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SECM/13/35

FRAGILITY CURVES FOR TSUNAMI LOADING

Isuru Nanayakkara1 and Priyan Dias

2

1Department of Civil Engineering, University of Moratuwa, Sri Lanka

E-mail: isuru_nanayakkara@live.com

2Department of Civil Engineering, University of Moratuwa, Sri Lanka

E-mail: priyan@uom.lk

Abstract

Vulnerability to structural damage can be characterized by a fragility curve, which is expressed as the

conditional probability of reaching or exceeding a particular damage state, expressed by a lognormal

cumulative probability distribution, given a certain value of the demand parameter. Such curves have

been produced for a variety of damage states in different categories of buildings that have been

subjected to tsunami loading in different parts of the world, with the demand parameter taken as

inundation depth. Harmonization was sought across these studies with respect to the median

inundation depths. Three categories of buildings were identified based on construction material;

namely reinforced concrete, masonry and timber. The median inundation depths for the complete

damage state decreased from reinforced concrete (5.4-7.3m) through masonry (2.3-2.5m) to timber

(~1.6m) structures. The steeper fragility curves for the weaker structures suggest that they display a

single failure mode, probably sliding. The fairly narrow ranges above represent a number of different

studies and indicate that a common family of curves can be used in damage assessments worldwide.

Such ranges were identified for two partial damage states too.

Keywords: Fragility curves, Damage state, Inundation depth, Construction material

1.0 Introduction

During the past decade an unprecedented number of tsunami events have struck coastal regions, all

over the world, with 2004 Indian Ocean Tsunami and 2011 Great East Japan Tsunami being the most

destructive.

Vulnerability for structural damage of a category of building can be characterized by a set of fragility

curves, each of which is expressed as the conditional probability of reaching or exceeding a particular

damage state, given a certain value of demand parameter, namely inundation depth in the case of a

tsunami event. It is common practice to present the fragility curves in the form of a cumulative log

normal (Eq.1) or cumulative normal (Eq.2) distribution (Table1). Here andare means and and

are standard deviations. The fragility function used by Peiris (2006) should be noted for using

inundation depth to median inundation depth ratio )( HH as the variable, rather than the

conventional inundation depth )(H . Here is used for standard deviation.

HxP

ln (1)

Special Session on Loading Effects, 4th

International Conference on Structural Engineering and Construction Management 2013, Kandy, Sri Lanka, 13

th, 14

th & 15

th December 2013

24

HxP

(2)

Although fragility curves have conventionally been used in seismic risk analysis of structural systems

(Koshimura et al., 2009a), occurrence of tsunami events has been too scarce to generate focused

attention on using fragility functions to characterize tsunami damage. A fair amount of separate

studies have been carried out however and fragility curves developed. The tsunami events considered

in this study includes five tsunamis from 2004 Indian Ocean Tsunami to 2011 Great East Japan

Tsunami (see Table 1). These events have primarily occurred in the Indian and Pacific Oceans and the

damaged areas range from Sri Lanka, Thailand, Indonesia, Japan through Solomon Islands and Samoa

to Dichato in Chile.

Two broad methodologies used in developing fragility curves; namely 1) Field survey data, 2) GIS/

numerical modelling. Both of these methods have their advantages and disadvantages. Detailed

damage level classifications can be obtained from field survey data, but only a limited number of data,

due to practical constraints in surveying large areas. In contrast GIS data provide a significantly large

number of data although it can only identify the completely damaged state. Furthermore, field survey

data method uses physical markings on walls and trees to determine the inundation depth while the

GIS based method uses numerical modelling of tsunami flow to measure inundation depth. In addition

to the above, Koshimura et al., (2009a) have developed fragility curves for 1896 Meiji–Sanriku, 1933

Showa-Sanriku and 1960 Chile tsunamis, based on secondary data obtained from historical sources.

Furthermore, Dias et al. (2009) have carried out probabilistic modelling to obtain a synthetic fragility

curve for the case of single storey masonry buildings.

There are important conclusions arrived at by observation of fragility functions for tsunamis. Peiris

(2006) has compared fragility curves for buildings in East and South coast of Sri Lanka and has

concluded that they behave similarly. By comparison of fragility curves for different building types

under different damage states, Reese et al., (2011) has concluded that non-structural damage states are

independent of the building typology. Reese et al., (2011) have further attempted to quantify the

effects of debris and shielding, while Koshimura et al., (2009a) have compared the effect of the

methodology of obtaining data for fragility curves. Further they have noted the importance of

statistical considerations (such as bin size) in developing fragility curves.

