Sediment Transport Mechanism and Grain Size Distributionsin Stony Bed Rivers
S.FUKUOKA1 and K.OSADA2
1Professor, Research and Development Initiative, Chuo-University, 1-13-27 Kasuga
Bunkyo-ku, Tokyo, 112-8551, Japan; PH &FAX；(3)3817-1625;
email:sfuku@tamacc.chuo-u.ac.jp
2
Research Associate, ditto, email:osada@tamacc.chuo-u.ac.jp
ABSTRACTThe riverbed elevation of stony-bed rivers is controlled by boulders andcobbles. The authors have determined the mechanism of riverbed variation,
characteristic grain size groups, and riverbed stability in stony-bed rivers from theresults of field experiments on straight channels conducted in the Joganji River .
In this study, we analyzed the results of field experiments using a meanderingchannel of the Joganji River. We examined characteristic grain-size distribution inmeandering rivers with boulders and cobble and effects of meander and bankrevetment on riverbed elevation and grain size distribution. Furthermore, we
determined dimensionless physical parameter governing the forming of stable crosssections in stony-bed rivers.
1. Introduction
To implement effective and efficient countermeasures to bed scouring andbank erosion in a stony-bed river, it is first necessary to understand how boulders andcobbles give effects the river’s bed elevation and grain size distribution. In 2004 and2005, we carried out large-scale field experiments using straight channels dug into a
sandbar on a typical Japanese stony river, the Joganji, determining the bed variation
mechanism and characteristic grain size distributions at various discharges, as well as
the mechanism of bed stabilization brought by boulders and cobbles (Kuroda et al.
2005, Fukuoka et al. 2007).
A stony-bed river ordinarily has a complex planform, the result of repeateddivergence and rejoining of the main water route. In such rivers, bank revetments areoften built to prevent bed scouring and bank erosion where the water route is close to
the bank. To minimize damage in and near rapidly flowing sections of stony-bed
rivers, it is critical to develop the capability to predict bank erosion and local scouring
by clarifying the mechanism of water route formation and the effect of revetmentbank on bed elevation and bed grain size distribution.
In this paper, the authors first use data from field experiments conducted inthe Joganji River in 2006 to consider differences in bed elevation and characteristic
grain size distribution in a meandering stony-bed river where revetment bank is in
33rd IAHR Congress: Water Engineering for a Sustainable Environment
c 2009 by International Association of Hydraulic Engineering & Research (IAHR)
Copyright °ISBN: 978-94-90365-01-1

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100

S3 left bank water levelS3 right bank water lavel
S7 left bank water levelS7 right bank water levelmean bed level

60level(m)percentage of grain surface area (%)

Figure1. Plan view of the test channel

5958

570

W02

W04 W08 W12 W16 W20

2040

60

80

100

W22120

W17 right
W16 right
W15 right
W16 left
W13 left
W08 left
W07 left
W06 left
W05 left

8060
40
200
1

140

10finemediumsand gravel gravel

longitudinal distance(m)Figure2. Longitudinal distribution ofwater level and mean bed levelcoarsegravel1001000size(mm)cobbleboulder

Figure3. Bed material grain size
distribution by the surface image analysis
place versus those without revetments. Next, we examine the results of all previous
Joganji river field experiments to consider the stable cross-section of stony-bed rivers.
2. Field Experiments in the Joganji River
Figure 1 is a top view of the meandering waterway. This waterway contained
two meanders and was dug into a sandbar at the 11.1 km point in the Joganji River.
Meander 1 contained natural riverbanks, while revetments were built along the outerbank of meander 2. We measured water level, discharge, bed cross-section, and bed
grain size distribution, the last of which was measured with surface image analysis
and sieve analysis. As the experimental waterway was made of actual bed material,
we released a discharge with a unit width discharge equivalent to the annual meandischarge of the Joganji river, and measured longitudinal distribution of water levels
and discharge at the point where the channel achieved stability at that discharge. After506

