The 28th International Tsunami Sysmposium (ITS),
22 August 2017, Bali-Flores, Indonesia

Quantitative effect of uncertainty intsunami hazard on building risk
assessment
Yo Fukutani1 , Anawat Suppasri2 , Fumihiko Imamura2
1Kanto Gakuin University
2International Research Institute of Disaster Science, Tohoku University

Objective and Targets【Objective】◆ This study demonstrate thatquantitative effect of uncertainty
in tsunami hazard variability onbuilding risk assessment.

Japan island

Tohoku area

Kesennuma
気仙沼◆Uncertainty assessment is anindispensable work to understandthe risk.

【Targets】◆Targets of the risk assessment
arebuildings
locatedinKesennuma city, Sendai city andSoma city in Tohoku area, Japan.

仙台SendaiSoma
相馬

Miyagi Prefecture
Fukushima PrefectureEvaluation methods for hazard uncertainty◆ Epistemic uncertainty

Alternative models are captured by branches of logic tree.

This uncertainty arises from a lack of knowledge or data.
MomentLog normal
計算波高のAsperity
position
Returnperiod
magnitude
Sourcearea
マグニチュード範囲 アスペリティ位置 平均発生間隔 standard deviation
波源域
対数標準偏差σNorthern
三陸沖北部
Sanriku
earthqauke 1/3
プレート間大地震

Mw=8.21/3

Mw=8.3

JTN1_1※繰り返し発生する地震

1/3

Mw=8.4

1/3

North
北端

0.25

1/3

Center
中央

0.5

South
南端

0.25

1/3

58 58年
years
9797年
years

0.40

σ = 0.223

0.35

σ = 0.300

0.20

197
years
197年

0.05

σ = 0.372

対数標準偏差Truncatedvalueの打切り

0.75

±2.3σ

0.25±10σσ = 0.438◆ Aleatory uncertainty

This uncertainty is difference between a model prediction and observed data.
Aleatory uncertainty can bequantified by a probability
density function.

P.D.F

P.D.F
Information for aleatory uncertainty isincorporated into the logic tree.

Targetearthquake
zonesandand logic
Targetearthquake
zones
logictrees
trees
波源域
Source三陸沖北部
プレート間大地震◆We selected elevenearthquake zones along
the Japan trench
including the March 11
Tohoku Earthquake
type fault

JTN1_1※繰り返し発生する地震

MomentMomentmagnitude

1/3
1/3
1/3

Mw=8.4

North
北端

0.25

1/3

中央
Central

0.5

1/3

南端
South

0.25

58年
97年

Mw=7.5※繰り返し発生する地震
以外の地震

Mw=7.621年

宮城県沖地震Mw=7.3

15年

JTN2

Mw=7.4

Central中央

中央Central

14年

38年

North
北端

37年

Mw=7.9Central中央

109年※繰り返し発生する地震

Mw=8.0

南端
South

161年

三陸沖南部海溝寄り地震

Mw=7.4

中央
Central42年

Mw=7.6

宮城県沖＋三陸沖南部海溝寄り連動地震

Mw=8.0

North
北端

66年

Mw=8.1

中央
Central

218年

三陸沖北部から房総沖の海溝寄りのプレート内大地震（正断層型地震）

JTNR

福島県沖プレート間地震

JTS1

過去110年で4回発生

過去220年で3回発生

21年

Mw=7.5※繰り返し発生する地震
以外の地震

JTT

過去127年で9回発生

53年

Mw=7.5
Mw=7.8三陸沖北部から房総沖の海溝寄りのプレート間大地震（津波断層）

過去412年で4回発生

10年

JTN3_1

JTN2+JTN3

設定根拠（※）

197年

JTN1_2

JTN3_2

Target earthquake zone (above figure)and logic trees (right figure)

Mw=8.3

1/3再現期間・Return
Period 信頼区間の平均発生間隔

Mw=7.4※繰り返し発生する地震◆Numbers of all
branches in the logic
trees are 1800.

Mw=8.2

アスペリティ位置
position

三陸沖北部
プレート間大地震

三陸沖南部海溝寄り地震◆We constructed logic
trees corresponding toeach earthquake zone.

