SEISMIC RISK AND COST-EFFECTIVENESS OF BASE
ISOLATED BUILDINGS IN PERU
Luis A. BEDRIÑANA∗MEE09195

Supervisor: Taiki SAITO∗∗ABSTRACTThe principal objective of this study is to evaluate the cost-effectiveness as well as the seismic safetyof a base isolated building located in Peru. A methodology to evaluate quantitatively the seismic risk
and the cost-effectiveness of 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 isconsidered in this study. Series of artificial earthquake ground motions are generated by a stochastic
method in the studied area. Then a preliminary seismic design of the target building is carried out, byusing 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 threestructural parameters such as: interstory drift ratio (IDR), floor acceleration (FA) and the structural
damage index (DI). The damage of the target building is evaluated by using damage index. Finally, thecost-effectiveness of using base isolation system is examined, by comparing exceendance probabilityof repair cost in the target building with and without base isolation during a given time period.
Keywords: Cost-Effectiveness, Seismic Risk, Base Isolation, Damage index, repair cost.
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. Many
important lessons have been learned from theses events and the most important problems noticed inbuildings are: low resistance, high level of damage, and no protection of contents. To increase
resistance in buildings several improvements have been made in 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 and contents of buildings.
One of the best alternatives to reduce the damage and to provide protection of contents inbuildings is the use of base isolation. Base isolation has proved to be a reliable technology to prevent
damage in buildings and to increase its performance; however current seismic provisions do notprovide information of the real safety of base isolated buildings. Furthermore, in developing countries
the use of base isolation is not massive due to the high construction cost of isolation system. So, amethodology to evaluate the real seismic safety and cost-effectiveness in base isolation is needed tomeet current performance requirements in buildings.
2. SEISMIC HAZARD AND GROUND MOTION MODELINGThe historical data of past earthquakes (Figure 1) from the Peruvian seismic catalog (Tavera et al.
2007) are used to model the earthquake occurrence of magnitude (M) and hypocentral distance (R)∗Center for Earthquake Engineering Research and Disaster Mitigation (CISMID), Peru.
International Institute of Seismology and Earthquake Engineering, Building Research Institute, Japan.

∗∗− 97 −The earthquake occurrence of magnitude andhypocentral distance is modeled by a truncatedG-R formula and the Beta probability function
respectively as is shown in Figure 2. To generate
the artificial ground motions, sets of M and R arerandomly generated according to their probability
distributions. Each set of values of M and R isrelated to ground motions by an attenuation
formula in terms of spectral acceleration for Peru
subduction earthquakes. Then, the earthquake
ground motion is generated as a nonstationary
stochastic process compatible with the response
spectrum calculated with the attenuation formula.
Using random vibration theory, a simple model ofearthquake ground motion A(t) is expressed as a
Figure 1. Distribution of earthquake epicentersproduct of a wave x(t) from a stationary randomaround Lima from 1963 to 2005.
process, with a power spectral density PS(ω), andan 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 is used (Jennings et al. 1969). This function
takes into account the transient effects in time of earthquake ground motions. The sample wave x(t) isgenerated by a combination of harmonic functions, with a given power spectral density PS(ω)(Gasparini et al. 1976). This power spectral density PS(ω) represents the importance of the harmonic
function, in some specified band frequencies, and it matches the target spectrum defined previously. A
total number of 800 artificial earthquake ground motions are generated for the studied area.
5.0E-03

1.E+004.5E-03

Probability D ensity

N/N0

Data
Beta Dist.

4.0E-03

Data
Trun G-R

1.E-01

1.E-02

1.E-03

3.5E-033.0E-03
2.5E-032.0E-03
1.5E-03
1.0E-035.0E-04

0.0E+00

1.E-04
5.5

6.0

6.5

7.0

7.5

8.08.59.0Magnitude (Mw)050100150200250300R (Km)350400450500

Figure 2. Earthquake occurrence of magnitude M and hypocentral distance R (1963 to 2005).

3. TARGET BUILDING AND STRUCTURAL RESPONSE
3.1. Design of the target building
The target building for this study is an RC office building with 8 stories as is shown in Figure 3. Thisbuilding is assumed to be located in Lima downtown and is a representative mid-rise building.
Concrete used in this building has a nominal strength of f’c=21MPa, and the nominal strength of steel
is fy=412MPa. The total weight of the structure is around 46174kN, and the fundamental period is0.65s 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 and 0.09 in Y direction.

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C.L

DCB

AYX
1

2

3

4

5678

91011DCAB

123456Figure 3. Plan and elevation view of target building.

3.2. Design of base isolation
In this study, the equivalent SDOF
method (Okamoto et al. 2002) is used todesign the base isolation system in thetarget building. This method considers anisolated building as rigid body moving
with hysteretic properties of isolation
devices, with a bilinear model. The leadrubber bearing LRB is used as isolation
devices in this study. The total design
yield force of the isolation system is set to4% 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 thedimensions of isolation devices.

