ORIGINAL RESEARCH PAPER

Seismic fragility assessment for reinforced concretehigh-rise buildings in Southern Euro-Mediterraneanzone

Jelena Pejovic1 • Srdjan Jankovic1

Received: 29 December 2014 / Accepted: 4 September 2015� Springer Science+Business Media Dordrecht 2015

Abstract This paper presents seismic fragility assessment of RC high rise-buildings for

seismic excitation, typical for Southern Euro-Mediterranean zone. The fragility curves

were derived and log-normal cumulative distribution function parameters were obtained

for the four defined damage states by conducting 3600 nonlinear time-history analyses on

the basis of 60 ground motions with wide range of magnitudes, distance to source and

different site conditions, including in this way uncertainties during ground motion selec-

tion. As a prototype buildings, 20-story, 30-story and 40-story RC high-rise buildings with

core wall structural system were chosen. The key points of the process for obtaining the

fragility curves are shown by using algorithm, defined in this paper, and generally appli-

cable to all types of RC high-rise buildings. For the purpose of conducting nonlinear time-

history analyses, non-linear 3D models of the buildings were designed. A detailed prob-

abilistic seismic damage analysis was done and as its result the limit states as well as

corresponding damage states for RC high-rise buildings were defined, where the damage

states were treated as random variables. Inter-storey drifts at threshold of damage state

were defined as random variables with the range of possible values. Since no probabilistic

fragility curves exist for this class of buildings and for this seismic zone, this work partially

fills the void in Southern Euro-Mediterranean seismic risk assessment. The whole approach

presented in this paper may be used for efficient obtaining probabilistic fragility curves for

RC high-rise buildings of different configurations.

Keywords Reinforced concrete high-rise buildings � Seismic fragility assessment �Fragility curves � Probabilistic seismic damage analysis � Non-linear time-history analysis �Log-normal distribution function parameters

& Jelena Pejovicjelenar@t-com.me

Srdjan Jankovicsrdjanj@t-com.me

1 Faculty of Civil Engineering, University of Montenegro, Podgorica, Montenegro

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Bull Earthquake EngDOI 10.1007/s10518-015-9812-4

1 Introduction

In the last decades, urbanization and massive migrations of people, high land prices and

rapid economic development are just some of the reasons leading to the design of tall

buildings, which have become the norm in the architectural projects worldwide. In

December 2011, The Council on Tall Buildings, (The Council on Tall Buildings and Urban

Habitat 2011) claimed, that only in two decades, from 2000 to 2020, the average height of

building will be doubled. A similar trend has occurred in the Southern Euro-Mediterranean

zone. Since the entire Mediterranean zone is a seismically active zone, it is necessary to

perform detailed seismic risk assessment analyses of these populations of buildings. Within

the process of seismic risk assessment for the certain types of facilities and for certain

locations as well, a seismic vulnerability analysis of buildings is conducted resulted in

obtaining the fragility curves. Today, in literature, there is a lack of information regarding

obtaining fragility curves for RC high-rise buildings. Until today in Southern Euro-

Mediterranean seismic zone, for the population of RC high-rise buildings, such fragility

curves have not been obtained. The topic of this paper is related to the seismic fragility

assessment for RC high-rise buildings and to the derivation of fragility curves for seismic

excitation, specific for Southern Euro-Mediterranean zone. As a prototype buildings,

Fig. 1 Proposed fragility assessment framework

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20-story, 30-story and 40-story RC high-rise buildings are chosen, with core wall structural

system. The ground motions are chosen from Southern Euro-Mediterranean zone.

Fragility curves are defined as the conditional probability of exceedance of particular

damage (DS) or limit state for a given ground motion intensity measure (IM). Fragility

curves can be written in mathematical form as follows (DM is a demand measure, dmDS is

limit value of demand measure for particular damage state DS) (Eq. 1):

P DS=IM½ � ¼ P DM[ dmDS=IM� �

ð1Þ

There are different ways for obtaining fragility curves, from simple to more complex.

Simple methods provide approximated fragility curves while more complicated methods

provide more realistic and accurate curves. Rossetto and Elnashai (2003) classify the

existing fragility curves into four groups: empirical fragility curves, expert fragility curves,

analytical fragility curves and hybrid fragility curves. Empirical fragility curves are

obtained by statistical analyses of damaged buildings in the occurred earthquakes. The

example for empirical fragility curves for the region of Europe and for RC buildings are the

curves done by Rossetto and Elnashai (2003). Expert fragility curves are based partially or

completely on expert’s opinion and represent the simplest way for obtaining the curves.

The example for expert fragility curves are the curves implemented into HAZUS database

(National Institute of Building Sciences 1999). Analytical fragility curves are derived using

numerical models to simulate the behavior of systems. In the absence of experimental data,

observational data or an opinion of an expert, the only way to explore vulnerability of

buildings is by using analytical methods. Due to the lack of experimental data and data on

field in the occurred earthquake, the fragility curves for RC high-rise buildings could only

be derived by analytical methods (Ji et al. 2007b). Hybrid fragility curves are derived by

combining the above mentioned curves.

For obtaining fragility curves, in this paper analytical method is used. The key points of

the process of obtaining fragility curves are shown by using algorithm, defined in this

paper, and generally applicable to all types of RC high-rise buildings (Fig. 1). The fragility

curves were derived, as well as log-normal cumulative distribution function parameters

were obtained for the four defined damage states by conducting 3600 nonlinear time-

history analyses on the basis of 60 ground motions with wide range of magnitudes, distance

to source and different site condition. In this way uncertainties during ground motion

selection are included. Ground motion uncertainties are usually much higher than other

types of uncertainties in the probabilistic seismic risk analysis (Ji et al. 2009). Therefore,

the ground motions are in this paper treated as the main source of uncertainty in the process

of obtaining the fragility curves. In order to obtain fragility curves, due to their complexity

and large scope of work, the authors of this paper adapted the process by creating the

program in MATLAB (2013).

One of the most important phases in the process of obtaining fragility curves is defining

the limit states and corresponding damage states because they directly affect on derived

fragility curves (Erberik and Elnashai 2004). This paper provides a detailed damage

analysis of the prototype structures in order to define limit states and corresponding

damage states for RC high-rise buildings. A detailed quantitative approach is applied and

certain inter-storey drifts are determined at threshold of each defined damage state. These

analyses resulted in the four damage states for which, the fragility curves are obtained.

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2 Selection and description of prototype RC high-rise buildings

As a prototype buildings, in this paper, 20-story, 30-story and 40-story RC high-rise

buildings with core wall structural system are selected. The specific plan view of the story

characteristic for all prototype buildings, ETABS model (CSI 2013) and PERFORM-3D

model (CSI 2006) of the 30-story prototype RC high-rise building are shown on Fig. 2. RC

core wall structural system is a system which is applicable for RC high-rise buildings up to

the 50 storey (Taranath 2010).

