ARTICLE

Analysis of a damaged 12-storey frame-wall concrete building duringthe 2010 Haiti earthquake Part I: Dynamic behaviour assessment1

Benoit Boulanger, Charles-Philippe Lamarche, Jean Proulx, and Patrick Paultre

Abstract: Despite all the damages encountered during the 2010 Haiti earthquake, the 12-storey reinforced-concrete Digicelbuilding behaved well, sustaining only reparable damages. Visual assessment to characterize the damages sustained andambient vibration tests (AVT) were carried out to identify the building's key dynamics properties (natural vibration frequencies,mode shapes, and damping ratios). ETABS was used to generate finite element (FE) models before and after the AVT, to evaluatethe capabilities of common modelling assumptions to predict the dynamic behaviour of structures. Nonautomated modelupdating was carried out to generate a model representing the building's actual dynamic behaviour in its damaged state. Thestudy showed that the finite element method (FEM) is reliable for predicting the dynamic behaviour of structures, but is verysensitive to the modelling assumptions. The models could predict the vibration frequencies precisely, but an accurate represen-tation of the mode shapes required careful model updating.

Key words: ambient vibration, reinforced concrete building, structural dynamic, Haiti earthquake, mode shapes, frequencies,damping, FE modelling.

Résumé : Malgré la destruction massive survenue lors du séisme d'Haïti en 2010, le bâtiment de 12 étages en béton armé de Digicela bien résisté, ne subissant que des dommages réparables. L'évaluation de sa structure ainsi qu'une série d'essais sous vibrationsambiantes ont permis de caractériser son comportement dynamique (fréquences propres, modes propres et amortissement). Desmodèles par éléments finis sur ETABS, avant et après les essais, ont permis d'évaluer la capacité de prédiction des techniques demodélisation courantes. Une calibration dumodèle de base a ensuite permis d'élaborer un nouveaumodèle numérique représentantbien le comportement réel du bâtiment. Cette étude a montré que la méthode des éléments finis permet de bien représenter lecomportement dynamique de structures, mais que la méthode est sensible aux hypothèses considérées. Il a aussi été observé qu'unmodèle peut prédire les fréquences propres sans pour autant représenter fidèlement le comportement dynamique (modes). Unecalibration efficace a été nécessaire afin d'avoir un modèle représentant bien le comportement du bâtiment.

Mots-clés : vibrations ambiantes, bâtiment en béton armé, dynamique des structures, séisme d'Haïti, modes propres, fréquences,amortissement, éléments finis.

1. IntroductionAdvances in earthquake engineering during the last few decades

have been driven by experimental and theoretical research, and,more importantly, by the lessons learned from historical seismicevents. The cases of the 1985 Mexico City earthquake, where soil–structure interaction was a key factor, and of the 1994 Northridgeearthquake, where fragile steel connections were observed, are twowell-known examples.

The magnitude 7.0 earthquake that struck Haiti on 12 January2010 left the capital city, Port-au-Prince, in a state of massive de-struction. Government estimates place the earthquake's deathtoll at more than 300 000. In addition, 1.5 million people were lefthomeless and over 500 000 displaced. The epicentre's proximity tothe vulnerable population of Port-au-Princewas directly related tothe extent of damage (Paultre et al. 2013). The vulnerability of thispopulation living in an active seismic zone can also be explainedby the lack of adequate seismic design codes, poor constructiontechniques, and inconsistency in materials quality.

In some areas of Port-au-Prince, more than 60% of the structureswere extensively damaged during the earthquake. Some buildingssustained very little damage and remained operational after theevent. This is the case of the city's tallest building: the 12-storey rein-

forced concrete Digicel tower. Located in a neighbourhood that wasalmost completely destroyed, the Digicel building withstood theearthquake and sustained only local damage. To give a comparativeidea of the intensity of ground motion, a recent four-storey rein-forced concrete hospital building collapsed across the street fromthe Digicel tower (see Fig. 1).

The Digicel building owners granted access to the structure, pro-viding a unique opportunity to assess its seismic performance basedon the observed damage. A series of ambient vibration tests (AVTs)was carried out to characterize the dynamic behaviour of the build-ing alongwith a thorough visual assessment of the structure to char-acterize the damage sustained. Nonlinear numerical analyses ofcalibrated models using various modelling hypotheses were subse-quently carried out to understand the earthquake's effects on thebuilding's structure.

This research project is presented in two companion papers. Thepresent paper (Part I) focuses on the field investigation and the finiteelement model (FEM) calibration. The building and its damage aredescribed, followed by the description of the ambient vibration sur-vey and results. In the third section, the effects of both structural andnonstructural components on the dynamic response are investi-gated by calibrating the FE models with the experimental data.