Table 1. Dimensions of isolation devices.
LRB-600

LRB-500

Shear Modulus (N/mm2)0.390.39

Shear Modulus lead (N/mm2)

0.59

0.59

Exterior Diameter (mm)600500Interior Diameter (mm)100100Thickness of rubber layer (mm)43.5

Primary Shape Factor S1

144
4ȿ36
37.5

123
3.5ȿ3535.7

Secondary Shape Factor S2

4.2

4.1

Number of Bearings

368Total rubber thickness (mm)

1.0

1.0
0.9
0.8

Lognormal-Fixed
Xm=0.0014; ζ=1.83

0.9
0.8
0.7

0.5

Lognormal-Isolated
Xm=0.0010; ζ=1.66

Probability

Probability0.70.6

0.4

0.6
0.5

Lognormal-Isolated
Xm=4.02; ζ=1.19

0.4
0.3

0.3
0.2

0.2

Isolated
Fixed

0.1
0.0
1.E-07

Lognormal-Fixed
Xm=7.21; ζ=1.15

Isolated
Fixed

0.1
0.0
1.E-02Drift Ratio (%)

1.E+00
1.E+01
Floor acceleration (gal)Figure 4. Lognormal distribution of IDR in 1st story.

Figure 5. Lognormal distribution of FA in 1st story

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E-01

1.E+02

1.E+033.3. Structural response distribution
A total of 800 nonlinear dynamic analyses are carried out in the target building, with and without baseisolation, by using artificial earthquake ground motions previously generated. In this study structural
uncertainty is assumed to be small compared with uncertainties of ground motions. With informationof structural maximum response in each analysis, the probability distribution of the interstory drift− 99 −

ratio (IDR) and peak floor acceleration (FA) are obtained. The structural response is modeled by alognormal distribution in this study. Figure 4 and Figure 5 show the distribution of IDR and FA
respectively in the first story of the target building.
3.4. Structural damage distribution
Additionally to the structural response, the structural damage in the target building is evaluated. To
correlate the values of IDR with damage, the Park-Ang’s damage index (1985) is used. This damage
index considers earthquake damage in RC members is composed of the damage caused by themaximum displacement and the absorbed hysteretic energy. The damage index DI is expressed byequation (2), where Qy is the yield strength, Eh is the total hysteretic energy dissipated during
earthquake, δm is the maximum drift during earthquake, δu is the ultimate drift under monotonic loads,
and βc is a constant to take into account the number of cycles (a value of 0.05 is taken in this study).

DI =δmEh+ βcδuQyδ u

1.0
0.9
0.8

Lognormal-Fixed
Xm=0.0014; ζ=1.79

Probability

0.7
0.6
0.5

Lognormal-Isolated
Xm=0.0011; ζ=1.58

0.4
0.3

Isolated
Fixed

0.2
0.1
0.0
1.E-07

1.E-06

1.E-05

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

1.E-02

1.E-01

1.E+00Figure 6. Lognormal distribution of DIT.

(2)

Based on the 800 values of maximum IDR
showed previously, the damage index iscalculated for each and every case.
Additionally, the total damage index in thebuilding is calculated as an average ofdamage indices in each story (Park et al.
1985). Park and Ang (1985) determined thatthe damage index is reasonably lognormal
distributed. Figure 6 shows the lognormal
probability distribution of total damage (DIT)in the target building. It can be seen from thisplot that the median value and the standard
deviation of damage distribution of isolatedbuilding are lower than fixed building.

4. SEISMIC RISK ANALYSIS
4.1. Exceedance probability of a random variable
To evaluate the exceedance probability of a random variable X, which represents structural response,
the Poisson process model is used. 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 int years is given as follows (Saito and Wen 1994)

p f = P (X > X m [0, t ]) = 1 − exp[− ν t (1 − F ( X m )](3)

4.2. Seismic risk in terms of exceedance probability
The seismic risk of the building can be quantified in terms of exceedance probability of the structural
response. To estimate the probability that the IDR will exceed some threshold value, the Poissonprocess model is assumed for the earthquake occurrence. The annual earthquake occurrence is ν=2.98
in this study. Figure 7, shows the expected values of IDR with 10% of exceedance probability. Thevalues of IDR for the isolated building are much lower than values for fixed building. So, it can be said
that isolated building has better seismic safety than fixed building.