The structural system with RC core wall is very suitable for architectonic reasons and is

very often used in high-rise buildings. RC ductile walls are placed in the central part of the

building around communication core, (lifts, staircase), forming in that way the spatial

system capable to resist to lateral loads in both directions. The space between central RC

core to the building exterior usually stays free or rarely filled with gravity RC columns

connected with beams or flat slab, providing more space in that way. At the building

perimeter, RC frames, used only as gravity load system, are formed. In these systems of

RC high-rise buildings, RC core wall accept all of the lateral load (Taranath 2010). The

main features of the prototype RC high-rise buildings are shown in the Table 1.

Seismic design of the prototype RC buildings was done in accordance with Eurocode 2

(CEN EC2 2004) and Eurocode 8-1 (CEN EC8 2004). The dimensions of the structural

elements of prototype buildings are obtained according to the requirements defined in

Eurocode’s provisions. Seismic linear analysis of buildings was done using a multi-modal

response spectrum analysis, which is quite appropriate due to higher-mode effects in high-

rise RC buildings. The modal periods of buildings and mass participation factors of first

four modes are shown in the Table 2. The elastic flexural and shear stiffness properties of

structural elements are taken to be equal to one-half of the corresponding stiffness of the

uncracked elements, according to Eurocode 8-1 (CEN EC8 2004). For linear analysis and

seismic design of buildings, ETABS spatial models of buildings (CSI 2013) were used.

Seismic forces are dominantly accepted by RC core walls. For this reason, RC core walls

were subject of further detailed seismic design in accordance with relevant provisions of

Eurocode and thereafter nonlinear time-history analyses.

Fig. 2 30-story prototype building ETABS2013 model (left), plan view of the story (middle) and 30-storyprototype building PERFORM3D model (right)

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3 Nonlinear modeling of prototype RC high-rise buildings

In the study, the PERFORM-3D program (CSI 2006) was used for the nonlinear time-

history analyses. The nonlinear models are designed as a spatial models and they consist of

RC core walls. The mathematical models used for elastic analysis are extended to include

the strength of structural elements and their post-elastic behaviour. Element properties are

based on mean values of the properties of the materials. Stress–strain relationship for

unconfined concrete, confined concrete and reinforcement steel are adopted in accordance

with the recommendations of Eurocode 8-2 (CEN 2005). Stress–strain relationship for

unconfined concrete with concrete mean strength of 53 MPa and confined concrete for

typical confining reinforcement in boundary wall elements are shown in Fig. 3. The steel

material is modeled with a bi-linear stress–strain relationship according to Eurocode 8-2

(CEN 2005) with expected yield mean strength of 575 MPa and ultimate strength of

660 MPa, both in compression and tension. The floor slabs are modeled as rigid

diaphragms.

The core walls are modeled using non-linear vertical fiber elements representing the

expected behavior of the concrete and reinforcing steel (CSI 2007). The area and location

of reinforcement within the cross-section and the properties of the concrete are defined

using individual fibers. The shear behavior is modeled as elastic. The behavior for out-of-

plane bending and behavior in horizontal transverse plane are assumed to be elastic. The

hinge lengths at the base of the wall are adopted according to Eurocode 8-1 (CEN EC8

2004). The coupling beams are defined as elastic beam elements with a nonlinear dis-

placement shear hinge at the mid-span of the beam. These are connected to the shear walls

using embedded elements as suggested by Powell (CSI 2007). The shear hinge behavior is

based on test results by Wallace (2012).

Table 1 Main features of the prototype RC high-rise buildings

Features 20-story prototypebuilding

30-story prototypebuilding

40-story prototypebuilding

Total height (m) 60 90 120

Storey height (m) 3 3 3

Floor RC slab thickness 20 cm 20 cm 20 cm

RC beams 40 9 65 cm 40 9 65 cm 40 9 65 cm

RC columns 80 9 80 cm 80 9 80 cm 90 9 90 cm

Core walls thickness 1–5 storey: 30 cm 1–5 storey: 40 cm 1–10 storey: 55 cm

6–20 storey: 20 cm 6–30 storey: 30 cm 11–40 storey: 45 cm

Coupling beams in Xdirection

20 9 80 cm and30 9 80 cm

30 9 80 cm and40 9 80 cm

45 9 80 cm and55 9 80 cm

Concrete fck (fcm) (MPa) 35 (43) 45 (53) 55 (63)

Reinforcement fyk (fym)(MPa)

500 (575) 500 (575) 500 (575)

Modulus of elasticity Ecm

(MPa)34,000 36,000 38,000

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4 Ground motion records selection

In the study, Southern Euro-Mediterranean seismic zone is selected. Therefore, the ground

motions selection was done within this zone. The data of Seismological Institute of

Montenegro and European strong motion database were used as database of ground

motions (Ambraseys et al. 2002). Ground motions were selected depending on the value of

magnitude M, distance to source R and site conditions. From the large number of available

records, there were chosen 60 ground motions out of which, 25 selected ground motions

were recorded on the rock which correspond to soil type A and 35 selected ground motions

recorded on stiff soil which correspond to soil type B, according to Eurocode 8-1 (CEN

EC8 2004). The values of magnitude of selected ground motions are in the range between

5.1 and 7.0 while the distances to source are in the range from 5 to 70 km. By using larger

number of ground motions with wider range of magnitudes, distance to source and

Table 2 Modal periods and mass participation factors for the prototype RC high-rise buildings

Prototype buildings 20-story prototypebuilding

30-story prototypebuilding

40-story prototypebuilding

Period in Y direction (s)

Mode

1 1.652 2.880 4.097

2 0.389 0.623 0.858

3 0.181 0.270 0.355

4 0.117 0.164 0.207

Period in X direction (s)

Mode

1 1.641 2.597 3.511

2 0.480 0.702 0.880

3 0.250 0.347 0.423

4 0.164 0.228 0.275

Mass participation factors in Y direction (%)

Mode

1 64.26 63.53 63.24

2 20.32 19.43 18.94

3 7.04 7.05 7.05

4 3.23 3.57 3.65

Sum of mass part factors in Ydirection (%)

94.85 93.58 92.88

Mass participation factors in X direction (%)

Mode

1 69.36 67.70 66.08

2 15.96 17.40 18.78

3 5.49 5.23 5.68

4 2.83 2.78 2.64

Sum of mass part factors in Xdirection (%)

93.64 93.11 93.18

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different site conditions, uncertainties during ground motions selection are being included.

High-rise buildings are specific, due to fact that their response frequency range is much

wider than for low-rise or mid-rise buildings. Accordingly, it is necessary to include a

larger number of ground motions, various magnitudes and distances to source. Uncer-

tainties during ground motions selection are usually much higher than other types of

uncertainties in the probabilistic analysis of seismic risk.

