Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanTSUNAMI LOAD EVALUATION BASED ONDAMAGE OBSERVATION AFTER
THE 2011 GREAT EAST JAPAN EARTHQUAKE
Tatsuya ASAI1, Yoshiaki NAKANO2, Tomokazu TATENO3, Hiroshi FUKUYAMA4
Koji FUJIMA5, Yuji HAGA6, Tadashi SUGANO6 and Tsuneo OKADA7
1

Graduate Student, Department of Architecture, The University of Tokyo,
Tokyo, Japan, tasai@iis.u-tokyo.ac.jp
2
Professor, Institute of Industrial Science, The University of Tokyo,
Tokyo, Japan, iisnak@iis.u-tokyo.ac.jp
3
Counselor, The Japan Building Disaster Prevention Association,
Tokyo, Japan, kenbokyo@kenchiku-bosai.or.jp
4
Chief Researcher, Building Research Institute, Tsukuba, Japanfukuyama@kenken.go.jp
5Professor, Department of Civil and Environmental Engineering, National Defense Academy,
Yokosuka, Japan, fujima@nda.ac.jp
6
Senior Technical Adviser, The Japan Building Disaster Prevention Association,
Tokyo, Japan, kenbokyo@kenchiku-bosai.or.jp
7
President, The Japan Building Disaster Prevention Association,
Tokyo, Japan, kenbokyo@kenchiku-bosai.or.jp

ABSTRACT: To design and construct buildings resistive to tsunami loads, quantitative evaluationsof tsunami load applicable to structural design is most essential. The practical design load for tsunami
shelters proposed by The Building Center of Japan in 2004 were examined through surveys ofstructures after the Indian Ocean Tsunami in December 2004. Nonetheless researches on tsunami
load against structures based on damage observations are yet insufficient. In this paper, structures thatexperienced the Great East Japan Earthquake were surveyed, and the relationship between their
damage, strengths, and inundation depth is quantitatively investigated to examine the design load.
Key Words: The Great East Japan Earthquake, Tsunami, Tsunami shelter, Design load

INTRODUCTION
To design and construct buildings resistive to tsunami loads, quantitative evaluations of tsunami load
applicable to structural design is most essential. The design guidelines for tsunami shelters weredeveloped by a task committee under the Japanese Cabinet Office in 2005 referring “Structural Design
Method of Building to Seismic Sea Wave” (Okada et al. 2004a and 2004b), which introduced aformula to compute tsunami loads expected to act on shelters constructed on coastlines (JCO 2005).
The formula was developed primarily based on laboratory tests of 2-dimensional scaled model(Asakura et al. 2000) and examined through surveys of structures after the Indian Ocean Tsunami in516

December 2004 (Nakano 2008). However, since researches on tsunami loads against structures basedon damage observations are yet insufficient and tsunami damage caused by the 2011 Great East Japan
Earthquake was devastating, quantitative evaluations of tsunami loads is currently in urgent need interms of tsunami disaster prevention in the future. The authors therefore made extensive damage
surveys of structures that experienced the tsunami caused by the 2011 Great East Japan Earthquake toinvestigate the relationship between their lateral strength and observed damage, and to verify theappropriateness of the design formula. In this paper, the outline of the damage surveys andinvestigated results on design tsunami loads is presented.

OUTLINE OF DAMAGE SURVEYS
Surveyed areas
Damage surveys were made in Tohoku area (from Hachinohe city in Aomori Prefecture to Soma city in
Fukushima Prefecture as shown in Fig. 1) from the beginning of April through the end of June, 2011.