Received 7 March 2012. Accepted 9 May 2013.

B. Boulanger. Department of Civil Engineering, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada; Read Jones Christofferson, Suite 500, 144 Front Street West, Toronto,ON M5J 2L7, Canada.C.P. Lamarche, J. Proulx, and P. Paultre. Department of Civil Engineering, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada.

Corresponding author: Patrick Paultre (e-mail: Patrick.Paultre@usherbrooke.ca).1This paper is one of a selection of papers in this Special Issue on Lessons Learned from Recent Earthquakes.

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Can. J. Civ. Eng. 40: 791–802 (2013) dx.doi.org/10.1139/cjce-2012-0098 Published at www.nrcresearchpress.com/cjce on 28 May 2013.

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The objectives of this work were to characterize the damagessustained by the 12-storey building, identify the building's keydynamics properties in its damaged state (natural vibration fre-quencies, mode shapes, and damping ratios), and generate a FEmodel representative of the “true” structure, as built, based onthe AVT results and a thorough inspection.

2. The Digicel building

2.1. Building descriptionThe Digicel mobile-phone company building is located in the

Turgeau district of Port-au-Prince (Fig. 2). Construction started atthe end of 2006 and continued throughout 2007. The building wasconstructed in four consecutive phases, identified as 1–4 in theplan view of the ground level shown in Fig. 3. All the axes are 6 mapart and each storey is 3.8 m high.

Phases 1, 2, and 4 are located between axes A and D with a totalwidth of 18m. Phases 1 and 2 have bays that extend from axis 1 to 10,but are separated at axis 6, with respective lengths of 24 and 30 m.They both have two floors and a common underground parkingarea, which also extends through phase 4. Large steel trusses span-ning from axis A to D made it possible to avoid using columns inconstructing an atrium from axis 1 to 8 at the second level of thesetwo phases. At the time of the earthquake, the atrium was almostempty, and the rest of phases 1 and 2 were filled with light telecom-munications equipment. Phase 4 has eight identical bays (not shownin Fig. 3), with a total length of 48 m. This latter phase only hasunderground parking and a single floor above that, likely serving asoutdoor parking. The soil grade is at the parking level (basement) forthe entire north–west (NW) part.

Phase 3 represents the high-rise building that consists of onebasement (B in Fig. 4), a ground level (GL in Fig. 4), eleven floors,and the roof (R in Fig. 4), with a total height of 49 m from theground level to the roof. A square helicopter landing pad centeredat axis G-4 spans two bays on the roof. Themain floors are 24m by42 m, with a total area of 1008 m2, and are mostly open officespace. At the time of the earthquake, some storeys were com-pletely empty. The soil grade is at ground level on the sides of axis2 and L, but slopes gradually from ground level at L-6 to thebasement at D-6. Figure 4 shows an elevation view of a sectiongoing through the NW staircase, between axes 4 and 5.

2.2. Description of the structural systemA set of as-built drawings and several photos of the construction

sites were made available to the research team. No direct discus-sions with the design engineer ever took place. The only addi-tional information provided was that ASCE 7-05 provisions wereused to design the building. Many differences were observed be-tween the drawings and the visual inspection of the structure.Dimensions measured at the site were used in all the analysespresented herein (such as column diameters, beam depts., etc.).The steel reinforcement details in the drawings were taken asaccurate. Moreover, because phase 4 was added a posteriori, andthe drawings were not available, the necessary information wasobtained by visual assessment and on-site measurements.

The four phases of the building shown in Fig. 3 were apparentlydesigned as independent structures, because they were built in-dependently with no monolithic casting or steel rebars passingthrough adjacent members. Figure 5a illustrates the junction ofthe two columns at A-6, between phases 1 and 2. The connectionbetween the tower (phase 3) and phase 2 is similar.

The lateral force-resisting system for phases 1 and 2 is amoment-resisting frame. All columns and beams have rectangu-lar dimensions of 600 mm by 300 mm with a 200 mm-thick one-way slab. All beams have seismically detailed stirrups with 135°hooks. In the short direction, the designer added stirrups in theslabs in the vicinity of the beams, probably to confine a greaterconcrete area therefore providing larger-beam secondmoment ofinertia and ductility for the weak building direction. Phase 1 hasits perimeter bays filled with masonry on every level as well asalong axis 8. In phase 2, all the upper-level perimeter bays havemasonry infill. At the parking level, the infill only goes up to halfthe column height. No detail was found in the drawings for thereinforcement for those masonry walls. The number of out-of-plane collapses during the earthquake suggests that the masonrywalls are unreinforced. Square isolated footings are all joined byburied beams to form a monolithic foundation.

