THESIS 2013 June 10-12, Chatou France, K. OSADA et al

Two-dimensional riverbed variation analysis method focused on
bed surface unevenness and mechanism of sediment transport
in stony-bed rivers
Kengo Osada
Anan National College of Technology / Japan
265, Aoki, Minobayashi, Anan City, Tokushima, 774-0017
Tel. +81 (8) 84 23 7190, Fax: +81 (8) 84 23 7199
e-mail : osada@anan-nct.ac.jp

Shoji Fukuoka
Research and Development Initiative, Chuo University / Japan
1-13-27, Kasuga, Bunkyo-ku, Tokyo, 112-8551
Tel. +81 (3) 3817 1625, Fax: +81 (3) 3817 1625
e-mail : sfuku@tamacc.chuo-u.ac.jp

In a stony-bed river with a wide range of particle size distribution, large stones act as a strong fluidresistance element during a flood. Sands and gravels often tend to remain in unevenness of the bed
surface formed by large stones of various sizes. A stony-bed river will be in a stable bed condition
when the cross sectional form and particle size distributions corresponding to the flow force areestablished. However, it is difficult to predict riverbed variations in stony-bed rivers by theconventional riverbed variation analysis methods, which do not account for these essential
mechanisms resulting from the unevenness of the bed surface. In this study, we developed a new modelof two-dimensional riverbed variation by considering the mechanism of riverbed variation andcharacteristics of bed surface unevenness. We applied the new model to the field experiment results
carried out in the Jyoganji River. The model is capable of explaining water surface profiles, dischargehydrographs, bed variations, sediment transport rate, particle size distribution and height of eachparticle size in stony-bed rivers.

Key words
Stony-bed river, new bed variation analysis model, bed surface unevenness, sediment transport, field
experiment, gravel bed river.

IBACKGROUND AND OBJECTIVE OF THE RESEARCH

In a stony bed river with wide range of particle size distribution, stones and gravels are moved
violently during flood, readily leading to bed scouring and bank erosion. A model predicting
reasonably both two-dimensional flood flow and riverbed variation is required for the channel design
and planning in stony-bed rivers [2]. The authors have conducted large scale field experiments in theJyoganji River to elucidate the mechanism of bed variation in stony-bed rivers [3] [5]. Large stones
exert great resistances on the flood flow. Sands and gravels tend to remain in unevenness of the bed
surface formed by large stones of various sizes. A stony-bed river will be in a stable condition when
the cross sectional form and particle size distributions corresponding to flow force are established.
In this study, we develop a new model of two-dimensional riverbed variation by considering
the mechanism of riverbed variation and characteristics of bed surface unevenness. We verify theapplicability of the new model with the results of the field experiment carried out in the Jyoganji Riverin 2009 [5].

THESIS 2013 June 10-12, Chatou France, K. OSADA et al

Velocity

Sediment transport
Pick-up DBCdeposition

ABed surface layer
Average ofriverbed elevation
Subsurface layer

Figure 1 Relationship between bed surface, flow and sediment transport

Figure 2 Procedure of the two-dimensional riverbed variation analysis

IITWO-DIMENSIONAL BED VARIATION MODEL IN STONY-BED RIVERS

Figure 1 illustrates sediment transport mechanism resulting from bed surface unevenness instony-bed rivers. Figure 2 shows an analysis procedure of the new two-dimensional riverbed variation.
The bed elevation in the conventional model has been treated as a constant within an analytical grid. In
our new model, we calculate the height of each particle size on the bed surface in order to express
unevenness of the bed surface. Moreover, we developed the form resistance using d90 to consider
effects of large stones in the bed surface. The sediment transport model is composed of pick-up ratefrom the riverbed, deposit rate to the riverbed and particle velocity on the bed. Pick-up rate iscalculated by considering the sheltering effect of large stones. Deposit rate is evaluated by using therest ratio of each particle Pck and the volume of sediment transport Vmk. The rest ratio Pck is estimatedby saltation analysis which is calculated in consideration of particle size distribution on the bed andbed surface unevenness.

1:1

0.5m
1:1

8m
3m
0.5m

Case 3boulderflow

2m

No.6 No.4 No.2 No.0 No.-2No.8
Water level (level surveying)
Channel cross section
No.10
Discharge measurement section

2m

No.16 No.14

No.12

After Case 3

Water level (pressure-type gauge)

170m

Figure 3 Plan view and initial cross sectional form of the field experimental channel

THESIS 2013 June 10-12, Chatou France, K. OSADA et al

Initial grain size distribution for calculation

Percent finer (%)

Surface layer : Main channel
Surface layer : Flood plain
Substrate layer

100

No.0
No.2
The surface image analysis
No.8(main channel ; Case 1)
No.13
No.15
No.2(Left)
No.2(main channel)
No.7(left)
The sieve analysis(Case 4)No.7(main channel)
No.13(right)
No.13(main channel)

80
60
40
2000.01

0.1

110100particle size (mm)Figure 4 Particle size distribution used for the computation
31.0

Case4 left (EXP)
Case4 right (EXP)
Case4 left (CAL)
Case4 right (CAL)

Z(m)
30.5
30.0

Q(m3/s)

No.0
No.4

14
12
108
6
4
20

No.8

29.5

Case3 left (EXP)
Case3 right (EXP)
Case3 left (CAL)
Case3 right (CAL)

