ROGER LF.B. HOOKE. Laboratory Study of the Influence of. Granules on Flow over a Sand Bed

ROGER LF.B. HOOKE Laboratory Study of the Influence of Granules on Flow over a Sand Bed Abstract: A flume was used to study the effect of granules on the equilibrium of a stream flowing over a movable bed of fine sand. Addition of granules to flows over a dune-covered sand bed resulted in armouring of troughs between dunes, and in a decrease in the friction factor and sediment discharge. It is inferred that the latter two effects resulted from a decrease in amplitude of bed forms due to the armouring. Addition of granules to a flow over an initially flat sand bed caused an increase in both friction factor and sediment discharge. Similar results were obtained by Guy and others (1966, p. 72-73) for both the dune and flat bed configurations. During some runs a long low hump formed on the bed in a reach where granule concentration was slightly higher than average. By means of this hump, the depth and velocity were adjusted to yield a sediment discharge in the reach of high granule concentration that was equal to sediment discharge elsewhere in the flume. Introduction The mechanics of streams flowing over movable beds have been studied extensively in laboratory flumes during the past decade (Vanoni and Brooks, 1957; Brooks, 1958; Kennedy, 1961; Simons and Richardson, 1962; Guy and others, 1966). However, with a few notable exceptions (Gilbert, 1914; Guy and others, 1966), the size range of bed material used in these experiments has been limited. The ellect of coarse material on the equilibrium of a laboratory stream is the subject of the present study. Runs 1, 2, and 3 were made with a bed of fine sand (Table 1). Following run 1, a one particle-diameter thick layer of granules was added to the artificially leveled bed surface. Granules and sand were mixed by the flow during a series of test runs which preceded run 1G. Granules were removed by screening following run 1G and were reintroduced in the same way after run 3. During runs \G->, 2G, and 3G the granule concentration in the upper 0.1 ft of the bed was about 15 percent (Table 1). Granule concentration during run 1G may have been slightly higher. Few if any granules were found at depths greater than 0.1 ft (PL 1, fig. 1). Each run over the mixed bed differed from the correspondingly numbered run over a sand bed only in the slope of the energy grade line (= water-surface slope). Discharge, mean depth, and mean velocity were all held nearly constant (Table 2). Because all seven runs were made at the same depth, discharge (or velocity) was the only factor varied between sets of correspondingly numbered runs. Acknowledgments Discussions with N. II. Brooks, F. Raichlen, R. P. Sharp, and especially V. A. Vanoni have been helpful in clarifying and interpreting the results of this study. Sharp, Vanoni, H. P. Guy, D. B. Simons, and E. V. Richardson read and made valuable suggestions on a draft of this paper. Vanoni and Brooks arranged for use of the flume which is located in the W. M. Keck Laboratory of Hydraulics and Water Resources of the California Institute of Technology. E. Daly, R. Greenway, and my wife assisted in various phases of the work. The experiments were run in 1962 while the author was a graduate student in geology at Caltech. Apparatus and Procedure The 40-foot long, 10 1/2-inch wide, closedcircuit, tilting flume described by Brooks (1958, Fig. 1), with minor modifications to the inlet as described by Kennedy (1961, Fig. 3-15), was used. As all sediment is recirculated in a closed-circuit flume, a stable or equilibrium condition can be maintained for several hours. Bed and water-surface elevations were measured to the nearest 0.001 ft with a point gage Geological Society of America Bulletin, v. 79, p. 495-500, 1 fig., f pi., April 1968 495