Asperity

マグニチュード範囲
magnitude

過去127年で3回発生

93年

Mw=8.2

南端
South

1260年

Mw=7.9

North
北端

56年

Mw=8.0Central
中央

103年

Mw=8.1

南端
South

191年

Mw=8.1

North
北端

174年

Mw=8.2Central中央

575年

Mw=8.3

南端
South

3324年

中央
Central

206年

過去218年で1回発生

過去400年で4回発生

過去575年で1回発生

89年

Mw=7.3

Mw=7.4
Mw=7.5582年

茨城県沖地震Mw=7.4

15年

IBRK

Mw=7.5

中央
Central

26年

浅部の北端
North

45年

Mw=7.60.20

東北地方太平洋沖地震

Mw=8.90.20

中間Middle

335年

TOHOKU

Mw=9.0

0.20
0.20

浅部の中央
Central

600年

中間Middle

1148年

Mw=9.1

0.20

浅部の南端
South

過去412年で2回発生

過去127年で5回発生

過去2400年で4回発生

Targetearthquake
zones andlogic trees
Tsunaminumericalsimulation◆The fault parameters are determined based on
the conditions of every branches of the logic trees.
◆Using the fault parameters, we implemented
tsunami numerical simulations and calculated
maximum tsunami height at the target points.
【Earthquake fault parameters】
Longitude, Latitude, Length,
Width, Dip, Rake, Slip, Depth,
Strike (9 parameters)( UNESCO, 1997)
Governing equation

2D non-linear shallow water equation（Tohoku University TUNAMI model）

Coordination system

Lon-Lat coordination

Numerical integration method

Staggered leap-frog differential method

Mesh size

810m → 270m → 90m → 30m → 10m

Time step

0.9s → 0.3s → 0.1s → 0.03s → 0.01s

Ground displacement

Okada(1985) equation

Calculation condition

SomaportElevation

Calculation area

Computing
stochastictsunami
tsunami heightin Soma
port port
Computingstochasticheightin Soma
◆After statistical treatment of the tsunami numerical simulation results and 1800
logic trees, we can obtain each fractile hazard curves and Simple average curve.
◆We can understand tsunami height uncertainty derived from the uncertainty ofeleven earthquakes.
1

Output point of waveforms
and hazard curves

0.05 fractile curve

Annual Exceedance
Probability
年超過確率(year-1)

0.50 fractile curve
Simple average curve

0.1

0.95 fractile curve
0.01

0.001

4m

0.000109m
510
津波波高Tsunami
Height(m)(m)

15Tsunami hazard curve off the Soma port
( at Red point in the right figure)Soma portComputing
stochastictsunami
tsunami heightin Somaport port
Computingstochasticheightin Soma◆By using the tsunami hazard curves, we can specify an earthquake fault thatgenerate tsunami with some return period.
No.

The return period of such anearthquake that causes a 7.1m
tsunami is 1566 years.
1Source
nameMoment
magnitude

Position ofasperity

Tsunamiheight (m)Return period(years)0.05 fractile curve

Annual Exceedance
Probability
年超過確率(year-1)

0.50 fractile curve
Simple average curve

0.1

0.95 fractile curve
0.01

0.001

1566
years
0.000105 7.1m 10
津波波高
TsunamiHeight(m)(m)

15

Numerical simulation results

Return period estimated from tsunami hazard curve (0.50 fractile curve)Probabilistic
inundationassessment
Tsunamitsunami
inundationassessment◆We made a probabilistic tsunami hazard map by conducting tsunami
inundation simulation using fault parameters of a specified earthquake withsome return period.