Hachinohe
Kuji

GoogleTanohata
Taro
MiyakoOtsuchi
Kamaishi
OfunatoRikuzentakata
Kesennuma
Minamisanriku
Ishinomaki / Onagawa
Shiogama / Tagajo
Sendai / Natori
Watari / Yamamoto
Soma

Fig. 1 Surveyed areas
Survey strategy
Surveys were made to review the overall damage in the areas, and to record structural dimension andreinforcement arrangement etc. to further investigate the relationship between their lateral strength andtsunami load that acted on them since they met the following three conditions:(1) The lateral strength of the surveyed structures could be simply estimated based on the structuralproperties obtained on site, because (i)their sectional properties (cross-sectional size, reinforcement
arrangement, etc.) were measured; (ii)their damage (or collapse) mechanism was simple and theboundary between damaged and intact part of the structure was not complicated; and (iii)they were
small and/or regular enough in their plan and height that their lateral strength could be calculated
through simple modeling and assumptions.
(2) The tsunami inundation depth was clearly found on the surveyed site through water marks left onbuilding’s walls, where it was defined and measured as the water depth above the ground level atthe building’s site.
(3) The tsunami load could be simply estimated because the surveyed structures were located in areas
close to the coastlines and the direct effects by tsunami attack were the primary source of the damage.
In this paper, the measured tsunami inundation depth ηm corresponding to the design tsunami
inundation depth h (m), which will be described later, was defined not to be affected by the local water517

splash-up on the front face of buildings. This is because the design tsunami inundation depth isgenerally simulated neglecting local effects of buildings. The measured tsunami inundation depth ηm is,therefore, defined as:(1) the tsunami trace found on a rear or side walls of a building in flatland areas from Ishinomaki city to
Soma city because it was higher on a front face than on the other faces due to water splash-up, and(2) the highest tsunami trace around a building in saw-tooth Sanriku area from Kuji city to Onagawa
town because no major differences in tsunami height were found among traces on all sides ofexterior walls. This is due primarily to the fact that the flow velocity was not high enough at its
maximum inundation depth in Sanriku area to cause water splash-up on the front face as evidenced
by the tsunami videos recorded during the event.
Detailed information recorded on investigated structures
Photo 1 shows the typical structures investigated in this study. Considering three conditions fordetailed surveys described earlier, more than 130 structures including (a)buildings with simple
configuration, (b)fence walls, (c)RC or masonry columns (bridge piers, gate piers, etc.), (d)stonemonuments, (e)seawalls, and (f)steel fences, were investigated and detailed structural data werecollected. They include (1)locations with GPS data, (2)topographical information of the site, (3)use
and type of structure (RC, CB (concrete block), stone, etc.), (4)damage pattern, (5)tsunami inundation
depth ηm, (6)structure and/or member dimension (B x D x H, wall thickness, etc.), (7)reinforcement
arrangement (diameter, spacing, cover concrete depth, etc.), (8)general view photos, and (9)structuralconfigurations.

Collapsed building (a)Survived building (a) Collapsed fence wall (b) Survived fence wall (b)(Watari, CB)(Ofunato, RC)(Rikuzentakata, RC 1-story) (Onagawa, RC 4-story)

Collapsed Railway bridge (c)(Tanohata, RC)

Collapsed column (c) Overturned monument (d) Collapsed seawall (e)(Watari, CB)(Watari, stone)(Yamada, RC)

Photo 1 Typical investigated structures (Letters (a) to (e) show categories of structures)

EVALUATION OF LATERAL STRENGTH OF INVESTIGATED STRUCTURES
Lateral strength of buildings
The lateral strength of the buildings categorized in (a) as exemplified in Photo 1 is evaluated based on
the first level screening of seismic evaluation procedure which is generally applied in Japan (JBDPA

518

2001), using the measured structure dimension and the material test results. Buoyant forces are
neglected in the evaluation because overturned buildings are not discussed in this paper.
Lateral strength of simple structures
According to the damage and failure mode observed, the cracking strength Mc, the flexural yielding
strength My, the ultimate flexural strength at rebar fracture Mu, the overturning strength MOT, thesliding strength Ps are calculated for simple structures categorized in (b) through (e) described earlier,using the conventional equations widely applied in Japanese design practice and the material test
results. MOT is applied for the overturned structures such as gravity-type seawalls, gate piers, stonemonuments, etc. and Ps is applied for the slid stone monument. The buoyant force is neglected in
calculating MOT and Ps herein, because it is negligibly small when a tsunami applies impulsive force
to a structure.

