8CUEE CONFERENCE PROCEEDINGS
8th International Conference on Urban Earthquake Engineering
March 7-8, 2011, Tokyo Institute of Technology, Tokyo, JapanSEISMIC RISK AND DAMAGE COST ANALYSIS OF MID-RISE BASE ISOLATEDBUILDINGS IN PERU

Luis A. Bedrinana1) and Taiki Saito2)
1) Assistant Researcher, Center for Earthquake Engineering Research and Disaster Mitigation (CISMID), Peru
2) Chief Research Engineer, International Institute of Seismology and Earthquake Engineering, Building Research Institute, Japanluisbedrim@gmail.com, tsaito@kenken.go.jp

Abstract: The principal objective of this study is to evaluate the cost-effectiveness as well as the seismic safety of abase isolated building located in Peru. A methodology to evaluate quantitatively the seismic risk and the cost-effectivenessof a base isolated building during its lifetime is presented. The process starts with the hazard analysis and the earthquake
ground motion generation in the studied area. Lima area is considered in this study. Series of artificial earthquake groundmotions are generated by a stochastic method in the studied area. Then a preliminary seismic design of the target building
is carried out, by using the Peruvian seismic code. To get the response distribution of the target building, several dynamic
nonlinear analyses are performed by using the generated artificial motions as input waves. By assuming a structural
response distribution, the seismic risk analysis is performed in terms of three structural parameters such as: interstory drift
ratio (IDR), floor acceleration (FA) and the structural damage index (DI). The damage of the target building is evaluatedby using a damage index. Finally, the cost-effectiveness of using base isolation system is examined, by comparing theexceedance probability of repair cost in the target building with and without base isolation during a given time period.

2.
SEISMIC HAZARD AND EARTHQUAKEGROUND MOTION MODELING

1. INTRODUCTION
Peru is an earthquake prone country, which has
experienced many severe earthquakes in its history. Most of
those severe earthquakes have been a big disaster, producing
huge losses and fatalities. Most important problems noticed
in buildings during these events, are: low resistance, highlevel of damage, and no protection of contents. To increase
resistance in buildings several improvements have been
made in the seismic code; however, there is no any
regulation about damage limit levels in buildings in current
codes. Moreover, current provisions do not provide any
protection to nonstructural components, equipment andcontents of buildings.
One of the best alternatives to reduce the damage and toprovide protection of contents in buildings is the use of baseisolation. Base isolation has proved to be a reliable
technology to prevent damage in buildings and to increase
the seismic performance; however current seismic
provisions do not provide information of the real safety ofbase isolated buildings. Furthermore, in developing
countries the use of base isolation is not wide due to the highconstruction cost of isolation system. So, a methodology toevaluate the real seismic safety and cost-effectiveness of thebase isolation system is needed to meet current performancerequirements in buildings. This methodology has to provide
a rational basis and clear procedures to achieve the target inorder to be used normally.

Seismic hazard of studied area is determined using pastearthquake data. The historical data of past earthquakes(Figure 1) from the Peruvian seismic catalog (Tavera et al.
2007) are used to model the earthquake occurrence ofmagnitude (M) and hypocentral distance (R) around Lima
area.

LIMA

Figure 1 Distribution of earthquake epicenters around Lima
from 1963 to 2005.

- 1707 -1.E+00

Data
Trun G-R
1.E-01spectral density PS(ω) represents the importance of theharmonic function, in some specified band frequencies, andit matches the target spectrum defined previously. A total
number of 800 artificial earthquake ground motions aregenerated for the studied area. Figure 3 shows the response
spectrum of a sample generated wave (Sample 128) RSX
which is compared with the target response spectrum RST.
1800
Sample 128

Acceleration (gal)The earthquake occurrence of magnitude andhypocentral distance is modeled by a truncated G-R formulaand the Beta probability function respectively as is shown in
Figure 2. To generate the artificial ground motions, several
sets of M and R are randomly generated according to theirprobability distributions by standard procedures. Then, each
set of values of M and R is related to ground motions bymeans of an attenuation formula in terms of spectral
acceleration for Peru subduction earthquakes. In this study
the attenuation relationship for spectral acceleration in Peru
is used (Chavez 2006), which was proposed for different soil
conditions of the Peruvian coastal area.