○●Soma port
20m water depth
10m water depth

Annual Exceedance Probability

Risk assessment point○ Output point of tsunami hazard curve (at water depth 20m)
Hazard curve output point● Output point of tsunami hazard curve (at water depth 10m)
2011 Tohoku Tsunami area
10m water depth (Corr: -0.92)
2011 Tohoku Tsunami area

Return period 200 years
Return period 600 years
Return period 1200 years

20m water depth (Corr: -0.60)
50m water depth (Corr: -0.63)

Tsunami inundation depth (m)確率論的津波ハザードマップ
Probabilistic
tsunami hazard map Tsunami hazard information at risk assessment point

Probabilistic
inundationassessment
Tsunamitsunami
inundationassessment◆In the same way, we implemented tsunami inundation assessment for Sendai
city and Kesennuma city.
◆The area of tsunami inundation spread as the return period is longer.

Sendai city

Kesennuma city

Return period 200 years

Return period 200 years

Return period 700 years

Return period 700 years

Return period 1500 years

Return period over 1500 years

Quantificationofoftsunami
tsunamirisk
risk using
using tsunami hazard
Quantification
hazardand
andfragility
fragility

20m water depth (Corr: -0.60)
50m water depth (Corr: -0.63)

Tsunamiinundation
inundationdepthdepth (m)(m)
TsunamiReinforced concrete
Steel
Brick
Wood

Tsunami inundation depth (m)Reinforced concrete
Steel
Brick
Wood

Annual Exceedance Probability

10m water depth (Corr: -0.92)

Damage probability (%)

Risk is the product of severity of damage and its generation probability.
Therefore, area below risk curve is an expected value of tsunami risk.
年超過確率（発生確率）
Exceedance Probability
AnnualDamage probability

Probability
Annual Exceedance
Probability
Annual Exceedance◆We can derive the relationships between damage probability and generation probability
by eliminating tsunami inundation depth from tsunami hazard and fragility curve.

津波リスクの定量化
Quantificationof tsunami risk

3

Integration 2.5
関数を積分∫ 𝑃 𝑅 𝑑𝑅2

𝑌y ==P(R)
𝑃(𝑅)

1.5
1
0.5

面積
Area
DamageProbability
建物の損害確率
DamageProbability

0
鉄筋コンクリート造
（RC造）

RC

鉄骨造

（S造）
Steel

れんが造

（B造）
Block

木造（W造）Wood

Quantification of tsunami
risk usingResults
tsunami hazard and fragility
CalculationKesennuma
気仙沼(5 percentilehazardhazard)(a)Expected
Invaluecaseofoftsunami
usingrisk
5 percentile

仙台SendaiSoma
相馬◆ There are big differences theorders of values listed in the threegraphs.
◆ The risk of steel buildings inSendai and Kesennuma is lower than
the risk of concrete buildings inSoma.

Annual expected tsunami loss ratio (%/year)

1.00E-04

1.00E-05

1.00E-06
Wood Brick Wood Brick Wood Steel BrickRCSteelRCSteelRCSoma Soma Kesen Kesen Sendai Soma Sendai Soma Kesen Kesen SendaiSendai
numa numa
numa numa

10 times(b)
caseofofusing
percentile
hazardExpectedInvalue
tsunamirisk50(50percentile hazard)
1.00E-03

1.00E-04

1.00E-05

Wood Brick Wood Wood Steel Brick BrickRC

Steel SteelRCRC

Soma Soma Kesen Sendai Soma Kesen Sendai Soma Kesen SendaiKesen Sendai
numanumanuma
numa

10 times(c)
Invaluecaseofusing
95(95percentilehazard
In caseof ofusing
95riskpercentile
hazardExpectedtsunami
percentilehazard)
1.00E-02

1.00E-03

The tsunami risk cannot be explainedby only fragility assessment.
We clearly showed uncertainty oftsunami risk due to hazard variability.

1.00E-04
Wood Brick Wood Wood Steel Brick BrickRC

Steel Steel

RCRC

Soma Soma SendaiKesen Soma Kesen Sendai Soma Kesen SendaiKesen Sendai
numa
numa
numa
numa

1.00E-05

Quantification of tsunami
risk usingResults
tsunami hazard and fragility
Calculation
1.00E-06

Wood Brick Steel95(%*year-1 )Kesennuma
気仙沼

9595

RC95

Wood Brick Steel
505050RC

Wood Brick Steel505(c)(a)Kesennuma city
津波リスクの期待値（気仙沼）Wood Brick Steel

RC

55RC
51.00E-02

仙台SendaiSoma相馬◆In any three cities and building
structures, there is a difference of
100 times from 5 percentile
hazard to 95 percentile hazard.