COMPARISON BETWEEN TSUNAMI LOAD AND OBSERVED DAMAGE
Definition of tsunami pressure distribution acting on structures
In the guidelines (JCO 2005), the design tsunami load is defined by Eq. (1). In the subsequent
investigations, Eq. (2) that is analogous to Eq. (1) is first defined, and the water depth coefficient a isevaluated (Nakano 2008) setting the lateral strength of the investigated structures equal to the tsunami
load computed from Eq. (2):qz = ρ g ( 3 h - z )pz = ρ g ( a ηm - z )(0 < z < 3h)(0 < z < aηm)

(1)
(2)

where qz (kN/m2) and pz (kN/m2) are the tsunami pressure acting on a structure at a distance z (m)above the ground level, defined in the guidelines (JCO 2005) for design load and defined in this study
to investigate a rational value of a, respectively; ρ (t/m3) is the mass per unit volume of water (1.0
assumed herein); g (m/s2) is the gravity acceleration; h (m) and ηm (m) are the design tsunami
inundation depth and the measured tsunami inundation depth, respectively; and a is the water depth
coefficient defined by the ratio of the water depth aηm equivalent to the structure’s strength to themeasured tsunami inundation depth ηm (i.e., a = aηm /ηm ).
Figure 2 illustrates the background concept employed in Eq. (1). The design tsunami pressure
distribution acting along the structure’s height is assumed a triangular shape with the height reaching 3
times of the design tsunami inundation depth h (i.e., the pressure at the bottom is assumed 3 times of
the hydrostatic pressure) based on the experimental results (Asakura et al. 2000). In calculating thecoefficient a, two typical cases of inundation depth and structure’s height, which can be found in theFig. 2 Design tsunami pressure
distribution (JCO 2005)

structure

Case 2structure

Case1

Fig. 3 Measured tsunami inundation depth η m, structure’s height H,
and tsunami pressure distribution pz

