See discussions, stats, and author profiles for this publication at: https://www.researchgate.

net/publication/277901456

Seismic Fragility Assessment of RC Frame-Shear Wall Structures Designed

According to the Current Chinese Seismic Design Code

Article in Journal of Asian Architecture and Building Engineering · May 2015

DOI: 10.3130/jaabe.14.459

CITATIONS READS

6 348

3 authors, including:

Huanjun Jiang Liu Xiaojuan

Tongji University National Huaqiao University
147 PUBLICATIONS 1,598 CITATIONS 3 PUBLICATIONS 99 CITATIONS

SEE PROFILE SEE PROFILE

All content following this page was uploaded by Huanjun Jiang on 11 November 2015.

The user has requested enhancement of the downloaded file.

 Seismic Fragility Assessment of RC Frame-Shear Wall Structures Designed According to the
Current Chinese Seismic Design Code

Huanjun Jiang1, Xiaojuan Liu*2 and Lingling Hu3

1
Professor, State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, China
2
Doctoral Candidate, State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, China
3
Assistant Engineer, Shanghai Sunyat Architecture Design Co., Ltd., China

Abstract
After learning from several devastating earthquakes in China in recent years, stricter design criteria have
been introduced in the current Chinese seismic design code. To investigate the reliability of the current
seismic design code, seismic fragility analyses were performed for 45 10-story reinforced concrete (RC)
frame-shear wall structures designed according to the current Chinese seismic design code by analytical
methods, considering the uncertainty of earthquake ground motions. The plastic rotation at the ends of
the structural component (or the total chord rotation) and the maximum inter-story drift were employed as
damage identifiers to quantify the four performance levels, i.e., fully operational, operational, repairable
and collapse prevention. Thus, seismic fragility curves corresponding to individual performance levels were
developed on the basis of nonlinear time history analyses for the reference RC frame-shear wall structure.
The influences of the site soil type, the seismic protection intensity and the performance index on the fragility
curves were analyzed. The structural reliability of RC frame-shear wall structures was examined using the
developed fragility curves. The results indicate that the seismic performance objectives of RC frame-shear
wall structures designed according to the current Chinese seismic design code can be achieved with good
reliability.

Keywords: RC frame-shear wall structure; seismic fragility; performance-based seismic design

1. Introduction examine the appropriateness of the current CCSDB,

Severe damage and collapse of buildings were seismic fragility analyses of RC moment-resisting
observed in recent devastating earthquakes in China, frames designed according to the current CCSDB
such as the 2008 Wenchuan Earthquake and the 2010 have been conducted by some researchers. Jiang et
Yushu Earthquake, which resulted in a series of social al. (2012) performed seismic fragility analysis of RC
and economic problems. The lessons learned from past frame structures designed according to the current
earthquakes raise the need to introduce stricter seismic CCSDB. The results indicate that seismic performance
design criteria for building structures in the newly objectives for RC frame structures designed in line
revised seismic design code. The updated Chinese with the current Chinese code can be achieved in good
seismic design code, Code for Seismic Design of reliability. Similar study was conducted by Wu et al.
Buildings (GB50011-2010) (MOHURD, 2010), has (2012). It is concluded that the seismic performance
been implemented since December 1st, 2010. More of the RC frame structures designed according to the
rigorous seismic design measures are specified in the current CCSDB is strongly enhanced compared with
current Chinese Code for Seismic Design of Buildings that of the structures built before the implementation of
(CCSDB), and additionally, performance-based the current CCSDB. The fragility analysis performed
seismic design (PBSD) is introduced in the code. To by Yang and He (2013) revealed that the RC frame
structures designed according to the current CCSDB
can meet the performance objective of collapse
*Contact Author: Xiaojuan Liu, Doctoral Candidate, prevention under the rare earthquake.
Research Institute of Structural Engineering and Disaster Fragility analysis, a useful tool for showing the
Reduction, College of Civil Engineering, Tongji University, probability of structural damage due to earthquakes
1239 Siping Road, Shanghai 200092, China as a function of ground motion intensity indices, is
Tel: +86-21-65986151 Fax: +86-21-65982668 essential for seismic risk assessment and performance-
E-mail: 2liuxjty@tongji.edu.cn based earthquake engineering. Due to its critical role in
( Received October 7, 2014 ; accepted March 9, 2015 ) regional seismic risk and loss estimation, many studies

