System Identification of a Two-Story Infilled RC

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System Identification of a Two-Story Infilled RC Building in Different Damage States S. Yousefianmoghadam1; M. Song2; A. Stavridis3; and B. Moaveni4 1

Ph.D. Candidate, University at Buffalo, 116 Ketter Hall, Buffalo, NY 14260. E-mail: [email protected] 2 Ph.D. Student, Tufts University, 574 Boston Ave., Medford, MA 02155. E-mail: [email protected] 3 Assistant Professor, University at Buffalo, 224 Ketter Hall, Buffalo, NY 14260. Email: [email protected] 4 Associate Professor, Tufts University, 200 College Ave., Medford, MA 02155. Email: [email protected] Abstract This study focuses on vibration-based system identification of an actual structure located in El Centro, California. The structure had already been subjected to four earthquakes with epicenters in close proximity and was to be demolished due to the extended damage. Four damage levels were introduced to the structure by gradually removing four perimeter infill walls. A series of dynamic tests were conducted in each damage state using an eccentric mass shaker. The ambient vibration of the structure was also recorded through an array of 60 accelerometers mounted on the structure. The system identification discussed in this paper was conducted using the ambient vibration recordings. Moreover, a preliminary finite element model of the building was created to estimate numerically the dynamic characteristics of the structure. These were compared to the properties obtained from the system identification. The results indicate that the frequencies estimated by the model overestimate those obtained from the system identification results, while the experimentally and numerically obtained mode shapes are in good agreement. INTRODUCTION The dynamic properties of structures such as natural frequencies, mode shapes, and damping ratios and their changes can provide a powerful tool to detect and evaluate the damage induced on the structures by extreme loads such as earthquakes. Damage detection methods using these properties are classified as global algorithms and can be utilized in a rapid manner using sparse measurements (Sohn et al. 2004; Baghaei Naeini 2011). Such methods have been used by researchers on specimens damaged gradually during shake-table tests (Stavridis et al. 2012; Belleri et al. 2014; Astroza et al. 2013) or quasi-statically (Angel et al. 1994; Anil and Altin 2007). However, they do not present the same challenges as real structures due to the simplified test set ups. This is not the case for the studies focusing on actual bridges and buildings (Behmanesh and Moaveni 2014; Farrar and Jauregui 1998; Yu et al. 2008). However,

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in these cases the induced damage is typically local and minor because imposing damage to healthy and in service structures is often not feasible. As a result of these limitations, there is a lack of studies implementing system identification methods on actual structures at different levels of induced damage. Such studies can provide valuable information for damage assessment of buildings and also for the calibration of numerical models and the validation of model updating algorithms. This paper, describes the system identification performed on a two-story reinforced concrete frame with masonry infills which was hit by four major historic earthquakes. The severe damage to the building provided the opportunity to investigate the characteristics of a damaged structure which has exhibited significant nonlinear response. The study involved recordings of ambient vibration, as well as dynamic loading of the building using eccentric mass shakers. In the study presented here, the ambient vibration recordings have been used to obtain the dynamic properties of the building. A finite element model of the building was also built and calibrated based on the geometric and material data obtained before the tests. TEST STRUCTURE The two-story reinforced concrete moment frame structure with a basement, located in El Centro, CA is shown in Figure 1. The building was constructed in the 1920s and it was typical of the construction practice in California in that era. It had sustained damage during the Imperial Valley Earthquakes of 1940 and 1979, and the 1987 West Westmoreland Earthquake. The exterior frames and infills of the first floor were repaired and retrofitted after the first three earthquakes. However, the structure was red tagged and evacuated after the 2010 Baja California Earthquake due to extensive damage in the second story. With all non-structural components removed from the building, only its structural members, including the RC frame and the infill walls, was in place during the tests. The structure was scheduled to be demolished after the completion of the tests as it could not be repaired cost-effectively considering the economy in the area. North

West

Figure 1. Test Structure (photo by S. Yousefianmoghadam) Figure 2 shows the 26 m by 32 m (88 ft. by 106 ft.) plan view of the structure at the second floor level. The plan was rectangular except for the west exterior frame which was curved. Plan view of the first floor was similar to that shown in Figure 2 except that the exterior infills on the northern side had one frame recess to allow for a © ASCE and ATC 2015 Improving the Seismic Performance of Existing Buildings and Other Structures 2015

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ped destrian sidee walk passaage as shown n in Figure 1. On the ssouth, there was a onestorry wooden structure attaached to the main m buildinng as indicatted in Figuree 2.