519

guidelines (JCO 2005), are taken into consideration as shown in Fig. 3 since they are the basic patterns
of tsunami attack to existing structures in the surveyed areas. The tsunami pressure is uniformly
reduced by the ratio α defined as [1 - (opening area)/(loaded area)] as shown in Fig. 3 when thebuilding has openings.
Procedure to compute the water depth coefficient a
The coefficient a can be computed assuming that the lateral strength of an investigated structure isequal to the overall tsunami load acting on it under the pressure distribution along its height defined by
Eq. (2) and Fig. 3. The coefficient a therefore denotes the ratio of the equivalent water depth aηmcorresponding to the structure’s lateral strength under a triangular hydrostatic pressure profile to themeasured tsunami inundation depth ηm. If the coefficient a categorizes collapsed and survived structuresat its value of 3, one can say that Eq. (1) with a equal to 3 is a rational design formula to compute thetsunami load. The procedure to compute the coefficient a is described in detail below (Nakano 2008).
1. Compute the lateral strength of investigated structures considering their failure mode as shown in
the previous chapter.
2. Then compute shear force or bending moment acting at the failure point u (defined as the distance
between the failure point and the ground surface) assuming the tsunami pressure distribution as
defined in Eq. (2). Setting the force or moment at the height u equal to the lateral strength obtainedin step 1. above, evaluate the equivalent water depth aηm corresponding to the strength. Note thatthe tsunami pressure above structures is neglected and the depth aηm is evaluated assuming thetrapezoidal instead of triangular pressure distribution in computing the force or moment as shownin case 2 of Fig. 3.
3. Finally compute the coefficient a, which is defined as the ratio of equivalent water depth aηm tomeasured tsunami inundation depth ηm (i.e., a = aηm /ηm).
Tsunami load evaluation based on structure’s damage
Of all surveyed structures, 43 simple structures and 8 RC buildings are employed to evaluate thecoefficient a. To overview the relationship between damage, measured tsunami inundation depth ηm,and other data, they are plotted from north to south in Fig. 4, starting from left, together with theirstructural type, height, 0.5ηm, and 1.5ηm. Note that 0.5ηm, ηm, and 1.5ηm in the figure correspond to 0.5,
1.0, and 1.5 in coefficient a. A dashed line in Fig. 4 shows the boundary between ria coast area
(Sanriku area) and flatland area such as Sendai plain. As can be found in the figure, the measured
tsunami inundation depth ηm in Sanriku area is found generally higher than that in flatland area. Eachplot in Fig. 4 explains that the collapsed structures (designated as x and *) were exposed to the force
higher than the hydrostatic force due to the water depth aηm (corresponding to the structure’s strength)plotted in the vertical axis, while the survived structures (designated as  and ) were exposed to theforce lower than that, and the cracked structures (designated as ) were just exposed to the hydrostaticforce due to aηm. Therefore, the actual tsunami load can be found as the boundary value between
collapsed (x and *) and survived ( and ) structures.
In general, structures with high coefficient a survived and those with low coefficient a collapsed
as shown in Fig. 4. Although one may expect higher value of a in flatland area due to higher flow
velocity, no such a tendency is found and the topographical difference may not be the major parameterto find a rational value of a.
It should be noted, however, that some structures located just close to the coastlines such asseawalls collapsed even though their strengths are high as shown in the hatched area of Fig. 4.
Assuming that the tsunami load differs depending on the site environment, the surveyed structures arethen divided into two groups, i.e., those in areas with or without structures on the sea side that are
deemed effective to reduce the tsunami power such as breakwater. Fig. 5 shows the relationshipbetween the coefficient a and the measured tsunami inundation depth ηm for each area with different
site environment.

520

30

Structure’s height
Measured inundation depth ηm (a=1.0)
1.5 ηm (a=1.5)
0.5 ηm (a=0.5)

25
20

Values in vertical axis correspond to aηmSurvived (simple structures)
Cracked(simple structures)
Collapsed (simple structures)
Survived (buildings)
Collapsed (buildings)

15
10
5
0

Tanohata
Railway bridge
Tanohata
Sea wall
YamadaSea wall
YamadaSea wall
YamadaSea wallOtsuchi
Sea wall
Kamaishi
RC 3-story
Kamaishi
CB fence wall
OfunatoCB fence wall
Ofunato Stone monument
OfunatoCB fence wall
OfunatoRC 2-story
OfunatoRC fence wall
OfunatoRC fence wall
OfunatoCB fence wall
Rikuzentakata RC 5-story
Rikuzentakata RC 1-story
Rikuzentakata RC 3-story
Kesennuma RC fence wall
Kesennuma RC fence wall
Onagawa
RC 4-story
Onagawa
RC 2-story
Onagawa
RC 4-story
Ishinomaki RC fence wall
Ishinomaki RC fence wall
Shiogama
CB fence wall
SendaiRC fence wall
SendaiRC fence wall
SendaiRC fence wall
SendaiRC fence wall
NatoriRC column
WatariCB column
WatariStone monument
WatariCB fence wall
Yamamoto CB fence wall
Yamamoto Stone gate pier
Yamamoto Stone gate pier
Yamamoto Stone monument
Yamamoto Stone monument
Yamamoto Stone monument
Yamamoto Stone monument
Yamamoto CB fence wall
Yamamoto CB fence wall
Yamamoto CB fence wall
Yamamoto CB fence wall
Yamamoto
RC column
Yamamoto RC fence wall
Yamamoto RC fence wall
Yamamoto RC fence wallSoma
CB wall

Mesured inundation depth ηm and equivalent water depth aηm (m)Areas without structures
to reduce tsunami power▼

Fukushima Pref.
South

Miyagi Pref.

