Research ArticleSeismic Vulnerability Assessment of School Buildings in SeismicZone 4 of Pakistan

Muhammad Zain 1 MuhammadUsman 1 Syed Hassan Farooq1 and TahirMehmood2

1School of Civil amp Environmental Engineering National University of Science and Technology (NUST) Sector H-12Islamabad Pakistan2Civil Engineering Department COMSATS University Islamabad Wah Campus Wah Cantt Pakistan

Correspondence should be addressed to Muhammad Usman musmankaistackr

Received 24 June 2019 Revised 28 August 2019 Accepted 6 September 2019 Published 2 October 2019

Academic Editor Constantin Chalioris

Copyright copy 2019 Muhammad Zain et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

ick population density and its escalation propensity in seismically active regions of Pakistan has raised sincere concerns aboutthe performance of building stock whose suboptimal performance and complete collapses led to a colossal number of casualtiesduring the past earthquakes e current research is inspired by the Kashmir earthquake of 2005 which consumed more than80000 lives out of which approximately 19000 were children due to wide spread collapse of school buildings A new database forexisting reinforced concrete (RC) school buildings in seismic zone 4 of Pakistan has been developed using the surveyed in-formation and presented briefly e paper presents the statistics of the data collected through field surveys and professionalinterviews It was found that the infrastructural authorities in the considered region developed some specific designs for schoolbuildings with varying architectural and structural configurations which were eventually replicated throughout the area In thecurrent study almost 2500 schools were surveyed for identifying versatile architectural and structural configurations andsubsequently 19 different types had been identified which were eventually used as representative stock for the schools in seismiczone 4 of Pakistan Muzaffarabad district e results of the study yield the brief of the collected data from the field and aconsolidated methodology for establishing the analytical fragility relationships for one of the 19 structural configurations of theschool buildings A sample building from the collected data has been selected by considering the maximum number of studentsand afterwards the vulnerability is assessed by employing incremental dynamic analysis (IDA) which constitutes the presentedmethodology Finally the fragility curves are developed and presented for the said building type e derived analytical fragilitycurves for the considered building type indicate its structural vulnerability and as a whole represent its satisfactory behavior evulnerability assessment process and the fragility development are described in an easy manner so that the domestic practicingengineers can readily become able to extend the application towards other school buildings in the region e developed re-lationships can be employed for rational decision making so that essential disaster preparedness can be carried out by identifyingany need for structural strengthening and interventions

1 Introduction

e earthquake and its aftershocks that struck Pakistan inOctober 2005 were extremely catastrophic and served as aneye-opener for policy makers engineers and the hoi polloion the necessity of having safe buildings and structures thatmust be resilient enough to sustain natural calamitiesSeismically undermined infrastructural facilities and poorconstruction specifically of school buildings make the lives

of youth severely vulnerable eir safety and continuity ofeducation is of paramount importance not only for theparents but also for the long-term social growth and eco-nomic prosperity of the nation A structure may get sub-jected to extreme seismic loading conditions during its lifespan so an adequate engineering proficiency to assess di-minishing structural capacity is essential to avoid completestructural collapse or to decide any specific intervention [1]e 2005 Kashmir earthquake caused approximately 87000

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 5808256 14 pageshttpsdoiorg10115520195808256

casualties out of which almost 19000 were school goingchildren and cumulatively it affected about 35 millionpeople [2] It was also stated by the Earthquake EngineeringResearch Institute Report [2] that approximately 67 of theeducational institutions in the area faced complete de-struction Despite of the deaths and socioeconomic rami-fications the 2005 earthquake yielded the phenomenon ofldquoBuild Back Betterrdquo in Pakistan and the Building Code ofPakistan (BCP)ndashSeismic Provisions 2007 [3] is essentially atangible example of it In 2015 United Nations DevelopmentProgramme (UNDP) reviewed the status of building designcodes and bylaws with a precise focus on 2007 Building Codeof Pakistan (BCP) and in its report [4] UNDP stated that athin and tight development schedule forced a large-scaleincorporation of American source documents and preventedthe creation of a truly Pakistani code

In major cities developmental authorities with juris-diction do most regulation over the respective cities andsuburbs but with respect to the BCP and earthquake designissues the bylaws of leading local developmental authoritiesare incomplete and even inconsistent and at times evencontradictory [4] From the prevailing information it can beinferred that the design professional bears all the re-sponsibility for structural design

Considering the prevailing state of the vague practice ofBCP 2007 and its provisions the current research is targetedto assess the seismic vulnerability of RC school buildings thatwere designed and constructed in Pakistanrsquos seismic zone 4after the 2005 Kashmir earthquake Data collection wasmade in the whole of Muzaffarabad district of Kashmir as itis one of the most vulnerable zones and faced colossaldevastation in the past due to earthquakes

Numerous field visits were conducted and professionalinterviews were taken with different organizations includingNational Engineering Services Pakistan (NESPAK) the mostprominent organization to develop designs for most of theschool buildings in the earthquake-prone regions Acuteeffort was made to accurately develop the analytical modelfor vulnerability assessment e field visits were conductedto visually inspect the contemporary condition of the schoolbuildings and to take the essential measurements of struc-tural members so that they may substantially be comparedwith the drawings obtained through professional interviewsSubsequently using the incremental dynamic analysis(IDA) structural vulnerability is assessed and fragility curvesare developed As indicated by the literature fragility curvesare widely employed to represent the vulnerability ofbuildings [5 6] Tangible examples can be observed in theliterature for instance Zain et al [7] developed the ana-lytical fragility curves for a reinforced concrete building inPhilippines by considering two damage states It is pertinentto mention that the damage itself characterizes undesirablechanges in a system that adversely affects a structurersquos be-havior [8] e development of fragility curves is not onlylimited to building structures Pang et al [9] and Rasheedet al [10] conducted their researches for bridges whileWanget al [11] and Yazdani and Alembagheri [12] established thefragility curves for dams e present paper specificallyconsiders the building structure only for developing the

analytical fragility curves e analytical fragility curves canbe generated using nonlinear static and dynamic analysis[13 14] though nonlinear dynamic analysis is considered tobe the most rigorous and reliable for their derivation[15 16]

e present paper provides a brief insight into thecollected data and presents a consolidated framework toassess the vulnerability of school buildings in seismic zone 4of Pakistan A newly developed database for the existingschool buildings in the Muzaffarabad district of AzadJammu and Kashmir (AJK) province of Pakistan is pre-sented For the purpose of developing analytical fragilityrelationships a building typology representative of thetypical school building stock with certain structural con-figuration is selected for developing its fragility relation-ships against seismic loading ough some work has beendone in this sphere in the developed world but developingcountries still lack such researches and presently no otherwork exists that can specifically address the development ofanalytical fragility relationships for school buildings inPakistane outcomes of the presented study can be readilyadopted by relevant authorities and disaster preparednessand mitigation agencies to decide any need for specificstructural or nonstructural intervention e application ofthe presented framework can be further extended to es-tablish analytical fragility relationships for other types ofschool buildings whose information are briefly presented inthis work

2 Data Collection and Methodology

21 Data Collection Data collection was made from wholeof Muzaffarabad district to establish a database for existingreinforced concrete (RC) school buildings e databasecontains all the information pertaining to structural featuresof schools ie number of stories locations of staircaseslocations and dimensions of beams and columns thicknessof slabs and the width and locations of infills e databasealso contains the structural drawings ie design and as builtthat were collected as part of the data collection processLater on the obtained drawings were compared with theexisting structures to obtain insight into the actual executionand the contemporary condition of the school buildingstructures

22 Development of Database for Existing School Buildings inMuzaffarabad District A total of 2417 schools were visitedand visual inspection was made in accordance with FEMA154 [17] Detailed plans indicating the locations and sizes ofstructural components were developed for all the buildingsand were eventually compared with the obtained drawingsfrom different domestic sources Out of 2417 schools en-trance was granted for 1933 school buildings and the localstaff for measuring the dimensions of the structural com-ponents extended appropriate cooperation and elaboratedabout the behavior of the buildings during the earthquakeswhich came after 2005 While for the rest of the buildingsie 484 only exterior was available for observance from

2 Advances in Civil Engineering

which the number of bays external columns and beamscould be observed It was found that out of 2417 schoolbuildings 1158 were single story 847 were double story and412 were three-story structures It can be convenientlydeciphered from the collected data that most of the buildingpopulation in the region consists of single story schoolbuildings with obvious variation in the number of their baysand story heights

It was found out that domestic authorities developedsome typical architectural and structural designs whichwere subsequently replicated throughout the consideredregion for constructing RC schools For the purpose ofdeveloping categories of school buildings with varyingstructural configurations to assess their vulnerability 19different types of RC school buildings were identifiedthrough the field surveys and professional interviews einventory developed after the identification of the buildingtypes along with their structural features is given in Ta-ble 1 e first column of the Table 1 denotes the name ofthe model aimed to represent the generic nonlinear modelfor that category of schools All the names start fromldquoBLRrdquo and subsequently the model number is mentionedie BLR-1 BLR-2 up to BLR-19 representing all the 19school building typologies with varying structural andarchitectural configurations ldquoBLRrdquo in the names meansldquoBuilding-Low-Riserdquo essentially representing the low-risenature of the construction in the considered region as thenumber of stories for school buildings remains between 1and 3 only e 2nd column presents the number of storiescolumn 3 and 4 provide the number of bays in x and ydirections respectively e x and y directions are referredas the direction along the front side and the orthogonaldirection respectively It was observed that mostly two baysexisted in the y-direction ie one for the pedestrianwalkway which mainly served as a corridor so that studentscould walk to get in and out of the classrooms while theother one served the purpose of a classroom e totalheight of the buildings is given in column 5 Column 6presents the typical floor area while column 7 correspondswith the area of slab openings placed above the staircasesTypical floor area means the area for a single floor only

Figure 1 provides the number of schools under each ofthe 19 school building categories It was found that BLR-5was the mostly constructed school building in one-storystructures BLR-11 was the mostly constructed schoolbuilding in two-story structures while BLR-18 was themostly constructed school building in three-story structuresin the considered region

In the present study the vulnerability is assessed byconsidering a two-story structure BLR-11 e BLR-11 isspecifically considered as this typology has the maximumnumber of students as per the collected information ebuilding categories with 3 number of stories housed alliedfacilities ie libraries and laboratories but it was found thatamong all typologies BLR-11 accommodates most of thepupils from the considered seismic zone e altruistic in-tention is to produce building class-specific fragility re-lationships that can be easily adopted by the researchers andmore practically by practicing engineerse fragility curves

have been developed using the IDA the details of which havebeen provided under the subsequent section

23 Methodology For conducting the vulnerability assess-ment of school buildings in seismic zone 4 of Pakistan thecurrent study employs nonlinear incremental dynamicanalysis (IDA) to capture the structural response againstapplied and incrementally scaled set of ground motions Forthis purpose 20 ground motions were carefully selected andscaled at increments of 020 g starting from 020 g up to 140 g

Since earthquake loading parameters are usually char-acterized by single numerical values ie peak ground ac-celeration (PGA) or pseudo spectra acceleration at thefundamental period of the building (T1) single-value in-dicators PGA and Sa at the fundamental period of thebuilding (T1) have also been used in the current study tocorrelate with the structural damage As low-rise buildingsare the primary focus of this research the current studyemploys global drift to decide the threshold damage limits todecide different damage states also known as limit states ofthe building Dynamic instability is usually caused by largeglobal drift due to large interstory drift and P-delta effectKeeping this in view global drift is selected as the damageindicator to incorporate the overall structural global stabilityin the presented work

Figure 2 qualitatively depicts the illustration of the de-formational-based response corresponding with differentlimit states used by the HAZUS [18] e figure illustratesfour damage states ranging from slight damage to completecollapse of the building by relating the base shear with thedeformational-based structural response while the de-formational-based response itself can be considered innumerous forms ie global drift interstory drift or thespectral displacements

Finally using a probabilistic seismic demand modelattained by the virtue of simulated damage data fragilitycurves for each of the considered damage state were ob-tained e framework and procedure through which thevulnerability assessment has been conducted is presented inFigure 3 Detail for every step is given hereafter

3 Application of the Framework

For demonstrating the established framework a nonlinearmodel for a selected school building type BLR-11 from thedeveloped database is created using CSI Perform 3D V 70[19] as it contains the vital inelastic elements that canmonitor the strains in structural members For the con-sidered typology nonlinear inelastic fiber elements wereused to monitor the strains in the members and sub-stantially to set threshold limits for the attainment ofdamage states e configuration of the selected buildingemployed analytical tools and material strengths are dis-cussed in the forthcoming sections

31 Configuration of the Selected Building Typology eselected school building represents a typical two-storystructure that comprises 11 bays in the x-direction and 2

Advances in Civil Engineering 3

bays in the y-direction It consists of different sizes of beamsand columns Figure 4 shows the plan of the selectedbuilding that has been considered in the present study whileFigure 5 exhibits the elevation of the considered building inthe longer dimension to indicate the story height

In Figure 4 FB means the floor beams while FC meansthe floor columns e actual buildings are constructed onrelatively stiff soil type but it was found during the pro-fessional interviews that all of them have been designedaccording to the soft soil type Sd soil according to BCP emain structural system of the buildings consists of moment-resisting RC frames in both of the directions e typicalfloor area for the selected building is 3445m2 Table 2 showsthe X-sectional dimensions of structural members iedifferent FBs and FCs e amount of reinforcement ob-tained through field surveys and professional interviews isalso indicated in the same table

32 Nonlinear Structural Modelling Full three-dimensionalnonlinear structural model was created in software CSIPerform 3D v 70e analytical tools in the software possess

BLR-2BLR-1 BLR-3

BLR-4 BLR-5

BLR-6 BLR-7 BLR-8

BLR-10

BLR-11

BLR-12BLR-13

BLR-14

BLR-15

BLR-16BLR-17

BLR-18

BLR-19

One storyTwo stories

ree stories0

50

100

150

200

250

300

Tota

l num

ber o

f bui

ldin

gs

BLR-9

Figure 1 Number of schools in each of the 19 school building configurations

Table 1 General properties of the buildings in developed database

Building ID(col 1)

No of stories(col 2)

No of bays in x-direction (col 3)

No of bays in y-direction (col 4)

Total buildingheight (m) (col 5)

Typical floor area(m2) (col 6)

Area of slab opening(m2) (col 7)

BLR-1 1 6 3 38 3286 mdashBLR-2 1 3 3 30 1015 mdashBLR-3 1 4 2 38 1431 mdashBLR-4 1 4 2 38 1466 mdashBLR-5 1 5 2 36 1970 mdashBLR-6 1 6 3 36 328 mdashBLR-7 1 6 3 30 3066 mdashBLR-8 1 3 2 38 808 mdashBLR-9 2 4 2 76 1452 93BLR-10 2 4 2 76 1255 93BLR-11 2 11 2 61 3445 216BLR-12 2 2 2 61 664 68BLR-13 2 5 2 67 1927 163BLR-14 2 8 3 67 2536 235BLR-15 2 3 2 61 58 57BLR-16 2 5 2 61 223 77BLR-17 3 4 2 11 3902 248BLR-18 3 5 2 11 2092 153BLR-19 3 12 2 91 3776 214

Slight damage

Moderate damage

Extensive damage

Complete collapse

Yield

Deformational-based response

Base

shea

r

Figure 2 HAZUS-based illustration of different structural damagestates depending upon the structural deformation-based response

4 Advances in Civil Engineering

excellent capability to capture different aspects of structuralperformance ranging from hinge rotations to materialsrsquostrains in members In order to capture the actual behaviorit was pertinent to take into account the properties of locallydeveloped concrete materials using the domestically avail-able cement aggregates and other constituents For thispurpose a study conducted by Rafi and Nasir [20] wasutilized to extract a mean value for concretersquos strength at

28 days subsequently as per the recommendations of ASCE41 [21] expected strength was ultimately employed duringthe analysis For reinforcing steel bars it was inferred frommost of the professional interviews that Grade 40 reinforcingbars were used during the design and construction processconsequently the current study uses Grade 40 steel re-inforcements in the analytical models in accordance with therecommendations of ASCE 41 [21]

Defining an RC building category from the database that represents the typical

building stock

Establish nonlinear analytical model using inelastic fiber

sections for structural elementsie beams columns and shear

walls

Execute nonlinear static analysis of the buildings to

obtain capacity curves

Establish the limit states (LS) of buildings depending upon the

strength and stiffness degradation (u k)

Selection of ground motions depending upon

the fault mechanism magnitude Mw distance to rupture (Rrup) and shear

wave velocity (Vs30)(ldquonrdquonumber of ground

motions)

Execution of incremental dynamic analysis (IDA) by incrementally scaling the selected ground motions

(i = 1 n)

Development of damage-hazard relationships IM

vs response parameter iePGA Sa Sd etc

Select the seismic intensity measure (IM) ie PGA PGV

Sa Sd etc (previously used during IDA)

Aer processing of results

Determine the parameters for lognormal distribution to match

the sampling probabilities (λc βc)

Plotting of fragility curves for each limit

state (LS)

Maximizeλc and βc using the

maximum likelihood

method (MLE)

Estimate the sampling

probabilities

Figure 3 Framework for the vulnerability assessment of RC school buildings in the current study

FB-1

FB-1

X

Y

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-138m 38m 38m 38m 38m 38m 38m 38m 38m 38m

58m

25m

FC-1

FC-1

FB-2

FB-2

FB-3

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FC-1 FC-1 FC-1 FC-1 FC-2 FC-1 FC-2 FC-1 FC-2 FC-1 FC-1

FC-1

FC-2

FC-1

FC-2

FC-1

FC-2

FC-1

FC-1

FC-1

FC-2

FC-2

FC-1

FC-2

FC-2

FC-2

FC-1

FC-2

FC-2

FC-2

FC-1

FC-2

FC-1

FC-2

38m

Figure 4 Plan view of the considered building typology

XZ

38m 38m 38m38m 38m38m38m 38m 38m38m38m

3 m

3 m

Figure 5 Elevation view of the considered building indicating the story height of the superstructure

Table 2 Beam and column X-sectional and reinforcement details

Structural element(s) Label Width (mm) Height (mm) Top steel Bottom steel Mid steel

BeamsFB-1 305 455 3_19 3_19 mdashFB-2 305 455 3_19 3_19 mdashFB-3 305 455 3_19 3_19 mdash

Columns FC-1 305 455 3_19 3_19 2_19FC-2 305 305 3_19 3_19 2_19

Advances in Civil Engineering 5

Nonlinear inelastic fiber sections were created forlayer-by-layer modelling of concrete and reinforcing re-bars for all of the X-sections except slabs which weremodelled as linear By the virtue of fiber modelling theforce-deformation relationship of columns and beams istransformed into the stress-strain relationship of con-struction materials ie concrete and reinforcement Byemploying fibers an appropriate division may be in-troduced for confined and unconfined concrete fibers andconsequently a composite section can easily be taken intoaccount [22]

In the current study the Mander model provided byMander et al [23] was used for concrete Complete con-finement effect and strength loss were considered during theanalysis according to the details given in the X-sections ofbeams and columns (Table 2)

Steel models that can capture the buckling and non-buckling behavior of the reinforcements are available withinthe Perform 3D For this case the nonbuckling steel modelwas utilized as ductility design is mainly based on the factthat reinforcement cannot be abruptly brittle Expectedmaterial strength was used in the analysis as per the rec-ommendations of ASCE 41 [21]e numerical modelling ofstrength degradation at high ductility levels was also con-sidered by modelling the strengths of the materials in anonlinear range Table 3 summarizes all the materialstrengths live loads and infill-partitioning loads that wereused during the analysis in accordance with the professionalinterviews conducted during the field surveys

4 Uncertainty Treatment

e uncertainties can be divided into two categories iealeatory and epistemic during any sort of vulnerability andrisk assessments [24] e uncertainty associated with theinherent variability in the nature of ground motionresulting from the natural earthquakes comes under theheading of aleatory uncertainty us the intrinsic ran-domness and variability of ground motion record describesuch uncertainties

e epistemic uncertainties on the other hand char-acterize the qualms related to paucity of available knowledgeConventionally during the vulnerability assessments thelack of knowledge related to the materialsrsquo strengths comesunder the category of such uncertainty On the contraryZain et al [25] have shown that variation in materialcharacteristics do not induce any significant disparity in thestructural response and variation in the ground motionsmust be considered as the majorly significant factor ininfluencing the dynamic response of the structures as re-cord-to-record variability may persuade severe changes inthe structural response of any building against the propertiesof different ground motions

e current study employs 20 different ground motionsto cover a wide range of variation in the characteristics ofseismic loading Since the variations in the materialsrsquostrengths do not incite any major uncertain structural re-sponse hence their variation is not considered in this studye details about the selection procedure and incremental

scaling for the ground motions are discussed under theproceeding section

41 Ground Motion Uncertainty e biggest source ofuncertainty lies in the seismic demand during the vulner-ability assessment process Path attenuation characteristicsof the originating source and the site conditions all playtheir respective parts in contributing to such uncertainty Onaccount of the structural dynamic response it is imperativeto consider a wide range of seismic energy levels for selectingthe ground motions Typically a target spectrum is con-sidered for the anticipated seismic hazard level and thespectrum-matching technique is usually adopted to selectthe most suitable ground motions Although the BuildingCode of Pakistan (referred at [3]) provides a target spectrumfor the region considered seismic zone 4 of Pakistanhowever as explained in Section 1 the reliability of thedomestic code is questionable erefore in the presentstudy ground motions are selected by considering the bestavailable information of the case study area In this research20 natural ground motion records are selected by consid-ering the domestic fault mechanism magnitude source-to-site distance and the shear wave velocityVs in the upper 100feet of the soil layers and only the large magnitude earth-quakes ie 650 up until 80 are considered

For the current research the range of source-to-sitedistance has been kept between 0 and 30 kilometers forselecting the ground motions to consider the effects of pathattenuation so that any possibility of diversified site-specificsoil layers in near and far sites can be taken into account Forshear wave velocity Vs in the upper 30meters of the soil therange has been kept varying between 175 and 350msecwhich corresponds with the soil type Sd according to BCP-2007 (referred at [3])

e selected ground motions are given in the Table 4which presents the names of earthquake motion time his-tories magnitudes distances to rupture shear wave veloc-ities and associated PGA with some other minor details

By using numerous records with the consideration ofdomestic geological conditions the selected records may beconsidered as the representative of future shaking at the zonein question us with a variety of magnitudes PGA andother characteristics the aleatory uncertainty is adequatelytreated in the present study

5 Incremental Dynamic Analysis and GroundExcitation Random Effects

Incremental dynamic analysis (IDA) serves as the mostreliable method to assess the structural performance againstseismic excitations [26] Several researchers ie Kostinakisand Athanatopoulou [27] Fereshtehnejad et al [28] andZarfam and Mofid [29] adopted the technique for theevaluation of dynamic responses of different structures iebuildings and bridges and despite of its extensive compu-tational effort IDA has proved to be a splendid tool forprobabilistic vulnerability and risk assessments DuringIDA the ground motions are incrementally scaled in a way

6 Advances in Civil Engineering

that during each iteration of the analysis the accelerationsincrease at specific intended intervals e current studyutilizes the IDA for considering various levels of seismicintensity to predict the structural response against earth-quakes ranging from 02 g to 14 g with 020 g as theaugmenting acceleration for each successive iteration thusat this stage it is imperative to select the appropriateseismic intensity measure (IM) for representation ofseismic Subsequent subsection addresses the selection ofIM in the current study Apart from selecting the IM theremust also be a damage indicator that can amply relate theseismic IM with the observed structural damage As de-scribed earlier the current study employs global drift as thedamage indicator and the details have been given inSection 61

51 Seismic Intensity Measure Seismic intensity measure(IM) correlates the ground motion with the structuraldamage hence any IM employed must be rationally able toproject the dynamic response of the structure by the virtue ofthe damage indicator PGA is one of the IMs that has beenfrequently used by the experts for fragility derivations but itis generally comprehended that Sa is a better option as an IMto correlate with the structural damage as it actually rep-resents the effect of ground shaking on the building itselfPang and Wu [30] and Jiang et al [31] employed PGA fortheir researches Apart from the PGA Omine et al [32] andEden et al [33] used peak ground velocity (PGV) as an IM

Eden et al [33] also used Sa at the fundamental period of thestructure as an IM Frankie et al [34] and Choudhury andKaushik [35] utilized spectral displacement (Sd) as IM fortheir study on open ground story RC frames with openingsin walls during the vulnerability assessment Buratti [36]analyzed the sufficiency and the efficiency of numerous IMsas indicated in their study and employed the cloud analysistechnique for 1704 unscaled accelerograms Bojorquez et al[37] proposed a procedure to obtain the interstory driftdemands for midrise frame structures in terms of a spectral-shape-based IM (INp

) and eventually concluded that INpwas

the best parameter to relate with the structural response offrames with 4 6 8 and 10 stories under the narrow-bandground motions in Europe Some other vector-valued in-tensity measures have also been proposed and discussed byModica and Stafford [38] Baker and Cornell [39] Polsakand Nicolas [40] and Kohrangi et al [41] Bojorquez andIervolino [42] also performed their research to establish avector-based IM however their research also proposed ascalar-based IM as they apprehended that the use of thescalar-based IM is easier than the vector-based IM forpractical purposes

Pejovic and Jankovic [43] investigated different groundmotion IMs which are conventionally used to investigate thedynamic behavior and concluded that despite being the mostcommon IM PGA provided the greatest dispersion in re-sults in comparison with the PGV Sa(T1) Sv(T1) and Sd(T1) e research portrayed spectral response velocity valueSv(T1) as the most efficient IM for the RC frames while

Table 4 Selected natural ground motions

Sr No Earthquake name Year Station name Mag PGA (g) Rrup (KMs) Vs30 (msec)1 San Fernando 1971 LA - hollywood stor FF 661 0225 2277 316462 Gazli USSR 1976 Karakyr 68 0864 547 259593 Tabas Iran 1978 Boshrooyeh 735 0106 2879 324574 Spitak Armenia 1988 Gukasian 677 020 240 343535 Loma Prieta 1989 Agnews State Hospital 693 01695 2457 239696 Loma Prieta 1989 Saratoga-W Valley Coll 693 0331 930 347907 Northridge-01 1994 Arleta-Nordhoff fire station 669 0345 866 297718 Northridge-01 1994 N Hollywood - coldwater can 669 0309 1251 326479 Chi-Chi Taiwan 1999 CHY002 762 0137 2496 2351310 Chi-Chi Taiwan 1999 CHY036 762 0273 1604 2331411 Chi-Chi Taiwan 1999 TCU038 762 01448 2542 2978612 Chi-Chi Taiwan 1999 TCU059 762 0165 1711 2726713 Chi-Chi Taiwan 1999 TCU110 762 01918 1157 2127214 Kashmir earthquake 1999 ABD-Abbottabad 760 02517 260 2230415 St Elias Alaska 1979 Icy Bay 754 01759 2645 3063716 Niigata Japan 2004 NIG017 663 04764 1281 2741717 Montenegro Yugoslavia 1979 Ulcinj-Hotel Olimpic 71 02928 576 3187418 Chuetsu-oki Japan 2007 Joetsu Kita 68 0176 2945 334019 Iwate Japan 2008 IWT011 69 02194 843 2793620 Iwate Japan 2008 Kitakami Yanagihara 69 02057 1667 34898

Table 3 Material strengths and loading values used for the structural modelling

Materials LoadsCharacteristics Strength Units Name Value UnitsConcretersquos strength (fcprime) 21 MPa Live 26 kNm2

Reinforcing steelrsquos yielding stress (fy) 275 MPa Infill-partitioning 43 kNm

Advances in Civil Engineering 7

stating the other two spectral response parameters ieSa(T1) and Sd(T1) were similarly adequate as they in-corporated the dynamic characteristics of the consideredstructure e current study chooses both ie PGA andspectral acceleration at the fundamental time period (Sa(T1))of the structure as intensity measures As indicated by theprevious literature provided by Jelena and Srdjan [43] PGAis the most commonly employed IM which is easy to un-derstand for normal people with no specific engineeringbackground while Sa(T1) incorporates the structural char-acteristics during the execution of analyses

52 Results of IDA Figure 6 shows the results of IDA in theform of plots between global drift and the selected IMs ieincrementally scaled PGA and Sa(T1) from 020 g to 14 g Itcan be observed that intrinsic nature of different groundmotions produces different results despite of having thesame intensity of acceleration at a given pointere are total20 curves in each part of Figure 6 while each curve char-acterizes structural damage indicated by global drift causedby the single corresponding earthquake at discretely con-sidered seismic intensity levels ranging from 02 g to 14 g

In Figure 6(a) the curves manifest the maximum globaldrift ranging from 020 to more than 50 when PGA isused to indicate seismic intensity While in Figure 6(b)when Sa(T1) is used to characterize the seismic intensity themaximum global drift reaches 247 against the Sa of 14 gthe maximum considered in this study

e results of IDA indicate that intrinsic properties ofground motions project substantial sensitivities to theseismic demand e disparity in the structural responseagainst different ground motions of the same intensities isprimarily attributed to differences in the inherent nature ofground motions ie energy distribution over frequencycontent and duration that predominantly affects thestructural response Moreover when Sa(T1) is used as anindicator of the seismic intensity the global drift observeslower values because of the scaling of the ground motions atthe fundamental period of the structure which is directlyrelated with the structural inertia and stiffness

6 Vulnerability Assessment

e fundamental process of the risk assessment against anyhazard consists of two parts ie the hazard and the vul-nerability of structural systems to that hazard For earth-quakes the first portion is primarily concerned withseismologists who can provide a realistic estimate of thepotential seismic hazard that can hit a specific geographicalarea while the second part vulnerability is usuallyaddressed by the engineers and experts who design thefacilities for versatile purposes e current study is relatedwith the second part and assesses the vulnerability of theconsidered typology of school buildings by establishing thehazard-damage relationships for the considered typology ofstructures and subsequently by developing the genericfragility relationships Hazard-damage relationships depictthe structural performance against seismic excitations and

exhibit the dynamic response for all considered groundmotion intensities Figures 7(a) and 7(b) present a directrelationship between the seismic intensities and the struc-tural damage e structural damage is quantified using theglobal response and seismic intensities are provided in-crementally in terms of PGA as well as in terms of spectralacceleration at the fundamental modersquos time period Everysingle dot in each part of Figure 7 represents the maximumvalue of the global drift in terms of percentage against aspecific earthquake scaled at a specific intensity For in-stance at the seismic intensity of 14 g there are 20 dots fromall 20 ground motions indicating the uncertainty in thestructural response by depicting that one earthquake havingthe seismic intensity of 14 g produces global drift less than1 while some other earthquake with the same seismicintensity produces more than 5 of global drift

With increasing intensity of PGA from 020 g to 080 gin Figure 7(a) the global drift remains between 009 and119 While at higher PGA levels from 10 g to 14 g theglobal drift drastically remains between 044 and 516 forall the considered ground motions At the maximum con-sidered PGA of 140 g the global drift varies from 097 to516 for all 20 ground motions All this disparity in thestructural response arises because of the inherent charac-teristics of ground motions which vary from record to re-cord thus instigating different response against the samescaled intensity level

When Sa(T1) is used for representing seismic intensitythe global drift varied between 022 and 24 at the Sa of140 g as shown by Figure 7(b) e dotted line inFigures 7(a) and 7(b) shows the mean structural responseobtained at each intensity level

On the other hand the fragility curve as described byEquation (1) represents a conditional probability ofexceedance for specific damage or limit states of a structureagainst a particular seismic intensity given in terms of PGASa or some other seismic intensity describing the indicator

Pfragility P[LS | IM x] (1)

e aforementioned equation describes the conditionalprobability Pfragility of achieving or exceeding a specific limitstate LS when seismic intensity defined by a particularintensity measure (IM) is equal to ldquoxrdquo Fragility relationshipsfor different damage states must be probabilistically able topredict the structural vulnerability against a realistic range ofseismic ground excitations is probabilistic evaluation isonly possible when a large variation of seismic demands isconsidered so that ample variation in the dynamic structuralresponse can be obtained e vulnerability assessment re-quires the definition of specific limit states damage indicatorsand seismic intensity indicators e impending sectionsaddress all the requirements to develop fragility curvesConsequently fragility curves are developed for the selectedtypology to elucidate the established framework

61 Damage Indicator and the Definition of Limit Statese derivation of analytical fragility curves requires thedefinition of specific limit states in both terms ie

8 Advances in Civil Engineering

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Peak

gro

und

acce

lera

tion

(g)

05 1 15 2 25 3 35 4 45 5 550Maximum global drift ()

(a)

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Spec

tral

acce

lera

tion

(T1)

05 1 15 2 250Maximum global drift ()

(b)

Figure 6 IDA curves (a) maximum global drift vs PGA (b) maximum global drift vs spectral acceleration scaled at the fundamental timeperiod of the structure (Sa(T1))

0 02 04 06 08 1 12 14PGA (g)

0

1

2

3

4

5

Glo

bal d

ri (

)

(a)

0

05

1

15

2

25

3

0 02 04 06 08 1 12 14

Glo

bal d

ri (

)

Sa(T1)

(b)

Figure 7 Hazard-damage relationships (a) PGA vs global drift in percentage (b) Sa(T1) vs global drift in percentage

Advances in Civil Engineering 9

qualitative and quantitative For this purpose a researcherhas to employ a specific damage indicator also known asengineering demand parameter (EDP) or may also propose anew damage measure that can represent the structuraldamage in a rational manner to correlate the damage withseismic loading Once the damage indicator has been set orselected different limit states often known as the damagestates of a structure may be defined

