Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Porto, Portugal, 30 June - 2 July 2014
A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)
ISSN: 2311-9020; ISBN: 978-972-752-165-4
Development of fragility curves for base isolated RC structures
A. Bakhshi1, S.A. Mostafavi2
Associate Professor, Department of Civil Engineering, Sharif University of Technology, Tehran, Iran
2
M.Sc. Graduate Student, Department of Civil Engineering, Sharif University of Technology, Tehran, Iran
Email: [email protected], [email protected]
1
ABSTRACT: Despite assessing the efficacy of base isolation systems on seismic performance of existing structures in former
investigations using deterministic methods, it will be useful to assess the effect of these systems on the structural performance of
buildings through probabilistic methods such as developing fragility curves. This study considers three 2-D reinforced concrete
moment-resisting frame structures with different heights (3, 7, 12 stories). These structures are rehabilitated using Lead Rubber
Bearing (LRB) isolators based on FEMA 356 instructions. Two sets of 7 records including near-fault and far-field records
resting on stiff soil are selected to consider seismic uncertainty. Structural uncertainties are considered through modeling
different material properties as random variables using Monte Carlo simulation method. Nonlinear time-history analyses will be
conducted using open-source platform OpenSees for each level of seismic intensity parameter (here CAV) and using Park-Ang
damage index for RC building and shear strain for isolators finally fragility curves are developed. There is a high correlation
between CAV levels and mean damage. These fragility curves can be helpful to assess effects of adding base isolation systems
in seismic demand of structures in each damage state. Although near- fault earthquakes have high vulnerability on fixed base
buildings, their effects on base isolated are more.
KEY WORDS: Fragility curve, Base isolation, Near-fault earthquake, Seismic intensity measure parameters, Damage model,
Nonlinear dynamic analysis
1
INTRODUCTION
One of the best ways to control structure seismic performance
is to use base isolation systems due to their ductility and
energy dissipation mechanism which leads to increase in
damping and fundamental period of structure and as a result a
reduction in amplification occurring during earthquakes will
happen, especially for common short building, which their
natural fundamental frequency is near to earthquake
frequency. Owing to the performance of base isolation
systems during ground motions excitations and result of
experimental and analytical assessments, these systems are
widely used in both new structures and old structures (in order
to rehabilitate them).
On the other hand Near-Fault (NF) earthquakes have
destructive effects on isolation systems. These effects are due
to the pulses existing in displacement time-history in periods
near to the base isolated systems'. So it will be useful to
evaluate the effect of proximity of the isolated structures to
the seismic source.
It is important to define the structural damage
corresponding to a specific level of ground motion intensity
which will provide a good situation for decision makers in
governments, insurers and structures' owners to reduce the
consequences of the earthquakes. If we obtain the structural
vulnerability of a component under some levels of ground
motion intensity measure parameters (IM s) such as PGA, it
will result to develop a seismic Fragility curve. In this
method, it is required to define some Damage states and then
according to those states the existence probability of damage
related to each state by considering an IM can be compute as
fragility curve of that state.
Many investigations have been done on developing fragility
curves for each structure type especially for bridges.
Furthermore fragility curves can be used for assessing
different structural control systems to find the best retrofit
choice and seismic risk management.
Some investigations has been done on the base-isolated
highway bridges but in this project the effect of adding
isolators on reinforced concrete moment resisting frame
buildings will be include.
Karim & Yamazaki[1] assessed the effect of adding isolator
on fragility curve of highway bridges and proposed a
simplified approach for deriving their fragility curves. They
modeled 30 types of bridges with different height, weight and
over strength ratio factor and excited them under a suite of
250 ground motion records using PGA, PGV as IM. They
compared the curves of isolated and not-isolated structures
with different pier height and found that isolation increases
the fragility for tall piers bridges despite for short pier bridges.
They designed one type isolator for all pier height and they
didn’t consider the effect of isolator damage.
Zhang & Huo[2] used fragility functions to evaluate the
effectiveness of isolation devices for highway bridges using
both IDA , PSDA methods. They modeled 2- , 3- dimensional
bridge models to compare their fragility using Opensees
program[3]. They selected a suite of 250 ground motion
records and used PGA as IM. For damage computing column
curvature ductility was selected as pier damage index and
shear strain as isolator damage index and the system (super
structure and isolator) damage was computed by combination
of them. By illustrating the similar fragility for 2-, 3-D
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
structures, the 2-D model used for optimization of isolation
design.
