MECHANISM OF LOW WATER CHANNEL FORMATION AND
THE ROLE OF GRAIN-SIZE DISTRIBUTION IN GRAVEL-BED
RIVERS
Shoji FUKUOKA *, Tomonori ABE*** Research and Development Initiative, Chuo University,
1-13-27 Kasuga Bunkyo-ku, Tokyo, Japan, email; sfuku@tamacc.chuo-u.ac.jp**Toyama River and Road Office, Hokuriku Regional Construction Office, Ministry ofLand, Infrastructure and Transport, 1-425-2 hakusanura, Niigata, JapanINTRODUCTION
Most of Japan's rivers have a steep bed gradient. Areas along rivers have large
populations and important assets located near sediment-yield regions, which are
therefore susceptible to disaster. In a steep river, major flooding often does not
involve excessively high water levels, but the rapid flow velocities can erode bed
and banks and alter the watercourse. Even bed scouring during small- to mediumscale flooding can lead to levee failure. Currently, the primary flood-control
response to such dangers is to increase the setting depth of revetments or to build
underpinnings for foot protection. For reasons of cost and doubts about
effectiveness, however, such measures need to be re-examined. Research on floodrelated phenomena and engineering methods in steep rivers are limited. Previously,
Fukuoka and Tsuchiya2) have discussed the channel and flood properties of steep
rivers compared the results of both numerical analysis and field and hydraulicmodel experiments to assess flows and bed variation, and discussed theeffectiveness of each approach. However, the relationship between hydraulicquantities during flooding and such factors as scour depth and bed grain-size
distribution is still unclear and no method for predicting maximum scour depth has
been established. For this reason, the authors, in this project, aimed to identify thefactors behind bed variation in the Joganji River—one of Japan's steepest rivers—
and use this to establish a method for predicting maximum scour depth. Bedvariation reflects net sediment transport rate which in turn is determined by thegrain-size composition of bed material. Although grain-size distribution is highly
useful in determining maximum scour depth, roughness coefficient during flooding,and aspects of river environment, no objective-specific methods have been
established for studying bed material. Instead, a single sample collection method
has been used in such research. That bed material in a steep gravel-bed river spans abroad distribution of grain sizes makes it important to establish bed-material
investigation methods that are suited to the needs of specific applications.
The authors began this research by considering flood-induced bed variation in
gravel-bed rivers by analyzing existing temporal data on bed height, bed material
grain-size distribution, flood discharge, and other factors. We then performed largescale experiments in the Joganji River in 2005 to ascertain the process of channel
formation and channel bed stability in gravel-bed rivers.

Analysis of Temporal Data on the Joganji River(1) River Overview
The Joganji is one of Japan's steepest alluvial river. The bed gradient transition pointis roughly 7 km upstream from the river's mouth (Fig. 1). From a bed gradient of 1:1300,
the riverbed rises sharply to 1:70 in only 10 km. The longitudinal distribution of bed
material grain size (D60) increases from several centimeters in the lower reaches to alarge 30 cm at the 10-km point. The bed regime of the Joganji River is classified into
multiple-row bars separating multiple low-water channels.

E levation (km )

