Experiments on surface structure and partial sediment

Transcription

1 WATER RESOURCES RESEARCH, VOL. 36, NO. 7, PAGES , JULY 2000 Experiments on surface structure and partial sediment transport on a gravel bed Marwan A. Hassan and Michael Church Department of Geography, University of British Columbia, Vancouver Abstract. Eight flume experiments were conducted to study the development of bed surface texture and structure in the presence of partial bed material transport. The experiments have two phases, a no-feed degradational phase followed by a feeding phase. A surface structure of irregular, reticulate stone nets and clusters was developed before sediment feeding commenced. Bed load transport equaled or slightly exceeded the fed supply, except at the highest feed rate. The bed structure was maintained, but bed surface texture fined with increasing sediment load. The two phenomena may coexist because the largest grains on the bed moved only very sporadically. The actual sediment transport rates were much less than the expected rate calculated from the ratio of bed surface grain size to transported grain size. The difference reflects the increase in bed stability introduced by the bed structure. Between 17% and 47% of the bed shear stress is estimated to be carried by the structure, <4% being absorbed by the load, while the bed grains carried the balance of the stress. Bed material transport is exceedingly sensitive to bed surface structure and grain size, which raises concerns about the realizable precision of grain size measurements and characterization of the structure. 1. Introduction Bed material transport in gravel bed stream channels commonly occurs at low rates. In this condition, the bed is only partially mobilized [Wilcock and McArdell, 1993], and much or most of the bed material remains in place for extended periods of time. Both bed surface coarsening and bed surface structures make up the armor surface found in many gravel bed rivers [e.g., Proffitt and Sutherland, 1983; Sutherland, 1987]. As the result of grain-grain interference during tractive transport of sediment over the bed, the resident material becomes arranged into recognizable structures [Johnston, 1922; Laronne and Carson, 1976] that increase the reluctance of individual grains to move [Brayshaw et al., 1983], reduce the bed material transport, and reinforce the overall stability of the channel bed [Church et al., 1998]. The development of bed structures has been investigated experimentally by Church et al. [1998] under the condition of zero sediment influx, and the nature of the grain-grain interaction has been studied computationally by Tribe and Church [1999]. Here we report the extension of our experiments to the condition of low rates of bed material influx over an already structured bed, the usual condition of bed material transport in most gravel bed channels in nature. Our specific objectives are to examine the character of the bed surface texture and structure, and their influence on the sediment transport process, in the presence of sediment feed in a laboratory generic scale model. XNow at Department of Geography, The Hebrew University of Jerusalem, Jerusalem, Israel. Copyright 2000 by the American Geophysical Union. Paper number 2000WR /00/2000WR $ Guiding Prototype and Experimental Arrangements The experimental arrangements were guided by conditions observed in Harris Creek, British Columbia, Canada, as described by Church et al. [1998]. Arrangements of surface stones, consisting of interconnected irregular cells with characteristic diameter of order 1 m, cover large areas of the bed in Harris Creek. The cell borders consist of pebble to cobble size material and, sometimes, boulders. Usually, the cell edges consist of material that is larger than 384 of the bed surface material. The center of the cell contains very poorly sorted material that is significantly finer than that at the edges. The median size of the subsurface material ranges between 22 and 45 mm (Figure 1) in the study reach. The average water surface slope of the study reach ranges between in low flows and in high flows. The bed is well armored, and the median size of the surface layer is -64 mm in pools and 76 mm in riffles. During the study period, , material up to 200 mm moved, but material up to 500 mm diameter is present. It seems that the larger fractions move only during extreme events. Streamflows are dominated by a gradually varying freshet from melting snow, but the largest flood events are created by late spring cyclonic storms with embedded convectional activity. On the basis of 20 years' record from a gage located 6 km downstream of the study site, the estimated mean annual flood at the study site is -19 m 3 s - and the largest flows are -35 m 3 s -. The duration of an average snowmelt event in the river is -3 weeks. Pit traps (described by Church et al. [1991]) were used to measure bed material transport during snowmelt freshet. Sizespecific sediment rating relations and for total bed load mate- rial were examined for the 1989 and 1991 flow seasons. An example of a sediment rating curve for total bed load material is presented in Figure 2. The exponents of the size-specific rating relations range between 4 and 14 (M. A. Hassan and M. Church, manuscript in preparation, 2000). The relatively high 1885

2 1886 HASSAN AND CHURCH: GRAVEL BED STRUCTURE AND SEDIMENT TRANSPORT "'--.x ß.oo, '.',' '"".._'i Subsurface Bar ".., \'[ Riffle Experimental 20 Mixture \ l 11;i o, Grain Size (mm) Figure 1. Surface and subsurface sediment grain size distributions in Harris Creek, the prototype stream for the study, and the grain size distribution of the experimental sediment. exponent values indicate that gravels move near the threshold conditions. Field observations and textural analyses showed that sand is transported at low discharges and the size distribution is unimodal. As the discharge increases, a gradual increase is evident in the size of mobile grains, and the size distributions become bimodal. The pebble and cobble fractions which constitute the true bed material in the channel were found to be mobile for <10% of the flood duration, whereas during >90% of the flood, sand was found to be mobile. In comparison with some of the lower reported values (e.g., Oak Creek [Klingeman and Emmett, 1982], Sagehen Creek [Andrews, 1994]) the rates of sedimentransport in Harris Creek remain low (see Figure 2). Eight experiments were carried out in a recirculating flume which is 10 m long, 0.80 m wide, and 0.50 m deep. Flow and sediment data