Mobility of bed material in Harris Creek

Mobility of bed material in Harris Creek

Michael Church and Marwan A. Hassan

Department of Geography, University of British Columbia, Vancouver, British Columbia, Canada

Received 29 June 2001; revised 16 February 2002; accepted 16 February 2002; published 15 November 2002.

[1] The mobility of bed material is investigated in a small gravel bed river in which the bedis weakly bimodal in texture and relatively stable. The bed surface remained intactthroughout the freshet, and scour was limited to small areas of the bed. Observations ofbedload caught in pit traps and displacement of magnetically tagged particles during twospring freshets permit analysis of the mobility of each size fraction. Fractional transportrates plot up to three orders of magnitude below the reference transport rate suggested in theliterature. At low flows, no size fraction was fully mobile. At intermediate flows (shearstress >27 Pa) sand was fully mobile while larger material remained partially mobile. Athigh flows (>43 Pa) the division between the full and partial mobility regimes occurredaround 16 mm, which remains finer than the median size of the subsurface material. Thelargest material scarcely moves at mean annual flood. Magnetic tracers confirmed resultsobtained from the pit traps. Three distinct zones of mobility can be defined in fractionaltransport plots: partial mobility, full mobility, and overpassing/suspended. Critical shearstress for incipient motion varied over an order of magnitude; a qualitatively similar resultfor bimodal sediment was reported by Wilcock and McArdell [1993]. Incipient motionanalysis based on the largest grain observed to move yielded an upper envelope implyingtransport similarity for sizes found on the bed surface, and a lower envelope thatcorresponds with our (nonsimilar) entrainment criterion. INDEX TERMS: 1815 Hydrology:

Erosion and sedimentation; 1821 Hydrology: Floods; 1824 Hydrology: Geomorphology (1625); KEYWORDS:

bedload, sediment transport, floods, channel stability, sediment mobility

Citation: Church, M., and M. A. Hassan, Mobility of bed material in Harris Creek, Water Resour. Res., 38(11), 1237, doi:10.1029/

2001WR000753, 2002.

1. Introduction

[2] It is commonly assumed that grains are entrained instream channels when the force of the water acting on thebed material overcomes particle inertia. Shields [1936]established a ratio to express this force balance and deter-mined its value at the threshold of particle entrainment to benear 0.06 for sufficiently large material in a turbulent flow(grain Reynolds number > 100) on the basis of experimentsusing relatively narrowly graded sediments. However, nat-ural alluvial sediments have heterogeneous particle sizedistributions which reflect their source, the flow regime,and the history of sediment transport and deposition. More-over, it is widely known that individual size fractions doinfluence each other’s mobility. Field and experimentalstudies dealing with the entrainment of clastic grains haveyielded a wide range of observations [see Buffington andMontgomery, 1997], with Shields numbers varying from 0.2for strongly imbricated, natural streambeds to 0.01 for fullyexposed grains [e.g., Paintal, 1971; Fenton and Abbott,1977; Church, 1978]. The wide variation has been ascribedto effects of particle grading, relative protrusion, shelteringeffect of large particles, and pivot point constraints. In fact,the threshold ratio depends on the combined effect of thesurface texture and the more specific arrangement of thesurface layer grains [Church et al., 1998]. This is a

consequence of the adjustment of the bed surface to matchthe local sediment transport with that supplied fromupstream, and from adjacent slopes and banks.[3] In gravel bed channels, the surface nearly always

appears to be coarser than the bulk sediment depositbeneath. The bed surface is said to be ‘armoured’. Largeparticles covering less than half of the bed surface aresufficient to limit erosion and stabilize the bed [Harrison,1950]. Morris [1955] provided a rationale for variation inflow resistance that occurs as the density of dominantroughness elements changes. The highest values of resist-ance are associated with intermediate densities of the rough-ness elements because vortex generation and dissipation inthe lee side of one element is then not complete before thenext element is met by the flow. In channels with lowtransport rates, the arrangement of the dominant elementsappears to take characteristic forms, including imbrication,stone clusters [Dal Cin, 1968; Brayshaw, 1984], stone lines[Laronne and Carson, 1976], and irregular, cell-like struc-tures termed stone cells [Church et al., 1998]. These particleaggregations are associated with an increase in the resist-ance to flow [Martin et al., 2001] and with large reductionsin sediment transport rate [Church et al., 1998].[4] Under a given flow a size fraction may include both

grains that move and grains that remain stable, even thoughthey are all exposed on the bed surface. Wilcock andMcArdell [1993, 1997] termed this condition, which maybe defined for the bed as a whole or for individual sizefractions, ‘‘partial transport.’’ They [Wilcock and McArdell,

Copyright 2002 by the American Geophysical Union.0043-1397/02/2001WR000753

19 - 1

WATER RESOURCES RESEARCH, VOL. 38, NO. 11, 1237, doi:10.1029/2001WR000753, 2002

1997, p.235] suggested that ‘‘the entrainment frequency of asize fraction depends not just on the rate at which individualgrains are entrained but also on the proportion of grains of agiven size that are never entrained over the duration of atransporting event.’’ Consequently, they asserted thatentrainment would be more accurately modeled if theproportion entrained and the entrainment rates of activegrains are considered separately.[5] The objective of this study is to examine bed material

mobility on a lateral bar in a small river that has a relativelystable bed due to the existence of well-developed surfacearmour and structures. Rates of bed material transport are,therefore, small. Much of the bed surface remains stablemost or all of the time. Of particular interest are the relativemobility of particles of given sizes over a range of flows andthe changes in grain mobility over time at a given flow. Ineffect, then, the purpose of the paper is to examine the

application to a field case of the concept of partial mobilityintroduced by Wilcock and McArdell [1993, 1997].