Damage states represent a physical categorization ofdamages by using damage indices which suggest thresholdlimits for different damage states by relaying upon theparameters of structural behavior eg energy dissipationcapability ductility and strength Damage indices are usedfor correlating the accumulated damage with differentspecific damage states and numerous nonidentical damageindices may exist for the same structure For instance Khanet al [44] used global displacement of the structure tocharacterize the structural damage Crowley et al [45]considered damage limit states based on the strain levels inconcrete and steel Guneyisi and Altay [46] considered theinterstory drift ratio for representing the response pa-rameter corresponding to the four damage states takenfrom the HAZUS Casotto et al [47] considered themember flexural strength to characterize the first limit state(LS1) when the reinforcement steel yields in the columnsand 3 interstory drift for flexural collapse limit state(LS2) and subsequently related his LS2 with the loss ofsupport of the beam Chaulagain et al [48] and Gautamet al [49] used 3 damage states ranging from slight damageto complete collapse and developed empirical fragilityrelationships for buildings in Nepal ey further relatedtheir results with FEMA356 [50] classifications for buildingdamage levels

Since this study primarily relates with the generation offragilities for a specific building stock it would not bepractical to define damage or limit states depending uponthe member behavior or local strains In the current studythe global drift ratio has been considered as the damageindicator to correlate with the structural damage

ree damage states namely serviceability limit state(LS1) damage control limit state (LS2) and collapseprevention (LS3) are qualitatively defined in this studyLS1 corresponds with the 1st yield of longitudinal steelreinforcement in the structure Conventionally the firstlimit states are usually related with the formation of the firsthinge in the structure but since the current study employsnonlinear fibers to model the structure therefore the LS1primarily describes the yielding strain reaching in astructural element located anywhere in the structure edeformation and strength govern the LS2 It is defined as75 of LS3 e LS3 collapse prevention is generallydirected by the deformation Altug [51] defined the collapseprevention limit state as 75 of ultimate structural de-formation or the value for which more than 20 strengthdrop can be observed relative to the maximum strengthvalue e smaller of these two values would govern theLS3

e mathematical quantification for these damage statescould not be adopted from the previous research as there

exists no analogous research for Pakistanrsquos constructionindustry or for Pakistanrsquos seismic zone 4 In the currentstudy the mathematical values are assigned to each of thediscrete damage state by using the capacity curve of theselected structure However the obtained values were ap-proximately similar to those obtained by Altug [51] whichused the low-rise buildings of the Turkish region in theirresearch thus the obtained values amply represent the low-rise structural behavior e mathematical values for each ofthe considered damage state against the global drift arepresented in Table 5

62 Fragility Assessment for the School Buildings Seismicfragility curves are widely employed to obtain an articu-lated insight of structural performance against seismicloads and they represent the probability of entering orexceeding different damage states for considered in-tensities of ground shaking After attaining the structuralresponse established limit state definitions are applied forevaluating the structural performance for each limit stateOnce the computed value comes out to be greater than alimit statersquos value an event shall be counted within thesample comprising all the ground motions scalesereby for each IM direct sampling probabilities overthe 20 selected ground motions on all incrementing scaleswere obtained

It is a commonly accepted assumption that for a fragilitycurve a lognormal cumulative distribution function can beconveniently utilized for the representation of conditionalprobabilities [52ndash54] From viewpoint of literature log-normal distribution was also assumed and used for theregression of fragility relationships as mentioned in thefollowing equation

P(LS | IM) ϕln IM minus λc

βc1113888 1113889 (2)

where P(LS | IM) describes the probability of exceedance ofa particular LS given an IM value ϕ represents the standardnormal cumulative distribution function (CDF)

e controlling parameters λc and βc represent themedian point and the slope of the curve respectively It isimperative to evaluate their optimized values for a best fit ofCDF against the calculated probabilities Shinozuka et al[53] Dang et al [54] and Baker [55] stated that the max-imum likelihood method (MLM) is one of the most suitablemethod to achieve best possible values of these two pa-rameters In the current study MLM is utilized to obtain themedian point and the slope of the fragility curve Formultiple IM levels as considered in this study the likelihoodfunction is given as follows

Likelihood 1113945m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠ϕln IMiλc( 1113857

βc1113888 1113889

zj

1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 1113889

njminus zj

(3)

wherem is the number of IM levels andΠ denotes a productover all levels It is assumed that the observation of attaininga specific limit state from each ground motion is

10 Advances in Civil Engineering

independent of the observations from other ground mo-tions In the above equation zj denotes the number ofattaining particular limit state out of nj ground motions witha particular value of IM IMie fragility curve parameterscan be obtained by maximizing the likelihood function inEquation (3) as given in following equation

λc βc1113864 1113865 argmaxλc βc 1113944

m

j1ln

nj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnϕln IMiλ( 1113857c

βc1113888 1113889

⎧⎪⎨

⎪⎩

+ nj minus zj1113872 1113873ln 1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 11138891113897

(4)

A MATLAB code was written to control the maximi-zation of the likelihood function so that optimum values ofthese two parameters can be obtained for establishingseismic fragility

Figure 8 presents the developed fragility relationships forthe considered typology of the RC school building in seismiczone 4 of Pakistan Each portion of Figure 8 contains threefragility relationships correlating with each limit stateagainst both of the IMs ie PGA and Sa(T1) Directsampling probabilities obtained from the IDA are alsoplotted in Figure 8 along with lognormally fitted fragilityfunctions

Table 6 provides the simulated values for λc and βc foreach limit state against each IM for the derivation of fragilitycurves

7 Conclusion

Pakistan has numerous seismotectonically active regionsincluding Muzaffarabad and past earthquakes especially the2005 Kashmir earthquake have proven this fact In thisstudy a new database of RC school buildings constructed inMuzaffarabad district after 2005 earthquake has beenpresented Subsequently the structural vulnerability of aspecific category of RC school buildings is assessed andpresented by using IDA so that practicing engineers atdomestic and regional level can further extend the evalua-tion to other categories of RC buildings e procedurepresented utilizes the fiber-based model which is the mostreliable at present In the current study both PGA andSa(T1) have been used to characterize the seismic intensityough Sa(T1) is a more appropriate IM PGA has beeneasily understandable with the normal public therefore thefragility relationships have also been developed using thePGA as an IM At the PGA of 06 g there exists

Table 5 Limit state criteria for the considered building typology

Buildingmodel nameDamagelimit state (based of global drift )

Serviceability (LS1) Damage control (LS2) Collapse prevention (LS3)BLR-11 035 066 089

Table 6 Lognormal distribution parameters for fragilities againstPGA and Sa(T1) for the considered school building typology

Fragilityparameter

Serviceability(LS1)

Damagecontrol (LS2)

Collapseprevention

(LS3)PGA Sa(T1) PGA Sa(T1) PGA Sa(T1)

λc 04842 08908 07156 13094 0957 18399βc 0327 03266 01974 02606 01742 03353

LS1-lognormalLS2-lognormalLS3-lognormal

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty

LS3 directLS2 directLS1 direct

02 04 06 08 1 12 140PGA (g)

(a)

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty02 04 06 08 1 12 140

Sa(T1)

LS1-lognormalLS2-lognormalLS3-lognormalLS3 direct

LS2 directLS1 direct

(b)

Figure 8 Derived fragility relationships for all IMs (a) seismic fragility for PGA (b) seismic fragility for Sa(T1)

Advances in Civil Engineering 11

approximately 82 probability of exceedance for the firstlimit state (LS1) while only around 20 probability ofexceedance has been achieved against the same seismicintensity for the second limit state (LS2) is essentiallyindicates the structural behavior dominated by the yieldingof the members instead of their complete failures At theseismic intensity of 140 g of PGA the structure seems to bein LS3 with almost around 100 of probability while whenSa(T1) is used as an IM the probability of being in LS3 at theseismic intensity of 140 g remains only around 20 isspecific variation in structural behavior is primarily attrib-uted to the inherent structural characteristics ie stiffnessand ductility that influence the response when the spectralacceleration is used as an IM after being scaled at thefundamental time period of the structure Since the selectedstructure is engineered the results are not so admonishingfor the considered school building typology neverthelessthe results might not be encouraging for other schoolbuilding types in the presented database e presentedconsolidated procedure is relatively simple and can bereadily adopted by the domestic and regional disaster pre-paredness and mitigation agencies to extend the applicationSuch studies are relatively new for under developingcountries like Pakistan and contemporarily no other workexists that may specifically address the vulnerability ofschools in seismic zone 4 of Pakistan Assessment of vul-nerabilities for other types of school buildings may yield aneed for immediate intervention in order to safeguard thelife of students and other users e presented study isspecifically targeted to assess the vulnerability and does notaddress the assessment of risk therefore the developedfragility curves can be further integrated with the hazardcurves of the considered area to evaluate the total riskinvolved

Data Availability

e data used to support the findings of this study are in-cluded within the article Any other data used to support thefindings of this study may be released upon request to theauthor(s) who can be contacted at musmankaistackr

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] M Zain M Usman S H Farooq and A Hanif ldquoProgressivestructural capacity loss assessmentmdasha framework for modernreinforced concrete buildingsrdquo PLoS One vol 13 no 12Article ID e0208149 2018

[2] Report from earthquake engineering research Institute (ERRI)httpswwweeriorglfepdfkashmir_eeri_2nd_reportpdf

[3] Government of Pakistan Building Code of Pakistan PakistanEngineering Council Government of Pakistan IslamabadPakistan 2007

[4] D Bonowitz Seismic Design in Pakistan Be Building CodesBylaws and Recommendations for Earthquake Risk Reduction

United Nations Development Programme New York NYUSA 2015

[5] C Xu J Deng S Peng and C Li ldquoSeismic fragility analysis ofsteel reinforced concrete frame structures based on differentengineering demand parametersrdquo Journal of Building Engi-neering vol 20 pp 736ndash749 2018

[6] J Ji A S Elnashai and D A Kuchma ldquoAn analyticalframework for seismic fragility analysis of RC high-risebuildingsrdquo Engineering Structures vol 29 no 12 pp 3197ndash3209 2007

[7] M Zain N Anwar F A Najam and T Mehmood ldquoSeismicfragility assessment of reinforced concrete high-rise buildingsusing the uncoupled modal response history analysis(UMRHA)rdquo in Proceedings of the International Conference onEarthquake Engineering and Structural Dynamics ReykjavikIceland June 2017

[8] A Ali T Sandhu and M Usman ldquoAmbient vibration testingof a pedestrian bridge using low-cost accelerometers for SHMapplicationsrdquo Smart Cities vol 2 no 1 pp 20ndash30 2019

[9] Y Pang X Wu G Shen and W Yuan ldquoSeismic fragilityanalysis of cable-stayed bridges considering different sourcesof uncertaintiesrdquo Journal of Bridge Engineering vol 19 no 4Article ID 04013015 2014

[10] A Rasheed S H Farooq M Usman A Hanif N A Khanand R A Khushnood ldquoStructural reliability analysis of su-perstructure of highway bridges on China-Pakistan economiccorridor (CPEC) a case studyrdquo Journal of Structural Integrityand Maintenance vol 3 no 3 pp 197ndash207 2018

[11] J-T Wang M-X Zhang A-Y Jin and C-H ZhangldquoSeismic fragility of arch dams based on damage analysisrdquo SoilDynamics and Earthquake Engineering vol 109 pp 58ndash682018

[12] Y Yazdani and M Alembagheri ldquoSeismic vulnerability ofgravity dams in near-fault areasrdquo Soil Dynamics and Earth-quake Engineering vol 102 pp 15ndash24 2017

[13] S Leonidas and A Kappos ldquoDerivation of fragility curves fortraditional timber-framed masonry buildings using nonlinearstatic analysisrdquo in Proceedings of the 4th International Con-ference on Computational Methods in Structural Dynamicsand Earthquake Engineering Kos Island Greece June 2013

[14] J Alam M S Islam M Hussan and A Sarraz ldquoSeismicfragility assessment of RC building using nonlinear staticpushover analysisrdquo in Proceedings of the International Con-ference on Planning Architecture and Civil Engineering(ICPAC) Rajshahi India February 2017

[15] M Ni Choine M M Kashani L N Lowes et al ldquoNonlineardynamic analysis and seismic fragility assessment of a cor-rosion damaged integral bridgerdquo International Journal ofStructural Integrity vol 7 no 2 pp 227ndash239 2016

[16] K Bakalis and D Vamvatsikos ldquoSeismic fragility functions vianonlinear response history analysisrdquo Journal of StructuralEngineering vol 144 no 10 Article ID 04018181 2018

[17] FEMA Rapid Visual Screening of Buildings for PotentialSeismic Hazards A Handbook Federal Emergency Manage-ment Agency (FEMA) Washington DC USA third edition2015

[18] FEMA Technical and Userrsquos Manual HAZUSndashMH 21 De-partment of Homeland Security Federal Emergency Man-agement Agency (FEMA) Washington DC USA

[19] User Guide Perform 3D Nonlinear Analysis and PerformanceAssessment for 3D Structures Computers and Structures IncBerkeley CA USA 2011

[20] M M Rafi and M M Nasir ldquoExperimental investigation ofchemical and physical properties of cements manufactured in

12 Advances in Civil Engineering

which the number of bays external columns and beamscould be observed It was found that out of 2417 schoolbuildings 1158 were single story 847 were double story and412 were three-story structures It can be convenientlydeciphered from the collected data that most of the buildingpopulation in the region consists of single story schoolbuildings with obvious variation in the number of their baysand story heights

It was found out that domestic authorities developedsome typical architectural and structural designs whichwere subsequently replicated throughout the consideredregion for constructing RC schools For the purpose ofdeveloping categories of school buildings with varyingstructural configurations to assess their vulnerability 19different types of RC school buildings were identifiedthrough the field surveys and professional interviews einventory developed after the identification of the buildingtypes along with their structural features is given in Ta-ble 1 e first column of the Table 1 denotes the name ofthe model aimed to represent the generic nonlinear modelfor that category of schools All the names start fromldquoBLRrdquo and subsequently the model number is mentionedie BLR-1 BLR-2 up to BLR-19 representing all the 19school building typologies with varying structural andarchitectural configurations ldquoBLRrdquo in the names meansldquoBuilding-Low-Riserdquo essentially representing the low-risenature of the construction in the considered region as thenumber of stories for school buildings remains between 1and 3 only e 2nd column presents the number of storiescolumn 3 and 4 provide the number of bays in x and ydirections respectively e x and y directions are referredas the direction along the front side and the orthogonaldirection respectively It was observed that mostly two baysexisted in the y-direction ie one for the pedestrianwalkway which mainly served as a corridor so that studentscould walk to get in and out of the classrooms while theother one served the purpose of a classroom e totalheight of the buildings is given in column 5 Column 6presents the typical floor area while column 7 correspondswith the area of slab openings placed above the staircasesTypical floor area means the area for a single floor only

Figure 1 provides the number of schools under each ofthe 19 school building categories It was found that BLR-5was the mostly constructed school building in one-storystructures BLR-11 was the mostly constructed schoolbuilding in two-story structures while BLR-18 was themostly constructed school building in three-story structuresin the considered region

In the present study the vulnerability is assessed byconsidering a two-story structure BLR-11 e BLR-11 isspecifically considered as this typology has the maximumnumber of students as per the collected information ebuilding categories with 3 number of stories housed alliedfacilities ie libraries and laboratories but it was found thatamong all typologies BLR-11 accommodates most of thepupils from the considered seismic zone e altruistic in-tention is to produce building class-specific fragility re-lationships that can be easily adopted by the researchers andmore practically by practicing engineerse fragility curves

have been developed using the IDA the details of which havebeen provided under the subsequent section

23 Methodology For conducting the vulnerability assess-ment of school buildings in seismic zone 4 of Pakistan thecurrent study employs nonlinear incremental dynamicanalysis (IDA) to capture the structural response againstapplied and incrementally scaled set of ground motions Forthis purpose 20 ground motions were carefully selected andscaled at increments of 020 g starting from 020 g up to 140 g

Since earthquake loading parameters are usually char-acterized by single numerical values ie peak ground ac-celeration (PGA) or pseudo spectra acceleration at thefundamental period of the building (T1) single-value in-dicators PGA and Sa at the fundamental period of thebuilding (T1) have also been used in the current study tocorrelate with the structural damage As low-rise buildingsare the primary focus of this research the current studyemploys global drift to decide the threshold damage limits todecide different damage states also known as limit states ofthe building Dynamic instability is usually caused by largeglobal drift due to large interstory drift and P-delta effectKeeping this in view global drift is selected as the damageindicator to incorporate the overall structural global stabilityin the presented work

Figure 2 qualitatively depicts the illustration of the de-formational-based response corresponding with differentlimit states used by the HAZUS [18] e figure illustratesfour damage states ranging from slight damage to completecollapse of the building by relating the base shear with thedeformational-based structural response while the de-formational-based response itself can be considered innumerous forms ie global drift interstory drift or thespectral displacements

Finally using a probabilistic seismic demand modelattained by the virtue of simulated damage data fragilitycurves for each of the considered damage state were ob-tained e framework and procedure through which thevulnerability assessment has been conducted is presented inFigure 3 Detail for every step is given hereafter

3 Application of the Framework

For demonstrating the established framework a nonlinearmodel for a selected school building type BLR-11 from thedeveloped database is created using CSI Perform 3D V 70[19] as it contains the vital inelastic elements that canmonitor the strains in structural members For the con-sidered typology nonlinear inelastic fiber elements wereused to monitor the strains in the members and sub-stantially to set threshold limits for the attainment ofdamage states e configuration of the selected buildingemployed analytical tools and material strengths are dis-cussed in the forthcoming sections

31 Configuration of the Selected Building Typology eselected school building represents a typical two-storystructure that comprises 11 bays in the x-direction and 2

Advances in Civil Engineering 3

bays in the y-direction It consists of different sizes of beamsand columns Figure 4 shows the plan of the selectedbuilding that has been considered in the present study whileFigure 5 exhibits the elevation of the considered building inthe longer dimension to indicate the story height

In Figure 4 FB means the floor beams while FC meansthe floor columns e actual buildings are constructed onrelatively stiff soil type but it was found during the pro-fessional interviews that all of them have been designedaccording to the soft soil type Sd soil according to BCP emain structural system of the buildings consists of moment-resisting RC frames in both of the directions e typicalfloor area for the selected building is 3445m2 Table 2 showsthe X-sectional dimensions of structural members iedifferent FBs and FCs e amount of reinforcement ob-tained through field surveys and professional interviews isalso indicated in the same table

32 Nonlinear Structural Modelling Full three-dimensionalnonlinear structural model was created in software CSIPerform 3D v 70e analytical tools in the software possess

BLR-2BLR-1 BLR-3

BLR-4 BLR-5

BLR-6 BLR-7 BLR-8

BLR-10

BLR-11

BLR-12BLR-13

BLR-14

BLR-15

BLR-16BLR-17

BLR-18

BLR-19

One storyTwo stories

ree stories0

50

100

150

200

250

300

Tota

l num

ber o

f bui

ldin

gs

BLR-9

Figure 1 Number of schools in each of the 19 school building configurations

Table 1 General properties of the buildings in developed database

Building ID(col 1)

No of stories(col 2)

No of bays in x-direction (col 3)

No of bays in y-direction (col 4)

Total buildingheight (m) (col 5)

Typical floor area(m2) (col 6)

Area of slab opening(m2) (col 7)

BLR-1 1 6 3 38 3286 mdashBLR-2 1 3 3 30 1015 mdashBLR-3 1 4 2 38 1431 mdashBLR-4 1 4 2 38 1466 mdashBLR-5 1 5 2 36 1970 mdashBLR-6 1 6 3 36 328 mdashBLR-7 1 6 3 30 3066 mdashBLR-8 1 3 2 38 808 mdashBLR-9 2 4 2 76 1452 93BLR-10 2 4 2 76 1255 93BLR-11 2 11 2 61 3445 216BLR-12 2 2 2 61 664 68BLR-13 2 5 2 67 1927 163BLR-14 2 8 3 67 2536 235BLR-15 2 3 2 61 58 57BLR-16 2 5 2 61 223 77BLR-17 3 4 2 11 3902 248BLR-18 3 5 2 11 2092 153BLR-19 3 12 2 91 3776 214

Slight damage

Moderate damage

Extensive damage

Complete collapse

Yield

Deformational-based response

Base

shea

r

Figure 2 HAZUS-based illustration of different structural damagestates depending upon the structural deformation-based response

4 Advances in Civil Engineering

excellent capability to capture different aspects of structuralperformance ranging from hinge rotations to materialsrsquostrains in members In order to capture the actual behaviorit was pertinent to take into account the properties of locallydeveloped concrete materials using the domestically avail-able cement aggregates and other constituents For thispurpose a study conducted by Rafi and Nasir [20] wasutilized to extract a mean value for concretersquos strength at

28 days subsequently as per the recommendations of ASCE41 [21] expected strength was ultimately employed duringthe analysis For reinforcing steel bars it was inferred frommost of the professional interviews that Grade 40 reinforcingbars were used during the design and construction processconsequently the current study uses Grade 40 steel re-inforcements in the analytical models in accordance with therecommendations of ASCE 41 [21]

Defining an RC building category from the database that represents the typical

building stock

Establish nonlinear analytical model using inelastic fiber

sections for structural elementsie beams columns and shear

walls

Execute nonlinear static analysis of the buildings to

obtain capacity curves

Establish the limit states (LS) of buildings depending upon the

strength and stiffness degradation (u k)

Selection of ground motions depending upon

the fault mechanism magnitude Mw distance to rupture (Rrup) and shear

wave velocity (Vs30)(ldquonrdquonumber of ground

motions)

Execution of incremental dynamic analysis (IDA) by incrementally scaling the selected ground motions

(i = 1 n)

Development of damage-hazard relationships IM

vs response parameter iePGA Sa Sd etc

Select the seismic intensity measure (IM) ie PGA PGV

Sa Sd etc (previously used during IDA)

Aer processing of results

Determine the parameters for lognormal distribution to match

the sampling probabilities (λc βc)

Plotting of fragility curves for each limit

state (LS)

Maximizeλc and βc using the

maximum likelihood

method (MLE)

Estimate the sampling

probabilities

Figure 3 Framework for the vulnerability assessment of RC school buildings in the current study

FB-1

FB-1

X

Y

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-138m 38m 38m 38m 38m 38m 38m 38m 38m 38m

58m

25m

FC-1

FC-1

FB-2

FB-2

FB-3

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FC-1 FC-1 FC-1 FC-1 FC-2 FC-1 FC-2 FC-1 FC-2 FC-1 FC-1

FC-1

FC-2

FC-1

FC-2

FC-1

FC-2

FC-1

FC-1

FC-1

FC-2

FC-2

FC-1

FC-2

FC-2

FC-2

FC-1

FC-2

FC-2

FC-2

FC-1

FC-2

FC-1

FC-2

38m

Figure 4 Plan view of the considered building typology

XZ

38m 38m 38m38m 38m38m38m 38m 38m38m38m

3 m

3 m

Figure 5 Elevation view of the considered building indicating the story height of the superstructure

Table 2 Beam and column X-sectional and reinforcement details

Structural element(s) Label Width (mm) Height (mm) Top steel Bottom steel Mid steel

BeamsFB-1 305 455 3_19 3_19 mdashFB-2 305 455 3_19 3_19 mdashFB-3 305 455 3_19 3_19 mdash

Columns FC-1 305 455 3_19 3_19 2_19FC-2 305 305 3_19 3_19 2_19

Advances in Civil Engineering 5

Nonlinear inelastic fiber sections were created forlayer-by-layer modelling of concrete and reinforcing re-bars for all of the X-sections except slabs which weremodelled as linear By the virtue of fiber modelling theforce-deformation relationship of columns and beams istransformed into the stress-strain relationship of con-struction materials ie concrete and reinforcement Byemploying fibers an appropriate division may be in-troduced for confined and unconfined concrete fibers andconsequently a composite section can easily be taken intoaccount [22]

In the current study the Mander model provided byMander et al [23] was used for concrete Complete con-finement effect and strength loss were considered during theanalysis according to the details given in the X-sections ofbeams and columns (Table 2)

Steel models that can capture the buckling and non-buckling behavior of the reinforcements are available withinthe Perform 3D For this case the nonbuckling steel modelwas utilized as ductility design is mainly based on the factthat reinforcement cannot be abruptly brittle Expectedmaterial strength was used in the analysis as per the rec-ommendations of ASCE 41 [21]e numerical modelling ofstrength degradation at high ductility levels was also con-sidered by modelling the strengths of the materials in anonlinear range Table 3 summarizes all the materialstrengths live loads and infill-partitioning loads that wereused during the analysis in accordance with the professionalinterviews conducted during the field surveys

4 Uncertainty Treatment

e uncertainties can be divided into two categories iealeatory and epistemic during any sort of vulnerability andrisk assessments [24] e uncertainty associated with theinherent variability in the nature of ground motionresulting from the natural earthquakes comes under theheading of aleatory uncertainty us the intrinsic ran-domness and variability of ground motion record describesuch uncertainties

e epistemic uncertainties on the other hand char-acterize the qualms related to paucity of available knowledgeConventionally during the vulnerability assessments thelack of knowledge related to the materialsrsquo strengths comesunder the category of such uncertainty On the contraryZain et al [25] have shown that variation in materialcharacteristics do not induce any significant disparity in thestructural response and variation in the ground motionsmust be considered as the majorly significant factor ininfluencing the dynamic response of the structures as re-cord-to-record variability may persuade severe changes inthe structural response of any building against the propertiesof different ground motions

e current study employs 20 different ground motionsto cover a wide range of variation in the characteristics ofseismic loading Since the variations in the materialsrsquostrengths do not incite any major uncertain structural re-sponse hence their variation is not considered in this studye details about the selection procedure and incremental

scaling for the ground motions are discussed under theproceeding section

41 Ground Motion Uncertainty e biggest source ofuncertainty lies in the seismic demand during the vulner-ability assessment process Path attenuation characteristicsof the originating source and the site conditions all playtheir respective parts in contributing to such uncertainty Onaccount of the structural dynamic response it is imperativeto consider a wide range of seismic energy levels for selectingthe ground motions Typically a target spectrum is con-sidered for the anticipated seismic hazard level and thespectrum-matching technique is usually adopted to selectthe most suitable ground motions Although the BuildingCode of Pakistan (referred at [3]) provides a target spectrumfor the region considered seismic zone 4 of Pakistanhowever as explained in Section 1 the reliability of thedomestic code is questionable erefore in the presentstudy ground motions are selected by considering the bestavailable information of the case study area In this research20 natural ground motion records are selected by consid-ering the domestic fault mechanism magnitude source-to-site distance and the shear wave velocityVs in the upper 100feet of the soil layers and only the large magnitude earth-quakes ie 650 up until 80 are considered

For the current research the range of source-to-sitedistance has been kept between 0 and 30 kilometers forselecting the ground motions to consider the effects of pathattenuation so that any possibility of diversified site-specificsoil layers in near and far sites can be taken into account Forshear wave velocity Vs in the upper 30meters of the soil therange has been kept varying between 175 and 350msecwhich corresponds with the soil type Sd according to BCP-2007 (referred at [3])

e selected ground motions are given in the Table 4which presents the names of earthquake motion time his-tories magnitudes distances to rupture shear wave veloc-ities and associated PGA with some other minor details

By using numerous records with the consideration ofdomestic geological conditions the selected records may beconsidered as the representative of future shaking at the zonein question us with a variety of magnitudes PGA andother characteristics the aleatory uncertainty is adequatelytreated in the present study

5 Incremental Dynamic Analysis and GroundExcitation Random Effects

Incremental dynamic analysis (IDA) serves as the mostreliable method to assess the structural performance againstseismic excitations [26] Several researchers ie Kostinakisand Athanatopoulou [27] Fereshtehnejad et al [28] andZarfam and Mofid [29] adopted the technique for theevaluation of dynamic responses of different structures iebuildings and bridges and despite of its extensive compu-tational effort IDA has proved to be a splendid tool forprobabilistic vulnerability and risk assessments DuringIDA the ground motions are incrementally scaled in a way

6 Advances in Civil Engineering

that during each iteration of the analysis the accelerationsincrease at specific intended intervals e current studyutilizes the IDA for considering various levels of seismicintensity to predict the structural response against earth-quakes ranging from 02 g to 14 g with 020 g as theaugmenting acceleration for each successive iteration thusat this stage it is imperative to select the appropriateseismic intensity measure (IM) for representation ofseismic Subsequent subsection addresses the selection ofIM in the current study Apart from selecting the IM theremust also be a damage indicator that can amply relate theseismic IM with the observed structural damage As de-scribed earlier the current study employs global drift as thedamage indicator and the details have been given inSection 61

51 Seismic Intensity Measure Seismic intensity measure(IM) correlates the ground motion with the structuraldamage hence any IM employed must be rationally able toproject the dynamic response of the structure by the virtue ofthe damage indicator PGA is one of the IMs that has beenfrequently used by the experts for fragility derivations but itis generally comprehended that Sa is a better option as an IMto correlate with the structural damage as it actually rep-resents the effect of ground shaking on the building itselfPang and Wu [30] and Jiang et al [31] employed PGA fortheir researches Apart from the PGA Omine et al [32] andEden et al [33] used peak ground velocity (PGV) as an IM

Eden et al [33] also used Sa at the fundamental period of thestructure as an IM Frankie et al [34] and Choudhury andKaushik [35] utilized spectral displacement (Sd) as IM fortheir study on open ground story RC frames with openingsin walls during the vulnerability assessment Buratti [36]analyzed the sufficiency and the efficiency of numerous IMsas indicated in their study and employed the cloud analysistechnique for 1704 unscaled accelerograms Bojorquez et al[37] proposed a procedure to obtain the interstory driftdemands for midrise frame structures in terms of a spectral-shape-based IM (INp

) and eventually concluded that INpwas

the best parameter to relate with the structural response offrames with 4 6 8 and 10 stories under the narrow-bandground motions in Europe Some other vector-valued in-tensity measures have also been proposed and discussed byModica and Stafford [38] Baker and Cornell [39] Polsakand Nicolas [40] and Kohrangi et al [41] Bojorquez andIervolino [42] also performed their research to establish avector-based IM however their research also proposed ascalar-based IM as they apprehended that the use of thescalar-based IM is easier than the vector-based IM forpractical purposes

Pejovic and Jankovic [43] investigated different groundmotion IMs which are conventionally used to investigate thedynamic behavior and concluded that despite being the mostcommon IM PGA provided the greatest dispersion in re-sults in comparison with the PGV Sa(T1) Sv(T1) and Sd(T1) e research portrayed spectral response velocity valueSv(T1) as the most efficient IM for the RC frames while

Table 4 Selected natural ground motions

Sr No Earthquake name Year Station name Mag PGA (g) Rrup (KMs) Vs30 (msec)1 San Fernando 1971 LA - hollywood stor FF 661 0225 2277 316462 Gazli USSR 1976 Karakyr 68 0864 547 259593 Tabas Iran 1978 Boshrooyeh 735 0106 2879 324574 Spitak Armenia 1988 Gukasian 677 020 240 343535 Loma Prieta 1989 Agnews State Hospital 693 01695 2457 239696 Loma Prieta 1989 Saratoga-W Valley Coll 693 0331 930 347907 Northridge-01 1994 Arleta-Nordhoff fire station 669 0345 866 297718 Northridge-01 1994 N Hollywood - coldwater can 669 0309 1251 326479 Chi-Chi Taiwan 1999 CHY002 762 0137 2496 2351310 Chi-Chi Taiwan 1999 CHY036 762 0273 1604 2331411 Chi-Chi Taiwan 1999 TCU038 762 01448 2542 2978612 Chi-Chi Taiwan 1999 TCU059 762 0165 1711 2726713 Chi-Chi Taiwan 1999 TCU110 762 01918 1157 2127214 Kashmir earthquake 1999 ABD-Abbottabad 760 02517 260 2230415 St Elias Alaska 1979 Icy Bay 754 01759 2645 3063716 Niigata Japan 2004 NIG017 663 04764 1281 2741717 Montenegro Yugoslavia 1979 Ulcinj-Hotel Olimpic 71 02928 576 3187418 Chuetsu-oki Japan 2007 Joetsu Kita 68 0176 2945 334019 Iwate Japan 2008 IWT011 69 02194 843 2793620 Iwate Japan 2008 Kitakami Yanagihara 69 02057 1667 34898

Table 3 Material strengths and loading values used for the structural modelling

Materials LoadsCharacteristics Strength Units Name Value UnitsConcretersquos strength (fcprime) 21 MPa Live 26 kNm2

Reinforcing steelrsquos yielding stress (fy) 275 MPa Infill-partitioning 43 kNm

Advances in Civil Engineering 7

stating the other two spectral response parameters ieSa(T1) and Sd(T1) were similarly adequate as they in-corporated the dynamic characteristics of the consideredstructure e current study chooses both ie PGA andspectral acceleration at the fundamental time period (Sa(T1))of the structure as intensity measures As indicated by theprevious literature provided by Jelena and Srdjan [43] PGAis the most commonly employed IM which is easy to un-derstand for normal people with no specific engineeringbackground while Sa(T1) incorporates the structural char-acteristics during the execution of analyses

52 Results of IDA Figure 6 shows the results of IDA in theform of plots between global drift and the selected IMs ieincrementally scaled PGA and Sa(T1) from 020 g to 14 g Itcan be observed that intrinsic nature of different groundmotions produces different results despite of having thesame intensity of acceleration at a given pointere are total20 curves in each part of Figure 6 while each curve char-acterizes structural damage indicated by global drift causedby the single corresponding earthquake at discretely con-sidered seismic intensity levels ranging from 02 g to 14 g

In Figure 6(a) the curves manifest the maximum globaldrift ranging from 020 to more than 50 when PGA isused to indicate seismic intensity While in Figure 6(b)when Sa(T1) is used to characterize the seismic intensity themaximum global drift reaches 247 against the Sa of 14 gthe maximum considered in this study

e results of IDA indicate that intrinsic properties ofground motions project substantial sensitivities to theseismic demand e disparity in the structural responseagainst different ground motions of the same intensities isprimarily attributed to differences in the inherent nature ofground motions ie energy distribution over frequencycontent and duration that predominantly affects thestructural response Moreover when Sa(T1) is used as anindicator of the seismic intensity the global drift observeslower values because of the scaling of the ground motions atthe fundamental period of the structure which is directlyrelated with the structural inertia and stiffness

