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Engineering Structures 32 (2010) 1876–1887

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Engineering Structures

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Case study: Analytical investigation on the failure of a two-story RC buildingdamaged during the 2007 Pisco-Chincha earthquakeOh-Sung Kwon, Eungsoo Kim ∗Department of Civil, Architectural, and Environmental Engineering, Missouri University of Science and Technology. 1401 N. Pine Street, Rolla MO, 65409, USA

a r t i c l e i n f o

Article history:Available online 29 December 2009

Keywords:Pisco-Chincha earthquakePost-earthquake analysisShort column effectsInfill masonry wallConfinement effectSeismic performanceReinforced concrete structures

a b s t r a c t

The Pisco-Chincha earthquake hit the western shore of Peru on 15 Aug 2007. More than five hundredpeople perished and numerous residential structures made of masonry and adobe collapsed. Manybuildings were severely damaged by settlement due to liquefaction. In general, engineered reinforcedconcrete structures experienced less damage compared with structures constructed with traditionalconstruction practice. This paper presents a case study on a two-story RC building in Ica, Peru which wasseverely damaged during the earthquake. Field observations suggest that causes of the structural failureare: (1) short column effects resulting from masonry infill walls; (2) an overloaded second floor; and(3) insufficient stirrups in the columns. To test these hypothesized causes of column failure, analyticalmodels based on measured section dimensions and reinforcement bar configurations from the fieldinvestigation are used. Nonlinear response history analyses are carried outwith groundmotions recordedat a seismic station located 500 m from the reference structure. The analysis results show that the partialinfill walls and a lack of shear reinforcement were the leading causes of the column failures. The resultsalso show that the overloaded columns do not significantly influence the seismic demand of the referencestructure. Stirrups in the columns mainly affect seismic capacity and have relatively no effect on seismicdemand for the ground motion that the building was subjected to.

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1. Introduction

On August 15, 2007, the Pisco-Chincha earthquake, of magni-tude 8.0±0.1 struck the coastal region of central Peru, causing con-siderable damage and loss of life. The earthquake was attributedto the highly active source created by the subduction of the Nazcaoceanic plate under the South American continental plate. Themechanism of the earthquake was complex with two major rup-tures approximately 50 s apart. The loss of life was estimated at600 and several hundreds were injured. The earthquake destroyedover 50,000 buildings and severely damaged at least 20,000 others.A team of researchers from the Mid-America Earthquake Center inUS, Peru–Japan Center for Seismological Investigations and Disas-ter Mitigation in Peru, and National University of Peru jointly in-vestigated the resultant damage to building structures and bridges,road failures, effects of land slide and liquefaction, and the seismichazards of the affected area [1]. The majority of structural failureswere in clay and brick masonry structures. However, several rein-forced concrete (RC) structures also suffered major damage or col-lapse, often due to soft story effects and lack of vertical continuity.

∗ Corresponding author. Tel.: +1 573 341 4046.E-mail address: [email protected] (E. Kim).

0141-0296/$ – see front matter© 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2009.12.022

The lack of ductile detailing was clear and repetitive even in mod-ern constructions. The field investigation provided a valuable op-portunity to closely investigate one of the damaged RC structures,which is the topic of this study.The objective of this study is to investigate the failure

mechanism of one of the RC structures damaged from theearthquake. The failure in this study refers to the loss of lateralload resisting capacity due to the earthquake. The referenceRC structure is a two-story building which housed chemistrylabs and class rooms at the National University of Ica locatedapproximately 117 km from the epicenter of the earthquake asshown in Fig. 1. Many residential structures in Ica are constructedwith adobe and masonry and were heavily damaged while mostengineered structures survived the earthquake without significantdamage. However, a few engineered structures, including theone investigated in this study, suffered irrepairable damage. Thereference building in this studywas of high interest to investigatorsas it was one of a few engineered structures which were severelydamaged in the earthquake. In addition, ground accelerations ofthe eventwere recorded at a seismic station located approximately500 m from the building. With actual dimensions of structuralelements along with the close-to-actual input ground motiondata, the main causes of the structural failure can be identifiedthrough numerical analyses. The numerical model also allows forparametric studies to be conducted such that the relative effects of

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Fig. 1. Location of the reference structure.

Fig. 2. First floor plan of the reference building.

several structural deficiencies on the seismic performance of thebuilding can be investigated.In the following sections, the configuration of the building

and characteristics of recorded ground motions at nearby groundmotion station is introduced. The observed structural damagesfrom the field investigation and hypotheses on the causes of thestructural damages are introduced. Finally, the analytical modelof the building, the analysis parameters, and the analysis resultsare presented followed by summary of key findings from this casestudy.