250
200
150
100
50
0
0

10
15
5
Distance from river mouth (km)1/1295 1/443 1/209 1/95

1/75

1/60

20
1/71

Bed slopeFigure 1. Bed Profile(2) Bed Variation Properties
Figs. 3 and 4 show, respectively, temporal change in average annual maximum
discharge and the bed profile at the 13.1-km point. Flood discharges of 1,200 m3/s
occurred from 1995 to 1996 and of 1,700 m3/s in 1998. As Fig. 4 shows, such flood
flows exceeding 1,000 m3/s have caused bed variation through the channel, greatlychanging scour depth and the relative positions of the low-water channels and bars.
Flood mark water levels from 1998 flooding indicate an above-bar depth of 1 to 2 m,which would suggest considerable movement of bed material on the bars. In
contrast, flooding of roughly 500 m3/s from 1991 through 1994 but resulted inalmost no changes in the bars, although low-water channel scouring did increase.
These phenomena indicate that any consideration of the problem of low-water
channel scouring in a steep river must also consider scouring caused by small- to
medium-scale flooding. Because maximum scour depth occurs in the low-water
channel, it is essential to understand low-water channel formation and variation
properties when considering scour problems. Fig. 5 shows the longitudinal
distribution of the number of low-water channels. Here, for convenience's sake, alow-water channel is defined as that portion below the main channel's average bedheight. Also, five cross-sectional surveys were conducted between 1991 and 2002,
and "maximum number of low-water channels" refers to the maximum observed ateach cross-section in all five surveys. Similarly, "average number of low-water
channels" refers to the average number for all five surveys. The Joganji River ismultiple-row bars waterway containing two or three low-water channels on average.
The number of low-water channels is strongly dependent on main channel widthand floodplain width: Wide sections contain a larger number of low-water channels,
narrow sections fewer. This suggests that main channel and flood channel width areimportant factors in characterizing flood flows and sediment transport: The greater
the degree of freedom in transport is the more water channels are formed. It has also
been verified that where structures such as bridges, groundsills, or dams are present,
the restriction of flow and sediment movement results in fewer low-water channels
and less change in the lateral position of those low-water channels.
1000.0Grain size (mm)

100.0

図-2

D60 の縦断変化

10.0

1988
1993
1996

.1.0

1998

0.1
0

2

4

6

8

10 12

4 16 1 8

20 2 2 2 4 2 6 2 8Longitudinal distance (km)Figure 2. Longitudinal change in D60

Annual maximum discharge (m3/s)

Fig. 6 shows the temporal change in low-water channel area at three sections.
Low-water channel area is defined as the cross-sectional area of all low-water
channels in a section. As the graph shows, the temporal change in average lowwater channel area in each section is not that great. That this is so even in the 19.1km section (Fig. 5), where temporal change in the number of low-water channels isgreat, suggests that average low-water channel area at a given section is roughly
fixed, i.e., even if flooding causes changes in the number or position of the lowwater channels, the channel structure maintains roughly the same average area.
(3) Properties of Bed Material Grain Size Distribution
To determine the differences in grain size distribution properties according tochannel morphology, the authors surveyed bed material in both the river's bars andlow-water channels at the 7.1-km and 13.1-km sections (Fig. 7).
20 00

Average annual maximum discharge
Q=787m3/s

15 00

10 00

5 00

0
1990

1992

1994

1996

1998

2000

2002

Year of flooding

Figure 3. Annual maximum discharge

800River width (m)9Main channel widthInterlevee distance
Maximum number of low-water channel
Average number of low-water channel

700
600
500

8
7
6

400
5
300

4

200

3

100

2

0

Number of low water channel

Figure 4. Bed cross-section (13.1km point)

1

5

0

Tokiwa Br.

Rita Br.

10

15
20
Raicho Br.
Miyaji groundsill
Kamitaki groundsill

Joganji Br.

Yokoe weir

Figure 5. Longitudinal distribution of number of low-water channels (1991 to 2002)

Figure 6. Variation in low-water channel area

⑪

30cm

Surface layer

50cm

Middle layer⑥③ ②⑤ ④⑩⑨①⑧

Low water channel
Sandbars

50cm

Lower layer⑦

Fig.7 Surveyed locations in 2002
(13.1-km point)

Fig. 8. Bed layers in perpendicular survey

Lower channel surface layer
Lower channel middle layer
Lower channel lower layer
Bar surface layer
Bar middle layer
Bar lower layer

0.1

1

10

100

1000

Grain size (mm)Fig. 9. Each layer's average grain-size
distribution (13.1-km point)

Volume percentage finer than (%)

Volume percentage finer than (%)

100
90
80
70
60
50
40
30
20
10
0

Location

100

①
③
⑤
⑦
⑨
⑪

80
60

②
④
⑥
⑧
⑩

①

⑥

40
20
0
0.1

1

10

100

1000

Grain size (mm)Fig. 10. Surface-layer grain-size
distribution (13.1-km point)