1600

M=8.2, R=117.8

1400

PGA=590gal

RST(gals)
RSX(gals)

1200
1000
800
600

N/N0400
1.E-02200

a = 2.1
b = 0.80
0.0

1.E-03

0.5

1.0

1.5

2.0
Period (sec)

2.5

3.0

3.5

4.0

No=125

1.E-04
5.5

6.0

6.5

7.0
7.5
Magnitude (Mw)

8.0

8.5

9.0

0.00503. STRUCTURAL AND DAMAGE ANALYSIS

0.0045
Data
Beta Dist.

0.0040
Probability Density

Figure 3 Comparison between target response spectrum andresponse spectrum of generated sample wave.

0.00350.00300.00250.00200.00150.00100.00050.0000
050

100

150

200

250
300
R (Km)

350

400

450500Figure 2 Earthquake occurrence of magnitude M andhypocentral distance R (1963 to 2005).
The artificial earthquake ground motions are generated
as a nonstationary stochastic process compatible with theresponse spectrum calculated previously with the attenuation
formula. By using the random vibration theory, a simple
model of earthquake ground motion A(t) is expressed as a
product of a wave x(t) from a stationary random process,with a power spectral density PS(ω), and an intensity
envelope function E(t) (Shibata 2010) as follows

A(t ) = E(t ) .x(t )(1)

In this study, the Jennings’s intensity envelope function
E(t) is used (Jennings et al. 1969). This function takes into
account the transient effects in time of earthquake groundmotions. The sample wave x(t) is generated by a
combination of harmonic functions, with a given power
spectral density PS(ω) (Gasparini et al. 1976). This power

3.1 Target building
The target building for this study is an RC officebuilding with 8 stories as is shown in Figure 4. This building
is assumed to be located in Lima downtown and it is a
representative mid-rise building. The concrete used in thisbuilding has a nominal strength of f’c=21MPa, and thenominal strength of steel is fy=412MPa. The total weight ofthe structure is around 46174kN, and the fundamental period
is 0.65s in X direction and 0.54s in Y direction. The target
building is designed according to the Peruvian seismic code.
The design base shear coefficient is 0.08 in X direction and0.09 in Y direction.
3.2 Design of base isolation system
In this study, the equivalent SDOF method (Okamoto etal. 2002) is used to design the base isolation system in thetarget building. This method considers an isolated building
as a rigid body moving with hysteretic properties of isolation
devices, with a bilinear model. The lead rubber bearing LRB
is used as isolation devices in this study. The total design
yield force of the isolation system is set to 4% of the total
weight and the design limit displacement is 300mm.
Moreover, the design target period of the isolation system is
2.24s. Table 1 shows the dimensions of isolation devices.
3.3 Dynamic Analysis
To obtain structural response of the target building aseries of nonlinear dynamic analyses are carried out, using
artificial ground motions generated previously as input
motions. These artificial ground motions represent future- 1708 -earthquakes that would occur in the life cycle of the building.
In this study structural uncertainty is assumed to be small
compared with uncertainties of ground motions, andstructural uncertainty is not taken into account. The
nonlinear dynamic analyses are carried out in the building
with conventional design as well as with base isolation.
Dcomposed of the damage caused by the maximum
displacement and the absorbed hysteretic energy. The
damage index DI is expressed by.

DI =δmEh+ βcδuQ yδ u(2)Where Qy the yield strength, Eh is the total hystereticenergy dissipated during earthquake, δm is the maximum
drift during earthquake, δu is the ultimate drift undermonotonic loads, and βc is a constant.

CB

Moreover, the overall damage of entire buildings ischecked by means of the total damage index DIT, (Park et al.
1985) as follows

AYX

12

4

3

765

98

1011DIT = ∑ λi DI i

λi =Ehi
∑ Ehi

(3)

1.0
0.9
0.8

Probability

0.7
0.6
0.5

Lognormal-Isolated
Xm=0.0010; ζ=1.66

0.4
0.3
0.2DCBADCB

0.0
1.E-07

Figure 4 Plan and elevation view of the target building.

