JOINT CONFERENCE PROCEEDINGS
9th International Conference on Urban Earthquake Engineering/ 4th Asia Conference on Earthquake Engineering
March 6-8, 2012, Tokyo Institute of Technology, Tokyo, JapanEVALUATION OF TSUNAMI FLUID FORCE ACTING ON THE BRIDGE DECKDAMAGED BY THE 2011 OFF THE PACIFIC COAST OFTOHOKU EARTHQUAKE TSUNAMI

Gaku Shoji1), Yu Hiraki2), and Yoshiyuki Ezura3)
1) Associate Professor, Faculty of Engineering, Information and Systems, University of Tsukuba, Ibaraki, Japan
2) Graduate Student, Graduate School of Systems and Information Engineering, University of Tsukuba, Ibaraki, Japan
3) College of Engineering Systems, University of Tsukuba, Ibaraki, Japan
gshoji@kz.tsukuba.ac.jp, s1021008@u.tsukuba.ac, s0811167@u.tsukuba.ac.jp

Abstract: The 2011 off the Pacific Coast of Tohoku earthquake tsunami caused the catastrophic damage ofinfrastructures such as coastal structures, utilities and transportation facilities. First we carried out the tsunami flow
simulation at the affected five areas such as Rikuzentakata city by using the finite difference method with a staggered leap
frog scheme. From the simulation we obtained the inundation heights at the sites where the wash-away nine bridges arelocated. Second, by using the simulated inundation heights, we estimated the horizontal and vertical hydraulic pressures
acting on the bridge decks based on the previously proposed formulas on evaluation of the relationship of the position ofa bridge deck to an inundation height with the horizontal and vertical wave pressures acting on a bridge deck.

1. INTRODUCTION
The 2011 off the Pacific Coast of Tohoku earthquake
tsunami caused the catastrophic damage of infrastructures
such as coastal structures, utilities and transportation
facilities. Among them a bridge structure plays importantroles to carry out emergency response by related
stakeholders and to support their recovery activities.
The issues are strongly recognized since weexperienced the 2004 Indian Ocean tsunami disaster. Since
the 2004 tsunami disaster, evaluation of tsunami fluid
force acting on a bridge deck is urgently required fordesigning a tsunami-proof bridge structure, and many
academic researchers and practitioners are involved in it.
From view of the point of numerical analysis, Yeh (2006)
evaluated the tsunami force and velocity in the run-up zone
by using the numerical algorithm developed by Carrier et al.
(2003) based on fully nonlinear shallow-water wave theory.
Ikari and Goto (2007) simulated the run-up tsunami wave
and the damage of a bridge deck by MPS (Moving Particle
Semi-implicit) method, and Shigihara et al. (2009) validated
the damage of the bridge deck at Sumatra island, Indonesia
subjected to the 2004 tsunami by three dimensional
numerical fluid analysis by adapting a staggered leap-frog
method. However, the effect of tsunami fluid force on thebridge deck damage has not been clarified enough.
From the reason above, we estimate the horizontal andvertical tsunami wave pressures on the wash-away ninebridge decks by combining the previously proposed

experimental formulas with the numerical inundation
heights. First we carry out the tsunami flow simulation at theaffected five areas by using the finite difference method witha staggered leap frog scheme. From the simulation we obtain
the inundation heights at the sites where the wash-away ninebridges are located. Second, by using the simulated
inundation heights, we estimate the horizontal and verticalhydraulic pressures acting on the bridge decks based on theformulas on evaluation of the relationship of the position ofa bridge deck to an inundation height with the horizontal andvertical wave pressures acting on a bridge deck.

2.

NUMERICAL SIMULATION OF TSUNAMIWAVE PROPAGATION AND INUNDATION
AREAS

2.1 Governing Equations
The tsunami wave propagation is computed by using
TSUNAMI-CODE (Tohoku University‟s Numerical
Analysis Model for Investigation of Tsunami). The
governing equations are based on shallow water theory as
shown in Eq. (1a)-(1c), which are discretized by using thefinite difference method with a staggered leap flog scheme(DCRC 2009).