The tower's structure (phase 3) is a dual system ofmoment framesand shearwalls acting together to resist lateral loads (Fig. 6). L-shapedwalls are present at the north and south corners. U-shaped wallsenclosing a staircase and an elevator are found at the east corner,with a door opening on the ground level along axis L. The U-shaped

Fig. 1. In background: the Digicel Building located in a damaged area of Port-au-Prince; on the left: the collapsed “Hopital de Turgeau”.

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Fig. 3. Plan view of the ground level.

Fig. 2. Southwest elevation of the Digicel building.

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wall is closedbyamasonry infillwall alongaxisK.At thewest corner,U-shapedwalls enclosing the elevator shafts have been placed in thesecond bay for architectural considerations. Their open side facesNW; doors on axis 3 and 4 provide access to the elevator shaft. Thisyields a system of U-shaped walls coupled with two T-shaped col-umns. From the basement to the seventh floor, the beams are400 mm wide, changing to 300 mm for the remaining storey. Allbeams are 600 mm deep, including the 200 mm-thick slabs, whichare identical on all floors. All walls are 300mmthick. For the bottomparts, all perimeter columns measure 400 mm by 800 mm, reducedto 300mm by 600mm on the upper floors. All the interior columnsare circularwith diameters varying from800mmat the basement to500 mm on the top floors. Infill walls are present on all floors nearthe north shear walls, as illustrated in Fig. 6.

Apart from the infill walls shown in Fig. 6, very few interiorpartitions are present. Most of the offices consist of movable par-titions or gypsumwallboard, which are not likely to influence thedynamic behaviour of the entire building. The exterior claddingconsists of a light glass wall attached outside the structure with aconnection system of slotted holes that allow a certain amount ofmovement (Fig. 5b). This system was chosen to make up for struc-tural defects. This building is therefore an ideal candidate for aresearch project because the nonstructural components have verylimited effect on the structure's overall stiffness. On the otherhand, material uniformity and quality are uncertain parametersin this project. Studies of FE model updating of buildings in Van-couver revealed that material properties can diverge from ex-pected values by more than 50% (Ventura et al. 2005). Suchvariations are most certainly greater than usual in Haiti, becausematerial quality controls aren't as strict as in industrialized coun-tries. This uncertainty could very well apply to steel-rebar detail-ing also.

2.3. Description of the observed damagesAs in most buildings subject to strong ground accelerations, non-

structural damage tookplace in thehighest part of the tower. Fallingof suspended ceilings and tumbling of many desks and bookcasestook place. The exterior cladding's flexible connection system savedalmost all of the exterior windows. The masonry walls clearly con-tributed to the lateral resisting process because many infill wallssustained severe shear cracks and even partial collapse (Fig. 7a).

The greatest damage to the tower occurred as flexural damageto beams and columns on the top storeys in the longitudinaldirection. From the 7th storey up, most columns exhibited appar-

ent concrete crushing (Fig. 7b). Segregation of large aggregates atcolumnbases yielded poor concrete quality in regionswhere largeinelastic member rotation is expected (plastic hinges). This kindof segregation often results from poor vibration of the fresh con-crete during casting. Light concrete crushing, bond splitting, andeven rebar buckling were observed in many beams directly con-nected to shear walls (Fig. 7c). The most damaged beams werethose connecting to the east U-shaped wall on axes 5 and 6 on thetop four storeys. Other cracks in beam–column joints as well asceramic floor damage around columns suggest significant flexuraldeformations. The greatest damage to the concrete walls was ob-served around the opening at the bottom of the east wall (Fig. 7d).Some local crushing of the outer armof the U-shapedwall at K-6 alsooccurredon thebottomfloors. Largeopenings in the couplingbeamsyielded some local damage as well. Despite the observed level ofdamage, the building was deemed safe for occupancy after a com-plete inspection by a structural engineer immediately after theearthquake. The required repairs were carried out after a completestructural analysis of the building by a foreign engineering firm. Therepairs consisted in chipping of the spalled cover concrete andfillingof the voids with grout. Most damaged elements were repaired withcomposite confinement wrapping.

The low-rise part of the building (i.e., phases 1, 2, and 4) sufferedirreparable damage, therefore requiring their demolition. The de-molition had not started when our investigation took place. Forsafety reasons, the parking level (phase 2) was the only area avail-able for inspection and damage assessment. Important shear andflexural failures were observed in many interior columns on theparking level. These diagonal shear cracks were present at severalplaces on almost all columns in the transverse direction, as illus-trated in Fig. 8. For the exterior columns, the half-storey masonryinfill wall led to shear failure, which is often observed with shortcolumns (Fig. 9a). Most infill walls in phases 1 and 2 were alsodamaged, along with the columns enclosing them. The steel roofof the atrium collapsed during the earthquake. The trusses onaxes 5 and 6 lost seating at their exterior ends when the masonryparapet wall fell on the steel roof (Fig. 9b).