Journal of Asian Architecture and Building Engineering/May 2015/466 459

have been conducted to determine the seismic fragility Wan, 2010; Chen, 2011), the limit values of damage
of structures under the effect of potential earthquake indexes corresponding to each performance level were
ground motions (Lagaros, 2008; Vargas et al., 2013; determined, as shown in Table 1. To be comparable, the
Unnikrishnan et al., 2013; Sengupta and Li, 2014). deformation indexes of structural components adopted
In the last 20 years, a large number of approaches in this study conform to FEMA 356 (FEMA, 2000).
have been proposed to compute fragility functions, For RC beams, the limit value of the plastic rotation
which can be classified into the four generic groups, corresponding to each performance level is related to
i.e., the empirical method, the judgmental method, the the parameter k, which is determined by the following
analytical method, and the hybrid method (Rossetto equation:
and Elnashai, 2003). In addition, experimental seismic
fragility curves have been developed in recent years f y As  As
(Retamales et al., 2013; Cosenza et al., 2014). (1)
k 1
The RC frame-shear wall structure is one of the 1 f c bh0b
most common structure types for high-rise buildings
around the world. Its structural behavior depends where fy is the design yielding strength of longitudinal
heavily on the behavior of the frame and the shear steel reinforcement; A s and A s' are the total area of
wall, leading to more complex dynamic behavior than tensile and compressive longitudinal reinforcement,
the pure frame structure and the shear wall structure. respectively, and A s'/A s should be larger than 0.3,
For rational estimation and reduction of the potential as specified in the current CCSDB; α1 is the factor
seismic risk associated with RC frame-shear wall depending on the concrete strength grade, which is
structures, it is necessary to evaluate the structural 1.0 for concrete with a strength grade not exceeding
seismic reliability of such structures by seismic C50, 0.94 for concrete with a strength grade exceeding
fragility analysis. However, in the literature, there C80, and the linear interpolated value for concrete
is very limited information available concerning the with strength grades between those values; fc is the
seismic vulnerability of RC frame-shear wall structures design compressive strength of concrete; b and h0 are
designed according to the current CCSDB from the the width and effective depth of the cross section,
perspective of performance-based seismic design. respectively; and ξb is the relative balanced depth of
In this study, the fragility curves for RC frame- compressive area of concrete.
shear wall structures designed according to the current For RC columns, three failure modes depending
CCSDB were developed by an analytical method. on shear span ratio λ, i.e., flexural failure, shear-
Fragility curves corresponding to four performance flexural failure and shear failure, were considered.
levels, quantified by the plastic rotation at the ends of For flexure dominating RC columns, the plastic hinge
structural components (or the total chord rotation) and rotation is adopted as the performance index. For
the inter-story drift ratio, which reflect the damage shear dominating RC columns, the plastic drift ratio
state of the structure at the structural component level is adopted as the performance index. Both the plastic
and the story level, respectively, were generated using hinge rotation and the plastic drift ratio are denoted by
regression analysis of the results obtained from a plastic rotation, as shown in Table 1. The limit value of
large number of nonlinear time histories of reference the plastic rotation corresponding to each performance
structural models. The effects of site soil and seismic level is related to the axial compressive ratio μ. For
protection intensity on the resulting fragility curves RC coupling beams, the total chord rotation or plastic
were investigated. The appropriateness of the current rotation is selected as the damage measure depending
CCSDB was examined using the results of this work. on the shear span ratio λ. The limit value of the total
chord rotation corresponding to each performance level
2. Damage Measure and Performance Levels is related to the parameter β, which is calculated by the
Defining limit states and selecting appropriate following equation:
damage indexes to quantify the seismic damage state
of the building structure is the first important step
  2.1 f c h /  s (2)
in fragility analysis. In this study, four performance For flexure dominating shear walls, the plastic hinge
levels, i.e., fully operational, operational, repairable, rotation is adopted as the performance index. For shear
and collapse prevention, were considered. Both dominating shear walls, the total drift ratio is adopted
the maximum inter-story drift ratio and the plastic as the performance index. The limit values of plastic
rotation at the ends of structural components (or the rotation and total drift ratio of each performance level
total chord rotation), which reflect the damage state are related to the parameters β1, β2 and β3, which are
of the structure at the story level and the component calculated by the following equations:
level, respectively, were used as damage indicators.
Based on a comprehensive review of past research 0 8 s f y
0.8
1  (3)
work on the quantification of seismic damage levels  fc
of building structures (MOHURD, 2010; Lu, 2009;

