River Basin Management X 71

ESTIMATION OF LEVEE FAILURE POINTS BASEDON LEVEE VULNERABILITY INDEX AND FLOODRISK ANALYSIS BY INTEGRATING SIMULATION
OF FLOOD FLOW AND INUNDATIONKOSUKE TABATA & SHOJI FUKUOKA
Research Development Initiative, Chuo University, Japan

ABSTRACTTo examine the flood risk management measures, it is important to estimate the levee breach points,
inundation discharge hydrograph and motion of the inundation water in the basin as precisely as
possible. The purpose of this paper is to conduct the above series of studies on the Kinu River (Japan)
suffered from inundation in the range of 40 km2 due to overflowing and levee breach during the 2015
large flood. First, a simulation model integrating flood flow and inundation is developed. The
inundation discharge hydrographs due to the overflowing and levee breach are estimated by the flood
flow analysis based on observed temporal changes in water surface profiles in the Kinu River. The
inundation is calculated by a two-dimensional model. The mesh of the inundation analysis model isgenerated by regular grid with 5 m size in order to express the microtopography obtained by DSM(Digital Surface Model). Manning’s roughness coefficients are given according to the situation of theland use and inundation depth. It is confirmed that the developed model is useful by the inundation
arrival time read from camera images and the spread of the actual inundation water in the basin. Next,
the suitability of the levee vulnerability index t* which has been derived by the authors is examined
for the levees of the Kinu River. Finally, the inundation flow analysis is conducted under the actualand hypothetical levee breach conditions based on the value of t*. It is concluded that the differencein the location and time of the levee breach influences on the motion of the inundation water andinundation areas in the Kinu River basin.
Keywords: Kinu River 2015 flood, inundation flow, flood flow, levee vulnerability index, flood risk.

1 INTRODUCTION
It is important to estimate the levee breach points, inundation discharge hydrograph andmotion of the inundation water in the basin as precisely as possible to examine the floodrisk management measures.
Tabata et al. [1] developed a flood flow analysis model based on the temporary changesof observed water surface profiles during the 2015 flood in the Kinu River, Japan, whichsuffered from damage in the huge inundation area due to levee breach. The inundation
discharge hydrographs were estimated accurately by the developed flood flow model. Also,in the Joso City which faces the left bank of the Kinu River and inundated in the 2015
flood, the inundation time and depth were obtained from camera images installed at somelocations in the Kinu River basin. These data will make it possible to verify the inundation
analysis model.
In general flood risk assessment [2], levee breach points are usually set up at levee
failure points where the water level exceeds the design water level. However, serious levee
damage such as a levee breach and sliding or collapse has occurred at points where thebody of the levee is vulnerable to seepage flow even in the section where the water level isbelow the design water level. In recent years, Fukuoka and Tabata [3] have proposed thelevee vulnerable index t* which is represented by the combination of water level, duration
time of flood, levee width, porosity and permeability of the levee. It has been confirmed

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72 River Basin Management X

that the levee vulnerability index can represent the risk of levee failure due to seepage flow.
By using this index, the levee breach points will be estimated rationally.
The purpose of this paper is to estimate the flood risk by integrating simulation of flood
flow and inundation in the Kinu River basin. First, the inundation flow analysis model isdeveloped by using the inundation discharge hydrographs due to the overflowing and levee
breach. Then, the inundation model is verified by the filed inundation data. Next, the levee
failure risk due to seepage flow in the Kinu River is evaluated by the use of the levee
vulnerability index t*. Finally, the inundation flow analysis is conducted under the levee
breach condition based on the value of t*. It is concluded that the difference in the locationand time of the levee breach considerably influences on the motion of the inundation waterand inundation area in the Kinu River basin.
2 DEVELOPING THE INTEGRATING SIMULATION MODEL OF
FLOOD FLOW AND INUNDATION
2.1 Integrated simulation model of flood flow and inundation in the Kinu River
Fukuoka and Watanabe [4] have proposed the numerical method for flood flows and bed
variations using time series of observed flood water surface profiles on the basis of the ideathat effects such as plan forms, cross-sections and outflowing water from the river appear intime series of observed water surface profiles of flood flows. Based on this idea, theintegrated simulation model of flood flow and inundation was developed by using timeseries of the observed water surface profiles during the 2015 flood in the Kinu River [1].
Since overflowing and collapse of the levee occurred around 25.35 k, the inundation flow
was calculated so that the collapse occurred when the water level exceeded the levee height.
Also, the inundation flow from the levee breach point at 21.0 k was calculated so that thecalculated water surface profiles agreed with the observed ones around the levee breachedpoint [5] considering observed breach time and temporary change of breach width (Fig. 1).
This model could not only elucidate the flood propagation in the Kinu River but also
estimate inundation discharge hydrographs due to the overflowing and levee breach.
Levee breach at 12:50