2. Reference building and recorded ground motions

2.1. Configuration of the reference building

The reference building is a two-story reinforced concretestructure consisting of 12 bays in the east–west (EW) direction and3 bays in the north–south (NS) direction as depicted in Fig. 2. Thebuilding was constructed as two independent modules separated

by slabs and beams at the interface of themodules. A stairwell wasalso independently constructed. The height of the both stories is4.1 m and the spans of each bay are 4.2 m × 8.0 m. At the eastand west facades of the building, additional columns, CW21–23and CE21–23 were constructed on the first floor to support gravityloads of story-high infillwalls on the second floor as shown in Fig. 2.Fig. 3 illustrates the elevation of the west and north facades of thebuilding indicated in Fig. 2. Exterior walls facing east and westinclude story-high infill walls as shown in Fig. 3(a). Partial infillwalls were constructed between most columns in north and southfacades of the building, Fig. 3(b). Openings forwindows are presentinmost of the infill walls in the north and south facadeswhile otherwalls include openings used as entrances. Damage to the structuralelements is indicated in Fig. 3 which will be discussed in detailin Section 3. Infill walls are made of clay bricks with thickness of175 mm. On the second floor, slabs are extended as cantilevers onwhich cladding was constructed.Column dimensions of the building are 350 mm× 550 mm for

all columns except intermediate columns (350 mm × 480 mm)

1878 O.-S. Kwon, E. Kim / Engineering Structures 32 (2010) 1876–1887

Fig. 3. Elevation of west and north face of the building and damage patterns.

350

350

480550 550

350

(a) Columns. (b) Beam.

Fig. 4. Section dimensions.

in the west and east facades as shown in Fig. 4. Eight #5 (diam-eter φ = 15.8 mm) longitudinal reinforcement bars are used forexterior columns and four #5 bars are used for interior columns.From field observations of the columns, which experienced a lossof cover concrete during the earthquake, it was found that an in-sufficient amount of stirrups were used in the columns. Only one#3 (φ = 9.52mm) stirrup was used at the end of each column andsmoothwires (φ = 5mm)were used to hold the longitudinal rein-forcement bars in place. Beams were 350mm×650mm includinga 250 mm slab thickness. Reinforcement bars of beams and slabscould not be identified as the beams were not damaged during theearthquake and their interiors were not exposed.

2.2. Recorded ground motions

The accelerometer at the ICA2 station in Fig. 1 was locatedon the first floor of a two-story building similar to the referencestructure. Since the accelerometer was installed on the firstfloor of the building, it was anticipated that the recordedground motion includes vibration components resulting fromsoil–structure interaction. With limited information on soilprofiles, it was assumed that soil profiles at the reference buildingand at the building housing the accelerometer are similar. Hence,soil–structure interaction is not explicitly accounted for in theanalysis as it is implicitly considered by applying recorded motionon the first floor of a similar building.Fig. 5 shows the time history of the EW component ground

motion recorded at the ICA2 station. The ground motion has

two distinctive peaks at an interval of approximately 50 s. Thisenvelope of the acceleration time history was observed from allrecorded ground motions at other stations, from which it canbe inferred that the two distinctive peaks are from consecutiveruptures at the source of the earthquake rather than local siteeffects. Elastic response spectra with 2%, 5%, and 10% damping arepresented in Fig. 6. The ground motion has spectral acceleration of0.7–0.8g between 0.1 s to 0.6 s of period range.The earthquake lasted longer than 150 s. Damage likely resulted

from the many large amplitude cycles and the long duration ofthe earthquake which were devastating to non-ductile structures.Several intensity parameters of the ground motion are comparedwith those of ground motions recorded from different earthquakeevents. Peak values in the time domain, such as PGA, PGV, and PGD,are the most frequently used parameters to define the intensityof ground motions. However, these parameters lack many otherimportant features of ground motions such as number of cyclesand frequency content. The nonlinear response of structures can beinfluenced by other ground motion parameters such as frequencycontent, duration, number of large amplitude cycles, energy flux,etc. The following ground motion parameters summarized inKramer [2] are evaluated for the ground motions recorded atstation ICA2 after baseline correction.PGA = max |a(t)| (1)vmax/amax = PGV/PGA (2)

arms =

√1tr

∫ tr

0[a(t)]2 dt (3)


Fig. 5. Recorded acceleration from station ICA2 (EW component).

Fig. 6. Acceleration–displacement response spectra of the EW component.