To determine differences in grain size properties according to bed depth, we
conducted sieve analysis of bed material collected from the surface layer (depth 0–
30 cm), middle layer (30–80 cm), and lower layer (80–130 cm).
Fig. 9 shows the average grain-size distribution of each layer for each bed
morphology. Both grain sizes of the surface layer and middle layer in the low-water
channel area exceed the grain sizes in the bar area. This is because the flow's greater
tractive force in the low-water channel causes the bed material to be sorted out. In
addition, the predominance of sedimentation in the bar area sometimes results in thecharacteristic grain-size distribution seen at points ① and ⑥ in Fig. 10. Although
the surface and middle layers exhibit different characteristic grain-size distributionsin the bar and low-water channel areas, the distribution of the lower layer is roughly
the same in both areas of the river. From the lateral survey locations shown in Fig.
11, we see that the bar lower layer is roughly the same as the low-water channel bed
height, which suggests that the layer was formed by sediment movement caused by
the area becoming a low-water channel during large flooding. In short, the lower
layer in the bar area is likely similar to the low-water channel surface layer becauseof the deposition of mixed bed materials. Results of examination of the low-water
channel lower area (Fig. 12) show particularly small grain sizes at location ⑨.
Focusing on the lateral survey locations, we see that the middle layer was thelocation of bars in 1997, i.e., it was the same as surveying a sandbar. Conversely,
middle layers in bar areas had once been low-water channels in other cases. The
preceding shows that because the bed material grain-size distribution of steep rivers
are affected by differences in channel morphology and by bed changes caused bypast flooding, such factors must be taking into consideration when assessing themethodology of bed material surveys and the results obtained therewith.

18

Elevation
標高(m)(m)Volume percentage finer than (%)

H14
Bed河床
in 2002

Bed
in 1997
H9
河床

17

16

④

15

⑥

⑤

⑫

⑨

⑪

14
70

120

170

220

270

320

370

420

100

⑦
⑨
⑫
⑭

80
60

Fig. 11. Perpendicular and lateral sample
collection locations (7.1-km point)

average

⑨

40
20
0
0.1

Lateral横断距離(m)distance (m)

⑧
⑪
⑬

1

10

Grain size (mm)

100

1000

Fig. 12. Grain-size distribution in middle bed
layer of low-water channel (7.1-km point)

Joganji River Field Experiments
Overview of Experimentation
L1-12.5m
L1 L2-25m L2

L1-25mL-1 L0-25m

L0Artificial waterway
N2
N5
N7

Natural waterway
BO2

N21
BO1

N15

N18
BO1

L0+10
L1-20m L1-5m
BO1(右)
BO4(
N29
N34.5
BO1(左)
BO11(右)BO4(左)
BO7
BO11(左)Flow

BO1Natural waterway sieve analysis
Natural waterway image analysis

50m

Artificial waterway image analysis

Fig. 13. Channel planform diagram and bed grain-size sample collection points

To determine the mechanism of water channel formation in gravel-bed rivers,
and to determine the associated properties of water channel and investigate methods
for surveying bed materials, the authors conducted experimentation in 2005 using awaterway dug on the bed in the Joganji River. This field experimentation was
carried out near the river's 13.1-km point (Fig. 13). This waterway dug into thechannel for the purpose of experimentation, is referred to as the "artificial
waterway," and the low-water channels naturally existing in the channel as the"natural waterway." The artificial waterway was a 170-m-long, 4-m-wide straightwaterway. The upstream end was blocked with a mound of earth. Water wasdiverted from the natural waterway to the artificial waterway by removing themound and blocking the natural waterway. Cutting off the flow of water in thenatural waterway made it possible to measure bed material grain-size distribution
and bed shape of the natural waterway. After bed height equilibrium was reached inthe artificial waterway, the flow of water was returned to the natural waterway.
From measurements of the artificial waterway's bed surface grain-size distribution
and bed profile, the authors then investigated the relationship between tractive force,
bed variation, bed material grain-size distribution, and other factors. To assess bed
grain-size distribution, the authors captured digital images of a 2-by-3-m section of
bed surface, divided it into 24 sections (each 50 by 50 cm), determined the grainsize distribution of each section, then calculated the overall average. This method
was also employed for the natural waterway, and the results were compared to thoseof sieve analysis of bed material from the surface layer (0–40 cm) and the middle
layer (40–80 cm). Discharge in the artificial waterway was 8.10 m3/s on November
16, 2005 (the first day of experimentation) due to rain, but on the 17th this fell to
7.00 m3/s.
(2) Bed Variation and Bed Grain-Size Distributions in the Artificial Waterway
Fig. 14 shows the longitudinal distribution of water level, total head, bed height,
and tractive force. Tractive force was calculated using peak discharge (8.10 m3/s),
at which the bed shape is believed to have formed. After water was diverted into
this waterway, the bed in the section (L1-25m~L1) having a large initial bed
gradient was extensively scoured, further increasing the gradient. Tractive force
was great in section L1-25m–L1, and significant erosion was also observed there.
This suggests that bed variation and bank erosion are strongly correlated withtractive force, and that in a straight river section where watercourse width isuniform, maximum scouring will occur in steep areas where tractive force is also
greatest.
87

