京都
 大 学 防 災 研 究 所 年 報 第 49 号 C 平 成 18 年 4 月
Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No. 49 C, 2006

Study on Earthquake Damage Prediction
by Considering Variations of Seismic Performance of Wooden Houses

Takeshi MORII and Yasuhiro HAYASHI** Graduate School of Engineering, Kyoto University
Synopsis
In order to promote aseismic retrofit and to mitigate earthquake damage, it is necessary forinhabitants to recognize the seismic risk of their own houses. This paper presents a method fordamage prediction of a wooden house based on the results of seismic capacity evaluation andstrong motion evaluation. The method is developed so as to simulate the wooden house damage
in recent earthquakes in Japan. Finally, we confirm the effect of aseismic retrofit on seismic
damage mitigation from predicting seismic damage of wooden houses by the proposed method.
Keywords: earthquake damage prediction, wooden houses, seismic performance,
maximum drift angles, damage probability, strong ground motions


1.

Introduction

To mitigate the earthquake damage of wooden
houses that influences life safety during strong groundmotions, promotion of aseismic retrofit is required.
Therefore, it is important to let the inhabitants recognize
earthquake risk of the area they live in and the effect ofaseismic retrofit; and it is necessary to develop a methodof earthquake damage prediction which not only evaluate
the damage based on analysis results of strong groundmotions but also take into consideration the difference ofseismic performance, strength and deformation, ofwooden houses.
In the promotion of aseismic retrofit of wooden
houses, both the damage predictions for a group ofhouses and an individual one are necessary. The
evaluation results for wooden houses in a local area areimportant data for making disaster prevention plan of thearea. On the other hand, the evaluation results of anindividual house make the owner understand earthquake
hazard and the effect of aseismic retrofit concretely, andraise the incentive to conduct aseismic retrofit.

In this study, we present two methods for earthquake
damage prediction of wooden houses based on theevaluation results of seismic capacity and strong groundmotions. One is the method for individual wooden house,
which predict damage probability of wooden house.
Another is the method for wooden houses in an area,
which predict the damage ratio of wooden houses. Bothin the method, the earthquake damage of wooden houseis predicted from estimated maximum drift angles byusing the fragility functions, which are constructed basedon seismic damage data in recent earthquakes. Then, theproposed methods are applied to wooden houses in
Kyoto city, and the mitigation effects of retrofit are
discussed.
2. Method of earthquake damage prediction for anindividual wooden house
2.1 Outline of the method
The method of damage prediction for an individual
wooden house is based on the results of seismic capacity
and strong motions.

㧙㧙Figure 1(a) shows the flowchart. First, with theproperties available from an investigation of the house,
the analysis model of an individual wooden house isconstructed by using the steps of seismic capacity
evaluation used in the calculation method of response
and limit strength (Suzuki et al., 2001). Second, themaximum drift angle of wooden houses is estimatedfrom the response analysis of constructed model underthe estimated ground motions (Hayashi, 2002). Finally,
the probability of damage of a wooden house is predictedfrom estimated maximum drift angle by using thefragility functions. An example of a 2-storied wooden
house is used to explain each step in detail, from 2.2 to
2.4.
2.2 Modeling of a wooden house
Modeling of a wooden house follows the method ofseismic performance evaluation used in the calculation
method of response and limit strength (Suzuki et al.,2001).
First, the main structural properties, such as plans,height, seismic performance elements, etc., of a wooden
house are investigated, and the seismic performanceelements, such as mud wall, handing wall, etc., areextracted (Fig.2(a)). Then the standard forcedisplacement curve is used each seismic performanceelement, and the force- displacement curve of the wholewooden house is calculated by adding the curve of eachelement (Fig. 2 (b)). Besides, with the investigated story
height and mass of the 2-storied wooden house, anequivalent 1-storied one, which is a single-degree-offreedom (SDOF) system, is obtained based on the steps
in the calculation method of response and limit strength(Fig. 2 (c)).
Estimatedground motion