When two insufficiently spaced buildings with different dy-namic behaviours oscillate and collide, significant local damagetypically occurs. An obvious damage pattern resulting frompounding was observed between the tower (phase 3) and the low-rise part (phases 1, 2, and 4). As mentioned earlier, these phaseswere built separately and independently. Figure 9c shows the re-sults of such pounding. The pounding left a clear separation be-tween the two building structures, as shown in Fig. 9d. Suchobservations suggest that pounding influenced the building'searthquake response.

3. Dynamic behaviour survey

3.1. Ambient vibration testsIn recent years, the development of numerical methods and the

rapid evolution of technologies have led to several numericaltools for assessing the dynamic behaviour of structures. Thesetools, however, may have led many engineers to overlook thedifficulties in the importance of finding the “true” structural char-acteristics of structures. The structural engineering communityhas thoroughly discussed and recognized that FEM accuracy isgreatly enhanced if updated based upon experimental evidence.Dynamic characteristics (natural vibration frequencies, modeshapes, and damping) are usually determined by either forced-vibration tests or AVTs.

AVT reliability was assessed and proven by Lamarche et al.(2008) by comparing ambient test results with forced vibrationtest results. The AVTmethod is generallymuch faster and cheaperto perform, because it typically requires less equipment and in-frastructure. The fact that AVT is nondestructive also represents amajor advantage, making it very popular. Such experiments have

Fig. 4. Elevation of axis 4.

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been performed on dams (Darbre and Proulx 2002), bridges(Brownjohn and Xia 2000), stadiums (Saudi et al. 2009), and build-ings (Ventura and Schuster 1996; Lamarche et al. 2009). Resultsfrom these various field investigations were primarily used to findkey dynamic properties and update FE models (Ventura et al.2005). Ambient vibration tests were carried out on the Digicelbuilding to calibrate its structural properties in its damaged state.

3.2. Signal processingOf the methods for extracting the modal properties from AVT

data, frequency–domain decomposition (FDD) has become one ofthe most popular method used nowadays (Brincker et al. 2001).This method can be viewed as an extension of the traditionalfrequency–domain basic-peak-picking method. In the FDDmethod, the modal frequencies are identified by analysing thepower-spectral-density matrices that are decomposed at every fre-

quency line by performing singular-value decomposition (SVD).This process results in sets of principal values and orthogonalvectors. In the FDDmethod, the natural frequencies are identifiedby “peak picking.” By peak picking the frequencies of interest onthe singular values curves, the first vector obtained by the SVDwill give an estimate of the mode shape for that given frequency.The user can then inspect the mode shape corresponding to acertain peak and decide if it is actually a vibration mode. The FDDmethod is based on the following hypotheses: (i) the excitation ispure white noise; (ii) the damping is small; and (iii) all modeshapes are orthogonal (Brincker et al. 2001). After identifying fre-quencies by peak picking and extracting the corresponding modeshapes from the singular vectors, equivalent single-degree-of-freedom spectral bells are identified. The modal assurance crite-rion (MAC) is used to compare the mode shape and determinewhich singular values should be kept in the single-degree-of-freedom spectral bell. The bell is then transformed back into thetime domain using the inverse fast Fourier transform (FFT), there-fore yielding the corresponding autocorrelation function. Thenatural frequency is then re-evaluated by counting the number ofzero crossings in a finite time interval of the autocorrelation func-tion, and damping ratios are estimated from the logarithmicdecrement of the same autocorrelation function. This special pro-cedure is referred to as the enhanced FDDmethod (Brincker et al.2001). The reliability of the FDD and enhanced FDD methods hasbeen addressed thoroughly in recent literature. The reader canfind more details on FDD in Brincker et al. (2001) and Lamarcheet al. (2008). Its application has also been further discussed inVentura et al. (2003).

3.3. Instrumentation and testing procedureThe ambient vibration survey of the Digicel tower took place on

18 and 19 May 2010, four months after the earthquake. The firstday of testing was clear and sunny with light winds. The buildingwas nearly unoccupied as it was a national holiday. On the secondday of testing, the winds were much stronger. In addition, officeactivities and construction workers around the building — notpresent the first day of testing — induced higher levels of excita-tion. Work in the building included regular office work as well asceiling and masonry repairs. Excavation and other heavy workalso took place outside the building.

