E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands

NUMERICAL ASSESSMENT TECHNIQUE ON DAMAGES OF RIVER FLOOD AND INUNDATIONSCAUSED BY LARGE FLOODSTATSUFUMI MIYAZAKI(1) & SHOJI FUKUOKA(2)(1) Graduate School of Science and Engineering, Chuo University, Kasuga 1-13-27, Bunkyo-ku, Tokyo 112-8551, JAPAN,

E-mail: miyazaki@civil.chuo-u.ac.jp(2) Research and Development Initiative, Chuo University, Kasuga 1-13-27, Bunkyo-ku, Tokyo 112-8551, JAPAN,

E-mail: sfuku@tamacc.chuo-u.ac.jp

ABSTRACT
Successive large floods exceeding the designed discharge occurred in the Kagetsu River in July 3 and 14, 2012. The
floods caused serious damages such as levee breaches and flood inundations in densely residential area. In this paper,
we analyzed both flood behavior in the river channel and inundation area by numerical analyses of quasi-three
dimensional flows and two-dimensional bed variations. Causes of levee breaches were investigated by field survey andnumerical computation results of velocity distributions and bed variations during the floods. Numerical simulation showedthat the river-crossing structure (Yuuta Bridge) caused severe overbank flows by the driftwood accumulations and large
inundation over dense housing areas.
Keywords: driftwoods, flood flow, levee breach, inundation, numerical computation
1.

INTRODUCTION

The Kagetsu River lying on the northwest of Oita Prefecture in Japan (see Figure 1) joins the upper Chikugo River. The
drainage area of the Kagetsu River is about 136.1 km2. Figure 2 shows the planform of ministerial management section of
the Kagetsu River. In this area, the river channel runs through built-up areas with mean slope of 1/250 and width of 60m.
The Arita River having the comparable drainage area meets the Kagetsu River at a right angle at 5.3km point (see Figure2). The main problem of the Kagetsu River is the discharge capacity of the river channel.

0

Oita
Prefecture

500kmJapan sea
the Pacific

Chikugo River
Kagetsu River

Figure 1. Location of the Kagetsu River.

帝国書院

Successive large floods exceeding the designed discharge (1,200m3/s) occurred in the Kagetsu River at July 3 and July
14, 2012. The peak discharge of these floods were about 1,284m3/s and 1,349m3/s, respectively. Levee breaches
occurred at the right bank of 6.0km and the left bank of 5.8km points (see Figure 3), and overbank flows occurred at
concrete embankment in the downstream area of the Arita River confluence during the first flood. It brought large
inundations of approximately 121 hectares and 721 buildings were damaged by the inundation water as shown in Figure
2. Emergency rehabilitation was conducted place after the July 3 flood and levee breaches were escaped during the July
14 flood, but overbank flows inundated approximately 79 hectares areas and 282 buildings were damaged. It is believedthat water level increase due to the driftwood accumulations around the Yuuta Bridge at 4.7km point (see Figure 3)
expanded the flood inundation damages at the middle Kagetsu River (see Figure 2). The driftwood accumulations arounda bridge during flood events have been serious problem for many middle and small-scale rivers in Japan. Fujimori et al.
(2008) quantitatively estimated fluid forces acting on the bridge railing from hydraulic experiments. Maeno et al. (2014)1

E-proceedings of the 36th IAHR World Congress,
28 June – 3 July, 2015, The Hague, the Netherlands

0.0k

Inundation areas(7/3)

1.0kInundation areas(7/14)

2.0k

Kagetsu River
Levee breaches points

8.0k
7.0k

3.0k

6.0k
4.0k
5.0k

Arita River

Yuuta Bridge
Figure 2. Inundation areas of the Kagetsu River basin at July 2012.

clarified that the force acting on the bridge could be estimated by using the three-dimensional flow model. But three
dimensional models have extremely high computational cost. Moreover there are few studies about resistances andblockage effects of the bridge covered by driftwoods because it is difficult to observe the amount over time of thedriftwood accumulations around a bridge during floods.
In this study, we constructed the numerical model which could compute flood flows and bed variations in the river channel
and inundation flows in the built-up area considering the driftwood accumulations around the Yuuta Bridge based on thedepth-integral model. By using the numerical model and measured data during the Kagetsu River floods, we investigatedthe cause of the levee breaches, and mechanics of the overbank flows and return flows over the concrete embankment
from the inundation area to the river channel.

Flow
Flow

(a) Right bank of 6.0km point.

(b) Left bank of 5.8km point.

Figure 3. Soil levee breaches of the Kagetsu River during the first flood.