Ia =π

2g

∫∞

0[a(t)]2 dt (4)

SED =∫ tr

0[v(t)]2 dt (5)

where a(t), v(t), and tr are recorded acceleration, velocity, andtotal duration of record, respectively. arms is root-mean-squareof acceleration, vmax/amax is peak velocity to peak accelerationratio, Ia is Arias intensity, and SED is specific energy density. Sincethe method adopted for baseline correction significantly affectsthe velocity and displacement time history, PGV and PGD arenot compared. The evaluated intensity measures are presented inTable 1. As a reference, the parameters of a few representativeearthquake groundmotions are also presented. For the comparisonwith the groundmotion record at ICA2 station with PGA of 0.341g ,ground motions with similar PGA (around 0.3g) are selected.It can be noted from Table 1 that while other parameters donot show large differences between recorded ground motions,the Arias intensity and specific energy density of the earthquakerecord from ICA2 station are much larger than those from otherearthquake events. The Arias intensity and specific energy densityare greatly affected by earthquake duration in comparison withother intensity parameters. Fig. 7 compares the energy flux ofthe record from ICA2 station with records from other earthquakeevents. The 2007 Pisco-Chincha earthquake is characterized bya much larger energy flux when compared to other earthquakeevents with similar PGA due to its prolonged ground motiondurationwhichmay have been the primary cause of buildingswithpoor ductility capacity.

3. Observed damage and assumed causes of the damage

The first-story columns of the west module of the structure inFig. 2 were heavily damaged by the earthquake. Many columns

Fig. 7. Energy flux comparison of the Pisco-Chincha earthquake with otherearthquake events.

completely lost their capacities to resist gravity loads. Fieldinvestigation of the damaged structure suggest three possiblecauses for the structural failure: short column effect, insufficientstirrups and overloaded columns.

3.1. Short column effects due to infill walls

At the south and north facades of the building, partial infill wallswere constructed between columns. Most infill walls remainedintact while some of the infill walls developed minor cracks andcrushing at the corners. Fig. 3 depicts the severity of columndamage with three damage indices ranging from DI1 to DI3, whichcorrespond to minor cracks (DI1), loss of cover concrete andexposure of longitudinal bars (DI2), and buckling of longitudinalbars, fracture of stirrups, and loss of core concrete (DI3). Thesedamage indices qualitatively correspond to usable, repairable, andirrepairable damage state. From Fig. 3(b), it can be observed thatcolumns CW16, CW18, CW19, and CW20 suffered more severedamage (DI3) than columns CW15 and CW17. The columns withless damage have partial infill wall on one side and no wall onthe other side of the columns. From this observation, it can bepresumed that the restraints of infill walls to the columns mighthave had an influenced on the observed column damage.Fig. 8 shows two examples of column failure from the

earthquake. In Fig. 8(a), the infill wall on the left side of thecolumn is higher than the infill wall on the right side, which leadto non-symmetric deformation capacity of the column and theformation of shear cracks in one direction. In Fig. 8(b), due tothe restraints from the infill walls, damage is concentrated at oneend of the column. The damage patterns of these columns clearlyshow that the infill walls influenced the column damage. It is welldocumented that short columns reduce structural periods, whichin general increase the seismic force demand. In addition, shortcolumns are subject to non-ductile shear failure rather than ductile


(a) Column CW18. (b) Column CW16.

Fig. 8. Typical column failure modes of the reference building.

Table 1Intensity measures of ground motions from the Pisco-Chincha earthquake.

Earthquake Station Component PGA (g) vmax/amax (s) arms (g) Ia (m/s) SED (m2/s)

Pisco-Chincha, 2007 ICA2 NS 0.341 0.190 0.033 3.698 13074LomaPrieta, 1989 Gilroy Array #2 0 0.367 0.091 0.044 1.197 875Northridge, 1994 Beverly Hills Vertical 0.327 0.053 0.054 1.349 415Kobe, 1995 Kakogawa 90 0.345 0.082 0.052 1.687 1625Kocaeli, 1999 Duzce 180 0.312 0.192 0.051 1.085 7339

flexural failure. The effects of short column on shear capacity anddemand are analytically investigated in Sections 4 and 5.

3.2. Inappropriate stirrups

Several damaged columns experienced loss of cover concreteand core fromwhich information pertaining to columndimensionsand number of reinforcement bars were extracted. Fig. 9 is a close-up view of the two damaged columns with exposed stirrups andlongitudinal reinforcements. The field investigation revealed thatonly one stirrup with regular deformed bar was used at the end ofthe column. For the remaining parts of the columns, smooth wireswith diameters of 5 mm or less were used as stirrups instead ofregular deformed reinforcement bars.Poor confinement characterized by the usage of smooth wires

stirrups resulted in crushing of the core concrete and subsequentlybuckling of the longitudinal reinforcements. The combinationof increased shear force demand from column shortening andreduced shear capacity from inappropriate stirrups are expected tobe the major contributing factor to the column failure. The effectsof confinement on the seismic demand and shear capacity areinvestigated analytically in Section 4.