2.0 Objectives

The primary objectives of this study are:

I. To compare fragility curves from different researchers in order to explore

similarities

II. To discriminating fragility curves on the basis of different building types

3.0 Analysis and results

3.1 Common basis for fragility curves

As mentioned earlier fragility functions indicate the probability that a given structure meets or

exceeds a given damage state (DS) under the given level of demand parameter (d), and could be

derived by the use of Eq.(3).

d| structures exposed of No

d|DS ds structures of No|

dDSdsP

(3)

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Table 1: Fragility curves for Tsunami damage developed by different researchers

Author Tsunami Area Methodology Main Building

typology Fragility function

Peiris

(2006)

2004 Indian

Ocean

Sri Lanka Field Survey data Single story

masonry

H

Hln

1

Dias et al

(2009)

2004 Indian

Ocean

Sri Lanka Field Survey data,

Probabilistic

modeling

Single story

masonry

H

Hln

1

Koshimura

et al

(2009a)

2004 Indian

Ocean

Banda Ache,

Indonesia

GIS /numerical

modeling,

Field Survey Data

H 1933 Showa

Historical Data 1896 Meiji

1960 Chile

Koshimura

et al

(2009b)

2004 Indian

Ocean

Banda Ache,

Indonesia

GIS /numerical

modeling

Low rise wooden

houses and non-

engineered RC

construction

H

Murao and

Nakazato

(2010)

2004 Indian

Ocean

South coast of

Sri Lanka

Field Survey data

brick, block or

woodwork

H

Koshimura

et al (2010)

2007

Solomon

Island

Ghizo Island,

Solomon

Islands

GIS /numerical

modeling

H

Reese et al

(2011)

2009 South

Pacific

Samoa and

American

Samoa

Field Survey data

masonry

residential

structures

Hln

Suppasri et

al (2011)

2004 Indian

Ocean

Phang Nga,

Thailand

GIS /numerical

modeling,

Field Survey Data

(for RC

structures)

concrete and

brick

Hln

Phuket,

Thailand

Concrete and

brickwork.

Gokon et al

(2011)

2009 South

Pacific

Tutuila Island,

American

Samoa

GIS/ numerical

modelling

H

Suppasri et

al (2012)

2011 Great

East Japan

Miyagi

Prefecture,

Japan

Field Survey data

wooden houses

H

Mas et al

(2012)

2010 Chile Dichato, Chile GIS /numerical

modeling

masonry + wood,

wood +

corrugated metal

Hln

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However, Peiris (2006) has used a slightly different definition. Hence an attempt was made to adjust

the Peiris (2006) fragility curves to meet the above definition. The field survey data of the tsunami

damage in Sri Lanka due to 2004 Indian Ocean tsunami, published by the Department of Census and

Statistics (DCS) was used to adjust the Peiris (2006) fragility curves. This was the same source used

by Peiris (2006) in his study, and has been extended since to include data from all tsunami affected

districts. DCS data includes the number of structures exceeding three damage states (complete,

partial–unusable and partial–usable) under six inundation depth levels. Since there were no data

available on structures experiencing no damage, it was assumed that the numbers of those were very

small. The following definition was used to recalculate the new data points of the fragility curves for

various damage states.

(usable) partial ,(unusable) partial complete,i

d| ds structures of No

d|D ds structures of No|

iDS

SdDSdsP

(4)

The data points and fragility function parameters for the complete damage state, by the method used

by Peiris (2006) extended to the full DCS data, and by the method proposed above (New Method) is

given in Table 2. It should be noted that the raw data used in both methodologies is the same and the

only difference is in data manipulation.

Table 2: Comparison of fragility curves developed from complete DCS data using two methods

Cumulative % of housing units damaged by submerged

depth (m)

H median <=

1.5

1.83 -

2.13

2.44 -

3.05

3.35 -

6.10

6.40 -

9.14

> 9.14

1.5 2 2.7 4.7 7.8 10

Peiris Method 10.5 23.2 50.8 91.8 97.7 99.5 2.67 0.4756

New Method 13.2 36.8 58.4 83.9 90.5 93.3 2.32 0.5247

3.2 Harmonizing damage state classifications

The researchers who determined fragility curves based on field survey data have classified buildings

under different damage states. These differing damage states proposed or used by different

researchers were brought to a common platform based on the damage descriptions they have given for

each damage category. A five level damage scale presented in Table 3 was produced harmonizing

damage states of Peiris (2006), Reese et al. (2011) and Suppasri et al. (2011).

Observation of fragility curves for different damage states developed by above researchers validated

the attempt to harmonize damage states. Figure 1 shows fragility curves for masonry and reinforced

concrete structures under different damage states proposed/used by Peiris (2006), Reese et al. (2011)

and Suppasri et al. (2011). Note that these fragility curves show similarity in shapes and compatibility

in damage classification despite being produced by different researchers for different tsunami events

in different countries, using different fragility functions.