40

water leve （Y.P.m）

35
30
25
20
15

Lines: calculated
Plots: observed

105
9/9 18:00

9/10 6:00

9/10 18:00

Water level hydrographs.

Cal. at 45.5k
Cal. at 37.3k
Cal. at 27.3k
Cals. at 21.3k
Cals. at 11k
Obs. at 45.5k
Obs. at 37.3k
Obs. at 27.3k
Obs. at 21.3k
Obs. at 11k

9/11 6:00

Water level
observed
point at 21.3k

Water level (Y.P.m)

5m/s

Inundation flowfrom levee breachpoint at 21.0k

Water level contour and velocity vectors
at 9/10 14:00 (3 hours after breach)

Figure 1: Calculated water level and inundation flows in the levee breach point at 21.0 k.
Fig. 2 shows the inundation discharge hydrographs which were estimated by this model.
The first wave was caused by overflowing and collapse of levee around 25.35 k, whichstarted at 06:00 on 10 September 2015, and the second one was caused by the levee breachat the 21 k left bank at 12:50 on 10 September 2015. The calculated inundation discharge

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River Basin Management X 73

Inundation
discharge(m3/s)

exceeded 500 m3/s at the maximum and the volume was estimated to be 32,000,000 m3.
The measured total inundation volume was about 38,000,000 m3, which agreed well withthe computed result. The inundation flow analysis is carried out by using these inundation
discharge hydrographs as the boundary conditions.
1,200
1,000
Overflowing and800
collapse (25.35k)
600
400
200
0
9/10 0:00
9/10 6:00

Total amount
Levee breach (21.0k)

9/10 12:00

9/10 18:00

9/11 0:00

9/11 6:00

Figure 2: Estimated inundation discharge during the 2015 flood event in the Kinu River.
2.2 Inundation flow analysis in Joso City
A two-dimensional inundation analysis model for Joso City which faces the left bank leveein the Kinu River is developed by using the inundation discharge during the 2015 flood
estimated by the analysis model in Section 2.1.
Fig. 3 shows the developed model for inundation analysis model in Joso City. The meshis generated by regular grid with 5 m size in order to express the microtopography obtainedby DSM (Digital Surface Model). Also, the mean ground level of each mesh is given by
DSM. The land use classifications were set based on GIS data of farmlands, road networks
and water area published by the Geophysical Survey Institute of Japan, and they were given
to each mesh. Manning’s roughness coefficients are given according to the land use andinundation depth. The roughness coefficients of farmland and water areas are given as
0.070 and 0.020 respectively. The roughness of the road is given small as 0.025 since it isgenerally known that the inundation water flows with high velocity on the road [6]. A large
resistance acts on the inundation front flowing into the dry area, and the resistance isreduced at the place where was wet once. Therefore, a depth threshold h0 (1.0 m in thisstudy) related to dry or wet state is introduced. If the water depth is less than h0 or has neverbeen flooded, the roughness coefficient is given as 0.100, otherwise the one for each land
use is given.
Fig. 4 shows a comparison between the observation and calculation of the temporalchanges of the inundation depth at observed points St.1 and 2 in Fig. 1. The observed data
were read from camera images at St.1 and 2. It can be confirmed that the inundation starts
immediately after the levee breach at St.1. Also, the calculated data can roughly explain theobserved one at St.2 which is far from the site of overflowing and levee breach. Therefore,
it is shown that the developed model can express the spread of the inundation water fromthe Kinu River and the distribution of inundation water depth in Joso City.
Fig. 4 shows the inundation depth contours at 15:00 on 10 September and 0:00 on 11
September. First, part of the inundation water around 25.35 k flows into the main drainage
channel and reaches the downstream part via the channel. At this time, the inundation water
due to the levee breach at 21.0 k left bank was combined with the inundation water due tooverflowing and collapse around 25.35 k. Also, the main body of the inundation waterreached near the Joso City hall at 0:00 on 11 September (Fig. 4(b)), and a large-scale
inundation occurred around the Joso City hall.