Yuuta Bridge

Flow
Flow

Levee

(a) Driftwood accumulations around the Yuuta Bridge.

(b) Overbank flows around the Yuuta Bridge.

Figure 4. Driftwood accumulations and overbank flows around the Yuuta Bridge.
2E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands

2.

ANALYSIS METHOD AND CONDITIONS

2.1 Analysis method
In this paper, we developed the calculation method to solve simultaneously flood flows and bed variations in the river
channel and inundation flows in the built-up area considering the driftwood accumulation around the Yuuta Bridge. The
BVC method by Uchida and Fukuoka (2011) was adopted in order to analyze flood flows in the channel. And unsteady
two-dimensional flow analysis was adopted for the inundation flow analysis.
The BVC method is composed of a set of governing equations of Eq. [1] to Eq. [5] for the following unknown quantities:
water depth h, Depth Averaged (DA) horizontal velocities Ui, DA horizontal vorticities Ωi, water surface velocities usi andbottom velocities ubi. The bottom velocity is derived by integrating horizontal vorticities respect to depth (Eq. [1]).

ubi  usi   j h[1]where, ubi is bottom velocity in i direction, usi is water surface velocity, h is water depth and Ωj is DA horizontal vorticity.
Bottom velocity by Eq. [1] is obtained by depth-integrated horizontal vorticity equation [2] and water surface velocity
equation [3] in addition to shallow water equations [4], [5]. In this study, Eq. [2] to Eq. [5] are converted to the generalcurvilinear coordinate system.

hDiji h ERi  Pi 
t
x j

[2]

where, ERσi is rotation term of vertical vorticity, Pωi is production term of vorticity from the bottom thin vortex layer and Dωij
is horizontal vorticity flux due to convection, rotation, dispersion and turbulence diffusion.

usi
u
z
 usj si   g s  Psi
t
xi
xi

[3]

where, g is the acceleration of gravity, zs is water level and Psi is production term due to shear stress acting on thin water
surface layer.

fh fU j h

0
t
x j

[4]

Τ ij
U i
U i
z
1

U j
 g s ( Di  Pi ) 
 bi
t
x j
xi hxyhx j h[5]where, Τij is horizontal shear stress due to turbulence and vertical velocity distribution, ρ is water density, τbi is bed shear
stress, Di is drag force of bridge piers, Pi is force on a bridge railing and f is occupancy ratio of water considering bridge
railing and piers. Detail discussions of drag forces of bridge piers Di, force on a bridge railing Pi and occupancy ratio ofwater f were given in section 2.2. The two dimensional bed-variation analysis took into account the bed load. A rate of the
bed load transport was calculated by Ashida and Michiue formula (Ashida & Michiue., 1972).
2.2 Analysis conditions
The discharge hydrograph at 8.6km point of the Kagetsu River and inflow discharge hydrograph from the Arita River used
for the upstream boundary conditions were given by the runoff analysis. The downstream boundary condition was givenby the water level hydrograph estimated at 0.0km point which was created with considering the shape of the measured
85

Elevation (T.p.m)84

Kagetsu observation station(3.3 km point)

83
82
81
80
79
0:00

6:00

12:00

18:00

Time (hour)

2012/7/3
Figure 5. Observed water level hydrographs.
3E-proceedings of the 36th IAHR World Congress,
28 June – 3 July, 2015, The Hague, the Netherlands

water level hydrograph at the Kagetsu observation station at 3.3 km point (see Figure 5) and the flood mark elevations at
0.0km point. The Manning roughness coefficients were determined so as to explain the longitudinal distribution of flood
marks obtained after each flood. They were set as 0.035 and 0.025 in the channel and inundation areas, respectively.
Bed elevations in the river channel were given by the cross-sectional profiles of the Kagetsu River measured at 200 m
intervals in August 2010. Particle size distributions used for the bed variation analysis shown by Figure 6 were determinedfrom the data of bed materials survey of the study area in 2010.
Volume percentage finer than (%)

100

90
80
70
60
50
40
30

20
10
0
0.1

1

10

100

1000

Grain size (mm)Figure 6. Particle size distributions used to the analysis.