In this investigation the effect of adding LRB to reinforced
concrete building is assessed using fragility curve under a
suite of 7 near-field and 7 far-field earthquakes separately.
Despite of the other investigations CAV, which has a good
correlation with structural damage potential[4], is selected as
intensity measure parameter. By modeling 3- , 7- , 12-story 2D RC moderate moment resist frames in 2 conditions fixedbase and LRB isolated, the analysis will be done by IDA
method. Also 5 models with different characteristic
parameters which are random variables are used for each
building in order to consider structural uncertainty. A
modified Park-Ang damage index is selected for RC buildings
and by assuming a log-normal distribution fragility curves are
derived.
2
DEVELOPMENT OF FRAGILITY CURVES
Fragility curves are useful and powerful tools for seismic
reliability, economic analysis, risk evaluating and
management. Seismic fragility curve as illustrated in equation
(1) is the conditional exceedance probability of engineering
demand parameter related to capacity of the structure at each
damage state (e.g. collapse) under an IM level of ground
motion.
|
(1)
There are 3 methods for developing fragility curves:
Empirical, Analytical and simplified approach.
2.1
Empirical fragility curves
Yamazaki et al. [5] developed a set of empirical fragility
curves based on actual damage data from the 1995 Kobe
earthquake, and showed the relationship between the damages
that occurred to the expressway bridge structures and the
ground motion indices. In this approach, the damage data of
the expressway structures due to the Kobe earthquake were
collected, and the ground motion indices along the
expressways were estimated based on the estimated strong
motion distribution using Kriging technique. The damage data
and ground motion indices were related to each damage rank,
and the damage ratio for each damage rank was obtained.
Finally, using the damage ratio for each damage rank, the
empirical fragility curves for the expressway bridge structures
were constructed assuming a lognormal distribution. [1]
2.2
Analytical fragility curves
Developing fragility curves using empirical approach is not
always possible because of lack of data from happened
earthquakes and defining damage states problems and also
sometimes it is required to do pre-earthquake planning or
retrofit prioritizing. So in such situations, by using analytical
approach the fragility curves can be developed.
In this approach, the response of structure can be
determined using numerical analysis results and damage state
will be computed by using a damage model and finally by
understanding a probabilistic distribution fragility curves
would be derived.
Usually two methods are used to develop fragility curves in
probabilistic seismic demand model which are: probabilistic
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seismic demand analysis (PSDA) that uses cloud approach
(uses un-scaled records) and incremental dynamic analysis
(IDA) that uses scaling approach. The PSDA method obtains
the mean and standard deviation by using a regression
analysis for each limit state but the IDA method scales records
to some pre-defined levels of IMs and do analysis for each IM
level so it has more computational efforts and more accuracy.
The analysis can be done by using nonlinear dynamic or static
analysis. Finally by assuming a probabilistic distribution
function such as normal cumulative distribution function or
log-normal cumulative distribution function can be selected to
fit the fragility curves.
2.3
Simplified Approach
Because of much computational effort of analytical approach
sometimes it is better to use a simplified approach instead
with accepting a little error.
In this investigation IDA method is used and a log-normal
cumulative distribution is assigned to damage measures to
define the fragility curves, as following in equation 2 :
1
3
(2)
STRUCTURAL MODEL OF BUILDING
In this section, first assumptions made in design process of
RC buildings and LRB isolators will be defined and then the
nonlinear modeling of structures in OpenSess will be
explained.
3.1
RC structure design
In this investigation, the buildings which are worked on are a
middle frame of a regular 3-D building. The buildings are
assumed as 3-, 7- and 12-story to evaluate height effect. 3and 7-story frames have 3 bays and 12-story frame has 4 bays.
Story heights are assumed 4.5m for first story and 3.5m for
other stories. Specified concrete compression strength (f’c) is
equal to 30MPa and reinforce yield stress (fy) 400MPa. By
assuming hospital utilization that is highly important and
moderate moment frame resting on a zone which is with
highest hazard level of Iranian seismic code(2800 standard)
(i.e. PGA=0.35g), base shear calculated. The buildings
designed for 60 percent of calculated base shear based on
ACI-318-05 and demand inter-story drift checked to be lower
than allowable related limit. Drift limitations controlled
designed sections for taller buildings than strength limits.