SixMR2003 + Syscomunidirectional horizontal velocity sensorswere used to measure the building's ambient vibrations. Dataacquisition was carried out with a 16-bit National InstrumentsDAQ systemwith eight channels, allowing high-pass and low-passfiltering capabilities and adjustable gains. The measurementswere taken at a sample rate of 200 Hz and an 80 Hz low-pass

Fig. 5. (a) Connection of phases 1 and 2; (b) flexible connection system used for exterior cladding.

Fig. 6. Plan view of a typical storey with the sensor positions.

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antialiasing filter was used. Prior to the field work, a FEmodel wasprepared using the as-built plans available, to pre-establish thebuilding's dynamic properties. The details of the model and re-sults will be presented later in this paper. The FE model helpeddetermine where to place the reference sensors and to plan effi-cient configuration patterns. Based on the FEmodelmode shapes,we decided to place the reference sensors at the east corner (axisL-6) of the fifth floor. The roof was not an option because of cablelength considerations. This location was chosen to get both trans-lational and torsional modes, and because it was not located onany mode shape nodes. The other four sensors were movedaround the building to accurately describe the mode shapes. Twoconfigurations of four sensors per floor were used to record data atthree corners and at the geometrical centre in both horizontal direc-tions (Fig. 6). The acquisition time was set to 10 min per configura-tion, corresponding to approximately 400 times the first vibrationperiod obtained numerically. This value is within the recommendedrange discussed by Lamarche (2005).

3.4. Test results

3.4.1. Time domain resultsA total of 27 data acquisition configurations were taken during

the two days. Figures 10a and 10b display short time windows oftypical velocity responses for the reference sensors in both hori-zontal directions. Figure 10c and 10d illustrate similar strongerresponses recorded on the second day when stronger winds

were observed. Their root mean square (RMS) values of 0.161 and0.176 mm/s are significantly higher than those observed on theprevious day with RMS values around 0.02 mm/s. These graphsalso show the predominance of the first period of vibrations ineach signal. Based on the distance between the responses peaks inthe time domain, the first periods of vibration were estimated tobe approximately T1Y = 1.4 s in the longitudinal direction andT1X = 1.2 s in the transverse direction, which strongly correlateswith the frequency domain results that will be discussed later.Because these periods correspond to frequencies below 1 Hz, anamplitude-correction transfer was applied in the frequency do-main to correct the transducer response below 1 Hz. The uncor-rected and corrected responses were plotted, showing the greatercorrection of the low-frequency amplitudes.

3.4.2. Singular values and mode shapesThe singular value decomposition of the power-spectral matri-

ces separates the energy of a dominating mode from the energyrelated to noise or other close modes. The ARTeMIS Extractor(Structural Vibration Solutions 2005) software package was usedto compute the SVD curves. A total of 8192 data points were usedwith a Nyquist frequency of 100 Hz to compute the FFT corre-sponding to a 0.012 Hz frequency resolution. An overlap averagingof 66.7% was used. Figure 11a shows the first four SVD lines of atypical setup. Sixmodes can be identified from the clear peaks of thefirst SVDaverage line. The spectral bells corresponding to thefirst six

Fig. 7. (a) Masonry-wall damage; (b) flexural damage and concrete segregation; (c) bond splitting failure in a beam; (d) concrete crushing in theeast wall.

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vibrationmodes are represented by bold lines in Fig. 11a. These spec-tral bells were identified using a MAC rejection level of 0.8.

Figure 11b presents the average of the first SVD line of all con-figurations. The bold curve with the most energy represents thetest configurations recorded during stronger wind episodes (testday 2). The lower bold curve was obtained during lighter windepisodes (test day 1). The shaded area represents the upper andlower limits corresponding to the mean, plus or minus one stan-dard deviation. The fact that these shaded areas are rather thinillustrates good correlation between all acquisitions. The first sixmodes are summarised in Table 1. Separating the acquisitionsaccording to the level of ambient excitation (wind) confirms thatthe analysis method remains accurate even with low vibrationlevels. Furthermore, isolating the higher amplitude vibrationsmakes it possible to identify highermodes. Two extramodes wereidentified at 5.3 and 6.7 Hz. These modes were not identifiablefrom the lower amplitude recordings. Nevertheless, the corre-spondingmode shapes were difficult to plot because of their weakenergy level. Isolating the helipad setup also allowed for identify-ing local modes at 6 and 10 Hz (not shown in Fig. 12).