2. Study Area

[6] The study was conducted in Harris Creek, BritishColumbia, Canada. At the study site, the river drains 220km2 of glaciated terrain. Floods from melting snow domi-nate streamflows, but the largest events are created by latespring cyclonic storms with embedded convectional activ-ity. Based on 20 years’ record from a gauge located 6 kmdownstream from the study site, the estimated mean annualflood at the study site is about 19 m3/s. The largest flowsexceed 35 m3/s.[7] A map of the study reach is shown in Figure 1. The

median size of the subsurface material (D50sub) rangesbetween 16 and 45 mm, with a composite median of 20

Figure 1. Location map of the study area showing the staff gauge, sediment traps, and size distributionof the bed material. Four bulk subsurface samples (1–3 and 6) were taken from the bar (about 600 kgeach) and two (�350 particles each) grid by number surface samples (4 and 5) were taken from a pooland riffle located immediately upstream of the study bar. Bulk sample 1 is known to have been depositedrecently. Panel 7 is a composite of the four bulk samples, and panel 8 shows the two surface samples.

19 - 2 CHURCH AND HASSAN: MOBILITY OF BED MATERIAL IN HARRIS CREEK

mm (Figure 1, panel 7). The size distribution of thesubsurface material is weakly bimodal. The bed is wellarmoured, the median size on the surface (D50surf) rangingfrom 64 mm in pools (panel 5) to 76 mm in riffles (panel4). The composite median on the surface is 68 mm (Figure1, panel 8). Small pebbles and sand fill the voids betweenthe large stones on the bar surface. Cellular arrangementsof surface stones (stone cells) have been observed to coverlarge areas of the bed in the study reach. They are presentbut not prominent on the study bar. The bed is, however,strongly imbricated on the bar. Bed material transport inthe reach has been described by Hassan and Church[2001].

3. Data Collection

[8] Bed load samples were collected in pit traps duringthe 1989 and 1991 freshets. During 1989, a peak flow of15.0 m3/s was recorded followed by several minor rises. In1991, a peak flow of 19.1 m3/s was measured, close to themean annual flood, followed by two further major peaksand several small ones. Traps were installed at the head,midsection and tail of the lateral bar (Figure 1). They eachconsisted of a 20-litre removable plastic pail placed inside a50.0 cm long, 30.5 cm diameter concrete pipe set verticallyin the bar [Church et al., 1991]. The efficiency of the pittraps in comparison with a Helley-Smith sampler wasexamined by Sterling and Church [2002]. Their analysisshowed that at discharges of about 4 m3/s the traps seem tobe reliable for material coarser than 0.25 mm. At about 10m3/s, they appear to be reliable for material coarser than 1mm. The traps collect all material larger than 4 mm (that is,all displaced surface material) over all flows. Analysis ofsuspended sediment samples collected at the study site andof the limit sizes between bedload and overpassing/sus-pended material confirmed the findings of Sterling andChurch [Hassan and Church, 2001].[9] The sampling duration ranged between 1 hour during

high flows and one day during low flows. This procedureavoids short-term, random fluctuations in transport rate (asidentified, for example, by Klingeman and Emmett [1982]and analyzed by Gomez et al. [1989]) and increases thechance of collecting large particles, so is apt to provide arepresentative sample of mobile sizes. The amount of sedi-ment collected in each trap ranged from a few tens of gramsduring low flows to about 30 kg during high flows. Most ofthe samples ranged between 10 and 20 kg and yielded alargest clast of weight less than 1% of total sample size; afew had a largest clast approaching 5% of sample weight.The 1% results compare reasonably with the criteria ofChurch et al. [1987] for a representative sample. However,neither the finest nor the coarsest mobile fractions may bewell represented in the traps. Overpassing in suspension isthe main reason for the low catch in the case of the fines,whereas underrepresentation of the coarsest fractions couldbe due to their sporadic movement and the shift in the locusof the bedload movement over the bar during high flows[see Hassan and Church, 2001].[10] The bedload samples were dried and sieved at 1/2-

psi intervals ( psi = log2D = �phi, phi being the traditionalsedimentological unit). In this paper we report data col-lected at traps 3B during 1989 and 1991 freshets and 1Aduring 1991. These traps were left fully open to collect all

mobile sizes, whereas the other traps were covered eitherwith 10 mm wire screen or with rocks in order to study theinfiltration of fines. Although trap 5A was left uncoveredduring the 1991 freshet, we do not include it in theanalysis because the main flow is directed away from thetrap and mostly sand and fine gravels (<16 mm) werefound in it. Although traps 3B and 1A also reflect localhydraulic conditions, they collect all mobile sizes andtherefore better represent the sediment transport regimeof the stream.[11] To support bedload measurements along the bar,