2.3 Estimated maximum drift angle
Next, maximum drift angle of wooden house duringstrong ground motions is estimated by using equivalentperformance response spectrum developed by Hayashi(2002).
In the method, a wooden house is simplified as asingle-degree-of-freedom (SDOF) system. Analysis isconducted based on the simplified SDOF system, andresults are applied to the original wooden house. The
main results of the method are outlined below. An
equivalent period Tet is related to the drift angle Re as
follows
2S H et  Re /(CBe  g )Tet ( Re , CBe )[1]where Me and Tet are the effective mass and effective
height, respectively, M, CBe and g are the total mass, theyield base shear coefficient, and the gravitational
constant, respectively. The equivalent acceleration
response spectrum corresponding to the specified drift
angle Re can be calculated fromS aeS ( Re , C Be , h0.05) C Be  g / Fh (het ( Re ))[2]

where Fh is the reduction factor of acceleration spectrum.
Fh depends on the damping ratio h, and in turn depends
on the drift angle with the following relations
1.5
1  10  het (Re )Fh (het (Re ))het ( Re )heq ( Re )  h0­° het Re®
°̄ het Re

[4]

㧨

0.05

h0

0.05  het Re

҈

0.05

h0

0

Estimatedground motion

Modeling of wooden
house (fig.2)[3]

Modeling ofwooden house

Modeling of a group ofwooden houses

Estimation of distribution of
maximum drift angles

Estimation of
maximum drift angle (fig.3)
Method of seismic
capacity evaluation

Prediction of damage ratio

Prediction of damage probability (fig.4)(a) An individual wooden house(b) A group of wooden houses
Fig.1 Outline of the method of earthquake damage prediction

㧙㧙



For a given drift angle R, both Tet and SaeS can becalculated from [1] and [2]. A pair of Tet and SaeS
corresponds to a point in the response spectrum-period
plane, as shown in Figure 3. For a fixed CBe, anequivalent response spectrum curve can be drawn by
varying the drift angle Re.
2.4 Prediction of the damage probability
Finally, the damage probability of a wooden houseis predicted from the maximum response drift angle R
by using fragility functions.
It is assumed that the variation of damage by the
maximum drift angle R could be expressed by lognormal
distribution. The damage probability, Pf(R), is calculatedas
Pf ( R ) ) ln R  ln Rm / ] R[5]where Ǟ is a standard normal distribution functions
and Rm is the median value ; (ln(Rm)) =ǳR , ǳR is theaverage of ln(R)) and ǮR is the standard deviation ofln(R). Equations [5] is referred to as fragility functions
here in.
In this study, damage levels are categorized into 5groups : No damage, Slight, Minor, Moderate, Sever(Hayashi et al., 2001). Rm andǮR are decided based ondamage ratios of wooden houses at Hino-town in 2000
Western Tottori earthquake, as shown in Figure 4 (Morii
et al., 2005).
3. Method of earthquake damage prediction for agroup of wooden houses
3.1 Outline of the method
Figure 1(b) shows the flowchart of the method ofearthquake damage prediction for a group of wooden
house. Fundamentally, it is the same process as themethod for individual wooden house.
First, modeling of the seismic performance of thegroup is expressed by lognormal distribution function
based on the investigation results of individual wooden

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(c) Modeling of equivalent SDOF system
Fig.2 Evaluation of seismic performance of wooden house based on
the calculation method of response and limit strength㧙㧙houses. Next, for given estimated strong ground motions,the maximum drift angle of an individual house iscalculated by using the equivalent-performance response
spectra, and then the distribution of the maximum drift
angle for the group is obtained. Finally, with the damage
probability of each house available by using the fragility
functions, the damage ratios of the group is calculated as
the average of the damage probabilities.

method) (Howard et al., 1990) is used for calculating the
distribution of the maximum drift angle. The LHS
method is adopted because it could use smaller numberof samples to obtain a stable solution. In this study, thenumber of samples of the LHS method is calculated as
N=10.