Figure 12 presents the first six mode shapes extracted from theFDD. The in-plane rigid-diaphragm hypothesis for the floor slabswas verified from the shapes obtained from the acquisitions takenat three corners as well as the centre of each floor. The fourthcorner's position was then calculated accordingly. The first modeis longitudinal in the Y direction and the first transverse mode inthe X direction has an atypical shape with the south–east parthaving much larger amplitude than the NW part, adding sometorsional behaviour (see Fig. 6 for X and Y sensor directions). This

amplitude difference between both ends of the building can beexplained by the eccentricity between the torsion centre and thecentre of mass. This eccentricity is obviously due to an irregularpattern in the lateral force-resisting systems, because the in-planemass distributions of the various floors are uniform. The third andsixth modes are two typical torsional modes with a slight trans-verse component in the X direction. Mode 4 is the second longi-tudinal mode, with a little more transverse component than thefirst mode. Mode 5 is a second transverse mode with the sameasymmetric pattern as mode 4.

3.4.3. DampingThe difficulties in estimating damping ratios from AVTs have

been an issue since the early beginnings of dynamic testing. Tri-funac (1972) compared AVT results with forced-vibration test re-sults and found damping ratios differed depending on themethodof analysis. Trifunac (1972) concluded that estimating dampingfrom AVT was not accurate unless very small frequency resolu-tions were used. Ventura and Schuster (1996) also discussed thatthe damping ratios found with AVTs were very sensitive to analy-sis parameters. In addition, Tamura et al. (2004) studied the loga-rithmic decrement technique of FDD and found that dampingratios tended to converge as the number of data points used in theFFT increased. This can be explained by the bias error introducedby the spectral leakage that has not been completely eliminatedin the postprocessing windowing process. Because the bias erroris proportional to the square of the frequency resolution (Bendatand Piersol 2000), increasing the number of data points reduces

Fig. 8. Damage to columns in the parking area of the low-rise building.

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leakage. This phenomenon is illustrated in Fig. 13 as the dampingratios of the first five modes are plotted as a function of the num-ber of data points used to compute the FFTs.

The values converge when asmany as 8192 or 16 384 data pointsare used. In recent years, Lamarche (2005) and Lamarche et al.(2008) verified this statement and obtained realistic values ofdamping with AVT results at times when the method's reliabilitywas still questioned.

Table 2 shows the average damping ratios obtained for the firstfive modes of vibration. The spectral bell of mode 6 was not clearenough to get reasonable damping estimates. The damping valueswere obtained from an average of the 27 recordings acquired fromsix velocity sensors. The results show that the damping ratiosranged from 1.0% to 1.5%. It must be kept inmind that these valueswere obtained from AVTs and that they are related to very smallamplitudes of motion. It is expected that higher damping valueswould be obtained from forced vibration tests and during strongground motions with significantly higher input forces as the mi-crocracks in the concrete would open and close, thus adding hys-teretic damping to the structure (Lamarche et al. 2008).

The inclusion of five acquisitions datasets that occurred duringhigh wind periods raised the possibility of investigating the effectof motion amplitude on the damping ratios. Li et al. (2004) illus-trated the nonlinear energy dissipation characteristics of a tallbuilding in China by comparing the different damping ratiosfound in functions of the building motion's amplitude. Increasesof 0.2%–0.4% were observed. The average RMS of the referencesensors increased from0.05 to 0.16mm/swith thewind during the

AVT. The damping ratios for all modes increased from 0.1% to 0.8%depending on the level of wind speeds, showing that the level ofexcitation has an effect on the identified damping ratios.

4. Finite element modellingThe level of confidence in FE models is greatly increased when

calibrated with experimental data. The following sections illus-trate a typical FE model built from the original drawings, aswould be used during design. The calibration of the FE modelusing the modal analyses results from the AVT data are pre-sented in Sect. 4.2.

4.1. Pretest FE modelThe ETABS software was used to model the structure of the

Digicel tower. Amodel was developedwith the available drawingsand visual assessment information obtained during the in-situsurvey. All beams and columns were modelled with simple frameelements, using their true section size. T-beam sections withflange widths calculated according to the formulas given inPaulay and Priestley (1992) were used to include the slab effect.Shell elements were used tomodel the shear walls; their openingswere included. Rigid diaphragms were used at each floor withlumped masses. Rigid links were used at every connection. Thereduced stiffness of the beams and columns used in the modelswere adjusted to account for the joint stiffnesses. The concretedensity was assumed to be 2400 kg/m3. A 24 GPa Young'smodulus,

Fig. 9. (a) Short-column damage; (b) top view of the steel-roof collapse; (c) evidence of pounding; (d) postquake separation between phases 2and 3.