Y X

Fiigure 2. Second floor pllan view inccluding the typical fram ming and jooists detail Thee structure comprised of six rein nforced conncrete framees in the nnorth‐south direection conneected by arcch-type joistts in the easst‐west direection. The dimensions and d reinforcem ment details of the joistss are shown in Figure 22. The interiior columns werre 40 cm (16 6 in.) diametter circular. The T exteriorr columns weere 40 cm byy 40 cm (16 by 16 in.) squaare except fo or the colum mns in south side and thee first-story columns in norrth side whicch were 40 cm (16 in.) diiameter circuular. Thee first story of o the structu ure had been n repaired annd retrofittedd in the late 1980s after the 1987 earthq quake. The retrofit r had focused f on sstrengtheningg of the massonry infills t first floo or. As a resu ult, there weere three typpes of infill iin this floor: reinforced of the con ncrete, unreinforced massonry and co ombinations of the two. The exterioor frames in the basement had h reinforcced concretee walls withh openings nnear the topp, while the second story had h a mason nry infill off two indeppendent wytthes in all tthe exterior fram mes. The wy ythes had a distance d of 10 1 cm (4 in.)) and the gapp in betweenn was filled witth a powderr; most prob bably for in nsulation reeasons. The stiffness annd strength disccontinuity between b the first and second storiess resulted inn severe dam mage of the second story in nfills and fraames in the North, Wesst, and Southh bays durinng the 2010 Bajja Californiaa Earthquakee. The east side s on the ssecond floorr that had a solid infill, and d the entire first f story thaat was streng gthened did nnot develop any visible cracks. Ind duced dama age Thee exterior in nfill walls were w part of o the lateraal load resissting system m and their rem moval could affect the lateral stiffn ness and strrength of thhe structure. Four infill wallls were rem moved at threee stages intrroducing fouur levels of damage to tthe building refeerred to as damage stattes in this paper. p The ffirst damagee state (DS1), was the inittial conditio on of the sttructure prio or to the exxperiment, w which incluuded a wall



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alreeady removeed in the bay y A3-A4 of the second ffloor. This w wall was rem moved prior to the t tests to allow a the slid ding of the shaker s inside. The seconnd damage sstate (DS2), resu ulted once th he infill in D6-E6 D bay in the secondd floor (Y-ddirection) waas removed, the third damag ge state (DS S3) resulted from the rem moval of thee infill in E66-F6 bay in n the second floor, and tthe fourth daamage state (DS4) was the same exteriior frame in intrroduced afteer the remov val of infills in F6-G6 annd G5-G6 inn the secondd floor. The locations and seequence of the t removed walls are shhown in Figuure 3.

Figure 3. Damage D statees and wall removal sequence.

DY YNAMIC TE ESTING Insstrumentatio on A total t of 97 seensors includ ding accelerrometers, striing pots andd LVDTs weere installed on the buildin ng to meassure accelerrations and displacemeents. To m measure the 2 uniaxial and a 39 triaxial force-ballance acceleerometers weere utilized. acccelerations, 21 Thee acceleromeeters were in nstalled closse to the fouur corners annd the centerr of the first and d second flo oor and the roof. r In everry location, they measuured the acceleration in two o horizontall directions and one vertical v direcction (X, Y Y, and Z), so that 15 accceleration meeasurementss were obtain ned at each llevel as show wn in Figuree 4a. The X direection corresponds to th he east-west direction w with positivve measurem ments being tow wards the weest and the Y direction correspondss to the norrth-south dirrection with possitive toward ds the north h. Moreover,, two triaxiaal accelerom meters were installed at the north-west and south-east corner of the basem ment, while thhree additionnal uniaxial acccelerometers were moun nted on the extension e buuilding at itss north and west sides. Fin nally, two triaxial accelerrometers weere installed oon the grounnd close to thhe structure at the t north and d west side of o it. To measure thee relative dissplacement between b the floor slabs, LVDTs andd string pots werre used. Thee former werre mounted on stiff polees with smaall masses neear the four corrners and ceenter of the first and second s floorr. Hence, thhey could m measure the relaative displaccement betw ween those stories s in tw wo horizontaal directionss (X, Y) at eacch location. The T stringpo ots were insttalled at the F1-G1 and F6-G6 bayss in the first