- 2049 - M N


0
t
x
y

(1a)

Table 1 Subject Bridges
Group
Name of Dameged Bridges Longtitude Latitude
Name of Roads
Prefectures
No.
1
Koizumi Long-bridge
141.50738.769National Route 45
Miyagi
Mizushiri Bridge
141.443
38.673National Route 45
Miyagi2
Oritate Bridge
141.43738.648 National Route 398
MiyagiYokotsu Bridge
141.456
38.638 National Route 398
Miyagi3
Utatsu Bridge
141.524
38.717National Route 45
Miyagi4
Shinkitakami Bridge
141.420
38.549 National Route 398
MiyagiKawaharagawa Bridge
141.630
39.009National Route 45
Iwate
5
Numata Bridge
141.650
39.009National Route 45
Iwate
Kesen Bridge
141.62239.006
National Route 45
IwateM   M 2    MN  gn 22
2
      gD  7 3 M M  N (1b)t x  D  y  D 
x DN   MN    N 2  gn 2
2
2
(1c)
 
      gD  7 3 N M  N
t x  D  y  D 
y D

where η is a tsunami wave height measured from sea surface
level, M and N are the discharge fluxs of x-direction andy-direction. D is a total water depth (η+h), h is a water depth,
g is the gravitational acceleration, n is the Manningroughness coefficient. n is set as 0.25 in the simulation.
Inundation area(GSI)

2.2 Details of Computational Data Set
Five affected areas by the 2011 of the Pacific Coast of
Tohoku earthquake tsunami are focused for the simulationand totally nine wash-away bridges at the areas are selected
for the analysis. Table 1 and Figure 1 show the information

Numata Bridge

Kawaharagawa Bridge
39°0'0"N

Kesen Bridge
38°50'0"N

Koizumi Long-bridge
Utatsu Bridge
Mizushiri Bridge

38°40'0"N

Oritate Bridge
Yokotsu Bridge

38°30'0"N

Shinkitakami Bridge

300 km

500 km

700 km

900 km(a)

141°10'0"E 141°20'0"E 141°30'0"E 141°40'0"E

Figure 1 Location of the Bridges
Table 2 Number of Grids for All Groups
Group
No.
All Group
1, 2, 4
3, 5
1
2
3
4
5

Region X -direction Y -direction Grid Size[m]
1
2
3
4
4
5
6
5
6
5
6
5
6
5
6

480
481
481
541
481
511
781
601
811
481
721
1090
1090
721
931

720
721
721
901
721
781
811
721
811
721
721
889
1090
481
931

1350
450
150
50
50
16.67(50/3)
5.55(50/9)
16.67(50/3)
5.55(50/9)
16.67(50/3)
5.55(50/9)
16.67(50/3)
5.55(50/9)
16.67(50/3)
5.55(50/9)

545 km555 km565 km(b)

Figure 2 Computatinal Boundary(a) Region 1 to Region 3, and (b) Region 4 to Region 6- 2050 -of subject bridges. Six computational regions (Region 1 toRegion 6) are used in the nested grid system.
Region 1 is used together in five groups. Region 2,
Region 3, and Region 4 are used together in Group 1, Group
2 and Group 4. Region 2, Region 3, and Region 4 are used
together in Group 3 and Group 5. Region 5 and Region 6 arefor each group separately. Region 1 is generated by using
GEBCO 30 second data with the grid size of 1,350m.
Region 2, Region 3, and Region 4 are generated by using
GEBCO 30 second data for topography and JHA
1m-increment-line data for bathymetry with the grid size of
450m, 150m, and 50m, respectively. Region 5 and Region 6
are generated by using GSI DEM 10m-point data for
topography and JHA 1m-increment-line data for bathymetry
with the grid size of 16.67 (50/3)m and 5.56 (50/9)m. Figure
2 (a) shows the computational area of Region 1, Region 2,
and Region 3 for Group 5. Figure 2 (b) shows thecomputational area of Region 4, Region 5, and Region 6 forGroup 5. Table 2 shows the number of grids in x-direction
and y-direction in WGS-1984-UTM-54-N coordinate system.
The time step for computation is 0.15 second, and total
computational time is 120 minutes for all groups.