496 K. [,. IIOOKli TMT.UFNCF Ol ; GKANULFS OK FLOW TAI'.I.I-!. SIJAI: A\\i.Y.si.s <)] Hi:n MATKKIAI. Sand ( Iranules 0.220 2.35 I.52 1.18 13 5 Sand Granules 0.225 2.80 1.47 1.19 15.7 mounted on a carriage which rode on rails along the sides of the flume. Discharge was measured with an accuracy of + 1 percent with the use o! a 4 inch by 3 inch venturi meter and water manometer. Slopes were measured using a vernier gage attached to the Hume, and also by measuring water-surface elevations relative to the sloping instrument-carriage rails before starting the flow. Water temperature was maintamed'at 25 C + 2 with lour 1000-watt manually controlled immersion heaters. Sediment discharge was measured by sampling the How m the return pipe just below the inlet to the flume. The sediment sampler has been described by Kennedy (1961, p. 53-55). Bc- Iwccu 9 and 15 one-liter samples were taken near the end of each run. A liter of clear water was returned to the flume lor each liter removed. I'.quilibnum was established using the methods described by Brooks (1958, p. 530 532, Fig. 2). Criteria lor equilibrium were: (1) the mean depth of flow was constant over a working section of the flume (uniform flow); (2) the energy grade line was parallel to the bed and water surface and there was negligible scatter of the points through which the energy grade line was drawn; and, (3) bed forms moved downstream but did not change in gross characteristics for several hours. The equilibrium was delicate and reproducible. In two instances trial runs were made at depths from 2 to 4 percent lower than the depth in the final run for a particular discharge. The resultant steepening ol the slope by deposition at the inlet was apparent in both the bed profile and the energy grade line. In another case a 2 percent increase in velocity also produced a slight increase in energy grade lineslope. I'lffect of granules on it transitional flow regime. During run 1 the bed configuration was typical depth, tt hydraulic raditis, ft velocity ft/sec. 1 )arcy- \Yeisbach Friction iactor sediment concent rations g/1 lied C Configuration^.00251.00251.00231.00241.00304.00252.00276.00251.153. 146.14').149.149.150.150. 151 1.86 2. 00 1.90 l.')2 1. 30 1.28 ].04 1.04.0284.0284.0255.0235.0244.0251.0251.0693.0588.09X5.0895.0693.0588.09X5.0895.73 1 '.984 /.476.407.275.219 dunes \ flat / Transitional I' ripples * ^ Transitional \ or flat f (Pi. 1, Figs. 3 and 5) ' dunes dunes dunes dunes (I'l. 1, Figs. 2 and 4) * Hed-configuralion nomenclature corresponds to that recommended by Kennedy and others (1966), except that the term ripple is reserved for linear features with amplitudes less than about 0.02 ft. ^ Sediment samples taken while sandwave was at downstream end of flume. d = dune-covered part ot bed 1 = flat part of bed G mixed bed

--- - ---------- - --- - -------- - ---------- - --- - ---------- - --- - --------- ----------- Figure 1. Solidified block removed after run 3G. Note layer of granules exposed on sawed surface. Gouging of sawed surface occurred when granules tore loose during sawing. Length of block about 18". Photo: Keck Laboratory of Hydraulics and Water Resources, Caltech. Figures 2 and 4. Bed configuration during run 3G. Fig. 4 taken through window in side of flume. Figures 3 and 5. Bed configuration during run 162. Dark spots on Fig. 3 are granules. Fig. 5 taken through window in side of flume. Points A correspond on two photographs. BED CONFIGURATIONS ARROWS SHOW FLOW DIRECTION HOOKE, PLATE 1 Geological Society of America Bulletin, volume 79

NOTES AND DISCUSSIONS of the transitional flow regime described by Kennedy and others (1966), in that part of the bed was covered by dunes while the remainder was flat. For some reason, granules prevented regeneration of the dunes during runs 1G and IGo. However sand accumulated in patches which extended across the channel and which moved over the granule layer. These sand accumulations occasionally had distinct lee slopes and could be called ripples. More commonly they were symmetrical, and in some cases the water surface above them was elevated, suggesting an antidunc flow regime. Some of the sand accumulations were essentially flat, and appeared to do little more than fill void space between granules (PI. 1, figs. 3, 5). The friction iactor and total sediment discharge were higher for flows over the mixed bed of runs 1G and IGz than for flows over the flat bed of sand alone (run If) (Table 2; Fig. 1). The higher friction factor is attributed to an increase in skin-friction drag due to the presence of the granules and to an increase in form drag due to the low sand accumulations. The higher sediment discharge was probably largely due to the fact that the sand accumulations projected up into the flow, and hence were exposed to higher