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Table 1. observed discharge

60.0

59.0

58.0

57.0(m)Section W05

level(m)••••floflow••••••••••••• • ••• • ••after flow S3 experiment• • ••• • ••• ••• ••• •• • • • • • • • • • • • • • • • • • • • • • • • • •transverse distance (m)Section W16••
level(m)••••oflow••••••••after flow S7 experiment

Figure 4. Bed elevation contour••••• • ••• • ••• • ••• ••• ••• ••• •• • • • • • • • • • • • • • • • • • • • • • • • •transverse distance (m)Figure5. Bed cross-section and bed
surface photographflow experiment S3 (discharge approx. 10 m3/s) and after the experiment S7, at which
maximum discharge was approximately 15.5 m3/s, we drained the waterway bysealing off the waterway’s upstream end, then performed bed cross-sectionalsurveying.
Figure 2 shows the longitudinal distribution of water level and mean bed
elevation. The bed slope was 1:90 overall and increased at the transition points inmeanders 1 and 2. As shown in Table 1 (observed discharge), discharge at theupstream discharge observation cross-section was 10.9 m3/s for flow S3 and peaked
at 15.4 m3/s for flow S7. In Figure 3—the distribution of bed material grain sizes inthe meanders as calculated with surface image analysis—we see that grain size varied
from small gravel 2 mm in diameter to large stones 50 cm in diameter. Because of thedifferences in bed profile and bed materials between the inner and outer banks of themeanders, grain size distribution was calculated separately for the left and right banks,
taking bed transverse slope into account. As seen in Figure 4—bed elevation contour
after flow S3, flow S7,—we see that during flow S3, a characteristic channel shape ofa meander flow formed. Particularly in meander 2, which contained revetments,507

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localized scouring occurred on the revetment face, with sediment accumulation along
the inner bank. It is also apparent that in meander 1, which is formed by natural banks,
more bank erosion was caused by flow S7 than by flow S3. It also shows that along
natural bank, sediment caused by bank erosion accumulated at the locations oflocalized scouring. Figure 5 shows the bed cross-section and a bed surface
photograph for locations W05 and W16. These show that the large-diameter bed
materials are all aligned in the downstream direction (i.e., in a flattened state). This isbecause the force from the flow causes the stones to align in the same orientation as
the flow, making it smaller for resistance to act on them. Large-diameter materials
were predominant at the outer banks of the meanders, smaller-diameter materials at
the inner banks. Along the left bank at location W05, the revetment prevented bankerosion, although bed elevation dropped at the base of the revetments. Along the leftbank at W16, the natural bank was eroded, and sediment was deposited on the bed,resulting in a bed smoothly sloping in the transverse direction from the outer bank.
This demonstrates that in a sufficiently wide river with sufficiently large bed
materials, the relationship between bed shape and bed materials clearly reflects theflow conditions.
3. Mechanism of Channel Formation in Stony-Bed Rivers(1) Characteristic Grain Size Distribution in Meandering Stony-Bed Rivers
Using the results of field experiments, this section discusses the effects thatchannel alignment and revetments have on the bed profile and bed grain size
distribution of a stony-bed river. From grain size distribution in the meander reach(Fig. 3), we see that along an outer natural bank, grain size is large overall, with little
fine-grained material, while large amounts of fine-grained sediment accumulated
along the inner bank due to secondary flow. We also see that along a revetment, incontrast, grain size was smaller overall compared to that observed along natural outerbanks. In addition, the bed material at W08 and W05 differed from that of otherrevetment locations in that it exhibited a distribution shape approximating that of anatural bank. Figure 6 shows the channel cross-sectional shape at W07 and W08—
where revetments were built—and at W16—the site of natural banks. At meander 1(natural bank), the friction velocity was 0.5 m/s, indicating stronger friction force atwork than in the straight section upstream. Along a natural bank, the earth that falls
into the waterway due to bank erosion caused by this large fluid force results in a lesssteep transverse slope [Fig. 6(a)]. Repetition of this process at various discharges
ultimately results in a stable channel like that shown in Fig. 7(a). When earth
containing cobbles and boulders are deposited into the waterway from the banks inthis state, static equilibrium results, and the bed comes to exhibit a broad grain size
distribution. Static equilibrium is a state in which even small-diameter bed materials
remain in place; this is due to the absorption of the tractive force by large-diametermaterials capable of withstanding it and which are exposed on the bed surface by bedand bank scouring. In meander 2 (revetment bank), the friction velocity along therevetment was a high 0.7 m/s, and the main flow velocity line ran close to therevetment. Despite local scouring [Fig. 6(c)] at the revetment face due to508

