Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanTHE GENERATION OF EARTHQUAKE DAMAGE
PROBABILITY CURVES FOR BUILDING FACILITIESIN TAIWAN
George C. YAO1, Ying-Lieh TU2
1

Professor, Department of Architecture, National Cheng Kung University,
Tainan, Taiwan, gcyao@mail.ncku.edu.tw
2
Ph.D. Candidate, Department of Architecture, National Cheng Kung University,
Tainan, Taiwan, kentu@mail.ncku.edu.tw

ABSTRACT: This paper describes earthquake vulnerability curves for nonstructuralcomponents developed from hospital and school buildings. Authors investigatednonstructural components damage of 41 hospital buildings in the Chi-Chi earthquake,and concluded data with fragility curves and probability curves. Authors also
investigated nonstructural components damage of 56 schools buildings from the Taitungand Heng-Chun earthquake in 2006. Using these curves, the damage prediction for
nonstructural components in important buildings can be exercised in Taiwan.
Key Words: hospital, school, fragility curve, nonstructural component, probability curveof repair cost, probability curve of recovery time

INTRODUCTION
In the 1999 Chi-Chi earthquake, Taiwan found that the emergency hospitals’ medical capability isinadequate owing to nonstructural component damage inside hospital buildings. (Yao and Lin, 1999).
It was later concluded that the importance of nonstructural components’ seismic safety in hospitals’
continual operation should not be compromised. In order to safeguard the medical capability to
execute disaster relief work after an earthquake, a hospital needs to improve the seismic performanceof both building structures and its nonstructural components. The same approach should also be
applied to school buildings because many of them will be needed to serve as the community shelter
after a major earthquake. Also because the nonstructural components in the typical buildings
constituted 82%-92% of total investment which could be the main proportion of earthquake damage
loss ( Taghavi and Miranda , 2003) as shown in Figure 1, the seismic damage of nonstructuralcomponents were paid much attention by researchers in order to reduce economic loss in earthquakes.
The damage investigation after an earthquake and the derivation of fragility curves, have increased
gradually in the past twenty years. The fragility curves can describe damage probability with peakground acceleration (PGA) in earthquake engineering community. William (William, 1998) compared
the damage of nonstructural components in the Northridge earthquake with that in previous earthquake
experience, and generalized a suggestion of seismic performance in nonstructural components. Kuo etal. (Kuo, Hayashi and Kambara, 2004) performed a questionnaire investigation to find out that993

nonstructural components damage begin to take place at seismic intensity 5+, and the damaged
condition rises rapidly at seismic intensity 6. Tien and Pai (Tien and Pai, 2006) built the fragility curveon the ratio of building damage and personnel death. Porter (Porter, 2007) estimated the fragility curveof elevator with the method of Binary Regression Analysis.

Figure 1 The investment ratio of nonstructural components in buildings
Recently, Yeh (Yeh, 2002) established the Taiwan Earthquake Loss Estimation System (TELES)
with local data in Taiwan to estimate the probable damage loss of structures and nonstructuralcomponents. However, the fragility curve of nonstructural components in TELES adopts much
American materials, lacks of the domestic data of nonstructural components in Taiwan. After the 1999
Chi-Chi earthquake, Taiwan experienced many moderate ones. These earthquakes produce different
levels of damage to nonstructural components and we collect and analyze them to produce local
nonstructural damage data.
This study describes a nonstructural component database of hospital and school buildings frompast earthquakes in Taiwan. It includes data from 3 earthquakes namely, the 1999 Chi-Chi earthquake,
Taitung earthquake on April 1st 2006, and the Heng-Chun earthquake on December 26th in 2006.
The derived data from questionnaires includes: damage probability curves of different nonstructuralcomponents, probability of repair cost, and probability of recovery time of nonstructural components.