Iwate Pref.
North
SANRIKU AREA

FLATLAND AREA

Fig. 4 Relationship between measured inundation depth, equivalent water depth and structure’s damage
16
Survived (Simple structures)
Cracked (Simple structures)
Collapsed (Simple structures)
Survived (Buildings)
Collapsed (Buildings)

14
12

Measured tsunami inundation depth ηm(m)Measured tsunami inundation depth ηm(m)16Collapsed (Simple structures)

14
12

10

10

8
6

*1
*2

4

*2

2
0

8
6
4
2
0

0.0

1.0
2.0
Coefficient a (aηm/ηm)

3.0

0.0

1.0
2.0
Coefficient a (aηm/ηm)3.0(a) Areas with structures to reduce tsunami power (b) Areas without structures to reduce tsunami power
Fig. 5 Computed coefficient a vs. measured tsunami inundation depth ηm
Figure 5(a) shows structures other than those plotted in the hatched area in Fig. 4. They are locatedin Kamaishi city, Ofunato city, and Onagawa town where breakwaters are provided at its bay mouth;
Rikuzentakata city, Ishinomaki city, Sendai city, etc. where breakwaters and seawalls which areconsidered high enough to reduce the tsunami power are provided; Kesen-numa city where the bay
holds Hachigasaki area off the coast which served as a natural breakwater. Note that the521

data denoted by *1 are structures oriented parallel to the direction of the tsunami flow and survived
despite the coefficient a was much smaller than 1 due to the water pressure acting on both front andrear sides of them. Also note that the structures denoted by *2 are stone gate piers embedded in the
ground but its contribution to the overturning resistance is neglected for simple calculation andtherefore their actual coefficient a shuold be larger than the value shown in Fig. 5(a). Considering
those mentioned above, Fig. 5(a) shows that the coefficient a to discriminate between collapsed andsurvived structures is around 1 (i.e., equivalent to the measured tsunami inundation depth ηm) when themeasured depth ηm is smaller than 10m. Fig. 5(a) also shows that the buildings whose coefficient a issmaller than 1 survived when ηm is larger than 13m. It implies that the tsunami load was smaller thanthe hydrostatic force of inundation depth ηm, because the water had flown all around the buildings
when the inundation depth reached ηm and loaded on all sides of the building.
Figure 5(b) shows structures plotted in the hatched area in Fig. 4. They are located in areas
without structures to reduce the tsunami power. Fig. 5(b) shows that the coefficient a to discriminate
between collapsed and survived structures is above 1.7. Note that the upper bound of the coefficient acannot be determined from Fig. 5(b) because survived structures are not plotted in Fig. 5(b). Table 1
summarizes the results found in the above discussions.
It should be noted that the results based on the damage observations after the 2004 Indian Ocean
Tsunami (Nakano 2008) concluded that the boundary coefficient a lies in the range of 2 to 2.5, which
is much larger than the result obtained in this study. This is probably because structures investigatedafter the Indian Ocean Tsunami were located just close to the coastlines with no built environment to
reduce tsunami power and high tsunami waves directly attacked the structures.
Table 1 Coefficient a to discriminate collapsed and survived structures