Design parameters of these RC buildings are listed in Table 1.
Table 1. Design parameters
No. of
stories
Height(m)
Ductility
coefficient
Bay
length(m)
3
7
12
10.5
25.5
43
7
7
7
5
6
6
Base
shear
coefficient
0.15
0.11
0.08
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
3.2
LRB design
Isolators have been designed based on FEMA356 for these
weak hospital buildings. The LRB hysteretic model assumed
as bilinear with first stiffness k1 and secondary stiffness k2 as
illustrated in Figure 1. The ratio between primary stiffness to
secondary stiffness (k1/k2) is assumed 10.0. The
characteristics of designed LRB isolators are listed in Table 2.
Figure 2. Hysteretic behavior of concrete02[3]
Figure 1. LRB bilinear model
Table 2. Characteristics of LRB
No.
Of
stor
ies
Design
displac
ement
(cm)
3
23.2
7
26.1
12
28.6
3.3
Col.
Positi
on
Q
(KN)
Q/W
K2
(KN/m
)
Rubber
height tr
(mm)
Mid.
Cor.
Mid.
Cor.
Mid.
40.7
20.3
103.7
51.9
172.2
0.048
0.048
0.045
0.045
0.043
354.7
177.3
614.7
307.3
673.8
150
150
200
200
200
Cor.
86.1
0.043
336.9
200
RC frame nonlinear modeling
In order to nonlinear analyze of designed buildings, it is
required to model them in opensees platform; so the used
material is Concrete02 for concrete that include tension
linearly as in Figure 2 and Steel02 for reinforcement as in
Figure 3. For considering the effect of confinement of stirrups
on core concrete that increase both the strength and ductility,
Mander model[6] is used and defined section has different
patched fibers for cover and concrete. Linear P-delta effect
has been used for columns.
Figure 3. Hysteretic behavior of steel 02[3]
3.4
LRB nonlinear modeling
If a linear spring with stiffness equal to k2 becomes parallel
with a elastic perfect plastic spring with stiffness equal to (k1k2) which yields at a point with displacement equal to Fy/k1,
the behavior illustrated at Figure 1 will be resulted.
4
GROUND
MOTION
PARAMETER
INTENSITY
MEASURE
Although many other investigations use PGA or PGV for
developing fragility curves which are useful and well-known
parameters between engineers, here CAV is selected. CAV
encompass both intensity and duration of the accelerogram
and is defined as equation3 .
|
|
(3)
CAV has a good correlation with structure damage potential
where CAV=3m/s (which is computed after filtering
frequencies higher than 10 Hz) is as like as an event with
lower limit of MMI equal to 7 [4]. Also Bakhshi et al. find
that for short to mid rise reinforce concrete buildings, CAV
correlate well with structure damage[7]. By the way it is
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
required to develop a relation between CAV and other wellknown IMs such as MMI which Bozorgnia et al. has done it
for standardized CAV with MMI and JMA [8].
5
UNCERTAINTIES
Uncertainties can be taken as seismic, structural and site. Here
the first and second one are considered.
5.1
Seismic uncertainty
It is important to use a large suite of earthquake ground
motion records to minimize the error of uncertainty in results,
but because of computational efforts 7 records selected for
far-field and 7 for near-fault earthquakes. 10 Km displacement
to fault was the limit of being near and far. One of the
directions, which is perpendicular to fault and has pulse in
itself, is selected for analysis.
In order to select ground motion accelerogram, the events
happened at soil type C of NEHRP, magnitude larger than 5.5
PGA>0.2g and PGV>0.15 m/sec was the qualification. The
selected records was according to FEMA P695[9].
5.2
Structural uncertainty
Because of construction problems sometimes a difference
between material properties happens. In this investigation
Specified concrete compression strength (f’c), reinforce yield
stress (fy), concrete Young’s modulus (E) and viscous
damping coefficient (ξ) are the selected random variables. For
each structural property mean value and standard deviation
and corresponding statistical distribution are selected based on
prior researches for example for concrete based on
Ellingwood et. al. [10] and for reinforcement based on Mirza
et. al.[11] investigations as listed in Table 3. Also for damping
a uniform distribution between 0.02-0.05 of critical damping
is used. By constructing 5 random numbers for each one using
Monte Carlo simulation method, structural uncertainty is
concluded by analyzing these 5 numerical models.