from the typical simulation to validate the simulated
inundation data with observed data.
Figure 4 shows the elevation from the topography andbathymetry data used for the Group 5 simulation. It also
shows the positions of subject three bridges and the related
twenty three observation sites for twenty inundation heights
and three run-up heights with reliability A and B, by the

2.3 Tsunami Source Model

Figure 4 Elevation for Group 5 Simulation(Red denotes the positions of subject bridges, blue
denotes the positions of observation sites for inundation
height, yellow denotes those for runup heights)

The tsunami source model proposed by Imamura et al.
(2011) is used for the simulation. We give the initial waterlevel based on the tsunami source model by using Okada‟smethod (Okada 1985). Figure 3 shows the initial water
elevation for the tsunami simulation.

30m
25m

3．COMPARISON OF SIMULATED INUNDATIONDATA WITH OBSERVED DATA

20m
15m

By the limitation of paper lengths, we show the results

10m
5m
0.01m
0m

Figure 5 Inundation Areas for Group 5 Simulation(Red, blue and yellow dots denote same meanings
as those in Figure 4)30Group1（Inundation height）

Simulate inundation height [m]3030Group1（Inundationheight）
height）
Group2（Inundation
Group1（Inundation

Computatinal value[m]25Figure 3 Initial Water Level(Tohoku University Model Ver1.1)

2525

20

2.33

Group2（Inundationheight）
height）
Group2（Inundation
Group3（Inundation

2.33
2.33

Group3（Inundationheight）
height）
Group3（Inundation
Group4（Inundation

2020

Group4（Inundationheight）
height）
Group4（Inundation
height）
Group5（Inundation

15

Group5（Inundation
height）
Group5（Inundation
height）
Group1（Runup
height）

1515

10

1010

5

55

0

Group1（Runup height）

Group1（Runup height）
height）
Group2（Runup

0.87

0.87
0.87

Group2（Runupheight）
height）
Group2（RunupGroup3（Runup height）
Group3（Runupheight）
height）
Group3（RunupGroup4（Runup height）

Group4（Runupheight）
height）
Group4（RunupGroup5（Runupheight）
height）
Group5（RunupGroup5（Runup height）

00
0 0 5 5 1010 1515 2020 25
25 30
30
0Observed
5
10
15
20height
25
30
inundation
andrun-up height [m]Observed
inundation
height andrunup height[m]Figure 6 Comparison of Observed Inundation Heights
and Run-up Heights with Simulated Results- 2051 -Inundation height [m]three points for the Group 3, and one point for Group 4.
From Figure 6, the magnification factors of simulated
inundation data with observed data are 0.84 to 2.33. Basedon this validation, we use the simulated inundation heights
data at subject bridges as input tsunami waves acting on theirbridge decks in consideration of accuracy for simulated
results as shown in Figure 6. In addition, we obtain timeseries of inundation heights at subject bridges for the Group
5 as shown in Figure 7.

20
10

(a)

0
20
10

(b)

0
20
10
0
0

(c)
20

40

60

80

100

120

Time
0
20
40 [minutes]
60
80
100 120
Figure 7 Time Series of Inundation Heights at
Subject Bridges for Group5 Simulation(a) Kawaharagawa Bridge,(b) Numata Bridge, and (c) Kesen Bridge

4. ESTIMATION OF TSUNAMI WAVE PRESSURESON THE WASH-AWAY BRIDGE DECKS

2011 Tohoku Earthquake Tsunami Joint Survey Group(2011). Figure 5 shows the inundation areas by Group 5
simulation. The elevation data at point 11 is estimatedpossibly to have the difference with the real value since
point 11 is located near the steep slope.
From the results by the Group 5 simulation for
Rikuzentakata city, simulated inundation heights show thevalues of 11.15m to 18.87m, which have the differences by-3.04m to 3.04m compared with observed values. It
indicates that simulated inundation heights become 0.82 to1.22 times ones compared with the observation data.
Figure 6 shows the relationship between the simulated
inundation data from the Group 1 to Group 5 simulations
and the related observation data. We validate the simulated
inundation heights with seven points for Group 1, sevenpoints for the Group 2, six points for the Group 3, and four
points for Group 4. We validate the simulated run-up heights
with five points for Group 1, four points for the Group 2,