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and d second floor measurin ng horizontal, vertical annd diagonal relative dissplacements betw ween the flo oors as show wn in Figure 4b. 4

(a) accelerometters on main n structure (b) string ppots on the eeast and westt sides Figure F 4. Insstrumentatiion plan. In this paper, the system m identificattion results from the data recordded by the acccelerometers on the main n structure during d the am mbient vibraation of the bbuilding are presented. The sensors werre connected d to a dataloggger with daata sampling rate of 200 Hz and were sy ynchronized by GPS timing. od and Sequ uence Tessting Metho A series s of shaake tests weere performeed on the sttructure to iinvestigate iits dynamic pro operties in th he quasilineaar and nonlin near ranges oof behavior.. The experiments were con nducted usin ng two mobille shakers ow wned and opperated by N NEES@UCL LA. Initially a sm mall, linear, one-man po ortable shak ker was usedd to identify the natural frequencies of the t building g. The other shaker, wass a mobile eeccentric maass shaker w with a force cap pacity of 100 0 kips. The shaker could d produce harmonic exccitations witthin a range of frequencies f (0-5.5 Hz). The shaker was mounteed on the seccond floor aat the northwesst corner and bolted to the concretee slab (Figurre 5). The eexcitations pproduced by the latter shakeer were sine sweeps and d sine steps w which were used to excite both the a Y directiions. X and

Figure 5. MK15 Sha aker (photo by A. Stavrridis)



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Forced vibration and ambient vibration tests were conducted in all damage states, before and after the wall removal. A total of 26 forced vibration tests were performed and 166 ambient vibration recordings (80 hours) were obtained in the four damage states over a four-day period. SYSTEM IDENTIFICATION Modal parameters of the test structure were estimated at each damage state from the ambient measurements. The system identification was performed using time-domain (NExT-ERA) and frequency-domain (Peak picking) methods which will be discussed further. NExT-ERA method The natural excitation technique combined with the eigensystem realization algorithm (NExT-ERA) was used to identify the modal parameters of the building. The data cleaning process included: (1) filtering between 0.5 and 7 Hz with a Finite Impulse Response (FIR) band-pass filter, and (2) down-sampling the data from 200 Hz to 50 Hz. Based on the length of available data in each damage state, the ambient acceleration measurements were divided into 30 sets for DS1, 5 sets for DS2, 2 sets for DS3, and 20 sets for DS4. Each set of data corresponds to approximately 10 minutes of measurements for DS1-DS3 and 5 minutes for DS4. The system identification algorithm was applied for all 57 datasets. For each set, the signal was divided into 4 Hamming windows with 50% overlap to compute the cross power spectral density. SW-X on 2nd floor and SW-X on roof were chosen as two reference channels for computing cross-correlation functions which were then used as free vibration data and fed into the ERA method. The order of ERA was chosen manually for each of the 57 sets based on the stabilization diagrams. The modal parameters (natural frequencies, damping ratios and mode shapes) were then identified for each set of DS1 and DS4. Peak picking method The peak-picking method was also used to find the natural frequencies and mode shapes of the building at different damage states. The transfer functions between all of the accelerometers recordings (outputs) and a reference accelerometer were computed from their power spectral densities using one set of data in each damage state, with each set corresponding to approximately 20 minutes of measurements for DS1,DS2, and DS4 and 10 minutes of measurements for DS3. As reference, the accelerometers at north-west corner of the second floor measuring in either the X direction or Y direction depending on the direction considered, were selected. In the next step, the peak and the corresponding frequencies were estimated from the transfer function between the signals at the roof and at the reference location. The mode-shape components were then estimated using the values of the transfer functions between all the locations and the reference accelerometer at the identified frequency. The damping ratios of the reference channels were also found and averaged using the half power bandwidth method on their power spectral densities. Power-cross spectral densities of the acceleration measurements were estimated using