sediment mobility was also investigated using over 1000tracer clasts. Such tracers can provide information on flowcompetence and mobility of different size fractions. Sincethe movement of the coarse fractions in gravel bed rivers issporadic, the tracers are likely to provide a more accuratemeasure of the movement of such sizes and thereforecomplement sediment transport data obtained from the pittraps. The basis for using the tracers to examine sedimentmobility has been provided by Wilcock [1997]. They rangedin size between 16 and 500 mm and had a similar shape,density and roundness to sediment found in the channel bed.The clasts were magnetically tagged and initially placed inlines on the bed surface across the channel, 300 m upstreamof the study bar. The size range of the tracers matches thatabove D42 of the subsurface material and almost the entiresize distribution of surface material (>D03 of the surface).They were introduced in three groups, before the freshets of1989, 1990, and 1991. After each flood season, theirpositions were mapped and their distance of movementand depth of burial were recorded.[12] A water level recorder was installed adjacent to the

bar (Figure 1) and calibrated against discharge from cross-section measurements of stream velocity, width, and depth.During the 1991 freshet, velocity profiles were measurednear traps 3B and 1A, though for a relatively narrow rangeof flows. The daily fluctuation in streamflow during thefreshet was small, so the difference between the minimumand the maximum flow during the collection of an indi-vidual bedload sample was about 10% or less. Since weare concerned with sediment entrainment and mobility, themaximum discharge was adopted to represent the sampledperiod. The shear stress was calculated using the depth-slope method. Water depth measurements in the vicinity ofthe traps were correlated with flow discharge. The watersurface slope was determined locally using HEC2 for arange of flows. The hydraulic model was calibrated usingthe available velocity profiles. The shear stress was calcu-lated using the local depth and computed slope at eachtrap.

4. Observations and Analysis

[13] The texture of the transported material varied withflow magnitude. At low flows, the transported materialwas composed mainly of sand and the size distributionwas unimodal. At higher flows an increasing proportionof gravel was entrained and the size distribution becamebimodal. At about 7 m3/s (shear stress, t, of 27 Pa),particles approaching the median size of the subsurfacematerial were mobile. The maximum size collected in atrap did not exceed 128 mm during either season and thesize distribution of trapped material always remained finer

CHURCH AND HASSAN: MOBILITY OF BED MATERIAL IN HARRIS CREEK 19 - 3

than that of the subsurface material [Hassan and Church,2001]. Little scour or fill was observed on the study bar.

4.1. Fractional Transport Rates

[14] In order to study the relative mobility of various sizeclasses, the fractional transport rate, piqb [Wilcock andSouthard, 1988], was plotted as a function of the particlesize for all samples. In the foregoing expression pi is thefraction of the load made up of particles in the ith sizerange, and qb is the total transport, calculated as the meanfor the sampling period. Following Wilcock and Southard,the fractional transport rate was scaled using the sizedistribution (fi) of the bed material. The resulting expressionis not straightforwardly interpreted. We are interested in therelative mobility of various sizes, a measure of which is theratio pi/fi. Retention of qb in the argument adds no infor-mation. However, it serves to separate successive plots of pi/fi in a multisample diagram designed to show how fractionaltransport changes with flow or with time. We have found ituseful to examine both measures.[15] Wilcock and Southard originally used the size dis-

tribution of the bulk bed material (fi) as their scale. How-ever, Wilcock and McArdell [1993] later argued that the sizedistribution of the surface material (Fi) is more relevant, asthis represents the material that may potentially be mobi-lized. They also pointed out that using the bulk materialrather than the surface material yielded a less distinct breakbetween partial and full mobility. Reference to the surfacematerial is appropriate for spatially uniform transport (asrealized in their experimental flume). But it is not obviouslyso in a stream channel, where material advected over a sitemay be entrained from various different surfaces, includingstream banks, some distance upstream, and does not neces-sarily reflect just the local exchange of sediment betweenbed and flow. Furthermore, there is no guarantee at all thatthe bed surface when it is accessible to be sampled repre-sents surface conditions at the time of the transport measure-ments. Nor is there any guarantee that the bed surface in thefield is adjusted to the time-varying transport. In thesecircumstances, it can reasonably be argued that the bulksediment deposit in the bed accumulated over time by thefull range of competent flows in the stream is the mostrelevant reference material. There are also practical reasonsto prefer the bulk material as the reference material. Oursurface samples were obtained by the Wolman method (asare nearly all surface sample in the field) and consequentlyare limited to material larger than 8 mm. The absence fromthe sample, and, largely, from the surface, of the finer sizestrapped in the load renders certain of the surface-basedfractional ratios uncomputable. For substantive and expe-dient reasons, then, we used the bulk size distribution as thereference distribution.[16] The variation of the fractional transport rate with

particle size was determined at each trap for both seasons,separately. Both traps yielded similar results; some exam-ples are presented in Figure 2. Figure 2a, which plots pi/fi,shows that, at the lowest flows, sand is very greatly over-represented in the transport and, in comparison, larger sizesare greatly under-represented (in fact, they are nearlyabsent). In contrast, at the high flows, sand becomesgreatly under-represented. The largest sizes remain rela-tively scarce, but a range of intermediate sizes has 2 < pi/fI