We estimate tsunami wave pressures on the wash-away
nine bridge decks by applying the following experimental
formulas by Shoji et al. (2011) to the simulated data. These
formulas are for surging breaker bores (SBB) and plunging
breaker bores (PBB).
  1.54  0.69 8.38

:SBB (2a)4  1.73  10 3  1.74  10 3 3.7710:SBB (2b)  1.73  0.63 5.42

:PBB (2c)4  1.56  10 3  1.56  10 3 3.6410

Table 3 shows inundation heights and elevation at
subject bridges, and η, κ, λ,,defined as thefollowing equations. Figure 8 shows also the wash-awaybridge data in the relationships of κ-η and λ-η.

Table 3 Wave Pressures Act on Subject Bridges(a) For Surging Breaker Bores, and (b) For Plunging Braker Bores
Group
No.
1
2
3
4
5

Group
No.
1
2
3
4
5

Name of Dameged Dridge
Koizumi Long-bridge
Mizushiri Bridge
Oritate Bridge
Yokotsu Bridge
Utatsu Bridge
Utatsu Bridge by Secondary Wave
Shinkitakami Bridge
Kawaharagawa Bridge
Numata Bridge
Kesen Bridge

Name of Dameged Bridge
Koizumi Long-bridge
Mizushiri Bridge
Oritate Bridge
Yokotsu Bridge
Utatsu Bridge
Utatsu Bridge by Secondary Wave
Shinkitakami Bridge
Kawaharagawa Bridge
Numata Bridge
Kesen Bridge:PBB (2d)Inundation
Elevation
Height
[m]
[m]
18.27
6.53
19.97
7.17
20.27
7.09
17.43
1.58
17.35
2.04
13.76
2.04
9.38
7.29
15.375
1.81
15.75
3.179
14.576
5.757
Inundation
Elevation
Height
[m]
[m]
18.27
6.53
19.97
7.17
20.27
7.09
17.43
1.58
17.35
2.04
13.76
2.04
9.38
7.29
15.375
1.81
15.75
3.179
14.5765.757- 2052 -

η

κ

λ

0.64
0.64
0.65
0.91
0.88
0.85
0.22
0.88
0.80
0.61

1.53 0.21
1.53 0.21
1.52 0.22
1.23 0.44
1.30 0.42
1.36 0.39
1.54 -0.48
1.30 0.42
1.44 0.35
1.53 0.17

η

κ

0.64
0.64
0.65
0.91
0.88
0.85
0.22
0.88
0.80
0.61

1.67 0.25
1.67 0.25
1.67 0.25
1.36 0.45
1.41 0.43
1.47 0.41
1.73 -0.35
1.41 0.43
1.55 0.37
1.69 0.21

λF X /A s

F Z /A b[kN/m2] [kN/m2]
279.97306.11
310.29215.91226.95
188.50145.39201.10227.63224.38

38.72
41.92
44.48
76.64
72.87
54.57
-45.28
64.56
55.77
25.10

F X /A s

F Z /A b(a)[kN/m2] [kN/m2]
306.89335.64339.77237.28246.03202.77162.99218.00244.41
247.22

45.56
49.45
51.88
78.04
74.71
56.45
-33.3666.19
58.78
31.31 (b)a  hc
a

(3a)



Fx As
ga

(3b)



Fz Ab
ga

(3c)

and
of 58.58kN/m2. Kesen Bridge decks with
η=0.61 are estimated to be affected by κ=1.69 and λ=0.21
tsunami wave pressures, which areof 247.22kN/m2
2
andof 31.31kN/m . At Numata Bridge and Kesen
Bridge, higher horizontal pressure and lower uplift verticalpressure act on their bridge decks compared with those at
Kawaharagawa Bridge.
From the similar analyses, we find that the mechanismof horizontal and vertical wave pressures on the wash-away
nine bridge decks are classified into three categories :
relatively lower κ and higher positive λ acts at Yokotsu
Bridge, Kawaharagawa Bridge and Utatsu Bridge, relatively
middle κ and positive λ acts at Numata Bridge, Oritate
Bridge, Koizumi Long-bridge, Mizushiri Bridge and Kesen
Bridge, and relatively higher κ and negative λ acts at
Shinkitakami Bridge.