Table 3. Material properties with their average value, type of
distribution function and coefficient of variation
Average
parame
Distribution
value
COV.(%)
ter
(Mpa)
f'c
Normal
30
19
Fy
log Normal
445
7.3
Ec
Normal
25743
19
6
DAMAGE INDEX AND STATES
In order to determine the occurred damage in the structure
after an event it is required to define a damage index, which
model the damage accurately. So in this investigation a local
damage index for each component is selected and the global
damage is computed using weighting average of them with
respect to absorbed energy of each element. Although some
damage indices which are displacement based are more
useful, here a combined damage index is selected to include
the effect of absorbed energy in element. This damage model
is a modified index of well-known Park-Ang damage model
[12] that is moment and curvature based and the recoverable
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deformation is removed from the first term[13] as defined in
equation (4)
DIPA
β
dE
M .
( 4)
In which Øm is taken from the maximum curvature happened
in each element edge that is more critical than other points, βe
structural type coefficient is assumed 0.15, The integral part
of second term is the area under M- Ø hysteretic diagram
under corresponding IM level of ground motion. Also Øu is
the ultimate curvature of the component and Øy, My are the
yield point at M-Ø pushover diagram. This M- Ø diagram is
created in opensess program for each beam and column
section using a “zero-length element section” that is fixed in
one side and is loaded monotonically with an increasing
moment at other side. The yield point is obvious and the point
in which the stiffness is suddenly reduced is the ultimate point
for finding Øu.
After calculating the occurred damage at each element, the
global damage of story and building is calculated as illustrated
in equations (5) and (6):
DI
DI
∑ E
. DI
∑E
∑ E
∑E
(5)
. DI
(6)
The corresponding damage states of Park-Ang damage index
which is result of calibration according to damaged buildings
in the 1985 Mexico earthquake is represented in Table 4 at 5
states[14]. The best estimate value for various damage states
are set as the middle point of each range.
Table 4. RC building damage states
Damage state
Nonstructural
Slight
Moderate
Severe
Collapse
Damage
range
0.01 - 0.1
0.1 - 0.2
0.2 - 0.5
0.5 – 0.85
0.85-1.15
Best
estimate
0.05
0.15
0.35
0.67
1
For determining the damage occurred at the isolators shear
strain (γ) is used because of better characterizing the bearing
behavior due to the its effect on the shear modulus and
damping of rubber [15]. The corresponding damage states of
this damage index are listed as shown in Table 5.[2]
Table 5. Isolator damage states
Damage state
Minor
Slight
Moderate
Severe
Collapse
Damage
range
25‐75
75‐125
125‐175
175‐225
225‐275
Best
estimate
50
100
150
200
250
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
(7)
In which DSs is structure damage state and DSI is isolator
damage state.
Here damage of both components are normalized to 5 ranges
between 0.5-5.5 . In other words in this method amount of
damaged are combined and not damage states. Also in their
investigations there is no difference between DS equal to 2.01
and 2.99. But again these normalized damage indices are
combined with those weights of 25 and 75 for isolator and
building because of higher importance of building. This
normalization is shown in equation (8)
DI
DS
DI DI
UL
LL
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
0
(8)
Where DI is the damage occurred to each component ( ParkAng for RC building and shear strain for isolator) ,
is best
estimate of corresponding damage state, ULi and LLi are
upper bound and lower bound of that damage state. Also DSi
is the best estimate of corresponding new normalized damage
states (i.e. 1,2,3,4 and 5).
7
0,9
RESULTS AND DISCUSSION
After analyzing the 3 height type buildings, that each one has
modeled in 5 models to include structural uncertainty, under a
suit of 14 earthquake records at levels of CAV from 3 to 27
m/s in 10 levels, the resulting fragility curve of each building
in fixed base and base isolated situation is derived separately.
The related statistical distribution function is log-normal as
defined in equation (2).
The Pearson correlation between CAV levels and median of
damage index at each structure and a result of 97.3-99.9
percent for both isolated and fixed base structures is found. So
the selected intensity measure parameter and damage model
correlate well.
The result fragility curves for fixed base versus base isolated
building under near and far earthquakes are shown in Figure 4
to Figure 9. In these figures FB, BI means fixed base structure
and base isolated structure. Also LS=1, 2, 3, 4 , 5 respectively,
represent nonstructural(minor) , slight, moderate, severe and
collapse damage state.