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74 River Basin Management X

Kinu River

Route
294

Overflowing
and collapse(25.35k)
St.1
Levee breach(21.0k)Ground level(Y.P.m)Kokai River

Building

Crowded urban district

Road

Hachikenbori River(Main drainage channel)

Route123

St.2

Joso City hall

Crowded urban district
0

Route294

5㎞

Figure 3: Developed inundation analysis model in Joso City.
3 EVALUATION OF LEVEE FAILURE RISK AND LEVEE BREACH POINTSBASED ON LEVEE VULNERABILITY INDEX
3.1 Levee vulnerability index t* by the seepage flow
Fukuoka and Tabata [3] have proposed the dimensionless index for the levee failure due toseepage flow during a flood event; levee vulnerability index t* (eqn (1)).
t* =5 kHt ' .
2 b 2(1)

Here, H is water level, b is horizontal length from the water front of waterside levee to thetoe of the landside levee, t’ is duration time from when the flood water level exceeds theground level of the landside toe. k,  and Sr are averaged permeability, porosity and degreeof saturation of the levee, respectively (see Fig. 5(a)).
The levee vulnerability index t* has been applied to many field levees where the damage
had occurred, and it has become clear that when the value of t* exceeds 0.1, the risk oflevee breach due to the seepage flow tends to increase [3].

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0.4
0.2
0
9/10 3:00

1.2
1

9/10 15:00

Cal.

0.8

Obs.

0.6

0.4
0.2
9/10 15:00

9/11 3:00

9/11 15:00

0.8

Obs.

0.6

0.4

River Basin Management X 75

0.2
09/10 3:00

9/11 15:00【St.1】

0
9/10 3:00

Inundation depth(m)9/11 3:00

Inundation de

0.6

Inundation depth(m)Inundation dept

Inundation depth(m)

Obs.

0.8

(a)

1.2

1

9/10 15:00

1

0.4

Cal.

0.2

Obs.

0
9/10 3:00

9/10 15:00

St.1

Levee breach

9/11 3:00

9/11 3:00

9/11 15:00

0.8

0.6
0.4

Cal.

0.2

Obs.

0
9/10 3:00

9/10 15:00

Inundation
depth (m)Crowdedurban district

Overtopping
0.6
and collapse

9/11 15:00【St.2】

1.2
0.8

9/11 3:00

Ground level(Y.P.m)9/11 15:00

Flowing through thedrainage channel

St.2

0

Huge flooding
due to main bodyof Inundation

5㎞

Joso City hall
9/10 15:00
・9 hours after overflowing
・4 hours after breachFigure 4:(b)

9/11 0:00
・18 hours after overflowing
・13 hours after breachInundation depth distribution in the Kinu River basin. (a) Comparison between
calculation and observation at St.1 and St.2; and (b) Calculated inundation
depth contour.

When the water level recedes, the top of the seepage line in the levee gradually moves tothe landside toe. Therefore, the seepage flow from the top of the seepage line to thelandside toe of the levee keeps on going and maintaining a high risk of levee failure. This ismainly caused by the reduction of the horizontal length b in eqn (1) due to the shift of theseepage peak height. Uemura and Fukuoka [7] have proposed the analysis method that canaccurately represent the above-mentioned unsteady seepage phenomenon during the flood
water receding stage. The outline of this method is shown below.
Consider the continuity condition that the volume change of water in the levee V
coincides with the displacement qt from the body of the levee to the waterside due to thewater level receding (see Fig. 5(b)).

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76 River Basin Management X

H: water levelH

k: coefficient of permeability
: porosity

Risingflood plain

landsidett’: duration time from when the water levelexceeds the ground level of the landside toe

b: horizontal length from water front
to levee toe of landside

(a)

①

b

z

H0

Hmax

Receding

flood plainb’(b)Figure 5:

x’

Ht+t

q

V

a

f

Hmax

②

0

x

f

h

3


  x 2 ①： h1 = H 0 1 −     0    x ' 2 
②： h2 =  h 1 − 
 
 

  f  Definition of variables of levee vulnerability index t*. (a) During water level
rising (definition of variables in eqn (1)); and (b) During water level receding(definition of variables in eqns (2)–(5)) [7].
 V = q t .