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00Drift Ratio (%)

Table 1 Dimensions of isolation devices.

Figure 5 Lognormal distribution of IDR in 1st story.

LRB-500

Shear Modulus (N/mm2)

0.39

0.39

1.0

Shear Modulus lead (N/mm2)

0.59

0.59

0.9

Exterior Diameter (mm)

600

500

0.8

Interior Diameter (mm)1001000.7

Thickness of rubber layer (mm)

43.5

144
4 x 36123
3.5 x 35

Steel layer thickness (mm)2.5

2.50.3

Primary Shape Factor S1

37.535.70.2

Secondary Shape Factor S2

4.2

4.1

0.1

Number of Bearings

3680.0
1.E-02

Probability

LRB-600

Total rubber thickness (mm)Isolated
Fixed

0.1

A

3.4 Damage Analysis
Additionally to the structural response in terms of IDRand FA, the structural damage in the target building isevaluated. To correlate the values of IDR with damage, thePark-Ang’s damage index (1985) is used. This damage
index considers earthquake damage in RC members is0.6
0.5

Lognormal-Isolated
Xm=4.02; ζ=1.19

0.4

Isolated
Fixed
1.E-011.E+00
1.E+01
Floor acceleration (gal)

1.E+02

Figure 6 Lognormal distribution of FA in 1st story.

- 1709 -1.E+03

X
4. STRUCTURAL RESPONSE DISTRIBUTION

F(X)
Xm

Timet

Figure 8 Exceedance probability of random variable
based on the Poisson process.
850-Isolated
100-Isolated
200-Isolated
50-Fixed
100-Fixed
200-Fixed

76Story

A total of 800 nonlinear dynamic analyses are carriedout in the target building, with and without base isolation, byusing artificial earthquake ground motions previously
generated. With information of structural maximumresponse in each analysis, the probability distribution of theinterstory drift ratio (IDR) and peak floor acceleration (FA) isobtained. The structural response is modeled by a lognormal
distribution in this study and Figure 5 and Figure 6 show thedistribution of IDR and FA respectively in the first story of
the target building.
Based on the 800 values of maximum IDR showed
previously, the damage index is calculated for each andevery case. Park and Ang (1985) determined that the damage
index is reasonably lognormal distributed. Figure 7 shows
the lognormal probability distribution of total damage (DIT)in the target building. It can be seen from this plot thatstructural damage in isolated building is considerablyreduced. Additionally, the median value and the standard
deviation of damage distribution of isolated building arelower than conventional one.

543

1.0
0.9
0.8

2

Lognormal-Fixed
Xm=0.0014; ζ=1.79

10.0

Probability

0.7
0.6
0.5

Lognormal-Isolated
Xm=0.0011; ζ=1.58

0.4

0.6
0.8
Drift ratio (%)

1.0

1.2

1.4

Figure 9 Values of IDR with 10% of exceedanceprobability in 50, 100 and 200 years.

0.40.38Isolated
Fixed

0.2
0.1

750-Isolated
100-Isolated
200-Isolated
50-Fixed
100-Fixed
200-Fixed

61.E-06

1.E-05

1.E-04 1.E-03 1.E-02
Total damage index

1.E-01

1.E+00Story

0.0
1.E-070.2

Figure 7 Probability distribution of DIT.

543

5. SEISMIC RISK ANALYSIS

2The seismic safety of a building can be quantified interms of the exceedance probability of the structural
response. To evaluate the exceedance probability of arandom variable X, which represents structural response, thePoisson process model is used as is shown in Figure 8. If X
is the random variable evaluated, F(X) is the cumulative
distribution of X, and ν is the annual occurrence of the event;the exceedance probability that X>Xm in t years is given as
follows (Saito and Wen 1994)

1p f = P(X > X m [0, t ]) = 1 − exp[−ν t (1 − F ( X m )]

(4)