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which roughly correspond to a concrete with f ′c = 30 MPa, wasconsidered.

The gross moments of inertia, Ig, were reduced to account forcracking. In the case of the columns, 0.7Ig was used, correspond-ing to axial load levels ranging between 0.2Agf

′cand 0.5Agf

′c,

where Ag is the gross area. For the beams, 0.35Ig was used, while0.7Ig was used for the shear walls. These values correspond tothose proposed by Paulay and Priestley (1992) and in the CSA-A23.3Design of Concrete Structures Standard. The masonry infill wallswere not included in this preliminary “pretest” model, as is oftenthe case at the design state.

The periods of vibration of the first sixth modes are shown inTable 1 and graphically compared in Fig. 14. The pretest modelresults in frequencies all within 15% of the experimental data,which was deemed “quite” acceptable for a noncalibrated model.The mode shapes, however, do not correspond to the structure'sobserved behaviour, as shown in Fig. 15. The pretestmodel yieldedto coupled modes, in x and y, for the first two modes. Experimen-tally, the first mode is clearly in the Y direction, and the second inthe X direction with a slight torsion component. This patternsuggests that the stiffness in the X direction was underestimatedin the preliminary model, leading to poor MAC values, as shownin Fig. 16.

From these results, it is clear that the model based on the avail-able drawings and the aforementioned design assumptions doesnot accurately reproduce the true dynamic behaviour of the Digi-cel structure. Moreover, a model with good correlation with thevibration periods can still inaccurately represent the actual build-ing's dynamic behaviour (mode shapes).

It is of interest to note that the measured fundamental period inboth orthogonal directions T1Y = 1.42 s and T1X = 1.15 s, fall within theempirical period range prescribed by the National Building Code ofCanada (NBCC) for the seismic design of buildings with concreteshear walls as themain seismic force resisting system (i.e., Ta = 0.93–1.85 s). This reflects the fact that only secondary load carrying mem-bersweredamaged in restricted areas in thebuildingwhile the shearwalls were not damaged during the earthquake.

Fig. 10. Typical corrected and uncorrected responses of referencesensors for light and high winds.

Fig. 11. (a) Four first SVD lines of setup 18 with the spectral bells fora 0.8 MAC rejection level; (b) SVD lines with standard deviationlimits for the setups with and without high winds.

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4.2. Updated FE modelThe model was calibrated to converge towards the experi-

mental dynamic behaviour. The major change to the originalmodel is the addition of the masonry wall on axis E, whichstiffened the NW transverse direction (X direction). This stiff-ening shifts the torsion centre from the geometrical centretoward this end of the building as observed experimentally.The infill walls were modelled by diagonal equivalent strutswith a Young's modulus E = 10 GPa. The equivalent section wasset to 250 mm thick, which corresponds to the wall's actualthickness, by 800 mm deep, which correspond to approxi-

mately 25% of the clear diagonal length of the infill bays, asrecommended by Paulay and Priestley (1992).

Resulting from this addition, the MAC values were significantlyimproved to almost perfect values (Table 1 and Fig. 16). The addedstiffness in the X direction left a weaker Y direction, bringing thefirst mode in the Y direction, as observed experimentally. Theunbalanced stiffness brought on by the infill wall is responsiblefor the torsion component in the second mode. This shows theimportance of the infill walls in the building's dynamic behaviour.Their participation in sustaining lateral forces was confirmedfrom all the diagonal cracks that were observed on site.

Several iterations were necessary to converge toward a finalupdated model with vibration periods and MAC values that al-most perfectly corresponded to the experimentally identified val-ues (Table 1, Figs. 14 and 16). Infillwallswere addedonaxesEandK. Theiteration process includes the variation of the concrete density, �,and the elastic moduli, E, of the various elements. The effective

Table 1. Comparison between the experimental and the numerical natural periods of the first sixvibration modes identified.

Experimental Pretest FEM Updated FEM

Mode Type Freq. [Hz] T [s] T [s] Diff [%] MAC T [s] Diff [%] MAC

1 1-Y 0.70 1.42 1.28 −10.2% 0.42 1.42 −0.1% 0.992 1-X 0.87 1.15 1.17 1.9% 0.30 1.11 −3.4% 0.983 1-T 1.24 0.81 0.92 13.8% 0.85 0.87 7.9% 0.984 2-Y 2.47 0.40 0.34 −15.4% 0.49 0.35 −14.2% 0.985 2-X 2.97 0.34 0.30 −11.6% 0.37 0.28 −16.4% 0.986 2-T 4.25 0.24 0.22 −6.3% 0.68 0.21 −8.8% 0.76

Fig. 12. Mode shapes found experimentally.