3.3 Variation of fragility curves by building type

Fragility curves developed for three distinct building types were encountered; masonry, timber and

reinforced concrete. In most of the cases the building typologies were defined as mixed type since the

building lot included structures built using different materials. Figure 2 shows fragility curves for

complete damage state for distinct building types, as produced by various researchers. It clearly shows

that timber constructions perform poorly in tsunamis while reinforced concrete structures perform the

best. It should be further noted that Peiris (2006) data includes up to 30% temporary constructions

27

(using mud, wood and tin sheets). Furthermore the fragility curves produced by Suppasri et al (2012)

for wooden houses under 2011 Great East Japan Tsunami was not considered as its author notes that

the wooden structures in the study area has performed better than wooden structures elsewhere, given

that they were newly constructed with proper control procedures (Suppasri et al., 2012).

Table 3: Harmonizing damage states presented by different researchers into a common scale

Reese et al (2011) Suppasri et al (2011) Peiris (2006) This Paper

[DS0]

None -

[No Damage]

No visible structural

damage

[DS 00]

No visible damage

[DS1]

Non-structural

damage only

[Damage Level 1]

Structural damage in

secondary members

(roof and wall) only

[Partial Damage

(Usable)]

Repairable damage

not compromising

structural integrity

[DS 01]

Non-structural

damage

[DS2]

Significant non-

structural damage,

minor structural

damage

[Damage Level 2]

Damage in primary

members (beam,

columns, footing)

[Partial Damage

(Unusable)]

Collapse of walls

beyond repair.

Structural integrity

compromised.

[DS 02a]

Moderate structural

damage [DS3]

Significant structural

and non-structural

damage

[DS4]

Irreparable structural

damage, will require

demolition

[DS 02b]

Significant structural

damage. Structural

integrity

compromised

[DS5]

Complete structural

collapse

[Damage Level 3]

Collapse

[Complete Damage]

Complete structural

damage or collapse

[DS 03]

Complete collapse

3.4 Median inundation depth ranges

Considering the different damage states and construction material encountered, we suggest that

buildings be classified into four distinct damage levels; namely no damage (DS00), non-structural

damage (DS01), structural damage (DS02) and complete collapse (DS03). Furthermore, median

inundation depth limits for timber, masonry and reinforced concrete structures for the above damage

states are suggested in the Table 4. These values are based on fragility curves developed by Peiris

(2006), Reese et al. (2011) and Suppasri et al. (2011).The choice of median inundation depth as the

representative parameter is due to the physical significance and comparability. Median inundation

depth indicates the inundation depth at which half of the building lot will exceed the damage state

considered. In addition, the median inundation depth will have this physical significance regardless of

whether the fragility function is cumulative normal or cumulative log-normal. Values given in Table 4

are general values and due recognition should be given to extreme cases where the building lot is

known or expected to be of significantly high quality, as in Japan’s Miyagi Prefecture (Suppasri et

al.,2012) or of significantly low quality, as in Dichato, Chile (Mas et al.,2012).

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a) Masonry structures

b) Reinforced Concrete (RC) structures

Figure 1: Fragility curves for different damage states of a) masonry and b) reinforced concrete

structures

Figure 2: Fragility curves for complete damage state by construction material

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Table 4: Proposed median inundation depth ranges

Damage Level Reinforced

Concrete Masonry Timber

DS 03 - Complete 5.4 to 7.3m

2.3 to 2.5 m

~ 1.6 m

DS 02b - Heavy

0.5 to 3.5m

~1.9m

~ 1.3 m

DS 02a - Moderate ~ 0.5m

0.5 to 1.2m

DS 01 - Minor 0.3 to 0.4m

~ 0.3m

~ 0.3m

DS 00 - No Damage

Figure 3 gives the median inundation depth of the fragility curves for complete damage developed by

other researchers mentioned in Table 1.These researchers’ fragility functions have not been used in

the building type and damage state analyses above, since they have either lumped multiple building

types together or did not consider multiple damage states. Figure 3 also includes the median

inundation depth ranges suggested for complete damage state (DS 03) in Table 4. It can be observed

in Figure 3 that median inundation depths for a building lot with a given mix of building types fit

within the values suggested for the individual building types that make up the particular mix of

building types.

Figure 3: Median inundation depth of fragility curves developed by various researchers

4.0 Conclusion

Building damage due to tsunami loading could be classified under four damage states; namely no

damage, non-structural damage, structural damage and complete collapse, and various damage states

identified by a number of researchers can be collapsed into the four states above. This can be justified

by demonstrating the clustering of fragility curves into the three states with damage above.

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Three main building types, based on the building material, were identified. The median inundation

depth of the fragility curve for the complete collapse damage state showed increasing values and

ranges from timber (1.6m), through masonry (2.3 to 2.5m) to reinforced concrete (5.4 to 7.3m).Such

median inundation depths were identified for other damage states as well. These values can be used in

carrying out risk assessments for building lots subject to tsunamis.

The median inundation depth for a building lot with a given mix of building types was shown to fit

within the values suggested for the individual building types that make up the particular mix of

building types.

References

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surveys and Monte Carlo simulation.Civil Engineering and Environmental Systems, 26(2),

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destruction in American Samoa.Journal of Japan Society of Civil Engineering,67(2), pp.1321-

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