Seismic performance of deficientmasonry infill reinforced-concretestructures&1 Muhammad Usman Ali MSc
Graduate Student, School of Civil and Environmental Engineering,National University of Sciences and Technology, Islamabad, Pakistan(corresponding author: [email protected])
&2 Shaukat Ali Khan PhDAssociate Professor, Department of Civil Engineering, AbasynUniversity, Peshawar, Pakistan
&3 Muhammad Yousaf Anwar MScGraduate Student, Department of Civil Engineering, Yildiz TechnicalUniversity, Istanbul, Turkey
&4 Abdul Aleem MScStructural Engineer, Design Inn Consulting Engineers & Architects(Pvt.) Ltd, Islamabad, Pakistan
&5 Saim Raza BScGraduate Student, Swinburne University of Technology, Australia
Literature from previous years of research studies reveals that the effect of masonry infills is significant and cannot be
neglected. This study is aimed at the seismic vulnerability assessment of masonry infilled reinforced-concrete frame
structures in developing countries, taking Pakistan as a case study. Typical two-dimensional reinforced-concrete frames
with and without infill panels, and with infill openings are considered. A three-strut model is employed for analytical
modelling of infill panels. Compressive strength of a typical Pakistani brick masonry prism is evaluated for modelling the
equivalent strut. It is concluded that the study’s masonry infilled structural configurations give better performance than
bare frame structures. Openings in masonry panels, however, increase the seismic vulnerability of infilled structures.
NotationCa seismic coefficient (acceleration)Cv seismic coefficient (velocity)Ec elastic modulus of frameEm elastic modulus of masonryFcr cracking loadFmax crushing loadFr residual strengthf′m compression strength of masonryhw height of masonry panelsIc moment of inertia of columnKe initial stiffnesst thickness of masonryz infill-frame contact lengthαcap post peak strength degradationαh hardening strengthαw ratio of area of opening to the area of infill wallδc displacement at zero wall strengthδcap displacement at peak loadη reduction factorθ angle between infill height and bay lengthλ relative stiffness of masonry infill panel
1. IntroductionThe construction of multi-storey buildings is associatedwith infilled frames. In most of the constructions, especiallyin developing countries, masonry is used for infill (Alwashaliand Maeda, 2013) because it is faster, easier and even cheaperthan other materials used for similar construction. Masonrywalls fill in the portal spaces inside bounding frames. Inthis type of composite structural system, frames carry thegravity loads while non-load-bearing infill panels provideinternal partitioning and enclosure to the buildings. As theiruse is aesthetic or functional rather than structural, therefore,they have been considered as non-structural elements and theirpresence neglected in the design process (Agrawal et al., 2013;Jinya and Patel, 2014; Kauffman and Memari, 2014;Mohamed, 2012).
Research carried out over the years has revealed that masonryinfill interacts with the reinforced-concrete (RC) frame, result-ing in positive or negative impacts during earthquake events(Furtado et al., 2015). Many researchers have reported that thepresence of masonry infill improves the lateral capacity of thebuilding; however, a reverse trend has also been observed in
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Seismic performance of deficient masonryinfill reinforced-concrete structuresAli, Khan, Anwar et al.
Proceedings of the Institution of Civil EngineersStructures and Buildings 170 February 2017 Issue SB2Pages 143–155 http://dx.doi.org/10.1680/jstbu.15.00115Paper 1500115Received 15/10/2015 Accepted 27/07/2016Published online 10/11/2016Keywords: concrete structures/seismic engineering/structural frameworks
many of the past earthquake events, for example, the Kashmirearthquake in 2005, the Wenchuan earthquake in 2008 and theHaiti earthquake in 2010 (Alwashali and Maeda, 2013).Earthquake damage has been observed by the structural modi-fications of the frame caused by infill panels, as shown inFigure 1.
Initial lateral stiffness is considerably increased by infill panels(Furtado et al., 2015; Kauffman and Memari, 2014), reducingthe time period of the building and in turn leading to largeshear forces (Jinya and Patel, 2014). Consequently, the increasein stiffness due to interaction of the infill panel alters the loadtransfer mechanism from frame action to truss action (Jinyaand Patel, 2014; Razzaghi and Javidnia, 2015). The verticaland plan irregularities, resultant from infill panels, may inducenegative impacts, causing short column and soft-storey effects(Furtado et al., 2015; Ko et al., 2014). For low-rise structures,the presence of openings in these walls can influence their per-formance. Openings significantly affect the stiffness and lateralstrength of RC structures and consequently change theirfailure modes. In most cases, the failure is largely due to stressconcentrations at the corners of the openings (Surendran andKaushik, 2012).