3.3. Overload on the second floor

Even though the structure consists of two identical modules asshown in Fig. 2, the columns in the west module were significantlymore damaged than those in the right module. Fig. 10 shows thatcolumns CW06, and CW07 were severely damaged and crusheddue to the loss of core concrete. A close look at the plans of thesecond floor and load carrying system suggests that the columns

in the west module of the building might have been overloadedin comparison with those in the right module. From the fieldinvestigation, it was found that the span surrounded by columnsCW06, CW07, CW14, and CW13 was heavily loaded with partitionwalls. In addition, there was fairly heavy cladding on the canopy ofthe span which can be seen in Fig. 10. The west and east facadeof the building also have story-high infill walls on the secondfloor as shown in Fig. 3(a). However, the load from the infill wallsis distributed to additional intermediate columns CW21, CW22,CE22, and CE 23 in Fig. 2. On the other hand, the shaded span inFig. 2 has no additional load carrying columns which can sharethe load of infill walls on the second floor. It is hypothesized thatthe failure of columns CW06 and CW07 may have resulted fromlarge overload on the second floor. Crushing and shortening of thecolumns of this span might have redistributed gravity loads overother columns CW04 and CW05 resulting in progressive columnfailures. The effect of overload is analytically studied in Section 4.

4. Analytical model of the reference building

A 3D analytical model was developed to understand the causesof the structural failures. The columns and beams are modeledwith fiber-based section elements in Zeus-NL [3]. Infill walls aremodeled as diagonal struts as shown in Fig. 11. In the followingsections, employed assumptions and numerical models of frameelements and infill walls are presented.

4.1. Reinforced concrete frames

The building consists of two modules separated by a small gap.Considering the very similar geometry of the two modules, it is

Administrator

Highlight


(a) Column CW05. (b) Column CW16.

Fig. 9. Exposed reinforcement bars from damaged columns.

Fig. 10. Overloads on columns CW06 and CW07.

assumed that the modules have similar fundamental periods andpounding of the twomodules is unlikely and can be ignored. Hence,the west module of the building in Fig. 2 is modeled for responsehistory analysis. The material properties of the concrete and steelreinforcements could not be identified from the field investigation.Thus, the strengths of concrete and steel reinforcements areassumed based on typical material properties commonly used inPeru. Loaiza and Blondet [4] reported that concrete strength forbuilding structures in Peru ranges from 21 MPa to 35 MPa andthe steel yield strength is 410 MPa. Based on the study by Loaizaand Blondet [4], the strength of concrete used in the analysisis set to 27 MPa and the yield strength of steel at 410 MPa.Dimensions of column and beam sections were obtained from thefield. The diameters and number of longitudinal and transversereinforcements of columns are as shown in Fig. 4. Beam elementsaremodeled as T -beams to account for the contribution of slabs onflexural stiffness and strength. The effective flange width of the T -beams is determined according to ACI 318-08 [5]. The dimensionsand number of the beam reinforcement bars could not be obtainedfrom the field investigation as the beams were not damagedby the earthquake. The beam reinforcements are determined bydesigning the T -beam sections against gravity load.

Beam and column elements are modeled with fiber-basedsection elements while accounting for material and geometricnonlinearity. During the analysis, the sectional stress–strain stateis obtained through the integration of the inelastic materialresponse of the individual fibers describing the section. Eulerian-based geometric nonlinearity is employed on the element level.In doing so, the spread of inelasticity along the member lengthand across the section depth as well as the effect of large memberdeformations are all considered. Since the sectional response iscalculated at each loading step from inelastic material models thataccount for stiffness and strength degradation, there is no needfor sweeping assumptions on themoment–curvature relationshipsrequired by other analysis approaches. The concrete is modeledusing a nonlinear hysteretic uniaxial concretemodel with constantconfinement based on the model presented by Mander et al. [6].Steel is modeled with the bilinear elasto-plastic model withkinematic strain hardening.

4.2. Masonry infill walls

Masonry walls are modeled with compression-only diagonalstruts as illustrated in Fig. 12. The strut strength can be determinedconsidering the three possible failure modes of infill walls: namelycompression failure of diagonal strut, sliding shear failure of themasonry along horizontalmortar, and diagonal tensile cracking [7].Among these failure modes, the first and the second failure modesare the most common failure modes for infill walls. In this study,the shear strengths of the infill walls corresponding to the firstand the second failure modes are calculated for each infill wall.The minimum of the shear strengths from the two failure modes isconsidered as the ultimate strength. Themodeling of the infillwallsfollows the method presented in Mostafaei and Kabeyasawa [8]and is summarized below.