6 Vulnerability Assessment

e fundamental process of the risk assessment against anyhazard consists of two parts ie the hazard and the vul-nerability of structural systems to that hazard For earth-quakes the first portion is primarily concerned withseismologists who can provide a realistic estimate of thepotential seismic hazard that can hit a specific geographicalarea while the second part vulnerability is usuallyaddressed by the engineers and experts who design thefacilities for versatile purposes e current study is relatedwith the second part and assesses the vulnerability of theconsidered typology of school buildings by establishing thehazard-damage relationships for the considered typology ofstructures and subsequently by developing the genericfragility relationships Hazard-damage relationships depictthe structural performance against seismic excitations and

exhibit the dynamic response for all considered groundmotion intensities Figures 7(a) and 7(b) present a directrelationship between the seismic intensities and the struc-tural damage e structural damage is quantified using theglobal response and seismic intensities are provided in-crementally in terms of PGA as well as in terms of spectralacceleration at the fundamental modersquos time period Everysingle dot in each part of Figure 7 represents the maximumvalue of the global drift in terms of percentage against aspecific earthquake scaled at a specific intensity For in-stance at the seismic intensity of 14 g there are 20 dots fromall 20 ground motions indicating the uncertainty in thestructural response by depicting that one earthquake havingthe seismic intensity of 14 g produces global drift less than1 while some other earthquake with the same seismicintensity produces more than 5 of global drift

With increasing intensity of PGA from 020 g to 080 gin Figure 7(a) the global drift remains between 009 and119 While at higher PGA levels from 10 g to 14 g theglobal drift drastically remains between 044 and 516 forall the considered ground motions At the maximum con-sidered PGA of 140 g the global drift varies from 097 to516 for all 20 ground motions All this disparity in thestructural response arises because of the inherent charac-teristics of ground motions which vary from record to re-cord thus instigating different response against the samescaled intensity level

When Sa(T1) is used for representing seismic intensitythe global drift varied between 022 and 24 at the Sa of140 g as shown by Figure 7(b) e dotted line inFigures 7(a) and 7(b) shows the mean structural responseobtained at each intensity level

On the other hand the fragility curve as described byEquation (1) represents a conditional probability ofexceedance for specific damage or limit states of a structureagainst a particular seismic intensity given in terms of PGASa or some other seismic intensity describing the indicator

Pfragility P[LS | IM x] (1)

e aforementioned equation describes the conditionalprobability Pfragility of achieving or exceeding a specific limitstate LS when seismic intensity defined by a particularintensity measure (IM) is equal to ldquoxrdquo Fragility relationshipsfor different damage states must be probabilistically able topredict the structural vulnerability against a realistic range ofseismic ground excitations is probabilistic evaluation isonly possible when a large variation of seismic demands isconsidered so that ample variation in the dynamic structuralresponse can be obtained e vulnerability assessment re-quires the definition of specific limit states damage indicatorsand seismic intensity indicators e impending sectionsaddress all the requirements to develop fragility curvesConsequently fragility curves are developed for the selectedtypology to elucidate the established framework

61 Damage Indicator and the Definition of Limit Statese derivation of analytical fragility curves requires thedefinition of specific limit states in both terms ie

8 Advances in Civil Engineering

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Peak

gro

und

acce

lera

tion

(g)

05 1 15 2 25 3 35 4 45 5 550Maximum global drift ()

(a)

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Spec

tral

acce

lera

tion

(T1)

05 1 15 2 250Maximum global drift ()

(b)

Figure 6 IDA curves (a) maximum global drift vs PGA (b) maximum global drift vs spectral acceleration scaled at the fundamental timeperiod of the structure (Sa(T1))

0 02 04 06 08 1 12 14PGA (g)

0

1

2

3

4

5

Glo

bal d

ri (

)

(a)

0

05

1

15

2

25

3

0 02 04 06 08 1 12 14

Glo

bal d

ri (

)

Sa(T1)

(b)

Figure 7 Hazard-damage relationships (a) PGA vs global drift in percentage (b) Sa(T1) vs global drift in percentage

Advances in Civil Engineering 9

qualitative and quantitative For this purpose a researcherhas to employ a specific damage indicator also known asengineering demand parameter (EDP) or may also propose anew damage measure that can represent the structuraldamage in a rational manner to correlate the damage withseismic loading Once the damage indicator has been set orselected different limit states often known as the damagestates of a structure may be defined

Damage states represent a physical categorization ofdamages by using damage indices which suggest thresholdlimits for different damage states by relaying upon theparameters of structural behavior eg energy dissipationcapability ductility and strength Damage indices are usedfor correlating the accumulated damage with differentspecific damage states and numerous nonidentical damageindices may exist for the same structure For instance Khanet al [44] used global displacement of the structure tocharacterize the structural damage Crowley et al [45]considered damage limit states based on the strain levels inconcrete and steel Guneyisi and Altay [46] considered theinterstory drift ratio for representing the response pa-rameter corresponding to the four damage states takenfrom the HAZUS Casotto et al [47] considered themember flexural strength to characterize the first limit state(LS1) when the reinforcement steel yields in the columnsand 3 interstory drift for flexural collapse limit state(LS2) and subsequently related his LS2 with the loss ofsupport of the beam Chaulagain et al [48] and Gautamet al [49] used 3 damage states ranging from slight damageto complete collapse and developed empirical fragilityrelationships for buildings in Nepal ey further relatedtheir results with FEMA356 [50] classifications for buildingdamage levels

Since this study primarily relates with the generation offragilities for a specific building stock it would not bepractical to define damage or limit states depending uponthe member behavior or local strains In the current studythe global drift ratio has been considered as the damageindicator to correlate with the structural damage

ree damage states namely serviceability limit state(LS1) damage control limit state (LS2) and collapseprevention (LS3) are qualitatively defined in this studyLS1 corresponds with the 1st yield of longitudinal steelreinforcement in the structure Conventionally the firstlimit states are usually related with the formation of the firsthinge in the structure but since the current study employsnonlinear fibers to model the structure therefore the LS1primarily describes the yielding strain reaching in astructural element located anywhere in the structure edeformation and strength govern the LS2 It is defined as75 of LS3 e LS3 collapse prevention is generallydirected by the deformation Altug [51] defined the collapseprevention limit state as 75 of ultimate structural de-formation or the value for which more than 20 strengthdrop can be observed relative to the maximum strengthvalue e smaller of these two values would govern theLS3

e mathematical quantification for these damage statescould not be adopted from the previous research as there

exists no analogous research for Pakistanrsquos constructionindustry or for Pakistanrsquos seismic zone 4 In the currentstudy the mathematical values are assigned to each of thediscrete damage state by using the capacity curve of theselected structure However the obtained values were ap-proximately similar to those obtained by Altug [51] whichused the low-rise buildings of the Turkish region in theirresearch thus the obtained values amply represent the low-rise structural behavior e mathematical values for each ofthe considered damage state against the global drift arepresented in Table 5

62 Fragility Assessment for the School Buildings Seismicfragility curves are widely employed to obtain an articu-lated insight of structural performance against seismicloads and they represent the probability of entering orexceeding different damage states for considered in-tensities of ground shaking After attaining the structuralresponse established limit state definitions are applied forevaluating the structural performance for each limit stateOnce the computed value comes out to be greater than alimit statersquos value an event shall be counted within thesample comprising all the ground motions scalesereby for each IM direct sampling probabilities overthe 20 selected ground motions on all incrementing scaleswere obtained

It is a commonly accepted assumption that for a fragilitycurve a lognormal cumulative distribution function can beconveniently utilized for the representation of conditionalprobabilities [52ndash54] From viewpoint of literature log-normal distribution was also assumed and used for theregression of fragility relationships as mentioned in thefollowing equation

P(LS | IM) ϕln IM minus λc

βc1113888 1113889 (2)

where P(LS | IM) describes the probability of exceedance ofa particular LS given an IM value ϕ represents the standardnormal cumulative distribution function (CDF)

e controlling parameters λc and βc represent themedian point and the slope of the curve respectively It isimperative to evaluate their optimized values for a best fit ofCDF against the calculated probabilities Shinozuka et al[53] Dang et al [54] and Baker [55] stated that the max-imum likelihood method (MLM) is one of the most suitablemethod to achieve best possible values of these two pa-rameters In the current study MLM is utilized to obtain themedian point and the slope of the fragility curve Formultiple IM levels as considered in this study the likelihoodfunction is given as follows

Likelihood 1113945m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠ϕln IMiλc( 1113857

βc1113888 1113889

zj

1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 1113889

njminus zj

(3)

wherem is the number of IM levels andΠ denotes a productover all levels It is assumed that the observation of attaininga specific limit state from each ground motion is

10 Advances in Civil Engineering

independent of the observations from other ground mo-tions In the above equation zj denotes the number ofattaining particular limit state out of nj ground motions witha particular value of IM IMie fragility curve parameterscan be obtained by maximizing the likelihood function inEquation (3) as given in following equation

λc βc1113864 1113865 argmaxλc βc 1113944

m

j1ln

nj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnϕln IMiλ( 1113857c

βc1113888 1113889

⎧⎪⎨

⎪⎩

+ nj minus zj1113872 1113873ln 1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 11138891113897

(4)

A MATLAB code was written to control the maximi-zation of the likelihood function so that optimum values ofthese two parameters can be obtained for establishingseismic fragility

Figure 8 presents the developed fragility relationships forthe considered typology of the RC school building in seismiczone 4 of Pakistan Each portion of Figure 8 contains threefragility relationships correlating with each limit stateagainst both of the IMs ie PGA and Sa(T1) Directsampling probabilities obtained from the IDA are alsoplotted in Figure 8 along with lognormally fitted fragilityfunctions

Table 6 provides the simulated values for λc and βc foreach limit state against each IM for the derivation of fragilitycurves

7 Conclusion

Pakistan has numerous seismotectonically active regionsincluding Muzaffarabad and past earthquakes especially the2005 Kashmir earthquake have proven this fact In thisstudy a new database of RC school buildings constructed inMuzaffarabad district after 2005 earthquake has beenpresented Subsequently the structural vulnerability of aspecific category of RC school buildings is assessed andpresented by using IDA so that practicing engineers atdomestic and regional level can further extend the evalua-tion to other categories of RC buildings e procedurepresented utilizes the fiber-based model which is the mostreliable at present In the current study both PGA andSa(T1) have been used to characterize the seismic intensityough Sa(T1) is a more appropriate IM PGA has beeneasily understandable with the normal public therefore thefragility relationships have also been developed using thePGA as an IM At the PGA of 06 g there exists

Table 5 Limit state criteria for the considered building typology

Buildingmodel nameDamagelimit state (based of global drift )

Serviceability (LS1) Damage control (LS2) Collapse prevention (LS3)BLR-11 035 066 089

Table 6 Lognormal distribution parameters for fragilities againstPGA and Sa(T1) for the considered school building typology

Fragilityparameter

Serviceability(LS1)

Damagecontrol (LS2)

Collapseprevention

(LS3)PGA Sa(T1) PGA Sa(T1) PGA Sa(T1)

λc 04842 08908 07156 13094 0957 18399βc 0327 03266 01974 02606 01742 03353

LS1-lognormalLS2-lognormalLS3-lognormal

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty

LS3 directLS2 directLS1 direct

02 04 06 08 1 12 140PGA (g)

(a)

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty02 04 06 08 1 12 140

Sa(T1)

LS1-lognormalLS2-lognormalLS3-lognormalLS3 direct

LS2 directLS1 direct

(b)

Figure 8 Derived fragility relationships for all IMs (a) seismic fragility for PGA (b) seismic fragility for Sa(T1)

Advances in Civil Engineering 11

approximately 82 probability of exceedance for the firstlimit state (LS1) while only around 20 probability ofexceedance has been achieved against the same seismicintensity for the second limit state (LS2) is essentiallyindicates the structural behavior dominated by the yieldingof the members instead of their complete failures At theseismic intensity of 140 g of PGA the structure seems to bein LS3 with almost around 100 of probability while whenSa(T1) is used as an IM the probability of being in LS3 at theseismic intensity of 140 g remains only around 20 isspecific variation in structural behavior is primarily attrib-uted to the inherent structural characteristics ie stiffnessand ductility that influence the response when the spectralacceleration is used as an IM after being scaled at thefundamental time period of the structure Since the selectedstructure is engineered the results are not so admonishingfor the considered school building typology neverthelessthe results might not be encouraging for other schoolbuilding types in the presented database e presentedconsolidated procedure is relatively simple and can bereadily adopted by the domestic and regional disaster pre-paredness and mitigation agencies to extend the applicationSuch studies are relatively new for under developingcountries like Pakistan and contemporarily no other workexists that may specifically address the vulnerability ofschools in seismic zone 4 of Pakistan Assessment of vul-nerabilities for other types of school buildings may yield aneed for immediate intervention in order to safeguard thelife of students and other users e presented study isspecifically targeted to assess the vulnerability and does notaddress the assessment of risk therefore the developedfragility curves can be further integrated with the hazardcurves of the considered area to evaluate the total riskinvolved

Data Availability

e data used to support the findings of this study are in-cluded within the article Any other data used to support thefindings of this study may be released upon request to theauthor(s) who can be contacted at musmankaistackr

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] M Zain M Usman S H Farooq and A Hanif ldquoProgressivestructural capacity loss assessmentmdasha framework for modernreinforced concrete buildingsrdquo PLoS One vol 13 no 12Article ID e0208149 2018

[2] Report from earthquake engineering research Institute (ERRI)httpswwweeriorglfepdfkashmir_eeri_2nd_reportpdf

[3] Government of Pakistan Building Code of Pakistan PakistanEngineering Council Government of Pakistan IslamabadPakistan 2007

[4] D Bonowitz Seismic Design in Pakistan Be Building CodesBylaws and Recommendations for Earthquake Risk Reduction

United Nations Development Programme New York NYUSA 2015

[5] C Xu J Deng S Peng and C Li ldquoSeismic fragility analysis ofsteel reinforced concrete frame structures based on differentengineering demand parametersrdquo Journal of Building Engi-neering vol 20 pp 736ndash749 2018

[6] J Ji A S Elnashai and D A Kuchma ldquoAn analyticalframework for seismic fragility analysis of RC high-risebuildingsrdquo Engineering Structures vol 29 no 12 pp 3197ndash3209 2007

[7] M Zain N Anwar F A Najam and T Mehmood ldquoSeismicfragility assessment of reinforced concrete high-rise buildingsusing the uncoupled modal response history analysis(UMRHA)rdquo in Proceedings of the International Conference onEarthquake Engineering and Structural Dynamics ReykjavikIceland June 2017

[8] A Ali T Sandhu and M Usman ldquoAmbient vibration testingof a pedestrian bridge using low-cost accelerometers for SHMapplicationsrdquo Smart Cities vol 2 no 1 pp 20ndash30 2019

[9] Y Pang X Wu G Shen and W Yuan ldquoSeismic fragilityanalysis of cable-stayed bridges considering different sourcesof uncertaintiesrdquo Journal of Bridge Engineering vol 19 no 4Article ID 04013015 2014

[10] A Rasheed S H Farooq M Usman A Hanif N A Khanand R A Khushnood ldquoStructural reliability analysis of su-perstructure of highway bridges on China-Pakistan economiccorridor (CPEC) a case studyrdquo Journal of Structural Integrityand Maintenance vol 3 no 3 pp 197ndash207 2018

[11] J-T Wang M-X Zhang A-Y Jin and C-H ZhangldquoSeismic fragility of arch dams based on damage analysisrdquo SoilDynamics and Earthquake Engineering vol 109 pp 58ndash682018

[12] Y Yazdani and M Alembagheri ldquoSeismic vulnerability ofgravity dams in near-fault areasrdquo Soil Dynamics and Earth-quake Engineering vol 102 pp 15ndash24 2017

[13] S Leonidas and A Kappos ldquoDerivation of fragility curves fortraditional timber-framed masonry buildings using nonlinearstatic analysisrdquo in Proceedings of the 4th International Con-ference on Computational Methods in Structural Dynamicsand Earthquake Engineering Kos Island Greece June 2013

[14] J Alam M S Islam M Hussan and A Sarraz ldquoSeismicfragility assessment of RC building using nonlinear staticpushover analysisrdquo in Proceedings of the International Con-ference on Planning Architecture and Civil Engineering(ICPAC) Rajshahi India February 2017

[15] M Ni Choine M M Kashani L N Lowes et al ldquoNonlineardynamic analysis and seismic fragility assessment of a cor-rosion damaged integral bridgerdquo International Journal ofStructural Integrity vol 7 no 2 pp 227ndash239 2016

[16] K Bakalis and D Vamvatsikos ldquoSeismic fragility functions vianonlinear response history analysisrdquo Journal of StructuralEngineering vol 144 no 10 Article ID 04018181 2018

[17] FEMA Rapid Visual Screening of Buildings for PotentialSeismic Hazards A Handbook Federal Emergency Manage-ment Agency (FEMA) Washington DC USA third edition2015

[18] FEMA Technical and Userrsquos Manual HAZUSndashMH 21 De-partment of Homeland Security Federal Emergency Man-agement Agency (FEMA) Washington DC USA

[19] User Guide Perform 3D Nonlinear Analysis and PerformanceAssessment for 3D Structures Computers and Structures IncBerkeley CA USA 2011

[20] M M Rafi and M M Nasir ldquoExperimental investigation ofchemical and physical properties of cements manufactured in

12 Advances in Civil Engineering

bays in the y-direction It consists of different sizes of beamsand columns Figure 4 shows the plan of the selectedbuilding that has been considered in the present study whileFigure 5 exhibits the elevation of the considered building inthe longer dimension to indicate the story height

In Figure 4 FB means the floor beams while FC meansthe floor columns e actual buildings are constructed onrelatively stiff soil type but it was found during the pro-fessional interviews that all of them have been designedaccording to the soft soil type Sd soil according to BCP emain structural system of the buildings consists of moment-resisting RC frames in both of the directions e typicalfloor area for the selected building is 3445m2 Table 2 showsthe X-sectional dimensions of structural members iedifferent FBs and FCs e amount of reinforcement ob-tained through field surveys and professional interviews isalso indicated in the same table

32 Nonlinear Structural Modelling Full three-dimensionalnonlinear structural model was created in software CSIPerform 3D v 70e analytical tools in the software possess

BLR-2BLR-1 BLR-3

BLR-4 BLR-5

BLR-6 BLR-7 BLR-8

BLR-10

BLR-11

BLR-12BLR-13

BLR-14

BLR-15

BLR-16BLR-17

BLR-18

BLR-19

One storyTwo stories

ree stories0

50

100

150

200

250

300

Tota

l num

ber o

f bui

ldin

gs

BLR-9

Figure 1 Number of schools in each of the 19 school building configurations

Table 1 General properties of the buildings in developed database

Building ID(col 1)

No of stories(col 2)

No of bays in x-direction (col 3)

No of bays in y-direction (col 4)

Total buildingheight (m) (col 5)

Typical floor area(m2) (col 6)

Area of slab opening(m2) (col 7)

BLR-1 1 6 3 38 3286 mdashBLR-2 1 3 3 30 1015 mdashBLR-3 1 4 2 38 1431 mdashBLR-4 1 4 2 38 1466 mdashBLR-5 1 5 2 36 1970 mdashBLR-6 1 6 3 36 328 mdashBLR-7 1 6 3 30 3066 mdashBLR-8 1 3 2 38 808 mdashBLR-9 2 4 2 76 1452 93BLR-10 2 4 2 76 1255 93BLR-11 2 11 2 61 3445 216BLR-12 2 2 2 61 664 68BLR-13 2 5 2 67 1927 163BLR-14 2 8 3 67 2536 235BLR-15 2 3 2 61 58 57BLR-16 2 5 2 61 223 77BLR-17 3 4 2 11 3902 248BLR-18 3 5 2 11 2092 153BLR-19 3 12 2 91 3776 214

Slight damage

Moderate damage

Extensive damage

Complete collapse

Yield

Deformational-based response

Base

shea

r

Figure 2 HAZUS-based illustration of different structural damagestates depending upon the structural deformation-based response

4 Advances in Civil Engineering

excellent capability to capture different aspects of structuralperformance ranging from hinge rotations to materialsrsquostrains in members In order to capture the actual behaviorit was pertinent to take into account the properties of locallydeveloped concrete materials using the domestically avail-able cement aggregates and other constituents For thispurpose a study conducted by Rafi and Nasir [20] wasutilized to extract a mean value for concretersquos strength at

28 days subsequently as per the recommendations of ASCE41 [21] expected strength was ultimately employed duringthe analysis For reinforcing steel bars it was inferred frommost of the professional interviews that Grade 40 reinforcingbars were used during the design and construction processconsequently the current study uses Grade 40 steel re-inforcements in the analytical models in accordance with therecommendations of ASCE 41 [21]

Defining an RC building category from the database that represents the typical

building stock

Establish nonlinear analytical model using inelastic fiber

sections for structural elementsie beams columns and shear

walls

Execute nonlinear static analysis of the buildings to

obtain capacity curves

Establish the limit states (LS) of buildings depending upon the

strength and stiffness degradation (u k)

Selection of ground motions depending upon

the fault mechanism magnitude Mw distance to rupture (Rrup) and shear

wave velocity (Vs30)(ldquonrdquonumber of ground

motions)

Execution of incremental dynamic analysis (IDA) by incrementally scaling the selected ground motions

(i = 1 n)

Development of damage-hazard relationships IM

vs response parameter iePGA Sa Sd etc

Select the seismic intensity measure (IM) ie PGA PGV

Sa Sd etc (previously used during IDA)

Aer processing of results

Determine the parameters for lognormal distribution to match

the sampling probabilities (λc βc)

Plotting of fragility curves for each limit

state (LS)

Maximizeλc and βc using the

maximum likelihood

method (MLE)

Estimate the sampling

probabilities

Figure 3 Framework for the vulnerability assessment of RC school buildings in the current study

FB-1

FB-1

X

Y

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-138m 38m 38m 38m 38m 38m 38m 38m 38m 38m

58m

25m

FC-1

FC-1

FB-2

FB-2

FB-3

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FC-1 FC-1 FC-1 FC-1 FC-2 FC-1 FC-2 FC-1 FC-2 FC-1 FC-1

FC-1

FC-2

FC-1

FC-2

FC-1

FC-2

FC-1

FC-1

FC-1

FC-2

FC-2

FC-1

FC-2

FC-2

FC-2

FC-1

FC-2

FC-2

FC-2

FC-1

FC-2

FC-1

FC-2

38m

Figure 4 Plan view of the considered building typology

XZ

38m 38m 38m38m 38m38m38m 38m 38m38m38m

3 m

3 m

Figure 5 Elevation view of the considered building indicating the story height of the superstructure

Table 2 Beam and column X-sectional and reinforcement details

Structural element(s) Label Width (mm) Height (mm) Top steel Bottom steel Mid steel

BeamsFB-1 305 455 3_19 3_19 mdashFB-2 305 455 3_19 3_19 mdashFB-3 305 455 3_19 3_19 mdash

Columns FC-1 305 455 3_19 3_19 2_19FC-2 305 305 3_19 3_19 2_19

Advances in Civil Engineering 5

Nonlinear inelastic fiber sections were created forlayer-by-layer modelling of concrete and reinforcing re-bars for all of the X-sections except slabs which weremodelled as linear By the virtue of fiber modelling theforce-deformation relationship of columns and beams istransformed into the stress-strain relationship of con-struction materials ie concrete and reinforcement Byemploying fibers an appropriate division may be in-troduced for confined and unconfined concrete fibers andconsequently a composite section can easily be taken intoaccount [22]

In the current study the Mander model provided byMander et al [23] was used for concrete Complete con-finement effect and strength loss were considered during theanalysis according to the details given in the X-sections ofbeams and columns (Table 2)

Steel models that can capture the buckling and non-buckling behavior of the reinforcements are available withinthe Perform 3D For this case the nonbuckling steel modelwas utilized as ductility design is mainly based on the factthat reinforcement cannot be abruptly brittle Expectedmaterial strength was used in the analysis as per the rec-ommendations of ASCE 41 [21]e numerical modelling ofstrength degradation at high ductility levels was also con-sidered by modelling the strengths of the materials in anonlinear range Table 3 summarizes all the materialstrengths live loads and infill-partitioning loads that wereused during the analysis in accordance with the professionalinterviews conducted during the field surveys

4 Uncertainty Treatment

e uncertainties can be divided into two categories iealeatory and epistemic during any sort of vulnerability andrisk assessments [24] e uncertainty associated with theinherent variability in the nature of ground motionresulting from the natural earthquakes comes under theheading of aleatory uncertainty us the intrinsic ran-domness and variability of ground motion record describesuch uncertainties

e epistemic uncertainties on the other hand char-acterize the qualms related to paucity of available knowledgeConventionally during the vulnerability assessments thelack of knowledge related to the materialsrsquo strengths comesunder the category of such uncertainty On the contraryZain et al [25] have shown that variation in materialcharacteristics do not induce any significant disparity in thestructural response and variation in the ground motionsmust be considered as the majorly significant factor ininfluencing the dynamic response of the structures as re-cord-to-record variability may persuade severe changes inthe structural response of any building against the propertiesof different ground motions

e current study employs 20 different ground motionsto cover a wide range of variation in the characteristics ofseismic loading Since the variations in the materialsrsquostrengths do not incite any major uncertain structural re-sponse hence their variation is not considered in this studye details about the selection procedure and incremental

scaling for the ground motions are discussed under theproceeding section

41 Ground Motion Uncertainty e biggest source ofuncertainty lies in the seismic demand during the vulner-ability assessment process Path attenuation characteristicsof the originating source and the site conditions all playtheir respective parts in contributing to such uncertainty Onaccount of the structural dynamic response it is imperativeto consider a wide range of seismic energy levels for selectingthe ground motions Typically a target spectrum is con-sidered for the anticipated seismic hazard level and thespectrum-matching technique is usually adopted to selectthe most suitable ground motions Although the BuildingCode of Pakistan (referred at [3]) provides a target spectrumfor the region considered seismic zone 4 of Pakistanhowever as explained in Section 1 the reliability of thedomestic code is questionable erefore in the presentstudy ground motions are selected by considering the bestavailable information of the case study area In this research20 natural ground motion records are selected by consid-ering the domestic fault mechanism magnitude source-to-site distance and the shear wave velocityVs in the upper 100feet of the soil layers and only the large magnitude earth-quakes ie 650 up until 80 are considered

For the current research the range of source-to-sitedistance has been kept between 0 and 30 kilometers forselecting the ground motions to consider the effects of pathattenuation so that any possibility of diversified site-specificsoil layers in near and far sites can be taken into account Forshear wave velocity Vs in the upper 30meters of the soil therange has been kept varying between 175 and 350msecwhich corresponds with the soil type Sd according to BCP-2007 (referred at [3])

e selected ground motions are given in the Table 4which presents the names of earthquake motion time his-tories magnitudes distances to rupture shear wave veloc-ities and associated PGA with some other minor details

By using numerous records with the consideration ofdomestic geological conditions the selected records may beconsidered as the representative of future shaking at the zonein question us with a variety of magnitudes PGA andother characteristics the aleatory uncertainty is adequatelytreated in the present study

5 Incremental Dynamic Analysis and GroundExcitation Random Effects

Incremental dynamic analysis (IDA) serves as the mostreliable method to assess the structural performance againstseismic excitations [26] Several researchers ie Kostinakisand Athanatopoulou [27] Fereshtehnejad et al [28] andZarfam and Mofid [29] adopted the technique for theevaluation of dynamic responses of different structures iebuildings and bridges and despite of its extensive compu-tational effort IDA has proved to be a splendid tool forprobabilistic vulnerability and risk assessments DuringIDA the ground motions are incrementally scaled in a way

6 Advances in Civil Engineering

that during each iteration of the analysis the accelerationsincrease at specific intended intervals e current studyutilizes the IDA for considering various levels of seismicintensity to predict the structural response against earth-quakes ranging from 02 g to 14 g with 020 g as theaugmenting acceleration for each successive iteration thusat this stage it is imperative to select the appropriateseismic intensity measure (IM) for representation ofseismic Subsequent subsection addresses the selection ofIM in the current study Apart from selecting the IM theremust also be a damage indicator that can amply relate theseismic IM with the observed structural damage As de-scribed earlier the current study employs global drift as thedamage indicator and the details have been given inSection 61

51 Seismic Intensity Measure Seismic intensity measure(IM) correlates the ground motion with the structuraldamage hence any IM employed must be rationally able toproject the dynamic response of the structure by the virtue ofthe damage indicator PGA is one of the IMs that has beenfrequently used by the experts for fragility derivations but itis generally comprehended that Sa is a better option as an IMto correlate with the structural damage as it actually rep-resents the effect of ground shaking on the building itselfPang and Wu [30] and Jiang et al [31] employed PGA fortheir researches Apart from the PGA Omine et al [32] andEden et al [33] used peak ground velocity (PGV) as an IM

Eden et al [33] also used Sa at the fundamental period of thestructure as an IM Frankie et al [34] and Choudhury andKaushik [35] utilized spectral displacement (Sd) as IM fortheir study on open ground story RC frames with openingsin walls during the vulnerability assessment Buratti [36]analyzed the sufficiency and the efficiency of numerous IMsas indicated in their study and employed the cloud analysistechnique for 1704 unscaled accelerograms Bojorquez et al[37] proposed a procedure to obtain the interstory driftdemands for midrise frame structures in terms of a spectral-shape-based IM (INp

) and eventually concluded that INpwas

the best parameter to relate with the structural response offrames with 4 6 8 and 10 stories under the narrow-bandground motions in Europe Some other vector-valued in-tensity measures have also been proposed and discussed byModica and Stafford [38] Baker and Cornell [39] Polsakand Nicolas [40] and Kohrangi et al [41] Bojorquez andIervolino [42] also performed their research to establish avector-based IM however their research also proposed ascalar-based IM as they apprehended that the use of thescalar-based IM is easier than the vector-based IM forpractical purposes

Pejovic and Jankovic [43] investigated different groundmotion IMs which are conventionally used to investigate thedynamic behavior and concluded that despite being the mostcommon IM PGA provided the greatest dispersion in re-sults in comparison with the PGV Sa(T1) Sv(T1) and Sd(T1) e research portrayed spectral response velocity valueSv(T1) as the most efficient IM for the RC frames while

Table 4 Selected natural ground motions

Sr No Earthquake name Year Station name Mag PGA (g) Rrup (KMs) Vs30 (msec)1 San Fernando 1971 LA - hollywood stor FF 661 0225 2277 316462 Gazli USSR 1976 Karakyr 68 0864 547 259593 Tabas Iran 1978 Boshrooyeh 735 0106 2879 324574 Spitak Armenia 1988 Gukasian 677 020 240 343535 Loma Prieta 1989 Agnews State Hospital 693 01695 2457 239696 Loma Prieta 1989 Saratoga-W Valley Coll 693 0331 930 347907 Northridge-01 1994 Arleta-Nordhoff fire station 669 0345 866 297718 Northridge-01 1994 N Hollywood - coldwater can 669 0309 1251 326479 Chi-Chi Taiwan 1999 CHY002 762 0137 2496 2351310 Chi-Chi Taiwan 1999 CHY036 762 0273 1604 2331411 Chi-Chi Taiwan 1999 TCU038 762 01448 2542 2978612 Chi-Chi Taiwan 1999 TCU059 762 0165 1711 2726713 Chi-Chi Taiwan 1999 TCU110 762 01918 1157 2127214 Kashmir earthquake 1999 ABD-Abbottabad 760 02517 260 2230415 St Elias Alaska 1979 Icy Bay 754 01759 2645 3063716 Niigata Japan 2004 NIG017 663 04764 1281 2741717 Montenegro Yugoslavia 1979 Ulcinj-Hotel Olimpic 71 02928 576 3187418 Chuetsu-oki Japan 2007 Joetsu Kita 68 0176 2945 334019 Iwate Japan 2008 IWT011 69 02194 843 2793620 Iwate Japan 2008 Kitakami Yanagihara 69 02057 1667 34898

Table 3 Material strengths and loading values used for the structural modelling

Materials LoadsCharacteristics Strength Units Name Value UnitsConcretersquos strength (fcprime) 21 MPa Live 26 kNm2

Reinforcing steelrsquos yielding stress (fy) 275 MPa Infill-partitioning 43 kNm

Advances in Civil Engineering 7

stating the other two spectral response parameters ieSa(T1) and Sd(T1) were similarly adequate as they in-corporated the dynamic characteristics of the consideredstructure e current study chooses both ie PGA andspectral acceleration at the fundamental time period (Sa(T1))of the structure as intensity measures As indicated by theprevious literature provided by Jelena and Srdjan [43] PGAis the most commonly employed IM which is easy to un-derstand for normal people with no specific engineeringbackground while Sa(T1) incorporates the structural char-acteristics during the execution of analyses

52 Results of IDA Figure 6 shows the results of IDA in theform of plots between global drift and the selected IMs ieincrementally scaled PGA and Sa(T1) from 020 g to 14 g Itcan be observed that intrinsic nature of different groundmotions produces different results despite of having thesame intensity of acceleration at a given pointere are total20 curves in each part of Figure 6 while each curve char-acterizes structural damage indicated by global drift causedby the single corresponding earthquake at discretely con-sidered seismic intensity levels ranging from 02 g to 14 g

In Figure 6(a) the curves manifest the maximum globaldrift ranging from 020 to more than 50 when PGA isused to indicate seismic intensity While in Figure 6(b)when Sa(T1) is used to characterize the seismic intensity themaximum global drift reaches 247 against the Sa of 14 gthe maximum considered in this study

e results of IDA indicate that intrinsic properties ofground motions project substantial sensitivities to theseismic demand e disparity in the structural responseagainst different ground motions of the same intensities isprimarily attributed to differences in the inherent nature ofground motions ie energy distribution over frequencycontent and duration that predominantly affects thestructural response Moreover when Sa(T1) is used as anindicator of the seismic intensity the global drift observeslower values because of the scaling of the ground motions atthe fundamental period of the structure which is directlyrelated with the structural inertia and stiffness