10
20
CAV (m/s)
30
FB-LS=1
FB-LS=2
FB-LS=3
FB-LS=4
FB-LS=5
BI-LS=1
BI-LS=2
BI-LS=3
BI-LS=4
BI-LS=5
Figure 4. Fragility curve of 3 story building under near-fault
records isolated vs. fixed base
1
0,9
0,8
Probability of Exceedance
DS
int 0.75 . DSS 0.25 . DSI , DSS , DSI 4 4 , DSS or DSI 4
1
Probability of Exceedance
For computing the damage occurred at system of RC
building and isolator (system damage), some investigations
assumed the system serial or parallel with maximum and
minimum damage state of each component although the
system damage state is between them where Zhang&Huo [2]
prefer an average combination when 4 damage levels are
defined as shown in equation (7). They assumed a serial
system when one component ( Structure or Isolator) reaches
collapse.
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
0
10
20
30
CAV (m/s)
FB-LS=1
FB-LS=2
FB-LS=3
FB-LS=4
FB-LS=5
BI-LS=1
BI-LS=2
BI-LS=3
BI-LS=4
BI-LS=5
Figure 5. Fragility curve of 3 story building under far-field
records isolated vs. fixed base
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1
1
0,9
0,9
0,8
0,8
Probability of Exceedance
Probability of Exceedance
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
0,7
0,6
0,5
0,4
0,3
0,7
0,6
0,5
0,4
0,3
0,2
0,2
0,1
0,1
0
0
0
10
20
30
0
CAV (m/s)
FB-LS=1
FB-LS=4
BI-LS=2
BI-LS=5
20
30
CAV (m/s)
FB-LS=2
FB-LS=5
BI-LS=3
FB-LS=1
FB-LS=4
BI-LS=2
BI-LS=5
FB-LS=3
BI-LS=1
BI-LS=4
Figure 6. . Fragility curve of 7 story building under near-fault
records isolated vs. fixed base
0,9
0,9
0,8
0,8
0,7
0,7
Probability of Exceedance
Probability of Exceedance
1
0,5
0,4
0,3
FB-LS=3
BI-LS=1
BI-LS=4
0,6
0,5
0,4
0,3
0,2
0,2
0,1
0,1
0
FB-LS=2
FB-LS=5
BI-LS=3
Figure 8. Fragility curve of 12 story building under near-fault
records isolated vs. fixed base
1
0,6
0
0
10
FB-LS=1
FB-LS=4
BI-LS=2
BI-LS=5
CAV (m/s)
FB-LS=2
FB-LS=5
BI-LS=3
20
30
FB-LS=3
BI-LS=1
BI-LS=4
Figure 7. Fragility curve of 7 story building under far-field
records isolated vs. fixed base
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10
0
10
CAV (m/s)
20
30
FB-LS=1
FB-LS=2
FB-LS=3
FB-LS=4
FB-LS=5
BI-LS=1
BI-LS=2
BI-LS=3
BI-LS=4
BI-LS=5
Figure 9. Fragility curve of 12 story building under far-field
records isolated vs. fixed base
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
As shown in these curves retrofitting theses RC buildings
by using LRB isolators have reduced the probability of
exceeding damage significantly for example 20 percent
decrease of total (100 percent probability of exceedance) at
collapse state under near and 5 to 10 percent decrease under
far field earthquakes. Also in repairable states (LS=1 to 3),
more amount of decrease occurs.
By comparing the fragility curves under near- vs. far-source
events, more destroying potential is clear for near-source
event for both fixed base and base isolated cases but the
fragility curve of isolated building at minor state (LS=1) is
between moderate and slight states of fixed base building
when under near-fault earthquakes and between severe and
moderate when under far-field earthquakes, so it becomes
obvious that isolators are more vulnerable under near source
records and it is because of existence of strong displacement
pulses at some periods near to first period of isolated structure
By comparing the results of different fixed base buildings
although it was expected to have more vulnerability at taller
buildings but it did not happened specially for 12-story
building because at designing of them, the displacement
controlled related to strength and in order to increase stiffness
, the section size increased; in other words it is clear that they
are over designed and moment frames are not suitable
structure system for tall buildings and increasing stiffness by
using shear wall or bracing systems is better for a more
economic design. Also by comparing isolation effect on
decreasing damage probability for theses 3 buildings when
under near-fault earthquakes it found that isolation moves
collapse state to between slight to moderate for 3 story
building (as in Fig. 4) and for 7 story from collapse to severe
and for 12 story from collapse to slight state (as in Figs 6,8)
but for when under far-field earthquakes fragility of fixed base
for all buildings in collapse and severe damage states is
between fragility of isolated building at nonstructural and
slight damage states. More efficiency of isolators for 12 story
building is due to high design period and damping of designed
LRB isolator used for them respect to others.