4.2.1. Compression failure of diagonal strutsCompressive strength of the masonry prism is a key parameter

in themodeling of infill walls. Paulay and Priestley [7] proposed thefollowing equation for the estimation of the compressive strengthof the masonry prism, f ′m.

f ′m = fy ={f ′cb(f ′tb + αf

′

j

)}/{Uu(f ′tb + αf

′

cb

)}(6)

where α is j/4.1h, j is thickness of mortar, h is height of themasonry unit, Uu is stress nonuniformity coefficient (Uu = 1.5following Hilsdorf [9]), f ′tb is tension strength of brick (= 0.1f

′

cb), f′

cbis compression strength of brick, and f ′j is mortar compressionstrength. Eq. (6) requires material parameters of brick and mortar,


Fig. 11. Analytical model for the frame-infill wall system.

Fig. 12. Infill masonry walls and the equivalent diagonal strut parameters.

which could not be identified from the field investigation. Loaizaand Blondet [4] reported that the strength of masonry prism oftypical masonry walls in Peru ranges from 13 to 16MN/m2. In thisstudy, the median value of this range, 14.5 MN/m2, is used for thecompression masonry prism strength.Compression failure of infill walls occurs due to the compres-

sion failure of the equivalent diagonal strut. The horizontal com-ponent of the diagonal strut capacity (shear force) is,

Vc = ztwf ′m cos θ (7)

where f ′m ismasonry compression strength for ungrouted clay brick(14.5 MPa [4]), and z is equivalent strut width based on FEMA306 [10].

4.2.2. Sliding shear failure modeShear strength for the sliding shear failure mode, τf , can be

defined by the Mohr–Coulomb failure criteria:

τf = τo + µσN (8)

where τo is cohesive capacity of the mortar beds, µ is sliding fric-tion coefficient along the bed joint, and σN is vertical compressionstress in the infill wall. In terms of force,

Vf = τotw lm + µN (9)

where tw is infill wall thickness, lm is length of infill panel, and Nis vertical load in infill walls. The infill walls in the reference frameare not load bearing walls. Thus N can be approximated as verticalcomponent of the diagonal compression force, Rc sin θ , where Rc isdiagonal compression force, Fig. 12. Eq. (9) can be rewritten as

Rc cos θ = τotw lm + µRc sin θ

or,

Vf =τotw lm

1− µ tan θ. (10)

Typical ranges for τo and µ are 0.1 ≤ τo ≤ 1.5 MPa and 0.3 ≤µ ≤ 1.2 [8]. For analysis purposes, τo = 0.04 f ′m = 0.04 (14.5) =0.58 may be assumed [7]. Based on previously conducted experi-mental work, Chen [11] reported that the frictional coefficient, µ,can be defined as:

µ = 0.654+ 0.00525 f ′j (11)

where f ′j is mortar strength in MPa. Assuming f′

j = 4.9 MPa, fric-tional coefficient is calculated as µ = 0.68. Hence, Eq. (10) yieldsthe following:

Vf =0.58tw lm

1− 0.68 tan θ(12)

where Vf , tw , and lm are expressed in N, mm, andmm, respectively.

4.2.3. Hysteretic behavior of a diagonal strut elementThe shear strengths obtained from the sliding shear failure and

the diagonal compression failure may not exceed 0.83 MPa asrecommended in ACI 530-05/ASCE 5-05 [12].

Vmax/tw lm = 0.83 MPa. (13)

The two diagonal struts of infill walls provide resistance againstlateral load. In this study, it is assumed that force–displacementrelationship of each diagonal strut follows a tri-linear curve undercompression and zero tension strength as shown in Fig. 13. Thehysteretic behavior of diagonal struts is modeled with lumpedsprings at the end of the strut and the strut is modeled withrigid truss element. The tri-linear displacement–force relationshipconsists of yield shear force (Vy), maximum shear force (Vm),yield displacement (Uy) and maximum displacement at peak force(Um). The maximum displacement at the maximum lateral force isestimated by Eq. (14) following Madan et al. [13].

Um =ε′mdmcos θ

(14)


Vm

UmUy

K0

K0

α

Vy

Fig. 13. Hysteretic behavior of diagonal strut elements.

where ε′m is the masonry compression strain at the maximumcompression stress and assumed as 0.0018 and dm is the diagonalstrut length. Themaximum drift limitation of 0.8% is applied to theUm/hm ratio, based on the results from [11,14]. The initial stiffnessKo is determined as follows according to Madan et al. [13]:

K0 = 2(Vm/Um) (15)

where Vm is the maximum strength determined from Eqs. (11)–(13). The stiffness ratio, α, is assumed as 0.2 and Uy and Vy, areestimated based on Vm, Ko, and, α.