6 Vulnerability Assessment

e fundamental process of the risk assessment against anyhazard consists of two parts ie the hazard and the vul-nerability of structural systems to that hazard For earth-quakes the first portion is primarily concerned withseismologists who can provide a realistic estimate of thepotential seismic hazard that can hit a specific geographicalarea while the second part vulnerability is usuallyaddressed by the engineers and experts who design thefacilities for versatile purposes e current study is relatedwith the second part and assesses the vulnerability of theconsidered typology of school buildings by establishing thehazard-damage relationships for the considered typology ofstructures and subsequently by developing the genericfragility relationships Hazard-damage relationships depictthe structural performance against seismic excitations and

exhibit the dynamic response for all considered groundmotion intensities Figures 7(a) and 7(b) present a directrelationship between the seismic intensities and the struc-tural damage e structural damage is quantified using theglobal response and seismic intensities are provided in-crementally in terms of PGA as well as in terms of spectralacceleration at the fundamental modersquos time period Everysingle dot in each part of Figure 7 represents the maximumvalue of the global drift in terms of percentage against aspecific earthquake scaled at a specific intensity For in-stance at the seismic intensity of 14 g there are 20 dots fromall 20 ground motions indicating the uncertainty in thestructural response by depicting that one earthquake havingthe seismic intensity of 14 g produces global drift less than1 while some other earthquake with the same seismicintensity produces more than 5 of global drift

With increasing intensity of PGA from 020 g to 080 gin Figure 7(a) the global drift remains between 009 and119 While at higher PGA levels from 10 g to 14 g theglobal drift drastically remains between 044 and 516 forall the considered ground motions At the maximum con-sidered PGA of 140 g the global drift varies from 097 to516 for all 20 ground motions All this disparity in thestructural response arises because of the inherent charac-teristics of ground motions which vary from record to re-cord thus instigating different response against the samescaled intensity level

When Sa(T1) is used for representing seismic intensitythe global drift varied between 022 and 24 at the Sa of140 g as shown by Figure 7(b) e dotted line inFigures 7(a) and 7(b) shows the mean structural responseobtained at each intensity level

On the other hand the fragility curve as described byEquation (1) represents a conditional probability ofexceedance for specific damage or limit states of a structureagainst a particular seismic intensity given in terms of PGASa or some other seismic intensity describing the indicator

Pfragility P[LS | IM x] (1)

e aforementioned equation describes the conditionalprobability Pfragility of achieving or exceeding a specific limitstate LS when seismic intensity defined by a particularintensity measure (IM) is equal to ldquoxrdquo Fragility relationshipsfor different damage states must be probabilistically able topredict the structural vulnerability against a realistic range ofseismic ground excitations is probabilistic evaluation isonly possible when a large variation of seismic demands isconsidered so that ample variation in the dynamic structuralresponse can be obtained e vulnerability assessment re-quires the definition of specific limit states damage indicatorsand seismic intensity indicators e impending sectionsaddress all the requirements to develop fragility curvesConsequently fragility curves are developed for the selectedtypology to elucidate the established framework

61 Damage Indicator and the Definition of Limit Statese derivation of analytical fragility curves requires thedefinition of specific limit states in both terms ie

8 Advances in Civil Engineering

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Peak

gro

und

acce

lera

tion

(g)

05 1 15 2 25 3 35 4 45 5 550Maximum global drift ()

(a)

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Spec

tral

acce

lera

tion

(T1)

05 1 15 2 250Maximum global drift ()

(b)

Figure 6 IDA curves (a) maximum global drift vs PGA (b) maximum global drift vs spectral acceleration scaled at the fundamental timeperiod of the structure (Sa(T1))

0 02 04 06 08 1 12 14PGA (g)

0

1

2

3

4

5

Glo

bal d

ri (

)

(a)

0

05

1

15

2

25

3

0 02 04 06 08 1 12 14

Glo

bal d

ri (

)

Sa(T1)

(b)

Figure 7 Hazard-damage relationships (a) PGA vs global drift in percentage (b) Sa(T1) vs global drift in percentage

Advances in Civil Engineering 9

qualitative and quantitative For this purpose a researcherhas to employ a specific damage indicator also known asengineering demand parameter (EDP) or may also propose anew damage measure that can represent the structuraldamage in a rational manner to correlate the damage withseismic loading Once the damage indicator has been set orselected different limit states often known as the damagestates of a structure may be defined

Damage states represent a physical categorization ofdamages by using damage indices which suggest thresholdlimits for different damage states by relaying upon theparameters of structural behavior eg energy dissipationcapability ductility and strength Damage indices are usedfor correlating the accumulated damage with differentspecific damage states and numerous nonidentical damageindices may exist for the same structure For instance Khanet al [44] used global displacement of the structure tocharacterize the structural damage Crowley et al [45]considered damage limit states based on the strain levels inconcrete and steel Guneyisi and Altay [46] considered theinterstory drift ratio for representing the response pa-rameter corresponding to the four damage states takenfrom the HAZUS Casotto et al [47] considered themember flexural strength to characterize the first limit state(LS1) when the reinforcement steel yields in the columnsand 3 interstory drift for flexural collapse limit state(LS2) and subsequently related his LS2 with the loss ofsupport of the beam Chaulagain et al [48] and Gautamet al [49] used 3 damage states ranging from slight damageto complete collapse and developed empirical fragilityrelationships for buildings in Nepal ey further relatedtheir results with FEMA356 [50] classifications for buildingdamage levels

Since this study primarily relates with the generation offragilities for a specific building stock it would not bepractical to define damage or limit states depending uponthe member behavior or local strains In the current studythe global drift ratio has been considered as the damageindicator to correlate with the structural damage

ree damage states namely serviceability limit state(LS1) damage control limit state (LS2) and collapseprevention (LS3) are qualitatively defined in this studyLS1 corresponds with the 1st yield of longitudinal steelreinforcement in the structure Conventionally the firstlimit states are usually related with the formation of the firsthinge in the structure but since the current study employsnonlinear fibers to model the structure therefore the LS1primarily describes the yielding strain reaching in astructural element located anywhere in the structure edeformation and strength govern the LS2 It is defined as75 of LS3 e LS3 collapse prevention is generallydirected by the deformation Altug [51] defined the collapseprevention limit state as 75 of ultimate structural de-formation or the value for which more than 20 strengthdrop can be observed relative to the maximum strengthvalue e smaller of these two values would govern theLS3

e mathematical quantification for these damage statescould not be adopted from the previous research as there

exists no analogous research for Pakistanrsquos constructionindustry or for Pakistanrsquos seismic zone 4 In the currentstudy the mathematical values are assigned to each of thediscrete damage state by using the capacity curve of theselected structure However the obtained values were ap-proximately similar to those obtained by Altug [51] whichused the low-rise buildings of the Turkish region in theirresearch thus the obtained values amply represent the low-rise structural behavior e mathematical values for each ofthe considered damage state against the global drift arepresented in Table 5

62 Fragility Assessment for the School Buildings Seismicfragility curves are widely employed to obtain an articu-lated insight of structural performance against seismicloads and they represent the probability of entering orexceeding different damage states for considered in-tensities of ground shaking After attaining the structuralresponse established limit state definitions are applied forevaluating the structural performance for each limit stateOnce the computed value comes out to be greater than alimit statersquos value an event shall be counted within thesample comprising all the ground motions scalesereby for each IM direct sampling probabilities overthe 20 selected ground motions on all incrementing scaleswere obtained

It is a commonly accepted assumption that for a fragilitycurve a lognormal cumulative distribution function can beconveniently utilized for the representation of conditionalprobabilities [52ndash54] From viewpoint of literature log-normal distribution was also assumed and used for theregression of fragility relationships as mentioned in thefollowing equation

P(LS | IM) ϕln IM minus λc

βc1113888 1113889 (2)

where P(LS | IM) describes the probability of exceedance ofa particular LS given an IM value ϕ represents the standardnormal cumulative distribution function (CDF)

e controlling parameters λc and βc represent themedian point and the slope of the curve respectively It isimperative to evaluate their optimized values for a best fit ofCDF against the calculated probabilities Shinozuka et al[53] Dang et al [54] and Baker [55] stated that the max-imum likelihood method (MLM) is one of the most suitablemethod to achieve best possible values of these two pa-rameters In the current study MLM is utilized to obtain themedian point and the slope of the fragility curve Formultiple IM levels as considered in this study the likelihoodfunction is given as follows

Likelihood 1113945m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠ϕln IMiλc( 1113857

βc1113888 1113889

zj

1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 1113889

njminus zj

(3)

wherem is the number of IM levels andΠ denotes a productover all levels It is assumed that the observation of attaininga specific limit state from each ground motion is

10 Advances in Civil Engineering

independent of the observations from other ground mo-tions In the above equation zj denotes the number ofattaining particular limit state out of nj ground motions witha particular value of IM IMie fragility curve parameterscan be obtained by maximizing the likelihood function inEquation (3) as given in following equation

λc βc1113864 1113865 argmaxλc βc 1113944

m

j1ln

nj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnϕln IMiλ( 1113857c

βc1113888 1113889

⎧⎪⎨

⎪⎩

+ nj minus zj1113872 1113873ln 1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 11138891113897

(4)

A MATLAB code was written to control the maximi-zation of the likelihood function so that optimum values ofthese two parameters can be obtained for establishingseismic fragility

Figure 8 presents the developed fragility relationships forthe considered typology of the RC school building in seismiczone 4 of Pakistan Each portion of Figure 8 contains threefragility relationships correlating with each limit stateagainst both of the IMs ie PGA and Sa(T1) Directsampling probabilities obtained from the IDA are alsoplotted in Figure 8 along with lognormally fitted fragilityfunctions

Table 6 provides the simulated values for λc and βc foreach limit state against each IM for the derivation of fragilitycurves

7 Conclusion

Pakistan has numerous seismotectonically active regionsincluding Muzaffarabad and past earthquakes especially the2005 Kashmir earthquake have proven this fact In thisstudy a new database of RC school buildings constructed inMuzaffarabad district after 2005 earthquake has beenpresented Subsequently the structural vulnerability of aspecific category of RC school buildings is assessed andpresented by using IDA so that practicing engineers atdomestic and regional level can further extend the evalua-tion to other categories of RC buildings e procedurepresented utilizes the fiber-based model which is the mostreliable at present In the current study both PGA andSa(T1) have been used to characterize the seismic intensityough Sa(T1) is a more appropriate IM PGA has beeneasily understandable with the normal public therefore thefragility relationships have also been developed using thePGA as an IM At the PGA of 06 g there exists

Table 5 Limit state criteria for the considered building typology

Buildingmodel nameDamagelimit state (based of global drift )

Serviceability (LS1) Damage control (LS2) Collapse prevention (LS3)BLR-11 035 066 089

Table 6 Lognormal distribution parameters for fragilities againstPGA and Sa(T1) for the considered school building typology

Fragilityparameter

Serviceability(LS1)

Damagecontrol (LS2)

Collapseprevention

(LS3)PGA Sa(T1) PGA Sa(T1) PGA Sa(T1)

λc 04842 08908 07156 13094 0957 18399βc 0327 03266 01974 02606 01742 03353

LS1-lognormalLS2-lognormalLS3-lognormal

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty

LS3 directLS2 directLS1 direct

02 04 06 08 1 12 140PGA (g)

(a)

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty02 04 06 08 1 12 140

Sa(T1)

LS1-lognormalLS2-lognormalLS3-lognormalLS3 direct

LS2 directLS1 direct

(b)

Figure 8 Derived fragility relationships for all IMs (a) seismic fragility for PGA (b) seismic fragility for Sa(T1)

Advances in Civil Engineering 11

approximately 82 probability of exceedance for the firstlimit state (LS1) while only around 20 probability ofexceedance has been achieved against the same seismicintensity for the second limit state (LS2) is essentiallyindicates the structural behavior dominated by the yieldingof the members instead of their complete failures At theseismic intensity of 140 g of PGA the structure seems to bein LS3 with almost around 100 of probability while whenSa(T1) is used as an IM the probability of being in LS3 at theseismic intensity of 140 g remains only around 20 isspecific variation in structural behavior is primarily attrib-uted to the inherent structural characteristics ie stiffnessand ductility that influence the response when the spectralacceleration is used as an IM after being scaled at thefundamental time period of the structure Since the selectedstructure is engineered the results are not so admonishingfor the considered school building typology neverthelessthe results might not be encouraging for other schoolbuilding types in the presented database e presentedconsolidated procedure is relatively simple and can bereadily adopted by the domestic and regional disaster pre-paredness and mitigation agencies to extend the applicationSuch studies are relatively new for under developingcountries like Pakistan and contemporarily no other workexists that may specifically address the vulnerability ofschools in seismic zone 4 of Pakistan Assessment of vul-nerabilities for other types of school buildings may yield aneed for immediate intervention in order to safeguard thelife of students and other users e presented study isspecifically targeted to assess the vulnerability and does notaddress the assessment of risk therefore the developedfragility curves can be further integrated with the hazardcurves of the considered area to evaluate the total riskinvolved

Data Availability

e data used to support the findings of this study are in-cluded within the article Any other data used to support thefindings of this study may be released upon request to theauthor(s) who can be contacted at musmankaistackr

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] M Zain M Usman S H Farooq and A Hanif ldquoProgressivestructural capacity loss assessmentmdasha framework for modernreinforced concrete buildingsrdquo PLoS One vol 13 no 12Article ID e0208149 2018

[2] Report from earthquake engineering research Institute (ERRI)httpswwweeriorglfepdfkashmir_eeri_2nd_reportpdf

[3] Government of Pakistan Building Code of Pakistan PakistanEngineering Council Government of Pakistan IslamabadPakistan 2007

[4] D Bonowitz Seismic Design in Pakistan Be Building CodesBylaws and Recommendations for Earthquake Risk Reduction

United Nations Development Programme New York NYUSA 2015

[5] C Xu J Deng S Peng and C Li ldquoSeismic fragility analysis ofsteel reinforced concrete frame structures based on differentengineering demand parametersrdquo Journal of Building Engi-neering vol 20 pp 736ndash749 2018

[6] J Ji A S Elnashai and D A Kuchma ldquoAn analyticalframework for seismic fragility analysis of RC high-risebuildingsrdquo Engineering Structures vol 29 no 12 pp 3197ndash3209 2007

[7] M Zain N Anwar F A Najam and T Mehmood ldquoSeismicfragility assessment of reinforced concrete high-rise buildingsusing the uncoupled modal response history analysis(UMRHA)rdquo in Proceedings of the International Conference onEarthquake Engineering and Structural Dynamics ReykjavikIceland June 2017

[8] A Ali T Sandhu and M Usman ldquoAmbient vibration testingof a pedestrian bridge using low-cost accelerometers for SHMapplicationsrdquo Smart Cities vol 2 no 1 pp 20ndash30 2019

[9] Y Pang X Wu G Shen and W Yuan ldquoSeismic fragilityanalysis of cable-stayed bridges considering different sourcesof uncertaintiesrdquo Journal of Bridge Engineering vol 19 no 4Article ID 04013015 2014

[10] A Rasheed S H Farooq M Usman A Hanif N A Khanand R A Khushnood ldquoStructural reliability analysis of su-perstructure of highway bridges on China-Pakistan economiccorridor (CPEC) a case studyrdquo Journal of Structural Integrityand Maintenance vol 3 no 3 pp 197ndash207 2018

[11] J-T Wang M-X Zhang A-Y Jin and C-H ZhangldquoSeismic fragility of arch dams based on damage analysisrdquo SoilDynamics and Earthquake Engineering vol 109 pp 58ndash682018

[12] Y Yazdani and M Alembagheri ldquoSeismic vulnerability ofgravity dams in near-fault areasrdquo Soil Dynamics and Earth-quake Engineering vol 102 pp 15ndash24 2017

[13] S Leonidas and A Kappos ldquoDerivation of fragility curves fortraditional timber-framed masonry buildings using nonlinearstatic analysisrdquo in Proceedings of the 4th International Con-ference on Computational Methods in Structural Dynamicsand Earthquake Engineering Kos Island Greece June 2013

[14] J Alam M S Islam M Hussan and A Sarraz ldquoSeismicfragility assessment of RC building using nonlinear staticpushover analysisrdquo in Proceedings of the International Con-ference on Planning Architecture and Civil Engineering(ICPAC) Rajshahi India February 2017

[15] M Ni Choine M M Kashani L N Lowes et al ldquoNonlineardynamic analysis and seismic fragility assessment of a cor-rosion damaged integral bridgerdquo International Journal ofStructural Integrity vol 7 no 2 pp 227ndash239 2016

[16] K Bakalis and D Vamvatsikos ldquoSeismic fragility functions vianonlinear response history analysisrdquo Journal of StructuralEngineering vol 144 no 10 Article ID 04018181 2018

[17] FEMA Rapid Visual Screening of Buildings for PotentialSeismic Hazards A Handbook Federal Emergency Manage-ment Agency (FEMA) Washington DC USA third edition2015

[18] FEMA Technical and Userrsquos Manual HAZUSndashMH 21 De-partment of Homeland Security Federal Emergency Man-agement Agency (FEMA) Washington DC USA

[19] User Guide Perform 3D Nonlinear Analysis and PerformanceAssessment for 3D Structures Computers and Structures IncBerkeley CA USA 2011

[20] M M Rafi and M M Nasir ldquoExperimental investigation ofchemical and physical properties of cements manufactured in

12 Advances in Civil Engineering

excellent capability to capture different aspects of structuralperformance ranging from hinge rotations to materialsrsquostrains in members In order to capture the actual behaviorit was pertinent to take into account the properties of locallydeveloped concrete materials using the domestically avail-able cement aggregates and other constituents For thispurpose a study conducted by Rafi and Nasir [20] wasutilized to extract a mean value for concretersquos strength at

28 days subsequently as per the recommendations of ASCE41 [21] expected strength was ultimately employed duringthe analysis For reinforcing steel bars it was inferred frommost of the professional interviews that Grade 40 reinforcingbars were used during the design and construction processconsequently the current study uses Grade 40 steel re-inforcements in the analytical models in accordance with therecommendations of ASCE 41 [21]

Defining an RC building category from the database that represents the typical

building stock

Establish nonlinear analytical model using inelastic fiber

sections for structural elementsie beams columns and shear

walls

Execute nonlinear static analysis of the buildings to

obtain capacity curves

Establish the limit states (LS) of buildings depending upon the

strength and stiffness degradation (u k)

Selection of ground motions depending upon

the fault mechanism magnitude Mw distance to rupture (Rrup) and shear

wave velocity (Vs30)(ldquonrdquonumber of ground

motions)

Execution of incremental dynamic analysis (IDA) by incrementally scaling the selected ground motions

(i = 1 n)

Development of damage-hazard relationships IM

vs response parameter iePGA Sa Sd etc

Select the seismic intensity measure (IM) ie PGA PGV

Sa Sd etc (previously used during IDA)

Aer processing of results

Determine the parameters for lognormal distribution to match

the sampling probabilities (λc βc)

Plotting of fragility curves for each limit

state (LS)

Maximizeλc and βc using the

maximum likelihood

method (MLE)

Estimate the sampling

probabilities

Figure 3 Framework for the vulnerability assessment of RC school buildings in the current study

FB-1

FB-1

X

Y

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-1

FB-138m 38m 38m 38m 38m 38m 38m 38m 38m 38m

58m

25m

FC-1

FC-1

FB-2

FB-2

FB-3

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FB-2

FB-3

FC-1 FC-1 FC-1 FC-1 FC-2 FC-1 FC-2 FC-1 FC-2 FC-1 FC-1

FC-1

FC-2

FC-1

FC-2

FC-1

FC-2

FC-1

FC-1

FC-1

FC-2

FC-2

FC-1

FC-2

FC-2

FC-2

FC-1

FC-2

FC-2

FC-2

FC-1

FC-2

FC-1

FC-2

38m

Figure 4 Plan view of the considered building typology

XZ

38m 38m 38m38m 38m38m38m 38m 38m38m38m

3 m

3 m

Figure 5 Elevation view of the considered building indicating the story height of the superstructure

Table 2 Beam and column X-sectional and reinforcement details

Structural element(s) Label Width (mm) Height (mm) Top steel Bottom steel Mid steel

BeamsFB-1 305 455 3_19 3_19 mdashFB-2 305 455 3_19 3_19 mdashFB-3 305 455 3_19 3_19 mdash

Columns FC-1 305 455 3_19 3_19 2_19FC-2 305 305 3_19 3_19 2_19

Advances in Civil Engineering 5

Nonlinear inelastic fiber sections were created forlayer-by-layer modelling of concrete and reinforcing re-bars for all of the X-sections except slabs which weremodelled as linear By the virtue of fiber modelling theforce-deformation relationship of columns and beams istransformed into the stress-strain relationship of con-struction materials ie concrete and reinforcement Byemploying fibers an appropriate division may be in-troduced for confined and unconfined concrete fibers andconsequently a composite section can easily be taken intoaccount [22]

In the current study the Mander model provided byMander et al [23] was used for concrete Complete con-finement effect and strength loss were considered during theanalysis according to the details given in the X-sections ofbeams and columns (Table 2)

Steel models that can capture the buckling and non-buckling behavior of the reinforcements are available withinthe Perform 3D For this case the nonbuckling steel modelwas utilized as ductility design is mainly based on the factthat reinforcement cannot be abruptly brittle Expectedmaterial strength was used in the analysis as per the rec-ommendations of ASCE 41 [21]e numerical modelling ofstrength degradation at high ductility levels was also con-sidered by modelling the strengths of the materials in anonlinear range Table 3 summarizes all the materialstrengths live loads and infill-partitioning loads that wereused during the analysis in accordance with the professionalinterviews conducted during the field surveys

4 Uncertainty Treatment

e uncertainties can be divided into two categories iealeatory and epistemic during any sort of vulnerability andrisk assessments [24] e uncertainty associated with theinherent variability in the nature of ground motionresulting from the natural earthquakes comes under theheading of aleatory uncertainty us the intrinsic ran-domness and variability of ground motion record describesuch uncertainties

e epistemic uncertainties on the other hand char-acterize the qualms related to paucity of available knowledgeConventionally during the vulnerability assessments thelack of knowledge related to the materialsrsquo strengths comesunder the category of such uncertainty On the contraryZain et al [25] have shown that variation in materialcharacteristics do not induce any significant disparity in thestructural response and variation in the ground motionsmust be considered as the majorly significant factor ininfluencing the dynamic response of the structures as re-cord-to-record variability may persuade severe changes inthe structural response of any building against the propertiesof different ground motions

e current study employs 20 different ground motionsto cover a wide range of variation in the characteristics ofseismic loading Since the variations in the materialsrsquostrengths do not incite any major uncertain structural re-sponse hence their variation is not considered in this studye details about the selection procedure and incremental

scaling for the ground motions are discussed under theproceeding section

41 Ground Motion Uncertainty e biggest source ofuncertainty lies in the seismic demand during the vulner-ability assessment process Path attenuation characteristicsof the originating source and the site conditions all playtheir respective parts in contributing to such uncertainty Onaccount of the structural dynamic response it is imperativeto consider a wide range of seismic energy levels for selectingthe ground motions Typically a target spectrum is con-sidered for the anticipated seismic hazard level and thespectrum-matching technique is usually adopted to selectthe most suitable ground motions Although the BuildingCode of Pakistan (referred at [3]) provides a target spectrumfor the region considered seismic zone 4 of Pakistanhowever as explained in Section 1 the reliability of thedomestic code is questionable erefore in the presentstudy ground motions are selected by considering the bestavailable information of the case study area In this research20 natural ground motion records are selected by consid-ering the domestic fault mechanism magnitude source-to-site distance and the shear wave velocityVs in the upper 100feet of the soil layers and only the large magnitude earth-quakes ie 650 up until 80 are considered

For the current research the range of source-to-sitedistance has been kept between 0 and 30 kilometers forselecting the ground motions to consider the effects of pathattenuation so that any possibility of diversified site-specificsoil layers in near and far sites can be taken into account Forshear wave velocity Vs in the upper 30meters of the soil therange has been kept varying between 175 and 350msecwhich corresponds with the soil type Sd according to BCP-2007 (referred at [3])

e selected ground motions are given in the Table 4which presents the names of earthquake motion time his-tories magnitudes distances to rupture shear wave veloc-ities and associated PGA with some other minor details

By using numerous records with the consideration ofdomestic geological conditions the selected records may beconsidered as the representative of future shaking at the zonein question us with a variety of magnitudes PGA andother characteristics the aleatory uncertainty is adequatelytreated in the present study

5 Incremental Dynamic Analysis and GroundExcitation Random Effects

Incremental dynamic analysis (IDA) serves as the mostreliable method to assess the structural performance againstseismic excitations [26] Several researchers ie Kostinakisand Athanatopoulou [27] Fereshtehnejad et al [28] andZarfam and Mofid [29] adopted the technique for theevaluation of dynamic responses of different structures iebuildings and bridges and despite of its extensive compu-tational effort IDA has proved to be a splendid tool forprobabilistic vulnerability and risk assessments DuringIDA the ground motions are incrementally scaled in a way

6 Advances in Civil Engineering

that during each iteration of the analysis the accelerationsincrease at specific intended intervals e current studyutilizes the IDA for considering various levels of seismicintensity to predict the structural response against earth-quakes ranging from 02 g to 14 g with 020 g as theaugmenting acceleration for each successive iteration thusat this stage it is imperative to select the appropriateseismic intensity measure (IM) for representation ofseismic Subsequent subsection addresses the selection ofIM in the current study Apart from selecting the IM theremust also be a damage indicator that can amply relate theseismic IM with the observed structural damage As de-scribed earlier the current study employs global drift as thedamage indicator and the details have been given inSection 61

51 Seismic Intensity Measure Seismic intensity measure(IM) correlates the ground motion with the structuraldamage hence any IM employed must be rationally able toproject the dynamic response of the structure by the virtue ofthe damage indicator PGA is one of the IMs that has beenfrequently used by the experts for fragility derivations but itis generally comprehended that Sa is a better option as an IMto correlate with the structural damage as it actually rep-resents the effect of ground shaking on the building itselfPang and Wu [30] and Jiang et al [31] employed PGA fortheir researches Apart from the PGA Omine et al [32] andEden et al [33] used peak ground velocity (PGV) as an IM

Eden et al [33] also used Sa at the fundamental period of thestructure as an IM Frankie et al [34] and Choudhury andKaushik [35] utilized spectral displacement (Sd) as IM fortheir study on open ground story RC frames with openingsin walls during the vulnerability assessment Buratti [36]analyzed the sufficiency and the efficiency of numerous IMsas indicated in their study and employed the cloud analysistechnique for 1704 unscaled accelerograms Bojorquez et al[37] proposed a procedure to obtain the interstory driftdemands for midrise frame structures in terms of a spectral-shape-based IM (INp

) and eventually concluded that INpwas

the best parameter to relate with the structural response offrames with 4 6 8 and 10 stories under the narrow-bandground motions in Europe Some other vector-valued in-tensity measures have also been proposed and discussed byModica and Stafford [38] Baker and Cornell [39] Polsakand Nicolas [40] and Kohrangi et al [41] Bojorquez andIervolino [42] also performed their research to establish avector-based IM however their research also proposed ascalar-based IM as they apprehended that the use of thescalar-based IM is easier than the vector-based IM forpractical purposes

Pejovic and Jankovic [43] investigated different groundmotion IMs which are conventionally used to investigate thedynamic behavior and concluded that despite being the mostcommon IM PGA provided the greatest dispersion in re-sults in comparison with the PGV Sa(T1) Sv(T1) and Sd(T1) e research portrayed spectral response velocity valueSv(T1) as the most efficient IM for the RC frames while

Table 4 Selected natural ground motions

Sr No Earthquake name Year Station name Mag PGA (g) Rrup (KMs) Vs30 (msec)1 San Fernando 1971 LA - hollywood stor FF 661 0225 2277 316462 Gazli USSR 1976 Karakyr 68 0864 547 259593 Tabas Iran 1978 Boshrooyeh 735 0106 2879 324574 Spitak Armenia 1988 Gukasian 677 020 240 343535 Loma Prieta 1989 Agnews State Hospital 693 01695 2457 239696 Loma Prieta 1989 Saratoga-W Valley Coll 693 0331 930 347907 Northridge-01 1994 Arleta-Nordhoff fire station 669 0345 866 297718 Northridge-01 1994 N Hollywood - coldwater can 669 0309 1251 326479 Chi-Chi Taiwan 1999 CHY002 762 0137 2496 2351310 Chi-Chi Taiwan 1999 CHY036 762 0273 1604 2331411 Chi-Chi Taiwan 1999 TCU038 762 01448 2542 2978612 Chi-Chi Taiwan 1999 TCU059 762 0165 1711 2726713 Chi-Chi Taiwan 1999 TCU110 762 01918 1157 2127214 Kashmir earthquake 1999 ABD-Abbottabad 760 02517 260 2230415 St Elias Alaska 1979 Icy Bay 754 01759 2645 3063716 Niigata Japan 2004 NIG017 663 04764 1281 2741717 Montenegro Yugoslavia 1979 Ulcinj-Hotel Olimpic 71 02928 576 3187418 Chuetsu-oki Japan 2007 Joetsu Kita 68 0176 2945 334019 Iwate Japan 2008 IWT011 69 02194 843 2793620 Iwate Japan 2008 Kitakami Yanagihara 69 02057 1667 34898

Table 3 Material strengths and loading values used for the structural modelling

Materials LoadsCharacteristics Strength Units Name Value UnitsConcretersquos strength (fcprime) 21 MPa Live 26 kNm2

Reinforcing steelrsquos yielding stress (fy) 275 MPa Infill-partitioning 43 kNm

Advances in Civil Engineering 7

stating the other two spectral response parameters ieSa(T1) and Sd(T1) were similarly adequate as they in-corporated the dynamic characteristics of the consideredstructure e current study chooses both ie PGA andspectral acceleration at the fundamental time period (Sa(T1))of the structure as intensity measures As indicated by theprevious literature provided by Jelena and Srdjan [43] PGAis the most commonly employed IM which is easy to un-derstand for normal people with no specific engineeringbackground while Sa(T1) incorporates the structural char-acteristics during the execution of analyses

52 Results of IDA Figure 6 shows the results of IDA in theform of plots between global drift and the selected IMs ieincrementally scaled PGA and Sa(T1) from 020 g to 14 g Itcan be observed that intrinsic nature of different groundmotions produces different results despite of having thesame intensity of acceleration at a given pointere are total20 curves in each part of Figure 6 while each curve char-acterizes structural damage indicated by global drift causedby the single corresponding earthquake at discretely con-sidered seismic intensity levels ranging from 02 g to 14 g

In Figure 6(a) the curves manifest the maximum globaldrift ranging from 020 to more than 50 when PGA isused to indicate seismic intensity While in Figure 6(b)when Sa(T1) is used to characterize the seismic intensity themaximum global drift reaches 247 against the Sa of 14 gthe maximum considered in this study

e results of IDA indicate that intrinsic properties ofground motions project substantial sensitivities to theseismic demand e disparity in the structural responseagainst different ground motions of the same intensities isprimarily attributed to differences in the inherent nature ofground motions ie energy distribution over frequencycontent and duration that predominantly affects thestructural response Moreover when Sa(T1) is used as anindicator of the seismic intensity the global drift observeslower values because of the scaling of the ground motions atthe fundamental period of the structure which is directlyrelated with the structural inertia and stiffness

6 Vulnerability Assessment

e fundamental process of the risk assessment against anyhazard consists of two parts ie the hazard and the vul-nerability of structural systems to that hazard For earth-quakes the first portion is primarily concerned withseismologists who can provide a realistic estimate of thepotential seismic hazard that can hit a specific geographicalarea while the second part vulnerability is usuallyaddressed by the engineers and experts who design thefacilities for versatile purposes e current study is relatedwith the second part and assesses the vulnerability of theconsidered typology of school buildings by establishing thehazard-damage relationships for the considered typology ofstructures and subsequently by developing the genericfragility relationships Hazard-damage relationships depictthe structural performance against seismic excitations and

exhibit the dynamic response for all considered groundmotion intensities Figures 7(a) and 7(b) present a directrelationship between the seismic intensities and the struc-tural damage e structural damage is quantified using theglobal response and seismic intensities are provided in-crementally in terms of PGA as well as in terms of spectralacceleration at the fundamental modersquos time period Everysingle dot in each part of Figure 7 represents the maximumvalue of the global drift in terms of percentage against aspecific earthquake scaled at a specific intensity For in-stance at the seismic intensity of 14 g there are 20 dots fromall 20 ground motions indicating the uncertainty in thestructural response by depicting that one earthquake havingthe seismic intensity of 14 g produces global drift less than1 while some other earthquake with the same seismicintensity produces more than 5 of global drift

With increasing intensity of PGA from 020 g to 080 gin Figure 7(a) the global drift remains between 009 and119 While at higher PGA levels from 10 g to 14 g theglobal drift drastically remains between 044 and 516 forall the considered ground motions At the maximum con-sidered PGA of 140 g the global drift varies from 097 to516 for all 20 ground motions All this disparity in thestructural response arises because of the inherent charac-teristics of ground motions which vary from record to re-cord thus instigating different response against the samescaled intensity level

When Sa(T1) is used for representing seismic intensitythe global drift varied between 022 and 24 at the Sa of140 g as shown by Figure 7(b) e dotted line inFigures 7(a) and 7(b) shows the mean structural responseobtained at each intensity level

On the other hand the fragility curve as described byEquation (1) represents a conditional probability ofexceedance for specific damage or limit states of a structureagainst a particular seismic intensity given in terms of PGASa or some other seismic intensity describing the indicator

Pfragility P[LS | IM x] (1)

e aforementioned equation describes the conditionalprobability Pfragility of achieving or exceeding a specific limitstate LS when seismic intensity defined by a particularintensity measure (IM) is equal to ldquoxrdquo Fragility relationshipsfor different damage states must be probabilistically able topredict the structural vulnerability against a realistic range ofseismic ground excitations is probabilistic evaluation isonly possible when a large variation of seismic demands isconsidered so that ample variation in the dynamic structuralresponse can be obtained e vulnerability assessment re-quires the definition of specific limit states damage indicatorsand seismic intensity indicators e impending sectionsaddress all the requirements to develop fragility curvesConsequently fragility curves are developed for the selectedtypology to elucidate the established framework