Mode 1: T = 1.42 s Mode 2: T = 1.15 sMode 3: T = 0.81 s

Mode 4: T = 0.40 s Mode 5: T = 0.34 s Mode 6: T = 0.24 s

Fig. 13. Convergence of the damping ratios with the increase ofdata points used.

Table 2. Average damping ratios for all the ac-quisitions and for the five with high wind (val-ues in %).

All High wind

Avg ref RMS 0.05 mm/s 0.16 mm/sMode 1 1.45% 1.78%Mode 2 1.26% 1.42%Mode 3 1.22% 1.31%Mode 4 1.43% 2.20%Mode 5 1.20% 1.94%

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inertias of the various members that were considered in Section4.1 were kept unchanged, because they already represent severecracking. The claddings were not introduced in the updatedmodel because of the negligible rigidity introduced by the flexibleconnection system (Fig. 5b). Table 3 presents the final values of thematerial properties that led to the best correlation. Usually thematerial properties should be determined through laboratorytesting. This option was not possible in the present work and the

material properties were adjusted to correlate with the AVTresults. The results show that the concrete properties were notlikely to be as high as reported during construction. The signif-icant decrease in the elastic modulus of the concrete beams andcolumns, compared to the walls, reflects their greater damage.

The updatedmodel has periods that agree almost perfectly withthe experimental values for the first two modes. For the subse-quentmodes, the errors remain low. This is acceptable if we recallthat the project's main objective was to assess the importance ofeach modeling parameter to create nonlinear models that assessthe building's seismic behaviour to explain the observed damage.Because vibration periods change during a nonlinear analysis, themost important dynamic parameter is the mode shapes that dic-tate structures’ responses during an analysis. The MAC values of98% for the first five modes and the 75% MAC value for the sixthmode are high enough to assume that the building's dynamicbehaviour has been accurately modelled.

5. Summary and conclusionsDespite the severity of the 2010 Haiti earthquake, the 12-storey

Digicel building behaved well from a structural engineeringpoint of view, and sustained little damage. Experimental workconsisting of visual assessments to characterise the damagessustained, and AVTs were carried out and to identify the build-ing's key dynamic properties (natural vibration frequencies,mode shapes, and damping ratios). ETABS was used to generateFE models before and after the AVT to assess the capabilities ofcommon modelling assumptions in predicting the structure'sdynamic behaviour.

AVT yielded to the identification of the first six modes of vibra-tion and corresponding damping ratios of the building structurein its damaged state, confirming the efficiency and accuracy of theAVT method in identifying structural dynamic properties. Theseismic behaviour of the Digicel building was thenmodelled withaccuracy through model updating, laying the ground for a more

Fig. 14. Comparison of the pretest and updated model vibrationfrequencies with the experimental ones.

Fig. 15. Comparison of the pretest and updated model vibrationmodes with the experimental ones.

Pretest FEM modes Experimental modes

Mode 1: T = 1.28 s

x

y

Mode 1: T = 1.42 s

Mode 2: T = 1.175 s Mode 2: T = 1.15 s

Fig. 16. Comparison of the MAC values for the pretest and updatedmodels.

Table 3. Material properties for the pretestmodel and the updated model.

Model

Properties Pretest Updated

� concrete 2400 kg/m3 1800 kg/m3

E columns 24 GPa 13.9 GPaE beams 24 GPa 14.5 GPaE walls 24 GPa 20.7 GPaE masonry — 13.5 GPa

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sophisticated nonlinear analysis presented in the companion pa-per.

In this study, it was found that the infill walls had a majorimpact on the building's dynamic behaviour and that the concreteelastic modulus, E, was likely not as high as reported during con-struction. Without the inclusions of the infill masonry walls, theFE model would not have been truly representative of the actualdynamic behaviour of the structure. In essence, the study showsthat the FEM is reliable in predicting structure dynamic behaviour,but that it is very sensitive to the assumptions used during themod-elling process. Based on as-built drawings, the FEM could predict thevibration frequencies precisely, but an accurate representation ofthe mode shapes required careful model updating.

AcknowledgementsThe authors would like to acknowledge the financial support of

the Natural Sciences and Engineering Research Council of Canada(NSERC) for the Canadian Seismic Research Network (CSRN), theQuébec Fonds pour la Recherche sur la Nature et les Technologies(FQRNT) for the Centre d'Études Interuniversitaires des Structuressous Charges Extrêmes (CEISCE), and the Canadian Associationfor Earthquake Engineering (CAEE). The authors would also liketo acknowledge the cooperation of Ian Jones, construction man-ager of the Digicel building, who provided invaluable informa-tion.

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