velocities. Movement ol granules across the sand accumulations may also have increased the sediment discharge by dislodging sand grains. Effect of granules on a dune flow regime. During runs 2G and 3G, granules accumulated in troughs between dunes. Granules near the downstream ends of troughs were frequently dislodged; they rarely, if ever, came to rest on the upper parts of dunes, but instead were transported over the dune to the next trough downstream (PL 1, figs. 1,2). In upstream parts of troughs, a leeside eddy formed due to separation of flow over the upstream dune. Granules beneath this eddy were shielded from the full longitudinal force of the flow, and were thus less commonly eroded. Turbulent fluctuations of the eddy caused them to move about in a random fashion until they were buried by advancing dunes. After the dune passed, the granules were rc-cxposcd. Coarse material thus formed a continuous undulating layer extending from trough to trough beneath the dunes (PI. 1, fig. 1). Greater activity of granules in deeper troughs indicated that lee-side eddies in these troughs were stronger and better developed. This conclusion was supported by observations of the eddies with the use of a thread attached to a wire and emcrsed in the flow. In the deepest troughs eddies became strong enough to erode the granule layer. This process is important because in the absence of occasional scouring of granules from the deepest troughs, the layer might eventually become so deeply buried that it would no longer influence the flow. Armouring by granules prevents deepening of troughs by lee-side eddies. It is inferred that this armouring reduces dune amplitude ami thus is responsible for the lower friction factors and sediment-transport rates observed in flows over dune-covered mixed beds (Table 2; Fig. 1). Direct measurements of average dune amplitude before and after addition of the granules are not available to confirm this conclusion. Uniform sediment transport in non-uniform flow. A persistent hump about 8 ft long occurred on the bed at the upstream end of the flume during runs 2G and 3G. This hump had an average height of 0.0091 feet above the remainder of the bed in run 2G and 0.0129 feet in run 3G. In accord with energy requirements, the water surface was depressed over this feature and flow velocities were higher. (Data reported in Table 1 and Figure 1A are for the downstream part of the flume where uniform flow was established.) A higher concentration of granules was observed on the hump on several occasions, but sieve analyses designed to measure the concentration differences were not made. This higher concentration was probably caused by the procedure when granules were added to the flume. Despite this concentration difference, bed lorms on the hump did not differ noticeably from those elsewhere in the flume. Because mean flow velocities were 5 to 6} ^ percent higher over the hump, it might be expected that higher sediment transport rates would occur and that the sediment in the hump would be redistributed along the bed. From Figure IB it is estimated that a 5 to 6Jx> percent increase in velocity should increase the sediment transport rate by nearly 10 percent. Such an increase would be sufficient to destroy the hump in less than 5 hours. Its persistence during nearly 100 hours of operation demonstrates that it was a stable feature of the bed. The stability ol the hump indicates that sediment discharge over it must equal sediment discharge in the downstream part of the flume. The following explanation for this equality is proposed. First, higher flow velocities would tend to move more sand, but due to the higher

498 R. I,, IIOOKK INFI.UFA'CE OF GKANUUiS ON FLOW Approximate limits of 5 experimental error in friction factor Sand bed E a Runs with relatively higher amplitude bed forms Runs with relatively lower amplitude ^ bed forms 1.4 1.6 flow velocity, ft/sec Figure 1. (A) Relationship between friction factor and flow velocity. (B) Relationship between sediment discharge and flow velocity. Run numbers are explained in Table 2. 2.0 granule concentration, more effective armouring of the troughs would reduce dune amplitude and thus reduce sand transport. The two effects must just balance to make sand movement over the hump equal to that downstream. Second, higher flow velocities would tend to increase granule movement and higher granule concentration might have the same effect. However, lower dune amplitude would reduce the strength of lee-side eddies and hence inhibit