η is the ratio of bridge deck position from a still walllevel
by an averaged wave heightfrom a still waterlevel. κ is defined as the ratio ofwith an averaged
horizontal wave force
and projected area of a bridge
deck , by hydraulic static pressure. λ is also definedas the ratio ofwith an averaged vertical wave force
and area of bottom of a bridge deck, by hydraulicstatic pressure. In the following analysis, we assume awave height
to be the simulated inundation height, andto be the value of elevation as shown in Figure 9.
By focusing on the Group 5 simulation results, from
Table 3 and Figure 8 for plunging breaker bores,
Kawaharagawa Bridge decks with η=0.88 are estimated tobe affected by κ=1.41 and λ=0.43 tsunami wave pressures,
which areof 218.07kN/m2 andof
2
66.21kN/m . It is possible that Kawaharagawa Bridge isaffected by simultaneously strong horizontal wave pressure
and uplift vertical wave pressure. Numata Bridge decks with
η=0.80 are estimated to be affected by κ=1.55 and λ=0.37
tsunami wave pressures, which areof 244.41kN/m2
2

5. CONCLUSIONS
We estimated the horizontal and vertical tsunami wave
pressures on the wash-away nine bridge decks due to the2011 off the Pacific Coast of Tohoku earthquake tsunami bycombining the previously proposed experimental formulaswith the simulated inundation heights. First we carried out
the tsunami flow simulations at the affected five areas(Group 1 to Group 5) by using the finite difference methodwith a staggered leap frog scheme, and we obtained theinundation heights at the sites where the wash-away nine2

Mizushiri Bridge,
Koizumi Long- bridge
Shinkitakami Bridge
Kesen Bridge Oritate Bridge

1.5

Shinkitakami Bridge
Mizushiri Bridge,
Koizumi Long- bridge
Kesen Bridge
Oritate Bridge
Numata Bridge

1.5

Numata Bridge
Utatsu Bridgeby Secondary Wave

Utatsu Bridgeby Secondary Wave

Utatsu Bridge,
Kawaragawa Bridge
Yokotsu Bridge
Yokotsu Bridge
Utatsu Bridge,
Kawaharagawa Bridge
Utatsu Bridgeby Secondary Wave
Numata Bridge

0.5

1

Utatsu Bridge,
Kawaragawa Bridge Yokotsu Bridge
Yokotsu Bridge
Utatsu Bridge,
Kawaragawa Bridge

κ, λ

κ, λ

1

0.5

Utatsu Bridgeby Secondary Wave
Numata Bridge

Kesen Bridge

Kesen Bridge
0

0
0

0.2

0.4

0.6

0.8

0

1

0.2

0.4

0.6

Oritate Bridge-0.5

Mizushiri Bridge,
Koizumi Long- bridge

0.8

1

Oritate Bridge-0.5

Mizushiri Bridge,
Koizumi Long- bridge

Shinkitakami Bridge
-1

(a)

η

Shinkitakami Bridge-1ηFigure 8 Wash-away Bridge Decks Data in the Relationship of κ-η, λ-η(a) For Surging Breaker Bores, and (b) For Plunging Braker Bores- 2053 -(b)