3.2 Simplification of modeling individual wooden
house in group
When performing earthquake damage prediction fora group of wooden houses, the result of seismic capacity
evaluation, based on the steps in the calculation methodof response and limit strength, of an individual house isapproximated by an elasto-plastic model, in which theyielding angle Ry , is 1/100rad and the angle of limit stateis 1/30rad. Then it was converted to an equivalentperformance response spectrum by using equations [1] [4].

Finally, the proposed methods are applied to wooden
houses (Kyo-machiya) in Kyoto city, and the mitigation
effects of retrofit are discussed.

3.3 Modeling of a group of wooden houses
A group of wooden houses model is modeled bylognormal distribution of the base shear coefficient,which is estimated from the result of seismic capacity
evaluation of the individual ones modeled as a SDOF
system. The parameters in the lognormal distributionfunction are the average base shear coefficient, CBe, andthe standard deviation,ǮCBe.
In this study, the standard deviation of equivalentheightǮHet is added to ǮCBe . Then, the new standard
deviation of shear coefficient ǮCBe’ is calculated asBe '] C2  ] 2
Be

[6]

H et

3.4 Evaluation of the distribution of the maximum
drift angles
The Latin hypercube sampling method (the LHS
SaS,SaeS

Earthquake damage prediction in Kyoto city

4.1 Example of earthquake damage prediction for
an individual wooden house
In Kyoto city, strong ground motions are estimatedfrom eight active faults around Kyoto city, as shown in
Figure 5 (Kyoto-city, 2003). The proposed methods areapplied to KJ-house (Kyo-machiya) in Kyoto city byusing the estimated strong ground motions of the
Biwako-Seigan fault and Hanaore fault. One wave of
estimated strong ground motions is created for each area
without distinction of direction.
KJ-house is located the central of Kyoto city, as
shown in Fig.5. Figure 6 shows the plans of KJ-house,
which is long and slender in the longitudinal direction,
seismic performance elements, such as mud wall, aremostly arranged in the longitudinal direction. In the
results of seismic capacity evaluation, when the limit
drift angle is 1/30rad, the shear coefficient CBe(R30) of
equivalent SDOF model is 0.11 in transversal direction,
0.42 in longitudinal direction. The shear coefficient
CBe(R30) in transversal direction is lower than that inlongitudinal direction.
Figure 7 shows the result of earthquake damage
prediction of KJ-house subjected to the estimated strong
ground motions due to the Biwako-Seigan fault andHanaore fault. In the case of the Biwako-Seigan fault,

Response spectra䇭SaS
Maximum drift angle R䃂Equivalent-performance
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㧙㧙the damage probability of KJ-house changes greatly due
to differences in the strength. The damage probability issmaller as larger strength in longitudinal direction. On
the other hand, in the case of the Hanaore fault, thedifference in the damage probability due to the strengthof wooden houses is not observed.
Figure 8 portrays the maximum drift angle in eachestimated strong ground motions. In the case of the
Biwako-Seigan fault, the estimated strong groundmotions did not attain strong intensity and the
predominant period is about 0.4 second, which meansthat the main components of the ground motions areshort period ones. The maximum drift angle in thelongitudinal direction, where the strength is larger, andtransversal direction, where the strength is smaller, are
1/49 and 1/25rad, respectively. Therefore, the maximum
drift angle decrease as the strength increase. On the other
hand, in the estimated strong ground motions of Hanaore
fault, the acceleration response spectrum shows
predominant period of 1 to 3 seconds. Regardless of thestrength, both in the longitudinal and transversal

direction, the maximum drift angles are about 1/11 rad.
Accordingly damage probability in the two directions are
same.
From these results, the following can be pointed out
about damage mitigation for KJ-house. In the case of
the estimated strong ground motions caused by the
Biwako-Seigan fault, it is possible to reduce thedamage by raising the strength of transversal direction.
In contrast, in the case of the estimated strong groundmotions caused by Hanaore fault, increasing strengthof a wooden house will not decrease the damage, but
raising the deformation capacity will mitigate thedamage.
4.2 Example of earthquake damage prediction of agroup of wooden houses
In this section, earthquake damage prediction of the
2-storied wooden houses group in Kyoto city subjectedto the estimated ground motions of Hanaore fault is
performed.
From the seismic capacity evaluation, based on