METHODOLOGY
According to the Nonstructural Performance Levels of FEMA356 (FEMA, 2000), this study divides
the nonstructural components into Architectural Components (A), Mechanical or Electrical or
Plumbing Systems/Components (B), and Contents (C). However, the classification of FEMA356 in
nonstructural components was not designed specifically for hospitals or schools. In accordance withthe building characteristics in Taiwan, this study made a questionnaire of nonstructural components bymodifying Table C1-5 through C1-7 of FEMA356. Finally, 4 types of damage description: no damage,slight damage, moderate damage and extensive damage were used for statistical analysis to establish
fragility curves for nonstructural components.
The damage condition of nonstructural components was surveyed and their repair cost andrecovery time probability curves were also analyzed by using questionnaire data in this study. The
algorithms of the log-normal distribution curve fitting were used to plot the corresponding repair costprobability curves.
Selection of samples
This study collected three-component strong motion records of earthquakes from the Central Weather
Bureau (CWB). PGA of each building site could be estimated by using the Kriging interpolation.
The selection steps of buildings are as follows:
1. Selecting the hospitals with in-patient beds from 736 hospitals, and schools from Taitung and994

Pingtung.
2. The seismic intensity 5 of CWB (I=5) is based on the Weber-Fechner rule as Eq.1. andindicated an acceleration (αI) range from 80 ~ 250 gal.

α I = 0.8(10

I −1
2

I
2

~ 10 )(1)

If I=5.5 is used to separate intensity 5- and intensity 5+, we can calculate from Eq.1. toknow that the separation acceleration is 140 gal.

3. Select buildings in which the seismic intensity exceeded 5+（PGA > 140 gal）.
4. Telephone, inquiry and site visit them which can help to fill in the questionnaire

PROBABILITY CURVES OF NONSTRUCTURAL COMPONENTS
The probability curve in this study adopts the method of probability theory and Survival Analysis thatMCEER puts forward in the technical report (MCEER, 1999) to investigate the damaged situation of
nonstructural components of earthquakes in hospitals and schools. Analysis steps are as shown in Fig.
2 to calculate the average (λ) and standard deviation (ζ) value:x , y , θ0

F ( x , θi ) i = 1 ~ Nyi∑(y − y )2Min∑ ( y − yi )2iNonlinear Least Squares Curve Fitting

No

Yes

 x1 
 y1 
λ 
  ，
 
x =  x2 
y =  y2  ， θ = ζ 
 
x 
y 
 3
 3

θ N = θ$Figure 2 Process of non-linear regression995

Based on λ and ζ value, the probability curve could be estimated as Fig. 3 ~ 5.

Figure 3 Fragility curves

Figure 4 Probability curves of repair cost

Figure 5 Probability curves of recovery time996

APPLICATION
Hospital Buildings – Fragility curves
The λ and ζ value for nonstructural components in hospitals were estimated, as Table 1 shows.
Every fragility curve of nonstructural components can be shown as in Fig.6~8.

Table 1 The λ and ζ value of each nonstructural components in hospitals

No.

Nonstructural components

λSlightModerateζExtensive

SlightModerate

Extensive

A-1

Exterior Walls

-1.3

-1.03

-0.9

0.46

0.46

0.51

A-2

Glazing

-0.85

-0.7

-0.41

0.54

0.61

0.55

A-3

Partitions

-1.34

-0.8

-0.17

0.57

0.54

0.63

A-4

Suspending Ceilings

-1.13

-1

-0.88

0.46

0.47

0.48

A-5

Parapets

-1.03

-0.42

-0.14

0.46

0.61

0.74

A-6

Stairs

-0.89

-0.44

0.25

0.47

0.61

0.75

A-7

Doors

-0.85

-0.62

0.25

0.44

0.56

0.75

B-1

Elevators

-0.67

-0.52

-0.27

0.43

0.38

0.23

B-2

HVAC Equipment

-0.68

-0.42

-0.16

0.63

0.61

0.62

B-3

Boiler

-0.4

-0.23

-0.23

0.55

0.45

0.45

B-4

Mainframe of Ice Water

-0.66

-0.16

0.28

0.4

0.62

0.74

B-5

Cooling Tower

-0.59

-0.42

0.25

0.53

0.61

0.75

B-6

Air Conditioner Duct

-0.69

-0.41

0.25

0.44

0.55

0.75

B-7

Piping

-0.86

-0.39

-0.21

0.58

0.46

0.5

B-8

Fire Sprinkler Systems

-0.42

-0.16

0.28

0.61

0.62

0.74

B-9

Fire Alarm Systems

-0.58

-0.58

0.25

0.49

0.49

0.75

B-10

Emergency Lighting

-0.71

-0.71

-0.62

0.32

0.32

0.33

B-11

Light Fixtures

-0.78

-0.61

-0.41

0.51

0.53

0.55

B-12

Sanitary Equipment

-0.69

-0.53

0

0.44

0.4

0

C-1

Computer Systems

-0.77

-0.53

-0.4

0.37

0.4

0.39

C-2

Desktop Equipment

-1.39

-0.98

-0.78

0.53

0.39

0.39

C-3

File Cabinets

-1.2

-1

-0.49

0.48

0.47

0.7

C-4

Book Shelves

-1.19

-0.88

-0.69

0.39

0.35

0.43

C-5

Art Objects

-0.95

-0.95

-0.55

0.5

0.5

0.45

C-6

Medical Equipment

-1.06

-0.95

-0.14

0.46

0.5

0.74

997

Figure 6 Fragility curve of exterior wall (A-1)