are summarized in Table 1. The bed was fixed in the first 0.75 m downstream of the flume headbox with stones equivalent to about D84 of the experimental bed material. In the remainder of the flume the bed consisted initially of 0.07 m of loose material. The water depth was controlled by an adjustable gate at the downstream end of the flume. All of the flow measurements and photographs were made in a 1-m length centered 5.5 m downstream from the headbox. The primary observation area was selected in the middle of the flume so the upper part of the flume can serve as the feeding part of the flume and the sediment source. Measurements of water surface and bed slopes were conducted throughouthe experiment using a mechanical point gauge with precision +_0.001 m. Over a distance of 6 m, 12 water surface measurements were taken and then averaged to check that flow conditions remained constant. Water depth fluctuations at a point due to waves were 5% or less. Velocity measurements conducted every meter between 2 and 8 m using a hot film probe confirmed that uniform flow was maintained. Because of the flow and sediment conditions used in the experiments (see Table 1), there was no need to adjust the flume tailgate in order to maintain a uniform flow. Over the course of the experiments, water temperature ranged between 10 ø and 18 ø, but within a run it varied <3 ø and usually remained within 1 ø. In each set of experiments, flow was held constant so that bed surface development and sedimentransport changes could be related to changes in bed texture and structure. The experiments were scaled from field conditions at geo- metric scale ratios of 1:20. The base of the flume was covered with a layer of well-mixed sediment with particle size distribution (Figure 1) scaled from Harris Creek, excepthat material finer than 0.18 mm was excluded because it would become suspended. This scaling preserved the size distribution down to the 28th percentile (3.6 mm) of the bed material, with 32 mm being the maximum particle size limit in the flume. The water surface slope of the experiments was set to fit the slope of high flows at Harris Creek study site. The model was generic rather than specific because no attempt was made to reproduce geometrical details of the prototype channel. An axial pump recirculated water but not sediment. Flow was set to a desired level, and the bed surface was allowed to develop without sediment feed for a period of 16 hours. By this time, sedimentransport was reduced to - 1% of the transport during the first hour (Figure 3), and bed surface structures were substantially developed. In nonfeed experiments, only slow changes were recorded thereafter. Sediment feeding was initiated after 16 hours at a rate proportional to the transport observed between 8 and 16 hours. By this means we expected to reproduce the conditions of low bed material transport over a developed surface, as observed in Harris Creek. The texture of the fed sediment was the same as that of the material transported between 8 and 16 hours. The reference sediment feeding rate, nominally equal to the observed transport rate, was, in fact, a fixed value close to the mean of values observed in each sequence of experiments, set by the value observed in the initial (nonfeed) run. At the start of each experiment the sediment was slowly flooded and then drained to aid settlement. Then the surface was leveled, and a flat bed with a constant slope was produced. In order to remove overexposed particles and irregularities in the surface leveling, the bed was first exposed to a low flow that was gradually increased to the desired level, selected so that partial entrainment (in the sense of Wilcock and McArdell lo 5 ß n- 103 o 102 o3 101 lo o O Discharge (m3/s) Figure 2. Trap rating relations for all sizes based on period averages at trap 3B. The rating curve of the fitted line is q = x 10- (Q) ', where Q is the water discharge.

3 HASSAN AND CHURCH: GRAVEL BED STRUCTURE AND SEDIMENT TRANSPORT _ _ Feed rate %, exp. HM exp. HM exp. HM exp. HM ß,..,_ exp. HM I o 1 Feed begun ' i Elapsed Run Time (hr) Figure 3. Experimental observations of sediment transport in five experiments with sediment feeding initiated at 16 hours. The shaded zone on the graph falls between 0.75 and 1.25 of the transport rate after 16 hours. Details of the feeding arrangements are given in the text _0. [1993]) of the sediment occurred. The flow was selected to mobilize sufficient sediment so that bed surface structure developed but not bed forms such as dunes or bars. The truncation of the flume sediment means that all of the transport would correspond with gravel transport in the prototype stream. Material transported from the flume was trapped on a 0.18-mm mesh screen in the tail box. At intervals throughouthe experiments the flow was lowered to a level well below that required for particle entrainment. Then the bed was photographed, bed surface samples were taken, and the sedimentrap in the tail box was replaced. This procedure was adopted to keep the bed fully under water to avoid air penetration and surface settling. Bed load samples were dried, weighed, and sieved at half-phi intervals. The sampling procedure was designed to establish mean sediment transport rates and to avoid random fluctuations. Underwater areal bed surface samples were taken -1 m downflume of the observation area using a piston device [Fripp and Diplas, 1993]. The piston disk, with diameter 0.15 m and area m 2, was coated with clay sufficiently thick to surround the largest particles on the bed and to contact fine particles immediately adjacent. The clay was pressed onto the gravel surface so that the surface sediment was embedded in the clay. The disk was then removed and washed to suspend the clay. The remaining sediment was dried and sieved at half-phi intervals. The minimum required area of the clay samples was calculated following Fripp and Diplas [1993]. The largest particle in the flume was 0.03 m, and therefore the required area was 0.09 m 2, so that five samples were taken across the flume from the reach below the primary observation area. The areal samples were converted to bulk sample equivalents using the Kellerhals and Bray [1971] formula, the fidelity of which was checked during the course of the work. To examine the impact of the areal samples on surface development and sedimentransport, one of the experiments was repeated without taking any surface samples. Comparison between the two runs revealed a very similar pattern of sedimentransport and bed surface development.