4.3. Damping

The commonly used damping ratio for elastic analysis ofreinforced concrete structures is 5% of the critical damping.When a structure behaves in a nonlinear range, the hystereticbehavior of materials dissipates energy. Thus, the application ofthe same amount of damping to elastic and inelastic systems isnot feasible [15]. Considering that the reference structure showedsignificant excursion into the inelastic range, 2% of the criticaldamping is assumed in the analytical model.

5. Analysis cases and result

The nonlinear time history analysis is adopted to evaluate theseismic performance of the structure. There are several othermethods for the seismic performance evaluation. With the recenttrends on the adoption of the performance-based seismic designand evaluation, the displacement-based approach is widely usedin recent studies instead of the traditional force-based evaluation.The capacity spectrum methods in ATC-40 [16] and Chopra andGoel [17] can provide approximate seismic performance utilizingthe structural resistance and seismic demand represented in theacceleration–displacement response spectra format. But to applythe capacity spectrummethod, a structure’s pushover curve shouldbe able to represent the global force–deformation relationship.If a structure has very stiff elements, such as infill walls orbraces, or if the structure develop brittle failure due to shear,the performance evaluation using capacity spectrum can be verydifficult. As the reference structure have many masonry wallsand the columns failed with brittle shear failure, the force-based evaluation combined with nonlinear time history analysis isadopted rather than displacement-based evaluation. The analysiscases and results are presented in the following sections.

5.1. Analysis cases

The developed numerical model is analysed with several dif-ferent parameters to determine the causes of the structural fail-ures introduced in Section 3. Table 2 summarizes the analysis cases

considered in this study. Each row corresponds to different analy-sis case and each column represents the controlled parameter. Case1 is the as-built condition of the reference building which includesmasonry infill wall, columns with insufficient stirrups, and over-loaded columns. The actual gravity load on the second floor in theoverloaded span shown in Fig. 2 is included in themodel. The verti-cal groundmotion in addition to two components of the horizontalground motion is also included in the analysis case. The analyticalmodels for cases 2 through 5 are based on themodel for case 1. Dif-ferent parameters in cases 2 to 5 are controlled to investigate theeffects of these parameters. The effects of masonry infill wall onseismic force and displacement demands are investigated in case2 in which the first hypothesis on the causes of structural failure istested.Case 3 is concerned with the effect of confinement on seismic

response and structural capacity. The stirrups in the columns havetwo major functionalities, providing confinement which increasesconcrete strength and ductility, and increasing shear strength.In case 1, the confinement effect is ignored by employing aconfinement factor of 1.0 since the columns in the building do nothave structural grade stirrups. The contribution of 5 mm smoothwire to the confinement effect is ignored. In case 3, it is assumedthat the columns meet the minimum requirement for stirrups forseismic design according to ACI 318-08 [5] and the correspondingconfinement factors are determined by the method presented byMander et al. [6]. Based on ACI 318-08 [5], the column sectionsare assumed to have a #4 (φ = 12.7 mm) rectilinear hoop withone crosstie arranged with a spacing of 100 mm. The confinementfactor for the column sections C1, C2, and C3 in Fig. 4 withminimum required stirrups are 1.43, 1.32, and 1.32, respectively.The effects of stirrups on seismic demand and shear strength arecompared in Section 5.3.Case 4 evaluates the effect of overloading on the second floor. In

case 4, the gravity load from heavy cladding on the canopy of theoverloaded span shown in Fig. 2 is not considered which reducesaxial force on the columns CW06 and CW07. Since the fiber-based section elements adopted to model columns and beamsestimate stiffness and strength from stress–strain relationship ofindividual fiber. Therefore, the effects of different axial forceson axial capacity of columns are automatically reflected duringresponse history analysis.In case 5, the vertical ground motion is not included to

investigate the effect of vertical ground motion on seismicresponse. The PGA of the vertical ground motion of the site is0.19g , which may increase axial force on columns resulting in thecrushing of core concrete or resulting in low moment strengths incolumns. The vertical ground motion also can decrease the axialforce on columns which can affect the shear capacity of a concretesection. The effects of the variation of axial force due to verticalgroundmotion on the structural response are investigated througha comparison of cases 1 and 5.Response history analyses for the above five analysis cases

are carried out with the recorded ground motions at stationICA2. For each analysis case, story displacement demand, axialforce demand, shear force demand, and shear force capacityare evaluated at every time step. The employed elements forbeams and columns can simulate flexural deformation and flexuralfailure of reinforced concrete elements with a high level ofconfidence. But the load redistribution due to shear failure andshear deformation cannot be represented with the model. Evenwith more sophisticated finite element analysis approaches for RCstructures, the prediction of shear failure and post-failure behaviorof RC structures is still very challenging. Hence, in this studythe shear failure is evaluated through comparison of shear forcedemand and shear force capacity at each time step. Analysis resultsare presented in the following sections.