The main criterion used in this paper for the selection of ground motions, requires the

mean spectrum of the selected ground motions to be compatible with relevant target

spectrum over the wide spectral period range of interest. As a target spectrum, elastic EC8

spectrum for reference return period of 475 years with design ground acceleration of

0.37 g was chosen. Due to the lack of ground motions in the Southern Euro-Mediterranean

zone, which may be selected without being previously scaled and with mean spectrum to

be in accordance with Eurocode spectrum, it was necessary to scale the ground motions.

The mean squared error method (MSE) was chosen as a mode of scaling of ground motions

(PEER 2010). By this method ground motions are scaled in a way where the mean squared

error is minimized over the whole range of periods. The mean square error represents the

difference between the spectral acceleration of ground motion records and target spectrum

and it is calculated by Eq. (2).

MSE ¼Pn

i¼1 Stargeta Tið Þ � f � Srecorda Tið Þ� �2

nð2Þ

Parameter f in Eq. (2) is a linear scale factor. The geometric mean spectrum of the selected

ground motions is adopted to be the mean spectrum (PEER 2010). The MSE method is

especially effective in the selection of ground motions since it allows to choose, from the

large number of available records, ground motions whose response spectra the least deviate

from the target spectrum. In this way, the selected original ground motions scaled to

different intensity levels defined by peak ground acceleration (PGA) resulted in the small

dispersion of seismic response parameters (with coefficient of variation less than 0.3).

Except earthquakes which have reference return period of 475 years (or analogously the

seismic action associated with reference probability of exceedance, 10 %, in 50 years), the

Fig. 3 Stress–strain relationship for unconfined and confined concrete with concrete mean strength of53 MPa

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prototype buildings were tested on the seismic action which have reference return period of

2475 years (or analogously the seismic action associated with reference probability of

exceedance, 2 %, in 50 years). Since in Eurocode 8-1 (CEN EC8 2004) such high level of

seismic intensity is not defined, it was necessary to use the latest literature for defining

appropriate seismic action with 2 %/50. Data for this seismic intensity is defined by the

project called Seismic hazard harmonization in Europe-SHARE (Giardini et al. and the

SHARE consortium 2013). Seismic intensity which corresponds to return period of

2475 years for the territory of Mediterranean is two times higher than seismic intensity

which corresponds to return period of 475 years. In accordance with above mentioned, the

mean spectrum of ground motions with intensity of 2 %/50 is two times higher than the

mean spectrum of ground motions of 10 %50.

In the Figs. 4 and 5, response spectra of selected ground motions scaled by MSE

method for the intensity level of 10 %/50, the mean spectrum and relevant target spectra

(Eurocodes 8-1 elastic spectra) for the intensity level of 10 %/50 and the mean spectrum

for the intensity level of 2 %/50, for certain soil types are shown.

In this way scaled ground motions are directly used in probabilistic seismic damage

analysis of prototype RC high-rise buildings. For obtaining the fragility curves, selected

original ground motions are scaled to different intensity levels defined by PGA.

5 Probabilistic seismic damage analysis of prototype RC high-risebuildings

One of the most important phases of probabilistic performance-based analysis is defining

the limit states and corresponding damage states. Realistic and comprehensive limit states

determination and thus identification of the performance levels is one of the important

Fig. 4 Response spectra of the selected ground motions for soil type A, mean spectra of the selected groundmotions for intensity levels 10 %/50 and 2 %/50 and elastic EC8 spectrum for soil type A for intensity level10 %/50

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steps in the process of obtaining the fragility curves because of their direct influence on

derived fragility curves (Erberik and Elnashai 2004). Limit states are described with

possible and acceptable losses. The losses may be presented in different ways: through

possible levels of damage state (structural damage and nonstructural damage), number of

killed people in the earthquakes, economic losses, the time when the facility is out of

service, repairment costs and other. Limit states present discrete points on continuous scale

of damage states of structures. There are two basic approach of defining the limit states:

qualitative and quantitative approach. Qualitative approach in a description of structure’s

limit state is the most used in building regulations. FEMA 356 (2000) defines three basic

limit states for structural elements or performance levels: Immediate Occupancy IO, Life

Safety LS and Collapse Prevention CP. HAZUS (National Institute of Building Sciences

1999) defines four levels of structural and non-structural damage as follows: slight damage,

moderate damage, extensive damage and complete damage. Rossetto and Elnashai (2003)

defines seven limit states based on observational data of damages on buildings after the

earthquakes. They defined homogeneous scale of damage for RC structures (HRC scale)

for presenting the level of damage on RC structures with levels from 0 to 100 for four

characteristic RC structural systems.

Due to the lack of research in the case of RC high-rise buildings, particularly for

structural systems with core wall, current qualitative approaches can only serve as refer-

ences (Ji et al. 2007a). In order to obtain analytical fragility curves for RC high-rise

buildings, it is necessary to apply more detailed quantitative approach for defining limit

states and certain damage states. For quantification of limit states, it is necessary to express

the damage states in terms of deformation. Inter-storey drift is the most used parameter in

the literature for defining the limit states due to its simplicity. Nonlinear time-history

analyses and empirical observations suggest that there is a strong connection between

inter-storey drift and the level of structural damage. In the existing literature there are few

Fig. 5 Response spectra of the selected ground motions for soil type B, mean spectra of the selected groundmotions for intensity levels 10 %/50 and 2 %/50 and elastic EC8 spectrum for soil type B for intensity level10 %/50

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examples of defining the limit states by quantitative approach for structural system with

ductile walls using inter-storey drift such as Ghobarah (2004) and Rossetto and Elnashai

(2003). Specifically for RC high-rise buildings, Ji et al. (2007a) proposed the definition for

limit states and they determined relevant inter-storey drifts for certain limit states on the

basis of 54-story building with core wall and RC frames. In this paper limit states and

certain damage states for the prototype buildings with respect to inter-storey drifts at

threshold of damage state are defined. For that purpose, a detailed probabilistic seismic

damage analysis was conducted through performing a large number of nonlinear time-

history analyses.

5.1 Defining of limit states and damage states

In this paper the limit states are defined in the following way: Immediate Occupancy IO,

Life Safety LS and Collapse Prevention CP (Fig. 6). Structure at point of limit state

Immediate Occupancy IO has slight or no damage. Structure at point called Life Safety LS

can sustain moderate damage but still stays in the zone of high safety against collapse.

Structure at the point of limit state called Collapse Prevention CP has significant and large

damage and it is near to collapse. In compliance with limit states certain damage states are

defined. The four defined damage states are: slight damage DS1, moderate damage DS2,

extensive damage DS3 and complete damage DS4.

Such defined damage states are in compliance with damage scale of selected damage

index Park and Ang DIPA (Park and Ang 1985). Park and Ang index is adopted to be a

damage index in this paper. It is one of the most used damage indexes for its simplicity,

stability and confirmation through experimental research. Park and Ang damage index is

obtained by a linear combination of damage, caused by maximum inelastic deformation

and by the cumulative damage, resulting from repeated cyclic response (Eq. 3) (Park and

Ang 1985).