2.3 Method for evaluating the height and location of buildings in the inundation areas and the cross-river structure
2.3.1 Method for evaluating the height and location of buildings in inundation areas
The height and location of buildings and the road network patterns of inundation areas are extremely important for aninundation simulation at a built-up area. Bed elevations of inundation areas are usually given by the Digital Elevation
Models (DEM) which represents the elevations of the ground surface measured by the aerial laser profiling (e.g., P.D.
Bates et al. (2000)) and the effects of the buildings on inundation flows are evaluated by the equivalent roughness
coefficient and occupancy ratio of water of each computational grid. But, because many buildings exist in the built-up
area around the Kagetsu River, it is difficult to set properly the equivalent roughness and occupancy ratio of water foreach computational grid. Akiyama et al. (2007) made the computational grids along the buildings and road networks anddirectly considered the height of the buildings existing at the built-up areas by using the Digital Surface Models (DSM)
which represent the elevation of the ground surface and aboveground features measured by the aerial laser profiling. But
it takes enormous effort and time to make the computational grids in built-up area along the buildings and road networks.
For this reason, we created the computational grids in the built-up area by simply expanding the computational grids
made for the river channel by using the general curvilinear coordinate to the inundation area as shown in Figure 7 (a). In
order to consider the location of the buildings adequately, the computational grids were made finely and the bed
elevations of built-up area were given by using the DSM. Figure 7(b) shows the DSM data and the bed elevations of thenumerical model at the middle Kagetsu River. The bed elevations of the numerical model could reproduce the height andlocation of buildings and road network patterns very well.
Digital Surface
Models (DSM)

The grid shapes of the inundation area
The grid shapes of the river channel area
The cross-river lines

Bed elevations of
the analysis

5.2k

5.0k

3.0k

4.8k

4.0k
4.6k

450m

Elevation(T.p.m)

4.4k

5.0k

(a) The grid shapes around the built-up area that is adapted forthe numerical analysis.

(b) DSM data and the bed elevations of the numerical analysis.

Figure 7. The grid shapes and surface bed elevations around the built-up area.
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E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands

2.3.2 Method for evaluating the cross-river structure
In the Kagetsu River floods, it was expected that driftwood accumulations around the Yuuta Bridge railing and piers
obstructing flood flows and the considerable water level increase induced severe overbank flows at the just upstream of
the Yuuta Bridge. For this reason, it was needed to consider the resistances and blockage effects of the Yuuta bridge
railing and piers in the numerical analysis.
In this study, Eq. [4] and Eq. [5] were solved for the general curvilinear coordinate system at the computational grids
including the Yuuta bridge railing and piers. They were derived by considering the volume ratio of the Yuuta bridge railingand piers and their resistance. Because the plan form of the river channel around the Yuuta Bridge is almost straight andthe bridge was constructed at almost a right angle to the river channel, it can be assumed that the flow resistance of thebridge railing and piers mainly work in the main stream direction. So, the drag force received from the Yuuta bridge piersin the main stream direction was given asDi 

1CDU iUA1
2[6]

where, U is depth averaged horizontal velocity, CD is drag coefficient, A1 is projected area of river bridge piers in mainstream direction. Because the amount over time of the driftwood accumulations around the Yuuta Bridge piers during theflood events are unapparent, the drag coefficient was set as the value generally used for a river bridge pier (CD=1.0) andthe projected area considered only for the Yuuta Bridge piers. On the other hand, it was apparent from the photographsthat the driftwood accumulations on the Yuuta Bridge railing heavily obstructed flowing of the floods. In order to consider
the driftwood accumulations, we assumed the impermeable wall above the Yuuta Bridge railing and made the flood water
unable to flow over the wall as shown in Figure 8. The force received from the Yuuta Bridge railing in the main stream
direction was given by the form of the drag force as shown by Eq. [7].

Pi 

1
C D u si u s A22

[7]

where, us is water surface velocity, A2 is projected area of the Yuuta Bridge railing in main flow direction. Drag coefficientof the Yuuta Bridge railing was determined so as to explain the longitudinal distribution of the flood marks observed after
each flood. The occupancy ratio of water f found in Eq. [4] was determined so that the flood flow was unable to flow overthe Yuuta Bridge railing at the computational grids including the Yuuta Bridge railing and piers as shown in Figure 8.
Elevation point for water level, river bed and surface velocity
Elevation point for depth averaged horizontal velocity
Control volume of continuity equation
Control volume of horizontal momentum equation
Projected area of the Yuuta Bridge railingz

The Yuuta Bridge railing

u

h
fh

B

 (Lateral direction)
River bedProjected area of the Yuuta Bridge pier(a) Front view.

P

The Yuuta Bridge railing

Flow

z

h

B

fh


 (Longitudinal direction)
River bed(b) Side view.
Figure. 8. Computation method considering the driftwood accumulation around the Yuuta bridge railing.

5E-proceedings of the 36th IAHR World Congress,
28 June – 3 July, 2015, The Hague, the Netherlands

3.