< 3, approximately. These figures indicate transport inproportion to the presence in the bed of these sizes, thedeparture from the strict similarity value pi/fi = 1.0 beingthe numerical consequence of under-representation of theother sizes. At intermediate flows, the range of approx-imate similarity extends from the sands to about 10 or 20mm. In Figure 2b, the multiplication by qb separates theplots and shows that, for a given flow, the fractionalsediment transport ratio has a range of nearly constantvalues (the ‘‘similarity range’’) with one limit on the finesediment side (Figure 2b: line A, left side) and a second onthe coarse side (line B, right side). Fractions finer than thedeflection point on the fine sediment side are relativelymore rare in the bedload than in the bed. They are subjectto overpassing by suspension. In the large fractions, thesediment transport ratios decrease with particle size, imply-

Figure 2. Transport ratio as a function of grain size:selected observations at trap 3B during 1989 and 1991freshets. (a) The transport ratio pi/fi, where pi is theproportion of each size fraction i present in the transportedmaterial and fi is the proportion of each size fraction in thebulk bed sediment [cf. Wilcock and Southard, 1988]. (b)The scaled fractional transport rate computed as qbpi/fi,where qb is the sediment transport rate. See text fordiscussion.


ing partial mobility of these sizes. The horizontal part ofthe curve implies that the fractional transport ratio isindependent of the particle size so that the absolute trans-port rate of the fraction depends mostly on the proportionin the bed [Wilcock and McArdell, 1993]. At low flows (<5m3/s; t < 20 Pa), this range disappears, implying that nosize larger than sand is fully mobile. The diagram showsthat the largest material contributes very little to the sedi-ment transport in the river while the fine fraction isunderestimated by trapping due to material moving intosuspension and overpassing the traps. It remains a possi-bility that the transport rate of fine material may be verysmall because there are few fines on the surface to transportand, indeed, flows were observed to be essentially clearexcept early in the freshet. However, the comparison of co-located Helley-Smith samples with those recovered simul-taneously from the trap (the sampler was placed on thedownstream rim of the trap) indicated disproportionatevolumes of sand overpassing the trap [Sterling and Church,2002]. We conclude that our first interpretation is thecorrect one.

4.2. Incipient Motion

[17] The initial threshold for entrainment of individualsize fractions was estimated, following Wilcock and McAr-dell [1993], as the shear stress (tri) that produces a smallreference transport rate. Selected scaled sediment transportrates are presented in Figures 3a and 3b as a function ofbed shear stress. To gain a better understanding of theimpact of sediment transport hysteresis on the analysis,distinction is made between the rising and the falling stagesof the flow. Generally, all the traps yielded a pattern offractional transport ratios similar to that illustrated. Alsoshown in the figure is the reference scaled transport rate(W*ri) of Parker et al. [1982] that has been used todetermine the bed shear stress needed to initiate sedimenttransport:

W*ri ¼qbpi ðrs=rÞ�1�g½

firsu3

*

¼ 0:002 ð1Þ

where rs is sediment density; r, fluid density; g, theacceleration of gravity; and u*, the shear velocity. Forsediment transport rate in g m�1 s�1, shear stress in Pascals,and a sediment density of 2650 kg m3, equation (1) has thedimensioned form qbpi/fi = 0.0104tri

1.5 . For low flows inHarris Creek, this relation plots near the maximummeasured sediment transport rates. Harris Creek data plotorders of magnitude below the suggested reference transportrate. At high flows (shear stress >30 Pa), the Parker relationplots near the centre of our data. We plotted parallel linesnear the lowest transport rates that we observed in HarrisCreek. The observed transport rates for the fine fractions inFigure 3a straddle a line three orders of magnitude belowthe Parker relation, so this line still remains above theminimum detectable transport rate. Coarser fractions plotabove a reference rate that is two orders of magnitude belowthe Parker relation.[18] To examine the relation between fractional sediment

transport rate and shear stress for each size class, it isconvenient to replot the relations presented in Figures 3aand 3b for more restricted size ranges. Selected examples

are presented in Figures 3c through 3f at trap 3B. Similarresults were obtained for trap 1B. For sizes finer than 4mm, most of the rising stage data plot near the referencerelation of Parker et al., whereas most of falling stage datawith t < 25 Pa plot near the lower ‘‘Harris Creek’’reference line. Hassan and Church [2001] described aclockwise pattern of hysteresis in sediment transport ratebetween samples collected during the rising limb of ahydrograph and those collected during the falling limb. Inthe case of fine material, they argued that sediment supplydetermines the type and intensity of the hysteresis in thesediment transport regime. At t < 20 Pa, the fractionalsediment transport rates during the rising stages of flowwere greater than those measured during the falling stages(Figures 3c and 3d). At t > 27 Pa, material larger than themedian size of the subsurface bed material began movingand grain size distributions of transported material shiftedtoward the coarse fractions. At these flows, both rising andfalling stages revealed about the same rates of sedimenttransport. For material larger than 4 mm, no distinctionbetween the rising and falling stages was detected (Figures3e and 3f ) and, indeed, little material moved at t < 25 Pa.Rating relations also showed that the coarse fractions (>8mm) exhibit a less systematic relation with flow than thefine fractions [Hassan and Church, 2001]. This observationcould be attributed to the sporadic movement of the coarsefractions and, consequently, at least in part to samplingerror.[19] The critical shear stress needed to initiate transport