61 Damage Indicator and the Definition of Limit Statese derivation of analytical fragility curves requires thedefinition of specific limit states in both terms ie

8 Advances in Civil Engineering

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Peak

gro

und

acce

lera

tion

(g)

05 1 15 2 25 3 35 4 45 5 550Maximum global drift ()

(a)

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Spec

tral

acce

lera

tion

(T1)

05 1 15 2 250Maximum global drift ()

(b)

Figure 6 IDA curves (a) maximum global drift vs PGA (b) maximum global drift vs spectral acceleration scaled at the fundamental timeperiod of the structure (Sa(T1))

0 02 04 06 08 1 12 14PGA (g)

0

1

2

3

4

5

Glo

bal d

ri (

)

(a)

0

05

1

15

2

25

3

0 02 04 06 08 1 12 14

Glo

bal d

ri (

)

Sa(T1)

(b)

Figure 7 Hazard-damage relationships (a) PGA vs global drift in percentage (b) Sa(T1) vs global drift in percentage

Advances in Civil Engineering 9

qualitative and quantitative For this purpose a researcherhas to employ a specific damage indicator also known asengineering demand parameter (EDP) or may also propose anew damage measure that can represent the structuraldamage in a rational manner to correlate the damage withseismic loading Once the damage indicator has been set orselected different limit states often known as the damagestates of a structure may be defined

Damage states represent a physical categorization ofdamages by using damage indices which suggest thresholdlimits for different damage states by relaying upon theparameters of structural behavior eg energy dissipationcapability ductility and strength Damage indices are usedfor correlating the accumulated damage with differentspecific damage states and numerous nonidentical damageindices may exist for the same structure For instance Khanet al [44] used global displacement of the structure tocharacterize the structural damage Crowley et al [45]considered damage limit states based on the strain levels inconcrete and steel Guneyisi and Altay [46] considered theinterstory drift ratio for representing the response pa-rameter corresponding to the four damage states takenfrom the HAZUS Casotto et al [47] considered themember flexural strength to characterize the first limit state(LS1) when the reinforcement steel yields in the columnsand 3 interstory drift for flexural collapse limit state(LS2) and subsequently related his LS2 with the loss ofsupport of the beam Chaulagain et al [48] and Gautamet al [49] used 3 damage states ranging from slight damageto complete collapse and developed empirical fragilityrelationships for buildings in Nepal ey further relatedtheir results with FEMA356 [50] classifications for buildingdamage levels

Since this study primarily relates with the generation offragilities for a specific building stock it would not bepractical to define damage or limit states depending uponthe member behavior or local strains In the current studythe global drift ratio has been considered as the damageindicator to correlate with the structural damage

ree damage states namely serviceability limit state(LS1) damage control limit state (LS2) and collapseprevention (LS3) are qualitatively defined in this studyLS1 corresponds with the 1st yield of longitudinal steelreinforcement in the structure Conventionally the firstlimit states are usually related with the formation of the firsthinge in the structure but since the current study employsnonlinear fibers to model the structure therefore the LS1primarily describes the yielding strain reaching in astructural element located anywhere in the structure edeformation and strength govern the LS2 It is defined as75 of LS3 e LS3 collapse prevention is generallydirected by the deformation Altug [51] defined the collapseprevention limit state as 75 of ultimate structural de-formation or the value for which more than 20 strengthdrop can be observed relative to the maximum strengthvalue e smaller of these two values would govern theLS3

e mathematical quantification for these damage statescould not be adopted from the previous research as there

exists no analogous research for Pakistanrsquos constructionindustry or for Pakistanrsquos seismic zone 4 In the currentstudy the mathematical values are assigned to each of thediscrete damage state by using the capacity curve of theselected structure However the obtained values were ap-proximately similar to those obtained by Altug [51] whichused the low-rise buildings of the Turkish region in theirresearch thus the obtained values amply represent the low-rise structural behavior e mathematical values for each ofthe considered damage state against the global drift arepresented in Table 5

62 Fragility Assessment for the School Buildings Seismicfragility curves are widely employed to obtain an articu-lated insight of structural performance against seismicloads and they represent the probability of entering orexceeding different damage states for considered in-tensities of ground shaking After attaining the structuralresponse established limit state definitions are applied forevaluating the structural performance for each limit stateOnce the computed value comes out to be greater than alimit statersquos value an event shall be counted within thesample comprising all the ground motions scalesereby for each IM direct sampling probabilities overthe 20 selected ground motions on all incrementing scaleswere obtained

It is a commonly accepted assumption that for a fragilitycurve a lognormal cumulative distribution function can beconveniently utilized for the representation of conditionalprobabilities [52ndash54] From viewpoint of literature log-normal distribution was also assumed and used for theregression of fragility relationships as mentioned in thefollowing equation

P(LS | IM) ϕln IM minus λc

βc1113888 1113889 (2)

where P(LS | IM) describes the probability of exceedance ofa particular LS given an IM value ϕ represents the standardnormal cumulative distribution function (CDF)

e controlling parameters λc and βc represent themedian point and the slope of the curve respectively It isimperative to evaluate their optimized values for a best fit ofCDF against the calculated probabilities Shinozuka et al[53] Dang et al [54] and Baker [55] stated that the max-imum likelihood method (MLM) is one of the most suitablemethod to achieve best possible values of these two pa-rameters In the current study MLM is utilized to obtain themedian point and the slope of the fragility curve Formultiple IM levels as considered in this study the likelihoodfunction is given as follows

Likelihood 1113945m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠ϕln IMiλc( 1113857

βc1113888 1113889

zj

1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 1113889

njminus zj

(3)

wherem is the number of IM levels andΠ denotes a productover all levels It is assumed that the observation of attaininga specific limit state from each ground motion is

10 Advances in Civil Engineering

independent of the observations from other ground mo-tions In the above equation zj denotes the number ofattaining particular limit state out of nj ground motions witha particular value of IM IMie fragility curve parameterscan be obtained by maximizing the likelihood function inEquation (3) as given in following equation

λc βc1113864 1113865 argmaxλc βc 1113944

m

j1ln

nj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnϕln IMiλ( 1113857c

βc1113888 1113889

⎧⎪⎨

⎪⎩

+ nj minus zj1113872 1113873ln 1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 11138891113897

(4)

A MATLAB code was written to control the maximi-zation of the likelihood function so that optimum values ofthese two parameters can be obtained for establishingseismic fragility

Figure 8 presents the developed fragility relationships forthe considered typology of the RC school building in seismiczone 4 of Pakistan Each portion of Figure 8 contains threefragility relationships correlating with each limit stateagainst both of the IMs ie PGA and Sa(T1) Directsampling probabilities obtained from the IDA are alsoplotted in Figure 8 along with lognormally fitted fragilityfunctions

Table 6 provides the simulated values for λc and βc foreach limit state against each IM for the derivation of fragilitycurves

7 Conclusion

Pakistan has numerous seismotectonically active regionsincluding Muzaffarabad and past earthquakes especially the2005 Kashmir earthquake have proven this fact In thisstudy a new database of RC school buildings constructed inMuzaffarabad district after 2005 earthquake has beenpresented Subsequently the structural vulnerability of aspecific category of RC school buildings is assessed andpresented by using IDA so that practicing engineers atdomestic and regional level can further extend the evalua-tion to other categories of RC buildings e procedurepresented utilizes the fiber-based model which is the mostreliable at present In the current study both PGA andSa(T1) have been used to characterize the seismic intensityough Sa(T1) is a more appropriate IM PGA has beeneasily understandable with the normal public therefore thefragility relationships have also been developed using thePGA as an IM At the PGA of 06 g there exists

Table 5 Limit state criteria for the considered building typology

Buildingmodel nameDamagelimit state (based of global drift )

Serviceability (LS1) Damage control (LS2) Collapse prevention (LS3)BLR-11 035 066 089

Table 6 Lognormal distribution parameters for fragilities againstPGA and Sa(T1) for the considered school building typology

Fragilityparameter

Serviceability(LS1)

Damagecontrol (LS2)

Collapseprevention

(LS3)PGA Sa(T1) PGA Sa(T1) PGA Sa(T1)

λc 04842 08908 07156 13094 0957 18399βc 0327 03266 01974 02606 01742 03353

LS1-lognormalLS2-lognormalLS3-lognormal

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty

LS3 directLS2 directLS1 direct

02 04 06 08 1 12 140PGA (g)

(a)

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty02 04 06 08 1 12 140

Sa(T1)

LS1-lognormalLS2-lognormalLS3-lognormalLS3 direct

LS2 directLS1 direct

(b)

Figure 8 Derived fragility relationships for all IMs (a) seismic fragility for PGA (b) seismic fragility for Sa(T1)

Advances in Civil Engineering 11

approximately 82 probability of exceedance for the firstlimit state (LS1) while only around 20 probability ofexceedance has been achieved against the same seismicintensity for the second limit state (LS2) is essentiallyindicates the structural behavior dominated by the yieldingof the members instead of their complete failures At theseismic intensity of 140 g of PGA the structure seems to bein LS3 with almost around 100 of probability while whenSa(T1) is used as an IM the probability of being in LS3 at theseismic intensity of 140 g remains only around 20 isspecific variation in structural behavior is primarily attrib-uted to the inherent structural characteristics ie stiffnessand ductility that influence the response when the spectralacceleration is used as an IM after being scaled at thefundamental time period of the structure Since the selectedstructure is engineered the results are not so admonishingfor the considered school building typology neverthelessthe results might not be encouraging for other schoolbuilding types in the presented database e presentedconsolidated procedure is relatively simple and can bereadily adopted by the domestic and regional disaster pre-paredness and mitigation agencies to extend the applicationSuch studies are relatively new for under developingcountries like Pakistan and contemporarily no other workexists that may specifically address the vulnerability ofschools in seismic zone 4 of Pakistan Assessment of vul-nerabilities for other types of school buildings may yield aneed for immediate intervention in order to safeguard thelife of students and other users e presented study isspecifically targeted to assess the vulnerability and does notaddress the assessment of risk therefore the developedfragility curves can be further integrated with the hazardcurves of the considered area to evaluate the total riskinvolved

Data Availability

e data used to support the findings of this study are in-cluded within the article Any other data used to support thefindings of this study may be released upon request to theauthor(s) who can be contacted at musmankaistackr

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] M Zain M Usman S H Farooq and A Hanif ldquoProgressivestructural capacity loss assessmentmdasha framework for modernreinforced concrete buildingsrdquo PLoS One vol 13 no 12Article ID e0208149 2018

[2] Report from earthquake engineering research Institute (ERRI)httpswwweeriorglfepdfkashmir_eeri_2nd_reportpdf

[3] Government of Pakistan Building Code of Pakistan PakistanEngineering Council Government of Pakistan IslamabadPakistan 2007

[4] D Bonowitz Seismic Design in Pakistan Be Building CodesBylaws and Recommendations for Earthquake Risk Reduction

United Nations Development Programme New York NYUSA 2015

[5] C Xu J Deng S Peng and C Li ldquoSeismic fragility analysis ofsteel reinforced concrete frame structures based on differentengineering demand parametersrdquo Journal of Building Engi-neering vol 20 pp 736ndash749 2018

[6] J Ji A S Elnashai and D A Kuchma ldquoAn analyticalframework for seismic fragility analysis of RC high-risebuildingsrdquo Engineering Structures vol 29 no 12 pp 3197ndash3209 2007

[7] M Zain N Anwar F A Najam and T Mehmood ldquoSeismicfragility assessment of reinforced concrete high-rise buildingsusing the uncoupled modal response history analysis(UMRHA)rdquo in Proceedings of the International Conference onEarthquake Engineering and Structural Dynamics ReykjavikIceland June 2017

[8] A Ali T Sandhu and M Usman ldquoAmbient vibration testingof a pedestrian bridge using low-cost accelerometers for SHMapplicationsrdquo Smart Cities vol 2 no 1 pp 20ndash30 2019

[9] Y Pang X Wu G Shen and W Yuan ldquoSeismic fragilityanalysis of cable-stayed bridges considering different sourcesof uncertaintiesrdquo Journal of Bridge Engineering vol 19 no 4Article ID 04013015 2014

[10] A Rasheed S H Farooq M Usman A Hanif N A Khanand R A Khushnood ldquoStructural reliability analysis of su-perstructure of highway bridges on China-Pakistan economiccorridor (CPEC) a case studyrdquo Journal of Structural Integrityand Maintenance vol 3 no 3 pp 197ndash207 2018

[11] J-T Wang M-X Zhang A-Y Jin and C-H ZhangldquoSeismic fragility of arch dams based on damage analysisrdquo SoilDynamics and Earthquake Engineering vol 109 pp 58ndash682018

[12] Y Yazdani and M Alembagheri ldquoSeismic vulnerability ofgravity dams in near-fault areasrdquo Soil Dynamics and Earth-quake Engineering vol 102 pp 15ndash24 2017

[13] S Leonidas and A Kappos ldquoDerivation of fragility curves fortraditional timber-framed masonry buildings using nonlinearstatic analysisrdquo in Proceedings of the 4th International Con-ference on Computational Methods in Structural Dynamicsand Earthquake Engineering Kos Island Greece June 2013

[14] J Alam M S Islam M Hussan and A Sarraz ldquoSeismicfragility assessment of RC building using nonlinear staticpushover analysisrdquo in Proceedings of the International Con-ference on Planning Architecture and Civil Engineering(ICPAC) Rajshahi India February 2017

[15] M Ni Choine M M Kashani L N Lowes et al ldquoNonlineardynamic analysis and seismic fragility assessment of a cor-rosion damaged integral bridgerdquo International Journal ofStructural Integrity vol 7 no 2 pp 227ndash239 2016

[16] K Bakalis and D Vamvatsikos ldquoSeismic fragility functions vianonlinear response history analysisrdquo Journal of StructuralEngineering vol 144 no 10 Article ID 04018181 2018

[17] FEMA Rapid Visual Screening of Buildings for PotentialSeismic Hazards A Handbook Federal Emergency Manage-ment Agency (FEMA) Washington DC USA third edition2015

[18] FEMA Technical and Userrsquos Manual HAZUSndashMH 21 De-partment of Homeland Security Federal Emergency Man-agement Agency (FEMA) Washington DC USA

[19] User Guide Perform 3D Nonlinear Analysis and PerformanceAssessment for 3D Structures Computers and Structures IncBerkeley CA USA 2011

[20] M M Rafi and M M Nasir ldquoExperimental investigation ofchemical and physical properties of cements manufactured in

12 Advances in Civil Engineering

Nonlinear inelastic fiber sections were created forlayer-by-layer modelling of concrete and reinforcing re-bars for all of the X-sections except slabs which weremodelled as linear By the virtue of fiber modelling theforce-deformation relationship of columns and beams istransformed into the stress-strain relationship of con-struction materials ie concrete and reinforcement Byemploying fibers an appropriate division may be in-troduced for confined and unconfined concrete fibers andconsequently a composite section can easily be taken intoaccount [22]

In the current study the Mander model provided byMander et al [23] was used for concrete Complete con-finement effect and strength loss were considered during theanalysis according to the details given in the X-sections ofbeams and columns (Table 2)

Steel models that can capture the buckling and non-buckling behavior of the reinforcements are available withinthe Perform 3D For this case the nonbuckling steel modelwas utilized as ductility design is mainly based on the factthat reinforcement cannot be abruptly brittle Expectedmaterial strength was used in the analysis as per the rec-ommendations of ASCE 41 [21]e numerical modelling ofstrength degradation at high ductility levels was also con-sidered by modelling the strengths of the materials in anonlinear range Table 3 summarizes all the materialstrengths live loads and infill-partitioning loads that wereused during the analysis in accordance with the professionalinterviews conducted during the field surveys

4 Uncertainty Treatment

e uncertainties can be divided into two categories iealeatory and epistemic during any sort of vulnerability andrisk assessments [24] e uncertainty associated with theinherent variability in the nature of ground motionresulting from the natural earthquakes comes under theheading of aleatory uncertainty us the intrinsic ran-domness and variability of ground motion record describesuch uncertainties

e epistemic uncertainties on the other hand char-acterize the qualms related to paucity of available knowledgeConventionally during the vulnerability assessments thelack of knowledge related to the materialsrsquo strengths comesunder the category of such uncertainty On the contraryZain et al [25] have shown that variation in materialcharacteristics do not induce any significant disparity in thestructural response and variation in the ground motionsmust be considered as the majorly significant factor ininfluencing the dynamic response of the structures as re-cord-to-record variability may persuade severe changes inthe structural response of any building against the propertiesof different ground motions

e current study employs 20 different ground motionsto cover a wide range of variation in the characteristics ofseismic loading Since the variations in the materialsrsquostrengths do not incite any major uncertain structural re-sponse hence their variation is not considered in this studye details about the selection procedure and incremental

scaling for the ground motions are discussed under theproceeding section

41 Ground Motion Uncertainty e biggest source ofuncertainty lies in the seismic demand during the vulner-ability assessment process Path attenuation characteristicsof the originating source and the site conditions all playtheir respective parts in contributing to such uncertainty Onaccount of the structural dynamic response it is imperativeto consider a wide range of seismic energy levels for selectingthe ground motions Typically a target spectrum is con-sidered for the anticipated seismic hazard level and thespectrum-matching technique is usually adopted to selectthe most suitable ground motions Although the BuildingCode of Pakistan (referred at [3]) provides a target spectrumfor the region considered seismic zone 4 of Pakistanhowever as explained in Section 1 the reliability of thedomestic code is questionable erefore in the presentstudy ground motions are selected by considering the bestavailable information of the case study area In this research20 natural ground motion records are selected by consid-ering the domestic fault mechanism magnitude source-to-site distance and the shear wave velocityVs in the upper 100feet of the soil layers and only the large magnitude earth-quakes ie 650 up until 80 are considered

For the current research the range of source-to-sitedistance has been kept between 0 and 30 kilometers forselecting the ground motions to consider the effects of pathattenuation so that any possibility of diversified site-specificsoil layers in near and far sites can be taken into account Forshear wave velocity Vs in the upper 30meters of the soil therange has been kept varying between 175 and 350msecwhich corresponds with the soil type Sd according to BCP-2007 (referred at [3])

e selected ground motions are given in the Table 4which presents the names of earthquake motion time his-tories magnitudes distances to rupture shear wave veloc-ities and associated PGA with some other minor details

By using numerous records with the consideration ofdomestic geological conditions the selected records may beconsidered as the representative of future shaking at the zonein question us with a variety of magnitudes PGA andother characteristics the aleatory uncertainty is adequatelytreated in the present study

5 Incremental Dynamic Analysis and GroundExcitation Random Effects

Incremental dynamic analysis (IDA) serves as the mostreliable method to assess the structural performance againstseismic excitations [26] Several researchers ie Kostinakisand Athanatopoulou [27] Fereshtehnejad et al [28] andZarfam and Mofid [29] adopted the technique for theevaluation of dynamic responses of different structures iebuildings and bridges and despite of its extensive compu-tational effort IDA has proved to be a splendid tool forprobabilistic vulnerability and risk assessments DuringIDA the ground motions are incrementally scaled in a way

6 Advances in Civil Engineering

that during each iteration of the analysis the accelerationsincrease at specific intended intervals e current studyutilizes the IDA for considering various levels of seismicintensity to predict the structural response against earth-quakes ranging from 02 g to 14 g with 020 g as theaugmenting acceleration for each successive iteration thusat this stage it is imperative to select the appropriateseismic intensity measure (IM) for representation ofseismic Subsequent subsection addresses the selection ofIM in the current study Apart from selecting the IM theremust also be a damage indicator that can amply relate theseismic IM with the observed structural damage As de-scribed earlier the current study employs global drift as thedamage indicator and the details have been given inSection 61

51 Seismic Intensity Measure Seismic intensity measure(IM) correlates the ground motion with the structuraldamage hence any IM employed must be rationally able toproject the dynamic response of the structure by the virtue ofthe damage indicator PGA is one of the IMs that has beenfrequently used by the experts for fragility derivations but itis generally comprehended that Sa is a better option as an IMto correlate with the structural damage as it actually rep-resents the effect of ground shaking on the building itselfPang and Wu [30] and Jiang et al [31] employed PGA fortheir researches Apart from the PGA Omine et al [32] andEden et al [33] used peak ground velocity (PGV) as an IM

Eden et al [33] also used Sa at the fundamental period of thestructure as an IM Frankie et al [34] and Choudhury andKaushik [35] utilized spectral displacement (Sd) as IM fortheir study on open ground story RC frames with openingsin walls during the vulnerability assessment Buratti [36]analyzed the sufficiency and the efficiency of numerous IMsas indicated in their study and employed the cloud analysistechnique for 1704 unscaled accelerograms Bojorquez et al[37] proposed a procedure to obtain the interstory driftdemands for midrise frame structures in terms of a spectral-shape-based IM (INp

) and eventually concluded that INpwas

the best parameter to relate with the structural response offrames with 4 6 8 and 10 stories under the narrow-bandground motions in Europe Some other vector-valued in-tensity measures have also been proposed and discussed byModica and Stafford [38] Baker and Cornell [39] Polsakand Nicolas [40] and Kohrangi et al [41] Bojorquez andIervolino [42] also performed their research to establish avector-based IM however their research also proposed ascalar-based IM as they apprehended that the use of thescalar-based IM is easier than the vector-based IM forpractical purposes

Pejovic and Jankovic [43] investigated different groundmotion IMs which are conventionally used to investigate thedynamic behavior and concluded that despite being the mostcommon IM PGA provided the greatest dispersion in re-sults in comparison with the PGV Sa(T1) Sv(T1) and Sd(T1) e research portrayed spectral response velocity valueSv(T1) as the most efficient IM for the RC frames while

Table 4 Selected natural ground motions

Sr No Earthquake name Year Station name Mag PGA (g) Rrup (KMs) Vs30 (msec)1 San Fernando 1971 LA - hollywood stor FF 661 0225 2277 316462 Gazli USSR 1976 Karakyr 68 0864 547 259593 Tabas Iran 1978 Boshrooyeh 735 0106 2879 324574 Spitak Armenia 1988 Gukasian 677 020 240 343535 Loma Prieta 1989 Agnews State Hospital 693 01695 2457 239696 Loma Prieta 1989 Saratoga-W Valley Coll 693 0331 930 347907 Northridge-01 1994 Arleta-Nordhoff fire station 669 0345 866 297718 Northridge-01 1994 N Hollywood - coldwater can 669 0309 1251 326479 Chi-Chi Taiwan 1999 CHY002 762 0137 2496 2351310 Chi-Chi Taiwan 1999 CHY036 762 0273 1604 2331411 Chi-Chi Taiwan 1999 TCU038 762 01448 2542 2978612 Chi-Chi Taiwan 1999 TCU059 762 0165 1711 2726713 Chi-Chi Taiwan 1999 TCU110 762 01918 1157 2127214 Kashmir earthquake 1999 ABD-Abbottabad 760 02517 260 2230415 St Elias Alaska 1979 Icy Bay 754 01759 2645 3063716 Niigata Japan 2004 NIG017 663 04764 1281 2741717 Montenegro Yugoslavia 1979 Ulcinj-Hotel Olimpic 71 02928 576 3187418 Chuetsu-oki Japan 2007 Joetsu Kita 68 0176 2945 334019 Iwate Japan 2008 IWT011 69 02194 843 2793620 Iwate Japan 2008 Kitakami Yanagihara 69 02057 1667 34898

Table 3 Material strengths and loading values used for the structural modelling

Materials LoadsCharacteristics Strength Units Name Value UnitsConcretersquos strength (fcprime) 21 MPa Live 26 kNm2

Reinforcing steelrsquos yielding stress (fy) 275 MPa Infill-partitioning 43 kNm

Advances in Civil Engineering 7

stating the other two spectral response parameters ieSa(T1) and Sd(T1) were similarly adequate as they in-corporated the dynamic characteristics of the consideredstructure e current study chooses both ie PGA andspectral acceleration at the fundamental time period (Sa(T1))of the structure as intensity measures As indicated by theprevious literature provided by Jelena and Srdjan [43] PGAis the most commonly employed IM which is easy to un-derstand for normal people with no specific engineeringbackground while Sa(T1) incorporates the structural char-acteristics during the execution of analyses

52 Results of IDA Figure 6 shows the results of IDA in theform of plots between global drift and the selected IMs ieincrementally scaled PGA and Sa(T1) from 020 g to 14 g Itcan be observed that intrinsic nature of different groundmotions produces different results despite of having thesame intensity of acceleration at a given pointere are total20 curves in each part of Figure 6 while each curve char-acterizes structural damage indicated by global drift causedby the single corresponding earthquake at discretely con-sidered seismic intensity levels ranging from 02 g to 14 g

In Figure 6(a) the curves manifest the maximum globaldrift ranging from 020 to more than 50 when PGA isused to indicate seismic intensity While in Figure 6(b)when Sa(T1) is used to characterize the seismic intensity themaximum global drift reaches 247 against the Sa of 14 gthe maximum considered in this study

e results of IDA indicate that intrinsic properties ofground motions project substantial sensitivities to theseismic demand e disparity in the structural responseagainst different ground motions of the same intensities isprimarily attributed to differences in the inherent nature ofground motions ie energy distribution over frequencycontent and duration that predominantly affects thestructural response Moreover when Sa(T1) is used as anindicator of the seismic intensity the global drift observeslower values because of the scaling of the ground motions atthe fundamental period of the structure which is directlyrelated with the structural inertia and stiffness

6 Vulnerability Assessment

e fundamental process of the risk assessment against anyhazard consists of two parts ie the hazard and the vul-nerability of structural systems to that hazard For earth-quakes the first portion is primarily concerned withseismologists who can provide a realistic estimate of thepotential seismic hazard that can hit a specific geographicalarea while the second part vulnerability is usuallyaddressed by the engineers and experts who design thefacilities for versatile purposes e current study is relatedwith the second part and assesses the vulnerability of theconsidered typology of school buildings by establishing thehazard-damage relationships for the considered typology ofstructures and subsequently by developing the genericfragility relationships Hazard-damage relationships depictthe structural performance against seismic excitations and

exhibit the dynamic response for all considered groundmotion intensities Figures 7(a) and 7(b) present a directrelationship between the seismic intensities and the struc-tural damage e structural damage is quantified using theglobal response and seismic intensities are provided in-crementally in terms of PGA as well as in terms of spectralacceleration at the fundamental modersquos time period Everysingle dot in each part of Figure 7 represents the maximumvalue of the global drift in terms of percentage against aspecific earthquake scaled at a specific intensity For in-stance at the seismic intensity of 14 g there are 20 dots fromall 20 ground motions indicating the uncertainty in thestructural response by depicting that one earthquake havingthe seismic intensity of 14 g produces global drift less than1 while some other earthquake with the same seismicintensity produces more than 5 of global drift

With increasing intensity of PGA from 020 g to 080 gin Figure 7(a) the global drift remains between 009 and119 While at higher PGA levels from 10 g to 14 g theglobal drift drastically remains between 044 and 516 forall the considered ground motions At the maximum con-sidered PGA of 140 g the global drift varies from 097 to516 for all 20 ground motions All this disparity in thestructural response arises because of the inherent charac-teristics of ground motions which vary from record to re-cord thus instigating different response against the samescaled intensity level

When Sa(T1) is used for representing seismic intensitythe global drift varied between 022 and 24 at the Sa of140 g as shown by Figure 7(b) e dotted line inFigures 7(a) and 7(b) shows the mean structural responseobtained at each intensity level

On the other hand the fragility curve as described byEquation (1) represents a conditional probability ofexceedance for specific damage or limit states of a structureagainst a particular seismic intensity given in terms of PGASa or some other seismic intensity describing the indicator

Pfragility P[LS | IM x] (1)

e aforementioned equation describes the conditionalprobability Pfragility of achieving or exceeding a specific limitstate LS when seismic intensity defined by a particularintensity measure (IM) is equal to ldquoxrdquo Fragility relationshipsfor different damage states must be probabilistically able topredict the structural vulnerability against a realistic range ofseismic ground excitations is probabilistic evaluation isonly possible when a large variation of seismic demands isconsidered so that ample variation in the dynamic structuralresponse can be obtained e vulnerability assessment re-quires the definition of specific limit states damage indicatorsand seismic intensity indicators e impending sectionsaddress all the requirements to develop fragility curvesConsequently fragility curves are developed for the selectedtypology to elucidate the established framework

61 Damage Indicator and the Definition of Limit Statese derivation of analytical fragility curves requires thedefinition of specific limit states in both terms ie

8 Advances in Civil Engineering

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Peak

gro

und

acce

lera

tion

(g)

05 1 15 2 25 3 35 4 45 5 550Maximum global drift ()

(a)

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Spec

tral

acce

lera

tion

(T1)

05 1 15 2 250Maximum global drift ()

(b)

Figure 6 IDA curves (a) maximum global drift vs PGA (b) maximum global drift vs spectral acceleration scaled at the fundamental timeperiod of the structure (Sa(T1))

0 02 04 06 08 1 12 14PGA (g)

0

1

2

3

4

5

Glo

bal d

ri (

)

(a)

0

05

1

15

2

25

3

0 02 04 06 08 1 12 14

Glo

bal d

ri (

)

Sa(T1)

(b)

Figure 7 Hazard-damage relationships (a) PGA vs global drift in percentage (b) Sa(T1) vs global drift in percentage

Advances in Civil Engineering 9

qualitative and quantitative For this purpose a researcherhas to employ a specific damage indicator also known asengineering demand parameter (EDP) or may also propose anew damage measure that can represent the structuraldamage in a rational manner to correlate the damage withseismic loading Once the damage indicator has been set orselected different limit states often known as the damagestates of a structure may be defined

Damage states represent a physical categorization ofdamages by using damage indices which suggest thresholdlimits for different damage states by relaying upon theparameters of structural behavior eg energy dissipationcapability ductility and strength Damage indices are usedfor correlating the accumulated damage with differentspecific damage states and numerous nonidentical damageindices may exist for the same structure For instance Khanet al [44] used global displacement of the structure tocharacterize the structural damage Crowley et al [45]considered damage limit states based on the strain levels inconcrete and steel Guneyisi and Altay [46] considered theinterstory drift ratio for representing the response pa-rameter corresponding to the four damage states takenfrom the HAZUS Casotto et al [47] considered themember flexural strength to characterize the first limit state(LS1) when the reinforcement steel yields in the columnsand 3 interstory drift for flexural collapse limit state(LS2) and subsequently related his LS2 with the loss ofsupport of the beam Chaulagain et al [48] and Gautamet al [49] used 3 damage states ranging from slight damageto complete collapse and developed empirical fragilityrelationships for buildings in Nepal ey further relatedtheir results with FEMA356 [50] classifications for buildingdamage levels

Since this study primarily relates with the generation offragilities for a specific building stock it would not bepractical to define damage or limit states depending uponthe member behavior or local strains In the current studythe global drift ratio has been considered as the damageindicator to correlate with the structural damage

ree damage states namely serviceability limit state(LS1) damage control limit state (LS2) and collapseprevention (LS3) are qualitatively defined in this studyLS1 corresponds with the 1st yield of longitudinal steelreinforcement in the structure Conventionally the firstlimit states are usually related with the formation of the firsthinge in the structure but since the current study employsnonlinear fibers to model the structure therefore the LS1primarily describes the yielding strain reaching in astructural element located anywhere in the structure edeformation and strength govern the LS2 It is defined as75 of LS3 e LS3 collapse prevention is generallydirected by the deformation Altug [51] defined the collapseprevention limit state as 75 of ultimate structural de-formation or the value for which more than 20 strengthdrop can be observed relative to the maximum strengthvalue e smaller of these two values would govern theLS3

e mathematical quantification for these damage statescould not be adopted from the previous research as there

exists no analogous research for Pakistanrsquos constructionindustry or for Pakistanrsquos seismic zone 4 In the currentstudy the mathematical values are assigned to each of thediscrete damage state by using the capacity curve of theselected structure However the obtained values were ap-proximately similar to those obtained by Altug [51] whichused the low-rise buildings of the Turkish region in theirresearch thus the obtained values amply represent the low-rise structural behavior e mathematical values for each ofthe considered damage state against the global drift arepresented in Table 5

62 Fragility Assessment for the School Buildings Seismicfragility curves are widely employed to obtain an articu-lated insight of structural performance against seismicloads and they represent the probability of entering orexceeding different damage states for considered in-tensities of ground shaking After attaining the structuralresponse established limit state definitions are applied forevaluating the structural performance for each limit stateOnce the computed value comes out to be greater than alimit statersquos value an event shall be counted within thesample comprising all the ground motions scalesereby for each IM direct sampling probabilities overthe 20 selected ground motions on all incrementing scaleswere obtained

It is a commonly accepted assumption that for a fragilitycurve a lognormal cumulative distribution function can beconveniently utilized for the representation of conditionalprobabilities [52ndash54] From viewpoint of literature log-normal distribution was also assumed and used for theregression of fragility relationships as mentioned in thefollowing equation

P(LS | IM) ϕln IM minus λc

βc1113888 1113889 (2)

where P(LS | IM) describes the probability of exceedance ofa particular LS given an IM value ϕ represents the standardnormal cumulative distribution function (CDF)

e controlling parameters λc and βc represent themedian point and the slope of the curve respectively It isimperative to evaluate their optimized values for a best fit ofCDF against the calculated probabilities Shinozuka et al[53] Dang et al [54] and Baker [55] stated that the max-imum likelihood method (MLM) is one of the most suitablemethod to achieve best possible values of these two pa-rameters In the current study MLM is utilized to obtain themedian point and the slope of the fragility curve Formultiple IM levels as considered in this study the likelihoodfunction is given as follows

Likelihood 1113945m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠ϕln IMiλc( 1113857

βc1113888 1113889

zj

1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 1113889

njminus zj

(3)

wherem is the number of IM levels andΠ denotes a productover all levels It is assumed that the observation of attaininga specific limit state from each ground motion is

10 Advances in Civil Engineering

independent of the observations from other ground mo-tions In the above equation zj denotes the number ofattaining particular limit state out of nj ground motions witha particular value of IM IMie fragility curve parameterscan be obtained by maximizing the likelihood function inEquation (3) as given in following equation