Coefficient a

Areas with structures
to reduce tsunami power

Areas without structures
to reduce tsunami power1** a < 1 when ηm > 13

> 1.7

VALIDATION OF THE COEFFICIENT a BASED ON DRAG FORCE
Drag force evaluation
In the previous discussions, the tsunami pressure distribution acting along the structure’s height isassumed a triangular similar to the hydrostatic pressure as expressed by Eq. (2), which is supposed tobe applied for impulsive force on onshore structures. However the 2011 Great East Japan Earthquake
evidenced through numerous recorded videos that structures were gradually inundated and may havebeen affected more significantly by drag force rather than impulsive force. In this paper, the tsunami
load is evaluated based on drag force and compared to the result of the previous chapter.
The drag forces FD is generally expressed by Eq. (3).
FD =1
ρC u 2 AD
2 D(3)where FD (kN) is the drag force; ρ (t/m3) is the mass per unit volume of water (1.0 assumed herein);
CD is the drag coefficient; u (m/s) is the flow velocity; and AD (m2) is the loaded area of a structure in
the plane normal to the direction of flow. Assuming the drag coefficient CD 2.0 for the quadrilateralstructures surveyed (JSCE 1971), Eq. (3) leads to Eq. (4).
FD = ρ u 2 AD

522

(4)

Case1Case 2

Fig. 6 Measured inundation depth ηm, structure’s height H, and tsunami pressure distribution ω
Assuming that the tsunami pressure is uniformly distributed as shown in Fig. 6, the pressure ωR
under which the overall tsunami load is equal to the structure’s strength considering their failure
mechanism is obtained. Then the tsunami load V equal to the structure’s strength is expressed by Eq. (5).
Note that the tsunami pressure above the structures is neglected as shown in case 2 of Fig. 6.
V = ωR AD(5)

Setting FD equal to V, the flow velocity uR equivalent to the structure’s strength is expressed by
Eq. (6).
uR = ωR / ρ(6)Then the Froude number FrR equivalent to the structure’s strength is expressed by the equivalent
flow velocity uR and the measured tsunami inundation depth ηm (Eq. (7)).

FrR =

uR
gη m

=

ωR / ρgη m(7)

From the discussion above, the equivalent flow velocity uR and the Froude number FrR are
obtained from Eq. (6) and Eq. (7) using the equivalent tsunami pressure ωR. To estimate the actual
tsunami pressure, flow velocity, and Froude number, the equivalent values to discriminate between
collapsed and survived structures are estimated as discussed earlier.
Tsunami load evaluation based on relationship between structure’s damage and drag force
Figure 7 shows the equivalent tsunami pressure ωR, flow velocity uR, and Froude number FrR obtained
from Eqs. (5), (6), and (7). As was done earlier in this study, the structures are divided into two groups,
i.e., areas with or without structures to reduce the tsunami power. Then they are plotted from north tosouth in Fig. 7, starting from left, showing their structural type, damage category, and the equivalentwater depth aηm. Alphabets in Fig. 7 show the observed failure mode of each structure: “Y”, “U”, “S”,
and “O” correspond to rebar yielding, rebar fracture, sliding, and overturning, respectively. To
estimate the tsunami pressure, flow velocity, and Froude number, the boundary values to discriminate
between collapsed and survived structures are found and hatched as shown in Fig. 7. Note that thehatched horizontal lines in the area without structures to reduce the tsunami power corresponds to thelower bound because no data on structure survived in the area are available in this study.
The tsunami pressure acted on the structures, as shown in Figure 7(a), is more than 85kN/m2
where they have no structures to reduce tsunami power, while it lies in the range of 15 to 30kN/m2
where they have structures to reduce tsunami power, excluding the data denoted by *1.
The flow velocity, as shown in Fig. 7(b), is more than 9m/s where they have no structures toreduce tsunami, while it lies in the range of 4 to 6m/s where they have structures to reduce the tsunami

523

Equivalent flow velocity uR (m/s)

Equivalent tsunami pressure ωR (kN/m2)