for a given size fraction is given by the Harris Creekreference transport relations over most of the range oftrapped grain sizes. However, sizes finer than 4 mm werefound to be mobile during most of the field observationsand in order to estimate their threshold condition we had touse other means. Size specific rating relations reported byHassan and Church [2001] were used to estimate thedischarge needed to transport the smallest detectable trans-port rate for size fractions between 0.5 and 4 mm. Fieldobservations show that fine sand starts to be caught whenthe traps are about 7 cm submersed in the flow (t � 5 Pa).We assumed that this flow initiates the movement of 0.5mm grains; the same principle was applied to the 0.71 mmclass. In the case of 1, 1.41, and 2 mm sizes we used thesmallest transport rates and size-specific rating relations.For example, measurements during 1989 at trap 1A, notdetailed here, showed that material of about 2.8 mm wasmobile at 2.8 m3/s, so this flow was used to estimate theentrainment condition for this sediment size.[20] The magnetically tagged tracers were used to esti-

mate the initial conditions for sediment entrainmentbeyond the sizes found in the traps (>128 mm). Thedispersion of magnetic tracers as large as 500 mm showedthat sizes larger than 128 mm are rarely mobile. In fact, thelarge clasts moved only 1 to 2 m, in effect rolling fromtheir initial placement position into a natural position,apparently stable for the range of flows experienced. Weassumed that the maximum mobile size with a traveldistance of about 5 m or more is associated with peak flow.Therefore, the entrainment conditions of sizes larger than128 mm were estimated using the peak discharge of theflood that had occurred immediately before the observationsof tracer displacements.


[21] The estimated threshold relation as a function ofgrain size is presented in Figure 4. The fitted functionalrelation based on the lower Harris Creek reference rate is

tri ¼ 6:97D0:39�0:019i Di in mmð Þ: ð2aÞ

The threshold relation based on the upper Harris Creekreference rate is

tri ¼ 7:09D0:38�0:016i ð2bÞ

There is scarcely any difference between these two results.The reason is that, near the practical threshold of sedimentmotion, the rate of transport declines dramatically quickly[see Hassan and Church, 2001] so that there is scarcely anydifference in shear stress for a full order of magnitude changein the transport. A fortunate corollary of this situation is thatit is unnecessary to specify the threshold transport rate veryprecisely in order to obtain a realistic threshold relation.[22] Our exponent is significantly different than most

published values derived from flume experiments, which

Figure 3. Size-specific fractional sediment transport rate as a function of bed shear stress during the1989 freshet at trap 3B.The reference transport relation of Parker et al. [1982] is shown as well as parallellines two and three orders of magnitude lower that envelope Harris Creek data at the fine and coarse endsof the range in grain size, respectively. In determining the shear stress needed to initiate the motion ofdifferent sediment size fractions we followed Wilcock and McArdell [1993]. Note that the scale divisionsdiffer between the axes.


range between�0.1 and 0.1 [Wilcock, 1992b], indicating thatsediments of all sizes move at the same critical stress. InFigure 4, the classical Shields curve for narrowly gradedsediment is plotted for comparison. In the range of largegrains, it has exponent 1.0. Our result falls between theselimits. A similarly intermediate result was obtained fromflume experiments on strongly bimodal sediments by Wil-cock and McArdell [1993]. Their exponent, 0.55, is statisti-cally different ( p < 0.001) than that of Harris Creek. TheWilcock-McArdell relation actually fits our results wellbetween 4 and 64 mm but underestimates finer fractionsand overestimates larger sizes. In detail, then, our data appearto diverge from a power law, but the range of our mostreliable data (those based on the reference transport) are wellapproximated by the full-range interpolated relations.[23] In fact, Shields’ original result in the range of large

grains (exponent 1.0 in Figure 4) represents dynamicalsimilitude with respect to the forces necessary to mobilizegrains of increasing size. Fractional exponents appear torepresent varying levels of control over the entrainmentprocess by a restricted subset of the grains present, up to thelimit of transport similarity (exponent 0.0), when all grainsmove off at the same time, presumably under the control ofthe largest grains present. Our result represents someintermediate condition, suggesting that bed condition hasa significant influence on the entrainment condition.