4 1888 HASSAN AND CHURCH: GRAVEL BED STRUCTURE AND SEDIMENT TRANSPORT Two cameras were mounted over the 0.21 m 2 (0.3 m x 0.7 m) primary observation area to take stereophotographs of the bed surface. The photographs were used to evaluate changes in particle arrangement on the surface by mapping the positions of large clasts. To reduce the level of subjectivity in mapping, the four largest half-phi size classes of sediment (all material >8 mm) were color coded. To examine the level of subjectivity, the surface in one set of photographs was independently mapped by three operators. Because the procedure entails judgements about which stones constitute parts of recognizable structures, some differences were noted in detail, but the main pattern was identical in all of them. transport rates at 16 hours is _+24.5%(see Table 1). Similar trends were revealed by other experiments. It should be recognized that Figure 3 represents sediment transport at the end of the flume. During nonfeed conditions, transport increases downflume according to the net recruitment rate of sediment from the bed. If we suppose, to a first approximation, that the sediment recruitment rate was linear, then transport at our observation area should be -50% of the displayed results. Conditions probably departed from this assumption only during the first hour or two of the runs. The local exchange rate of particles will have exceeded net recruitment by a considerable margin since most actual grain dis- A range of methods for the estimation of bed shear stress placements were observed to be quite short. has been suggested in the literature (reviewed by Whiting and Progressive downstream reorganization of the bed was ob- Dietrich [1990] and Wilcock [1996]). In this study, shear stress served during nonfeed conditions. During the first hour, large was estimated using velocity profiles and depth-slope product. Our velocity measurements include between 6 and 10 points per profile. The calculated shear stress depends on the number of points which are used to estimate u. (shear velocity) and their distance from the bed surface. Secondary circulation and amounts of fine material were evacuated from the bed surface. After -3 hours an order of magnitude reduction in the sediment transport was observed, and by 16 hours the reduction surpassed 2 orders of magnitude. Longer continuation of nonfeed conditions had minor further impact on bed surface texbed surface roughness distort the velocity profiles and cause ture and structure evolution. Experiment HM-1, which was deviations from the supposed logarithmic profile. Therefore, to estimate the shear stress at the bed, it has been suggested that only the lower 10% or 20% of the velocity profile be used [Bathurst, 1982]. When profiles were fully logarithmic, we used all points except those taken in the upper 20% of the flow continued without feed to 96 hours duration, confirms this conclusion, but it also revealed a further order of magnitude reduction in transport during the extended period (consistent with the nonfeed experiments we have previously run). The total degradation in our experiments ranged between 2 and 13 (close to the water surface). In distorted profiles we restricted mm, equivalent to between 0.6Ds0 and 4Ds0 of the bed mathe calculation to the lower 20% of the flow, but we required at least three points to be included in the calculation. The depth-slope method estimates an areal average value of the shear stress. It was used for the following reasons: (1) we are interested in the mean sediment transport rates over the bed and require an expression of mean hydraulic conditions for terial. Most of the degradation occurred during the first hour of flow. With the start of feeding at 16 hours the decline in sediment transport with time stopped (Figure 3). Within the precision of the measurements, transport became essentially constant, although there was a persistent indication of an increase in comparison; (2) the mean condition controlling bed surface transport out to about 60 hours and a decrease thereafter. By development is of interest to us rather than the local point values obtained from the velocity profiles; and (3) for flows with well-developed surface roughness the velocity profiles do not follow a logarithmic curve, making point estimates difficult to establish and verify. the end of the experiments (at 96 hours) the transport rate had declined below the 16-hour value for the 50% and 75% feed rates but remained higher for 100% and 150% rates. Only the last result, however, represents a significant change (in comparison with the transport variance observed at 16 hours). The To estimate a parameter related to the hydraulic resistance, pattern of transport rate variation after the initiation of feedwe used z0, the roughness height, of the velocity profiles. Our velocity measurements include between 6 and 10 points per profile. The calculation of z0 depends on the number of points that were used and their distance from the bed surface. We examined each velocity profile; in the case of fully logarithmic profiles we used all points excepthose taken in the upper 20% ing suggest superposition of the influx of mobile material upon a continuing pattern of net entrainment from the bed, later modulated by adjustment downstream to the influx. By the end of the experiments the load was essentially the fed sediment, except in the case of HM-3 (50% feed rate; higher shear stress), which was still recruiting sediment from of the flow (close to the water surface). In the case of distorted the bed, hence degrading, and HM-6 (150% feed rate; higher profiles we restricted the calculation to the lower 20% of the flow, which had to include at least three points. Because of the high variability and the local nature of the velocity measurements we decided to average results from the five profiles stress), which was aggrading. In HM-3 the transport appears to be similar to the sum of sediment feed plus the degradation exhibited by the nonfeed control (i.e., the sum would be 0.76 kg h -, versus an observed rate of 0.81 kg h- ). In HM-6, aggrameasured in the observation area. dation appears to have been -0.3 kg h-, about 1/6 of the feed rate. This would yield mm h- of bed rise and -3.5 mm total for the experiment. 