0.0

0.2

0.4

0.6
0.8
Damage Index

1.01.2

Figure 10 Values of DI with 10% of exceedance
probability in 50, 100 and 200 years.
The seismic risk of the structure can be quantified interms of exceedance probability of the structural response.
To estimate the probability that the IDR will exceed somethreshold value, the Poisson process model is assumed forthe earthquake occurrence. The annual earthquake
occurrence is ν=2.98 in this study. Figure 9, shows the- 1710 -

150
140
130120110

Isolated
Fixed

1009080020406080 100 120
Time (year)

140

160

180200Figure 11 Expected values of total structural cost with
10% of exceedance probability in the lifetime of thebuilding.
7. CONCLUSIONS

6. COST-EFFECTIVENESS ANALYSISIn addition to the seismic risk analysis, thecost-effectiveness analysis of the target building, with andwithout base isolation, is carried out. In this study just thestructural cost is taken into account, principally due to thelack of reliable data of nonstructural components, contents
and maintenance of buildings in Peru. The cost-effectivenessis evaluated by a model which correlates damage index into
structural repair cost of each story, so the total cost is thesum of repair cost in each story. In this study the model tocorrelate damage and repair cost is based on the proposal ofTakahashi and Shiohara (1987). The repair cost is defined by
the structural repair cost ratio RS, which is the normalized
repair cost by the cost of total replacing with new one. The
repair cost ratio RS is defined by

DI < Dc
 0.0 ;
 DI − Dc
RS = ; Dc ≤ DI < 1 1 − Dc
DI ≥ 1
 1.0 ;

160
Total structural cost ratio (%)

values of IDR for the target building with 10% ofexceedance probability. The values of IDR for isolatedbuilding are much lower than values for conventionalbuilding. So, it can be said that isolated building has better
seismic safety than conventional building.
The seismic risk of the structure can be also
quantified in terms of exceedance probability of damage
index. The Poisson process model for earthquake occurrenceis also used to obtain the probability that DI will exceed
some threshold value. Figure 10 shows the values of DI with
10% of exceedance probability. It is observed thatconventional building suffer large damage for long time
periods and after 100 years there is a 10% exceedance
probability to have a value of DI equal or more than 0.60.
Damage in main structure is reduced by using the baseisolation system, so the probabilities to have severe damage
are significantly lower than the case of conventionalbuilding.

(5)

Where Dc is the minimum damage index in which
repair work is necessary and a value of 0.01 is taken.
Results obtained in damage analysis are related to
repair cost by the cost ratio. Using values of damage index
with 10% of exceedance probability, the structural cost
repair ratio can be obtained in every case. It is noticed fromthese tables that conventional building has large values ofRS; especially in long time intervals, it is observed that somestories need to be almost totally repaired. If the life time
were 100 years; it would be expected a value of 37.1% fortotal cost ratio in the conventional building, which is about
4.7 times larger than value of isolated building.

The methodology presented here is a useful tool toquantify the seismic risk and the cost effectiveness of baseisolated buildings. Additionally this procedure could be
extended to any kind of building structure.
The total damage in conventional building is
considerably larger than isolated building. The expectedvalue of the total damage index in 50 years, with 10% of
exceedance probability, for the fixed building has a value ofabout 2.47 times larger than isolated one.
Although the initial total structural cost in the isolatedbuilding is larger than in fixed one, the total structural cost in
isolated building is much smaller for long time interval. So,base isolated building is cheaper than fixed building during
the lifetime of the target building.
It can be concluded that the seismic risk is much lower
in isolated building; moreover, the cost-effectiveness in
isolated building is better than fixed building, during lifetime
period when large damage is expected.
An upgrade in seismic codes is needed in order toinclude probabilistic methodologies to evaluate the seismic
risk of buildings.

Acknowledgements:
Special thanks are given to CISMID and its director Dr. CarlosZavala for their valuable collaboration to this study. The
information from the seismic catalog of Peru was provided by H.
Tavera from the Geophysical Institute of Peru and the informationof the attenuation equation was provided by J. Chavez; theircollaboration is acknowledged. This study was supported by theJapanese Government through the Japan International Cooperation
Agency (JICA). This financial support is gratefully acknowledged.
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