λc βc1113864 1113865 argmaxλc βc 1113944

m

j1ln

nj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnϕln IMiλ( 1113857c

βc1113888 1113889

⎧⎪⎨

⎪⎩

+ nj minus zj1113872 1113873ln 1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 11138891113897

(4)

A MATLAB code was written to control the maximi-zation of the likelihood function so that optimum values ofthese two parameters can be obtained for establishingseismic fragility

Figure 8 presents the developed fragility relationships forthe considered typology of the RC school building in seismiczone 4 of Pakistan Each portion of Figure 8 contains threefragility relationships correlating with each limit stateagainst both of the IMs ie PGA and Sa(T1) Directsampling probabilities obtained from the IDA are alsoplotted in Figure 8 along with lognormally fitted fragilityfunctions

Table 6 provides the simulated values for λc and βc foreach limit state against each IM for the derivation of fragilitycurves

7 Conclusion

Pakistan has numerous seismotectonically active regionsincluding Muzaffarabad and past earthquakes especially the2005 Kashmir earthquake have proven this fact In thisstudy a new database of RC school buildings constructed inMuzaffarabad district after 2005 earthquake has beenpresented Subsequently the structural vulnerability of aspecific category of RC school buildings is assessed andpresented by using IDA so that practicing engineers atdomestic and regional level can further extend the evalua-tion to other categories of RC buildings e procedurepresented utilizes the fiber-based model which is the mostreliable at present In the current study both PGA andSa(T1) have been used to characterize the seismic intensityough Sa(T1) is a more appropriate IM PGA has beeneasily understandable with the normal public therefore thefragility relationships have also been developed using thePGA as an IM At the PGA of 06 g there exists

Table 5 Limit state criteria for the considered building typology

Buildingmodel nameDamagelimit state (based of global drift )

Serviceability (LS1) Damage control (LS2) Collapse prevention (LS3)BLR-11 035 066 089

Table 6 Lognormal distribution parameters for fragilities againstPGA and Sa(T1) for the considered school building typology

Fragilityparameter

Serviceability(LS1)

Damagecontrol (LS2)

Collapseprevention

(LS3)PGA Sa(T1) PGA Sa(T1) PGA Sa(T1)

λc 04842 08908 07156 13094 0957 18399βc 0327 03266 01974 02606 01742 03353

LS1-lognormalLS2-lognormalLS3-lognormal

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty

LS3 directLS2 directLS1 direct

02 04 06 08 1 12 140PGA (g)

(a)

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty02 04 06 08 1 12 140

Sa(T1)

LS1-lognormalLS2-lognormalLS3-lognormalLS3 direct

LS2 directLS1 direct

(b)

Figure 8 Derived fragility relationships for all IMs (a) seismic fragility for PGA (b) seismic fragility for Sa(T1)

Advances in Civil Engineering 11

approximately 82 probability of exceedance for the firstlimit state (LS1) while only around 20 probability ofexceedance has been achieved against the same seismicintensity for the second limit state (LS2) is essentiallyindicates the structural behavior dominated by the yieldingof the members instead of their complete failures At theseismic intensity of 140 g of PGA the structure seems to bein LS3 with almost around 100 of probability while whenSa(T1) is used as an IM the probability of being in LS3 at theseismic intensity of 140 g remains only around 20 isspecific variation in structural behavior is primarily attrib-uted to the inherent structural characteristics ie stiffnessand ductility that influence the response when the spectralacceleration is used as an IM after being scaled at thefundamental time period of the structure Since the selectedstructure is engineered the results are not so admonishingfor the considered school building typology neverthelessthe results might not be encouraging for other schoolbuilding types in the presented database e presentedconsolidated procedure is relatively simple and can bereadily adopted by the domestic and regional disaster pre-paredness and mitigation agencies to extend the applicationSuch studies are relatively new for under developingcountries like Pakistan and contemporarily no other workexists that may specifically address the vulnerability ofschools in seismic zone 4 of Pakistan Assessment of vul-nerabilities for other types of school buildings may yield aneed for immediate intervention in order to safeguard thelife of students and other users e presented study isspecifically targeted to assess the vulnerability and does notaddress the assessment of risk therefore the developedfragility curves can be further integrated with the hazardcurves of the considered area to evaluate the total riskinvolved

Data Availability

e data used to support the findings of this study are in-cluded within the article Any other data used to support thefindings of this study may be released upon request to theauthor(s) who can be contacted at musmankaistackr

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] M Zain M Usman S H Farooq and A Hanif ldquoProgressivestructural capacity loss assessmentmdasha framework for modernreinforced concrete buildingsrdquo PLoS One vol 13 no 12Article ID e0208149 2018

[2] Report from earthquake engineering research Institute (ERRI)httpswwweeriorglfepdfkashmir_eeri_2nd_reportpdf

[3] Government of Pakistan Building Code of Pakistan PakistanEngineering Council Government of Pakistan IslamabadPakistan 2007

[4] D Bonowitz Seismic Design in Pakistan Be Building CodesBylaws and Recommendations for Earthquake Risk Reduction

United Nations Development Programme New York NYUSA 2015

[5] C Xu J Deng S Peng and C Li ldquoSeismic fragility analysis ofsteel reinforced concrete frame structures based on differentengineering demand parametersrdquo Journal of Building Engi-neering vol 20 pp 736ndash749 2018

[6] J Ji A S Elnashai and D A Kuchma ldquoAn analyticalframework for seismic fragility analysis of RC high-risebuildingsrdquo Engineering Structures vol 29 no 12 pp 3197ndash3209 2007

[7] M Zain N Anwar F A Najam and T Mehmood ldquoSeismicfragility assessment of reinforced concrete high-rise buildingsusing the uncoupled modal response history analysis(UMRHA)rdquo in Proceedings of the International Conference onEarthquake Engineering and Structural Dynamics ReykjavikIceland June 2017

[8] A Ali T Sandhu and M Usman ldquoAmbient vibration testingof a pedestrian bridge using low-cost accelerometers for SHMapplicationsrdquo Smart Cities vol 2 no 1 pp 20ndash30 2019

[9] Y Pang X Wu G Shen and W Yuan ldquoSeismic fragilityanalysis of cable-stayed bridges considering different sourcesof uncertaintiesrdquo Journal of Bridge Engineering vol 19 no 4Article ID 04013015 2014

[10] A Rasheed S H Farooq M Usman A Hanif N A Khanand R A Khushnood ldquoStructural reliability analysis of su-perstructure of highway bridges on China-Pakistan economiccorridor (CPEC) a case studyrdquo Journal of Structural Integrityand Maintenance vol 3 no 3 pp 197ndash207 2018

[11] J-T Wang M-X Zhang A-Y Jin and C-H ZhangldquoSeismic fragility of arch dams based on damage analysisrdquo SoilDynamics and Earthquake Engineering vol 109 pp 58ndash682018

[12] Y Yazdani and M Alembagheri ldquoSeismic vulnerability ofgravity dams in near-fault areasrdquo Soil Dynamics and Earth-quake Engineering vol 102 pp 15ndash24 2017

[13] S Leonidas and A Kappos ldquoDerivation of fragility curves fortraditional timber-framed masonry buildings using nonlinearstatic analysisrdquo in Proceedings of the 4th International Con-ference on Computational Methods in Structural Dynamicsand Earthquake Engineering Kos Island Greece June 2013

[14] J Alam M S Islam M Hussan and A Sarraz ldquoSeismicfragility assessment of RC building using nonlinear staticpushover analysisrdquo in Proceedings of the International Con-ference on Planning Architecture and Civil Engineering(ICPAC) Rajshahi India February 2017

[15] M Ni Choine M M Kashani L N Lowes et al ldquoNonlineardynamic analysis and seismic fragility assessment of a cor-rosion damaged integral bridgerdquo International Journal ofStructural Integrity vol 7 no 2 pp 227ndash239 2016

[16] K Bakalis and D Vamvatsikos ldquoSeismic fragility functions vianonlinear response history analysisrdquo Journal of StructuralEngineering vol 144 no 10 Article ID 04018181 2018

[17] FEMA Rapid Visual Screening of Buildings for PotentialSeismic Hazards A Handbook Federal Emergency Manage-ment Agency (FEMA) Washington DC USA third edition2015

[18] FEMA Technical and Userrsquos Manual HAZUSndashMH 21 De-partment of Homeland Security Federal Emergency Man-agement Agency (FEMA) Washington DC USA

[19] User Guide Perform 3D Nonlinear Analysis and PerformanceAssessment for 3D Structures Computers and Structures IncBerkeley CA USA 2011

[20] M M Rafi and M M Nasir ldquoExperimental investigation ofchemical and physical properties of cements manufactured in

12 Advances in Civil Engineering

that during each iteration of the analysis the accelerationsincrease at specific intended intervals e current studyutilizes the IDA for considering various levels of seismicintensity to predict the structural response against earth-quakes ranging from 02 g to 14 g with 020 g as theaugmenting acceleration for each successive iteration thusat this stage it is imperative to select the appropriateseismic intensity measure (IM) for representation ofseismic Subsequent subsection addresses the selection ofIM in the current study Apart from selecting the IM theremust also be a damage indicator that can amply relate theseismic IM with the observed structural damage As de-scribed earlier the current study employs global drift as thedamage indicator and the details have been given inSection 61

51 Seismic Intensity Measure Seismic intensity measure(IM) correlates the ground motion with the structuraldamage hence any IM employed must be rationally able toproject the dynamic response of the structure by the virtue ofthe damage indicator PGA is one of the IMs that has beenfrequently used by the experts for fragility derivations but itis generally comprehended that Sa is a better option as an IMto correlate with the structural damage as it actually rep-resents the effect of ground shaking on the building itselfPang and Wu [30] and Jiang et al [31] employed PGA fortheir researches Apart from the PGA Omine et al [32] andEden et al [33] used peak ground velocity (PGV) as an IM

Eden et al [33] also used Sa at the fundamental period of thestructure as an IM Frankie et al [34] and Choudhury andKaushik [35] utilized spectral displacement (Sd) as IM fortheir study on open ground story RC frames with openingsin walls during the vulnerability assessment Buratti [36]analyzed the sufficiency and the efficiency of numerous IMsas indicated in their study and employed the cloud analysistechnique for 1704 unscaled accelerograms Bojorquez et al[37] proposed a procedure to obtain the interstory driftdemands for midrise frame structures in terms of a spectral-shape-based IM (INp

) and eventually concluded that INpwas

the best parameter to relate with the structural response offrames with 4 6 8 and 10 stories under the narrow-bandground motions in Europe Some other vector-valued in-tensity measures have also been proposed and discussed byModica and Stafford [38] Baker and Cornell [39] Polsakand Nicolas [40] and Kohrangi et al [41] Bojorquez andIervolino [42] also performed their research to establish avector-based IM however their research also proposed ascalar-based IM as they apprehended that the use of thescalar-based IM is easier than the vector-based IM forpractical purposes

Pejovic and Jankovic [43] investigated different groundmotion IMs which are conventionally used to investigate thedynamic behavior and concluded that despite being the mostcommon IM PGA provided the greatest dispersion in re-sults in comparison with the PGV Sa(T1) Sv(T1) and Sd(T1) e research portrayed spectral response velocity valueSv(T1) as the most efficient IM for the RC frames while

Table 4 Selected natural ground motions

Sr No Earthquake name Year Station name Mag PGA (g) Rrup (KMs) Vs30 (msec)1 San Fernando 1971 LA - hollywood stor FF 661 0225 2277 316462 Gazli USSR 1976 Karakyr 68 0864 547 259593 Tabas Iran 1978 Boshrooyeh 735 0106 2879 324574 Spitak Armenia 1988 Gukasian 677 020 240 343535 Loma Prieta 1989 Agnews State Hospital 693 01695 2457 239696 Loma Prieta 1989 Saratoga-W Valley Coll 693 0331 930 347907 Northridge-01 1994 Arleta-Nordhoff fire station 669 0345 866 297718 Northridge-01 1994 N Hollywood - coldwater can 669 0309 1251 326479 Chi-Chi Taiwan 1999 CHY002 762 0137 2496 2351310 Chi-Chi Taiwan 1999 CHY036 762 0273 1604 2331411 Chi-Chi Taiwan 1999 TCU038 762 01448 2542 2978612 Chi-Chi Taiwan 1999 TCU059 762 0165 1711 2726713 Chi-Chi Taiwan 1999 TCU110 762 01918 1157 2127214 Kashmir earthquake 1999 ABD-Abbottabad 760 02517 260 2230415 St Elias Alaska 1979 Icy Bay 754 01759 2645 3063716 Niigata Japan 2004 NIG017 663 04764 1281 2741717 Montenegro Yugoslavia 1979 Ulcinj-Hotel Olimpic 71 02928 576 3187418 Chuetsu-oki Japan 2007 Joetsu Kita 68 0176 2945 334019 Iwate Japan 2008 IWT011 69 02194 843 2793620 Iwate Japan 2008 Kitakami Yanagihara 69 02057 1667 34898

Table 3 Material strengths and loading values used for the structural modelling

Materials LoadsCharacteristics Strength Units Name Value UnitsConcretersquos strength (fcprime) 21 MPa Live 26 kNm2

Reinforcing steelrsquos yielding stress (fy) 275 MPa Infill-partitioning 43 kNm

Advances in Civil Engineering 7

stating the other two spectral response parameters ieSa(T1) and Sd(T1) were similarly adequate as they in-corporated the dynamic characteristics of the consideredstructure e current study chooses both ie PGA andspectral acceleration at the fundamental time period (Sa(T1))of the structure as intensity measures As indicated by theprevious literature provided by Jelena and Srdjan [43] PGAis the most commonly employed IM which is easy to un-derstand for normal people with no specific engineeringbackground while Sa(T1) incorporates the structural char-acteristics during the execution of analyses

52 Results of IDA Figure 6 shows the results of IDA in theform of plots between global drift and the selected IMs ieincrementally scaled PGA and Sa(T1) from 020 g to 14 g Itcan be observed that intrinsic nature of different groundmotions produces different results despite of having thesame intensity of acceleration at a given pointere are total20 curves in each part of Figure 6 while each curve char-acterizes structural damage indicated by global drift causedby the single corresponding earthquake at discretely con-sidered seismic intensity levels ranging from 02 g to 14 g

In Figure 6(a) the curves manifest the maximum globaldrift ranging from 020 to more than 50 when PGA isused to indicate seismic intensity While in Figure 6(b)when Sa(T1) is used to characterize the seismic intensity themaximum global drift reaches 247 against the Sa of 14 gthe maximum considered in this study

e results of IDA indicate that intrinsic properties ofground motions project substantial sensitivities to theseismic demand e disparity in the structural responseagainst different ground motions of the same intensities isprimarily attributed to differences in the inherent nature ofground motions ie energy distribution over frequencycontent and duration that predominantly affects thestructural response Moreover when Sa(T1) is used as anindicator of the seismic intensity the global drift observeslower values because of the scaling of the ground motions atthe fundamental period of the structure which is directlyrelated with the structural inertia and stiffness

6 Vulnerability Assessment

e fundamental process of the risk assessment against anyhazard consists of two parts ie the hazard and the vul-nerability of structural systems to that hazard For earth-quakes the first portion is primarily concerned withseismologists who can provide a realistic estimate of thepotential seismic hazard that can hit a specific geographicalarea while the second part vulnerability is usuallyaddressed by the engineers and experts who design thefacilities for versatile purposes e current study is relatedwith the second part and assesses the vulnerability of theconsidered typology of school buildings by establishing thehazard-damage relationships for the considered typology ofstructures and subsequently by developing the genericfragility relationships Hazard-damage relationships depictthe structural performance against seismic excitations and

exhibit the dynamic response for all considered groundmotion intensities Figures 7(a) and 7(b) present a directrelationship between the seismic intensities and the struc-tural damage e structural damage is quantified using theglobal response and seismic intensities are provided in-crementally in terms of PGA as well as in terms of spectralacceleration at the fundamental modersquos time period Everysingle dot in each part of Figure 7 represents the maximumvalue of the global drift in terms of percentage against aspecific earthquake scaled at a specific intensity For in-stance at the seismic intensity of 14 g there are 20 dots fromall 20 ground motions indicating the uncertainty in thestructural response by depicting that one earthquake havingthe seismic intensity of 14 g produces global drift less than1 while some other earthquake with the same seismicintensity produces more than 5 of global drift

With increasing intensity of PGA from 020 g to 080 gin Figure 7(a) the global drift remains between 009 and119 While at higher PGA levels from 10 g to 14 g theglobal drift drastically remains between 044 and 516 forall the considered ground motions At the maximum con-sidered PGA of 140 g the global drift varies from 097 to516 for all 20 ground motions All this disparity in thestructural response arises because of the inherent charac-teristics of ground motions which vary from record to re-cord thus instigating different response against the samescaled intensity level

When Sa(T1) is used for representing seismic intensitythe global drift varied between 022 and 24 at the Sa of140 g as shown by Figure 7(b) e dotted line inFigures 7(a) and 7(b) shows the mean structural responseobtained at each intensity level

On the other hand the fragility curve as described byEquation (1) represents a conditional probability ofexceedance for specific damage or limit states of a structureagainst a particular seismic intensity given in terms of PGASa or some other seismic intensity describing the indicator

Pfragility P[LS | IM x] (1)

e aforementioned equation describes the conditionalprobability Pfragility of achieving or exceeding a specific limitstate LS when seismic intensity defined by a particularintensity measure (IM) is equal to ldquoxrdquo Fragility relationshipsfor different damage states must be probabilistically able topredict the structural vulnerability against a realistic range ofseismic ground excitations is probabilistic evaluation isonly possible when a large variation of seismic demands isconsidered so that ample variation in the dynamic structuralresponse can be obtained e vulnerability assessment re-quires the definition of specific limit states damage indicatorsand seismic intensity indicators e impending sectionsaddress all the requirements to develop fragility curvesConsequently fragility curves are developed for the selectedtypology to elucidate the established framework

61 Damage Indicator and the Definition of Limit Statese derivation of analytical fragility curves requires thedefinition of specific limit states in both terms ie

8 Advances in Civil Engineering

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Peak

gro

und

acce

lera

tion

(g)

05 1 15 2 25 3 35 4 45 5 550Maximum global drift ()

(a)

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Spec

tral

acce

lera

tion

(T1)

05 1 15 2 250Maximum global drift ()

(b)

Figure 6 IDA curves (a) maximum global drift vs PGA (b) maximum global drift vs spectral acceleration scaled at the fundamental timeperiod of the structure (Sa(T1))

0 02 04 06 08 1 12 14PGA (g)

0

1

2

3

4

5

Glo

bal d

ri (

)

(a)

0

05

1

15

2

25

3

0 02 04 06 08 1 12 14

Glo

bal d

ri (

)

Sa(T1)

(b)

Figure 7 Hazard-damage relationships (a) PGA vs global drift in percentage (b) Sa(T1) vs global drift in percentage

Advances in Civil Engineering 9

qualitative and quantitative For this purpose a researcherhas to employ a specific damage indicator also known asengineering demand parameter (EDP) or may also propose anew damage measure that can represent the structuraldamage in a rational manner to correlate the damage withseismic loading Once the damage indicator has been set orselected different limit states often known as the damagestates of a structure may be defined

Damage states represent a physical categorization ofdamages by using damage indices which suggest thresholdlimits for different damage states by relaying upon theparameters of structural behavior eg energy dissipationcapability ductility and strength Damage indices are usedfor correlating the accumulated damage with differentspecific damage states and numerous nonidentical damageindices may exist for the same structure For instance Khanet al [44] used global displacement of the structure tocharacterize the structural damage Crowley et al [45]considered damage limit states based on the strain levels inconcrete and steel Guneyisi and Altay [46] considered theinterstory drift ratio for representing the response pa-rameter corresponding to the four damage states takenfrom the HAZUS Casotto et al [47] considered themember flexural strength to characterize the first limit state(LS1) when the reinforcement steel yields in the columnsand 3 interstory drift for flexural collapse limit state(LS2) and subsequently related his LS2 with the loss ofsupport of the beam Chaulagain et al [48] and Gautamet al [49] used 3 damage states ranging from slight damageto complete collapse and developed empirical fragilityrelationships for buildings in Nepal ey further relatedtheir results with FEMA356 [50] classifications for buildingdamage levels

Since this study primarily relates with the generation offragilities for a specific building stock it would not bepractical to define damage or limit states depending uponthe member behavior or local strains In the current studythe global drift ratio has been considered as the damageindicator to correlate with the structural damage

ree damage states namely serviceability limit state(LS1) damage control limit state (LS2) and collapseprevention (LS3) are qualitatively defined in this studyLS1 corresponds with the 1st yield of longitudinal steelreinforcement in the structure Conventionally the firstlimit states are usually related with the formation of the firsthinge in the structure but since the current study employsnonlinear fibers to model the structure therefore the LS1primarily describes the yielding strain reaching in astructural element located anywhere in the structure edeformation and strength govern the LS2 It is defined as75 of LS3 e LS3 collapse prevention is generallydirected by the deformation Altug [51] defined the collapseprevention limit state as 75 of ultimate structural de-formation or the value for which more than 20 strengthdrop can be observed relative to the maximum strengthvalue e smaller of these two values would govern theLS3

e mathematical quantification for these damage statescould not be adopted from the previous research as there

exists no analogous research for Pakistanrsquos constructionindustry or for Pakistanrsquos seismic zone 4 In the currentstudy the mathematical values are assigned to each of thediscrete damage state by using the capacity curve of theselected structure However the obtained values were ap-proximately similar to those obtained by Altug [51] whichused the low-rise buildings of the Turkish region in theirresearch thus the obtained values amply represent the low-rise structural behavior e mathematical values for each ofthe considered damage state against the global drift arepresented in Table 5

62 Fragility Assessment for the School Buildings Seismicfragility curves are widely employed to obtain an articu-lated insight of structural performance against seismicloads and they represent the probability of entering orexceeding different damage states for considered in-tensities of ground shaking After attaining the structuralresponse established limit state definitions are applied forevaluating the structural performance for each limit stateOnce the computed value comes out to be greater than alimit statersquos value an event shall be counted within thesample comprising all the ground motions scalesereby for each IM direct sampling probabilities overthe 20 selected ground motions on all incrementing scaleswere obtained

It is a commonly accepted assumption that for a fragilitycurve a lognormal cumulative distribution function can beconveniently utilized for the representation of conditionalprobabilities [52ndash54] From viewpoint of literature log-normal distribution was also assumed and used for theregression of fragility relationships as mentioned in thefollowing equation

P(LS | IM) ϕln IM minus λc

βc1113888 1113889 (2)

where P(LS | IM) describes the probability of exceedance ofa particular LS given an IM value ϕ represents the standardnormal cumulative distribution function (CDF)

e controlling parameters λc and βc represent themedian point and the slope of the curve respectively It isimperative to evaluate their optimized values for a best fit ofCDF against the calculated probabilities Shinozuka et al[53] Dang et al [54] and Baker [55] stated that the max-imum likelihood method (MLM) is one of the most suitablemethod to achieve best possible values of these two pa-rameters In the current study MLM is utilized to obtain themedian point and the slope of the fragility curve Formultiple IM levels as considered in this study the likelihoodfunction is given as follows

Likelihood 1113945m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠ϕln IMiλc( 1113857

βc1113888 1113889

zj

1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 1113889

njminus zj

(3)

wherem is the number of IM levels andΠ denotes a productover all levels It is assumed that the observation of attaininga specific limit state from each ground motion is

10 Advances in Civil Engineering

independent of the observations from other ground mo-tions In the above equation zj denotes the number ofattaining particular limit state out of nj ground motions witha particular value of IM IMie fragility curve parameterscan be obtained by maximizing the likelihood function inEquation (3) as given in following equation

λc βc1113864 1113865 argmaxλc βc 1113944

m

j1ln

nj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnϕln IMiλ( 1113857c

βc1113888 1113889

⎧⎪⎨

⎪⎩

+ nj minus zj1113872 1113873ln 1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 11138891113897

(4)

A MATLAB code was written to control the maximi-zation of the likelihood function so that optimum values ofthese two parameters can be obtained for establishingseismic fragility

Figure 8 presents the developed fragility relationships forthe considered typology of the RC school building in seismiczone 4 of Pakistan Each portion of Figure 8 contains threefragility relationships correlating with each limit stateagainst both of the IMs ie PGA and Sa(T1) Directsampling probabilities obtained from the IDA are alsoplotted in Figure 8 along with lognormally fitted fragilityfunctions

Table 6 provides the simulated values for λc and βc foreach limit state against each IM for the derivation of fragilitycurves

7 Conclusion

Pakistan has numerous seismotectonically active regionsincluding Muzaffarabad and past earthquakes especially the2005 Kashmir earthquake have proven this fact In thisstudy a new database of RC school buildings constructed inMuzaffarabad district after 2005 earthquake has beenpresented Subsequently the structural vulnerability of aspecific category of RC school buildings is assessed andpresented by using IDA so that practicing engineers atdomestic and regional level can further extend the evalua-tion to other categories of RC buildings e procedurepresented utilizes the fiber-based model which is the mostreliable at present In the current study both PGA andSa(T1) have been used to characterize the seismic intensityough Sa(T1) is a more appropriate IM PGA has beeneasily understandable with the normal public therefore thefragility relationships have also been developed using thePGA as an IM At the PGA of 06 g there exists

Table 5 Limit state criteria for the considered building typology

Buildingmodel nameDamagelimit state (based of global drift )

Serviceability (LS1) Damage control (LS2) Collapse prevention (LS3)BLR-11 035 066 089

Table 6 Lognormal distribution parameters for fragilities againstPGA and Sa(T1) for the considered school building typology

Fragilityparameter

Serviceability(LS1)

Damagecontrol (LS2)

Collapseprevention

(LS3)PGA Sa(T1) PGA Sa(T1) PGA Sa(T1)

λc 04842 08908 07156 13094 0957 18399βc 0327 03266 01974 02606 01742 03353

LS1-lognormalLS2-lognormalLS3-lognormal

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty

LS3 directLS2 directLS1 direct

02 04 06 08 1 12 140PGA (g)

(a)

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty02 04 06 08 1 12 140

Sa(T1)

LS1-lognormalLS2-lognormalLS3-lognormalLS3 direct

LS2 directLS1 direct

(b)

Figure 8 Derived fragility relationships for all IMs (a) seismic fragility for PGA (b) seismic fragility for Sa(T1)

Advances in Civil Engineering 11

approximately 82 probability of exceedance for the firstlimit state (LS1) while only around 20 probability ofexceedance has been achieved against the same seismicintensity for the second limit state (LS2) is essentiallyindicates the structural behavior dominated by the yieldingof the members instead of their complete failures At theseismic intensity of 140 g of PGA the structure seems to bein LS3 with almost around 100 of probability while whenSa(T1) is used as an IM the probability of being in LS3 at theseismic intensity of 140 g remains only around 20 isspecific variation in structural behavior is primarily attrib-uted to the inherent structural characteristics ie stiffnessand ductility that influence the response when the spectralacceleration is used as an IM after being scaled at thefundamental time period of the structure Since the selectedstructure is engineered the results are not so admonishingfor the considered school building typology neverthelessthe results might not be encouraging for other schoolbuilding types in the presented database e presentedconsolidated procedure is relatively simple and can bereadily adopted by the domestic and regional disaster pre-paredness and mitigation agencies to extend the applicationSuch studies are relatively new for under developingcountries like Pakistan and contemporarily no other workexists that may specifically address the vulnerability ofschools in seismic zone 4 of Pakistan Assessment of vul-nerabilities for other types of school buildings may yield aneed for immediate intervention in order to safeguard thelife of students and other users e presented study isspecifically targeted to assess the vulnerability and does notaddress the assessment of risk therefore the developedfragility curves can be further integrated with the hazardcurves of the considered area to evaluate the total riskinvolved

Data Availability

e data used to support the findings of this study are in-cluded within the article Any other data used to support thefindings of this study may be released upon request to theauthor(s) who can be contacted at musmankaistackr

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] M Zain M Usman S H Farooq and A Hanif ldquoProgressivestructural capacity loss assessmentmdasha framework for modernreinforced concrete buildingsrdquo PLoS One vol 13 no 12Article ID e0208149 2018

[2] Report from earthquake engineering research Institute (ERRI)httpswwweeriorglfepdfkashmir_eeri_2nd_reportpdf

[3] Government of Pakistan Building Code of Pakistan PakistanEngineering Council Government of Pakistan IslamabadPakistan 2007

[4] D Bonowitz Seismic Design in Pakistan Be Building CodesBylaws and Recommendations for Earthquake Risk Reduction

United Nations Development Programme New York NYUSA 2015

[5] C Xu J Deng S Peng and C Li ldquoSeismic fragility analysis ofsteel reinforced concrete frame structures based on differentengineering demand parametersrdquo Journal of Building Engi-neering vol 20 pp 736ndash749 2018

[6] J Ji A S Elnashai and D A Kuchma ldquoAn analyticalframework for seismic fragility analysis of RC high-risebuildingsrdquo Engineering Structures vol 29 no 12 pp 3197ndash3209 2007

[7] M Zain N Anwar F A Najam and T Mehmood ldquoSeismicfragility assessment of reinforced concrete high-rise buildingsusing the uncoupled modal response history analysis(UMRHA)rdquo in Proceedings of the International Conference onEarthquake Engineering and Structural Dynamics ReykjavikIceland June 2017

[8] A Ali T Sandhu and M Usman ldquoAmbient vibration testingof a pedestrian bridge using low-cost accelerometers for SHMapplicationsrdquo Smart Cities vol 2 no 1 pp 20ndash30 2019

[9] Y Pang X Wu G Shen and W Yuan ldquoSeismic fragilityanalysis of cable-stayed bridges considering different sourcesof uncertaintiesrdquo Journal of Bridge Engineering vol 19 no 4Article ID 04013015 2014

[10] A Rasheed S H Farooq M Usman A Hanif N A Khanand R A Khushnood ldquoStructural reliability analysis of su-perstructure of highway bridges on China-Pakistan economiccorridor (CPEC) a case studyrdquo Journal of Structural Integrityand Maintenance vol 3 no 3 pp 197ndash207 2018

[11] J-T Wang M-X Zhang A-Y Jin and C-H ZhangldquoSeismic fragility of arch dams based on damage analysisrdquo SoilDynamics and Earthquake Engineering vol 109 pp 58ndash682018

[12] Y Yazdani and M Alembagheri ldquoSeismic vulnerability ofgravity dams in near-fault areasrdquo Soil Dynamics and Earth-quake Engineering vol 102 pp 15ndash24 2017

[13] S Leonidas and A Kappos ldquoDerivation of fragility curves fortraditional timber-framed masonry buildings using nonlinearstatic analysisrdquo in Proceedings of the 4th International Con-ference on Computational Methods in Structural Dynamicsand Earthquake Engineering Kos Island Greece June 2013

[14] J Alam M S Islam M Hussan and A Sarraz ldquoSeismicfragility assessment of RC building using nonlinear staticpushover analysisrdquo in Proceedings of the International Con-ference on Planning Architecture and Civil Engineering(ICPAC) Rajshahi India February 2017

[15] M Ni Choine M M Kashani L N Lowes et al ldquoNonlineardynamic analysis and seismic fragility assessment of a cor-rosion damaged integral bridgerdquo International Journal ofStructural Integrity vol 7 no 2 pp 227ndash239 2016

[16] K Bakalis and D Vamvatsikos ldquoSeismic fragility functions vianonlinear response history analysisrdquo Journal of StructuralEngineering vol 144 no 10 Article ID 04018181 2018

[17] FEMA Rapid Visual Screening of Buildings for PotentialSeismic Hazards A Handbook Federal Emergency Manage-ment Agency (FEMA) Washington DC USA third edition2015

[18] FEMA Technical and Userrsquos Manual HAZUSndashMH 21 De-partment of Homeland Security Federal Emergency Man-agement Agency (FEMA) Washington DC USA

[19] User Guide Perform 3D Nonlinear Analysis and PerformanceAssessment for 3D Structures Computers and Structures IncBerkeley CA USA 2011

[20] M M Rafi and M M Nasir ldquoExperimental investigation ofchemical and physical properties of cements manufactured in

12 Advances in Civil Engineering

stating the other two spectral response parameters ieSa(T1) and Sd(T1) were similarly adequate as they in-corporated the dynamic characteristics of the consideredstructure e current study chooses both ie PGA andspectral acceleration at the fundamental time period (Sa(T1))of the structure as intensity measures As indicated by theprevious literature provided by Jelena and Srdjan [43] PGAis the most commonly employed IM which is easy to un-derstand for normal people with no specific engineeringbackground while Sa(T1) incorporates the structural char-acteristics during the execution of analyses

52 Results of IDA Figure 6 shows the results of IDA in theform of plots between global drift and the selected IMs ieincrementally scaled PGA and Sa(T1) from 020 g to 14 g Itcan be observed that intrinsic nature of different groundmotions produces different results despite of having thesame intensity of acceleration at a given pointere are total20 curves in each part of Figure 6 while each curve char-acterizes structural damage indicated by global drift causedby the single corresponding earthquake at discretely con-sidered seismic intensity levels ranging from 02 g to 14 g

In Figure 6(a) the curves manifest the maximum globaldrift ranging from 020 to more than 50 when PGA isused to indicate seismic intensity While in Figure 6(b)when Sa(T1) is used to characterize the seismic intensity themaximum global drift reaches 247 against the Sa of 14 gthe maximum considered in this study

e results of IDA indicate that intrinsic properties ofground motions project substantial sensitivities to theseismic demand e disparity in the structural responseagainst different ground motions of the same intensities isprimarily attributed to differences in the inherent nature ofground motions ie energy distribution over frequencycontent and duration that predominantly affects thestructural response Moreover when Sa(T1) is used as anindicator of the seismic intensity the global drift observeslower values because of the scaling of the ground motions atthe fundamental period of the structure which is directlyrelated with the structural inertia and stiffness

