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International Journal of Civil Engineering and Technology (IJCIET)

Volume 9, Issue 4, April 2018, pp. 1559–1571, Article ID: IJCIET_09_04_172

Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=9&IType=4

ISSN Print: 0976-6308 and ISSN Online: 0976-6316

© IAEME Publication Scopus Indexed

SEISMIC FRAGILITY OF LOW DUCTILE

REINFORCED CONCRETE FRAME IN

MALAYSIA

Nurul Nabila Fazilan, Nurul Amiera Rosman and Nur Amalina Anuar

Faculty of Civil Engineering, Universiti Teknologi Malaysia

Sophia C. Alih

Faculty of Civil Engineering, Institute of Noise and Vibration, Universiti Teknologi Malaysia

ABSTRACT

Seismic vulnerability of low-ductile reinforced concrete (RC) frames which have

not been designed for earthquake loads has been a concern for countries with low-to-

medium seismicity like Malaysia. These types of structures represent the majority of

existing buildings in Malaysia and their safety level is of interest for authorities to

plan for their retrofit. This study is conducted to assess the vulnerability of low-ductile

reinforced concrete frame in Malaysia when subjected earthquake records through the

development of seismic fragility curves. Three types of structural models were

designed for gravity and lateral loads based on the common practices in Malaysia

which included RC frames with three, six, and nine stories. The structures were

analyzed using incremental dynamic analysis (IDA). In addition, pushover analysis

was used to determine inter-story drift demands. The earthquake records were divided

into three groups based on their peak ground acceleration (PGA) to peak ground

velocity (PGV) ratios. Three structural performance levels namely immediate

occupancy (IO), life safety (LS), and collapse prevention (CP) were considered for the

selected frames. The results showed that records with the low PGA/PGV ratios that

represented far-field earthquakes imposed the highest level of damage to the low-

ductile RC frames. It was observed that the probability of seismic induced damage

increased as the height of structures increased. The three story RC frame showed

brittle failure mechanism when subjected to employed earthquake records. The

probability of exceeding CP level under far-field records and the PGA of 0.2g was

more than 50% for three and nine story RC frames. It was concluded that three and

nine stories RC frames constructed in the East Malaysia did not satisfy the no-

collapse requirements and needed to be retrofitted.

Key words: Incremental dynamic analysis, non-ductile reinforced concrete frame,

seismic fragility curves, seismic performance level, vulnerability assessment.

Nurul Nabila Fazilan, Nurul Amiera Rosman, Nur Amalina Anuar and Sophia C. Alih


Cite this Article: Nurul Nabila Fazilan, Nurul Amiera Rosman, Nur Amalina Anuar

and Sophia C. Alih, Seismic Fragility of Low Ductile Reinforced Concrete Frame in

Malaysia, International Journal of Civil Engineering and Technology, 9(4), 2018,

pp. 1559–1571.

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=9&IType=4

1. INTRODUCTION

Evaluation of structural safety and risks imposed by seismic events are challenging issues due

to the characteristic of seismic loads which have a complex and usually unpredictable effects

on structures [1]. Assessment of seismic induced damage to structures has been implemented

through several methods that often take advantage of non-linear static or dynamic analyses [2,

3]. Seismic fragility curves have been used by many researchers to estimate seismic

vulnerability of structures. This approach shows the probability of exceeding a given damage

level in a structure due to a seismic hazard.

Procedures involved in this method include determination of structural capacity for a

given seismic hazard, followed by the fragility estimation for a given limit state or damage

state [4]. The developed fragility curves enable rapid structural assessment after an earthquake

event and have been used to determine the effectiveness of different rehabilitation methods

[5]. Fragility curves can be derived through empirical approaches, experimental data, and

analytical methods. The later has been widely used due to its ability to assess different seismic

hazard scenarios and structural systems through extensive analytical simulations [6]. Several

researchers have applied the analytical method in developing seismic fragility curves for

specific type of structures including bridges [5, 7], tunnels [8], air traffic control towers [9],

steel and reinforced concrete frames [10-15] with different structural configurations, and

masonry structures [16].