3. Observations Fractional sediment transport rate is computed as q,pi, 3.1. Sediment Transport Figure 3 shows the variation in sedimentransport rate with time for five runs with the same sediment mixture and flow but with varying sediment feed rates after 16 hours. During the first 16 hours the runs revealed the same pattern of variation with low variability, indicating that we are able to replicate experimentsatisfactorily. The two standard deviation range in where q, is the sedimentransport rate andpi is the fraction of each half-phi size class, i, present in the transported sediment, and then is scaled by the proportion of each size fraction f in the bulk sediment mixture, following Wilcock and McArdell [1993]. The mean fractional transport rates are plotted as a function of the particle size. All experimentshow a clear declining trend of the transport rate as the particle size increases (Figure 4). Fractional trans-

5 _ HASSAN AND CHURCH: GRAVEL BED STRUCTURE AND SEDIMENT TRANSPORT 1889 port rates ranged over 2 orders of magnitude, with a slight decrease in the largest mobile fraction within the first 8 hours of flow. This observation is consistent with changes in the surface particle size composition during the early, nonfeed stages of the experiments. For example, in experiment HM-1 (Figure 4a) the proportion of large mobile material exposed at the bed surface dropped from 26% after 2 hours of flow to 16% and then increased back to -- 25% after 96 hours. By the end of the experiment all particles larger than 5.6 mm were immobile. Furthermore, the mobility of the mm fraction dropped from 2.8% of their proportion in the bed surface after 2 hours of flow to <0.7% after 96 hours of nonfeeding flow. This should not be taken to imply that all of the large fractions were immobile. Depending on flow strength, direct observations showed that large particles moved for a short distance but did not reach the sediment trap. Figure 4b shows the fractional transport rates obtained for the 100% feed experiment (HM-4). During the first 8 hours the experiment exhibited a pattern similar to that of the nonfeed one. However, at 32 hours the fractional transport was similar to that after 8 hours. The 96-hour results show a significant shift in the pattern of transport, with a relative increase in the fractional transport of fine sediment and a decrease in the mobility of large fractions. Most of the curves show a break in slope that shifts toward the coarse fractions as the fractional transport rates increase. The collected 96-hour results displayed in Figure 4c are similar to each other and similar to results obtained for equilibrium transport experiments conducted by Wilcock and McArdell [1993] and by Wilcock [1997]. They demonstrate that full mobility of the bed was not observed in any of our experiments. Furthermore, only partial mobility was attained by most size fractions in the sediment feed runs (by all size fractions in the nonfeed control experiment). The highest fractional mobilities were consistently displayed at the end of the feeding experiments by material in the mm size range. loo lo- 1.o -- 0, ' Exp. HM1 -.'7..' Feeding ',, 2hr '\ '.. \ X. '* 96hr \ 32hr. 8hr -"" '-..'"'" 100% Feeding c HM4 (100) / - " --- '., HM5 (75) "', HM3 (50),,,, 2hr 96h;', 32hr 8hr" -- HM6 (150) Particle Size (mm) 3.2. Surface and Bed Load Textures Figure 4. Fractional sedimentransport diagrams in selected Field and laboratory studies have used bed surface texture as experiments. (a) Four stages in the nonfeed experiment HM-1; an indicator of armor development. Changes in the surface and (b) four stages in the 100% feed experiment; (c) the final bed load compositions through time and between experiments condition after 96 hours in each of the experiments HM-1 through HM-6, showing the effect of varying sediment feed are based on bed surface samples and analyses of trapped rate. transported material. Experiment HM-1 demonstrates textural changes during nonfeeding conditions (Figure 5a). From the early stages of the experiments a progressive trend of surface coarsening is evident. A slight increase in the surface material was observed after 8 hours of flow. In fact, about a 30% and 96 hours were similar. Feeding at a rate of 150% (experiment HM-6) yielded a similar trend to that of 100% feed. The increase in the median size of the surface material was ob- grain size compositions of the armor layer at the end of several served between 2 and 96 hours of flow. In all experiments, feeding experiments are shown in Figure 5c; the higher the major changes in the bed surface composition occurred during the first 16 hours of flow (e.g., Figure 5b). The transition from fine to coarse surface seems to be relatively abrupt. This imfeeding rate, the finer the size distribution of the surface material. Considering bed load texture, experiment HM-1 exhibited a plies the evacuation or "sieving" into the bed of large amounts gradual coarsening of the transported sediment between 2 and of fines at early stages of the experiment and surface modifi- 8 hours of flow. After 8 hours a fining trend was observed, and cation and rearrangement at later stages of flow. the size distribution after 96 hours was similar to that of 2 Figures 5b and 5c show the grain size composition of the armor layers, bed load, and original material for the feed experiments. During experiment HM-4 (i.e., 100% feeding), surface particle size increased and reached maximum development after 8 hours of flow (Figure 5b). No changes were recorded between 8 and 16 hours. When feeding started, a trend of fining in surface particle size composition was obhours. However, the size distribution of the transported material remained significantly finer than the original mixture and the bed surface material (Figure 5a). A trend of increase in the particle size was evident as the feeding rate increased (Figure 5c). In all cases the bed surface material was significantly larger than that of the transported material, but the difference clearly declined with increasing feed rate. served. The size distributions of bed surface material after 16 In a nonfeed experiment the transported sediment must

6 1890 HASSAN AND CHURCH: GRAVEL BED STRUCTURE AND SEDIMENT TRANSPORT Exp. HM1 0 Feeding Surface Time Mixture J I ; i i i i i i loo 80- Exp. HM3 100% Feeding :."':'"':.'... Transported Surface Time '.,'"'".:... 2 o 40- o..o ' "-.! ; Mixture ' ' ' ' ' ' ''' I... ' i;''/'h', ', tl-, loo ß , Transported Surface Feed rate % 80- '.'<'... ", 0 ', ",,xx: 2,-,,x.,..., ', '"...,,.,X,; \'"' ', '"'::, %':' "-, ' ';'.%, '\','[,, Mixture _ '%', 20 - D 84 q.., - -x.7,,, - %-..'X.. '. ' 0 ' ' ' ' ''' I,,,--F:F¾-r-"', '-'F",, i Particle Size (mm) Figure 5, Bed surface and transported material texture: (a) nonfeed experiment HM-1; (b) 100% feed experiment HM-4; (c) variation in bed surface and transported sediment texture over a range of feed rates; measurements made at the close of the experiments at 96 hours. come from the bed. Therefore bed surface texture depends solely on the sizes that a flow can (and cannot) transport. In the case of feed (sediment influx) it depends also on the texture of the influx and on its rate relative to the local entrainment rate. For 100% feed most or all of the mobile sediment comes from the feeder, the size distribution of which was matched in these in transported material, implying continued selectivexchange with the bed Evolution of Surface Structure and Surface Resistance Observations of bed surface texture and structure were re- corded during the experiments and used to evaluate bed surexperiments to that of the sediment being transported imme- face development. Bed surface samples have been used to diately before the start of feeding. The outcome depends on evaluate changes in the sedimentexture while surface structhat circumstance. The above observations show that as the ture was studied by mapping the disposition of large particles feed rate increased, a fining trend was observed in bed surface utilizing the stereophotographs. particle size composition and a coarsening trend was observed Figures 6a and 6b present the bed surface development

7 HASSAN AND CHURCH: GRAVEL BED STRUCTURE AND SEDIMENT TRANSPORT 1891 Feed (HM1) -- 96hr 50% Feed (HM3) n ' 96hr 1,5 cm 75% Feed (HM5) 100% Feed (HM4) 96hr o o o o o o 150% Feed (HM6) 0 0 u o _ 96hr ß o o 0 0 Figure 6. Surface structure development after 96 hours in four experiments with varying feed rate. For comparison, 16-hour results are shown. The shaded stones are those larger than 11.6 mm (>D9o) and the small unshaded stones interlocked with them to form the reticulate structure. during experiment HM-1 after 16 and 96 hours of flow, respec- being winnowed away. Although the pavement development in tively. After 16 hours, large areas of the bed are covered by experiment HM-1 was slightly coarser than that of HM-3, the moderately developed stone cells. Little change in the location general pattern of bed surface development was similar. Exof the large particles ( D84) has been observed after 96 hours periment HM-4 had a feeding rate of 100%, i.e., similar to the of flow. The stone cells and clusters became very clear and well transport rate measured at 16 hours in experiment HM-1. At develope due to the entrapment of small stones within the the end of the run it was obvious that the armoring had not cell edges (Figure 6b), as previously described by Church et al. developed to the degree of the zero feeding experiment (Fig- [1998]. The main elements of the pattern, however, were al- ure 6d). Fines were much more abundant on the surface, which ready clear at 16 hours. In the case of 50% feeding (experiment implies that the feeding rate was sufficiento inhibit further HM-3, Figure 6c), the sediment feed rate was not high enough winnowing of the bed surface, as would be expected if the to disrupt surface development as fines on the surface were still transport rate is matched by the input. Clusters developed

8 _ 1892 HASSAN AND CHURCH: GRAVEL BED STRUCTURE AND SEDIMENT TRANSPORT Ixl 0.8 HM HM HM3 1.0 HM1 I et al. [1998])with different flows (Figure 7a), pattems of variation in roughness length early in the experiments were varied, with rapid increases in two cases. However, the three experiments converged after 96 hours toward a narrow range of values that were generally lower than the early ones. While the zero feeding experiment (HM-1) displayed a gradual increase the roughness length with time (Figure 7b), a more complex pattern was revealed by the feeding experiments. In spite of the high variability, Figure 7b shows that Zo decreased as the feeding rate increased, and at the end, the results exhibited consistent feed rate order. The results exhibited in Figure 7b may be interpreted as reflecting the effect of increased areas of fine surface material with feeding. An important complicating factor, however, is that most of the surface resistance to flow is carried by the larger particles on the bed. Throughout the experiments reported here, the fraction of large particles exposed at the bed surface does not vary greatly (see Figure 5c). In this light, it is perhaps not surprising that the variation in the flow resistance index does not reveal a clear pattern. To clarify this issue, more specifically contrived experiments are needed. 0.2 o io Timo (hr) Figure 7. Variation of Zo with time (a) in three nonfeed experiments and (b) in four feed experiments and a nonfeed control. 