0
14

0
3

Tanohata
Railway bridge
Tanohata
Sea wall
YamadaSea wall
YamadaSea wall
YamadaSea wallOtsuchi
Sea wallNatoriRC column
WatariCB column
WatariStone monument
WatariCB fence wall
Kamaishi
RC 3-story
Kamaishi
CB fence wall
OfunatoCB fence wall
Ofunato Stone monument
OfunatoCB fence wall
OfunatoRC 2-story
OfunatoRC fence wall
OfunatoRC fence wall
OfunatoCB fence wall
Rikuzentakata RC 5-story
Rikuzentakata RC 1-story
Rikuzentakata RC 3-story
Kesennuma RC fence wall
Kesennuma RC fence wall
Onagawa
RC 4-story
Onagawa
RC 2-story
Onagawa
RC 4-story
Ishinomaki RC fence wall
Ishinomaki RC fence wall
Shiogama
CB fence wall
SendaiRC fence wall
SendaiRC fence wall
SendaiRC fence wall
SendaiRC fence wall
Yamamoto CB fence wall
Yamamoto Stone gate pier
Yamamoto Stone gate pier
Yamamoto Stone monument
Yamamoto Stone monument
Yamamoto Stone monument
Yamamoto Stone monument
Yamamoto CB fence wall
Yamamoto CB fence wall
Yamamoto CB fence wall
Yamamoto CB fence wall
Yamamoto
RC column
Yamamoto RC fence wall
Yamamoto RC fence wall
Yamamoto RC fence wallSoma
CB wall

Failure mode

Equivalent Froude number FrR

power. To validate the estimated flow velocity in Fig. 7(b), it is compared to the velocity of thefloating objects recorded in the tsunami videos in the following 7 points: Kamaishi city (2 points),
Ofunato city (2 points), Onagawa town (2 points) in Sanriku area and Natori city (1 point) in flatlandarea. All of them have structures to reduce tsunami power such as breakwaters or seawalls. Note that

Areas without structures120
to reduce tsunami power
Survived

鉄 防 防 防 防 防Cracked

20

4

石

0.5

UOUUUOUUOUSanriku area Flatland area

Collapsed (simple structures)

石

UOU
p

U
(

U
p

1

Y
U

Sanriku area

524
UUUU

Survived

*1

6
*1

)

*1

UU

Collapsed (buildings)

Areas with structures
to reduce tsunami power

100

80

(a) Tsunami pressure

60

40
*2

*1

鉄 防 防 防 防 防 R C 石 C R C C 石 C R R R C R R R R R R R R R R C R R R R C 石 石 石 石 石 石 C C C C R R R R C

12(b) Flow velocity

10

8

*2

*1

2

石 石 石 石 石 石

p

OO
(

g)

2.5

(c) Froude number

2

1.5

*1
*2

0
S OUUUUUUYUFlatland area

Fig. 7 Relationship between equivalent tsunami pressure, flow velocity, Froude number and structure’s damage

50

100 150
Time [s]

200

250 0

50

100 150
Time [s]200

Dai in Ofunato

250 0

50

100 150
Time [s]Flow velocity [m/s]Nonoda in Ofunato Ohara in Onagawa Onagawa in Onagawa Konuma in Natori
16
16(Not the first attack)
14
14
12
12
10
10
8
8
6
6
4
4
2
2
0
0
0
50 100 0
50 10050 100 0
50 100 150 200 0
Time [s]Time [s]Time [s]Time [s]

200

16
14
12
10
8
6
4
2
0
250

Inundation depth [m]Minato-machi in Kamaishi

Inundation depth [m]Flow velocity [m/s]