2500

Elevation
標高(m)(m)86

Grain-size distribution sample
collection point

2000

τ

85

1500

84

1000

83

500
L-1
L0-25

L2

L1

L0

掃流力τ（g/cm2）
Tractive
force

11/16
water
level
11/16
水位
11/17
water
level
11/17
水位
Bed
before河床
water release
通水前
Bed
after
21
hours offlow
21時間通水後河床
11/17
total全水頭
head
11/17
Tractive
force
掃流力τ

L1-25m

L2-25m

50

100

82

0
-50

0

150

縦断距離(m)Longitudinal
distance (m)Fig. 14. Artificial waterway: bed height, water level, and tractive force profile

L-1
L0
L1-25m
L1-12.5m
L1
L2-25m

80
60
40
20
0
0.1

1.0

10.0

Grain 粒径(mm)size (mm)Fig. 15. Grain-size distribution in theartificial waterway

100.0

Percentile of limit-of-motion
D○%粒径 grain size (%)

Area percentage finer than (%)

100

80

60

40

20

0
0

500

1000

1500

Tractive force at the point surveyed2000

τ (g/cm2)

Fig. 16. Correlation between tractive force
and limit-of-motion grain size

Fig. 15 shows the grain-size distribution determined by the aforementioned
image analysis. Grain sizes were large in the steep section (L1~L1-25m) and small
in the gently sloping sections (L0~L-1 and L2-25m~L1+10m). Tractive-force
profile calculated using hydraulic quantities at peak discharge exhibits large force inthe steep sections and smaller force in the gently sloping sections, i.e., an inversely
proportional relationship with bed grain-size distribution. Fig. 16 shows that theordinate is tractive force at the point surveyed the abscissa denotes and thepercentile grain sizes calculated as limit-of-motion tractive force at the points
surveyed for grain size distribution. That limit-of-motion grain size is greater wheretractive force is greater indicates a correlation between tractive force and thedominant grain size in the bed material. From this we conclude that where tractive
force is great, the bed continues to erode until bed materials over a large grain-size
range have eroded in quantities sufficient for stabilization of the bed.
(3) Bed Material Grain-Size Distribution Curves
Fig. 17 compares the distribution curves of grain sizes at the surveyed locations
as nondimensionalized with D60. It shows that below D80, the natural and artificial
waterways exhibit roughly the same curve. The divergence above D80 is due to thedifference in large-diameter gravel reflected in the distribution. Comparison of thetwo waterways shows general similarity in grain-size distribution curves. This
indicates that the bed of the Joganji River has an extremely broad range of grain
sizes and, consequently, a grain-size distribution large enough to respond todifferences in tractive force. As we have shown, because roughly equal distribution
curves are obtained by the nondimensionalization with D60 of grain sizes of bed
surfaces affected by the flow, if it is possible to assess grain-size distribution
according to D60 and predict D60 from tractive force and other data, then it should bepossible to roughly calculate the grain-size distribution of bed material at the locationin question.
Fig. 18 shows the results of sieve analysis and image analysis for the natural
waterway. This waterway is comprised of a steep upstream, a gently sloping
midstream, and the downstream, which is the steepest. Great differences between
the two methods used to analyze the steep and steepest sections result withdiameters smaller than the D20~D30 range. This is because image analysis makes it

100
L0
L1-20m
N07
N21
N29

80

面積百分率(%)