4. Analysis Bed surface modification is not a simple process of random particle displacements but the result of interactions among flow, sedimentexture, particle shapes and densities, sediment supply, and surface conditions, leading to the development of coarser and well-packed surfaces in conditions of partial sediment transport. It appears that the sedimentransport itself is an exceedingly sensitive indicator of the process. The decline in the sedimentransport rate (and increase of particle resistance with time) under conditions of negligible or during the first 16 hours, before the onset of feeding, were inhibited from further development and partially hidden by the abundance of surface fines. Nonetheless, the outline of an no sediment feed has been attributed to increase in the size of organized pattern of the coarser clasts remained clearly evident. Results from a 75% feeding experiment (HM-5) were particles exposed on the bed surface [Gessler, 1970] and has intermediate between those of experiments HM-3 and HM-4. been regarded as the essence of the bed armoring process. A feeding rate of 150% resulted in weak surface armoring with However, results of Church et al. [1998] and observations in a large amount of fine sediment on the bed surface, even this study show that most changes in particle size occur during though the density of the coarser clasts exposed on the surface the first few hours, which cannot explain the continued decline remained greater than their proportion in the bulk sediment in sedimentransport and changes in surface resistance. These mix. changes are attributed rather to the development of surface structures that reduce sediment motion. The pattern of observations described above and illustrated The introduction of sediment feed arrests the decline in in Figure 6 is consistent with the systematic fining of the surface grain size distributionshown in Figure 5c. The amount of transport. At low transport rates, sediment continues to move fines on the surface and the level of the development of clusat approximately the feed rate. However, the textural and ters during sediment feeding evidently depend on the feeding pattern evolution of the bed appear to continue as the surface rate and upon the size distribution of the fed material. moves toward a condition in which the transport of the fed Surface resistance to flow in gravel bed river depends on sediment is just sustained under the influence of the texture both particle size and surface arrangement. For a given particle and achieved pattern of the surface. size distribution, particle arrangements may lead to temporal Bed material surface texture is incorporated in recent forand spatial changes in surface resistance. Because direct meamulations of fluvial sedimentransport [e.g., Parker, 1990], but surements of surface structure are difficult, we attempted to surface structure is not successfully parameterized. To estiexamine the impact of the observed particle arrangements on mate the impact of bed structure in particle entrainment and flow characteristics using velocity profiles measured in the censediment transport, we have to resort to indirect methods. ter of the controlled area. We would expecthat changes in the Dietrich et al. [1989] presented a means to investigate the surface roughness elements result in changes in velocity profile influence of bed surface armoring (meaning increase of grain characteristics. The roughness length (Zo) was used to evalusize over the subsurface values) by forming the ratio of exate the effect of changes in the surface character with time and pected sediment transport with and without armoring: with different sediment feed rates. q* = [(zb- Zcs)/(zb- Tct)] n, Changes in Zo over time are illustrated in Figure 7. Owing to high and inconsistent variability in Zo values between profiles, the in which q* is the transport ratio, zb is the shear stress imposed average of the five profiles taken for each flow conditions is on the bed, Zcs is the critical shear stress for the surface mapresented. In three nonfeeding experiments (reported by Church terial, and Tct is the indicated critical shear stress that would be

9 HASSAN AND CHURCH: GRAVEL BED STRUCTURE AND SEDIMENT TRANSPORT x õ x 0.5 / O Exp. MH7-MH9 I 61 q. $b/$ct Figure 8. Plot of equation (1'), showing loci for various q* and the data of the experiments. The solid circles represent values of q* computed from equation (1') for the sequence HM-1 to HM-6, and the open circles represent HM-7 to HM-9. Data are given in Table 1. The crosses represent data from sediment transport measurements in Harris Creek, for comparison. associated with the transported bed material load. We estimate rc as 0.045#(ps - p)dso, in which Dso is assigned from the appropriate sediment population, ps and p are sediment and fluid densities, respectively, and # is the acceleration of gravity. The constant is the Shields number for widely graded sediment mixtures [see, e.g., Wilcock and McArdell, 1993]. In (1), n for established transport in most sedimentransport formulae [e.g., Meyer-Peter and Muller, 1948]. Equation (1) can be reexpressed as 'cs/ 'ct = q,2/3 + (1 - q*2/3) ¾/ 'ct. (1') Assuming that the Shields number takes a constant value, we can replace rcs/zct by Dsos/Dsot, the median grain sizes of the bed surface and transported sediment populations, respectively. This gives us a means to study the effect of sediment transport on surface development. Church et al. [1998] used the limit form of this equation, when q* --> 0, to investigate surface development with zero feed. In this analysis we first compare the observed sediment transport with the expected transport for the observed surface texture. We suppose that the transport observed during the first hour of the experiment approximates transport under no surface constraint (the classical "potential transport rate"). Our data are given in Table 1, and equation (1') is plotted in Figure 8. Data from Harris Creek during the 1991 flow event are plotted for comparison (Figure 8). All of Harris Creek data are located around q* = 0, indicating that sediment was moving very near the threshold conditions and that the sediment transport rates in the river were marginal. For the observed grain sizes, q* is predicted to fall between 0.10 and Observed values of q* fall between and The difference is likely due to the effect of