Uogashi in Kamaishi
16
14
12
10
8
6
4
2
0
0

Inundation depth at
Front
Side or Rear
All sides
Flow velocitty

Fig. 8 Measured flow velocity and inundation depth derived from the tsunami recorded videos
one record in Onagawa town corresponds to the second or later attack, while the other 6 records are
confirmed the first attack since the first arrival of tsunami is recorded. The measured velocities areplotted in Fig. 8 only when the floating objects appear on the videos. As can be found in Fig. 8, theflow velocity lies in the range of 3 to 6m/s regardless the inundation depth and consistent with theestimated result (4 to 6m/s) based on drag force.
The Froude number Fr, as shown in Fig. 7(c), is more than 1.27 where they have no structures toreduce tsunami power. On the other hand, it lies in the range of 0.5 to 0.65 in Sanriku area and it isaround 0.8 in flatland area where they have structures to reduce tsunami power. The Froude numbers
in Sanriku area is rather smaller than that in flatland area with structures to reduce tsunami power
although the flow velocity in Sanriku area is the same or even higher than that in flatland area.
Therefore, the flow velocity in Sanriku area is found not so high despite the high inundation depth.
Evaluation of the coefficient a based on drag force
Since the estimated flow velocity is found consistent with that derived from the tsunami recorded
videos, the coefficient a is then evaluated in terms of the Froude number obtained earlier andcompared to those previously calculated.
Given that the equivalent water depth aηm is lower than a structure with no openings, the wave
force Fx under a triangular hydrostatic pressure profile by Eq. (2) and the drag force FD can be
expressed as Eq. (8) and Eq. (9), respectively, for a unit width (1m) of a structure.
1
a2
Fx = ( aη m ×1) aρgη m =η m 2 ρg
2
2

525

(8)

FD = ρu 2 AD(9)

= ρu 2 ( ηm × 1) = Fr2 ηm 2 ρg

Setting Fx equal FD, Eq. (10) is obtained. Then the relationship between the coefficient a andFroude number Fr is expressed by Eq. (11).
a2
= Fr2
2
a = 2 × Fr

(10)
(11)

Table 2 shows the result of the coefficient a calculated using Eq. (11) with the Froude number
estimated above. The coefficient a of Table 2 in each case with and without structures to reducetsunami power roughly corresponds to the result in Table 1.
Table 2 Froude number Fr and coefficient a to discriminate collapsed and survived structures
estimated based on drag forces
Areas with structures
to reduce tsunami power

Areas without structures
to reduce tsunami power

Sanriku area

Flatland area

Sanriku area

Flatland area

Froude number Fr

0.5 to 0.65

0.8

> 0.9

> 1.27

Coefficient a ( = 2 Fr )0.71 to 0.92

1.13

> 1.27> 1.8

CONCLUSIONS
To verify the design load specified in the Japanese guidelines for tsunami shelters, the coefficient a isevaluated based on the damage observations after the 2011 Great East Japan Earthquake. The major
findings can be summarized as follows:
1. The water depth coefficient a is larger than 1.7 in the areas without structures on the sea side thatare deemed effective to reduce the tsunami power, while it is around 1 (or smaller especially when
ηm is larger than 13m) in the areas with structures to reduce the tsunami power.
2. According to the discussion based on drag force, the tsunami pressure, the flow velocity, and the
Froude number are more than 85kN/m2, 9m/s, and 1.27 respectively, in the areas without structures
to reduce the tsunami power. In the areas with structures to reduce the tsunami power, they lie in
the range of 15 to 30kN/m2, 4 to 6m/s, and 0.5 to 0.65 in Sanriku area and 0.8 in flatland area,
respectively. The coefficient a computed based on the results above roughly correspond to the resultof conclusion 1.
3. The coefficient a obtained in this study is much smaller than the results obtained from the damage
observations after the 2004 Indian Ocean Tsunami. This is probably because structures investigatedafter the Indian Ocean Tsunami were located just close to the coastlines with no built environment
to reduce tsunami power and high tsunami waves therefore directly attacked the structures.
4. It should be noted therefore that the design lateral load for tsunami shelters should be determinedfurther considering evidences obtained in other events and experimental researches as well as thosefound in this study.

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ACKNOWLEDGMENTS
This paper includes discussions made under “Investigation on Building Code Development in
Tsunami Hazard Areas,” granted by the Ministry of Land, Infrastructure, Transport and Tourism(Principal Investigator: Yoshiaki NAKANO, Professor at IIS, The University of Tokyo). The fieldsurveys were made under extensive cooperation with Prof. Nishida T. et al. of Akita Prefectural
University, Research Associates Takahashi N. and Choi H. et al. of IIS, The University of Tokyo. The
authors gratefully acknowledge their valuable supports to complete the research project.

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