Fig. 14. First-story relative displacement.

Table 2Analysis cases.

Masonry infill wall Confinement effects Overload Vertical ground motion

Case 1 Yes No Yes YesCase 2 No No Yes YesCase 3 Yes Yes Yes YesCase 4 Yes No No YesCase 5 Yes No Yes No

Notes: ‘Yes’ indicates that the effect of the parameter is considered, while analysis cases with ‘No’ do not include the effect. Case 1 is as-is condition. Other cases are to seethe effects of several parameters on seismic performance of the reference building.

5.2. Relative story displacements

The maximum story displacements from the five analysiscases are summarized in Table 3. Time history of the first-storydisplacement from cases 1 and 2 are presented in Fig. 14. FromTable 3, it can be seen that cases 1, 3, 4, and 5 have very similarmaximum story displacements. On the other hand, in analysis case2, which does not include infill walls, the story displacement isalmost five times greater than the story displacements observedin the other four cases. The structural models for cases 1 and 2have fundamental periods of 0.47 s and 0.64 s, which correspondsto the differences in stiffness with a ratio of 1.8. Hence, the largedifferences in the maximum story displacement between case2 and other cases originate from the large stiffness of the infillwalls. In case 3, the confinement factors for theminimum requiredstirrups, which increases strength and ductility of concrete, areincluded in the concrete material model. The analysis results showthat the maximum displacement from cases 1 and 3 are verysimilar. This implies that the concrete does not develop large strainto reach the increased strength due to the applied confinementfactor. This observation shows that the confinement factor does notgreatly contribute to the seismic demandwith the levels of appliedground motion used in this study.Shear deformation and shear failure are not represented in

the analytical model. Thus, it is expected that the maximumdisplacements may not be accurate. If columns fail due to shear,the inter-story displacement from these cases may be greater thanthe displacements presented in Table 3. Therefore, rather thanusing displacements as failure criteria, the failure of the structureis evaluated through comparison of shear strength capacity anddemand at each time step as presented in Section 5.3.

5.3. Comparison of shear force capacity and demand

The shear strength of RC members can be evaluated usingseveral formulas as suggested in ACI 318-08 [5]. The mostsimplified code formula considers the contribution of concrete andtransverse reinforcement bars to the shear strength of the section.More sophisticated equations consider the effect of span-to-depthratio through the applied shear force and moment demands.

Table 3Comparison of the first-story displacement.

Case 1 Case 2 Case 3 Case 4 Case 5

Maximum (mm) 19.68 99.03 19.52 19.31 19.61

Minimum (mm) −15.61 −65.23 −15.51 −15.33 −15.69

Contribution of axial force demand to the shear force capacity isalso considered in the code formula in which the shear strengthcapacity of concrete increases with the compressive axial force. Inthis study, the formula that includes the effect of axial force onconcrete shear strength is adopted in order to evaluate shear failureof columns.The failure of columns is evaluated through comparison of the

shear force capacity and demand at each time step. For analysiscases 1, 2, 4, and 5, the contribution of transverse reinforcementis not included in the shear capacity as the structure does nothave structural grade shear reinforcement. For analysis case 3, thecontribution ofminimumrequired shear reinforcement is includedin the shear strength evaluation. For all analysis cases, the effectof axial load to shear strength of concrete, Vc , is considered usingEq. (16).

Vc (t) = 0.17λ[1+

Nu(t)14Ag

]√f ′c bwd (16)

where, Ag is gross sectional area in mm2, Nu is axial force in Nwith positive sign for compression, f ′c is the concrete compressivestrength in MPa, bw is the web width in mm, and d is the effectivedepth in mm. The variable λ is 1.0 for normal weight concrete and0.75 for light weight concrete. The shear capacity contribution ofconcrete for member subjected to axial tension is calculated as

Vc(t) = 0.17λ[1+ 0.29

Nu(t)Ag

]√f ′c bwd. (17)

Fig. 15 presents the temporal variation of shear force demandand capacity of column CW19 from analysis case 1. The shearforce demand is a resultant force of two orthogonal shear forcesat the ends of a column. The shear force capacity varies withtime as the axial load on columns varies with time. It can be


300

250

200

150

100

Shea

r fo

rce

or c

apac

ity

(kN

)

Time (sec)

50

00 10 20 30 40 50 60

Fig. 15. Time history of shear force demand and capacity for CW19 in case 1.

Time (sec)

Shea

r de

man

d / c

apac

ity

0 10 20 30 40 50 60

2.01.81.61.41.21.00.80.60.40.20.0

Fig. 16. Time history of shear force demand to capacity ratio for CW19 in case 1.

