposit and preserve fine-grained sediments in a flow regime typically thought to transport such materials.     

Modelling grain-size distributions. A comparison of two models and their numerical solution

Three main diffusion-based models are currently used to study grain-size distributions. In this paper, two of these approaches — perfect sorting and imperfect sorting — are compared in a parameter study. First, the numerical solution of the imperfect-sorting model is extensively discussed, and numerical tests are performed. Then, the two sedimentation models are compared for a basin under varying conditions. For some of the imposed variations, predictions of both models differ markedly due to the different approach. The position of the gravel front in the perfect sorting model depends on gravel input and proximal accommodation space. The position of grain-size boundaries in the imperfect-sorting model is strongly controlled by gravel input, the position of the basin axis and the difference in diffusivities. As a result, those two models may predict gravel progradation for different situations. Both models suggest that gravel progradation should always be coupled with sedimentation rates in order to suggest an explanation of gravel progradation observed in the geological record. Simulations with the imperfect sorting model show that this criterion may also fail, showing that a unique interpretation of gravel progradation may be impossible.     

Thresholds of aeolian sand transport: establishing suitable values

This paper assesses the practical use and applicability of the time fraction equivalence method (TFEM; Stout & Zobeck, 1996) of calculating a wind speed threshold for sand grain entrainment in field situations. A modification of the original method is used and is applied to 1 Hz measurements of wind speed and sand transport on a beach surface. Calculated grain entrainment thresholds are tested in terms of the percentage of sand transport events that they explain. It was found that the calculated thresholds offered a poor representation of the occurrence of saltation activity, explaining only about 50% of the measured transport events. Results are discussed in terms of system response time, wind speed measurement height, undetected events and sampling period. A shear velocity threshold for grain entrainment was also calculated, but this also failed to explain a high proportion of the sand transport events. The best results (67–91% of transport events explained) were found by calculating a threshold based on time‐averaged (≈ 40 s) wind velocity measurements. The applicability of a single threshold to a natural grain population is discussed. A natural surface is likely to possess a range of thresholds varying over short time scales in response to parameters such as grain rearrangement and changes in moisture conditions. The results show that calculated thresholds based on 40 s time‐averaged data consistently explain a high proportion of the recorded sand transport events. This is because such a time‐averaged approach accounts for higher frequency variability inherent in the sand transport system.     

Analysing laser‐scanned digital terrain models of gravel bed surfaces: linking morphology to sediment transport processes and hydraulics

The grain‐scale topography of a sediment surface is a key component of a fluvial system, affecting aspects including sediment transport, flow resistance and ecology. However, its effect is hard to quantify because of the need for grain‐scale elevation data from in situ fluvial gravel surfaces which are difficult to collect. The sediment surface properties are, therefore, commonly estimated as a function of the sediment grain‐size distribution; however, because of additional factors, such as grain packing and shape, there is not necessarily a unique relationship between the two. A new methodology has been developed that uses terrestrial laser scanning to collect grain‐scale topographic data from in situ fluvial gravel surfaces, from which digital terrain models are created. This paper investigates methods of analysing such digital terrain models, and possible sedimentological interpretations that can be drawn from the analysis. Eleven digital terrain models from exposed gravel surfaces in two contrasting rivers (the River Feshie and Bury Green Brook) were analysed by calculating: the distribution of surface elevations, semivariograms, surface inclinations, surface slopes and aspects and grain orientation. The distribution of surface elevations and surface slope and aspect analysis were found to be most informative. In the River Feshie, grain‐size was interpreted as being a dominant control on sediment surface structure and gravel imbrication was identified. In Bury Green Brook, the location of the digital terrain models within the riffle–pool sequence was the dominant control on surface structure and grain orientation. Such digital terrain models therefore provide a new approach to measuring and quantifying the topography of fluvial sediment surfaces.     

微粒对多晶冰流变行为的影响(Ⅰ):应力下的流变行为

研究了应力下微粒对多晶冰流变行为的影响.结果表明:微粒分布在晶界或同时分布在晶界和晶内都将增加多晶冰的流变速率.当微粒只分布在晶界时,含微粒浓度为1 wt.%的多晶冰有最高的最小流变速率;当微粒同时分布在晶内与晶界时,多晶冰的最小流变速率基本与微粒浓度无关.微粒提高流变速率的原因来源于提高了流变过程中的位错密度,分布在晶界和晶内的微粒可以分别通过阻碍晶界滑移,发展内应力及Frank-Read位错增值机制提高流变过程中的位错密度.     

Grain sorting in gravel-bed streams and the choice of particle sizes for flow-competence evaluations

Flow-competence assessments of floods have been based on the largest particle sizes transported, and yield either the mean flow stress, mean velocity, or discharge per unit flow width. The use of extreme particle sizes has potential problems in that they may have been transported by debris flows rather than by the flood, it may be difficult to locate the largest particles within the flood deposits, and there are questions concerning how representative one or a few large particles might be of the transported sediments and therefore of the flood hydraulics. Such problems would be eliminated for the most part if competence evaluations are based on median grain sizes of transported sediments, or perhaps on some coarse percentile that is established by a reasonable number of grains. In order to examine such issues, the gravel-transport data of Milhous from Oak Creek, Oregon, and of Carling from Great Eggleshope Beck, England, have been analysed in terms of changing grain-size percentiles with varying flow stresses. A comparison between these two data sets is of added interest because the bed material in Oak Creek is segregated into well-developed pavement and subpavement layers, while such a layering of bed materials is largely absent in Great Eggleshope Beck. The analyses show that the trend of increasing sizes of the largest particles in the bedload samples (diameter D_m) with increasing flow stresses is consistent with similar dependencies based on sieve percentiles ranging from the medians (D₅₀) to the 95th percentiles (D₉₅). This indicates that the largest particles are an integral part of the overall distributions of bedload grain sizes, and respond to changing flow hydraulics along with the rest of the size distribution. In Oak Creek, the median grain size shows the largest change with increasing flow stresses, followed by D₆₀, and so on to D₉₅ which shows the smallest change. The variations in D_m continue this trend, and are similar to those for D₉₅. This systematic variation of grain-size percentiles in Oak Creek is consistent with changes in the overall distributions which tend to be symmetrical and Gaussian for low discharges, but become skewed Rosin distributions for high discharges. In contrast, in Great Eggleshope Beck the several percentiles and D_m show the same rate of shift to coarser sizes as flow stresses increase. This results in part from differences in sampling techniques wherein the bedload samples from Great Eggleshope Beck represent a complete flood event, while shorterterm samples at a specific flow stage were obtained in Oak Creek. As a result of the integrated sampling in Great Eggleshope Beck, the bedload grain-size distributions are more complex, commonly with a bimodal pattern. However, after accounting for differences in sampling schemes in the two streams, contrasting patterns in changing grain-size distributions remain, and these are concluded to reflect grain sorting differences as the bedload grain-size distributions approach the distributions of the bed materials. It is surprising that if criteria commonly employed to demonstrate the equal mobility of different grain sizes are used in the comparison, then Great Eggleshope Beck is far closer to this condition in spite of its minimal development of a pavement. It is concluded that the respective shapes of the bed-material grain-size distributions, in particular their degrees of skewness, are more important to the observed sorting patterns than are the effects of a pavement layer regulating grain entrapment to produce an equal mobility of different grain sizes. Therefore, the comparison has established that flow-competence relationships will differ from one stream to another, depending on the pattern of grain sorting which is a function of the bedmaterial grain-size distribution.