Wave height : a

Inundation heightLand
elevationhc

Still water
Still water
level
level
Figure 9 Correspondence of Parameters in Experimental Formulas with Simulated Data

bridges are located. Second, by using the simulated aninundation heights, we estimated the horizontal and verticalhydraulic pressures acting on the bridge decks based on theformulas on evaluation of the relationship of the position ofa bridge deck η to a inundation height with the horizontal
and vertical wave pressures acting on a bridge deck κ and λ.
Following conclusions are deduced.
(1) We validated the simulated inundation heights with thesimulated inundation data of 44 inundation heights and 16
run-up heights with observation data. Among the data
simulated inundation heights for Group 5 with highest
accuracy show the values of 11.15m to 18.87m, which havethe differences by -3.04m to 3.04m compared with observed
values. In contrast, the data simulated inundation heights forGroup 1 with relatively lowest accuracy show the values of
17.37m to 26.76m, which have the differences by 0.24m to
15.28m compared with observed values.
(2) The mechanism of horizontal and vertical wave pressureson the wash-away nine bridge decks are classified into three
categories : relatively lower κ and higher positive λ acts at
Yokotsu Bridge, Kawaharagawa Bridge and Utatsu Bridge,
relatively middle κ and positive λ acts at Numata Bridge,
Oritate Bridge, Koizumi Long-bridge, Mizushiri Bridge andKesen Bridge, and relatively higher κ and negative λ acts at
Shinkitakami Bridge.
Acknowledgements:
The authors acknowledge variable supports from Tohoku
University, Disaster Control Research Center (Professor Imamura,F., and Professor Koshimura, S. ).

References:
Association of Japanese Geographers (AJG) (2011),“Maps of the
Area Hit by the Tsunami of 11 March 2011 Northeast Japan,”
http://www.ajg.or.jp/disaster/201103_Tohoku-eq.html (Accessedon 21 December 2011).
Carrier, G.F., Wu, T.T., and Yeh, H. (2003). „„Tsunami Run-up andDrawdown on a Plane Beach,‟‟ Journal of Fluid Mechanics, 475,
79-99.
Geospatial Information Authority of Japan (GSI), “Digital Elevation
Model,” http://www.gsi.go.jp/kiban/etsuran.html (Accessed on
21 December 2011).
Ikari, H., and Goto, H. (2007). „„Numerical Simulation of Washed
Process of Girder Bridge by Tsunami Run-up,‟‟ Proceedings of
Coastal Engineering, Japan Society of Civil Engineers, 54,
211-215.
Imamura, F., Koshimura, S., Murashima, Y., Akita, Y., and Aratani,
Y. (2011), „„The Tsunami Simulation for The 2011 off the Pacific
Coast of Tohoku Earthquake Tsunami, Tohoku University
Model (version1.1),” Disaster Control Research Center(DCRC),
1-6.
Japan Hydraulic Association (JHA), “Digital Topography of Ocean
Floor M7000 Series.”
Koshimura, S. (2009), „„TSUNAMI-CODE Tohoku University‟s
Numerical Analysis Model for Investigation of Tsunami,‟‟School of Engineering, Tohoku University, Japan.
Okada, Y., „„Surface Deformation due to Shear and Tensile Faults in
a Half-space,‟‟ Bull. Seismol. Soc. Am., 75, 1135-1154.
Shigihara, Y., Fujima, K., Kosa, K., Hirooka, A., Nii, S., Shoji, G.,
Miyajima, M., and Ono, Y. (2009), „„Numerical Calculation of2004 Indian Ocean Tsunami around the Damaged Bridges in the
Northwest Coast of Sumatra Island,‟‟ Journal of Japan Societyof Civil Engineers, Ser. B2, Japan Society of Civil Engineers, 65,
311-315.
Shoji, G., Hiraki, Y., Ezura, Y., Iidaka, M., Fujima, K., andShigihara, Y. (2011), „„Experimental Study on the Mechanism of
Horizontal and Vertical Wave Forces Acting on a Bridge Deck
Subjected to Breaker Bores,‟‟ Journal of Japan Society of Civil
Engineers, Ser. A1, Japan Society of Civil Engineers, 67, (Inreview).
The General Bathymetry Chart of the Oceans (GEBCO),
http://www.gebco.net/ (Accessed on 21 December 2011).
Yeh, H. (2006). „„Maximum Fluid Forces in the Tsunami Run-up
Zone,‟‟ Journal of Waterway, Port, Coastal, and Ocean
Engineering, American Society of Civil Engineers, 132(6),496-499.

- 2054 -