(2)Here, t is seepage time, V is volume change of water in the levee per t, q is outgoing
discharge from waterside slope of the levee as the water level of rivers recedes. The left
side of eqn (2) is indicated by the orange hatched area in Fig. 5(b) and expressed as eqn (3).
 − +  h / tan a  h2 2
 V =−  f  h − ( h + H t + t )  f
2 tan a 3
−





3/2

0







3/2

 − f +  h / tan a  h   2−  − f + −  h .
  ( h + H t + t ) tan a   5
− 0







(3)

The right side of eqn (2) is expressed as eqn (4) by using Depuit–Forchheimer’sequation [8]
2
3/2


.
k     − f +  h / tan a   H 0 1 − 
 − H t2+ t  *  t
q t =
2 f    
−0



  


(4)

The horizontal position of seepage line’s top f (see Fig. 5(b)) can be numerically solved
since eqn (3) is equal to eqn (4). Then, the peak height of the seepage line’s top Hmax will
be found by assuming that the position of the peak of the water level shifts along theseepage line. Therefore, the levee vulnerability index during the water level receding stage
is expressed as eqn (5) by substituting Hmax and b’ (=b-f) for H and b in eqn (1)WIT Transactions on Ecology and the Environment, Vol 234, © 2019 WIT Press
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River Basin Management X 77t* =5 kH maxt ' .
2 b '2(5)

3.2 Calculated levee vulnerability index t* and estimating of levee breach points

Levee vulnerability index

The levee vulnerability index t* was calculated longitudinally for the Kinu River’s leftbank which faces Joso City. Fig. 6 shows the longitudinal distribution of the levee
vulnerability index t* at peak water level (black plots) and the maximum value of t* during
the water level receding stage (red plots). t* around the actual breach point (21.0 k) areplotted in the range of 0.1 to 1.0 where the levee breach risk is very high. Besides these, t*around 11.75 k exceed 0.1. Therefore, if the levee breach did not occur at 21.0 k, it might
have occurred around 11.75k.
t* take large values
around 11.75k.

1.E+00t* take large values around
actual levee breach point (21.0k).

1.E-01
1.E-02
1.E-03

1.E-04t*(at peak water level)t*(maximum value)

1.E-05

Levee breach (21.0k)

1.E-06

5

10

15
20
Longitudinal distance (km)25

30Figure 6: Longitudinal distribution of t* along the left bank of the Kinu River.
Fig. 7 shows the temporary change of the water level and levee vulnerability index at 21
k and 11.75 k. It is confirmed that t* exceeds 0.1 around the actual levee breach time (12:50
on 10 September) at 21 k left bank. Assuming that the levee breach occurs when t* exceeds
0.1, the levee breach time at 11.75 k can be estimated as 17:00 on 10th September which is
two hours after the peak water level.
9/10 10:00(t*>0.1)

9/10 8:00

9/10 7:00

9/10 10:00

9/10 12:50(actual breach time)

9/10 11:00
9/10 15:00(peak water level )9/10 17:00(t*>0.1)
Data are plotted at 1hour interval.

Figure 7: Temporary changes of water level and t* at 21.0 and 11.75 k.

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78 River Basin Management X

4 INUNDATION ANALYSIS UNDER A LEVEE BREACH SCENARIO
BASED ON LEVEE VULNERABILITY INDEX
We need to conduct the inundation analysis under levee breach scenarios different from theactual flood inundation stated in Section 2.2 to investigate the inundation risk in the basin.
In this section, the inundation discharge hydrograph is estimated, and the inundation
analysis is performed under a hypothetical levee breach condition based on the result of thelevee vulnerability index.
The hypothetical levee breach point was set at 11.75 k left bank in which t* value took
the second largest value after the actual levee bleach point at 21.0 k (see Fig. 6). Also, thelevee breach time was set at 17:00 on 10 September when t* exceeds 0.1 (see Fig. 7). This
analysis was not taking account into the overflowing and collapse around 25.35 k. Fig. 8
shows the inundation discharge hydrograph due to the levee breach at 11.75 k left bankestimated by the simulation integrating the flood flow and inundation. The inundation
discharge becomes about 500 m3/s as well as the actual breach point at 21.0 k. However,since the levee breaches during the flood receding stage, the inundation volume is7,500,000 m3, which is smaller than the actual one.