4.3. Domains of Sediment Mobility

[24] The limit between full and partial mobility domainsof sediment transport for each size fraction was estimated inFigure 2. Beyond the deflection point toward the coarse sideof the grain size plot, the large sediment is only partiallymobile. The threshold for initiation of transport is shown inFigure 4. The resulting Harris Creek full and partial mobi-lity domains are presented in Figure 5a. For comparison, thefully mobilized and partial transport domains from Wilcockand McArdell’s [1993] flume experiments and the modifiedShields curve [after Miller et al., 1977] are plotted. InFigure 5a, the Harris Creek fractional reference shear stresscrosses the Shields’ curve near the median size of the

surface material, as has been observed in many other datasets [cf. Komar, 1987; Wilcock, 1998]. Harris Creek valuesplot much higher in the domain of stress than those ofWilcock and McArdell. We ascribe the difference betweenthe Harris Creek results and Wilcock and McArdell’sexperiments to differences in surface condition betweenthe two sets of observations, their surfaces being muchsandier. As in the flume results, the ratio of shear stress forfull mobilization of a given grain size to that for initialmobilization is relatively constant at about 2. The fieldresults span a wider range in grain size, but a smaller rangein shear stresses than do the flume results, confirming thatthe streambed mobilized over a smaller range in shearstress.[25] The fractional transport ratio can be used to deter-

mine the division between suspended and tractive modes ofsediment transport (at least insofar as the sediment transportmeasurements upon which the analysis is erected do so).Here the deflection point in the fine fraction presented inFigure 2 (left side) was considered as the division betweenthem. This limit is plotted in Figure 5a as a function of bedshear stress. Figure 5a shows that most of the suspended/bed load size limit data plot within the suspended sedimentdomain as defined by the line u* = w, the sediment settlingvelocity [cf. Komar, 1988]. Although the data are scattered,the lower envelope continues the trend in shear stressestablished by the data of larger grain sizes. Shields’classical diagram for sediment entrainment is presented inFigure 5b for comparison.

4.4. Tracer Data

[26] During the study period the distance of movement ofa small proportion (32 stones) of the tracer particlesexceeded the 300 m distance between their point ofintroduction and the bar, so some were found within thestudy bar, all on the surface or within the top 15 cm of thebed. This outcome implies that scour during flow eventswas limited and most of the movement occurred over arelatively stable bed surface (the detection limit for buriedtracers is near 1 meter with our equipment). Since most of

Figure 4. The relation between the shear stress needed to initiate the movement of sediment transport asestimated in Figure 3 and grain size. The plotted data are derived from the lower Harris Creek thresholdline and the plotted result is equation 2a. Adoption of the upper Harris Creek threshold line makes nosensible difference to the plotting positions. See text for details of special methods used to estimatethreshold shear stress for certain sizes. Shields’ relation, as modified by Miller et al. [1977] and therelation of Wilcock and McArdell [1993] with exponent 0.55 are plotted for comparison.


the tracers were collected from the bed surface, they couldbe considered to represent the mobility of the bed surfacematerial.[27] To investigate the influence of particle size on

entrainment of the tracers, the proportion that moved ofthe total labeled population in each size fraction wascalculated. The mobile proportion is plotted against tracerparticle size in Figure 6. For sizes finer than the median sizeof the bed material about 70% of all recovered particlesmoved during both 1989 and 1991 flood seasons. In 1990,

when an unusually large flood occurred, all of the materialfiner than 16 mm was moved. For material coarser than themedian size of the bed surface material, the three seasonsshow a steep decrease in the mobility with increasingparticle size. On average, 60% of the tracers moved during1989, 88% during 1990, and only 36% during the 1991freshet. In all three seasons, full mobility was approachedonly for sizes of about 16 mm or less. These results aresimilar to those of the fractional transport rate analysis.Recognizing that the 1989 results reflect the initial place-

Figure 5. (a) Bed shear stresses needed to initiate and to fully mobilize sediment in Harris Creek areplotted against grain size. The initial conditions were estimated based on analysis presented in Figure 4while the full mobility analysis is based on Figure 2. The line u* = w (where w is the grain settlingvelocity and u* is the shear velocity) and the suspended sediment domain for Harris Creek are alsoshown. Wilcock and McArdell’s [1993] results, based on flume experiments, and a modified form ofShields’ curve due toMiller et al. [1977] are plotted for comparison. We adopt the Miller curve because itincorporates the modern consensus that tc* = 0.045 estimates the critical tractive force for widely gradedgravels without constraints. (b) Shields diagram for sediment entrainment. The dimensionless shear stressis given as ti* = (to/[(rs � r)gDi]) and the Grain Reynolds Number as <i* = u*Di/n, where n is thekinematic viscosity. Harris Creek initial and full mobility curves, Wilcock and McArdell’s [1993]experimental results for initial and full mobility conditions, modified Shields’ curve, and u* = w line areshown. This graph is merely a rescaling of Figure 5a.


ment of the particles on the bed, it appears, furthermore, thatmaterial larger than 181 mm is rarely mobile within theobserved range of flows. The largest mobile tracers corre-spond closely with the maximum size of clasts caught in thetraps.