NUMERICAL ANALYSIS RESULTS

3.1 Comparison between numerical analysis results and observed data
Figure 9(a) and (b) show the longitudinal distributions of the computed peak-water level and flood marks in the first floodand the longitudinal distributions of the bed elevations before and after the flood. The computed peak-water levels could
explain the longitudinal distribution of the flood marks. But the computed peak-water levels were lower than the flood

overbank flow(right and left banks)

130
Slope I=1/95

Elevation(T.p.m)
標高(T.p.m)

125
120
115

overbank flow(right and left banks)

110
levee breach(right bank)

105
100
95

levee breach(left bank)

90
5.4

5.9

6.4

6.9

7.4

7.9

8.4

Longitudinal
distance (km)距離(km)(a) Upstream reach.
overbank flow(right and left banks)
94

Slope I=1/256

標高(T.p.m)

Elevation (T.p.m)89

overbank flow(right bank)84

overbank flow
79 (right and left banks)
overbank flow
(left bank)

74

69
64
0.0

1.0

2.0

3.0

4.0

Longitudinal距離(km)distance (km)5.0Arita River Confluence(b) Downstream reach.
Figure 9. Comparison between the longitudinal distributions of computed peak-water level and the flood marks in the firstflood and longitudinal distributions of the bed elevations before and after the floods.
Maximum water depth (m)

5.0k

5.0k

4.0k
4.0k

3.0k
(a) Observed data.

3.0k(b) Computed results.

Figure 10. Comparison between observed and computed inundation areas and maximum water depth
distributions in the first flood.
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E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands

marks in some locations. In addition, the computed bed elevations after the floods almost agreed with the observed
average and lowest bed-elevations. Figure 10(a) and (b) show the observed inundation areas after the first flood and thecomputed inundation areas and maximum water depth distributions at the first flood. The computed inundation area of thefirst flood could almost reproduce the observed data. The relatively poor reproducibility around the 3.0km point (seeFigure 10(a), (b)) was due to the absent of considering the inundation water from the tributary flowing into the Kagetsu
River around 2.8km point.
3.2 Flow and bed variation around the levee breach points
Figure 11 shows the contour map of the bed variations and depth averaged velocity vectors at the peak of the first floodfrom 5.8 km to 6.8 km points at the Kagetsu River. Higher velocities concentrated to the outer bank side due to the river
planform, and they caused the bed scouring at the right bank in 6.0km point and at the left bank in 5.8km point where thelevee breaches occurred as shown in Figure 11.

6.8k
6.8k

Bed variation (m)Scouring

6.6k
6.6k

Deposition: Depth averaged horizontal velocity (3m/s)

5.8k
levee
breach

6.0k

6.4k
6.4k

6.0k

6.2k
6.2k

5.8k
levee breachFigure 11.

Contour map of computed bed variations and velocity vectors around the levee breaches area at the peak of the firstflood.

Figure 12(a) and (b) show cross-sectional distributions of the computed depth-averaged velocity, river bed levels before
and after the floods and peak water levels at 6.0km and 5.8km points. The computed maximum velocity was 6.9 m/s andthe bed scouring was at least 1.0m near the right bank at 6.0km point (see Figure 12(a)). Similarly, the high velocity andbed scouring occurred near the left bank of 5.8km point. In addition, the computed maximum water level was lower thanthe levee height as shown in Figure 12(a) and (b). It is suggested that the bed scouring was the most influential factor forthe levee breaches at the first flood in the Kagetsu River.
Bed elevations during the peak water level (Cal.)

Peak water level (Cal.)

Depth averaged velocity during the peak water level(Cal.)

Elevation(T.p.m)
標高(T.p.m)

6

100

5

99

4

98

3

97

2

96

1

Scouring

95

0
0

20

40
60
80
Transverse
distance (m)
横断距離(m)

100

100

6

98

5

97

4

96

3

95

2

Scouring

94

1

93

120

(a) Cross-sectional form at 6.0km point.
Figure 12.

7

5.8k

99

0
0

20

40
60
80
100
Transverse
distance (m)
横断距離(m)Depth averaged
velocity (m/s)
流速分布(m/s)

7

6.0k

101

標高(T.p.m)
Elevation(T.p.m)102

流速分布(m/s)
Depth averaged
velocity (m/s)

Initial bed elevations

120(b) Cross-sectional form at 5.8km point.

Computed bed variations and velocity distributions at the peak of the first flood at 6.0km and 5.8km points.