Mud wallHanaore fault
Biwako-Seigan
faultTransverse
0.11
5.8

CBe(R30)
Het(R30)

Longitude
0.42
5.8

Hanging wall
10,780
8,330

2,450

15,680KJ house

Longitude

2-story

Transverse

Fig.5 Location of faults around Kyoto city

Fig.6 Plans of KJ-house (Kyomachiya)
Biwako-Seigan fault

Longitudinal direction

SaS, S aeS (m/s 2)

Damage Probability (%)

Hanaore fault

10Transversal direction100

1-story80
60
40

R=1/11●R=1/495Transverse●

R=1/2520h=0.050
BIWAKOHANAORE

Slight

BIWAKOHANAORE

Moderate

Fig. 7 Results of earthquake damage
prediction in KJ-house

00.2

Longitude

0.4 0.6 0.8 1
Period (s)R=1/11●●

3

5

Fig.8 Maximum drift angles of KJ-houseduring estimated strong ground motions

calculation method of response and limit strength, of 30
wooden houses (Kyo-machiya). The wooden houses
group model is constructed using the result 27 2-storied
wooden houses, as shown in Figure 9 (Suda et al., 2005).
The wooden houses group model is expressed bylognormal distribution of CBe that the standard deviationof the equivalent height, Het was added to the shear
coefficient, CBe’ . The average of shear coefficient CBe ofwooden houses group model is about 0.43 forlongitudinal direction, and about 0.15 for transversal
direction. The average of the equivalent height Het isabout 4.4m for both directions.
 The earthquake damage prediction results oftransversal direction and longitudinal direction
respectively are shown in Figure 10. On the whole, thedamage ratio of longitudinal direction with larger
strength is smaller than that of transversal direction. It is
confirmed that performing the aseismic retrofit to raise
the strength, the damage ratio fell. For example, although
the damage ratio of transversal direction is over 40% at B
point, in longitudinal direction with larger strength, theratio is less than 10%.
From Figure 11, when the acceleration response
spectrum shows predominant period of about 3 seconds
and the strength is smaller than 0.2, the maximum
response drift angle becomes large. That is to say, byincreasing the strength to be larger than 0.2, resulting the
maximum drift angle of about 1/15rad, so that thedamage ratio decreases. On the other hand, at A point,
no apparent difference of damage ratio is observed inboth directions, and both the ratios are larger than 40%.
As shown in Fig.11, the strength is less than 0.9, themaximum drift angle and the damage ratio will notdecrease.
Therefore, in the region near active faults, only byincreasing strength of a wooden house, it may be difficult
to reduce the earthquake damage ratio. That is mitigating
the deformation capacity of a wooden houses isnecessary.
5.