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System identification results The summary of the system identification results is presented in Table 1. There is an excellent agreement between the modal frequencies with a maximum error of 4% between the NExT-ERA and the Pick-Peaking methods. Figure 6 also presents the modal frequency changes of the structure from DS1 thorough DS4. The identified frequencies are decreasing for both modes as expected. The rate of change is different for different damage states showing different contribution of each removed wall on the overall stiffness due to the location but also due to the prior damage. Table 1. Summary of system Identification results Damage State

Mode 1 Frequency Mode 2 Frequency (Hz) (Hz)

Mode 1 Damping Ratio

Mode 2 Damping Ratio

MAC Between NExT-ERA and:

FEM Peak- NExT Peak- NExTPeak- NExT- Peak- NExT- Peak-Picking FEM FEM Picking -ERA Picking ERA Picking ERA Picking ERA Mode 1 Mode 2 Mode 1 Mode 2

DS1

2.29 2.26 3.00 3.32

3.37 4.40 1.7% 1.6% 3.1% 2.3%

0.97

0.97

0.93

0.93

DS2

2.17 2.14

*

3.03

3.08

*

2.2% 1.3% 2.1% 2.0%

1.00

1.00

*

*

DS3

2.12 2.07

*

3.00

2.96

*

2.4% 2.0% 2.5% 2.7%

1.00

0.99

*

*

DS4

2.05 1.97 3.00 2.81

2.72 3.60 1.4% 1.6% 2.5% 2.7%

1.00

1.00

0.79

0.83

* The preliminary FE model does not distinguish between DS1, DS2, and DS3 as the walls removed between these DS were already severely damaged and were ignored in the model of DS1.

Frequency (HZ)


the Welch method and averaged over Hanning windows of 8192 data points with 50% window overlap. The same window, window function, and overlap was used to find the Fourier transform of the measurements.

Mode 1-NExT-ERA Mode 2-NExT-ERA Mode 1-Peak-Picking Mode 2-Peak-Picking

3.55 3.35 3.15 2.95 2.75 2.55 2.35 2.15 1.95 DS1

DS2

DS3

DS4

Figure 6. Change in identified frequencies The identified mode shapes of the structure in DS1 for mode 1 and mode 2 are shown in Figure 7 and Figure 8, respectively. These results, along with the Modal Assurance Criterion (MAC) values from Table 1 show the agreement between the two system identification methods considered in this study. It is worth noting that the mode shape components were estimated at the locations near the four corners and the center of the structure, where the accelerometers were mounted. Hence, they provide the ability to



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iden ntify the torrsional motiion of the bu uilding and to have a bbetter underrstanding of dam mage induced either by the t shaker orr the removeed walls. It sshould be nooted that for eacch mode, thee mode shap pe is a 30-co omponent veector (five ccomponents for each of the two orthog gonal horizo ontal directio ons at the ffour cornerss and the ceenter of the buiilding at each h story) whicch was norm malized to unnity. Thee first modee involved motion m mainlly along thee X (east-weest) directionn, however, the west corneers of the bu uilding also moved in tthe Y (northh-south) direection. This hap ppened becau use of the damage d in th he west infillls that shifteed the centerr of rigidity tow wards the un ndamaged eaast well. Ass a result, a combinatioon of transllational and torssional motio on was introd duced.