DIPA ¼ u

uuþ b � Eh

Fy � uuð3Þ

where u is maximum inelastic displacement during a ground motion, uu is an ultimate

displacement capacity of the system under a monotonically increasing lateral deformation,

Eh is hysteretic energy, Fy is yield strength of the structure, b dimensionless constant that

Fig. 6 Defined limit states and corresponding damage states

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depends on the structural properties and for the usual RC structures has value from 0.10 to

0.25 with mean value of 0.15.

According to the data based on damage of RC buildings, which were slightly or severely

damaged during few earthquakes occurred in America and Japan, Park and Ang defined the

relation between damage level and damage index (Table 3) (Park and Ang 1985).

The value of damage index DIPA = 0 indicates non-damaged structure or structure

remains in elastic behavior during earthquake. For damage index values DIPA\ 0.2 the

structure is exposed to minor damage, accompanied by visible cracks in structural ele-

ments. There is no delay in the functioning of facility for this level of damage and

rehabilitation of the structure is relatively simple. The values of damage index between 0.2

and 0.5 correspond to moderate level of damage, accompanied by the appearance of

reinforcement yielding in critical zones of some structural elements, including spalling of

the concrete cover, as well as formation of larger cracks in the plastic hinge zones. The

value of damage index DIPA = 0.5 is considered as a boundary between moderate and

severe damages or boundary between damage that can be repaired and damage that is

irreparable or the costs of damage are not economically justified. In a case of severe

damage it occurs concrete crushing and local buckling of longitudinal bars in the plastic

hinge zones. The collapse of the structure occurs in case of damage index value DIPA[ 1.

At this stage a loss of shear and/or axial load bearing capacity occurs, which results in

partial or complete collapse of structure.

As a deformation measure for defining limit states, inter-storey drift is selected, which is

at the same time the most used seismic response parameter. Specifically, maximum inter-

storey drift (relative storey displacement divided by the height of the storey) for whole

structure IDRmax is selected. In order to define range of certain damage state it is necessary

to determine inter-storey drift at threshold of damage state. At threshold of each damage

state there is corresponding damage index DIPA according to the Park and Ang scale. For

that reason, it is necessary to maintain correlation between the maximum inter-storey drift

and damage index, assuming that maximum inter-storey drift is required, depending on a

damage index. In this paper the values of inter-storey drifts at threshold of damage state are

described as random variables with range of possible values not as a single value or

deterministic parameter.

5.2 Results of damage analysis and relationship between damage index DIPAand maximum inter-storey drift IDRmax for prototype buildings

For determination of inter-storey drifts at threshold of certain damage state for the pro-

totype RC high-rise buildings, nonlinear time-history analyses were used. The prototype

buildings are exposed to the selected 60 ground motions with two levels of intensity (10 %/

50 and 2 %/50) in both directions of structures, which, in total include: 720 nonlinear time-

history analyses. These analyses required approximately 180 h of runtime on computer

Table 3 Interpretation ofdamage index

Damage states Damage index State of structure

Slight damage 0.0–0.2 Serviceable

Moderate damage 0.2–0.5 Repairable

Extensive damage 0.5–1.0 Irreparable

Collapse [1.0 Loss of storey or buildings

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Intel� CoreTM i5-3470 CPU 3.20 GHz and 8 GB of memory. After performing nonlinear

time-history analyses for selected ground motions result diagram is obtained which pre-

sents 720 points of pairs (DIPA,i, IDRmax,i) (Fig. 7). For each ground motion Park and Ang

damage index DIPA,i and maximum inter-storey drift IDRmax,i were determined. Regression

analysis was conducted. According to the constructed diagram it can be noticed that

between these two parameters is possible to establish linear regression model with very

high coefficient of determination R2 = 0.7981 or the coefficient of correlation r = 0.8934

which show very strong mathematical connection of these two parameters. Small values of

dispersion rIDRmax/DI were obtained. Since the distribution of seismic response parameter

IDRmax corresponds to the log-normal distribution, dispersion rIDRmax/DI is defined as the

standard deviation of the natural logarithms of the residuals IDRmax data from the

regression line. Obtained regression line represent median of random variable IDRmax/

DIPA i.e. value for which the probability that the random variable will have less or equal

value is 50 %. In the Fig. 7 are shown the lines which correspond to plus–minus one

standard deviation away from the median and in a case of log-normal distribution represent

16 % percentile and 84 % percentile.

With obtained linear relationship between damage index DIPA and maximum inter-

storey drift IDRmax, the values of inter-storey drifts at threshold of each damage state in

accordance with Park and Ang damage scale are determined. The values of derived inter-

storey drifts, their mean values (50th percentiles), 16 % percentiles and 84th percentiles for

certain damage states are shown in the Table 4.

Besides that, in the Table 4 confidence intervals for each damage state are shown.

Confidence interval provides information regarding the closeness of the calculated mean

value to the population mean value and is expressed by the probability. Plus–minus one-

sigma confidence interval (L1, L2) which corresponds to the probability of 84 % (calcu-

lated by Eq. 5) is shown in Table 4. In analytical practice the acceptable relative width of

confidence interval is 10 %. For derived inter-storey drifts at threshold of damage states

were obtained relative width of confidence interval (calculated by Eq. 6) in the amount

Fig. 7 Relationship between damage index DIPA and maximum inter-storey drift IDRmax for prototypebuildings

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about 2 % what is a very small relative width of confidence interval and indicates the high

level of accuracy of calculated random variables. On the other hand, the obtained values of

inter-storey drifts are in compliance with drifts defined by Ghobarah (2004) as well as with

inter-storey drifts defined by Rossetto and Elnashai (2003) over homogeneous damage

scale for RC buildings (HRC scale) with small differences because they were not formed

for high-rise RC buildings. If we compare inter-storey drifts at threshold of extensive

damage state and complete damage state defined in HAZUS database (National Institute of

Building Sciences 1999) (0.2 %-slight, 0.5 %-moderate, 1.5 %-extensive, 4.0 %-com-

plete) for structural system with ductile walls and number of storey higher than 8 (HAZUS

definition of high-rise buildings) with herein derived values for damage states DS3 and

DS4, we notice that later values are lower. This is because, the prototype buildings have

20, 30 and 40 stories and belongs to the category of real high-rise buildings which are more

flexible and more fragile than high-rise buildings from HAZUS database, which are

defined as buildings with number of stories[8.