460 JAABE vol.14 no.2 May 2015 Huanjun Jiang

 2  1.4  s  f c (4) For seismic intensity 7, the PGA values of the three
earthquake levels are 35, 100 and 220 gal, respectively.
2 1 f cb
2.1 For seismic intensity 8, the PGA values of the three
3  (5)
 hazard levels are 70, 200 and 400 gal, respectively. In
the current CCSDB, there are five categories of site soil
where ρh is the area ratio of the stirrup reinforcement; conditions, ranging from stiff to soft soil, i.e., Class I0,
ρs is the area ratio of the longitudinal reinforcement; I1, II, III and IV, each of which is further classified into
μ is the axial compressive ratio. As specified in the three design groups, i.e., Group 1, 2 and 3, according
current CCSDB, for RC columns μ should be less than to the characteristic period of the ground motion. The
0.95, and for RC shear wall, μ should be less than 0.6; characteristic period of Group 3 is the longest. The
and λ is the shear span ratio. design group reflects the influence of the epicentral
Table 1. Limit Values of Damage Indexes Corresponding to Each Performance Level (Unit: Radian)
Limit Value of Damage Index
Damage
Conditions Fully Collapse
Index Operational Repairable
Operational Prevention
Story Level Damage Inter-story
1/800 1/400 1/200 1/100
Index Drift Ratio
Plastic
Beam 0 0.0026-0.0024k 0.0158-0.0142k 0.0231-0.0207k
Rotation
λ≥4 0 0.0027-0.0023μ 0.0162-0.0136μ 0.0205-0.0159μ
Plastic
Column 2<λ<4 0 0.0029-0.0026μ 0.0173-0.0156μ 0.0207-0.0160μ
Rotation
λ≤2 0 0.0028-0.0027μ 0.0169-0.0164μ 0.0184-0.0145μ
Plastic
3<λ≤5 0 0.0006×(λ-3)+0.002 0.0023×(λ-3)+0.006 0.004×(λ-3)+0.01
Rotation
Coupling 0.0133×β-1.3
Beam 2<λ≤3 Total Chord 0.0252×β-1.3+0.0014 0.0371×β-1.3+0.0021 0.07×β-1.3+0.004
+0.0076
Rotation
λ≤2 0.00095 0.0018 0.00265 0.005
Flexure Plastic 0.28
0 0.00175β1 0.0087β10.28+0.0031β2-0.187 0.0063β2-0.187
Shear Failure Rotation
Wall Shear Total Drift
0.0114β3-0.35 0.0216β3-0.35 0.0318β3-0.35 0.06β3-0.35
Failure Ratio
3. Analytical Model distance. All 15 types of site soil were considered,
A typical 10-story RC frame-shear wall structure in addition to 3 seismic intensity levels. Thus, a total
was chosen for this study. The site soil type and the of 45 RC frame-shear wall structures were designed
seismic protection intensity were considered to be according to the current CCSDB. The structural plan
the main design variables of the reference building layout was identical for all sample structures. The cross
structure. Three seismic protection intensities, 6, 7 and sectional dimensions of the structural components were
8, were selected because the seismic intensity of most different for structures with different seismic protection
areas in China ranges from 6 to 8. For seismic intensity intensities. The structural plan layout and the cross-
6, the PGA values of the three earthquake hazard sectional dimensions of the structures with intensity 7
levels, i.e., frequent earthquakes, basic earthquakes and are shown in Fig.1.
rare earthquakes, are 18, 50 and 125 gal, respectively.

Note: The red dashed line denotes the coupling beam.

Note: The red dashed line denotes the coupling beam.
Fig.1. Structural Plan Layout for Structures with Intensity 7 (Unit: mm)

JAABE vol.14 no.2 May 2015 Huanjun Jiang 461

 The story height of the ground floor was considered σs
to be 4.5 m, while the height of other stories was
taken to be 3.3 m. The dead load and live load applied fy 0 01Es
0.01E
on the floor slab were set as 4 kN/m2 and 2 kN/m2,
respectively. Considering the dead load of the infill
walls, the distributed load applied on the peripheral
beams and the interior beams was set as 12 kN/m 0
Es
and 10 kN/m, respectively. The material strength was εεy εsε
chosen as follows: the yielding strength of longitudinal
Fig.3. Constitutive Relationship for Steel Reinforcement
and stirrup reinforcement was 335 MPa and 300 MPa,
respectively, and the cubic compressive strength 4. Earthquake Ground Motion
of concrete was 35 MPa. The structural design was The demand and capacity of structures depend
performed with the aid of the software PKPM (CABR, significantly on earthquake ground motion and the
2013), which is the most widely used building structure properties of the structure. The random nature of the
design software in Chinese industry. The seismic earthquakes and the inherent variability of structural
action and vertical load were considered to be the main properties make the occurrence of structural damage
load applied to the reference structure. The design variable. However, the variability of structural
value of the load effect of the structural component is responses resulting from structural properties is much
determined as follows: smaller than the variability due to ground motion
(Jiang et al., 2012). In this study, the randomness of
S d  1.35SGk  1.4  0.7  SQk (6) earthquake ground motions was considered as the only
S d  1.2 SGE  1.3S EhK (7) source of uncertainty existing in the seismic demand,
while the properties of the structure were assumed to
where, Sd is the design value of the load effect; SGk be deterministic.
is the effect of the standard value of the dead load; In this study, natural earthquake ground motion
SQk is the effect of the standard value of the live load; records were carefully selected in line with the design
S GE is the effect of representative value of gravity acceleration spectra specified in the current CCSDB.
load; S Ehk is the effect of the standard value of the The 641 pairs of natural earthquake ground motion
horizontal earthquake. The steel reinforcement of records collected by the authors' laboratory were used
structural components was determined by the strength- in this study. These ground motions were classified
based seismic design method according to the current into 15 groups in accordance with the CCSDB.
CCSDB, which varied with site soil condition and In each group, 10 pairs of ground motions, whose
seismic protection intensity. elastic acceleration spectra agree best with the design
The analytical model was constructed with the spectrum specified in CCSDB, were selected from the
aid of the software Perform-3D (Computer and database. In total, 150 pairs of ground motions were
Structures Inc., 2006). Perform-3D is a powerful used as input motions in the time history analyses.
tool for implementing displacement-based seismic In general, the acceleration spectra of the selected
design and capacity design. The concentrated plastic ground motions agree well with the design spectra. The
hinge model was adopted for RC beams, while the acceleration spectra of the selected ground motions and
fiber model was applied for RC columns, shear walls the design spectra for the three design groups of Class
and coupling beams. The simplified Mander models IV are compared in Fig.4.
(Mander et al., 1988) for confined and unconfined For each sample structure, one group of 10 pairs
concrete were employed for core concrete and cover of selected ground motions covering the uncertainty
concrete, respectively, as shown in Fig.2.(a) and 2.(b). aspects, which was consistent with the design group
The bilinear stress-strain relationship considering of site soil for determining the strength and steel
the kinematic hardening effect was used for steel reinforcement of the structure, was used for the input
reinforcement, as shown in Fig.3. earthquake ground motions.
40
40
The ground motion intensity can be expressed by
35
Simplified 35 several commonly used intensity measures, such as
30 Actual 30
peak ground acceleration (PGA), spectral acceleration
Pa)