Seismic vulnerability assessment of such low- to medium-riseinfilled RC structures is carried out in this study to investigatethe effects of masonry infills. Eight typical RC building con-figurations, which are commonly used in developing countries,are considered with masonry infill panels. A single buildingwithout masonry infill is considered as the control specimen.Two buildings with central openings in the infill are also con-sidered. The effects of the presence of an infill panel arestudied by comparing the vulnerability curves of an infill struc-ture to that of a bare RC structure, and ultimately with thestructures having openings in infilled walls. The effects of vari-ation in the number of bays and storeys that a building has onits seismic performance are also evaluated.
2. Modelling of masonry infillsMasonry infilled frames exhibit complex structural behaviour,integrating numerous factors. Experimental studies show that,even at low-level loading, such structures show highly non-linear inelastic behaviour. Material non-linearity initiates fromthe material properties, that is, degradation of both the sur-rounding frame and the infill panels, variation of contactlength, the loss of bond friction mechanism at the interface,and so on. Geometric non-linearity also affects the behaviourof infilled frames when resisting large lateral displacements.The above-mentioned non-linear effects cause analytical com-plexities which require sophisticated computational techniquesfor their proper consideration in modelling.
Several analytical techniques have been proposed in the litera-ture in order to idealise this structural type (Furtado et al.,2015). These models can be classified into two groups: local ormicro models and simplified or macro models. In the firstgroup, to take into account the local effects in detail, the struc-ture is divided into various elements. Whereas in the secondgroup, simplified models in the form of diagonal struts(Furtado et al., 2015) are used, which are based on the phys-ical understanding of the general behaviour of the infill panels.Conceptual and experimental observations have indicated thata diagonal strut of suitable mechanical and geometrical char-acteristics could possibly provide a solution to the problem(Asteris et al., 2011). Strut models may be simple, for instancea single-strut model, or else multiple, for example double- andtriple-strut models (Crisafulli, 1997; Furtado et al., 2015).
Many studies (Holmes, 1961; Polyakov, 1960; Stafford-Smith,1966; Stafford-Smith and Carter, 1969) have been carried outusing a single equivalent strut model. But, during the lasttwo decades, it has become clear that the complex behaviourof infilled masonry cannot be properly modelled using a singlediagonal strut. Many researchers (Buonopane and White,1999; Reflak and Fajfar, 1991; Saneinejad and Hobbs, 1995)have reported that a single equivalent strut, connecting twocorners of the infill panel, cannot adequately represent theshearing forces and bending moments in the frame members.More complex macro-models comprising more than one diag-onal strut were therefore proposed.
One study (Chrysostomou et al., 2002) was conducted with theintention of obtaining the performance of a masonry infilledframe under lateral loading by considering both strength andstiffness degradation of infill panels. Consequently, a modelwas proposed in which each infill panel contained six inclinedstruts undergoing only compression.
The structural response of RC infilled frames using differentmulti-strut models has also been studied (Crisafulli, 1997),while focusing on the stiffness of the structure and inducedactions in the surrounding frame. It was observed that thesingle-strut model underestimates the shear forces and bending
(a) (b)
Figure 1. Failure of masonry infill walls due to the diagonal
compressive forces: (a) Kappos and Panagopoulos (2009);
(b) Kashmir earthquake, 2005 (Ahmad et al., 2014)
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moments, as lateral loads are mainly resisted by a truss mech-anism. It was also reported that the double-strut model leadsto much larger values of shear forces and bending moments.However, a three-strut model showed better approximation toexperimental work. In the present study, therefore, a three-strutmodel proposed by Crisafulli (1997) is employed.
It is a common assumption that the diagonal struts are activeonly when subjected to compressive forces. However, owing tothe unavailability of compression-only elements in commonelasticity-based computer programs, tension–compression trussmembers in both directions are recommended with half of theequivalent strut area in each diagonal direction. A three-strutmodel use three struts, one diagonal and two off diagonal. Thestruts are active only when the compression force is applied.In order to capture the true response, a force–deformationrelationship corresponding to the equivalent strut model mustbe appropriately defined. The thickness and contact length ofthe equivalent strut model are other parameters necessary toadequately predict the actual behaviour of the masonry infills.These are further explained later in Section 4. A three-strutmodel used by Crisafulli (1997) is shown in Figure 2.