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after flow S3 experiment
after flow S7 experiment

Level(m)60.5

W16 natural bank
59.5
58.5
57.5
-5.0

-3.0

-1.0

1.0

3.0

5.0

flow

transverse distance (m)(a)

Level(m)60.0(a) natural bank

W08

59.0
58.0

flow
57.0
-5.0

-3.0

-1.0

1.03.05.0transverse distance (m)(b)

Level(m)
60.0

W07
59.0
58.0

(b) revetment bank••

57.0
-5.0

-3.0

-1.0

1.0

3.0

5.0

Figure 7. Stable-state channeltransverse distance (m)(c)

Figure 6. Channel cross-sectional
concentration of the flow there, exposure of large-diameter bed materials causedscouring to stop, resulting in a stable state like that shown in Figure 7(b). In this case,because the revetment prevents the transport of earth and rock away from the bank,the bed contains smaller-diameter material than along a natural bank, to which
sediment is continuously transported from upstream.
At point W05—the boundary between the revetment banks and naturalbanks—the proximity of the fast flow to the outer bank due to the revetment [Fig.
7(b)] caused significant erosion to the natural bank just downstream from thetransition point, indicating the severe erosion occurring there—as is well known tooccur at the boundary between a hard revetment and a soft natural bank. In this case,the grain size distribution widened and a stable bank resulted due to the deposition
onto the bed of large rocks along with other material freed up by bank erosion.
Thus, the channel shape of a stony-bed river is determined by large rocks on
the bank and the bed. In addition, differences in the mechanism of sediment transportarising from channel alignment and the presence of revetments also affect bed shapeand the grain size distribution of bed materials.

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B d 80h d 80

40

6530
4320
straight channel

10straight channel

2meander (natural bank)meander (natural bank)1

meander (revetment bank)meander (revetment bank)Eq (1)

Eq (2)

0002000

4000

600002000

Q / gI e d 805

4000

6000

Q / gI e d 805

Figure 8. Relationship between
the discharge and surface widthof stony-bed river

Figure 9. Relationship between thedischarge and depth of stony-bedriver(2) The Stable Channel Cross-Section of a Stony-Bed River
In general, the cross-sectional form of rivers is determined largely by
dynamic relation of discharge Q, slope I, and bed material d. This section considers
the mechanism by which the cross-section of stony-bed rivers is determined. Ikeda etal. (1986) have investigated the stable cross-sectional shape of gravel-bed rivers.
Dimensionless consideration of the above dynamic relation leads to Eq(1)and Eq(2) for the width B and depth h respectively:
B / d 80

0.7 Q / gI e d 805

h / d 800.08 Q / gI e d 805

0 .50.5(1)(2)

Figure 8 shows the relationship between the dimensionless discharge anddimensionless width of a stony-bed river. Also shown in the figure are the results ofexperiments conducted in straight stony waterways. The horizontal axis showsdimensionless discharge based on discharge Q, representative grain diameter d80, andenergy gradient Ie; the vertical axis shows dimensionless width based on d80. As therepresentative grain diameter, d80 is used because the bed of a stony-bed river isstabilized by the presence of stones and other large-diameter bed material (Kuroda et510

33rd IAHR Congress: Water Engineering for a Sustainable Environmentfc

k s 4R

10-1

straight channel
straight channel
meandering channel
meandering channel
286fc
4§u ·2¨ * ¸©u¹4210-18624210-2010-2