Majority of buildings constructed in Malaysia are made of reinforced concrete frames.

The existing structures have been designed without consideration of seismic provisions.

Smooth reinforcing bars anchored with insufficient end-hooks, absence of transverse shear

reinforcement in the beam-column joint region, large distance between transverse shear

reinforcement, and strong beam-weak-column design are among the main design issues that

contribute to the low-ductile behavior of the RC frames especially in Malaysia [17]. It should

be also mentioned that this type of structure suffered significant damage during the 2015

Sabah earthquake in Malaysia. After this earthquake, many RC frame buildings experienced

structural damage and required major rehabilitation works. Some needed to be demolished or

temporarily closed. This event demonstrated the needs for well-designed structures and

implementation of seismic design codes in Malaysia. In addition, understanding the safety

level and seismic vulnerability of existing structures became an important matter especially

for the low-ductile RC frames.

In this study, seismic vulnerability of low ductile reinforced concrete frames was assessed

through the framework of fragility curve. Three types of structural model were selected with

differences in their height that include three, six, and nine story RC frames. The selected

structures were designed based on the common practices in Malaysia. Incremental dynamic

analyses together with pushover analysis were used to determine drift capacities of the

selected structures. Totally 45 earthquake records scaled between 0.1g to 0.5g were used. The

earthquake records were divided into three groups based on their PGA/PGV ratios. The three

groups included low, medium, and high class records which represented far, medium, and

near field earthquakes respectively. Three structural performance levels namely immediate

occupancy, life safety and collapse prevention were considered for structural elements.

Seismic fragility curves were developed for all three groups of earthquake records separately.

Seismic Fragility of Low Ductile Reinforced Concrete Frame in Malaysia


A total of nine fragility curves were developed in this study. Results from this study were

used to determine the probability of damage to RC frame buildings when subjected to seismic

hazard given in Malaysian National Annex [18]. These results can provide an insight to the

vulnerability of each type of structures under different earthquake intensities and frequency

content. This is an important input in determining seismic rehabilitation plan and estimating

required budget to increase safety level of existing low-ductile RC frames. This may include

strengthening of structural components through concrete jacketing, steel jacketing, Fiber

Reinforced Polymer (FRP) wrapping, application of pre-stress component, and dampers [19-

21].

2. SELECTED STRUCTURES

In this study, low ductile RC frames with three different heights were selected to be analyzed.

These included three, six, and nine story of building. Fig. 1 shows the layout plan used for all

building and the location of the reference frame selected for derivation of fragility curves. The

structural layout is regular with 6m and 5m span length in X and Y direction, respectively.

Fig. 2 shows the side elevation of the selected frames. Each frame has four spans with 6m

length and the story heights of 4 m for the first floor and 3m for the upper floors.

Figure 1 Plan view of the building and the location of selected frame

In order to simulate the common design practice of RC buildings in Malaysia, frames

were designed based on the British Standard [22]. Concrete strength of 20MPa was used for

all structural models. Yield and ultimate stress of reinforcing bars were 300 N/mm2 and 420

N/mm2, respectively. All frames were designed under the effect of dead, live and wind load.

In design process, the dead load was considered 31.08 kN/m and the live load 12 kN/m. Table

1 shows the dimensions of designed columns together with reinforcement details of columns.

The structural models were is developed and analyzed by using ETABS2015 software [35]. It

should be mentioned that in all frames beam had a rectangular cross section with the size of

350 x 250 mm.