Inundation
discharge(m3/s)

800
600
400
200
0
9/10 12:00

9/10 18:00

9/11 0:00

9/11 6:00

Figure 8: Estimated inundation discharge hydrograph due to the levee breach at 11.75 k.
The inundation flow analysis for the hypothetical levee breach condition at 11.75 k leftbank based on the value of t* was conducted. Fig. 9 shows the time change of theinundation depth contour. Although the inundation area is smaller than the actual one (Fig.
4), the inundation water spreads rapidly because the levee breach point is close to thecrowded urban district of Joso City. It is shown that the maximum inundation depth in thecrowded urban district (black dashed circle in Fig. 9) rises over 2.5 m, 4 hours after thelevee breach at 11.75 k. Then, much of the inundation water flows northward on the westside of the main drainage channel. 12 hours after the levee breach, inundation water also
spreads widely to the east of the main drainage channel. It is clear the crowded urban
district of Joso City would suffer from the comparable large flood damage even if either
21k or 11.75k levee breached.
5 CONCLUSION
The integral simulation model for flood flow and inundation in the Kinu River basin
suffered from inundation due to the levee breach at 21.0 k and overflowing and collapse
around 25.35 k during the 2015 large flood was developed. This model can approximately
elucidate the inundation arrival time read from camera images and the actual inundationwater spread in the basin.

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River Basin Management X 79

Kinu River

0Main
drainagechannel

5㎞
Ground level(Y.P.m)Inundation
depth (m)Levee breach(11.75k)

Joso City hall
Crowded urban district

9/10 21:00(4 hours after breach)

Figure 9:

9/11 1:00(8 hours after breach)

9/11 5:00(12 hours after breach)

Inundation depth contour which is calculated taking account into the levee
breach at 11.75 k left bank in the Kinu River.

Also, the levee vulnerability index t* was calculated along the levee in the Kinu Riverand took high values at not only the actual levee breach point in 21.0 k but also 11.75 k.
The hypothetical inundation flow analysis by assuming that the levee breach occurs at
11.75 k was conducted. It is clear that the south crowded urban district of Joso City would
suffer from the comparable huge flood damage even if either 21 k or 11.75 k levee
breached. Therefore, the levee reinforcement against the seepage flow is needed at theplaces where the levee vulnerability index t* take high values. It is expected to make anadvanced inundation hazard map by performing the inundation flow analysis under theseveral levee breach scenarios based on the levee vulnerability index t*.
REFERENCES[1] Tabata, K., Fukuoka, S. & Deguchi, K., Analysis of discharge capacity and flood
storage rate during 2015 large flood in the Kinu River. 12th International Conference
on Hydro-Science and Engineering for Environmental Resilience, ICHE 2016,15-0036, 2016.
[2] Bilal, M., Jerry, F. & William, L., Risk analysis of a protected hurricane-prone region.
I: model development. Natural Hazards Review, 10(2), pp. 38–53, 2009.
[3] Fukuoka, S. & Tabata, K., Index governing the seepage flow and dynamic similarity
condition of levee failure due to seepage flow: Seepage flow number and levee
vulnerability index. Annual Journal of Hydraulic Engineering, JSCE, 74(5), pp.
I_1435–1440, 2018. (In Japanese.)[4] Fukuoka, S. & Watanabe, A., Estimating Channel Storage and Discharge Hydrographsof Flooding. Proceedings of the 5th International Conference on Hydro-Science andEngineering, 2002.
[5] Fukuoka, S., Abe, T. & Tsukamoto, Y., Calculation method of inundation dischargehydrograph from the temporal changes in water surface profile due to levee breach.
Journal of JSCE, 65(3), pp. 166–178, 2009. (In Japanese.)

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80 River Basin Management X[6] Fukuoka, S., Kawashima, M., Matsunaga, N. & Maeuchi, H., Flooding water over a
crowded urban district. Journal of JSCE, 491(II-27), pp. 51–60, 1994. (In Japanese.)[7] Uemura, Y. & Fukuoka, S., On the backslope stability of levee during the flood fallingstage based on the levee vulnerability index. Advances in River Engineering, 24, pp.
571–576, 2018. (In Japanese.)[8] Muskat, M., The Flow of Homogeneous Fluid through Porous Media, McGraw-Hill,
pp. 316, 1937.

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