500

1000

1500
Q / gI e d2000

2500

3000

580

Figure 10. Resistance diagram of the flow in stony-bed riveral. 2005, Fukuoka et al. 2007, 2008) . Although d90 is preferable, we chose d80
because of the poor precision of calculation that would result from d90 due to its low
percentage of the total. Trends are seen nearly same between straight natural-bankchannels and meandering natural-bank channels. A little difference is believed to be
due to the larger grain sizes found in meandering natural-bank channels owing to thelarge stones deposited there by bank erosion. In addition, we obtained larger values
for dimensionless discharge and dimensionless width for meander sections withrevetment banks than for straight sections without revetment banks. This difference isbecause revetments prevent the supply large stone-containing earth from the banks,
resulting in relatively smaller bed material grain sizes compared to natural banks.
Figure 9, which like Figure 8 plots dimensionless discharge on the horizontal axis andbed material–derived dimensionless depth on the vertical axis, shows that in bothstraight and meandering sections, dimensionless depth increases with dimensionlessdischarge. These values correspond to the region where the resistance coefficient f’remains constant on the resistance graph for stony-bed rivers as shown Fig.10. This isthought to reflect that with the exposure of rocks effecting static bed stability, it is theresistance of stones that primarily determines the depth of flow.
To summarize the mechanism of channel formation in stony-bed rivers as
discussed above: As discharge increases, small-diameter bed material is moved by theflow’s tractive force, resulting in bed scouring, which eventually exposes large stones,
creating large bed irregularities. By absorbing the flow’s tractive force, the largestones help create static equilibrium and a broad grain size distribution. Whendischarge increases further, the river attempts to achieve stability by increasing its

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cross-sectional area through bank erosion rather than bed scouring owing to the nearstability of the bed due to the large stones. As more and more stone-containing earth
falls into the river due to bank erosion, the bank side slope becomes less steep. The
large rocks supplied by bank erosion also help achieve static equilibrium and stability
at the bank side, as well. Particularly in a meander, where fluid force is stronger thanin a straight section, bed scouring is severe, and more sediment is also deposited onto
the bed, resulting in larger grain sizes than in a straight section. At this stage, a static,
stable cross-sectional shape in which both bed and bank are unchanging takes form. If
revetments are in place, the flow will cause bed scouring in front of them, but theexposure of large stones will eventually stop scouring so that stability is achieved.
Because revetments prevent the supply of large stone-containing earth from the banks,
bed materials have a smaller grain size distribution compared to sections with naturalbanks. When discharge is even greater, the same series of processes is repeated,widening the river and eventually achieving a stable water channel.
5. Conclusions
The stones and other large-diameter materials in a stony-bed river create static
equilibrium, and differences in sediment transport—particularly in a meander oralong revetment banks—have been shown to effect both bed shape and bed materialgrain size distribution. In addition, we derived the relation of dimensionless widthand dimensionless depth versus dimensionless discharge which is related to discharge,
slope and representative bed material sizes of stable-bed rivers.
REFERENCES
Ikeda,S., Parker, G., Chiyoda,M.and Kimura,Y.(1986), ‘‘Stable channel cross-sectionof straight gravel rivers with actively transported bed materials”, Journal ofHydraulic, Coastal and Environmental Engineering, JSCE, vol.375, 117-126.
Kuroda,Y., Fukuoka, S., Yamamoto, T.(2005), ‘‘Formation mechanism of gravel bedrivers and it’s characteristics of grain size distribution”, Advance in River
Engineering, vol.11, JSCE, 363-368
Fukuoka, S., Terasawa, N., Yamazaki, N. and Tsukamoto, Y. (2007), ‘‘Hydraulics ingravel bed river with boulders”, Advance in River Engineering, vol.13, JSCE,339-344
Fukuoka, S. and Osada, K.(2008), ‘‘The role of stones on the river bed stability instony bed rivers’’, Annual Journal of Hydraulic Engineering, JSCE, vol.52.

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