No.12

29.0
No.160

28.5
-200

20

406080100 120 140 160 180 200 X(m)Figure 5 Comparison between observed andcalculated water surface profiles
Z B − Z B (m )0.15

CAL(Case4)
EXP(Case4;No.0)
EXP(Case4;No.9)309060120150min

Figure 6 Comparison between observedand calculated discharge hydrographs

Z B − Z B (m )Case3(CAL)

0.1

CAL(Case3)
EXP(Case3;No.0)
EXP(Case3;No.9)

0.15

No.0

Case4(CAL)

Case4(EXP)

0.05

0.05

000.05-0.05
1101000 d(mm)100No.16

2009-Case3終了時（解析）Case3(CAL)
Case4(CAL)
2009-Case4終了時（解析）Case4(EXP)
2009-Case4終了時（実測）0.11101000 d(mm)100Figure 7 Comparison between the observed and calculated bed elevation of each particle size
Case1
22Z(m)

QB(m /s) Z(m)31.00.0002 31.0

30.5

30.5

30.0

0.0001 30.0

29.5

29.5

QB(m /s)
0.0002220mm

0.0001-5-3-1

135Transverse distance (m)(a) Conventional model

130mm

Flow70mm

Case4

30mm

0.0000 29.0

29.0

320mm

0.0000-5-3-11358mm2mm

Transverse distance (m)(b) Authors’ model

Figure 8 Transverse profiles of sediment discharge for each particle

IIIAPPLICATION TO FIELD EXPERIMENTAL RESULTS

We applied the new model to the results of field experiment conducted in the Jyoganji River[5]. Figure 2 shows a plan view and initial cross-sectional form of the field-experimental channel. The
channel is 190m long, 8m wide and 1:130 in bed gradient. The model was validated by the results ofcase 3 (8m3/s) and case 4 (12m3/s). We use the observed water level hydrographs at No.1 and No.15 as
the boundary conditions. Figure 4 shows the initial particle size distribution for the calculation. The
calculation was made by the division of seven particle sizes (320mm, 220mm, 130mm, 70mm, 30mm,8mm, 2mm).

THESIS 2013 June 10-12, Chatou France, K. OSADA et al

Initial bed elevation
D60（CAL）
D60（EXP）
Z(m)Calculated bed elevation
D80（CAL）
D80（EXP）

Observed bed elevation
D90（CAL）
D90（EXP）

D20（CAL）
D20（EXP）
D60河岸（実測）

d(mm)

Z(m)

d(mm)

300

30.5

300
200
1000-100-200

30.5200
30.0

100029.5

30.0
29.5-10029.0-200-5-3-11Transverse distance (m)3529.0-5-3-1

135Transverse distance (m)(b) Authors’ model(a) Conventional model
Figure 9 Cross sectional form and particle size distributions (D20, D60, D80, D90) at No.4 section
Figure 5 shows the observed and calculated water surface profiles. The calculation reproduces
well the observed water surface profiles. Figure 6 shows the comparison between observed andcalculated discharge hydrographs. These calculated results almost agree with the observed results.
Figure 7 shows the comparison of the calculated and observed heights of each particle size. The
calculated results nearly reproduce the observed heights of each particle size. Figure 8 showstransverse sediment discharge profiles for each particle size. Which show the comparison between theresults of conventional model [1] [4] and new model. In the conventional model, small particle groups
are mainly transported. On the other hand, the new model gives the transportation of large gravel andcobble size groups. Actually, groups of large gravel and cobble were transported actively in Case 3and Case4. Figure 9 shows the comparisons of the cross sectional form and particle size distributions(D20, D60, D80, D90) between the conventional model and new model. The conventional model cannot
reproduce the observed particle size distributions on the bed surface. On the other hand, the authors’
new model is capable of explaining cross sectional form and particle size distributions. It isdemonstrated that bed variation, sediment transport rate, particle size distributions and height of eachbed surface particles in stony-bed rivers as well as water surface profiles and discharge hydrographs
are explained by the authors’ new model.

IVCONCLUSIONS

We developed the new model of two-dimensional riverbed variation considering the sedimenttransport mechanism related to bed surface unevenness in stony-bed rivers. Water surface profile,height of each particle, bed variation and particle size distribution in stony-bed rivers were reproduced
properly by the new model.

REFERENCES
[1]
[2]

[3]

[4]
[5]

Ashida, K. and Michiue, M., (1972). –Study on Hydraulic Resistance and Bed-Load Transport Ratein Alluvial Streams, Proceedings of the Japan Society of Civil Engineers, No.206, pp.59-69.
Fukuoka,S. (2008). –Flood Flow and Bed Variation Analysis Considering the Change in Sediment
Environment -Practical Issues and Perspectives of the Sediment Research-, Advance in River
Engineering, JSCE, Vol.14, pp.1-6.
Fukuoka,S. and Osada,K. (2009). –Sediment Transport Mechanism and Grain Size Distributions in
Stony Bed Rivers, 33rd IAHR Congress: Water Engineering for a Sustainable Environment,
Vancouver, Canada, pp.505-512.
Hirano, M., (1971). –River-Bed Degradation with Armoring, Proceedings of the Japan Society ofCivil Engineers, No.195, pp.55-65.
Maeshima,T., Iwasa,M., Osada,K. and Fukuoka,S.(2011). –Study on River-Bed Variation and Its
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Annual Journal of Hydraulic Engineering, JSCE, Vol.55, pp.769-774.