4.5. Maximum Mobile Size

[28] A conventional method for the determination ofthreshold conditions for particle entrainment is estimationfrom the largest particle found in a bedload sampler or trap[e.g., Andrews, 1983]. In this analysis, it is usual to plot thedimensionless shear stress against the scaled particle size.The exponent of the expected relation ranges between 0, inthe case of size-selective entrainment as defined byShields’ relation, and �1 for equal mobility of all grainsfound on the bed surface [e.g., Andrews and Parker, 1987].Equal mobility analysis using the largest mobile sizeimplies that the largest mobile grain should be the largestgrain found in the bed [cf. Wilcock and Southard, 1988].However, Wilcock [1992a] warned against the use of thelargest particle for the estimation of threshold conditions.He pointed out that these estimates are based on theextreme value of the transport grain size distribution, whichis poorly sampled.[29] The data presented in Figure 7 are based on

the largest single particle in the trap [cf. Andrews, 1983].The dimensionless shear stress fell between 1 and 0.01. Themedian relation for the data plotted in Figure 7 is

tri* ¼ 0:11 Di=D50subð Þ�0:75 ð3Þ

wherein Di is the grain size of the largest particle found inthe trap and D50sub is the median size of the subsurfacematerial. Exponent values have been reported rangingbetween �0.43 and �1 (summarized by Komar [1996],

Table 4.1, and Buffington and Montgomery [1997], Table1c). The above relation suggests a strong relative size effecton the entrainment of individual particles, and that selectivetransport occurs in the study reach. The coefficient, 0.11 (tri*for the median grain size), is very high, suggestingsignificant constraints to entrainment.[30] However, Wilcock [1992a] pointed out that, although

the best fit relation can be used to address the question ofwhat is the largest particle size that is likely to be sampledfor a given flow condition, it does not yield a good estimateof the threshold condition for entrainment. To answer thequestion what is the largest mobile grain, he recommendedthe use of an upper envelope to indicate that one isapproaching the threshold shear stress for the entrainmentof a given sampled particle size. Plotting an upper envelopein Figure 7 yielded a line which has two segments; the breakbetween the two segments is around Di/D50sub = 0.3 (Di isabout 6 mm) which is equivalent to a shear stress of 27 Pa.The exponent of the coarse fraction upper envelope is �1,and the coefficient is about 0.13, implying equal mobilityfor the coarse grains after a high threshold is surpassed. Thisis the same threshold that we previously identified forentrainment of the median subsurface material.[31] If equation 3 is recalculated using D50surf (as

observed by Wolman count), the coefficient declines to0.044, which is very close to the customary value assignedfor widely graded sediments [Wilcock and Southard, 1988].For the envelope, the adjusted value is 0.052, still within therange of conventionally expected Shields numbers. Theseresults apparently represent the consequence of entrainmentof grains from a surface with no particular constraints tomobility. Many other investigators have reported similarresults (summarized by Buffington and Montgomery [1997],Table 1c). The apparently contradictory interpretation of theresults derived from scaling by D50sub and D50surf can be

Figure 6. Percent of moved tracers as a function of grain size for three freshet seasons in Harris Creek.Shading denotes the range in the median size of the surface and subsurface material.


reconciled by recognizing that the data upon which therelation is based are derived from trapped mobile grains. AsWilcock noted, the results represent an approximation of thelargest grain that could be moved in the local flow, oncereleased from the bed, but it does not represent a localentrainment criterion, that is, a criterion for release of agrain from the bed, except under the special circumstance ofno bed structure.[32] For comparison, we plotted equation 2a, giving the

reference shear stress, using the same units as in equation 3.The reference shear stress plots near the lower limit ofHarris Creek data (Figure 7). We should expect no result toplot below this limit: the nominal threshold for motion. Theresult is consistent with the manner in which the referenceshear stress relation was defined using trapped mobilematerial.

5. Conclusions

[33] We have examined sediment entrainment and mobi-lity in a gravel bed stream using material collected in pittraps and tracers. The sampling period ranged from onehour during high flow to one day during low flow. Thelong sampling period was determined in order to obtain arepresentative sample of the mobile sediment, to avoidrandom fluctuations in the bedload movement and toreduce the effect of the sporadic movement of the coarsefractions.[34] The sediment transport in the river is low; move-

ment of fractions larger than the median size of thesurface material is rare and occurs at relatively highflows. At low flows sand was transported over a static

bed. As the discharge increased, the texture of the mobilesediment changed and the distribution became moreskewed and bimodal. The passage between the two phaseswas abrupt. A similarly abrupt transition between sandtransport and gravel has previously been reported in themuch larger Snake and Clearwater rivers [see Emmett,1976; Klingeman and Emmett, 1982]. In Harris Creek, themovement of the sand depends largely on its availabilitywithin the channel, leading to a decrease in the transportrates after the peak discharge. Such sediments are sup-plied from upstream tributaries, bank collapse, floodplain,adjacent slopes, and sediment stored behind logjams [seeRyder and Fletcher, 1991]. After the removal of finesediment stored on the surface, mostly during the risingstage, the entrainment and transportation of these fractionsdepends mainly on local sources from the bed, which arecontrolled by the movement of coarse material. Thisinduces hysteresis in the fine sediment movement. Themobilization of the coarse material, on the other hand,depends on the local flow conditions and on bed andchannel characteristics.[35] A summary of our principal observations follows.1. Fractional transport rate in Harris Creek spans more

than five orders of magnitude and most of the data plotbelow the Parker et al [1982] reference transport rate.