Columns with infill walls

Fig. 17. Shear force demand-to-capacity ratio comparison of analysis cases 1 and 2.

seen from Fig. 15 that the variation of shear force capacity withtime is not significant in comparison with the variation of shearforce demand. Nonetheless, as both the shear force demand andcapacity of columns vary with time, the ratio of the shear forcedemand-to-capacity, Vu(t)/Vn(t), is evaluated at each time step.In Fig. 16 it can be seen that column CW19 in analysis case 1may have failed as the demand-to-capacity ratio is greater than1. However, as the material properties of the reference building isassumed in this study, the absolute magnitude of shear demand tothe capacity ratio may not be used as a criterion to define failureof a column. Since the objective of this study is to understand therelative effects of various parameters to the failure of the building,the relative demand-to-capacity ratios from the five analysis casesare compared with each other.Fig. 17 compares themaximum shear demand-to-capacity ratio

from analysis cases 1 and 2. From the figure, it can be seen thatthe shear demand-to-capacity ratios are relatively uniform in case2 while the ratios greatly vary in case 1. More specifically, thecolumns adjacent to infill walls, marked with dashed rectangularboxes in the figure, have noticeably higher demand-to-capacityratios than other columns. From this comparison, it can be seenthat the infill walls concentrate shear force demand to columns

in contact with the infill walls. But the infill walls reduce shearforce demand to other columns. A comparison of the demand-to-capacity ratios of columns from analysis cases 1 and 3 in Fig. 18shows that analysis case 3 has significantly lower shear demand-to-capacity ratio than case 1 due to increased shear capacity incase 3. Table 3 shows that case 3 has very similar displacementdemand to analysis case 1, which indicates that the shear demandto columns in case 1 and case 3 are very similar. Hence, thelow demand-to-capacity ratio in Fig. 18 implies that the shearcapacities of the columns in case 3 are large due to the contributionof shear force reinforcement. This result suggests that the columnsin the analysed structure may not have failed even if the minimumrequired amount of shear reinforcement is used in the columns.Figs. 19 and 20 compare the demand-to-capacity ratios fromanalysis case 1 with analysis cases 4 and 5, respectively. In bothcases, the ratios are very similar to case 1. Thus even though therewas large overload on one of the spans and a vertical groundmotion with PGA of 0.2g , the effect of axial load to the shearcapacity of the studied reinforced buildings is not significant.The comparisons of the shear demand-to-capacity ratios con-

sidering several parameters show that the infill walls concentrateshear force demand to adjacent columns, the stirrups do not affect





seismic demand through confinement effects but significantly af-fect the shear capacity of columns, and overload and the verticalgroundmotionmay not have significantly influenced the failure ofthe columns.

6. Conclusion

To understand themain causes of the structural failure of a two-story RC building damaged by the 2007 Pisco-Chincha earthquake,numerical models are developed based on the measured sectiondimensions and reinforcement bar configurations. Groundmotionsrecorded at a station located 500m from the reference building siteare used as input ground motions. Effects of masonry infill wall,stirrups, overloading, and vertical ground motions on structuralfailure are examined in five analysis cases. The following is asummary of the findings from this study.

• The first-story displacement is not significantly affected byconfinement effect, overloading on the second story, andvertical ground motion. The main factor contributing to story

displacement are the masonry infill walls which increase thelateral stiffness of the reference building.• The infill walls, especially partial story-height infill walls,concentrate shear forces to columns in contact with the infillwall while decreasing shear force demands to other columns.• When stirrups of columns are included in the analytical model,the stirrups donot affect seismic response through confinementeffects. This is mainly due to the fact that the ground motionlevel recorded at ICA2 station was not large enough to induceincreased concrete strength and ductility by confinementfactor. The stirrups however significantly decrease the sheardemand-to-capacity ratio.• The overload and vertical ground motions do not affect shearforce demand and capacity for the studied structure.

Some of the above findings are very specific to the studiedbuilding and the input groundmotion. For example, if a structure’sfailure is dominated by flexural failure, and if the ground motionintensity is large enough, the increase in strength and ductilitydue to confinement effects may have an effect on seismic


demand. This case study identifies main causes of the structuralfailure of a two-story RC building damaged during the 2007Pisco-Chincha earthquake. From the failure investigation of thereference structure, it can be learned that the building shouldnot have experienced column failures if minimum required shearreinforcement was used in the columns.

Acknowledgements

The field investigation after 2007 Pisco-Chincha earthquakewas supported by Mid-America Earthquake Center. The MAECenter is an Engineering Research Center funded by the NationalScience Foundation under cooperative agreement reference EEC97-01785.

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