3.3 Inundation in the built-up area around the middle Kagetsu River
Figure 13 (a) and (b) show the contour maps of inundation water depth computed at the beginning of the overbank flows
and at the flood peak during the first flood, respectively. The computed water level at the Yuuta Bridge already reached
the elevation of the bridge railing at 8:40am July 3. In this time, overbank flows didn’t occur yet. But overbank flows7E-proceedings of the 36th IAHR World Congress,
28 June – 3 July, 2015, The Hague, the Netherlands

occurred at the right bank of just upstream of the Yuuta Bridge (4.7km point) in 8:50am July 3. The inundation water had
spread to the area shown by Figure 13(b) until the flood peak and to the area shown by Figure 10(b) an hour after theflood peak during the first flood. They demonstrate that the structural deficiency absence of the height of the Yuuta Bridge
brought the large overbank flows and spread inundation water to the built-up area in a short time.
Water depth (m)Yuuta Bridge

Yuuta Bridge

Siromachi Bridge

Siromachi Bridge(a) 8:50(b) 9:00

Figure 13. Contour map of water depth at the middle Kagetsu River during July 3 flood.

Figure 14 shows the contour map of depth-averaged velocity in the inundation water at the peak of the first flood. The
houses existing at built-up area were heavily damaged by the inundation water at black circled point in Figure 14.
Because the ground slope in the built-up area was almost similar to the slope of the river channel, the inundation water
flowed with high velocity through the built-up area. Especially, inundation water had the velocity of greater than or equal to
2 m/s and large water depth around the circle point as shown in Figure 13(b) and Figure 14. Similarly, the inundationwater had high velocity and large water depth when it passed through the other damaged points at the built-up area. It
can be estimated that the houses in the built-up area received large fluid forces and heavy damages from the inundationwater.

Depth averaged velocity (m/s)

Yuuta Bridge
Heavily damaged house point

Siromachi Bridge

Figure 14. Contour map of depth averaged velocity at the middle Kagetsu River at July 3, 9:00am

Figure 15 shows the photograph of 4.0km point at 9:40am July 3. The inundation water at the built-up area flowed backinto the river channel at just upstream of the Siromachi Bridge locating at 4.0km point. Figure 16 shows contour map of
the computed water depth and depth-averaged velocity of the channel flow and inundation flow around the same point at
9:30am July 3. The return flow from the built-up area to the river channel could be reproduced in numerical analysis,
although the area where the inundation water flowed back into river channel was narrower than observed data (seeFigure 15). In this area, densely-packed buildings blocked the spreading of the inundation water and pushed back theinundation water toward the river channel. The inundation flow through the built-up area returned into the river channel
around the Siromachi Bridge, since the bed elevation around the Siromachi Bridge were higher than surrounding area.

8

E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands

Figure 15. Photograph of return flows of inundation water to the river around 4.0km point at 9:40am July 3.

Water depth (m)LeveeRiver channel

Siromachi
Bridge: Depth averaged
velocity (2.0m/s)

Figure 16. Contour map of computed water depth and depth-averaged velocity of channel flow and inundation flow around 4.0km
point at 9:30am July 3.

4.

CONCLUSIONS

The following conclusions were drawn by using the numerical model and data measured during the Kagetsu River floods.
1) We developed the numerical model which could explain flood flows and bed variations in the Kagetsu River andinundation flows in the built-up area by considering driftwood accumulations at the Yuuta Bridge. Here, the height andlocation of buildings and road network patterns at the built-up area were directly given by the Digital Surface Models(DSM) to examine the behavior of the inundation water in the built-up area.
2) It is suggested that bed scouring was the most influential factor for breaches of soil levees at the first flood in 2012 in
the Kagetsu River.
3) Inundation water passing through the built-up area returned into the river channel over concrete embankment aroundthe Siromachi Bridge, since the densely-packed buildings blocked further spreading of the inundation water and the bed
elevation around the Siromachi Bridge were higher than surrounding areas.
4) Because the ground slope in the built-up area was almost similar to the slope of the river channel, houses in the builtup area received large fluid force and heavy damages from the inundation water during the floods.
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medium and small scale rivers. Proc. JSCE, 70, 883–888.
Uchida T., and Fukuoka S. (2011). Numerical simulation of bed variation in a channel with a series of submerged groins.
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P.D. Bates., and A.P.J De Roo. (2000). A simple raster-based model for flood inundation simulation. Journal of Hydrology
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Akiyama J., Shigeeda M., and Tanabe T. (2009). Numerical simulation of inundation flow with sewer networks in the Onga
River basin. Proc. JSCE, 53, 829–834.

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