Figure 2 Side elevation of the selected frames. (a) three-story, (b) six-story, (c) nine-story

Table 1 Dimension and reinforcement bars details of columns

Structure type Story Height (m) Middle column

(Dimension in mm)

End column

(Dimension in mm)

3 story

1 4 300 x 300 (8Ø18)

350 x 350 (8Ø25) 2 3 250 x 250 (8Ø18)

3 3 250 x 250 (8Ø14)

6 story

1 4 450 x 450 (8Ø28)

400 x 400 (8Ø25)

2 3 400 x 400 (8Ø25)

3 3 350 x 350 (8Ø22)

4 3 300 x 300 (8Ø20)

5 3 300 x 300 (8Ø14)

6 3 250 x 250 (8Ø14)

9 story

1 4 550 x 550 (8Ø32)

450 x 450 (8Ø20)

2 3 550 x 550 (8Ø32)

3 3 550 x 550 (8Ø32)

4 3 500 x 500 (8Ø28)

5 3 450 x 450 (8Ø20)

6 3 400 x 400 (8Ø25)

7 3 350 x 350 (8Ø20)

400 x 400 (8Ø25) 8 3 300 x 300 (8Ø14)

9 3 300 x 300 (8Ø14)

Nonlinear behavior of beams and columns was simulated by using lumped plastic hinges

assigned to the end of each member. Fig. 3 displays the typical force–deformation relationship

of a plastic hinge that can be defined in ETABS2015. In this figure, segment AB indicates the

elastic behavior, segment BC represents the post-yield behavior and segment CD shows the

beginning of the failure. The parameters for each member in the figure were extracted from

the tables provided in ASCE 41-13 [23] considering material properties, internal forces and

sizes of beams and columns.



Figure 3 Generalized chord rotation model used for inelastic behaviour of beams and columns [24]

3. CONSIDERATION OF UNCERTAINTIES

Uncertainties that contribute to the seismic fragility can be classified into two types; random

and the one caused by lack of knowledge [25]. It has been also demonstrated that the

variability in ground motions has a significant impact on fragility curves compared to

uncertainties in material properties [26, 27, 28]. This also applies to non-ductile RC frames in

which material and structural parameters like structural damping, concrete strength, and

cracking strain in beam–column joints have less impact on the obtained seismic fragilities

when compared to uncertainties in seismic demands from earthquakes [10]. Therefore, in

addition to the building height this study considered the variability in the ground motions for

the derivation of seismic fragilities.

To account for uncertainty in seismic demands, 45 natural earthquake records classified

into three specific groups (each containing 15 records) were selected. Classification of the

groups was determined based on the PGA/PGV ratio of the records. The PGA/PGV ratio is a

simple parameter that can indicate the relative frequency content and duration of earthquake

ground motions generated by different seismic environments [29]. The PGA/PGV ratio of

ground motion has also a significant effect on the peak inelastic response, hysteretic energy

dissipation and stiffness deterioration of stiffness degrading systems [30]. In this study, the

earthquake records are classified in three groups based on the PGA/PGV ratio that includes

low, medium and high groups. Records with PGA/PGV < 0.8 g/m/s were classified as low

range, while 0.8 ≤ PGA/PGV ≤ 1.2 and PGA/PGV > 1.2 were classified as medium and high

groups respectively [29]. This classification allows further analysis on the effect of PGA/PGV

ratio of earthquake records. Fig. 4 and 5 display the magnitude and PGA/PGV ratio of

selected earthquake records against their source distances, respectively. It can be seen that

high PGA/PGV ratio characterizes motions in the vicinity of earthquake sources while low

PGA/PGV ratio displays motions far from large earthquakes [29].



Figure 4 Magnitude of the selected records against their source distance

Figure 5 PGA/PGV ratios of the selected records against their source distance

4. DERIVATION OF FRAGILITY CURVES

A fragility curve describes the conditional probability of a structure when encounters or

surpasses an indicated damage level for given ground motion [31]. Equation (1) shown below

is used to develop the fragility curves [32].

( ⁄ ) (

⁄

√

) (1)

With √ ( ) (2)

Where, SE2 is the standard error of demand drift; DS is damage state; SI is seismic

intensity; Φ is standard normal distribution; λc is natural logarithm of the median of drift

capacities for particular damage state; ⁄

is natural logarithm of the median demand drift

given the seismic intensity from the best fit power law; while βc and are respectively,

uncertainties related to capacity and modelling that have been taken as 0.3 [32].