surface structure. Using the Shields number , we can estimate the expected critical grain size for stability of our experimental surfaces. Adopting the mean value of rt,, we obtain Dso c = 5.46 _ mm for experiments HM-1 to HM-6 and _ 0.05 mm for experiments HM-7 to HM-9. Actual surface D so values are smaller by between 19% and 38% in zero feed runs, which presumably represents the grain size equivalent effect of the structure. The relative importance of the bed surface grains and the structure in carrying the bed stress can be more explicitly estimated by rearranging equation (1) to estimate r s = Tceff, the critical shear stress for the actual, structured surface, using the observed values of q*. Results are reported in Table 1. Because the sediment transport ratio remains small, Tce ff remains nearly constant, with a value 3.87 _ Pa in the first experimental sequence and _ 0.04 Pa in the second. The remaining components of the stress disposition can now be computed by difference. The estimated division of shear stress is given in Table 1. Surprisingly, sediment transport consumes up to nearly 4%. The bed structure appears to carry between 17% and 47% of the stress, and this fraction actually increases as sediment transport increases because of the declining size of the surface D so. This appearance could be an experimental artifact: the incidence of large clasts on the surface, those which carry most of the bed stress, does not vary greatly (compare Figures 5 and 7). Nevertheless, the structured arrangement of the surface certainly plays a significant role in mediating sediment mobility and bed stability. In the foregoing analysis, it is assumed that n in equation (1). In fact, the transport of gravels near threshold is remarkably sensitive to hydraulic conditions, and values of n in the range 2 -< n -< 14 have been reported [Church et al., 1991; Wilcock et al., 1996; Emmett and Wolman, 1999, M. A. Hassan and M. Church, manuscript in preparation, 2000]. Increasing n reduces the influence of q* in equation (1'), pushing the description of bed/flow interaction closer to the limit condition investigated by Church et al. [1998], even in the presence of sustained sediment transport. So it is reasonable to ask what would be the value of n in equation (1) to produce the observed q*. Values of %, 'cs, and Tct were substituted into equation (1), which was then solved for n (Table 1). We found 4.4 < n < 11.7, with values increasing as transport increased. The latter result is, again, the computational consequence of surface fining with the increased transport. The increasing value of n is tantamount to an indication that the transport process is occurring closer to the practical threshold which would be defined, in each case, for the observed surface grain size, even though the absolute transport becomes larger. A

10 1894 HASSAN AND CHURCH: GRAVEL BED STRUCTURE AND SEDIMENT TRANSPORT consistent interpretation is that the surface structure, again, suppressed transport well below that that would occur over a texturally equivalent, unarranged bed. 5. Conclusions We have conducted two sequences of experiments to study the development of bed surface texture and structure in the presence of modest rates of bed material transport in the regime of partial transport. The experiments were generically scaled to a prototype stream in which modest transport of gravel occurs as bed load in the presence of a developed, highly structured bed, a situation that we believe to be widespread in gravel bed streams in nature. In the stream, and in our experiments, the bed load supply is controlled so that the actual transport is substantially lower than the classical "capacity" of the channel (which would occur with full transport in the condition of no significant surface development). In the experiments the bed load transport essentially equalled the fed supply, except at the extreme rates of feeding in the first experimental sequence (with higher shear stress). At the lowest feed rate the degrading condition characteristic of the nonfeed control experiment continued; at the highest feed rate, mild aggradation occurred. In these circumstances the surface structure (developed in the experiments before the commencement of sediment feeding) was maintained during sedimentransport. However, the bed surface material fined over time and with increasing sediment feed. This appearance may reflect chiefly the incorporation of mobile sediment into the bed sediment samples. The largest materials on the bed, which moved only very sporadically, remained present. The bed structures remained largely intact except at the highest transport rate observed in experiment HM-6. Even here, the outlines of a bed structure remained discernible. By using a ratio for sedimentransport mediated by critical shear stress for sediments exposed at the surface (equation (1)), we calculated the expected transport as a proportion of the classical capacity rate. The observed sediment transport was more than an order of magnitude less than that. We suppose that the difference is due to the increase in bed stability provided by bed structure. By further manipulation of equation (1) it was possible to partition the bed shear stress into components carried by the load, by the bed grains, and by the bed structure. This exercise revealed that the structure carries between 17 and 47% of the stress, the load <4%, and the bed grains >50%. A surprising result is the appearance that momentum is transferred from ometries (for example, bars). In gravel bed rivers the complex structure represented by reticulate granular structures, themselves made up of individually considerable bed grains, defies this simple partition. Our principal evidence for structure effects remains the discrepancy between computed and observed bed grain sizes and the dramatic reduction in sedimen transport below that predicted to occur over an armored bed. The sensitivity of the sedimentransport deserves attention. Near threshold, the sensitivity of gravel transport to small