6 Vulnerability Assessment

e fundamental process of the risk assessment against anyhazard consists of two parts ie the hazard and the vul-nerability of structural systems to that hazard For earth-quakes the first portion is primarily concerned withseismologists who can provide a realistic estimate of thepotential seismic hazard that can hit a specific geographicalarea while the second part vulnerability is usuallyaddressed by the engineers and experts who design thefacilities for versatile purposes e current study is relatedwith the second part and assesses the vulnerability of theconsidered typology of school buildings by establishing thehazard-damage relationships for the considered typology ofstructures and subsequently by developing the genericfragility relationships Hazard-damage relationships depictthe structural performance against seismic excitations and

exhibit the dynamic response for all considered groundmotion intensities Figures 7(a) and 7(b) present a directrelationship between the seismic intensities and the struc-tural damage e structural damage is quantified using theglobal response and seismic intensities are provided in-crementally in terms of PGA as well as in terms of spectralacceleration at the fundamental modersquos time period Everysingle dot in each part of Figure 7 represents the maximumvalue of the global drift in terms of percentage against aspecific earthquake scaled at a specific intensity For in-stance at the seismic intensity of 14 g there are 20 dots fromall 20 ground motions indicating the uncertainty in thestructural response by depicting that one earthquake havingthe seismic intensity of 14 g produces global drift less than1 while some other earthquake with the same seismicintensity produces more than 5 of global drift

With increasing intensity of PGA from 020 g to 080 gin Figure 7(a) the global drift remains between 009 and119 While at higher PGA levels from 10 g to 14 g theglobal drift drastically remains between 044 and 516 forall the considered ground motions At the maximum con-sidered PGA of 140 g the global drift varies from 097 to516 for all 20 ground motions All this disparity in thestructural response arises because of the inherent charac-teristics of ground motions which vary from record to re-cord thus instigating different response against the samescaled intensity level

When Sa(T1) is used for representing seismic intensitythe global drift varied between 022 and 24 at the Sa of140 g as shown by Figure 7(b) e dotted line inFigures 7(a) and 7(b) shows the mean structural responseobtained at each intensity level

On the other hand the fragility curve as described byEquation (1) represents a conditional probability ofexceedance for specific damage or limit states of a structureagainst a particular seismic intensity given in terms of PGASa or some other seismic intensity describing the indicator

Pfragility P[LS | IM x] (1)

e aforementioned equation describes the conditionalprobability Pfragility of achieving or exceeding a specific limitstate LS when seismic intensity defined by a particularintensity measure (IM) is equal to ldquoxrdquo Fragility relationshipsfor different damage states must be probabilistically able topredict the structural vulnerability against a realistic range ofseismic ground excitations is probabilistic evaluation isonly possible when a large variation of seismic demands isconsidered so that ample variation in the dynamic structuralresponse can be obtained e vulnerability assessment re-quires the definition of specific limit states damage indicatorsand seismic intensity indicators e impending sectionsaddress all the requirements to develop fragility curvesConsequently fragility curves are developed for the selectedtypology to elucidate the established framework

61 Damage Indicator and the Definition of Limit Statese derivation of analytical fragility curves requires thedefinition of specific limit states in both terms ie

8 Advances in Civil Engineering

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Peak

gro

und

acce

lera

tion

(g)

05 1 15 2 25 3 35 4 45 5 550Maximum global drift ()

(a)

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Spec

tral

acce

lera

tion

(T1)

05 1 15 2 250Maximum global drift ()

(b)

Figure 6 IDA curves (a) maximum global drift vs PGA (b) maximum global drift vs spectral acceleration scaled at the fundamental timeperiod of the structure (Sa(T1))

0 02 04 06 08 1 12 14PGA (g)

0

1

2

3

4

5

Glo

bal d

ri (

)

(a)

0

05

1

15

2

25

3

0 02 04 06 08 1 12 14

Glo

bal d

ri (

)

Sa(T1)

(b)

Figure 7 Hazard-damage relationships (a) PGA vs global drift in percentage (b) Sa(T1) vs global drift in percentage

Advances in Civil Engineering 9

qualitative and quantitative For this purpose a researcherhas to employ a specific damage indicator also known asengineering demand parameter (EDP) or may also propose anew damage measure that can represent the structuraldamage in a rational manner to correlate the damage withseismic loading Once the damage indicator has been set orselected different limit states often known as the damagestates of a structure may be defined

Damage states represent a physical categorization ofdamages by using damage indices which suggest thresholdlimits for different damage states by relaying upon theparameters of structural behavior eg energy dissipationcapability ductility and strength Damage indices are usedfor correlating the accumulated damage with differentspecific damage states and numerous nonidentical damageindices may exist for the same structure For instance Khanet al [44] used global displacement of the structure tocharacterize the structural damage Crowley et al [45]considered damage limit states based on the strain levels inconcrete and steel Guneyisi and Altay [46] considered theinterstory drift ratio for representing the response pa-rameter corresponding to the four damage states takenfrom the HAZUS Casotto et al [47] considered themember flexural strength to characterize the first limit state(LS1) when the reinforcement steel yields in the columnsand 3 interstory drift for flexural collapse limit state(LS2) and subsequently related his LS2 with the loss ofsupport of the beam Chaulagain et al [48] and Gautamet al [49] used 3 damage states ranging from slight damageto complete collapse and developed empirical fragilityrelationships for buildings in Nepal ey further relatedtheir results with FEMA356 [50] classifications for buildingdamage levels

Since this study primarily relates with the generation offragilities for a specific building stock it would not bepractical to define damage or limit states depending uponthe member behavior or local strains In the current studythe global drift ratio has been considered as the damageindicator to correlate with the structural damage

ree damage states namely serviceability limit state(LS1) damage control limit state (LS2) and collapseprevention (LS3) are qualitatively defined in this studyLS1 corresponds with the 1st yield of longitudinal steelreinforcement in the structure Conventionally the firstlimit states are usually related with the formation of the firsthinge in the structure but since the current study employsnonlinear fibers to model the structure therefore the LS1primarily describes the yielding strain reaching in astructural element located anywhere in the structure edeformation and strength govern the LS2 It is defined as75 of LS3 e LS3 collapse prevention is generallydirected by the deformation Altug [51] defined the collapseprevention limit state as 75 of ultimate structural de-formation or the value for which more than 20 strengthdrop can be observed relative to the maximum strengthvalue e smaller of these two values would govern theLS3

e mathematical quantification for these damage statescould not be adopted from the previous research as there

exists no analogous research for Pakistanrsquos constructionindustry or for Pakistanrsquos seismic zone 4 In the currentstudy the mathematical values are assigned to each of thediscrete damage state by using the capacity curve of theselected structure However the obtained values were ap-proximately similar to those obtained by Altug [51] whichused the low-rise buildings of the Turkish region in theirresearch thus the obtained values amply represent the low-rise structural behavior e mathematical values for each ofthe considered damage state against the global drift arepresented in Table 5

62 Fragility Assessment for the School Buildings Seismicfragility curves are widely employed to obtain an articu-lated insight of structural performance against seismicloads and they represent the probability of entering orexceeding different damage states for considered in-tensities of ground shaking After attaining the structuralresponse established limit state definitions are applied forevaluating the structural performance for each limit stateOnce the computed value comes out to be greater than alimit statersquos value an event shall be counted within thesample comprising all the ground motions scalesereby for each IM direct sampling probabilities overthe 20 selected ground motions on all incrementing scaleswere obtained

It is a commonly accepted assumption that for a fragilitycurve a lognormal cumulative distribution function can beconveniently utilized for the representation of conditionalprobabilities [52ndash54] From viewpoint of literature log-normal distribution was also assumed and used for theregression of fragility relationships as mentioned in thefollowing equation

P(LS | IM) ϕln IM minus λc

βc1113888 1113889 (2)

where P(LS | IM) describes the probability of exceedance ofa particular LS given an IM value ϕ represents the standardnormal cumulative distribution function (CDF)

e controlling parameters λc and βc represent themedian point and the slope of the curve respectively It isimperative to evaluate their optimized values for a best fit ofCDF against the calculated probabilities Shinozuka et al[53] Dang et al [54] and Baker [55] stated that the max-imum likelihood method (MLM) is one of the most suitablemethod to achieve best possible values of these two pa-rameters In the current study MLM is utilized to obtain themedian point and the slope of the fragility curve Formultiple IM levels as considered in this study the likelihoodfunction is given as follows

Likelihood 1113945m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠ϕln IMiλc( 1113857

βc1113888 1113889

zj

1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 1113889

njminus zj

(3)

wherem is the number of IM levels andΠ denotes a productover all levels It is assumed that the observation of attaininga specific limit state from each ground motion is

10 Advances in Civil Engineering

independent of the observations from other ground mo-tions In the above equation zj denotes the number ofattaining particular limit state out of nj ground motions witha particular value of IM IMie fragility curve parameterscan be obtained by maximizing the likelihood function inEquation (3) as given in following equation

λc βc1113864 1113865 argmaxλc βc 1113944

m

j1ln

nj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnϕln IMiλ( 1113857c

βc1113888 1113889

⎧⎪⎨

⎪⎩

+ nj minus zj1113872 1113873ln 1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 11138891113897

(4)

A MATLAB code was written to control the maximi-zation of the likelihood function so that optimum values ofthese two parameters can be obtained for establishingseismic fragility

Figure 8 presents the developed fragility relationships forthe considered typology of the RC school building in seismiczone 4 of Pakistan Each portion of Figure 8 contains threefragility relationships correlating with each limit stateagainst both of the IMs ie PGA and Sa(T1) Directsampling probabilities obtained from the IDA are alsoplotted in Figure 8 along with lognormally fitted fragilityfunctions

Table 6 provides the simulated values for λc and βc foreach limit state against each IM for the derivation of fragilitycurves

7 Conclusion

Pakistan has numerous seismotectonically active regionsincluding Muzaffarabad and past earthquakes especially the2005 Kashmir earthquake have proven this fact In thisstudy a new database of RC school buildings constructed inMuzaffarabad district after 2005 earthquake has beenpresented Subsequently the structural vulnerability of aspecific category of RC school buildings is assessed andpresented by using IDA so that practicing engineers atdomestic and regional level can further extend the evalua-tion to other categories of RC buildings e procedurepresented utilizes the fiber-based model which is the mostreliable at present In the current study both PGA andSa(T1) have been used to characterize the seismic intensityough Sa(T1) is a more appropriate IM PGA has beeneasily understandable with the normal public therefore thefragility relationships have also been developed using thePGA as an IM At the PGA of 06 g there exists

Table 5 Limit state criteria for the considered building typology

Buildingmodel nameDamagelimit state (based of global drift )

Serviceability (LS1) Damage control (LS2) Collapse prevention (LS3)BLR-11 035 066 089

Table 6 Lognormal distribution parameters for fragilities againstPGA and Sa(T1) for the considered school building typology

Fragilityparameter

Serviceability(LS1)

Damagecontrol (LS2)

Collapseprevention

(LS3)PGA Sa(T1) PGA Sa(T1) PGA Sa(T1)

λc 04842 08908 07156 13094 0957 18399βc 0327 03266 01974 02606 01742 03353

LS1-lognormalLS2-lognormalLS3-lognormal

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty

LS3 directLS2 directLS1 direct

02 04 06 08 1 12 140PGA (g)

(a)

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty02 04 06 08 1 12 140

Sa(T1)

LS1-lognormalLS2-lognormalLS3-lognormalLS3 direct

LS2 directLS1 direct

(b)

Figure 8 Derived fragility relationships for all IMs (a) seismic fragility for PGA (b) seismic fragility for Sa(T1)

Advances in Civil Engineering 11

approximately 82 probability of exceedance for the firstlimit state (LS1) while only around 20 probability ofexceedance has been achieved against the same seismicintensity for the second limit state (LS2) is essentiallyindicates the structural behavior dominated by the yieldingof the members instead of their complete failures At theseismic intensity of 140 g of PGA the structure seems to bein LS3 with almost around 100 of probability while whenSa(T1) is used as an IM the probability of being in LS3 at theseismic intensity of 140 g remains only around 20 isspecific variation in structural behavior is primarily attrib-uted to the inherent structural characteristics ie stiffnessand ductility that influence the response when the spectralacceleration is used as an IM after being scaled at thefundamental time period of the structure Since the selectedstructure is engineered the results are not so admonishingfor the considered school building typology neverthelessthe results might not be encouraging for other schoolbuilding types in the presented database e presentedconsolidated procedure is relatively simple and can bereadily adopted by the domestic and regional disaster pre-paredness and mitigation agencies to extend the applicationSuch studies are relatively new for under developingcountries like Pakistan and contemporarily no other workexists that may specifically address the vulnerability ofschools in seismic zone 4 of Pakistan Assessment of vul-nerabilities for other types of school buildings may yield aneed for immediate intervention in order to safeguard thelife of students and other users e presented study isspecifically targeted to assess the vulnerability and does notaddress the assessment of risk therefore the developedfragility curves can be further integrated with the hazardcurves of the considered area to evaluate the total riskinvolved

Data Availability

e data used to support the findings of this study are in-cluded within the article Any other data used to support thefindings of this study may be released upon request to theauthor(s) who can be contacted at musmankaistackr

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] M Zain M Usman S H Farooq and A Hanif ldquoProgressivestructural capacity loss assessmentmdasha framework for modernreinforced concrete buildingsrdquo PLoS One vol 13 no 12Article ID e0208149 2018

[2] Report from earthquake engineering research Institute (ERRI)httpswwweeriorglfepdfkashmir_eeri_2nd_reportpdf

[3] Government of Pakistan Building Code of Pakistan PakistanEngineering Council Government of Pakistan IslamabadPakistan 2007

[4] D Bonowitz Seismic Design in Pakistan Be Building CodesBylaws and Recommendations for Earthquake Risk Reduction

United Nations Development Programme New York NYUSA 2015

[5] C Xu J Deng S Peng and C Li ldquoSeismic fragility analysis ofsteel reinforced concrete frame structures based on differentengineering demand parametersrdquo Journal of Building Engi-neering vol 20 pp 736ndash749 2018

[6] J Ji A S Elnashai and D A Kuchma ldquoAn analyticalframework for seismic fragility analysis of RC high-risebuildingsrdquo Engineering Structures vol 29 no 12 pp 3197ndash3209 2007

[7] M Zain N Anwar F A Najam and T Mehmood ldquoSeismicfragility assessment of reinforced concrete high-rise buildingsusing the uncoupled modal response history analysis(UMRHA)rdquo in Proceedings of the International Conference onEarthquake Engineering and Structural Dynamics ReykjavikIceland June 2017

[8] A Ali T Sandhu and M Usman ldquoAmbient vibration testingof a pedestrian bridge using low-cost accelerometers for SHMapplicationsrdquo Smart Cities vol 2 no 1 pp 20ndash30 2019

[9] Y Pang X Wu G Shen and W Yuan ldquoSeismic fragilityanalysis of cable-stayed bridges considering different sourcesof uncertaintiesrdquo Journal of Bridge Engineering vol 19 no 4Article ID 04013015 2014

[10] A Rasheed S H Farooq M Usman A Hanif N A Khanand R A Khushnood ldquoStructural reliability analysis of su-perstructure of highway bridges on China-Pakistan economiccorridor (CPEC) a case studyrdquo Journal of Structural Integrityand Maintenance vol 3 no 3 pp 197ndash207 2018

[11] J-T Wang M-X Zhang A-Y Jin and C-H ZhangldquoSeismic fragility of arch dams based on damage analysisrdquo SoilDynamics and Earthquake Engineering vol 109 pp 58ndash682018

[12] Y Yazdani and M Alembagheri ldquoSeismic vulnerability ofgravity dams in near-fault areasrdquo Soil Dynamics and Earth-quake Engineering vol 102 pp 15ndash24 2017

[13] S Leonidas and A Kappos ldquoDerivation of fragility curves fortraditional timber-framed masonry buildings using nonlinearstatic analysisrdquo in Proceedings of the 4th International Con-ference on Computational Methods in Structural Dynamicsand Earthquake Engineering Kos Island Greece June 2013

[14] J Alam M S Islam M Hussan and A Sarraz ldquoSeismicfragility assessment of RC building using nonlinear staticpushover analysisrdquo in Proceedings of the International Con-ference on Planning Architecture and Civil Engineering(ICPAC) Rajshahi India February 2017

[15] M Ni Choine M M Kashani L N Lowes et al ldquoNonlineardynamic analysis and seismic fragility assessment of a cor-rosion damaged integral bridgerdquo International Journal ofStructural Integrity vol 7 no 2 pp 227ndash239 2016

[16] K Bakalis and D Vamvatsikos ldquoSeismic fragility functions vianonlinear response history analysisrdquo Journal of StructuralEngineering vol 144 no 10 Article ID 04018181 2018

[17] FEMA Rapid Visual Screening of Buildings for PotentialSeismic Hazards A Handbook Federal Emergency Manage-ment Agency (FEMA) Washington DC USA third edition2015

[18] FEMA Technical and Userrsquos Manual HAZUSndashMH 21 De-partment of Homeland Security Federal Emergency Man-agement Agency (FEMA) Washington DC USA

[19] User Guide Perform 3D Nonlinear Analysis and PerformanceAssessment for 3D Structures Computers and Structures IncBerkeley CA USA 2011

[20] M M Rafi and M M Nasir ldquoExperimental investigation ofchemical and physical properties of cements manufactured in

12 Advances in Civil Engineering

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Peak

gro

und

acce

lera

tion

(g)

05 1 15 2 25 3 35 4 45 5 550Maximum global drift ()

(a)

EQ1

EQ2

EQ8EQ15

EQ9

EQ3EQ10

EQ16 EQ4EQ17

EQ11EQ18

EQ5EQ12EQ19EQ6

EQ7

EQ13

EQ14

EQ20

0

02

04

06

08

1

12

14

Spec

tral

acce

lera

tion

(T1)

05 1 15 2 250Maximum global drift ()

(b)

Figure 6 IDA curves (a) maximum global drift vs PGA (b) maximum global drift vs spectral acceleration scaled at the fundamental timeperiod of the structure (Sa(T1))

0 02 04 06 08 1 12 14PGA (g)

0

1

2

3

4

5

Glo

bal d

ri (

)

(a)

0

05

1

15

2

25

3

0 02 04 06 08 1 12 14

Glo

bal d

ri (

)

Sa(T1)

(b)

Figure 7 Hazard-damage relationships (a) PGA vs global drift in percentage (b) Sa(T1) vs global drift in percentage

Advances in Civil Engineering 9

qualitative and quantitative For this purpose a researcherhas to employ a specific damage indicator also known asengineering demand parameter (EDP) or may also propose anew damage measure that can represent the structuraldamage in a rational manner to correlate the damage withseismic loading Once the damage indicator has been set orselected different limit states often known as the damagestates of a structure may be defined

Damage states represent a physical categorization ofdamages by using damage indices which suggest thresholdlimits for different damage states by relaying upon theparameters of structural behavior eg energy dissipationcapability ductility and strength Damage indices are usedfor correlating the accumulated damage with differentspecific damage states and numerous nonidentical damageindices may exist for the same structure For instance Khanet al [44] used global displacement of the structure tocharacterize the structural damage Crowley et al [45]considered damage limit states based on the strain levels inconcrete and steel Guneyisi and Altay [46] considered theinterstory drift ratio for representing the response pa-rameter corresponding to the four damage states takenfrom the HAZUS Casotto et al [47] considered themember flexural strength to characterize the first limit state(LS1) when the reinforcement steel yields in the columnsand 3 interstory drift for flexural collapse limit state(LS2) and subsequently related his LS2 with the loss ofsupport of the beam Chaulagain et al [48] and Gautamet al [49] used 3 damage states ranging from slight damageto complete collapse and developed empirical fragilityrelationships for buildings in Nepal ey further relatedtheir results with FEMA356 [50] classifications for buildingdamage levels

Since this study primarily relates with the generation offragilities for a specific building stock it would not bepractical to define damage or limit states depending uponthe member behavior or local strains In the current studythe global drift ratio has been considered as the damageindicator to correlate with the structural damage

ree damage states namely serviceability limit state(LS1) damage control limit state (LS2) and collapseprevention (LS3) are qualitatively defined in this studyLS1 corresponds with the 1st yield of longitudinal steelreinforcement in the structure Conventionally the firstlimit states are usually related with the formation of the firsthinge in the structure but since the current study employsnonlinear fibers to model the structure therefore the LS1primarily describes the yielding strain reaching in astructural element located anywhere in the structure edeformation and strength govern the LS2 It is defined as75 of LS3 e LS3 collapse prevention is generallydirected by the deformation Altug [51] defined the collapseprevention limit state as 75 of ultimate structural de-formation or the value for which more than 20 strengthdrop can be observed relative to the maximum strengthvalue e smaller of these two values would govern theLS3

e mathematical quantification for these damage statescould not be adopted from the previous research as there

exists no analogous research for Pakistanrsquos constructionindustry or for Pakistanrsquos seismic zone 4 In the currentstudy the mathematical values are assigned to each of thediscrete damage state by using the capacity curve of theselected structure However the obtained values were ap-proximately similar to those obtained by Altug [51] whichused the low-rise buildings of the Turkish region in theirresearch thus the obtained values amply represent the low-rise structural behavior e mathematical values for each ofthe considered damage state against the global drift arepresented in Table 5

62 Fragility Assessment for the School Buildings Seismicfragility curves are widely employed to obtain an articu-lated insight of structural performance against seismicloads and they represent the probability of entering orexceeding different damage states for considered in-tensities of ground shaking After attaining the structuralresponse established limit state definitions are applied forevaluating the structural performance for each limit stateOnce the computed value comes out to be greater than alimit statersquos value an event shall be counted within thesample comprising all the ground motions scalesereby for each IM direct sampling probabilities overthe 20 selected ground motions on all incrementing scaleswere obtained

It is a commonly accepted assumption that for a fragilitycurve a lognormal cumulative distribution function can beconveniently utilized for the representation of conditionalprobabilities [52ndash54] From viewpoint of literature log-normal distribution was also assumed and used for theregression of fragility relationships as mentioned in thefollowing equation

P(LS | IM) ϕln IM minus λc

βc1113888 1113889 (2)

where P(LS | IM) describes the probability of exceedance ofa particular LS given an IM value ϕ represents the standardnormal cumulative distribution function (CDF)

e controlling parameters λc and βc represent themedian point and the slope of the curve respectively It isimperative to evaluate their optimized values for a best fit ofCDF against the calculated probabilities Shinozuka et al[53] Dang et al [54] and Baker [55] stated that the max-imum likelihood method (MLM) is one of the most suitablemethod to achieve best possible values of these two pa-rameters In the current study MLM is utilized to obtain themedian point and the slope of the fragility curve Formultiple IM levels as considered in this study the likelihoodfunction is given as follows

Likelihood 1113945m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠ϕln IMiλc( 1113857

βc1113888 1113889

zj

1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 1113889

njminus zj

(3)

wherem is the number of IM levels andΠ denotes a productover all levels It is assumed that the observation of attaininga specific limit state from each ground motion is

10 Advances in Civil Engineering

independent of the observations from other ground mo-tions In the above equation zj denotes the number ofattaining particular limit state out of nj ground motions witha particular value of IM IMie fragility curve parameterscan be obtained by maximizing the likelihood function inEquation (3) as given in following equation

λc βc1113864 1113865 argmaxλc βc 1113944

m

j1ln

nj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnϕln IMiλ( 1113857c

βc1113888 1113889

⎧⎪⎨

⎪⎩

+ nj minus zj1113872 1113873ln 1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 11138891113897

(4)

A MATLAB code was written to control the maximi-zation of the likelihood function so that optimum values ofthese two parameters can be obtained for establishingseismic fragility

Figure 8 presents the developed fragility relationships forthe considered typology of the RC school building in seismiczone 4 of Pakistan Each portion of Figure 8 contains threefragility relationships correlating with each limit stateagainst both of the IMs ie PGA and Sa(T1) Directsampling probabilities obtained from the IDA are alsoplotted in Figure 8 along with lognormally fitted fragilityfunctions

Table 6 provides the simulated values for λc and βc foreach limit state against each IM for the derivation of fragilitycurves

7 Conclusion

Pakistan has numerous seismotectonically active regionsincluding Muzaffarabad and past earthquakes especially the2005 Kashmir earthquake have proven this fact In thisstudy a new database of RC school buildings constructed inMuzaffarabad district after 2005 earthquake has beenpresented Subsequently the structural vulnerability of aspecific category of RC school buildings is assessed andpresented by using IDA so that practicing engineers atdomestic and regional level can further extend the evalua-tion to other categories of RC buildings e procedurepresented utilizes the fiber-based model which is the mostreliable at present In the current study both PGA andSa(T1) have been used to characterize the seismic intensityough Sa(T1) is a more appropriate IM PGA has beeneasily understandable with the normal public therefore thefragility relationships have also been developed using thePGA as an IM At the PGA of 06 g there exists

Table 5 Limit state criteria for the considered building typology

Buildingmodel nameDamagelimit state (based of global drift )

Serviceability (LS1) Damage control (LS2) Collapse prevention (LS3)BLR-11 035 066 089

Table 6 Lognormal distribution parameters for fragilities againstPGA and Sa(T1) for the considered school building typology

Fragilityparameter

Serviceability(LS1)

Damagecontrol (LS2)

Collapseprevention

(LS3)PGA Sa(T1) PGA Sa(T1) PGA Sa(T1)

λc 04842 08908 07156 13094 0957 18399βc 0327 03266 01974 02606 01742 03353

LS1-lognormalLS2-lognormalLS3-lognormal

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty

LS3 directLS2 directLS1 direct

02 04 06 08 1 12 140PGA (g)

(a)

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty02 04 06 08 1 12 140

Sa(T1)

LS1-lognormalLS2-lognormalLS3-lognormalLS3 direct

LS2 directLS1 direct

(b)

Figure 8 Derived fragility relationships for all IMs (a) seismic fragility for PGA (b) seismic fragility for Sa(T1)

Advances in Civil Engineering 11

approximately 82 probability of exceedance for the firstlimit state (LS1) while only around 20 probability ofexceedance has been achieved against the same seismicintensity for the second limit state (LS2) is essentiallyindicates the structural behavior dominated by the yieldingof the members instead of their complete failures At theseismic intensity of 140 g of PGA the structure seems to bein LS3 with almost around 100 of probability while whenSa(T1) is used as an IM the probability of being in LS3 at theseismic intensity of 140 g remains only around 20 isspecific variation in structural behavior is primarily attrib-uted to the inherent structural characteristics ie stiffnessand ductility that influence the response when the spectralacceleration is used as an IM after being scaled at thefundamental time period of the structure Since the selectedstructure is engineered the results are not so admonishingfor the considered school building typology neverthelessthe results might not be encouraging for other schoolbuilding types in the presented database e presentedconsolidated procedure is relatively simple and can bereadily adopted by the domestic and regional disaster pre-paredness and mitigation agencies to extend the applicationSuch studies are relatively new for under developingcountries like Pakistan and contemporarily no other workexists that may specifically address the vulnerability ofschools in seismic zone 4 of Pakistan Assessment of vul-nerabilities for other types of school buildings may yield aneed for immediate intervention in order to safeguard thelife of students and other users e presented study isspecifically targeted to assess the vulnerability and does notaddress the assessment of risk therefore the developedfragility curves can be further integrated with the hazardcurves of the considered area to evaluate the total riskinvolved

Data Availability

e data used to support the findings of this study are in-cluded within the article Any other data used to support thefindings of this study may be released upon request to theauthor(s) who can be contacted at musmankaistackr

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] M Zain M Usman S H Farooq and A Hanif ldquoProgressivestructural capacity loss assessmentmdasha framework for modernreinforced concrete buildingsrdquo PLoS One vol 13 no 12Article ID e0208149 2018

[2] Report from earthquake engineering research Institute (ERRI)httpswwweeriorglfepdfkashmir_eeri_2nd_reportpdf

[3] Government of Pakistan Building Code of Pakistan PakistanEngineering Council Government of Pakistan IslamabadPakistan 2007

[4] D Bonowitz Seismic Design in Pakistan Be Building CodesBylaws and Recommendations for Earthquake Risk Reduction

United Nations Development Programme New York NYUSA 2015

[5] C Xu J Deng S Peng and C Li ldquoSeismic fragility analysis ofsteel reinforced concrete frame structures based on differentengineering demand parametersrdquo Journal of Building Engi-neering vol 20 pp 736ndash749 2018

[6] J Ji A S Elnashai and D A Kuchma ldquoAn analyticalframework for seismic fragility analysis of RC high-risebuildingsrdquo Engineering Structures vol 29 no 12 pp 3197ndash3209 2007

[7] M Zain N Anwar F A Najam and T Mehmood ldquoSeismicfragility assessment of reinforced concrete high-rise buildingsusing the uncoupled modal response history analysis(UMRHA)rdquo in Proceedings of the International Conference onEarthquake Engineering and Structural Dynamics ReykjavikIceland June 2017

[8] A Ali T Sandhu and M Usman ldquoAmbient vibration testingof a pedestrian bridge using low-cost accelerometers for SHMapplicationsrdquo Smart Cities vol 2 no 1 pp 20ndash30 2019

[9] Y Pang X Wu G Shen and W Yuan ldquoSeismic fragilityanalysis of cable-stayed bridges considering different sourcesof uncertaintiesrdquo Journal of Bridge Engineering vol 19 no 4Article ID 04013015 2014

[10] A Rasheed S H Farooq M Usman A Hanif N A Khanand R A Khushnood ldquoStructural reliability analysis of su-perstructure of highway bridges on China-Pakistan economiccorridor (CPEC) a case studyrdquo Journal of Structural Integrityand Maintenance vol 3 no 3 pp 197ndash207 2018

[11] J-T Wang M-X Zhang A-Y Jin and C-H ZhangldquoSeismic fragility of arch dams based on damage analysisrdquo SoilDynamics and Earthquake Engineering vol 109 pp 58ndash682018

[12] Y Yazdani and M Alembagheri ldquoSeismic vulnerability ofgravity dams in near-fault areasrdquo Soil Dynamics and Earth-quake Engineering vol 102 pp 15ndash24 2017

[13] S Leonidas and A Kappos ldquoDerivation of fragility curves fortraditional timber-framed masonry buildings using nonlinearstatic analysisrdquo in Proceedings of the 4th International Con-ference on Computational Methods in Structural Dynamicsand Earthquake Engineering Kos Island Greece June 2013

[14] J Alam M S Islam M Hussan and A Sarraz ldquoSeismicfragility assessment of RC building using nonlinear staticpushover analysisrdquo in Proceedings of the International Con-ference on Planning Architecture and Civil Engineering(ICPAC) Rajshahi India February 2017

[15] M Ni Choine M M Kashani L N Lowes et al ldquoNonlineardynamic analysis and seismic fragility assessment of a cor-rosion damaged integral bridgerdquo International Journal ofStructural Integrity vol 7 no 2 pp 227ndash239 2016

[16] K Bakalis and D Vamvatsikos ldquoSeismic fragility functions vianonlinear response history analysisrdquo Journal of StructuralEngineering vol 144 no 10 Article ID 04018181 2018

[17] FEMA Rapid Visual Screening of Buildings for PotentialSeismic Hazards A Handbook Federal Emergency Manage-ment Agency (FEMA) Washington DC USA third edition2015

[18] FEMA Technical and Userrsquos Manual HAZUSndashMH 21 De-partment of Homeland Security Federal Emergency Man-agement Agency (FEMA) Washington DC USA

[19] User Guide Perform 3D Nonlinear Analysis and PerformanceAssessment for 3D Structures Computers and Structures IncBerkeley CA USA 2011

[20] M M Rafi and M M Nasir ldquoExperimental investigation ofchemical and physical properties of cements manufactured in

12 Advances in Civil Engineering

qualitative and quantitative For this purpose a researcherhas to employ a specific damage indicator also known asengineering demand parameter (EDP) or may also propose anew damage measure that can represent the structuraldamage in a rational manner to correlate the damage withseismic loading Once the damage indicator has been set orselected different limit states often known as the damagestates of a structure may be defined

Damage states represent a physical categorization ofdamages by using damage indices which suggest thresholdlimits for different damage states by relaying upon theparameters of structural behavior eg energy dissipationcapability ductility and strength Damage indices are usedfor correlating the accumulated damage with differentspecific damage states and numerous nonidentical damageindices may exist for the same structure For instance Khanet al [44] used global displacement of the structure tocharacterize the structural damage Crowley et al [45]considered damage limit states based on the strain levels inconcrete and steel Guneyisi and Altay [46] considered theinterstory drift ratio for representing the response pa-rameter corresponding to the four damage states takenfrom the HAZUS Casotto et al [47] considered themember flexural strength to characterize the first limit state(LS1) when the reinforcement steel yields in the columnsand 3 interstory drift for flexural collapse limit state(LS2) and subsequently related his LS2 with the loss ofsupport of the beam Chaulagain et al [48] and Gautamet al [49] used 3 damage states ranging from slight damageto complete collapse and developed empirical fragilityrelationships for buildings in Nepal ey further relatedtheir results with FEMA356 [50] classifications for buildingdamage levels

Since this study primarily relates with the generation offragilities for a specific building stock it would not bepractical to define damage or limit states depending uponthe member behavior or local strains In the current studythe global drift ratio has been considered as the damageindicator to correlate with the structural damage

ree damage states namely serviceability limit state(LS1) damage control limit state (LS2) and collapseprevention (LS3) are qualitatively defined in this studyLS1 corresponds with the 1st yield of longitudinal steelreinforcement in the structure Conventionally the firstlimit states are usually related with the formation of the firsthinge in the structure but since the current study employsnonlinear fibers to model the structure therefore the LS1primarily describes the yielding strain reaching in astructural element located anywhere in the structure edeformation and strength govern the LS2 It is defined as75 of LS3 e LS3 collapse prevention is generallydirected by the deformation Altug [51] defined the collapseprevention limit state as 75 of ultimate structural de-formation or the value for which more than 20 strengthdrop can be observed relative to the maximum strengthvalue e smaller of these two values would govern theLS3

e mathematical quantification for these damage statescould not be adopted from the previous research as there

exists no analogous research for Pakistanrsquos constructionindustry or for Pakistanrsquos seismic zone 4 In the currentstudy the mathematical values are assigned to each of thediscrete damage state by using the capacity curve of theselected structure However the obtained values were ap-proximately similar to those obtained by Altug [51] whichused the low-rise buildings of the Turkish region in theirresearch thus the obtained values amply represent the low-rise structural behavior e mathematical values for each ofthe considered damage state against the global drift arepresented in Table 5