3. Experimental programmeExperimental testing was carried out to determine the com-pressive strength of masonry required for material modellingof equivalent struts. The testing was conducted to evaluate thecompressive strength of typical Pakistani brick masonry infillpanels. For the preparation of samples, cement–sand mortarand locally manufactured bricks collected from differentsources were used.
The masonry prisms were sampled and tested in accordancewith ASTM C-1314 (ASTM, 2014). The compressive strengthof brick masonry has been determined by testing standard
brick prisms of size 225� 110� 260 mm (length�width�height) under uniaxial compression. There are three bricks ina single masonry prism laid in a mortar joint 10 to 12 mmthick, as shown in Figure 3. An expert local mason was hiredto construct the sample masonry prisms. After preparation ofthe specimens, prisms were wet cured for 7 d and were kept inmoisture-tight polythene bags until the date of testing.
To obtain the overall displacements of the specimens, a rigwith two 19 mm thick steel plates was used. Two displacementgauges were connected on each side of the specimen. Theplates were lubricated with oil and grease to reduce the con-finement effect provided by the friction between the steel platesand the ends of the specimen. The specimens were loaded incompression at an average loading rate of 2·4 kN/s. The instru-mentation is shown in Figure 3. The compressive strengthvalues of the tested brick prisms are provided in Table 1.
The average stress–strain curve of brick masonry samples incompression is shown in Figure 4. The standard deviation incompressive strength of brick masonry obtained from this
Z/2
Ams/4
Ams/2
Ams/4
Figure 2. Diagonal three-strut masonry model
(a) (b)
Figure 3. (a) Brick masonry prism in testing rig with displacement
gauges. (b) Compression testing of brick masonry prisms
experimental work is 0·239, while the average value ( f ′m) is
1: f 0m ¼ 5�06 MPa
4. Structural modellingMost residential buildings are regular in plan and elevation(Badrashi et al., 2010) and, therefore, eight two-dimensional
(2D) frames with infill, without infill and with openings areinvestigated for this study. The selected building frames aredesigned for gravity loads only, without considering lateralloads. A typical bay width of 4·0 m and storey height of 3·3 mare considered (Ahmad et al., 2011; Badrashi et al., 2010) forall the structures investigated. As a first step, a typical singlebay, two-storey (1B2S) RC frame is considered with andwithout infill panel, as shown in Figures 5(a) and 5(b), forcomparison with the experimental results.
A specimen having one bay, two-storey bare frame (1B2SB)is taken as the control specimen. Buildings with masonry infillpanels are considered in seven configurations, namely, one bay,two storeys (1B2S); two bays, two storeys (2B2S); three bays,two storeys (3B2S); three bays, three storeys (3B3S); three bays,four storeys (3B4S); three bays, three storeys with openings(3B3SO); and three bays, four storeys with openings (3B4SO).Different models with varying material and geometric proper-ties are prepared to capture the probabilistic effect of structuralperformance. The material and geometric properties con-sidered for the structural members are provided in Table 2 andthe reinforcement details are given in Table 3.
Selected building frames are then modelled using the softwarePerform 3D (Perform-3D, 2008) for structural response assess-ment. Perform 3D is a finite-element method (FEM) basednon-linear analytical tool, specifically used for non-linearanalysis of structures subjected to earthquake ground motions.Like many finite-element programs, nodes are defined inPerform 3D which are connected with the elements of the
0
1
2
3
4
5
6
0 0·002 0·004 0·006 0·008 0·010 0·012
Stre
ss: M
Pa
Strain
Figure 4. Average stress–strain curve of brick masonry in
frame, namely, the beam and column elements. Beams andcolumns are modelled with inelastic fibre section for beamsand fibre section for columns. Force–displacement relations,deformation capacities and strength loss ratios are calculatedas per the guidelines of Fema (Fema 356 (Fema, 2000)).Eurocode (Eurocode (BSI, 2004)) constitutive models for con-crete and steel have been used for modelling material proper-ties. Frame masses are calculated considering concrete unitweight of 24 kN/m3 and are lumped at exterior nodes.
For modelling infill panels, an infill panel element of Perform3D with diagonal strut model was used. This model has threestruts which resist compression only. The force–displacementrelationship for struts is calculated using the model shown inFigure 6 and was proposed by Sattar and Liel (2010).