NOTES AND DISCUSSIONS 499 TABLE 3. SEDIMENT USED BY Guv AND OTHERS* Geometric mean sieve diameter, mm 0.33 Geometric standard deviation 1.25 *U<>66, p. 4) Uniform Mixed 0.33 2.07 erosion of granules from troughs, thus again balancing the tendency toward higher transport rates. Additional Data Data published by Guy and others (1966, p. 72-73), covering a greater range of velocity, provide independent confirmation of the results in Figure 1A. These data are from experiments in a 2-foot wide flume with a flow depth of 0.50 +.02 ft. Characteristics of the sediment used by Guy and others arc summarized in Table 3. In Guy's runs with a ripple- or dunecovered bed, Darcy-Weisbach friction factors were lower over the mixed bed. Conversely when the bed was flat, Iriction factors were generally higher for the mixed bed. Guy and others extended their runs into the higher velocity antidune region and again observed lower friction factors for runs over the mixed bed. The explanation for this last effect may well be the same as that advanced for the similar effect on dune-covered beds: that the amplitude of bed forms was reduced by accumulation of coarser debris in troughs. Guy and others (1966, p. 50-51) present several photographs and some sieve analyses which show a higher concentration of coarse material in troughs between dunes as in my experiments. Guy and others (1966, p. 72-73) also present data on sediment transport rates which confirm and extend that shown in Figure IB. Their data indicate lower transport rates for flow over dune-covered mixed beds and for flow over mixed beds with antidunes. Sediment discharge is higher for flows over transitional or flat mixed beds. Concluding Statement From flume studies it is inferred that the presence of coarse sand and granules in the bed of a natural stream will generally result in friction factors and sediment discharges that are lower than those found in comparable streams flowing over finer or more uniform material. Only in the flat-bed flow regime will friction factors and sediment discharges be higher over the mixed bed. With lower friction factors a given discharge can be carried at a lower slope. This should be taken into consideration in attempts to deduce ancient conditions from the grading of fluvial materials. It was further observed that local variations in concentration of coarse material in a laboratory flume may result in stable humps in the sand bed. Such humps may be analogous to gravel bars in natural streams. Owing to their stability, these bars, once formed, may significantly influence the subsequent history of a natural channel. References Cited Brooks, N. H., 1958, Mechanics of streams with movable beds of fine sand: Am. Soc. Civil Engineers Trans., v. 123, p. 526-549. Gilbert, G. K., 1914, Transportation of debris by running water: U. S. Geol. Survey Prof. Paper 86, 263 p. Guy, H. P., Simons, D. B., and Richardson, E. V., 1966, Summary of alluvial channel data from flume ' experiments, 1956-1961: U. S. Geol. Survey Prof. Paper 462T/185 p. Kennedy, J. F. (Chrm.), 1966, Nomenclature for bed forms in alluvial channels: Rept, of the Task Force on Bed Forms in Alluvial Channels of the Committee on Sedimentation: lour. Hy. Div., Am. Soc. Civil Engineers, v. 92, No. HY3, p. 51-64. 1961, Stationary waves and antidunes in alluvial channels: W. M. Keck Laboratory of Flydraulics and Water Resources, California Institute of Technology, Pasadena, California, Rept. No. KH-R-2, 146 p. Simons, D. B., and Richardson, E. V., 1962, Resistance to flow in alluvial channels: Am. Soc. Civil Engineers Trans., v. 127, Paper No. 3360, p. 927-954. Vanoni, V. A., and Brooks, N. H., 1957, Laboratory studies of the roughness and suspended load of alluvial streams: California Institute of Technology, Sedimentation Laboratory, in cooperation with I. S. Army Corps ol Engineers, Omaha, Nebr., MRD Sed. Series No. 11, 121 p. CALIFORNIA INSTITUTE OF 'I ECHNOLOGY, DIVISION OF GEOLOGICAL SCIENCES, PUB. No. 1437 MANUSCRIPT RECEIVED BY THE SOCIETY FEBRUARY 15, 1967 PRESENT ADDRESS: DEPT. OF GEOLOGY AND GEOPHYSICS, UNIV. MINNESOTA, MINNEAPOLIS, MINNESOTA