62 Fragility Assessment for the School Buildings Seismicfragility curves are widely employed to obtain an articu-lated insight of structural performance against seismicloads and they represent the probability of entering orexceeding different damage states for considered in-tensities of ground shaking After attaining the structuralresponse established limit state definitions are applied forevaluating the structural performance for each limit stateOnce the computed value comes out to be greater than alimit statersquos value an event shall be counted within thesample comprising all the ground motions scalesereby for each IM direct sampling probabilities overthe 20 selected ground motions on all incrementing scaleswere obtained

It is a commonly accepted assumption that for a fragilitycurve a lognormal cumulative distribution function can beconveniently utilized for the representation of conditionalprobabilities [52ndash54] From viewpoint of literature log-normal distribution was also assumed and used for theregression of fragility relationships as mentioned in thefollowing equation

P(LS | IM) ϕln IM minus λc

βc1113888 1113889 (2)

where P(LS | IM) describes the probability of exceedance ofa particular LS given an IM value ϕ represents the standardnormal cumulative distribution function (CDF)

e controlling parameters λc and βc represent themedian point and the slope of the curve respectively It isimperative to evaluate their optimized values for a best fit ofCDF against the calculated probabilities Shinozuka et al[53] Dang et al [54] and Baker [55] stated that the max-imum likelihood method (MLM) is one of the most suitablemethod to achieve best possible values of these two pa-rameters In the current study MLM is utilized to obtain themedian point and the slope of the fragility curve Formultiple IM levels as considered in this study the likelihoodfunction is given as follows

Likelihood 1113945m

j1

nj

zj

⎛⎜⎝ ⎞⎟⎠ϕln IMiλc( 1113857

βc1113888 1113889

zj

1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 1113889

njminus zj

(3)

wherem is the number of IM levels andΠ denotes a productover all levels It is assumed that the observation of attaininga specific limit state from each ground motion is

10 Advances in Civil Engineering

independent of the observations from other ground mo-tions In the above equation zj denotes the number ofattaining particular limit state out of nj ground motions witha particular value of IM IMie fragility curve parameterscan be obtained by maximizing the likelihood function inEquation (3) as given in following equation

λc βc1113864 1113865 argmaxλc βc 1113944

m

j1ln

nj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnϕln IMiλ( 1113857c

βc1113888 1113889

⎧⎪⎨

⎪⎩

+ nj minus zj1113872 1113873ln 1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 11138891113897

(4)

A MATLAB code was written to control the maximi-zation of the likelihood function so that optimum values ofthese two parameters can be obtained for establishingseismic fragility

Figure 8 presents the developed fragility relationships forthe considered typology of the RC school building in seismiczone 4 of Pakistan Each portion of Figure 8 contains threefragility relationships correlating with each limit stateagainst both of the IMs ie PGA and Sa(T1) Directsampling probabilities obtained from the IDA are alsoplotted in Figure 8 along with lognormally fitted fragilityfunctions

Table 6 provides the simulated values for λc and βc foreach limit state against each IM for the derivation of fragilitycurves

7 Conclusion

Pakistan has numerous seismotectonically active regionsincluding Muzaffarabad and past earthquakes especially the2005 Kashmir earthquake have proven this fact In thisstudy a new database of RC school buildings constructed inMuzaffarabad district after 2005 earthquake has beenpresented Subsequently the structural vulnerability of aspecific category of RC school buildings is assessed andpresented by using IDA so that practicing engineers atdomestic and regional level can further extend the evalua-tion to other categories of RC buildings e procedurepresented utilizes the fiber-based model which is the mostreliable at present In the current study both PGA andSa(T1) have been used to characterize the seismic intensityough Sa(T1) is a more appropriate IM PGA has beeneasily understandable with the normal public therefore thefragility relationships have also been developed using thePGA as an IM At the PGA of 06 g there exists

Table 5 Limit state criteria for the considered building typology

Buildingmodel nameDamagelimit state (based of global drift )

Serviceability (LS1) Damage control (LS2) Collapse prevention (LS3)BLR-11 035 066 089

Table 6 Lognormal distribution parameters for fragilities againstPGA and Sa(T1) for the considered school building typology

Fragilityparameter

Serviceability(LS1)

Damagecontrol (LS2)

Collapseprevention

(LS3)PGA Sa(T1) PGA Sa(T1) PGA Sa(T1)

λc 04842 08908 07156 13094 0957 18399βc 0327 03266 01974 02606 01742 03353

LS1-lognormalLS2-lognormalLS3-lognormal

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty

LS3 directLS2 directLS1 direct

02 04 06 08 1 12 140PGA (g)

(a)

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty02 04 06 08 1 12 140

Sa(T1)

LS1-lognormalLS2-lognormalLS3-lognormalLS3 direct

LS2 directLS1 direct

(b)

Figure 8 Derived fragility relationships for all IMs (a) seismic fragility for PGA (b) seismic fragility for Sa(T1)

Advances in Civil Engineering 11

approximately 82 probability of exceedance for the firstlimit state (LS1) while only around 20 probability ofexceedance has been achieved against the same seismicintensity for the second limit state (LS2) is essentiallyindicates the structural behavior dominated by the yieldingof the members instead of their complete failures At theseismic intensity of 140 g of PGA the structure seems to bein LS3 with almost around 100 of probability while whenSa(T1) is used as an IM the probability of being in LS3 at theseismic intensity of 140 g remains only around 20 isspecific variation in structural behavior is primarily attrib-uted to the inherent structural characteristics ie stiffnessand ductility that influence the response when the spectralacceleration is used as an IM after being scaled at thefundamental time period of the structure Since the selectedstructure is engineered the results are not so admonishingfor the considered school building typology neverthelessthe results might not be encouraging for other schoolbuilding types in the presented database e presentedconsolidated procedure is relatively simple and can bereadily adopted by the domestic and regional disaster pre-paredness and mitigation agencies to extend the applicationSuch studies are relatively new for under developingcountries like Pakistan and contemporarily no other workexists that may specifically address the vulnerability ofschools in seismic zone 4 of Pakistan Assessment of vul-nerabilities for other types of school buildings may yield aneed for immediate intervention in order to safeguard thelife of students and other users e presented study isspecifically targeted to assess the vulnerability and does notaddress the assessment of risk therefore the developedfragility curves can be further integrated with the hazardcurves of the considered area to evaluate the total riskinvolved

Data Availability

e data used to support the findings of this study are in-cluded within the article Any other data used to support thefindings of this study may be released upon request to theauthor(s) who can be contacted at musmankaistackr

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] M Zain M Usman S H Farooq and A Hanif ldquoProgressivestructural capacity loss assessmentmdasha framework for modernreinforced concrete buildingsrdquo PLoS One vol 13 no 12Article ID e0208149 2018

[2] Report from earthquake engineering research Institute (ERRI)httpswwweeriorglfepdfkashmir_eeri_2nd_reportpdf

[3] Government of Pakistan Building Code of Pakistan PakistanEngineering Council Government of Pakistan IslamabadPakistan 2007

[4] D Bonowitz Seismic Design in Pakistan Be Building CodesBylaws and Recommendations for Earthquake Risk Reduction

United Nations Development Programme New York NYUSA 2015

[5] C Xu J Deng S Peng and C Li ldquoSeismic fragility analysis ofsteel reinforced concrete frame structures based on differentengineering demand parametersrdquo Journal of Building Engi-neering vol 20 pp 736ndash749 2018

[6] J Ji A S Elnashai and D A Kuchma ldquoAn analyticalframework for seismic fragility analysis of RC high-risebuildingsrdquo Engineering Structures vol 29 no 12 pp 3197ndash3209 2007

[7] M Zain N Anwar F A Najam and T Mehmood ldquoSeismicfragility assessment of reinforced concrete high-rise buildingsusing the uncoupled modal response history analysis(UMRHA)rdquo in Proceedings of the International Conference onEarthquake Engineering and Structural Dynamics ReykjavikIceland June 2017

[8] A Ali T Sandhu and M Usman ldquoAmbient vibration testingof a pedestrian bridge using low-cost accelerometers for SHMapplicationsrdquo Smart Cities vol 2 no 1 pp 20ndash30 2019

[9] Y Pang X Wu G Shen and W Yuan ldquoSeismic fragilityanalysis of cable-stayed bridges considering different sourcesof uncertaintiesrdquo Journal of Bridge Engineering vol 19 no 4Article ID 04013015 2014

[10] A Rasheed S H Farooq M Usman A Hanif N A Khanand R A Khushnood ldquoStructural reliability analysis of su-perstructure of highway bridges on China-Pakistan economiccorridor (CPEC) a case studyrdquo Journal of Structural Integrityand Maintenance vol 3 no 3 pp 197ndash207 2018

[11] J-T Wang M-X Zhang A-Y Jin and C-H ZhangldquoSeismic fragility of arch dams based on damage analysisrdquo SoilDynamics and Earthquake Engineering vol 109 pp 58ndash682018

[12] Y Yazdani and M Alembagheri ldquoSeismic vulnerability ofgravity dams in near-fault areasrdquo Soil Dynamics and Earth-quake Engineering vol 102 pp 15ndash24 2017

[13] S Leonidas and A Kappos ldquoDerivation of fragility curves fortraditional timber-framed masonry buildings using nonlinearstatic analysisrdquo in Proceedings of the 4th International Con-ference on Computational Methods in Structural Dynamicsand Earthquake Engineering Kos Island Greece June 2013

[14] J Alam M S Islam M Hussan and A Sarraz ldquoSeismicfragility assessment of RC building using nonlinear staticpushover analysisrdquo in Proceedings of the International Con-ference on Planning Architecture and Civil Engineering(ICPAC) Rajshahi India February 2017

[15] M Ni Choine M M Kashani L N Lowes et al ldquoNonlineardynamic analysis and seismic fragility assessment of a cor-rosion damaged integral bridgerdquo International Journal ofStructural Integrity vol 7 no 2 pp 227ndash239 2016

[16] K Bakalis and D Vamvatsikos ldquoSeismic fragility functions vianonlinear response history analysisrdquo Journal of StructuralEngineering vol 144 no 10 Article ID 04018181 2018

[17] FEMA Rapid Visual Screening of Buildings for PotentialSeismic Hazards A Handbook Federal Emergency Manage-ment Agency (FEMA) Washington DC USA third edition2015

[18] FEMA Technical and Userrsquos Manual HAZUSndashMH 21 De-partment of Homeland Security Federal Emergency Man-agement Agency (FEMA) Washington DC USA

[19] User Guide Perform 3D Nonlinear Analysis and PerformanceAssessment for 3D Structures Computers and Structures IncBerkeley CA USA 2011

[20] M M Rafi and M M Nasir ldquoExperimental investigation ofchemical and physical properties of cements manufactured in

12 Advances in Civil Engineering

independent of the observations from other ground mo-tions In the above equation zj denotes the number ofattaining particular limit state out of nj ground motions witha particular value of IM IMie fragility curve parameterscan be obtained by maximizing the likelihood function inEquation (3) as given in following equation

λc βc1113864 1113865 argmaxλc βc 1113944

m

j1ln

nj

zj

⎛⎜⎝ ⎞⎟⎠ + zj lnϕln IMiλ( 1113857c

βc1113888 1113889

⎧⎪⎨

⎪⎩

+ nj minus zj1113872 1113873ln 1 minus ϕln IMiλc( 1113857

βc1113888 11138891113888 11138891113897

(4)

A MATLAB code was written to control the maximi-zation of the likelihood function so that optimum values ofthese two parameters can be obtained for establishingseismic fragility

Figure 8 presents the developed fragility relationships forthe considered typology of the RC school building in seismiczone 4 of Pakistan Each portion of Figure 8 contains threefragility relationships correlating with each limit stateagainst both of the IMs ie PGA and Sa(T1) Directsampling probabilities obtained from the IDA are alsoplotted in Figure 8 along with lognormally fitted fragilityfunctions

Table 6 provides the simulated values for λc and βc foreach limit state against each IM for the derivation of fragilitycurves

7 Conclusion

Pakistan has numerous seismotectonically active regionsincluding Muzaffarabad and past earthquakes especially the2005 Kashmir earthquake have proven this fact In thisstudy a new database of RC school buildings constructed inMuzaffarabad district after 2005 earthquake has beenpresented Subsequently the structural vulnerability of aspecific category of RC school buildings is assessed andpresented by using IDA so that practicing engineers atdomestic and regional level can further extend the evalua-tion to other categories of RC buildings e procedurepresented utilizes the fiber-based model which is the mostreliable at present In the current study both PGA andSa(T1) have been used to characterize the seismic intensityough Sa(T1) is a more appropriate IM PGA has beeneasily understandable with the normal public therefore thefragility relationships have also been developed using thePGA as an IM At the PGA of 06 g there exists

Table 5 Limit state criteria for the considered building typology

Buildingmodel nameDamagelimit state (based of global drift )

Serviceability (LS1) Damage control (LS2) Collapse prevention (LS3)BLR-11 035 066 089

Table 6 Lognormal distribution parameters for fragilities againstPGA and Sa(T1) for the considered school building typology

Fragilityparameter

Serviceability(LS1)

Damagecontrol (LS2)

Collapseprevention

(LS3)PGA Sa(T1) PGA Sa(T1) PGA Sa(T1)

λc 04842 08908 07156 13094 0957 18399βc 0327 03266 01974 02606 01742 03353

LS1-lognormalLS2-lognormalLS3-lognormal

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty

LS3 directLS2 directLS1 direct

02 04 06 08 1 12 140PGA (g)

(a)

0

01

02

03

04

05

06

07

08

09

1

Prob

abili

ty02 04 06 08 1 12 140

Sa(T1)

LS1-lognormalLS2-lognormalLS3-lognormalLS3 direct

LS2 directLS1 direct

(b)

Figure 8 Derived fragility relationships for all IMs (a) seismic fragility for PGA (b) seismic fragility for Sa(T1)

Advances in Civil Engineering 11

approximately 82 probability of exceedance for the firstlimit state (LS1) while only around 20 probability ofexceedance has been achieved against the same seismicintensity for the second limit state (LS2) is essentiallyindicates the structural behavior dominated by the yieldingof the members instead of their complete failures At theseismic intensity of 140 g of PGA the structure seems to bein LS3 with almost around 100 of probability while whenSa(T1) is used as an IM the probability of being in LS3 at theseismic intensity of 140 g remains only around 20 isspecific variation in structural behavior is primarily attrib-uted to the inherent structural characteristics ie stiffnessand ductility that influence the response when the spectralacceleration is used as an IM after being scaled at thefundamental time period of the structure Since the selectedstructure is engineered the results are not so admonishingfor the considered school building typology neverthelessthe results might not be encouraging for other schoolbuilding types in the presented database e presentedconsolidated procedure is relatively simple and can bereadily adopted by the domestic and regional disaster pre-paredness and mitigation agencies to extend the applicationSuch studies are relatively new for under developingcountries like Pakistan and contemporarily no other workexists that may specifically address the vulnerability ofschools in seismic zone 4 of Pakistan Assessment of vul-nerabilities for other types of school buildings may yield aneed for immediate intervention in order to safeguard thelife of students and other users e presented study isspecifically targeted to assess the vulnerability and does notaddress the assessment of risk therefore the developedfragility curves can be further integrated with the hazardcurves of the considered area to evaluate the total riskinvolved

Data Availability

e data used to support the findings of this study are in-cluded within the article Any other data used to support thefindings of this study may be released upon request to theauthor(s) who can be contacted at musmankaistackr

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] M Zain M Usman S H Farooq and A Hanif ldquoProgressivestructural capacity loss assessmentmdasha framework for modernreinforced concrete buildingsrdquo PLoS One vol 13 no 12Article ID e0208149 2018

[2] Report from earthquake engineering research Institute (ERRI)httpswwweeriorglfepdfkashmir_eeri_2nd_reportpdf

[3] Government of Pakistan Building Code of Pakistan PakistanEngineering Council Government of Pakistan IslamabadPakistan 2007

[4] D Bonowitz Seismic Design in Pakistan Be Building CodesBylaws and Recommendations for Earthquake Risk Reduction

United Nations Development Programme New York NYUSA 2015

[5] C Xu J Deng S Peng and C Li ldquoSeismic fragility analysis ofsteel reinforced concrete frame structures based on differentengineering demand parametersrdquo Journal of Building Engi-neering vol 20 pp 736ndash749 2018

[6] J Ji A S Elnashai and D A Kuchma ldquoAn analyticalframework for seismic fragility analysis of RC high-risebuildingsrdquo Engineering Structures vol 29 no 12 pp 3197ndash3209 2007

[7] M Zain N Anwar F A Najam and T Mehmood ldquoSeismicfragility assessment of reinforced concrete high-rise buildingsusing the uncoupled modal response history analysis(UMRHA)rdquo in Proceedings of the International Conference onEarthquake Engineering and Structural Dynamics ReykjavikIceland June 2017

[8] A Ali T Sandhu and M Usman ldquoAmbient vibration testingof a pedestrian bridge using low-cost accelerometers for SHMapplicationsrdquo Smart Cities vol 2 no 1 pp 20ndash30 2019

[9] Y Pang X Wu G Shen and W Yuan ldquoSeismic fragilityanalysis of cable-stayed bridges considering different sourcesof uncertaintiesrdquo Journal of Bridge Engineering vol 19 no 4Article ID 04013015 2014

[10] A Rasheed S H Farooq M Usman A Hanif N A Khanand R A Khushnood ldquoStructural reliability analysis of su-perstructure of highway bridges on China-Pakistan economiccorridor (CPEC) a case studyrdquo Journal of Structural Integrityand Maintenance vol 3 no 3 pp 197ndash207 2018

[11] J-T Wang M-X Zhang A-Y Jin and C-H ZhangldquoSeismic fragility of arch dams based on damage analysisrdquo SoilDynamics and Earthquake Engineering vol 109 pp 58ndash682018

[12] Y Yazdani and M Alembagheri ldquoSeismic vulnerability ofgravity dams in near-fault areasrdquo Soil Dynamics and Earth-quake Engineering vol 102 pp 15ndash24 2017

[13] S Leonidas and A Kappos ldquoDerivation of fragility curves fortraditional timber-framed masonry buildings using nonlinearstatic analysisrdquo in Proceedings of the 4th International Con-ference on Computational Methods in Structural Dynamicsand Earthquake Engineering Kos Island Greece June 2013

[14] J Alam M S Islam M Hussan and A Sarraz ldquoSeismicfragility assessment of RC building using nonlinear staticpushover analysisrdquo in Proceedings of the International Con-ference on Planning Architecture and Civil Engineering(ICPAC) Rajshahi India February 2017

[15] M Ni Choine M M Kashani L N Lowes et al ldquoNonlineardynamic analysis and seismic fragility assessment of a cor-rosion damaged integral bridgerdquo International Journal ofStructural Integrity vol 7 no 2 pp 227ndash239 2016

[16] K Bakalis and D Vamvatsikos ldquoSeismic fragility functions vianonlinear response history analysisrdquo Journal of StructuralEngineering vol 144 no 10 Article ID 04018181 2018

[17] FEMA Rapid Visual Screening of Buildings for PotentialSeismic Hazards A Handbook Federal Emergency Manage-ment Agency (FEMA) Washington DC USA third edition2015

[18] FEMA Technical and Userrsquos Manual HAZUSndashMH 21 De-partment of Homeland Security Federal Emergency Man-agement Agency (FEMA) Washington DC USA

[19] User Guide Perform 3D Nonlinear Analysis and PerformanceAssessment for 3D Structures Computers and Structures IncBerkeley CA USA 2011

[20] M M Rafi and M M Nasir ldquoExperimental investigation ofchemical and physical properties of cements manufactured in

12 Advances in Civil Engineering

approximately 82 probability of exceedance for the firstlimit state (LS1) while only around 20 probability ofexceedance has been achieved against the same seismicintensity for the second limit state (LS2) is essentiallyindicates the structural behavior dominated by the yieldingof the members instead of their complete failures At theseismic intensity of 140 g of PGA the structure seems to bein LS3 with almost around 100 of probability while whenSa(T1) is used as an IM the probability of being in LS3 at theseismic intensity of 140 g remains only around 20 isspecific variation in structural behavior is primarily attrib-uted to the inherent structural characteristics ie stiffnessand ductility that influence the response when the spectralacceleration is used as an IM after being scaled at thefundamental time period of the structure Since the selectedstructure is engineered the results are not so admonishingfor the considered school building typology neverthelessthe results might not be encouraging for other schoolbuilding types in the presented database e presentedconsolidated procedure is relatively simple and can bereadily adopted by the domestic and regional disaster pre-paredness and mitigation agencies to extend the applicationSuch studies are relatively new for under developingcountries like Pakistan and contemporarily no other workexists that may specifically address the vulnerability ofschools in seismic zone 4 of Pakistan Assessment of vul-nerabilities for other types of school buildings may yield aneed for immediate intervention in order to safeguard thelife of students and other users e presented study isspecifically targeted to assess the vulnerability and does notaddress the assessment of risk therefore the developedfragility curves can be further integrated with the hazardcurves of the considered area to evaluate the total riskinvolved

Data Availability

e data used to support the findings of this study are in-cluded within the article Any other data used to support thefindings of this study may be released upon request to theauthor(s) who can be contacted at musmankaistackr

Conflicts of Interest

e authors declare that they have no conflicts of interest

References

[1] M Zain M Usman S H Farooq and A Hanif ldquoProgressivestructural capacity loss assessmentmdasha framework for modernreinforced concrete buildingsrdquo PLoS One vol 13 no 12Article ID e0208149 2018

[2] Report from earthquake engineering research Institute (ERRI)httpswwweeriorglfepdfkashmir_eeri_2nd_reportpdf

[3] Government of Pakistan Building Code of Pakistan PakistanEngineering Council Government of Pakistan IslamabadPakistan 2007

[4] D Bonowitz Seismic Design in Pakistan Be Building CodesBylaws and Recommendations for Earthquake Risk Reduction

United Nations Development Programme New York NYUSA 2015

[5] C Xu J Deng S Peng and C Li ldquoSeismic fragility analysis ofsteel reinforced concrete frame structures based on differentengineering demand parametersrdquo Journal of Building Engi-neering vol 20 pp 736ndash749 2018

[6] J Ji A S Elnashai and D A Kuchma ldquoAn analyticalframework for seismic fragility analysis of RC high-risebuildingsrdquo Engineering Structures vol 29 no 12 pp 3197ndash3209 2007

[7] M Zain N Anwar F A Najam and T Mehmood ldquoSeismicfragility assessment of reinforced concrete high-rise buildingsusing the uncoupled modal response history analysis(UMRHA)rdquo in Proceedings of the International Conference onEarthquake Engineering and Structural Dynamics ReykjavikIceland June 2017

[8] A Ali T Sandhu and M Usman ldquoAmbient vibration testingof a pedestrian bridge using low-cost accelerometers for SHMapplicationsrdquo Smart Cities vol 2 no 1 pp 20ndash30 2019

[9] Y Pang X Wu G Shen and W Yuan ldquoSeismic fragilityanalysis of cable-stayed bridges considering different sourcesof uncertaintiesrdquo Journal of Bridge Engineering vol 19 no 4Article ID 04013015 2014

[10] A Rasheed S H Farooq M Usman A Hanif N A Khanand R A Khushnood ldquoStructural reliability analysis of su-perstructure of highway bridges on China-Pakistan economiccorridor (CPEC) a case studyrdquo Journal of Structural Integrityand Maintenance vol 3 no 3 pp 197ndash207 2018

[11] J-T Wang M-X Zhang A-Y Jin and C-H ZhangldquoSeismic fragility of arch dams based on damage analysisrdquo SoilDynamics and Earthquake Engineering vol 109 pp 58ndash682018

[12] Y Yazdani and M Alembagheri ldquoSeismic vulnerability ofgravity dams in near-fault areasrdquo Soil Dynamics and Earth-quake Engineering vol 102 pp 15ndash24 2017

[13] S Leonidas and A Kappos ldquoDerivation of fragility curves fortraditional timber-framed masonry buildings using nonlinearstatic analysisrdquo in Proceedings of the 4th International Con-ference on Computational Methods in Structural Dynamicsand Earthquake Engineering Kos Island Greece June 2013

[14] J Alam M S Islam M Hussan and A Sarraz ldquoSeismicfragility assessment of RC building using nonlinear staticpushover analysisrdquo in Proceedings of the International Con-ference on Planning Architecture and Civil Engineering(ICPAC) Rajshahi India February 2017

[15] M Ni Choine M M Kashani L N Lowes et al ldquoNonlineardynamic analysis and seismic fragility assessment of a cor-rosion damaged integral bridgerdquo International Journal ofStructural Integrity vol 7 no 2 pp 227ndash239 2016

[16] K Bakalis and D Vamvatsikos ldquoSeismic fragility functions vianonlinear response history analysisrdquo Journal of StructuralEngineering vol 144 no 10 Article ID 04018181 2018

[17] FEMA Rapid Visual Screening of Buildings for PotentialSeismic Hazards A Handbook Federal Emergency Manage-ment Agency (FEMA) Washington DC USA third edition2015

[18] FEMA Technical and Userrsquos Manual HAZUSndashMH 21 De-partment of Homeland Security Federal Emergency Man-agement Agency (FEMA) Washington DC USA

[19] User Guide Perform 3D Nonlinear Analysis and PerformanceAssessment for 3D Structures Computers and Structures IncBerkeley CA USA 2011

[20] M M Rafi and M M Nasir ldquoExperimental investigation ofchemical and physical properties of cements manufactured in

12 Advances in Civil Engineering

Pakistanrdquo Journal of Testing and Evaluation vol 42pp 774ndash786 2014

[21] American Society of Civil Engineers Seismic Evaluation andRetrofit of Existing Buildings (ASCE 41) American Society ofCivil Engineers Reston VA USA 2013

[22] C Xuewei H Xiaolei L Fan and W Shuang ldquoFiber elementbased elastic-plastic analysis procedure and engineering ap-plicationrdquo Procedia Engineering vol 14 pp 1807ndash1815 2011

[23] J B Mander M J N Priestley and R Park ldquoeoreticalstress-strain model for confined concreterdquo Journal of Struc-tural Engineering vol 114 no 8 1988

[24] R P Kennedy ldquoRisk based seismic design criteriardquo NuclearEngineering and Design vol 192 no 2-3 pp 117ndash135 1999

[25] M Zain N Anwar F Najam and T Mehmood ldquoA simplifiedmethodology for seismic fragility assessment of reinforcedconcrete high-rise buildingsrdquo in Proceedings of the In-ternational Conference on Earthquake Engineering andStructural Dynamics (ICESD) Reykjavik Iceland June 2017

[26] S Soleimani A Aziminejad and A S Moghadam ldquoAp-proximate two-component incremental dynamic analysisusing a bidirectional energy-based pushover procedurerdquoEngineering Structures vol 157 pp 86ndash95 2018

[27] K Kostinakis and A Athanatopoulou ldquoIncremental dynamicanalysis applied to assessment of structure-specific earth-quake IMs in 3D RC buildingsrdquo Engineering Structuresvol 125 pp 300ndash312 2016

[28] E Fereshtehnejad M Banazadeh and A ShafieezadehldquoSystem reliability-based seismic collapse assessment of steelmoment frames using incremental dynamic analysis andBayesian probability networkrdquo Engineering Structuresvol 118 pp 274ndash286 2016

[29] P Zarfam andMMofid ldquoOn the modal incremental dynamicanalysis of reinforced concrete structures using a trilinearidealization modelrdquo Engineering Structures vol 33 no 4pp 1117ndash1122 2011

[30] Y Pang and L Wu ldquoSeismic fragility analysis of multispanreinforced concrete bridges using mainshock-aftershock se-quencesrdquo Mathematical Problems in Engineering vol 2018Article ID 1537301 12 pages 2018

[31] H Jiang X Lu and L Chen ldquoSeismic fragility assessment ofRC moment-resisting frames designed according to thecurrent Chinese seismic design coderdquo Journal of Asian Ar-chitecture and Building Engineering vol 11 no 1 pp 153ndash160 2012

[32] H Omine T Hayashi H Yashiro and S FukushimaldquoSeismic risk analysis method using both PGA and PGVrdquo inProceedings of the the 14th WorldC Conference on EarthquakeEngineering Beijing China October 2008

[33] B Eden A Reyes Salazar E Hector et al ldquoEvaluation ofseismic fragility of steel frames using vector-valued IMsrdquo inProceedings of the 14th European Conference on EarthquakeEngineering pp 3622ndash3629 Ohrid Republic of MacedoniaAugust 2010

[34] T M Frankie B Gencturk A S Elnashai and ElnashaildquoSimulation-based fragility relationships for unreinforcedmasonry buildingsrdquo Journal of Structural Engineeringvol 139 no 3 pp 400ndash410 2013

[35] T Choudhury and H B Kaushik ldquoA simplified method forseismic vulnerability assessment of RC buildings with openground storeyrdquo in Proceedings of the 16th World Conferenceon Earthquake Engineering Santiago Chile January 2017

[36] N Buratti ldquoA comparison of the performances of variousgroundndashmotion intensity measuresrdquo in Proceedings of the

15th World Conference on Earthquake Engineering pp 24ndash28Lisbon Portugal September 2012

[37] E Bojorquez V Baca J Bojorquez A Reyes-SalazarR Chavez and M Barraza ldquoA simplified procedure to esti-mate peak drift demands for mid-rise steel and RC framesunder narrow-band motions in terms of the spectral-shape-based intensity measure Irdquo Engineering Structures vol 150pp 334ndash345 2017

[38] A Modica and P J Stafford ldquoVector fragility surfaces forreinforced concrete frames in Europerdquo Bulletin of EarthquakeEngineering vol 12 no 4 pp 1725ndash1753 2014

[39] J W Baker and C Allin Cornell ldquoSpectral shape epsilon andrecord selectionrdquo Earthquake Engineering amp Structural Dy-namics vol 35 no 9 pp 1077ndash1095 2006

[40] P Tothong and N Luco ldquoProbabilistic seismic demandanalysis using advanced ground motion intensity measuresrdquoEarthquake Engineering amp Structural Dynamics vol 36no 13 pp 1837ndash1860 2007

[41] M Kohrangi P Bazzurro and D Vamvatsikos ldquoVector andscalar IMs in structural response estimation part II buildingdemand assessmentrdquo Earthquake Spectra vol 32 no 3pp 1525ndash1543 2016

[42] E Bojorquez and I Iervolino ldquoSpectral shape proxies andnonlinear structural responserdquo Soil Dynamics and EarthquakeEngineering vol 31 no 7 pp 996ndash1008 2011

[43] J Pejovic and S Jankovic ldquoSelection of ground motion in-tensity measure for reinforced concrete structurerdquo ProcediaEngineering vol 117 pp 588ndash595 2015

[44] B L Khan H Farooq M Usman F Butt A Q Khan andA Hanif ldquoEffect of soil-structure interaction on a masonrystructure under train-induced vibrationsrdquo Proceedings of theInstitution of Civil EngineersndashStructures and Buildingspp 1ndash13 2018

[45] H Crowley R Pinho J J Bommer and Bommer ldquoAprobabilistic displacement-based vulnerability assessmentprocedure for earthquake loss estimationrdquo Bulletin ofEarthquake Engineering vol 2 no 2 pp 173ndash219 2004

[46] E M Guneyisi and G Altay ldquoSeismic fragility assessment ofeffectiveness of viscous dampers in reinforced concretebuildings under scenario earthquakesrdquo Journal of StructuralSafety vol 30 no 5 pp 461ndash480 2008

[47] C Casotto V Silva H Crowley R Nascimbene andR Pinho ldquoSeismic fragility of Italian RC precast industrialstructuresrdquo Engineering Structures vol 94 pp 122ndash136 2015

[48] H Chaulagain H Rodrigues V Silva E Spacone andH Varum ldquoEarthquake loss estimation for the Kathmanduvalleyrdquo Bulletin of Earthquake Engineering vol 14 no 1pp 59ndash88 2016

[49] D Gautam G Fabbrocino and F Santucci de MagistrisldquoDerive empirical fragility functions for Nepali residentialbuildingsrdquo Engineering Structures vol 171 pp 617ndash628 2018

[50] FEMA NEHRP Guidelines for the Seismic Rehabilitation ofBuildings Vol 273 Federal Emergency Management Agency(FEMA) Washington DC USA 1997

[51] M E Altug ldquoFragility-based assessment of typical mid-riseand low-rise RC buildings in Turkeyrdquo Engineering Structuresvol 30 no 5 pp 1360ndash1374 2008

[52] M Shinozuka M Q Feng H-K Kim and S-H KimldquoNonlinear static procedure for fragility curve developmentrdquoJournal of Engineering Mechanics vol 126 no 12 pp 1287ndash1295 2000

[53] M Shinozuka M Q Feng H Kim T Uzawa and T UedaldquoStatistical analysis of fragility curvesrdquo Technical Report

Advances in Civil Engineering 13

MCEER University of Southern California Los Angeles CAUSA 2001

[54] C-T Dang T-P Le and P Ray ldquoA novel method based onmaximum likelihood estimation for the construction ofseismic fragility curves using numerical simulationsrdquoComptes Rendus Mecanique vol 345 no 10 pp 678ndash6892017

[55] J W Baker ldquoEfficient analytical fragility function fitting usingdynamic structural analysisrdquo Earthquake Spectra vol 31no 1 pp 579ndash599 2015

14 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

MCEER University of Southern California Los Angeles CAUSA 2001

[54] C-T Dang T-P Le and P Ray ldquoA novel method based onmaximum likelihood estimation for the construction ofseismic fragility curves using numerical simulationsrdquoComptes Rendus Mecanique vol 345 no 10 pp 678ndash6892017

[55] J W Baker ldquoEfficient analytical fragility function fitting usingdynamic structural analysisrdquo Earthquake Spectra vol 31no 1 pp 579ndash599 2015

14 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom