River Sedimentation – Wieprecht et al. (Eds)© 2017 Taylor & Francis Group, London, ISBN 978-1-138-02945-3

Bed variation during floods in the Chikugo River estuary with complex
structures of bed layers
Y. Kaneko
Graduate Student of Science and Engineering, Chuo University, Tokyo, Japan

S. Fukuoka
Research and Development Initiative, Chuo University, Tokyo, Japan

ABSTRACT: It is known that the vertical structure of the river bed of the Chikugo River estuary makes complex
structures of cohesive soil (gata-soil) and sand. In this study, we develop a new model of bed variation analysis
in the river estuaries with complex structures of bed layers, and we clarify the mechanism of bed variation in
the Chikugo River estuary during a flood. In the model, when the volume ratio of gata-soil is larger than theporosity of sand, bed variations are calculated by the GBVC flood flow analysis method and continuity equationof sediment which takes into account the discharge rate of sand and erosion speed of the cohesive material. On
the other hand, when the volume ratio of gata-soil is less than the porosity of sand, variations of the river bed are
calculated by continuity equation for sand. This is because sand and mixture of sand and gata-soil have different
transportation mechanism and the gata-soil has great influence on the bed variation. The newly developed bed
variation model provides good explanations for bed variation in the Chikugo River estuary.

1

INTRODUCTION

Environmental issues of the Ariake Sea which has thelargest tideland in Japan attract concern of the public.
One of reasons for issues is the lack of sand supply
from the Chikugo River which has the largest catchment area out of several rivers flowing into the Ariake
Sea. The bed of the Chikugo River estuary is covered
with the cohesive sediment such as silty clay called‘gata-soil’ which is transported from the Ariake Sea
due to a maximum of 6 meters tidal level changes.
Therefore it is said that sands may not be transported
mostly from the Chikugo River. However it is confirmed that the vertical structure of the river bed isformed by complex structures of bed layers of the gatasoil and sand and sands exist sufficiently in the lower
layer of the river bed surface by the core sample survey and supersonic echo sounder around the Chikugo
River estuary (see Figs. 1, 3).
Suzuki et al. (2011) developed the bed variation
analysis model taking into account the characteristics
of sediment transport of gata-soil and sand, focusing
on the fact that the water content ratio and particle size
distribution of the gata-soil and sand were different.
They estimated the mechanism of the bed variation andamount of sand supply from the Chikugo River estuary
to the Ariake Sea during a flood. But some problems
are remained in the sediment transport model of thegata-soil river bed. In this study, we develop a new
analysis method of river bed variation with complex
structures of bed layers. And we clarify the mechanismof the bed variation and estimate the amount of sandsupply from the Chikugo River estuary to the Ariake
Sea during a flood.

2

STUDY OBJECTIVE AREA AND FLOOD

Figure 2 shows plan-form of the objective area andwater level and flood discharge observation points.The
time series data of the flood discharge are observedat the Senoshita (25.5 km) observation station. The
points designated by squares indicate the location of
simple pressure-type water level gauges with a built indata logger. Table 1 shows the details of the objective
floods that occurred in 2009. The peak discharges of
the two floods were greater than the average annual

Figure 1. Vertical profiles of river bed material.

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depth, W : depth averaged vertical velocity, z s : water
surface level, z b : bottom level, ws , wb : vertical velocity
on water surface and bottom.
To calculate Equations (1), it is required to solve
the depth-integrated continuity equations (Eq. 2),
the depth-integrated horizontal momentum equations(Eq. 3), the depth averaged turbulence energy transport
equations (Eq. 4), the depth-integrated horizontal vorticity equations (Eq. 5) and the water surface velocity
equations (Eq. 6).
Figure 2. Structure of river bed layer and its materials.
Table 1.

Details of objective floods.

where, U i : depth averaged horizontal velocity, g :gravity, dp : pressure deviation from hydrostatic pressure distribution (dp = p − ρg(zs − z)), dp0 : depth
averaged dp(dp0 = dpb /2), dpb : dp on the bottom,
τ bi : bed shear stress, τ ij : horizontal shear stress due
to turbulence, ui, uj : correlation of vertical distributions of horizontal velocities, k : depth averaged
turbulence energy, P k : production term, ε: dissipation
term (ε = Cε k 3/2 /), vt = Cµ k 2 /ε, σk = 1.0, Cε / =1.7/h(Cε = 0.17, /h = 0.1).
Figure 3. Plan-form and observation points in the objective
area of the Chikugo River.

maximum discharge. Floods duration time were about
three days. Both of the flood discharge hydrographs
had two peaks. Flood in June occurred at the time ofneap, and flood in July occurred at the time of middle
tide. The river bed profiles before and after 2 floods
in 2009 were measured at intervals of 200 m from theriver mouth to 23 km including the tidal reach of the
Ariake Sea. Also in the same year, the detailed coresampling data of river bed was obtained and used foranalysis (see Fig. 1).
3
3.1

where, Rσ i : rotation term of vertical vorticity, P ωι: production term of vorticity from the bottom thinvortex layer and Dωij : horizontal vorticity flux due
to convection, rotation, dispersion and turbulencediffusion.

where, P si : production term due to shear stress acting
on thin water surface layer.
The vertical distribution of velocity is described by
Equation (7).

NUMERICAL ANALYSIS METHOD
Flood flow analysis method

The GBVC method (Uchida & Fukuoka 2012) is able
to evaluate vertical velocity distributions and bottom velocities without the assumption of the shallow
water flow such as hydrostatic pressure distribution by
calculating following Equations (1)∼(6). The bottom
velocity is obtained in the depth-integrating horizontal
vorticity equations (Eq. 1).

where, η = (zs − z)/h, ui = usi – Ui , δ ui = usi – ubi ,z : vertical level.
The bottom pressure intensity is given by equation (8) which is derived from the integration of thevertical momentum equation over water depth.

Time variation in the depth integrated verticalvelocity is calculated in Equation (9).
where, i,j = 1,2(x,y), ubi : bottom velocity, usi : water
surface velocity, j : depth averaged vorticity, h: water626

where, k1 = 1/10, φ = (Wh)n+1 – (Wh)n , φ P = (Wh)P– (Wh)n , (Wh)P is calculated by the continuity equation with horizontal velocity field by using predictedbottom velocity (ubi )P :where, k 2 = 1/10, (ui )P = (usi )n+1 −(ubi )P , (ubi )P is
evaluated by Eq. (1) with (Wh)n , z m = (z s +z b )/2.
3.2

Bed variation analysis method

The gata-soil from the Ariake Sea deposit on the river
bed of the Chikugo River estuary. Also flood flows
from the upstream of the Chikugo River deposit thesand in the Chikugo River estuary. Therefore complex structures of bed layer are formed (see Figures 1,3). Very loose gata-soil which is about 200% in watercontent ratio deposits on the river bed in the reachof 10 km to 17 km because the groundsill at 17.2 km
prevents salt water intrusion except the spring tide.
The thickness of the gata-soil layer is about 2 m at
the maximum. The mechanism of bed variations in
the Chikugo river estuary is quite different from the
sandy or stony bed rivers because the gata-soil has aparticular cohesion property. The bed variation analysis of Suzuki is made by erosion speed equation of
the cohesive material when the water content ratio of
the gata-soil layer is larger than 70%. On the other
hand, when the water content ratio of sand layer isless than 70%, bed variations are calculated by continuity equation for sediment taking into account thedischarge rate of sand. Also he elucidated the temporalchanges in observed water surface profiles and river
bed variation in the Chikugo River estuary by adjusting the coefficient of sediment discharge equation ofsand. However, in the numerical analysis of Suzuki, theeffect of the adhesive strength of the gata-soil on the
movement of the sand in the mixed state of gata-soiland sand was not considered, and continuity equationof sand included in a gata-soil layer was not satisfied.
In this study, we develop a new analysis methodof river bed variation with complex structures of bed
layers taking into account the movement mechanismof the sand and gata-soil and clarify the mechanismof bed variation and the amount of sand supply fromthe Chikugo River estuary to the Ariake Sea during aflood.
3.2.1

Sediment transport equations for sand andgata-soil
The bed load transport rate of each grain size of thesand is calculated by Ashida and Michiue formula(Ashida & Michiue 1972). The critical tractive forces
for each particle size and mean particle size are calculated by modified Egiazaroff formula (Ashida &Michiue 1972) and Iwagaki formula (Iwagaki1956)

respectively. Effects of bed slope on tractive forces andcritical tractive forces of sediments particles are evaluated by Fukuoka and Yamasaka equations (Fukuoka& Yamasaka 1986).
The erosion rate of gata-soil is calculated by erosion speed equation of the cohesive material (Eq. 11)(Nishimori & Sekine 2009).

where, E s : erosion speed, α: coefficient depending onwater temperature, Rwc : water content ratio, u∗ : shear
velocity.
Yokoyama et al. (2008) gave to 0.21×10−5 the valueof the coefficient α by observing the change of river
bed temperature and the erosion rate of gata-soil in the2006 Chikugo River flood.
3.2.2 Bed variation analysis
The variations in river bed elevations are evaluatedby two-dimensional continuity equation for sedimenttransport. Figure 4 demonstrates the concept for thevariations of river bed of complex structure consistingof gata-soil and sand. The gata-soil has transport characteristics different from sand and has great influenceon the bed variation of the Chikugo River estuary. In
other words, the influences of the gata-soil upon theriver bed variation depends on whether the rate of volume of gata-soil is larger than the porosity of sand ornot.
Figure 4(a) shows the bed variation model of thecase that rate of volume of gata-soil is larger than theporosity of sand (VG  λ) that is the gata-soil contains
the sand. The gata-soil in such a state increases thecohesion of bed layer and has a great effect on the
movement of sand. Therefore, variations in river bed
are calculated by Equation (12) that is continuity equation for sediment taking into account both discharge
rate of sand and erosion speed of the cohesive material.

where, z b : bottom level, q : discharge rate of sand(particle size 75 µm or more), V G : Volume ratio of
gata-soil (particle size less than 75 µm) in the river
bed layer.
On the other hand, Figure 4(b) indicates the statethat the volume ratio of gata-soil is less than the porosity of sand (VG < λ). In other words, the gata-soil iscontained in the porosity of sand. So it is able to be
assumed that the gata-soil is flushed with the transportof the sand and washing away of the gata-soil hardly
has effect on the variation of river bed. Then, variationsof the river bed are calculated by continuity equation
for sand as expressed in Equation (13).

where, λ: porosity of sand (0.4).

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Figure 4. (a) Model of the variation of river bed consisting of complex structure of gata-soil and sand. (VG  λ). (b) Modelof the variation of river bed consisting of complex structure of gata-soil and sand. (VG < λ).

3.2.3 Variation of the particle size distributions
The variation of the particle size distributions is calculated by Equation (14), which is the continuity
equation for particle size ratio using a bed variation
calculated by Equations (12) and (13) (see Figure 5).

where, w = −z/t : time variation of the river bed
elevation (downward positive), P k : the existing proportion of particle size k. V G is calculated from thewater content ratio of gata-soil and the particle size
ratio estimated by Equation (14). In addition, the gatasoil is assumed not to deposit again on the channel bed
once it starts to be transported.

3.3 Analysis conditions
Boundary conditions at the upstream and downstream
ends of the Chikugo river estuaries are given byobserved water-level hydrographs of –0.2 km pointand 22 km point, respectively. The Manning’s roughness coefficients are determined so as to agree withobserved temporal changes in water surface profilesof June and July floods in 2009. The equilibrium sediment discharge at the downstream of the Chikugo weir
where the ground elevation change is relatively small,is given as the upstream boundary condition of sediment. Initial conditions of bed layers are set at the pitchof 10 cm in vertical downward direction from river bed
surface. The particle size distribution and water content in each layer are given by the core sampling dataof river bed materials.

4

RESULTS AND CONSIDERATIONS

Figure 6 shows comparisons between observed andcalculated temporal changes in water surface profiles
and calculated mean bed elevations in the Chikugo
River estuary. The calculated water surface profiles
agree well with observed ones. Also the calculated
mean bed elevations in the section from 10 km to
17 km decrease about 1.5 m in the rising period of Juneflood. This is because the gata-soil deposited on theriver bed was flushed away during the flood. Figure 7
shows observed and calculated discharge hydrographs628

Figure 5. Method of calculation for the variation of the particle size distribution in the exchange layer.

Figure 6. Comparisons between observed and calculated water surface profiles and calculated mean bed elevations.

Figure 7. Discharge hydrographs at Senoshita (25.5 km) and river mouth (0.0 km).

Figure 8. Sediment discharge hydrographs and cumulative sediment discharge at the Chikugo River and Hayatsue River(0.0 km).

at Senoshita (25.5 km) observation station and 0.0 km
point. The solid and dash lines in Figure 7 indicate
the temporal changes in the calculated discharge andobserved tidal level, respectively.The newly developed

numerical method is found to explain observed discharge hydrograph at Senoshita observation station.
It is also found that flood discharge hydrograph at theriver mouth (0.0 km) strongly receives the influence of629

Figure 9. Contours maps of time change of bed variationfrom 9.0 km to 17 km.

Figure 10. Contours maps of time change of volume ofgata-soil on the bed surface from 9.0 km to 17 km.

the tidal level change of the Ariake Sea and the peakdischarge appears at the time of ebb tide.
Figure 8 shows calculated sediment dischargehydrographs and cumulative sediment discharges at
0.0 km points of the Chikugo River and Hayatsue
River. The dash and solid lines in Figure 8 indicate
the calculated sediment discharges and cumulative
sediment discharges, respectively. In this figure, sediment discharge from the Chikugo River estuary to
the Ariake Sea varies with the tidal level changes
as well as discharge at the river mouth (0.0 km) andmost of the sand flows out at low tide period. About
2,800 m3 and 7,200 m3 sand flowed out from the
Chikugo River into the Ariake Sea during June andJuly floods, respectively. Although the peak discharges
at Senoshita (25.5 km) of the June and July floods arecomparable, cumulative sediment discharge from the
Chikugo River estuary to the Ariake Sea of July flood
is more than 2.5 times as much as the cumulative sediment discharge of June flood. This is because Julyflood 4,000 m3 peak discharge flowed out from theriver mouth but June flood 3,000 m3 .
Figure 9 shows the contour map of the bed variations from 9.0 km to 17 km at the time indicated by the

Figure 11. Contours maps of bed variation from Ariake Sea
to 23 km before and after the flood.

green lines in Figure 7 (a). Figure 10 shows the volume ratio of the gata-soil on the river bed surface. The
range from white to red and white to blue in Figure 10
indicate the sand bed and gata-soil bed, respectively. In
this figure, the gata-soil which deposited in the section
from 10 km to 17 km is flushed all during the flood rising period in June and the sand is exposed on the river
bed surface at the time of flood discharge peak. The

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roughness coefficient of this section are increased withthe time from 0.021 to 0.028 whose values reproduce
the observations of temporal water surface profiles inthis section during the flood. Figure 11 shows comparisons between observed and calculated contour map of
the bed variations from the Ariake Sea to 23 km during
the 2009 June flood. In this analysis, calculation resultsof the bed variations almost agree with observed onesin the section from the 10 km to 17 km where a lot ofgata-soil deposit and the change of the particle size
distribution is large in the vertical direction. However, calculation results of the bed variations in thedownstream from 6 km are smaller than observed ones.
This reason may be that the gata-soil in the river bed
weakens the engagement effect among sands, whichmakes the sand easier to move actually compared witha general sand bed river.
5

CONCLUSIONS

1. The numerical analysis results reproduce the temporal changes of the observed water surface profiles, discharge hydrographs at the observation
points and the bed variations before and after the2009 flood. It is concluded that the present computation method gives better understanding of bed
variations in the river estuary which has the complex bed structures consisting of cohesive sedimentand sand.
2. About 10,000 m3 sand (June: about 2,800 m3 , July:
about 7,200 m3 ) flows out from the Chikugo River
into the Ariake Sea during 2 floods occurred in
2009.

REFERENCES
Ashida, K. & Michiue, M. 1972. Study on hydraulic resistance and bed-load transport rate in alluvial streams,
Proceedings, JSCE, Vol. 206, pp. 59–69.
Fukuoka, S. & Yamasaka, M. 1984. Shear stress distribution on a continuous boundary and widening processof a straight alluvial channel, Proceedings of the JSCE,
No. 351, pp. 87–96.
Hirano, M. 1971. River-bed degradation with armoring,
Proceedings, JSCE, Vol. 195, pp. 55–65.
Nishimori, K. & Sekine, M. 2009. Erosion rate formura ofcohesive sediment, Proceedings, JSCE, Vol. 65, No. 2,
pp. 127–140.
Suzuki, K., Fukuoka, S. & Matsuo, K. 2009. Bed material
structure and sand transport by flood flows in the estuaryof the Chikugo River, Proceeding of the Third international conference on the estuaries and coasts, Vol. 1,
pp. 101–108.
Suzuki, K., Shimamoto, H., Kubo, S. & Fukuoka, S. 2011.
Bed variation analysis in the Chikugo River estuary by
the flood flows, Journal of JSCE, Ser. B1 (HydraulicEngineering), Vol. 67, No. 4, pp. 877–882.
Uchida, T. & Fukuoka, S. 2012. Bottom velocity computation method by depth integrated model without shallow
water assumption, Journal of JSCE, Ser. B1 (HydraulicEngineering), Vol. 68, No. 4, pp. 1225–1230.
Umita, T., Kusuda, T., Futawatari, T. & Awaya,Y. 1988. Studyon erosional process of soft muds, Journal of the JSCE,
Vol. 1988 (1988), No. 393, pp. 33–42.
Yokoyama, K., Yamamoto, K. & Kaneko, Y. 2008. Erosion
process of cohesive sediment and sediment transport in
the estuarine channel of the Chikugogawa River, Journalof the JSCE, Vol. 64 (2008), No. 1, pp. 71–82.

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