The area of a diagonal strut is taken as half of the total strutarea in one direction and the area of each off-diagonal strut is
half of the diagonal strut, while the vertical separation is takenas half of the contact length between the masonry infill andthe frame (Crisafulli, 1997). Contact length is computed fromEquation 2 below.
2: z ¼ π
2λ
where z is the infill–frame contact length and λ is the relativestiffness of masonry infill panel which can be calculated usingEquation 3.
masonry panels, Ic is moment of inertia of column and θ is theangle between infill height and bay length.
The effect of an opening in an infilled panel is modelled with areduced strut width (Mondal and Jain, 2008). This reductionfactor is obtained by multiplying the width of the masonrystrut with that of a reduction factor. Equation 4 is then used tocalculate the reduction factor for strut width (Asteris et al.,2011).
4: η ¼ 1� 2α0�54w þ α1�14w
In this equation η is the reduction factor and αw is the ratio ofarea of opening to the area of infill wall. For modelling inelasticshear behaviour, a shear hinge component is used at interactionpoints of frame members with off-diagonal struts, wheremaximum inelastic shear is expected. A shear strength modelwith displacement hinge is used (Sezen, 2002). It relates theshear capacity of frame members with the displacement ductility.
5. Seismic response evaluationStructural response is assessed using the guidelines providedin ATC-40 (ATC, 1996) and Fema-440 (Fema, 2005) whichuses static analysis as an alternative to time history analysis.For the course of this study, a reverse procedure proposed byKyriakides et al. (2014) has been adopted, which uses a modi-fied acceleration displacement response spectrum (MADRS)to represent the seismic demand. Non-linear static cyclic analy-sis is performed to obtain the capacity of the structure in theform of a capacity curve. Displacement-controlled static cyclicanalysis with a chained sequence of static analyses is employed.Each static analysis pushes the structure in the opposite direc-tion and would use stiffness from the preceding analysis. Thedirection of the load pattern is reversed after each cycle andthe cycles are repeated until the desired displacement has beenachieved.
The outcome of the static cyclic analysis is a hysteresis loop,which yielded the backbone curve (force–displacement envel-ope) upon joining the peaks obtained in each cycle of loading.The force–displacement envelope was compared with the experi-mental results (Karayannis et al., 2005) as shown in Figure 7.The shape of the backbone of this study resembles the shapeof experimental results performed with similar parameters.Early cracking in the masonry is followed by a decrease instiffness and the RC frame is available only to resist the lateralload. The cracking of RC started after the ultimate capacitywas reached. The stiffness and strength degradation continues,starting shear failure in RC members. The continued degra-dation ultimately results in a shear failure of the structure.Response of the structure is marked on the backbone curve ofFigure 7, which further shows that both analytical and exper-imental models exhibit stiffness and strength degradation in asimilar manner. It is, therefore, assumed that the analyticalmodel behaves reasonably analogously to the experiment con-ducted by Karayannis et al. (2005).
The backbone curve of the infilled frame obtained from thisstudy is also compared with a bare frame, as shown inFigure 8. From the figure it is clear that the infilled frame hasmore stiffness as compared to the bare frame and there is alsoa brittle failure of masonry at the peak value of base shear.After the cracking of the infill panel, to some extent it stillcontributes to load resistance, along with the frame members.
6. Vulnerability curvesA seismic vulnerability assessment framework, developed fordeficient buildings, is employed for the development of vulner-ability curves (Kyriakides et al., 2014). This framework usesthe same MADRS procedure defined by Fema (Fema-440
0
10
20
30
40
50
60
70
80
90
0 0·1 0·2 0·3 0·4
Base
she
ar: k
N
Top displacement: m
Karayannis et al. (2005)
Current study
Cracking
Yielding/crushing
Completeshear failure
Strength/stiffnessdegradation
Figure 7. Comparison of infill panel frame structure’s backbone
curve with experimental backbone curve (Karayannis et al., 2005)
Force: kips
Storeydrift: %
Fmax
αcap
αh
Fr
Fcr
Ke
δcδcap
Figure 6. Force–displacement relationship for strut model (Sattar
and Liel, 2010)
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(Fema, 2005)). After the capacity of the building has beenevaluated in the form of a backbone curve, the seismic hazardcorresponding to various levels of damage is required. Theresponse spectrum of the building code of Pakistan (BCP,2007) with ‘SD’ (stiff soil) soil type is used as the structuraldemand parameter. Structural damage is quantified using atime-period-based damage index (Kyriakides et al., 2012).Then for each damage index calculated, a corresponding peakground acceleration (PGA) is calculated which represents thehazard level.
In the context of the framework employed, the capacity anddemand curves are required to be represented in spectral coor-dinates. The point of intersection of the capacity and demandcurve (performance point) represents the performance of thestructure. Every point on the capacity curve is assumed as aperformance point and, using the reverse MADRS procedure,the corresponding hazard level (PGA) is calculated(Kyriakides et al., 2014). The final equation has the form asexpressed in Equation 5 below, which is employed for evalu-ation of PGA (Ali et al., 2015).
where in Cv and Ca are seismic coefficients obtained fromBCP (2007). The calculated PGA is then plotted against thestructural damage index, which gives the required vulnerabilitycurve. The curves derived for masonry infill structures areshown in Figures 9–11. For probability of exceedance (POE),the derived curves consist of mean, 5% and 95% POE curvesto address the probabilistic aspect of vulnerability.
7. Results and discussionThe mean curve of the 1B2S building, as plotted in Figure 9,initially indicated a sharp increase in damage with increase inPGA. The value of mean damage ratio (MDR) reaches 21%with just 0·03g. At this point, it becomes stabilized; that is, thevalue of PGA increases without further increase in damage.This implies that, initially, the cracks in masonry induce abrittle nature, and later on this adds to the stiffness (Kauffmanand Memari, 2014; Ko et al., 2014).
This stiffness adds to the moment resistance of the frame.However, once the infill is damaged completely, then onlyframe is available and the damage starts increasing somewhatlinearly. At about 0·44g, with a corresponding damage of 42%,the curve becomes even steeper, representing the initiation ofbrittle shear failure, before ultimately collapsing at 0·65g.Similar patterns of vulnerability are shown by 5% and 95%POE curves, with a delayed and earlier collapse, respectively.
A set of vulnerability curves for 2B2S and 3B2S is shown inFigures 10(a) and 10(b). Mean curves of both the structures
indicated a sharp increase in MDR, but this becomes stabilisedearlier than 1B2S (8·57% and 9·48% MDR, respectively, for2B2S and 3B2S). As stated before, this stabilisation is a resultof added stiffness from the masonry infills. The structures con-tinued to absorb more forces with a slight increase in damage.Then a sudden increase in damage occurs at 0·44g and 0·47g,corresponding to an MDR of 27·67% and 29·67% for 2B2Sand 3B2S, respectively. Once this phenomenon occurs, boththe buildings fail with a very small increase in PGA. In 2B2Sframe, a 26% increase in PGA increases the MDR value from27·67% to 100%, whereas in the case of 3B2S, a 17% increasein PGA takes the value of MDR from 29·675% to 100%. Thisbrittle failure is again indicated due to the initiation of shearfailure in a structural member. Another important finding inthese curves is that, with increasing number of bays, the failurebecomes more sudden due to a decrease in the time period ofthe building. An almost similar pattern is indicated by the 5%and 95% POE curves in both cases.
0
15
30
45
60
75
90
0 0·1 0·2 0·3 0·4
Base
she
ar: K
N
Top displacement: m
Infilled frameBare frame
Figure 8. Comparison of backbone curves of masonry infilled RC
frame and bare RC frame
0
20
40
60
80
100
0 0·1 0·2 0·3 0·4 0·5 0·6 0·7
MD
R: %
PGA: g
Mean
5% POE
95% POE
Figure 9. Vulnerability curve for masonry infilled frame 1B2S
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While considering vulnerability curves of 3B3S and 3B4Sframe structures in Figures 11(a) and 11(b), the value of MDRequals 13·40% and 15·22%, respectively, against a PGA valueof 0·04g. Added stiffness then plays its part, consequently lim-iting the damage.
Alternate crushing in concrete then causes the initiationof shear failure and damage starts increasing after 22·50%MDR value in 3B3S and 25·52% MDR value in 3B4S struc-tures. Increased shear failure ultimately causes the collapse at0·60g in 3B3S and at 0·68g in 3B4S building frames. Failureis still brittle in both these cases, but relatively less brittlethan for the 2B2S and 3B2S structures. At the same time,3B4S structures showed a delayed collapse compared with3B3S structures. There is no marked difference in mean, 5%POE and 95% POE curves at initial stages; however, later on,the curves spread out but the pattern of failure remains thesame.
Similarly, the vulnerability curve drawn for a bare frame is pre-sented and compared in Figure 12. Again initially the damageincreases linearly until the yielding in tension steel starts at0·12g. At this point, the steepness of the curve increases a bitbut goes on increasing after 0·25g until the building collapseat 0·47g. This increase is a clear representation of initiation ofbrittle failure modes (shear failure) at different locations indifferent structural members.
7.1 Comparison with bare frame andGESI expert curve
The vulnerability curve of the infill frame is then comparedwith the vulnerability curve of the bare frame (Figure 12)with similar parameters and the Global Earthquake SafetyInitiative (GESI) expert opinion (GESI, 2001) based curve, asshown in Figure 13. From comparison of these vulnerabilitycurves, it is clear that the structures with masonry infill canwithstand higher PGA as compared to the bare frames priorto their failure, but they are more vulnerable below 0·30g,although the damage at this stage is not critical.
0
20
40
60
80
100
MD
R: %
PGA: g
PGA: g
(a)
(b)
Mean
5% POE
95% POE
0
20
40
60
80
100
0 0·2 0·4 0·6 0·8
0 0·2 0·4 0·6 0·8
MD
R: %
Mean
5% POE
95% POE
Figure 11. (a) Vulnerability curve for masonry infilled frame 3B3S.
(b) Vulnerability curve for masonry infilled frame 3B4S
0
20
40
60
80
100
MD
R: %
MD
R: %
PGA: g
Mean
5% POE
95% POE
0
20
40
60
80
100
0 0·2 0·4 0·6 0·8
0 0·2 0·4 0·6 0·8
PGA: g
(a)
(b)
Mean
5% POE
95% POE
Figure 10. (a) Vulnerability curve for masonry infilled frame 2B2S.
(b) Vulnerability curve for masonry infilled frame 3B2S
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The GESI expert opinion based vulnerability curve is used bymany researchers in earthquake risk assessment (ERA). Thiscurve does not incorporate the brittle failure mode of masonryinfill panels. From Figure 13, it is clear that the linear GESIcurve does not depict the actual behaviour of masonry infilledRC frame structures, as it underestimates the damage inmasonry panels below 0·20g and overestimates the damage athigher PGA levels.
7.2 Effect of openings on seismic vulnerabilityThe introduction of openings in infill panels reduces the areaof the infill panels and, thus, the width of the equivalentmasonry strut. The shape, location and size of the openingmay also affect the performance of the masonry infill(Surendran and Kaushik, 2012). In this case, central openingsare considered in three- and four-storey structures only (3B3SO
and 3B4SO). In central bays, an opening area of 22% of thetotal infill panel, equivalent to a door, and in external bays a13% opening area, equivalent to a window, are considered.After the vulnerability assessment, the comparison indicatedan increased vulnerability of the structures with openings, asevident from the plots of Figures 14 and 15. In the case ofinfill openings, the initial sharp rise in vulnerability becomesstabilised earlier than for the fully infilled panel.
With further propagation of cracks, the stresses start to con-centrate at the opening ends and the stiffness of the masonrydiminishes. At this point, the stresses are now resisted by thebare frame, as the masonry panel remains no more workable.This happened at an MDR of 23% and 28% for 3B3SO and3B4SO, respectively. A relatively sharp rise in vulnerability isobserved at this point, with an earlier collapse than the fully
0
20
40
60
80
100
0 0·15 0·30 0·45 0·60 0·75
MD
R: %
PGA: g
Infilled frameBare frame
Figure 12. Comparison of infilled and bare frame vulnerability
curves
0
20
40
60
80
100
0 0·2 0·4 0·6 0·8
MD
R: %
PGA: g
GESI curve
1B2S
2B2S
3B3S
3B4S
Figure 13. Comparison of infilled frame and GESI expert
vulnerability curves
0
20
40
60
80
100
0 0·1 0·2 0·3 0·4 0·5 0·6 0·7
MD
R: %
PGA: g
3B3S3B3SO
Figure 14. Comparison of fully infilled frame (3B3S) and infilled
frame with openings (3B3SO)
0
20
40
60
80
100
0 0·1 0·2 0·3 0·4 0·5 0·6 0·7
MD
R: %
PGA: g
3B4S
3B4SO
Figure 15. Comparison of fully infilled frame (3B4S) and infilled
frame with openings (3B4SO)
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infilled panel frame. Thus, it can be said that the vulnerabilityof 3B3S and 3B4S is increased by 10% and 5·88%, respectively,when openings are considered in masonry, namely, in 3B3SOand 3B4SO.