Conclusions

In order to promote aseismic retrofit and to mitigate
earthquake damage, it is necessary for inhabitants torecognize the seismic risk of their own houses. This
papers presents a method for damage prediction of awooden house based on the results of seismic capacity
evaluation and strong motion evaluation. The method ofearthquake damage prediction of wooden houses isbased on the results of response analysis under theestimated ground motion. Then, the probability ofdamage of wooden house is predicted from estimatedmaximum drift angle by using the fragility functions,which are constructed based on seismic damage data, weconfirmed that the effect of variation of seismic
performance on seismic damage mitigation from theresults of analysis, the following conclusions can be
drawn.
1) The proposed method of earthquake damage
prediction can evaluate the seismic performance asprobability of damage of wooden house.
2) It is confirmed that wooden houses damage is
mitigated in large area by increasing the strength ofwooden houses from the analysis results in the case of
Hanaore-Fault in Kyoto city.
3) However, in the case of strong ground motions withpredominant period in the range of 1 to 3 seconds,
damage of wooden houses is not mitigated by increasing
the strength of wooden houses. Therefore, it is important
to consider not only the strength of wooden houses but
also capacity of deformation to mitigate earthquake
damage of wooden houses.
Acknowledgements
This research was supported by the Japanese
Ministry of Education, Culture, Sports, Science andTechnology 21st Century COE Program for DPRI,
Kyoto University. We are also grateful for using thevaluable seismic observation recordings such as the
Kyoshin Network (K-NET) and Kyoshin Network(KiK-net) distributed by the by National ResearchInstitute for Earth Science, Disaster Prevention (NIED)of Japan.
References
Suzuki,Y., Saito,Y., Katagihara,K., Ikago,K. andNojima,C. (2001) : Method of evaluation seismic
performance of wooden frames - Limit bearing capacity
analysis in wide range of deformation, Proceedings ofthe 11th Japan Earthquake Engineering Symposium,
pp.1523-1528. (in Japanese).
Hayashi,Y. (2002) : Evaluation of Seismic Design Loadbased on Equivalent-Performance Response Spectra,
The eleventh Japan earthquake engineering symposium,㧙㧙pp.651-656. (in Japanese).
Hayashi,Y., Kitahara,A., Hirayama,T. and Ssuzuki,Y.
(2001) : Evaluation of peak ground velocities inwestern Tottori earthquake of 2000, Journal ofstructural and construction engineering (transactions ofarchitectural institute of Japan), No.548, pp.35-41. (inJapanese)
Morii,T., Hayashi,Y. and Saratani,A. (2005) ：Semiempirical method for predicting seismic damageof wood houses based on seismic performance, Jounalof social safety science, No.7, pp.281-289.

Howard H.M ， Hwang and Jing-Wen Jaw(1990):
Probabilistic Damage Analysis of Structures, Journal ofstructural Engineering, Vol.116, No.7, ASCE,
pp.1992-2007.
Kyoto-city (2003): Report on the third earthquake
damage prediction in kyoto city. (in Japanese).
Suda,T., Suzuki,Y., Okuda,T. and Ogasawara,M.
(2005) ： Evaluation of structural characteristics of
traditional wood houses in Kyoto bases on detailinvestigation, Journal of social safety science, No.7,
pp.15-21. (in Japanese).

Distrubuion of seismic performanceof 27 wooden houses
Transeverse
けた行方向

20

10

5

0
0

0.5

1

1.5

C Be

Fig.9 Model of a group of wooden houses
Severe (%)

1/R

15
SaS, SaeS (m/s 2)

The number of houses

PGA:766 (cm/s )PGV:111 (cm/s)

ave. v alue：0.43
coef. of variation ：0.2 5

15B point
2

Longitude

ave. v alue：0.15
coef. of variation ：0.4 4

A point

20

20

10

PGA:495 (cm/s 2)
PGV: 75 (cm/s)

5
0.8

30
10

0.6

100 60

0.4
5

0.2
0.1

h=0.0500.2
0.4 0.6 0.8 1
Period (s)

3

A

B

5

Fig.11 Estimated maximum drift angles R
Severe (%)

A

CBe

B

(a) Transverse (λCBe=0.15)(b) Longitude (λCBe=0.43)
Fig.10 Results of earthquake damage prediction of the wooden houses
in Kyoto city during estimated Hanaore faultᧁㅧᑪ‛ߩ⠴㔡ᕈ⢻ߩᄌൻࠍ⠨ᘦߒߚ࿾㔡ⵍኂ੍᷹ߦ㑐ߔࠆ⎇ⓥ

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