0

50

100

150

200

250

300

350

400

5 5.5 6 6.5 7 7.5 8 8.5

Sourc

e D

ista

nce

(km

)

Magnitude

Low

Medium

0

50

100

150

200

250

300

350

400

0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7

Sourc

e D

ista

nce

(km

)

PGA/PGV (g/m/s)

Low

Medium



Different levels of damage were defined based on the maximum inter-story drifts

obtained for each structure. Three performance levels, namely immediate occupancy (IO), life

safety (LS) and collapse prevention (CP) were considered for the structural elements.

Immediate occupancy means that the structure is lightly damaged, facility can return to full

use as utility systems are back in operation and the cleanup is completed. Meanwhile, life

safety shows a significantly damaged structure that does not cause life-threatening injuries.

Sometimes in LS performance level reparability is economically questionable and demolition

may be preferable. The collapse prevention is referring to a structure that heavily damaged

and it is at the verge of collapse [33].

Accurate determination of drift capacities in structures is vital for the development of

fragility curves. Table 2 shows the drift capacities of the selected frame that are obtained from

conducted analysis. The results show that as the number of stories increase, drift capacities

decrease. RC frame with nine stories has the smallest capacities followed by the six and three

stories frames. This shows that as the height increases, the intensity of damage to the studied

low ductile RC frames increases. It should be mentioned that the 3-story frame experienced a

sudden transition from the IO damage level to the CP level without indication of the LS level.

This indicated that the 3-story frame had a brittle failure mechanism such that as the seismic

intensity was slightly increased the CP level was achieved without going through the life

safety level.

Table 2 Drift capacities of the selected structures for each damage state

IO LS CP

3 story 1.32% - 1.61%

6 story 0.79% 1.16% 1.22%

9 story 0.76% 0.93% 1.05%

The incremental dynamic analysis (IDA) was conducted using ETABS 2015. The IDA is

an analytical method used to determine structural responses under different intensities and

frequency content of ground motions. To analyses the models, earthquake records are scaled

in multiple levels, hence representation of parametric response diagram could be obtained for

various intensities of earthquakes [34]. By using the IDA, the relationship between maximum

drift ratio and peak ground acceleration (PGA) can be determined.

Seismic fragility curves developed for three, six, and nine stories of RC frame under low,

medium and high class earthquake records are shown in Fig. 6 to Fig. 14, respectively. It can

be observed that, the low-class earthquake imposes the highest damage to all studied RC

frames. On the other hand, the high-class earthquake results in minimum damage and almost

has no impact to all frames up to 0.4g. This shows that the non-ductile RC frames are more

sensitive to far-field earthquakes compared to near-field earthquakes. From the figures, it can

be observed that as the number of stories increase the intensity of seismic induced damage

also increases. Comparison in the slope of the developed fragility curves show that for low-

class earthquake, the slope is steeper for lower PGAs i.e., 0.1g to 0.3g. This indicates that, a

small increase in PGA will cause significant increase in the seismic induced damage to the

studied structures. On the other hand, high-class earthquakes impose no damages to the

structures for smaller PGAs. Medium-class earthquakes have the steepest slope when

compared with the other class of records. For this class of records, seismic induced damage

increases significantly as the PGA increases from 0.1g to 0.5g.

As mentioned earlier, the 3-story RC frame exhibited the CP damage level right after

passing the IO level. Hence, the derived fragility curves for the 3-story RC frame in Figs. 6, 7,

and 8 only represent the IO and CP damage levels. In other words, the 3-story RC frame that



was designed with less ductility shows a brittle seismic behavior and has the risk for sudden

collapse. The observed brittle failure mode for the 3-story frame disappears as the height of

the frame increases. As can be seen from Figs. 12, 13, and 14, the fragility curves obtained for

IO, LS and CP damage levels of the 9-story RC frame display a tangible difference in their

probability of exceedance.

In order to determine the probability of seismic induced damage to low ductile RC

buildings in Malaysia, the PGA values were determined from the National Annex [18]. For

the structures that are built on the ground type with the site natural period of more than 0.7s,

the maximum PGA for Peninsular and Sarawak is 0.1g while for Sabah is 0.2g. For the design

seismic action i.e., 475 return period where no-collapse requirement is expected, three and

nine stories RC frame located in Sabah do not satisfy the expected performance objective.