6 Fragility curve assessment

Schematic representation of methodology used for obtaining the fragility curves is shown

in Fig. 8. Accordingly, for each level of intensity measure IMj, demand measures (max-

imum inter-storey drifts IDRmax) are obtained by conducting nonlinear time-history

analyses for all selected ground motions. Thus, scatter plot of nonlinear time-history

analysis results in terms of IDRmax for different levels of intensity measure IMj are

obtained. Then, for each level of intensity measure IMj and corresponding IDRmax values

(obtained as vertical scattered data), the probability of exceedance Pi,j of a certain damage

state (defined by IDRmaxDSi ) is calculated using Monte Carlo method. In this way, obtained

pairs, intensity measure, and corresponding probability of exceedance (IMj, Pij) are drawn

on the graphic and a dotted fragility curve is obtained. The dotted diagram (diagram of

sample probabilities) is fitted with most similar curve which represents a log-normal

cumulative distribution function. In the process of curve fitting, optimal log-normal dis-

tribution function parameter l and r for fragility curves are derived. Due to its simple

implementation and satisfying accuracy, in this research Monte Carlo method was applied

for determination of sample probabilities.

Log-normal cumulative distribution function by which the diagram of sample proba-

bilities is fitted has the following form (Eq. 4):

Table 4 Derived values of inter-storey drifts at threshold of damage states for the prototype RC high-risebuildings

Damagestates

Inter-storey drift at threshold of damage stateIDRmax (%)

Lower and upperendpoint of the 84 %confidence interval

Relative width ofconfidence interval

Median(50th percentile)

16thpercentile

84thpercentile

L1 L2 i (%)

DS1 0.250 0.190 0.330 0.247 0.253 2.40

DS2 0.528 0.398 0.702 0.522 0.534 2.27

DS3 0.945 0.710 1.260 0.935 0.955 2.12

DS4 1.640 1.230 2.190 1.622 1.658 2.19

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P DSi ¼ IDR[ IDRDSi=IM� �

¼ UlnIM � l

r

� �ð4Þ

U is the standard normal cumulative distribution function. The basic parameters of fragility

curve are the mean value l and standard deviation r. For log-normal distribution, the mean

value l is the median value of intensity measure at which the building reaches the

threshold of the damage state, i.e. the value of intensity measure for which probability of

exceedance threshold of damage state is 50 %. r represents standard deviation of the

natural logarithms of intensity measure for certain damage state. During the process of

fitting of fragility curves, optimal values for these two parameters are derived. In order to

obtain fragility curves and their optimal parameters, the authors of this paper adapted the

process by creating the program in MATLAB (2013) in compliance with schematic rep-

resentation in the Fig. 8. This program includes the whole procedure of obtaining the

fragility curves.

In the literature, there are several intensity measures that have been used for obtaining

the fragility curves. The most used are the following: PGA, spectral acceleration at some

periods (Sa), and spectral displacement at some periods (Sd). In this paper, PGA was

chosen as an intensity measure for obtaining the fragility curves. PGA was chosen because

it is the most used intensity measure for obtaining the fragility curves and, for the reason of

comparison and incorporation of derived fragility curves into existing databases mostly

based on intensity measure of PGA (for example Syner-G European database). Moreover,

it was chosen due to the simplification of problem regarding obtaining the fragility curves

Fig. 8 Schematic representation of obtaining fragility curve

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for complex buildings, such as the prototype RC high-rise buildings. The next step in

research of this type of buildings is obtaining fragility curves with other intensity measures.

6.1 Derived fragility curves

The selected prototype RC high-rise buildings are exposed to the selected 60 original

ground motions which are scaled to different intensity levels defined by PGA. As the range

of PGA values a fixed range [0.1, 1.0 g] with increments of 0.1 g is adopted. Ten sets of

ground motions were formed, corresponding to each separate intensity level. For the

selected ground motions, 3600 nonlinear time-history analyses for the both directions of

seismic action are performed. This required approximately 900 h of runtime on computer

Intel� CoreTM i5-3470 CPU 3.20 GHz and 8 GB of memory. The fragility curves for each

damage state were obtained, by using created MATLAB program. The derived values of

inter-storey drifts at threshold of each damage state obtained by probabilistic damage

analysis in the previous chapter are used (Table 4). Derived fragility curves of the pro-

totype RC high-rise buildings for intensity measure PGA including fitted log-normal

cumulative distribution function are shown in the Fig. 9. Each of four derived fragility

curves correspond to one of defined damage states (DS1, DS2, DS3 i DS4). Parameters of

fitted log-normal cummulative distribution functions for each damage state are shown in

the Table 5.

The Table 5 and Fig. 9 show, for example, that mean value of intensity measure PGA

for damage state DS2 (moderate damage) is 0.3519 g and represents the median value of

intensity measure at which the building reaches the threshold of the damage state DS2.

This means, that by the probability of 50 % for the value PGA of 0.3519 g, the threshold of

damage state DS2 is reached (i.e. the appearance of reinforcement yielding at critical zones

of some structural elements, including spalling of the concrete cover as well as forming

larger cracks in the plastic hinge zones). 84th percentile for damage state DS2 is 0.6864 g

Fig. 9 Derived fragility curves for the prototype RC high-rise buildings

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while 16th percentile is 0.1804 g. For the mean value of intensity measure PGA for

damage state DS2 plus–minus one sigma confidence interval is [L1,

L2] = [0.3397–0.3645 g]. Plus–minus one sigma confidence interval for log-normal dis-

tribution random variable, which corresponds to the probability of 84 %, is calculated by

Eq. (5) in the following way:

L1;2 ¼ l � e�rffiffiN

p ð5Þ

where L1 and L2 are lower and upper endpoint of the 84 % confidence interval for the

mean of a log-normal distribution, l is the sample mean value of random variable, r/HN is

standard error of the mean, r is standard deviation of the sample mean value, N is sample

size.

The relative width of confidence interval is calculated by Eq. (6):

i ¼ 100 � L2 � L1

l% ð6Þ

For all damage states the relative width of confidence interval is lower than 10 %, which is

acceptable and indicates small width of interval containing the mean value with relatively

high probability of 84 %. All this indicate the achieved great accuracy of obtained fragility

curves as well as their possible implementation for the case of RC high-rise buildings with

RC core wall or similar structural system.

The fragility curves shown in the Fig. 9 are derived by obtained mean values (median—

50th percentile) of inter-storey drifts at thresholds of certain damage states. In the prob-

abilistic seismic damage analysis except mean values, the values of 16th percentile and

84th percentile are obtained (Table 4). In the Fig. 10 all three types of derived fragility

curves are shown (fragility curves obtained by mean values, by values of 16th and 84th

percentile of inter-storey drifts at threshold of damage state).

6.2 Analysis and comparison of fragility curves

The derived fragility curves were compared to each other, for the purpose of making

difference in relation to various characteristics of earthquakes. The effects of magnitude,

distance to source and site conditions, on fragility of RC high-rise buildings, were

analysed.

Table 5 Derived log-normal distribution function parameters l and r for fragility curves of the prototypeRC high-rise buildings

Damagestates

Mean l(arithmeticspace) PGA (g)

Standarddeviationr

84thpercentilePGA (g)

16thpercentilePGA (g)

Lower and upperendpoint of the 84 %confidence interval

Relative widthof confidenceinterval

L1 L2 i (%)

DS1 0.1683 0.6304 0.3161 0.0896 0.1628 0.1740 6.65

DS2 0.3519 0.6682 0.6864 0.1804 0.3397 0.3645 7.05

DS3 0.6220 0.6554 1.1979 0.3230 0.6009 0.6439 6.91

DS4 0.9520 0.5133 1.5906 0.5698 0.9266 0.9781 5.41

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6.2.1 Comparison of fragility curves with respect to the magnitude

The selected 60 ground motions with the values of magnitude in the range between 5.1 and

7.0, are divided into two groups depending on the level of the magnitude: group with range

of magnitudes M = [5.1–6.2] which contains 29 ground motions (out of which 14 ground

motions with range of distance to source R = [1–20 km] and 15 ground motions with

range R = [20–70 km]) and group with range of magnitudes M = [6.3–7.0] which con-

tains 31 ground motions (out of which 15 ground motions with range of distance to source

R = [1–20 km] and 16 ground motions with range R = [20–70 km]). Fragility curves for

particular groups are obtained in order to analyze the fragility of high-rise buildings in

relation to the magnitude. The derived fragility curves with two different levels of mag-

nitude, M = [5.1–6.2] and M = [6.3–7.0], and for the whole range of distance to source

are shown in the Fig. 11. In the Figs. 12 and 13 are shown derived fragility curves for the

above mentioned levels of magnitude and separately for two range of distance to source as

follows: R = [1–20 km] and R = [20–70 km]. From the Fig. 11 it can be easily noticed

that the fragility of high-rise buildings with higher level of magnitude is larger than the

fragility with smaller level of magnitude for the same damage states and the same PGA

values. The differences become more obvious as the damage state increases (from DS1 to

DS4). For example, for the value PGA of 0.3 g, the probability of exceedance the threshold

of damage state DS2 (moderate damage) for the range of magnitudes M = [5.1–6.2] is

17 % while for the range of magnitudes M = [6.3–7.0] the probability is 64 %. The huge

differences are also in the derived parameter l of fragility curves (Table 6). The Table 6

Fig. 10 Derived fragility curves for the prototype RC high-rise buildings obtained by 50th percentile, 16thpercentile and 84th percentile of inter-storey drifts at thresholds of certain damage states

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shows that medians of intensity measure PGA in the case of larger magnitudes are lower

than in the case of smaller magnitudes, what means that by the same probability of

exceedance of 50 % in case of larger magnitudes, the threshold of certain damage state is

reached for lower values of PGA. Hence magnitude has a significant influence on seismic

vulnerability assessment of RC high-rise buildings and it can be connected with damage

states of RC high-rise buildings.

From the Figs. 12 and 13 it can be noticed that the differences between fragility of RC

high-rise buildings for two observed range of magnitudes are greater when the distance to

source is smaller than when is larger. It is interesting to notice, that, when it comes to the

ground motions with smaller magnitudes larger fragilities are obtained in case of larger

distance to source while regarding the ground motions with larger magnitudes, the larger

fragilities are obtained in case of closer earthquakes.

6.2.2 Comparison of fragility curves with respect to distance to source

The Fig. 14 shows the comparison of derived fragility curves for two different range of

distance to source as follows: R = [1–20 km] which contains 15 ground motions and

R = [20–70 km] which contains 16 ground motions for higher level of magnitude

M = [6.3–7.0]. It is noticeable from the Fig. 14 that the fragility curves are nearly equal in

case of smaller and larger distance to source. For the higher PGA values, i.e. for values

over median for certain damage states, there is a larger probability of exceedance of

damage states for closer compared to distant earthquakes. For lower PGA values than

median, there is equal or larger probability of exceedance for distant earthquakes. There is

almost no difference in derived parameter l of fragility curves (Table 7). According to this

results, it is evident high fragility of RC high-rise buildings to the impact of distant

earthquakes. This happens because for ground motions with larger distance to source, after

Fig. 11 Fragility curves of the prototype RC high-rise buildings for different magnitude levels

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decreasing of high frequency, comes lower frequencies of records which still excite high

periodical high-rise buildings to considerable displacements. Such fragilities indicate the

fact that in case of RC high-rise buildings, distant earthquakes indicate the high seismic

Fig. 12 Fragility curves of the prototype RC high-rise buildings for different magnitude levels and distanceto source R = [1–20 km]

Fig. 13 Fragility curves of the prototype RC high-rise buildings for different magnitude levels and distanceto source R = [20–70 km]

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Table

6Log-norm

aldistributionfunctionparam

eterslandrforfragilitycurves

oftheprototypeRChigh-risebuildingsfordifferentmagnitudelevels

Dam

agestates

Meanl(arithmetic

space)

PGA

(g)

Standarddeviationr

84th

percentile

PGA

(g)

16th

percentile

PGA

(g)

M=

6.3–7

M=

5.1–6.2

M=

6.3–7

M=

5.1–6.2

M=

6.3–7

M=

5.1–6.2

M=

6.3–7

M=

5.1–6.2

DS1

0.1192

0.2427

0.5509

0.4676

0.2067

0.3874

0.0687

0.1521

DS2

0.2499

0.5081

0.5250

0.5426

0.4225

0.8742

0.1478

0.2953

DS3

0.4555

0.8919

0.5039

0.5941

0.7538

1.6157

0.2752

0.4924

DS4

0.7296

1.4350

0.3936

0.5470

1.0815

2.4797

0.4922

0.8305

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vulnerability. Thus, for high-rise buildings it is necessary to provide an adequate seismic

analysis, even in a case when they are far away from the active fault in the zones of lower

seismic risk.

In the Fig. 15 fragility curves for lower level of magnitude M = [5.1–6.2] and two

different range of distance to source, R = [1–20 km] which contains 14 ground motions

and R = [20–70 km] which contains 15 ground motions are shown. It is noticeable, from

the Fig. 15, the higher fragility of certain damage states, in case of distant earthquakes

compared to closer earthquakes. All this indicates the high seismic vulnerability of RC

high-rise buildings to the impact of distant earthquakes.

6.2.3 Comparison of fragility curves with respect to site soil condition

The Fig. 16 presents the comparison of fragility curves for two soil types, the rock and stiff

soil (soil types A and B according to Eurocode 8-1). The diagram describes a bit higher

fragility for the case of foundation of high-rise buildings on stiff soil. The differences are in

the derived parameter of fragility curves l (Table 8), where the median of PGA are smaller

in the case of foundation on stiff soil than on rock. It happens because ground motions at

stiff soil sites causes larger responses for longer period modes of structure, as in case of RC

high-rise buildings.

It can be concluded that seismic vulnerability is higher in the case of foundation of RC

high-rise buildings on the stiff soil (soil type A) than on the rock (soil type B).

6.3 Comparison of derived fragility curves with existing fragility curves

There is a lack of information in the literature regarding derived fragility curves for RC

high-rise buildings. The largest database of fragility curves in America is HAZUS database

Fig. 14 Fragility curves of the prototype RC high-rise buildings for large magnitude level M = [6.3–7.0]and different distances to source

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Table

7Log-norm

aldistributionfunctionparam

eterslandr

forfragilitycurves

oftheprototypeRC

high-risebuildingsforlargemagnitudelevel

M=

[6.3–7.0]and

differentdistancesto

source

Dam

agestates

Meanl(arithmetic

space)

PGA

(g)

Standarddeviationr

84th

percentile

PGA

(g)

16th

percentile

PGA

(g)

R=

1–20

R=

20–70

R=

1–20

R=

20–70

R=

1–20

R=

20–70

R=

1–20

R=

20–70

DS1

0.1206

0.1170

0.4641

0.6431

0.1919

0.2225

0.0758

0.0615

DS2

0.2452

0.2567

0.4339

0.5982

0.3784

0.4669

0.1589

0.1411

DS3

0.4340

0.4800

0.4377

0.5602

0.6724

0.8405

0.2802

0.2741

DS4

0.7197

0.7403

0.3672

0.4199

1.0390

1.1266

0.4985

0.4865

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(National Institute of Building Sciences 1999). HAZUS represents the database of expert

fragility curves and includes wide range of various structural systems. This database

includes fragility curves for structural system with ductile walls for the three types of

Fig. 15 Fragility curves of the prototype RC high-rise buildings for small magnitude level M = [5.1–6.2]and different distances to source

Fig. 16 Fragility curves of the prototype RC high-rise buildings for selected ground motions recorded atsoil type A and soil type B

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height range (low rise, medium rise, and high rise) where high-rise building type is defined

with number of stories[8 floors with typical value of 12 floors.

In the Fig. 17 HAZUS fragility curves with derived fragility curves for the prototype

RC high-rise buildings are compared. It can be noticed that fragility curves do not vary

significantly in terms of damage states (DS1-slight and DS2-moderate) where HAZUS

fragility curves are above the fragility curves for the prototype buildings, because the inter-

storey drifts at the thresholds of these damage states for HAZUS fragility curves are less

and thus, the fragility is increased. For the damage state DS3 which corresponds to HAZUS

extensive damage state fragility curves are also close, where HAZUS curve is below

derived curve due to the fact that inter-storey drift for HAZUS curve is bigger and the

fragility is decreased as well. Fragility curve for HAZUS collapse damage state, with inter-

storey drift in the amount of 4 %, is noticeably lower than fragility curve of DS4 damage

state for the prototype buildings, where the inter-storey drift is 1.64 %. Such results

indicate the high degree of matching of derived fragility curves for the prototype buildings

with HAZUS fragility curves. The comparison of HAZUS parameters with derived

parameters of fragility curves l and r is done in the Table 9.

It is interesting to compare these two types of fragility curves assuming the same inter-

storey drifts at the threshold of defined damage states which correspond to HAZUS drifts

(Fig. 18). It may be concluded from the Fig. 18, the great level of matching of fragility

curves for each damage state. The matching is also noticeable in the median values of PGA

(Table 10). Considering that derived fragility curves are analytically obtained, and HAZUS

curves are expert fragility curves, such results indicate the high level of matching and

accuracy. In literature there are empirical fragility curves as well, for the region of Europe

and RC structures done by Rossetto and Elnashai (2003). Rossetto and Elnashai (2003)

pointed out that their fragility curves are not applicable for the structural systems with

ductile walls, due to the lack of observational data from the site for this type of structural

systems.

6.4 Comparison of fragility curves with respect to number of stories

The derived fragility curves, separately for each considered prototype RC high-rise

building (20-story, 30-story and 40-story), are shown in the Fig. 19. From the Fig. 19 it can

be easily noticed that the fragility increases with building’s height increase, but with no

significant differences in fragility for certain heights of the building. Since three considered

prototype buildings represent the same type of height range (high-rise) and are designed

according to the same rules defined in Eurocode provisions, similar levels of fragility are

Table 8 Log-normal distribution function parameters l and r for fragility curves of the prototype RC high-rise buildings for selected ground motions recorded at soil type A and soil type B

Damagestates

Mean l (arithmeticspace) PGA (g)

Standard deviation r 84th percentile PGA(g)

16th percentile PGA(g)

Soil typeA

Soil typeB

Soil typeA

Soil typeB

Soil typeA

Soil typeB

Soil typeA

Soil typeB

DS1 0.1697 0.1679 0.7473 0.5463 0.3583 0.2899 0.0804 0.0972

DS2 0.3688 0.3423 0.7660 0.6013 0.7934 0.6245 0.1715 0.1876

DS3 0.6536 0.6025 0.7050 0.6229 1.3228 1.1233 0.3229 0.3232

DS4 0.9438 0.9578 0.4601 0.5525 1.4952 1.6642 0.5958 0.5512

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expected and suggest clearly the possibility of using fragility curves obtained on integrated

sample of three prototype high-rise buildings.

7 Conclusions

In this study, probabilistic fragility curves of RC high-rise buildings with RC core wall

structural system were obtained for seismic excitation typical for Southern Euro-

Mediterranean zone. The fragility curves and parameters of fitted log-normal cumulative

distribution functions for four damage states were derived by conducting 3600 nonlinear

time-history analyses on the basis of 60 ground motions with wide range of magnitudes,

distances to source and different site conditions. In the process of obtaining fragility curves

it was performed detailed probabilistic seismic damage analysis of the prototype RC high-

rise buildings and as a result of it, limit states and corresponding damage states for RC

Fig. 17 Comparison of HAZUS fragility curves with derived fragility curves for the prototype RC high-risebuildings

Table 9 Comparison of HAZUS and derived log-normal distribution function parameters for fragilitycurves

Damagestates

Mean l (arithmetic space)PGA (g) derived

Mean l (arithmetic space)PGA (g) HAZUS

Standarddeviation rderived

Standarddeviation rHAZUS

DS1 0.1683 0.1200 0.6304 0.6400

DS2 0.3519 0.2900 0.6682 0.6400

DS3 0.6220 0.8200 0.6554 0.6400

DS4 0.9520 1.8700 0.5133 0.6400

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high-rise buildings were defined, where damage states were treated as random variables.

The inter-storey drifts at threshold of each defined damage state were defined as random

variables with the range of possible values. Calculated confidence intervals for all inter-

storey drifts of certain damage states, with relative width less than 5 %, indicate the high

level of accuracy of derived inter-storey drifts. In this way, per three types of fragility

curves (the fragility curves obtained by mean values, by 16th percentile and 18th percentile

of inter-storey drifts at threshold of certain damage states) were derived for four damage

states of the prototype RC high-rise buildings. Calculated relative width of confidence

interval (lower than 10 %) for the derived log-normal cumulative distribution function

parameters l of fragility curves indicate high accuracy of derived fragility curves and their

possible implementation for RC high-rise buildings with RC core wall or similar structural

systems.

Fig. 18 Comparison of HAZUS fragility curves with derived fragility curves for the prototype RC high-risebuildings assuming the same inter-storey drifts at the threshold of damage states which correspond toHAZUS drifts

Table 10 Comparison of HAZUS and derived log-normal distribution function parameters for fragilitycurves assuming the same inter-storey drifts at the threshold of damage states which correspond to HAZUSdrifts

Damagestates

Mean l (arithmetic space)PGA (g) derived

Mean l (arithmetic space)PGA (g) HAZUS

Standarddeviation rderived

Standarddeviation rHAZUS

DS1 0.1290 0.1200 0.6648 0.6400

DS2 0.3290 0.2900 0.6686 0.6400

DS3 0.8960 0.8200 0.5545 0.6400

DS4 1.5080 1.8700 0.2908 0.6400

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The derived fragility curves were compared to each other in order to make difference

regarding various characteristics of earthquakes. The effects of magnitude, distance to

source and site conditions, on fragility of RC high-rise buildings, were analysed. The

fragility of RC high-rise buildings with large magnitude is larger than fragility with smaller

magnitude for each damage state and same PGA values. Magnitude has significant influ-

ence on seismic vulnerability assessment of RC high-rise buildings and can be connected

with damage states of RC high-rise buildings. The fragilities of RC high-rise buildings for

smaller and larger distance to source are nearly equal. It is evident high fragility of RC

high-rise buildings to the impact of distant earthquakes. Accordingly, high-rise buildings

require an adequate seismic analysis, even in the case when they are located far away from

active faults in the zones of lower seismic risk. The fragility of RC high-rise buildings is

larger in case of foundation of high-rise buildings on stiff soil (soil type B) than on the rock

(soil type A according to Eurocode 8). Derived analytical fragility curves are mostly

matched with expert HAZUS curves.

Since no probabilistic fragility relationships exist for this class of building and for this

seismic zone, the aim is to incorporate derived fragility curves into existing European

database of fragility curves.

Acknowledgments The authors sincerely thank Seismological Institute of Montenegro for sharing datafrom its ground motions database.

References

Ambraseys N, Smit P, Sigbjornsson R, Suhadolc P, Margaris B (2002) Internet-site for European strong-motion data. European Commission, Directorate-General XII, Environmental and Climate Programme,Brussels. http://www.isesd.cv.ic.ac.uk

Fig. 19 Comparison of fragility curves of prototype RC high-rise buildings with respect to number ofstories

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123

CEN EC8 (2004) Eurocode 8-1—design of structures for earthquake resistance. Part 1: general rules,seismic actions and rules for buildings. European standard EN 1998-1, December 2004, EuropeanCommittee for Standardization, Brussels

CEN EC2 (2004) Eurocode 2—design of concrete structures. Part 1: general rules and rules for buildings.European standard EN 1992-1-1, December 2004, European Committee for Standardization, Brussels

CEN EC8 (2005) Eurocode 8-2—design of structures for earthquake resistance. Part 2: bridges Annex Eprobable material properties and plastic hinge deformation capacities for non-linear analyses. Europeanstandard prEN 1998-2, November 2004, European Committee for Standardization, Brussels

CSI (2006) PERFORM 3D nonlinear analysis and performance assessment for 3D structures. Computers &Structures Inc., Berkeley

CSI (2007) PERFORM 3D detailed example of a tall shear wall building by Dr. Graham H. Powell.Nonlinear modeling, analysis and performance assessment for earthquake loads. Computers &Structures Inc., Berkeley

CSI (2013) ETABS 2013 integrated analysis, design and drafting of buildings systems. Computers &Structures Inc., Berkeley

Erberik M, Elnashai A (2004) Fragility analysis of flat-slab structures. Eng Struct 26(2004):937–948. doi:10.1016/j.engstruct.2004.02.012

FEMA 356 (2000) Prestandard and commentary for the seismic rehabilitation of buildings. FederalEmergency Management Agency, Washington

Ghobarah A (2004) On drift limits associated with different damage levels. In: Proceedings of an inter-national workshop on performance-based seismic design concepts and implementation, Bled Slovenia,pp 321–332

Giardini D, Woessner J, Danciu L, Crowley H, Cotton F, Grunthal G, Pinho R, Valensise G and the SHAREconsortium (2013) SHARE European seismic hazard map. European Commission. www.share-eu.org

Ji J et al. (2007) Seismic fragility assessment for reinforced concrete high-rise buildings. Report 07-14, Mid-America Earthquake Center, University of Illinois at Urbana-Champaign

Ji J, Elnashai AS, Kuchma DA (2007) An analytical framework for seismic fragility analysis of RC high-risebuildings. Eng Struct 29(2007):3197–3209. doi:10.1016/j.engstruct.2007.08.026

Ji J, Elnashai AS, Kuchma DA (2009) Seismic fragility relationships for reinforced concrete high-risebuildings. Struct Des Tall Spec Build 18:259–277. doi:10.1002/tal.408

MATLAB (2013) MATLAB—the language of technical computing, version R2013b 8.2.0.701. MathWorksInc., Natick

National Institute of Building Sciences (1999) HAZUS technical manual, prepared for Federal EmergencyManagement Agency, Washington, DC

Park YJ, Ang AHS (1985) Mechanistic seismic damage model for reinforced concrete. J Struct Eng111(4):722–739

PEER (2010) Technical report for the peer ground motion database web application. Pacific EarthquakeEngineering Research Center, University of California, Berkeley

Rossetto T, Elnashai A (2003) Derivation of vulnerability functions for European-type RC structures basedon observational data. Eng Struct 25(2003):1241–1263. doi:10.1016/S0141-0296(03)00060-9

Taranath BS (2010) Reinforced concrete design of tall buildings. International Code Council, ConcreteReinforcing Steel Institute, CRC Press Taylor & Francis Group, Boca Raton

The Council on Tall Buildings and Urban Habitat (2011) The tallest 20 in 2020: entering the era of theMegatall. Illinois Institute of Technology, Chicago. http://www.ctbuh.org/TallBuildings/HeightStatistics/BuildingsinNumbers/TheTallest20in2020/tabid/2926/language/en-US/Default.aspx

Wallace JW (2012) Behavior, design, and modeling of structural walls and coupling beams—lessons fromrecent laboratory tests and earthquakes. Int J Concr Struct Mater 6(1):3–18. doi:10.1007/s40069-012-0001-4

Bull Earthquake Eng

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