Probability of Failure

Figure 7 Fragility curve of elevator (B-1)

Figure 8 Fragility curve of file cabinets (C-3)

Hospital Buildings – Repair costThis study divided the repair cost of nonstructural components in hospital buildings into 3 parts,
medical equipment, machine equipment, and information equipment. Total repair cost was defined as
the repair cost sum of all equipment.
In order to use the data for all hospitals, a floor area of 500 m2 of the hospital building was treated as adenominator to normalize the repair cost. The repair cost calculation result of nonstructuralcomponents and estimated parameters in hospital buildings were shown in Table 2. Analysis steps canbe found in Yao’s and Tu’s researches ( Yao et al, 2008 and Tu et al, 2009). The results were shown as
Fig. 9 ~12.

998

Table 2 Repair cost of nonstructural components in hospital buildings
MedicalMachineInformation

Total

Equipment

Equipment

Equipment

Equipment

0.00-0.99

0.00-0.99

0.00-0.99

0.00-0.99

0.03

0.02

0.03

0.20

λ

-0.7742-0.7788-0.8737-1.0981ζ

0.87440.51170.52030.55541.00-9.99

1.00-4.99

1.00-4.99

1.00-19.99

3.19

3.72

2.83

9.19

λ

-0.6031-0.7196-0.6991-0.8023ζ

0.77170.44870.41910.353110.00-80.00

5.00-210.00

5.00-80.00

20.00-220.00

30.68

88.78

18.52

97.33

λ

0.1121-0.3286

0.0788-0.3286ζ

0.83870.45010.67800.4501

Interval（NT$10000/500m2）
SlightAverage（NT$10000/500m2）

Interval（NT$10000/500m2）
Moderate

Average（NT$10000/500m2）

Interval（NT$10000/500m2）
Average（NT$10000/500m2）

0.03

3.19

0.1

0.2

30.68

SlightModerate

Extensive

1.0

Probability of Repair Cost

Extensive

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0

0.3

0.4

0.5

0.6

0.7

PGA(g)

Figure 9 Repair cost probability curves of medical equipment

999

0.8

0.02

3.72

0.1

0.2

88.78

SlightModerate

Extensive

Probability of Repair Cost

1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0

0.3

0.4

0.5

0.6

0.7

0.8

PGA(g)

Figure 10 Repair cost probability curves of machine equipment

0.03

2.83

0.1

0.2

18.52

SlightModerate

Extensive

Probability of Repair Cost

1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0

0.3

0.4

0.5

0.6

0.7

0.8

PGA(g)

Figure 11 Repair cost probability curves of information equipment

0.20

9.19

0.1

0.2

97.33

SlightModerate

Extensive

Probability of Repair Cost

1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0

0.3

0.4

0.5

0.6

0.7

PGA(g)

Figure 12 Repair cost probability curves of total equipment

1000

0.8

From Fig. 9, the repair cost probability curves of medical equipment defined at slight, moderate,and extensive damage level corresponds to 0.03, 3.19, and 30.68 ( NT$10000/500m2 ) respectively.
The probabilities on PGA 0.40g (seismic intensity 7) indicated repair cost of 44%, 34%, and 1% asslight, moderate, and extensive respectively.
In the same approach, the repair cost probability curves of machine equipment, informationequipment, and total equipment could be estimated respectively shown as shown Fig.10~Fig.12.
School Buildings – Fragility curves
The λ and ζ value for nonstructural components in schools were estimated and is shown in Table 3..

Table 3 The λ and ζ value of each nonstructural components in school buildings
No.