2. The range of fractional transport rates can be dividedinto three zones: (1) a limit zone in the fine fractions whichare underrepresented in the bedload because they are subjectto overpassing in suspension: except at the lowest flows,fractional transport rates decline with decreasing particlesize; (2) a fully mobile zone in which sediments are presentin the load in similar proportions to those of their presence

Figure 7. Dimensionless shear stress as a function of relative grain size. In this plot we used the largestparticle found in the trap. Shading denotes the range in the median size of the surface and subsurfacematerial. The sand fractions are also plotted; however, we exclude these sizes from the functionalanalysis. The best fitted line and an envelope over the largest fractions are shown. See text for discussion.


in the bed, and fractional transport rates are approximatelyequal; (3) a limit zone in the coarse material in whichfractional transport ratios decline with increasing particlesize and move in the partial transport regime. At relativelylow flows (t < 20 Pa), the expressed zone of full mobility ispinched out and no size larger than sand is fully mobile.

3. The reference shear stress for entrainment in each sizefraction increases with particle size. The exponent of theHarris Creek threshold relation is different than thatobtained in flume experiments by Wilcock and McArdell[1993] using poorly sorted sediment but it is consistent withthe behaviour of bimodal sediment. The value falls betweenthat for dynamical similitude for sediment entrainment andthat for fractional sediment transport similarity, implyingcontrol of the entrainment process by the bed configuration.

4. The fully mobilized and partial transport domains ofHarris Creek plot higher in the range of shear stress thanthose obtained in flume experiments. Harris Creek resultsalso imply that the bed is mobilized over a relatively smallrange of shear stress.

5. The relation for the threshold of movement crossesShields’ relation at Di near the median value of the bedsurface, as has customarily been observed.

6. The pebble-cobble size fractions were found to bemobile for less than 10% of the freshet duration, while thesand fractions were found to be mobile for more than 90%of the freshet duration.

7. Both pit trap and tracer data show that full mobilitywas obtained only for sizes of about 16 mm or finer (that is,smaller than the subsurface D50), indicating that partialtransport is the dominant regime in the river.

8. Incipient motion analysis using the maximum mobileparticle size suggests a strong relative size effect on theentrainment of individual particles. Plotting an upperenvelope over the largest mobile data yielded a line withtwo segments. The upper envelope indicates the thresholdshear stress for the entrainment of a given particle size.However, the reference shear stress line plots near the lowerenvelope of the largest mobile sizes. Furthermore, the entireanalysis, based on trapped, mobile sediment, applies to themobilematerial and not necessarily to that resident on the bed.

9. Sand and coarser sizes behave differently [cf. Wilcock,1998]. Sand mobilizes at lower shear stresses than gravel;moves into suspension at moderate flows, and exhibitsdistinctive behaviour in incipient motion analysis.[36] Two main effects together determine bed condition

and control the movement of the coarse material. Bedsurface armoring is expressed by the existing coarse surfacerelative to the subsurface layer, and is further promoted bythe observed non-similarity of entrainment. Development ofsurface structures requires that movement of the largeparticles found on the bed surface be sporadic and local[Church et al., 1998]. The main development occurs in thepartial transport regime. In both seasons at Harris Creek, fullmobility was obtained only for sizes of about 16 mm or less,so conditions for structure development were persistentlypresent. On the bar surface, development was chiefly,though not entirely, restricted to imbrication.[37] The sediment transport in the river, even during

relatively high flow, remains very modest in comparisonwith published field data [e.g., Milhous, 1973; Klingemanand Emmett, 1982; Ryan and Laramie, 1996]. The move-

ment of fractions larger than the median size of the bedsurface material is rare and occurs only at relatively highflows. Such flows may occur once every few years and themovement might not last more than a few hours. Fieldobservations indicate that large parts of the bed remainedstable through both 1989 and 1991 freshets and the surfacescouring was local. Our reported entrainment results repre-sent a case in which the bed surface layer and surfacestructures are known to have remained intact through theflow event and the destruction of the armoured surface waslimited to small areas during relatively high flows. Ourstudy describes the sediment transport regime in the pres-ence of a persistently well-armoured and structurally rein-forced bed. We believe that this represents the normalsituation in a relatively large number of gravel bed streams.

[38] Acknowledgments. The research was funded by the NaturalSciences and Engineering Research Council of Canada through a ResearchGrant to M. Church. S. Babakaieff, T. Hou, B. Killam, E. Leboe, C. Nistor,P. Paopangsawan, D. Ramsay, S. Rice, S. Sterling, S. Tsang, and J. Wolcottassisted with field and laboratory work. Mitch Delcau performed HEC2simulations. Peter Wilcock kindly reviewed a draft and provided manysuggestions and comments that greatly improved the paper, and tworeferees for the journal provided a similar service.

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��M. Church and M. A. Hassan, Department of Geography, University of

British Columbia, Vancouver, British Columbia, Canada V6T 1Z2.([email protected]; [email protected])


Mobility of bed material in Harris Creek

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