More than 50% probability of exceedance can be observed for CP level in these structures

under the low-class earthquakes. This indicates the needs for structural retrofitting in these

types of structures to reduce the risk of structural collapse during earthquakes. The six-story

frame however, shows lower probability of damage due to their higher over-strength factor

and redundancy. As for the damage limitation requirement, all RC frames in Peninsular,

Sarawak and Sabah do not satisfy the IO performance objective when subjected to the low-

class earthquakes. When subjected to medium- and high-class earthquake records, most of the

studied frames satisfy the requirement of no-collapse and damage limitation.

Figure 6 Seismic fragility of three stories RC frame considering the low class PGA/PGV ratio

Figure 7 Seismic fragility of three stories RC frame considering the medium class PGA/PGV ratio

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5

Pro

bab

ilit

y o

f ex

ceed

ance

PGA(g)

IO

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5

Pro

bab

ilit

y o

f ex

ceed

ance

PGA(g)

IO



Figure 8 Seismic fragility of three stories RC frame considering the high class PGA/PGV ratio

Figure 9 Seismic fragility of six stories RC frame considering the low class PGA/PGV ratio

Figure 10 Seismic fragility of six stories RC frame considering the medium class PGA/PGV ratio

0

0.1

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0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5

Pro

bab

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y o

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ceed

ance

PGA(g)

IO

CP

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5

Pro

bab

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ance

PGA(g)

IO

0

0.1

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0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5

Pro

bab

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y o

f ex

ceed

ance

PGA(g)

IO



Figure 11 Seismic fragility of six stories RC frame considering the high class PGA/PGV ratio

Figure 12 Seismic fragility of nine stories RC frame considering the low class PGA/PGV ratio

Figure 13 Seismic fragility of nine stories RC frame considering the medium class PGA/PGV ratio

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5

Pro

bab

ilit

y o

f ex

ceed

ance

PGA(g)

IO

0

0.1

0.2

0.3

0.4

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0.6

0.7

0.8

0.9

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0 0.1 0.2 0.3 0.4 0.5

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ance

PGA(g)

IO

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5

Pro

bab

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y o

f ex

ceed

ance

PGA(g)

IOLS



Figure 14 Seismic fragility of nine stories RC frame considering the high class PGA/PGV ratio

5. CONCLUSIONS

Majority of RC frames in countries with low-to-medium seismicity like Malaysia have not

been designed for seismic actions. These structures mostly have low ductility and their

seismic behavior under different earthquakes has not been well studied. Seismic fragility

curves are able to provide an assessment to the probability of damage imposed by different

earthquake records to the structures. In this study, low-ductile RC frames were designed to

represent the common type of buildings in Malaysia with three different numbers of stories.

IDA was performed using 45 records of ground motions classified in three groups based on

their PGA/PGV ratios. Based on the fragility curves obtained for 3, 6 and 9 stories RC

frames, it was shown that the low-class earthquake records which represented the far-field

earthquakes imposed more damage to all studied structures when compared to other

earthquakes. For all classes of earthquake records, it was observed that, the probability of

exceeding damage levels of IO, LS and CP increased as the height of structures increased. A

brittle failure mechanism was observed for the 3-story frame as it exhibited the CP damage

level right after passing the IO level. The observed brittle failure mode for the 3-story frame

disappeared as the height of the frame was increased. The probability of exceeding CP level

under low-class earthquake records and the PGA of 0.2g was more than 50% for three and

nine-story RC frames. This showed that the low ductile RC frames that have been constructed

in Sabah did not satisfy the no-collapse requirements of seismic codes and needed to be

retrofitted.

ACKNOWLEDGEMENT

The authors would like to acknowledge supports from Universiti Teknologi Malaysia and

financial support from the Ministry of Higher Education of Malaysia through the RUG Vot.

No. of 17H80 and 19H36, and FRGS Vot. 4F716.

0

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0 0.1 0.2 0.3 0.4 0.5

Pro

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PGA(g)

IO



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