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The seismic risk of the structure can be also quantified in terms of exceedance probability ofdamage index. Figure 8 shows the values of DI with 10% of exceedance probability. It is observed that
fixed building suffers a 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 base isolation system, so the probabilities to have severe damage are significantly
lower than the case of fixed building.
8850-Isolated
100-Isolated
200-Isolated
50-Fixed
100-Fixed
200-Fixed

Story65750-Isolated
100-Isolated
200-Isolated
50-Fixed
100-Fixed
200-Fixed

6Story75443322
110.0

0.2

0.4

0.60.8Drift ratio (%)

1.0

1.2

0.0

1.4

Figure 7. Values of IDR with 10% of exceedance
probability in 50, 100 and 200 years.

0.2

0.4

0.6Damage Index0.8

1.01.2

Figure 8. Values of DI with 10% of exceedance
probability in 50, 100 and 200 years

5. COST-EFFECTIVENESS ANALYSIS
5.1. Repair cost model

Total structural cost ratio (%)

160150140130120110

Isolated
Fixed

100
90
80
020406080 100 120
Time (year)

140160180

200

Figure 9. Expected values of total cost with 10% ofexceedance probability in 50, 100 and 200 years

In addition to the seismic risk analysis, thecost-effectiveness analysis of the target
building is carried out. In this study just thestructural cost is taken into account. The
cost-effectiveness is evaluated by a model
which correlates damage index into
structural repair cost of each story, so thetotal cost is the sum of repair cost in eachstory. The repair cost is defined by thestructural repair cost ratio RS (Takahashiand Shiohara 1987), which is thenormalized repair cost by the cost of total
replacing with new one. The repair cost
ratio RS is defined by equation (4), where
Dc is taken as a value of 0.01.

DI < Dc­ 0.0 ;° DI − Dc
RS = ®
; Dc ≤ DI < 1Dc
1−°DI ≥ 1
¯ 1.0 ;

(4)

5.2. Structural cost based in exceedance probability of damage index
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.

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Figure 9 shows the expected value of total structural cost with 10% of exceedance probability. It isnoticed from this figure that fixed building has large values of RS; especially in long time period. If thelife time were 100 years; it would be expected a value of 37.1% for total cost ratio in the fixedbuilding, which is about 4.7 times larger than value of isolated building.
6. CONCLUSIONS
The methodology presented here is a useful tool to quantify the seismic risk and the cost-effectivenessof base isolated 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
expected value of the total damage index in 50 years, with 10% of exceedance probability, for thefixed building has a value of about 2.47 times larger than isolated one.
Although the initial total structural cost in the isolated building is larger that in fixed one, thetotal structural cost in isolated building is much smaller for long time interval. So, base isolatedbuilding 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, thecost-effectiveness in isolated building is better than fixed building, during lifetime period when large
damage is expected.
The use of seismic isolation should be encouraged in Peru to reduce seismic risk in buildings.
Moreover; an upgrade in the Peruvian seismic code is needed in order to include probabilistic
methodologies.
AKNOWLEDGEMENT
The information of the seismic catalog of Peru was provided by H. Tavera from the GeophysicalInstitute of Peru and the information of the attenuation equation was provided by J. Chavez; theircollaboration is acknowledged. Special thanks are also given to CISMID and its director Carlos Zavala
for their valuable collaboration.
REFERENCES
Gasparini D. A., Vanmarcke E. H., 1976, Simulated earthquake ground motions compatible withprescribed response spectra, Report R76-4, Dep. Civil Eng., MIT, Cambridge, Massachusetts.
Jennings P. C., Housner G. W., Tsai N. C., 1969, Simulated Earthquake Motion for Design Purpose,proc. 4th WCEE, Santiago, Vol. I A1, 145-160.
Midorikawa M., Iiba M., Koshika N., Kani N., 2006, Performance-Based Seismic Provisions for
Seismically Isolated buildings in Japan, proc. 3rd ICUEE, Tokyo.
Park Y. J., Ang A. H–S, 1985, Mechanistic Seismic Damage Model for Reinforced Concrete, Jour.
Struc. Eng., ASCE, Vol. 111, SE 4, 722-739.
Park Y. J., Ang A. H–S, Wen Y.K., 1985, Seismic Damage Analysis of Reinforced Concrete
Buildings, Jour. Struc. Eng., ASCE, Vol. 111, SE 4, pp. 740-757.
Saito T., Wen Y. K., 1994, Seismic Risk Evaluation of R.C. Buildings in Japan, Report
UILU-ENG-94-2003, Structural Research Series No 587, Univ. of Illinois, Illinois.
Shibata A., 2010, Dynamic Analysis of Earthquake Resistant Structures, Tohoku University Press,Sendai.
Takahashi N., Shiohara H., 2004, Life Cycle Economic Loss due to Seismic Damage of Nonstructuralelements, proc. 13th WCEE, Vancouver, paper No. 203.
Tavera H., Agüero C., Fernandez E., Rodriguez S., 2007, Seismic Catalogo of Peru, GeophysicalInstitute of Peru, Lima. (In Spanish).

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