Area percentage finer than (%)

difficult to analyze bed material smaller than several millimeters, while sieve
analysis has trouble analyzing the fine material of the middle bed layer. A marked
difference appears between the results of sieve analysis and image analysis of the
gently sloping section, where the bed surface layer contains large amounts of fineparticles. Nevertheless, both analyses produced roughly equivalent values for
maximum grain size as well as D60 and others. Moreover, image analysis of thesteep section captures the same properties as sieve analysis did. From this we canconclude that image analysis:

60
40
20
0
0.01

0.1

1

Di／D6010

Fig. 17. Comparison of grain-size distribution curves
Percentage finer than (%)

Steepest section
100

Gently sloping section
10 0

BO-21 Surface layer
BO-21 Middle layer
N02
N05 Image analysis
N07

80
60

Steep section
10 0

BO-14 Surface layer
BO-14 Middle layer
N15
Image analysis
N18

80
60

80
60

40

40

40

20

20

20

0
0.001

0
0 .00 1

0.01

0.1

1

Grain size (cm)

10

100

1000

0 .0 10 .1

1Grain size (cm)

10

1 00

0
0.0 0 1

BO-7 (left bank) surface layer
BO-7 (left bank)middle layer
N34.5
Image analysis
N29

0. 0 1

0.1

1

10

100

Grain size (cm)Fig. 18. Comparison of results of sieve and image analysis.

(4) Consideration of Methodology of Surveying Bed Material•Can be used to easily determine bed material grain sizes over a wide range, andto average a large number of points.
•Reveals the same general characteristics as sieve analysis.
•Is less suited to analysis of fine bed material.
In addition, because the grain-size distribution of a riverbed surface layer is a
product of tractive force and scouring depth, image analysis of bed surfaces is aneffective technique for determining tractive force and other flow characteristics
from grain-size distribution, or when estimating roughness coefficients, which arehighly dependent on the bed surface.
In addition to the preceding, the average grain-size distribution exhibited by thelower layer of the riverbed (Fig. 9) suggests that sieve analysis is effective fordetermining average grain sizes in a channel or when assessing a riverine
environment in which fine bed material plays an important role.
Conclusions and Issues for Further Consideration in Gravel Bed Rivers
Because a gravel riverbed encompasses a wide range of grain sizes, the structureof its low-water channels (e.g., size, depth, and number) is determined by the
predominant bed materials that have adapted to the scale (i.e., tractive force) of
flooding.
(1) Flooding equivalent to average annual maximum discharge (800 m3/s) did
result in some observed bed variation throughout the channel, but even small-scale
flooding caused bed variation in the low-water channels.
(2) The relationship between watercourse and bed variation and bed material
grain size is closely tied to the scale of flooding.
(3) Even in straight sections, considerable variation in water surface gradient canoccur locally. In the steepest section, where maximum local water surface gradientoccurs, maximum scouring is also found.
(4) Bed material grain-size distribution is affected by past bed variation anddifferences in bed morphology (e.g., water course or sandbar).
(5) Where tractive force is great, bed materials encompassing a wide range ofgrain sizes plays an important role in bed stability.
(6) Longitudinal distribution of grain-size distributions of the surface bed layer
are roughly the same when nondimensionalized with grain diameter D60.
(7) Grain-size distribution determined from image analysis of the riverbed
surface is roughly equivalent to that determined from sieve analysis. Further, grainsize distribution determined from image analysis is effective input for determining
tractive force, roughness coefficient, and other flow quantities.
The large-scale field experimentation described in this paper has shown that thecorrelation between watercourse and bed variation in a gravel-bed river is closely
related to the scale of flooding. Such knowledge opens the door to the possibility ofmanaging channel formation in gravel-bed rivers. The next step is to investigate
large flood discharges through field experimentation using an artificial waterway inorder to investigate the mechanisms of waterway change and bed material grainsize formation and verify whether the results obtained in this research are valid
across a wide range.
REFERENCES
Toyama Construction Office, Ministry of Construction, River Improvement Work in the
Joganji River, 1979.
Tsuchiya S., and Fukuoka,S., Evaluation of the Efficacy of Water Channel Planning for the
Ngaoka City area of the Shinano River, ThemeC, Vol.Ⅱ, XXX IAHR, pp389-396, 2003.

Fukuoka S. Flood Hydraulics and Channel Design, Morikita Publishing
Company, 2005