Stress(MPaa)

25 25
Stress(MP

20 20
Simplified
and spectral displacement. In this study, PGA was
15
10
15
10
Actual used as the only measure of earthquake intensity.
5 5 The accelerations of the input motions were scaled
0 0
0 0.001 0.002 0.003 0.004 0.005 0.006 0 0.003 0.006 0.009 0.012 0.015 according to the required PGA.
Strain Strain
(a) Unconfined Concrete (b) Confined Concrete

Fig.2. Constitutive Relationship for Concrete

462 JAABE vol.14 no.2 May 2015 Huanjun Jiang

 3.5
3.5
3.5
3.0 software Perform-3D. The probability that the plastic
3.0

spectrum(g)
3.0 rotation of the structural components (or the total chord
(g) (g)
spectrum(g)
(g)
2.5

Spectrum(g)
spectrum(g)
2.5
npectrum
Spectrum(g)
npectrum
2.5
Spectrum(g)
npectrum
2.0
2.0 rotation) and the maximum inter-story drift ratio of
2.0
the structures at a given intensity of ground excitation
Acceleration spS

1.5
Acceleration
Accelerationsp
Acceleration S

1.5
Acceleration S

exceed the limits specified for each performance level

Accelerationsp

1.5
Acceleration
Acceleration

1.0
Acceleration

1.0
1.0
0.5 was determined following Eq. 8. Based on previous
0.5
0.5
0.0 research work (Sucuoglu et al., 1998), the lognormal
0.0
0.00.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
P i3.0
Periods(s)
0.0 0.5 1.0 1.5 2.0 2.5 d (3.5
) 4.0 4.5 5.0 5.5 6.0
distribution, as shown in the following equation, was
P iPeriods
d ( ) (s)
Periods(s)
Periods
P i (s)
Periods(s)
d()
Periods (s)
assumed for the regression of the fragility relationship:
(a)(a)
(a)
Design
Design
Design
(a) Design
Group
Group
Group
1 of
Group1 1of
1ofof
Class
Class
Class
Class IVIV
IV IV  ln Y   
3.5 Pi     (9)
 
3.5
3.5
30
3.0 
(gg) (gg)

30
3.0
g)
spectrum(g)
Spectrum(g)(g
Spectrum(g)

30
3.0
spectrum
Accelerationspectrum(g)

2.5
where Φ is the standard normal accumulative
spectrum
spectrum(g)
Spectrum(g)

2.5
spectrum

2.5
2.0
2.0
distribution function; Y is the intensity measure of the
Acceleration

2.0
celeration

ground motions (here PGA); and χ and ζ are function

celeration

1.5
celeration
Acceleration
Accceleration

1.5
celeration
Accceleration

1.5
1.0
1.0 parameters, indicating the mean and standard deviation
Acc

1.0
0.5
0.5 of lnY. Nonlinear lease squares were used to optimize
0.5
0.0
0.0 0.0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
the two function parameters. Accordingly, the fragility
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
Periods(s)
0.0 0.5 1.0 1.5 2.0 2.5 3.5 4.0 4.5 5.0 5.5 6.0
3.0 (s)
Periods
Periods(s)
curves were derived.
Periods (s)
Periods(s)
Periods (s) 5.2 Parameter Analysis
(b)(b)
(b)(b)Design
Design
Design
Design
Group
Group
Group
Group
2 of
22 of
of Class
Class
Class
2 of IVIVIV
Class IV Three seismic hazard levels, i.e., frequent
3.5 earthquakes, basic earthquakes and rare earthquakes,
3.5
3.5
3.0
are adopted in the current CCSDB. The return periods
(g) (g)

3.0
of the three intensity levels of earthquake are 50,
ectrum (g)
ctrum(g)

3.0
ectrum
spectrum(g)
ctrum(g)

2.5
spectrum(g)
ctrum(g)

475 and 1642 to 2475 years, and the corresponding

ectrum
spectrum(g)

2.5
2.5
spec

2.0
Spe
Accelerationspec

2.0
exceeding probabilities in 50 years are 63%, 10% and
Spe
spec

2.0
Acceleration
Acceleration Spe
Acceleration

1.5
Acceleration
Acceleration

2 to 3%, respectively.
Acceleration
Acceleration

1.5
Acceleration

1.5
1.0
1.0
1.0 The fragility curves for the inter-story drift ratio with
0.5
0.5
0.5 different protection intensities are shown in Fig.5. In
0.0
0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
0.00.5
0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
general, the slope of the curve is steeper for performance
Periods(s)
2.5
Periods(s)
Periods (s)
3.5 4.0 4.5 5.0 5.5 6.0
3.0 (s)
0.0 0.5 1.0 1.5 2.0 Periods
Periods(s)
Periods (s)
levels with less severe damage conditions. At the
(c) Design Group 3 of Class IV same PGA, the probability of exceeding each damage
(c)(c) Design
Design Group
Group 3 of
3 of Class
Class IVIV level (exceeding probability) for intensity 6 is the
Fig.4.(c) Design
ComparisonGroup 3 of Class
of Acceleration IV
Spectra largest, while the exceeding probability for intensity
5. Fragility Curves 8 is the smallest. At the three earthquake hazard
5. 1 Derivation of Fragility Curves levels, i.e., frequent earthquakes, basic earthquakes
Fragility curves describe the conditional probability and rare earthquakes, the probability exceeding each
that a certain degree of damage will be met or performance level for intensity 8 is usually the largest
exceeded for a given intensity of ground excitation. while the value for intensity 6 is the smallest, but the
The conditional probability is defined as differences in the exceeding probability for different
protection intensities are not significant.
Pik  P  D  di Y 
yk  (8) Fig.6. shows the comparison of fragility curves for
different performance indexes with the intensity of 7.
where P ik is the conditional probability meeting or Some differences exist between different performance
exceeding the damage state di for a given intensity indexes. In general, most of the exceeding probabilities
of ground excitation y k; D is the damage measure; at each performance level at the story level are smaller
and Y is the variable that reflects the intensity of than at the structural component level. Among all the
ground excitation. The conditional probability could structural components, the exceeding probability at
be calculated if the probability distribution of the each performance level from high to low in order is
structural damage at a given earthquake level is as follows: coupling beams, shear walls, beams, and
obtained by accounting for stochastic variations of the columns, which indicates the order of the damage
ground motion. suffered and the degree of vulnerability to earthquakes.
The analytical method used in this study was based Therefore, the concept of reasonable multiple
on time history analysis, which was used to estimate seismic defense lines for a dual structural system
the seismic demand of the sample structure. In total, can be realized. The shear wall structure acts as the
4950 numerical simulations of time history analyses first defense line, while the moment-resisting frame
for the 45 reference structures were performed using structure serves as the second defense line.

JAABE vol.14 no.2 May 2015 Huanjun Jiang 463

 The effects of site soil class and design group are 6. Verification of Seismic Performance Objectives
significant. Fig.7. shows the exceeding probability Based on the fragility curves derived as described
results for plastic rotation of RC beams for the above, the average exceeding probability for each
same design group and different site soil class. The performance level at each specified earthquake design
exceeding probability of the structures with site soil level was determined. The average results are shown
Class IV is the largest, while the exceeding probability in Table 2. The reliability of the seismic performance
of the structures with site soil Class I0 is the smallest. objectives specified in the current CCSDB can be
Fig.8. shows the exceeding probability results for evaluated according to the results. In general, the
plastic rotation of RC beams for the same site soil exceeding probability with respect to the plastic
class and different design group. The exceeding rotation (or the total chord rotation) of the coupling
probability of each performance level is the largest beam is slightly larger than with respect to the other
for the structures with design group 3 and smallest performance indexes. For ordinary RC frame-shear
for the structures with design group 1. In general, the wall structures designed according to the current
exceeding probability tends to be greater for softer site CCSDB, the exceeding probabilities of performance
soils and longer characteristic periods. levels corresponding to the ordinary performance
objective, i.e., fully operational under frequent
100 100 100

80 80 80
100 100 100
Probabiliity (%)
ity (%)lity(%)

Probabillity(%)
(%)

ity (%)
ity(%)

60 80 8060 80 60
Probability

Probabili
Probabillity(%)

Probabillity(%)
Probabil
Probabili

(%)

ity (%)
ity(%)

60 6040 60 40
40
Probability

Probabili

Probabili
Probabili

40 40 40
20 20 20
20 20 20
0 0 0
0 0 0.4 0.8 1.2 1.6 2 0 0 0.5 1 1.5 2 2.50 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
PGA(m/s 0 0.5 1 PGA(m/s
1.5
PGA (m/s22)2) 2.5 0 0.5 1 1.5 2 2.5 3 PGA(m/s
3.5 4 4.522)
0 0.4
(m/s)21.2
0.8 1.6 2 PGA (m/s )
2
PGAPGA(m/s )2)2 PGA(m/s
PGA (m/s2)2) PGA(m/s
PGA (m/s2))
2
PGA (m/s )

(a) Intensity
(a)(a)
Intensity 6 66
Intensity (b)(b) Intensity
(b) 7 77
Intensity
Intensity (c)
(c)Intensity
(c) Intensity 8Intensity 8 8
Fully
Fully Operational
Operational Operational
Operational Repairable
Repairable Collapse Prevention
Collapse Prevention

Fig.5. Fragility Curves for Inter-story Drift Ratio with Different Seismic Protection Intensity

100 100
100 100
80 80
(%)) (%))

80 80
(%) (%)

60
Probability

60
Probability

60
Probability

60
40 100 10040
Probability

40 80 8040
20
P

20
Probability (%))
Probability (%)

6020
P

20 60
0 0
40 40 0 0 0.5 1 1.5 2 2.5
0 0 0.5 1 1.5 2 2.5
0 20 0.5 PGA
1 (m/s1.5
2)
2 2.5 20 0 0.5 PGA
1 (m/s1.5
2)
2 2.5
P

PGA (m/s2)
0 (a)Fully
(a) FullyOperational
PGA (m/s2)
Operational 0 (b)
(b)Operational
Operational
(a)
0
Fully
0.5
Operational
1 1.5 2 2.5 0 0.5
(b)PGA
1
Operational
1.5
(m/s )
2 2.5
2
100 PGA (m/s2) 100

100
80 (a) Fully Operational 100
80 (b) Operational
80 100 80
(%) (%)

100
(%) (%)

60 60
bability
ability

60 80 80 60
40 40
bability
ability
Proba

bability (%)
Prob
Probaability (%)

60 60
40 40
20
Proba

20
Prob

40 40
20 20
Prob

0 0
20 20
0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5
0 0
1PGA (m/s
1.5) 1PGA (m/s
1.5)
2 2
0 0 0.5 2 2.5 0 0 0.5 2 2.5
0 0.5 1 2 1.5 2 2.5 0 0.5 1 1.5 22 2.5
(c) Repairable
PGA (m/s )
PGA (m/s ) 2 (d) Collapse
PGA (m/s ) Prevention
PGA (m/s )
2

(c) Repairable
(c)(c)
Repairable
Repairable (d)
(d) (d)Collapse
Collapse
Collapse Prevention
Prevention
Prevention
Inter story drift ratio
Inter-story Plastic rotation of beam Plastic rotation of column
Inter-story
Inter storystory
driftdrift
Inter-story
Inter ratio
ratio Plastic rotationofof
Plastic rotation beam
beam Plastic
Plastic rotation
rotation of column
of column
Plastic rotation of coupling beam Plastic rotation of shear wall
Plastic rotation of coupling
Plastic rotation of coupling beam beam Plastic
Plasticrotation of shear
rotation wall wall
of shear

Fig.6. Comparison of Fragility Curves for Different Performance Indexes with Intensity 7

464 JAABE vol.14 no.2 May 2015 Huanjun Jiang

 100 100
100 100
80 80
80

%)
80

%)
(%
%)

%)
(%
%)

%)
%)
Probability(%

Probability(%
(%
Probability(%

Probability(%
(%

%)
(%
60

%)
60

%)
%)
Probability(%

Probability
Probability(%
(%

Probability
Probability
Probability
60 60

Probability
Probability
40 40
40 40
20 20
20 20
0 0
0 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0.5 1 1.5 2 2.5 3 3.5 4 4.5
0 0.5 1 1.5 PGA(m/s
2 2.5 22 3 3.5 4 4.5 0 0.5 1 1.5 PGA
2 (m/s
2.5 2222)) 3
PGA(m/s 3.5 4 4.5
PGA (m/s222)) PGA(m/s
(m/s2))
2
PGA (m/s2))
PGA(m/s PGA
((a)) Fully
FFully
ll Operational
O ti l (b)
( (a)
(a) F ll Operational
) Fully Operational
O ti l (b)(b)O
Operational
O ti
ti ll
Operational
Operational
100 100
100 100
80 80
80 80

%)
%)

%)
%)

(%
(%

Probability(%)
)(%))
Probability(%)
(%

Probability(%)
Probability(%)

%)
%)

60 60

(%
(%

Probability(%)
Probability(%)

Probability
Probability

Probability
Probability

60 60

Probability
Probability

40 40
40 40
20 20
20 20
0 0
0 0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0.5 1 1.5 2 2.5 3 3.5 4 4.5
0 0.5 1 1.5 PGA(m/s
2 2.522 ) 223 3.5 4 4.5 0 0.5 1 1.5 PGA(m/s
2 2.522) 223 3.5 4 4.5
PGA (m/s ) PGA (m/s )
PGA(m/s 2) 2
PGA (m/s ) PGA(m/s 2) 2
PGA (m/s )
((c))) Repairable
R ii bl (d) C
Collapse
ll P
Prevention
ti
( (c)
(c) Repairable
RRepairable
bl (d) (d)
C
Collapse
ll P
Prevention
Collapse ti
Prevention

Site soil Class I 0 Site soil Class I 1 Site soil Class II Site soil Class III Site soil Class IV
Site soil Class I 0 Site soil Class I 1 Site soil Class II Site soil Class III Site soil Class IV

Fig.7. Comparison of Fragility Curves for Different Site Soil Classes with Design Group 1 and Intensity 8

100 100
100
100

80 80
80
80
%)
(%)
))

%)
(%)

(%
Probability(%)
(%
Probability(%)
Probability(%)
Probability(%)

60 60
60
Probability

60
Probability

Probability
Probability

100 100 40
40
40
40
80 80
20 20
20
20
%)
(%))

(%
Probability(%)
Probability(%)

60 60
Probability
Probability

0 0
0
0 40
0 40 0
0 0.5
0.5 1
1 1.5
1.5 2
2 2.5
2.5 3
3 3.5
3.5 4
4 4.5
4.5
0 0.50.5 1
1 1.5
1.5 2
2 2.5
2.5 3 3 3.5
3.5 4
4 4.5
4.5
PGA(m/s PGA(m/s
PGA(m/s
PGA 2 )) 2
(m/s
2
2)
20 PGA (m/s22 ))22)
PGA(m/s 20

0 ( )Fully
(a)
(a) Fully
llOperational
Operational
i l 0 (b)Operational
(b) O
Operational
ti l
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
PGA(m/s PGA(m/s
PGA (m/s)2)
2

100 PGA (m/s2 )2) 100

100
100
( ) Fully
(a) ll Operational
i l (b) O
Operational
ti l
80 80
80
80
%)
(%)
))

%)

100
(%
(%)

100
Probability(%)
(%
Probability(%)
Probability(%)
Probability(%)

60 60
60
60
Probability
Probability
Probability
Probability

80 80
%)
(%))

(%
Probability(%)

40
40
Probability(%)

40
40 60 60
Probability
Probability

20 40 40 20
20
20
20
0
20 0
0
0
0 0
0 0.5
0.5 1
1 1.5
1.5 2
2 2.5
2.5 3 3 3.5
3.5 4
4 4.5
4.5
0 00.5
0.5 1
1 1.5
1.5 2
2 2.52.5 3 3 3.5
3.5 4
4 4.5
4.5 0
PGA(m/s 2 2.5 PGA
PGA(m/s22 )
PGA(m/s
(m/s4)22) 4.5
2.5)) 22) 3
2 0 0.5 1 1.5 3 3.5
0 0.5 1 PGA
1.5 2 (m/s
PGA(m/s 2
3.5 4 4.5
PGA(m/s2 ) 2 PGA(m/s
PGA (m/s)2)
2
PGA (m/s )
(c)
(c)(c)Repairable
Repairable (d) C(d)
ll C
(d) Collapse
llPPrevention
Collapse
Collapse tiP
Prevention
ti
Prevention (d) C
Collapse
ll P
Prevention
ti
Repairable

Design
DesignGroup
Group 11 Design
Design Group
Group 2 2 Design
Design Group 3 Group 3

Fig.8. Comparison of Fragility Curves for Different Design Groups of Site Soil Class I0 with Intensity 8

earthquakes, repairable under basic earthquakes and 7. Conclusions

collapse prevention under rare earthquakes, are less The seismic fragility curves of RC frame-shear wall
than 5%. The exceeding probability of the operational structures designed in line with the current CCSDB
performance level under basic earthquakes with respect were derived through a large number of nonlinear time
to different performance indexes ranges from 7.69 to history analyses, accounting for the uncertainty of
14.32%, indicating that stricter seismic design criteria earthquake ground motions. The site soil type and the
than for ordinary buildings with ordinary performance seismic protection intensity were considered as the main
objectives are needed if enhanced performance design variables for the reference building structures.
objectives are required. Fragility curves for four performance levels, i.e.,

JAABE vol.14 no.2 May 2015 Huanjun Jiang 465

 Table 2. Average Exceeding Probability with Respect to Different Performance Indexes (Unit: %)
Limit Value of Damage Index
Performance Index Design Earthquake
Fully Operational Operational Repairable Collapse Prevention
Frequent Earthquake 1.42 0 0 0
Inter-story Drift Ratio Basic Earthquake 93.48 7.69 2.33 0
Rare Earthquake 100 95.67 20.83 1.28
Frequent Earthquake 2.23 0 0 0
Plastic Rotation of Beam Basic Earthquake 92.22 11.34 3.81 0.01
Rare Earthquake 100 92.87 14.57 2.16
Frequent Earthquake 2.07 0 0 0
Plastic Rotation of Column Basic Earthquake 91.35 9.16 1.93 0
Rare Earthquake 100 90.69 11.24 1.96
Plastic Rotation Frequent Earthquake 3.55 0 0 0
(or Total Chord Rotation) Basic Earthquake 94.32 14.32 4.32 0
of Coupling Beam Rare Earthquake 100 96.67 14.93 2.88
Plastic Rotation Frequent Earthquake 2.89 0 0 0
(or Total Drift Ratio) of Basic Earthquake 92.41 10.32 2.56 0
Shear Wall Rare Earthquake 100 93.14 13.72 2.23

fully operational, operational, repairable and collapse 7) Lagaros, N. D. (2008) Probabilistic fragility analysis: A tool for
assessing design rules of RC buildings. Earthquake Engineering
prevention, were developed, using the maximum inter-
and Engineering Vibration, 2008, 7(1), pp.45-56.
story drift ratio and the plastic rotation (or the total 8) Lu, X. L. (2009) Seismic design guidelines for tall buildings
chord rotation) of the structural components as the beyond the scope of design codes. Shanghai: Tongji University
performance indexes. The reliability of the ordinary Press. (in Chinese)
performance objectives of the reference RC frame- 9) Mander, J. B., Priestley, M. J. N., and Park, R. (1988) Theoretical
stress-strain model for confined concrete. Journal of Structural
shear wall structures were evaluated in terms of their
Engineering, 1988, 114(8), pp.1804-1826.
exceeding probabilities. The results indicated that the 10) MOHURD (Ministry of Housing and Urban-Rural Development
ordinary seismic performance objectives of ordinary of the People's Republic of China). (2010) Code for seismic design
buildings designed according to the current CCSDB of buildings(GB50011-2010). Beijing: China Architecture &
can be achieved with good reliability. Furthermore, Building Press. ( in Chinese)
11) Retamales, R., Davies, R., Mosqueda, G., and Filiatrault, A.
reasonable multiple seismic defense lines of the dual
(2013) Experimental seismic fragility of cold-formed steel framed
frame-shear wall structural system can be achieved. gypsum partition walls. Journal of Structural Engineering, 139,
pp.1285-1293.
Acknowledgements 12) Rossetto, T. and Elnashai, A. (2003) Derivation of vulnerability
The authors are grateful for support from the functions for European-type RC structures based on observational
data. Engineering Structures, 25(10), pp.1241-1263.
Doctoral Program Funds of the Ministry of Education
13) Sengupta, P. and Li, B. (2014) Seismic fragility evaluation
of China under grant No. 20130072110011 and the of lightly reinforced concrete beam-column joints. Journal of
National Natural Science Foundation of China under Earthquake Engineering, 18, pp.1102-1128.
grant Nos. 51478354 and 91315301-4. 14) Sucuoglu, H., Yucemen, S., Gezer, A., and Erberik, A. (1998)
Statistical evaluation of the damage potential of earthquake ground
motions. Structural Safety, 20(4), pp.357-378.
References
15) Unnikrishnan, V. U., Prasad, A. M., and Rao, B. N. (2013)
1) Chen, X. W. (2011) Research on deformation limit state of
Development of fragility curves using high-dimensional model
components of shear-wall structure and development of the
representation. Earthquake Engineering and Structural Dynamics,
computing platform. Ph.D. thesis. Guangzhou: South China
42, pp.419-430.
University of Technology. (in Chinese)
16) Vargas, Y. F., Pujades, L. G. and Barbat, A. H. (2013) Capacity,
2) Coseza, E., Sarno, L. D., Maddaloni, G., et al. (2014) Shake
fragility and damage in reinforced concrete buildings: a
table tests for the seismic fragility evaluation of hospital rooms.
probabilistic approach. Bull Earthquake Engineering, 11, pp.2007-
Earthquake Engineering and Structural Dynamics, published on
2032.
line.
17) Wan, H. T. (2010) Seismic performance test of RC beams and
3) CABR (China Academy of Building Research). (2013) PKPM
columns and research on parameter of deformation performance.
architecture design software CAD. China Academy of Building
Ph.D. thesis. Guangzhou: South China University of Technology.
Research: Beijing, China. (in Chinese)
(in Chinese)
4) Computer and Structures, Inc. (2006) Perform-3D, nonlinear
18) Wu, D., Tesfamariam, S., Stimemer, S. F., and Qin D. (2010)
analysis and performance assessment for 3D structure user guide,
Seismic fragility assessment of RC frame structure designed
version 4. Computers and Structures, Inc.: Berkeley, CA.
according to modern Chinese code for seismic design of buildings.
5) FEMA (Federal Emergency Management Agency). (2000) Pre-
Earthquake Engineering and Engineering Vibration, 2012, 11(3),
standard and commentary for the seismic rehabilitation of
pp.331-341.
buildings (Report No. FEMA 356). Washington, D.C.
19) Yang, P., He, C. H. (2013) Seismic vulnerability analysis of RC
6) Jiang, H. J., Lu, X. L., and Chen, L. Z. (2012) Seismic fragility
moment resisting frames complied with requirement of different
assessment of RC moment-resisting frames designed according
performance in current seismic code. China Civil Engineering
to the current Chinese seismic design code. Journal of Asian
Journal, 46(S1): 63-68. (in Chinese)
Architecture and Building Engineering, 11(1), pp.153-160.

466 JAABE vol.14 no.2 May 2015 Huanjun Jiang

View publication stats