Nonstructural components

1
2
3
4
5
6
7
8
9
10

Exterior Walls
Partitions
Suspending Ceilings
Parapets
Doors
Sanitary Equipment
Computer Systems
Desktop Equipment
File Cabinets
Book Shelves

λModerate Extensive-1.0165-0.7701-0.8173------0.9853-0.88100.00000.00001.8371-----0.0000------0.9017-0.7927-0.8395-0.2844-0.9266-0.8350-0.6576-0.3949

Slight-1.3261-1.2098-1.1157-0.7753-0.1859-0.7927-1.0388-1.2190-1.1285-1.0890

Slight0.45220.47190.43050.51200.89150.31920.20520.22170.21400.3769ζModerate Extensive
0.53380.63000.3648-----0.4658
0.41760.00000.00002.3518-----0.0000-----0.3128
0.31920.41880.66860.27540.25410.52700.6015Every fragility curve of nonstructural components can be shown as in Fig.13~15.

SlightModerate

Extensive

SlightModerate

Extensive

1.0

Probability of Failure

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

PGA (g)Figure 13 Fragility curves of Exterior Walls (1)

1001

0.9

1.0

Slight

Moderate

SlightModerate

1.0

Probability of Failure

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

PGA (g)Figure 14 Fragility curves of Partitions (2)SlightModerate

Extensive

SlightModerate

Extensive

1.0

Probability of Failure

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

PGA (g)Figure 15 Fragility curves of Suspending Ceilings (3)School Buildings – Repair cost and Recovery time
This study surveyed the repair cost and recovery time of nonstructural components in school buildings
with 3 items only: exterior walls, partitions, and suspending ceilings. Total repair cost and recovery
time were defined as the sum of all 3 items in repair cost or recovery time.
In order to apply to all schools, a floor area of 500 m2 of school buildings was treated as a denominator
to normalize the repair cost. The repair cost and recovery time of nonstructural components andestimated parameters in school buildings were shown as Table 4.
Table 4 The λ and ζ value of each nonstructural components in school buildings
Nonstructural components
RepairCost

Exterior Walls
Partitions
Suspending Ceilings
Total School
Nonstructural components

RecoveryTime

Exterior Walls
Partitions
Suspending Ceilings
Total School

λSlight Moderate Extensive-1.2467-0.8530-0.2616-0.90640.22430.7140-1.0383-0.4432-0.0829-1.4342-1.1667-0.5886
λSlight Moderate Extensive-1.2269-0.91221.1403-0.9064-0.6510-0.3903-1.0748-0.62070.8563-1.4173-1.0229-0.19151002

ζSlight Moderate Extensive
0.43840.60430.78900.53071.19091.16960.36540.71120.72350.41680.4922
0.6941ζ
Slight Moderate Extensive
0.48510.57081.56880.53070.54820.61730.38390.56680.93650.40620.54060.9089

The repair cost and recovery time probability curves were shown as Fig. 16~17.
2

Repair Cost (NT$10000 / 500M )
0.14

0.80

2.68

0.14

0.80

2.68

0.4

0.5

0.6

0.5

0.6

1.0
0.9

Probability of Cost

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0

0.1

0.2

0.3

PGA (g)Figure 16 Repair cost probability curve

Recovery Time(Day / 500M2)
0.23

1.20

2.74

0.23

1.20

2.74

1.0

Probability of Time(day)

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0

0.1

0.2

0.3

0.4

PGA (g)Figure 17 Recovery time probability curves

CONCLUSIONSThe conclusions of this study are as follows:
1. The ζ, standard deviation of fragility curve, was obtained in this study by nonlinear regression. It
reflects real site data of each damage component, and is deferent from a fixed value of 0.3 used byother researchers.
2. In hospital, the probability of repair cost is higher when the unit area repair cost is less. As seismic
intensity increases, a higher probability of repair cost occurred at the same level of unit area repaircost.
3. The repair costs by definition at the slight level are almost the same and they are close at themoderate level. But, at the extensive level, the repair cost of machine equipment is the largest

1003

subset and the repair cost of information equipment is the smallest one. Therefore, the seismic
protection for machine equipment in hospitals should be placed at a higher priority.
4. From fragility curves, the probability of damage of each nonstructural component can be predicted.
The probability of repair cost or recovery time of nonstructural components at a certain PGA canbe predicted and evaluated from their respective probability curves.

ACKNOWLEDGMENTS
This study was supported by The Central Weather Bureau, Taiwan（MOTC-CWB-96-E-10 and
MOTC-CWB-97-E-12 ）, The National Science Council, Taiwan (NSC98-2625-M-006-003) , and The
Department of Health. The authors are grateful to their supports.

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