Annual expected tsunami loss ratio (%/year)

1.00E-03
1.00E-04
1.00E-05

1.00E-06
95(%*year-1 )9595(a)(b)

95

Wood Brick Steel

50

5050

RC50

Wood Brick Steel

55RC

55

Wood Brick Steel

RCSendai city
津波リスクの期待値（相馬）1.00E-02

1.00E-03
1.00E-04
1.00E-05

1.00E-06
Wood Brick Steel95(%*year-1 )

95

95(c)
(b)

RC
95

Wood Brick Steel
50

5050

RC50

5555Somacity
Somacity
津波リスクの期待値（仙台）1.00E-02
1.00E-03
1.00E-04

1.00E-05
1.00E-06

Wood Brick Steel
95

9595

RC95

Wood Brick Steel
50

5050

RC50

Wood Brick Steel
555RC
5

SummarySummary◆ By combining a probabilistic tsunami inundation assessment and fragility
assessment, we can derive a risk curve and quantify tsunami risk considering
uncertainty.
Probabilistic tsunami height assessment

Fragility assessment

Risk quantification and uncertainty assessment

5 percentile
Average

0.1

50 percentile
95 percentile

0.01

0.001

(b)
0.0001
0.00

Reinforced
concrete
鉄筋コンクリート造
Steel鉄骨造
Brickれんが造
木造Wood1.0
Probability (%)
Damage損害確率

Exceedance
Annualprobability
exceedanceProbability
Annual10.8

value
tsunami5risk(5 percentile
hazard)(a)Expected
In caseofof using
percentile
hazard
1.00E-04

1.00E-05

0.6
0.4

1.00E-06
Wood Brick Wood Brick Wood Steel Brick RC

0.2

Suppasriら (2013)
5.00

SteelRC

SteelRC

Soma Soma Kesen Kesen Sendai Soma Sendai Soma Kesen Kesen SendaiSendai
numa numa
numa numa

0.0

10.00 15.00 20.00 25.00

0.0

TsunamiTsunamiheightheight(m)
(m)

2.0
4.0
6.0
8.0 10.0
Tsunami津波浸水深inundation(m)height (m)12.0(b)

In case of using 50 percentile hazard

Expected value of tsunami risk (50 percentile hazard)

1.00E-03

1.00E-04

Probabilistic tsunami inundation assessment

Risk assessment

20m water depth (Corr: -0.60)
50m water depth (Corr: -0.63)

Annual Exceedance Probability

Annual Exceedance Probability

10m water depth (Corr: -0.92)

Reinforced concrete
SteelBrickWood

1.00E-05

Wood Brick Wood Wood Steel Brick Brick RC

Steel SteelRCRCSoma Soma Kesen Sendai Soma Kesen Sendai Soma Kesen SendaiKesen Sendai
numanumanumanuma(c) In In
case
using
percentile
hazardcaseof ofusing
9595
percentile
hazardExpected value of tsunami risk (95 percentile hazard)

1.00E-02

1.00E-03

1.00E-04
Wood Brick Wood Wood Steel Brick Brick RC

Steel Steel

RCRC

Soma Soma SendaiKesen Soma Kesen Sendai Soma Kesen SendaiKesen Sendai
numa
numa
numanumaTsunami inundation height (m)Damage Probability (%)

SummarySummary◆ To evaluate tsunami risk, we considered two kinds ofuncertainties (epistemic and aleatory) in tsunami hazard
assessment by using the logic tree method.

◆We quantified the tsunami risk of three buildings located inthree places in the Tohoku area, Japan.
◆We clearly showed that there was a difference of 100 times in
the risk index (Annual expected tsunami loss ratio) from 5
percentile hazard to 95 percentile hazard, and the risk could not
be explained by only fragility assessment.
◆In the near future, we will analyze uncertainty of tsunami risk
due to variability of fragility assessment.

Thank you for your kind attention.