changes in flow or boundary conditions is well known. In this paper and in some other recent investigations [e.g., Dietrich et al., 1989; Lisle et al., 1993; Buffington and Montgomery, 1999] the remarkable sensitivity to changes in bed grain size has been noted. In our studies, 2 or 3 orders of magnitude of change in transport are correlated with changes in bed material size of order 4x or less. This makes very important the precise measurement of grain size. In nature, at least, this is difficult. There is, furthermore, the possibility that not all of the material resident on the streambed is effective in dissipating stream power. Acknowledgments. The work reported in this paper was supported by the Natural Sciences and Engineering Research Council of Canada through a grant to M. Church. The authors thank Hamish Weatherly for helping with the conduct of the experiments. This paper benefited from comments and suggestions made by E. D. Andrews, P. Diplas, T. B. Hoey, and T. Lisle. References Andrews, E. D., Marginal bed load transport in a gravel bed stream, Sagehen Creek, California, Water Resour. Res., 30, , Bathurst, J. C., Theoretical aspects of flow resistance, in Gravel-Bed Rivers, edited by R. D. Hey, J. C. Bathurst, and C. R. Thorne, pp , John Wiley, New York, Brayshaw, A. C., L. E. Frostick, and I. Reid, The hydrodynamics of particle clusters and sediment entrainment in coarse alluvial channels, Sedimentology, 30, , Buffington, J. M., and D. R. Montgomery, Effects of sediment supply on surface textures of gravel-bed rivers, Water Resour. Res., 35, , Church, M., J. F. Wolcott, and W. K. Fletcher, A test of equal mobility in fluvial sedimentransport: Behavior of the sand fraction, Water Resour. Res., 27, , Church, M., M. A. Hassan, and J. F. Wolcott, Stabilizing self-organized structures in gravel-bed stream channels: Field and experimental observations, Water Resour. Res., 34, , Dietrich, W. E., J. F. Kirchner, H. Ikeda, and F. Iseya, Sediment supply and the development of the coarse surface layer in gravel-bedded rivers, Nature, 340, , Emmett, W. W., and M. G. Wolman, Some comments on geomorphic effectiveness, paper presented at International Conference on Drainage Basin Dynamics and Morphology, Int. Assoc. of Hydrol. Sci., Jerusalem, May 22-29, Fripp, J. B., and P. Diplas, Surface sampling in gravel streams, J. Hydraul. Eng., 119, , the bed grains to the structure as sedimentransport increases. This may, in fact, be a computational artifact. Nonetheless, it would indicate a limitation of classical Shields analysis to in- Gessler, J., Self-stabilizing tendencies of alluvial channels, J. Waterw. vestigate structured beds. By relaxing the transport proportion- Harbors Coastal Eng. Div. Am. Sac. Civ. Eng., 96, , ality represented in equation (1) we further showed that the Johnston, W. A., Imbricated structure in river gravels, Am. J. $ci., $er. remarkable sensitivity of transport to hydraulic conditions at 5, 2, , low transport rates can be interpreted in terms of the inhibiting Kellerhals, R., and D. I. Bray, Sampling procedures for coarse fluvial sediments, J. Hydraul. Div. Am. Sac. Civ. Eng., 97, , effect on sediment mobility of surface structure. Klingeman, P. C., and W. W. Emmett, Gravel bedload transport pro- Our approach to investigating the effects on bed stability of cesses, in Gravel-Bed Rivers, edited by R. D. Hey, J. C. Bathurst, and a structured bed surface is indirect. A more direct approach C. R. Thorne, pp , John Wiley, New York, would be to compute the shear stress carried by the bed grains Laronne, J. B., and M. A. Carson, Interrelationships between bed [Wiberg and Smith, 1991], that carried by the bed form (struc- morphology and bed-material transport for a small, gravel-bed channel, Sedimentology, 23, 67-85, ture) [e.g., Parker and Peterson, 1980], and that assigned to the Lisle, T. E., F. Iseya, and H. Ikeda, Response of a channel with load. Computation of the form resistance and shear carried by alternate bars to a decrease in supply of mixed size bed load: A bed form has been accomplished for well-defined, simple ge- flume experiment, Water Resour. Res., 29, , 1993.

11 HASSAN AND CHURCH: GRAVEL BED STRUCTURE AND SEDIMENT TRANSPORT 1895 Meyer-Peter, E., and R. Muller, Formulas for bedload transport, paper presented at 2nd Meeting, Int. Assoc. of Hydraul. Res., Stockholm, Parker, G., Surface-based bedload transport relation for gravel rivers, J. Hydraul. Res., 28, , Parker, G., and A. W. Peterson, Bar resistance of gravel-bed streams, J. Hydraul. Div. Am. Soc. Civ. Eng., 106, , Proffitt, G. T., and A. J. Sutherland, Transport of non-uniform sedi- Wilcock, P. R., The components of fractional transport rate, Water Resour. Res., 33, , Wilcock, P. R., and B. W. McArdell, Surface-based fractional transport rates: Mobilization thresholds and partial transport of a sand-gravel sediment, Water Resour. Res., 29, , Wilcock, P. R., G. M. Kondolf, W. V. G. Matthews, and A. F. Barta, Specification of sediment maintenance flows for a large gravel-bed river, Water Resour. Res., 32, , ments, J. Hydraul. Res., 21, 33-43, Sutherland, A. J., Static armour layers by selective erosion, in Sediment Transport in Gravel-Bed Rivers, edited by C. R. Thorne, J. C. Bathurst, and R. D. Hey, pp , John Wiley, New York, M. Church, Department of Geography, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2. M. A. Hassan, Department of Geography, The Hebrew University Tribe, S., and M. Church, Simulations of cobble structure on a gravel of Jerusalem, Mount Scopus, Jerusalem, Israel. streambed, Water Resour. Res., 35, , (mshassan@mscc.huji.ac.il) Whiting, P. J., and W. E. Dietrich, Boundary shear stress and roughness of mobile alluvial beds, J. Hydraul. Eng., 116, , Wiberg, P. L., and J. D. Smith, Velocity distribution and bed roughness in high-gradient streams, Water Resour. Res., 27, , Wilcock, P. R., Estimating local bed shear stress from velocity observations, Water Resour. Res., 32, , (Received July 26, 1999; revised February 15, 2000; accepted February 28, 2000.)