7.3 Effect of variation in number of bays and storeysIncreasing the number of bays and storeys adds more columnlines and infill panels in the structure, and thus the stiffnessand the ductility of the structure changes considerably. It
has been observed in this study that this changed stiffnessand ductility greatly influences the capacity and failure modeof the structure. A comparison of the vulnerability curveswith varying numbers of bays and storeys is shown inFigures 16 and 17.
As can be seen, no generalised behaviour is shown by thecurves with increasing the number of bays and storeys. So, inorder to study the effect more deeply, different damage states
0
20
40
60
80
0
0 0·1 0·2 0·3 0·4 0·5 0·6 0·7
MD
R: %
PGA: g
1B2S 2B2S 3B2SM
oder
ate
dam
age
Exte
nsiv
eda
mag
e
Collapse
Slight damage
Ligh
tda
mag
e
Partial collapse
Figure 16. Comparison of vulnerability curves with variation in
number of bays
0
20
40
60
80
100
0 0·1 0·2 0·3 0·4 0·5 0·6 0·7
MD
R: %
PGA: g
3B2S 3B3S 3B4S
Slight damage
Ligh
tda
mag
eM
oder
ate
dam
age
Extensivedamage
Partial collapseCollapse
Figure 17. Comparison of vulnerability curves with variation in
number of storeys
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are marked on these curves. The homogenised reinforced con-crete (HRC) damage scale (Rossetto and Elnashai, 2003) isused to mark the threshold value of a certain damage state.As the number of bays increases with constant number ofstoreys, the vulnerability of the structures increases. It can beseen in Figure 16 that the 1B2S structure initially exhibitsmore damage than 2B2S and 3B2S, but collapses at a relativelyhigher PGA, whereas there is no considerable differenceobserved in 2B2S and 3B2S structures initially. However, thestructure with fewer bays collapses early. This trend is associ-ated with the decreased time period of the building withincreased number of bays, due to increased stiffness. A struc-ture with more stiffness, in other words a lower time period,attracts more forces (BCP, 2007) and owing to a large accumu-lation of forces they collapse early and in a more brittlemanner. Figure 16 further suggests that 2B2S is 7·69% morevulnerable to collapse than 1B2S, while 3B2S is 5% more vul-nerable to collapse than 2B2S. This implies that, above a par-ticular number, with a further increase in the number of baysthe trend may be shifted in contrast to what has just beenobserved. To verify the assumption, however, further analysisis needed.
On the other hand, when the number of bays is kept constantand the number of storeys is varied, the comparison showsan opposite trend and the vulnerability decreases with increas-ing number of storeys (within the scope of this study, i.e. amaximum of four storeys). With increasing number of storeysthe height of the building is increased as well as the timeperiod. Increased time period means that the building willattract less forces and can withstand a larger PGA beforecollapse. From Figure 17, it is obvious that 3B3S and 3B4Sstructures initially exhibit more damage than 3B2S, but thecollapse occurred earlier in 3B2S structures. Figure 17 furthersuggests that 3B2S is 8·09% more vulnerable to collapse than3B3S, while 3B3S is 9·37% more vulnerable to collapse than3B4S.
8. ConclusionsInitially masonry infill resists the forces induced by earthquakeloading, whereas the RC frame is critical for the performanceof the structure at stronger excitations. The vulnerability curvesdeveloped for typical Pakistani infilled RC frame structuresshowed the collapse at a PGA in the range of 0·57–0·68g. Interms of overall performance, the masonry infilled structureexhibited collapse damage at a 38% higher PGA level as com-pared to bare frame structures, thus enhancing the overallseismic response.
The GESI curve underestimates the damage in masonry panelsbelow 0·200g and overestimates at higher PGA; thus, thesecurves do not depict the actual behaviour of masonry infilledRC frame structures. An increased vulnerability is associatedwith increased number of bays and introduction of openingsin the masonry infill (2B2S is 7·69% more vulnerable than
1B2S; 3B2S is 5% more vulnerable than 2B2S). With respectto number of storeys, the seismic vulnerability is considerablyreduced with increasing number of storeys (3B2S is 8·09%more vulnerable than 3B3S; 3B3S is 9·37% more vulnerablethan 3B4S).
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