8
CONCLUTION
ACKNOWLEDGEMENTS
This research was supported by Civil Engineering Department
and Research and Technology Affairs of Sharif University of
Technology. Authors wish to thank gratefully this support.
REFRENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
K. R. Karim and F. Yamazaki, “Effect of isolation on fragility curves
of highway bridges based on simplified approach,” Soil Dynamics and
Earthquake Engineering, vol. 27, no. 5, pp. 414–426, May 2007.
J. Zhang and Y. Huo, “Evaluating effectiveness and optimum design of
isolation devices for highway bridges using the fragility function
method,” Engineering Structures, vol. 31, no. 8, pp. 1648–1660, Aug.
2009.
“Opensees.” Pacific Earthquake Engineering Research Center,
University of California,Berekeley, 2006.
S. L. Kramer, Geotechnical Earthquake Engineering. Prentice-Hall,
1996.
F. Yamazaki, H. Motomura, and T. Hamada, “DAMAGE
ASSESSMENT OF EXPRESSWAY NETWORKS IN JAPAN
BASED ON SEISMIC MONITORING,” in 12 WCEE, 2000, pp. 1–8.
R. Mander, J. B., Priestley, M. J., & Park, “Theoretical stress-strain
model for confined concrete,” ASCE Journal of Structural
Engineering, vol. 114, no. 8, pp. 1804–1826, 1988.
A. Bakhshi, H. Tavallali, and K. Karimi, “Evaluation of Structural
Damage using Simplified Methods,” 2007.
K. W. Campbell and Y. Bozorgnia, “Use of Cumulative Absolute
Velocity(CAV) in Damage Assessment,” in 15WCEE, 2012.
FEMA P695, Quantification of Building Seismic Performance Factors,
no. June. Federal Emergency Management Agency, Washington, D.C.,
2009.
B. Ellingwood and H. Hwang, “Probabilistic Descriptions of
Resistance of Safety-Related Structures in Nuclear plants,” Nuclear
Engineering and Design, vol. 88, pp. 169–178, 1985.
S. A. Mirza and J. G. MacGregor, “Variability of Mechanical
Properties of Reinforcing Bars,” Journal of The Structural Division,
vol. 105, no. 5, pp. 921–937, 1979.
A. H.-S. Park,Young-ji and Ang, “Mechanistic seismic damage model
for reinforced concrete,” ASCE Journal of Structural Engineering, vol.
111, no. 4, pp. 722–739, 1985.
M. S. Williams and R. G. Sexsmith., “Seismic damage indices for
concrete structures: a state-of-the-art review,” Earthquake Spectra, vol.
11, no. 2, pp. 319–349, 1995.
H. H. M. Hwang and J.-R. Huo, “Generation of hazard-consistent
fragility curves,” Soil Dynamics and Earthquake Engineering, vol. 13,
no. 5, pp. 345–354, Jan. 1994.
J. M. Naeim, F., Kelly, Design of Seismic Isolated Structures: From
Theory to Practice. wiely, 1999.
By using fragility curves as a middle instrument, it is possible
to evaluate different retrofit methods, decision making, risk
assessing and managing.
For 2-D RC buildings in 3, 7, and 12-story under 2 suites of
earthquakes near-fault and far-field, fragility curves in fixed
base and LRB isolated situation were derived when CAV is as
IM and high correlation found between it and corresponding
damage (upper than 97%).
By comparing these fragility curves it found that isolators
are a good retrofit method that can decrease the vulnerability
of RC buildings. In addition by assessing the effect of being
the earthquake near to source it was obvious that these records
are more vulnerable for isolated buildings; for example under
a near ground motion with CAV=10 g-s that has pulse the
exceedance probability of damage from nonstructural state
under near-source is about 20% but under far-field event it
will be zero.
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