Figure 7. Mode shap pe results foor mode1 att DS1

Figure 8. Mode shap pe results foor mode2 att DS1



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Mo ode 2 was mainly m torsion nal with the center of rootation closee to the eastt side of the buiilding. As in n the first mode, m the mo ovement in tthe X direction at the soouth side is more than the north side one. o The inffill walls at the east sidde appeared undamaged and d as a result, stiffer than the damaged walls at thhe west side.. Moreover, there was a staiirway shaft close to th he north-eaast corner oof the buildding having reinforced con ncrete walls which prov vided lateraal stiffness. Hence, the center of tthe rigidity moved toward the north-eaast corner off the structurre. Figure 9 iillustrates thhe deformed shaapes of the sttructure at ro oof level forr both modess in DS1 andd DS4. The comparison of these t two daamage statess in mode 1 indicates thhat the struccture tended to displace more in the Y direction affter the wall removal, w which was eexpected because three wallls were rem moved in this direction.

a) mode 1

b)) mode 2 ure 9. Deforrmed shape of the roof.. Figu

Tab ble 1 also sh hows the ideentified damp ping ratio reesults. Goodd agreement is observed betw ween the ressults of the two t system identificatio i n methods. One can notte that there is no n trend in th he changes of o the damping ratio chaanges betweeen the two aas expected for ambient vib bration resultts in general. NITE ELEM MENT MOD DEL FIN A finite f elemen nt model off the structurre was creatted using SA AP2000 V16 structural anaalysis softwaare (CSI 20 015) based on the geom metry and tthe materiall properties obttained prior to the testss. Hence, a preliminaryy model wass used to finnd the best opttion for the wall remov val strategy, namely, thhe walls withh larger efffects on the dyn namic behav vior of the strructure. Mo odeling Proccedure Thee model con nsists of con ntinuous beam m elements for main beeams and coolumns, and thin n shell elem ments for floor f slabs and infill walls. A ffour by fouur element disccretization is used for each e wall or slab based on a mesh ssensitivity aanalysis and the beam elem ments were discretized d to be coompatible w with the sheell element ubjected to linear moddal analysis in order to disccretization. The model has been su estiimate the modal propertties. Elastic modulus off the elemennts is assigneed based on the average vallues obtained d from the material m testiing of extraccted specimeens for each


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group. The mass of the structure is calculated based on the self-mass of the elements plus the mass of the 20-cm (8-in.) thick reinforced concrete parapet which is applied over the beams of the roof around the perimeter. As discussed before, the building was damaged mainly along the exterior frames and infills which made these elements challenging to model. Moreover, the exterior infills had openings adding more complexity to the model. To address these challenges, a stiffness reduction factor has been defined for each member as: =

×

Where, is the stiffness loss due to the damage to the infill which is a value between 0 and 1, with 1 corresponding to healthy and 0 to totally damaged walls, respectively. This parameter was estimated based on engineering judgment after the inspection of the walls. The parameter is the stiffness reduction due to the infill opening(s), estimated from the formula proposed by Stavridis (2009) for masonry infills : = (1 − 1.6 × Where,

) is the ratio of the opening area to the gross area of the infill.

The same stiffness reduction factor is used for the columns without the opening factor. The reduction factors are then applied to the stiffness parameters of the model for each element. It should be noted that the element is totally removed from the model if it is assigned a reduction factor of more than 0.6 for infills, and 0.5 for columns. Elements with more damage than that are not expected to participate in the stiffness of the structure during excitation at the ambient vibration level due to the severe cracks that tend to isolate these components. Moreover, modeling highly damaged elements can result in an ill-conditioned stiffness matrix for the structure. Test-Analysis correlation Table 1 includes the modal frequencies extracted from the model for each mode in DS1 and DS4. The frequencies do not match the ones from the system identification method as the FE model is preliminary and the effort is being done to make it more accurate for future studies. Figure 7 and Figure 8 include the mode shape results of the FE model. The model and the system identification results show good agreement except for the Y direction at the west side for mode1. As discussed before, the west side of the structure was damaged; hence, the exact stiffness of that side could not be determined exactly from the measured material and section properties. However, the modal assurance criterion (MAC) between the FE model and identified mode shapes is 93% for DS1 showing that the linear model can predict the mode shape with sufficient accuracy. For the second mode, good matching can be seen in the Y direction while there are mismatches in the other direction. The MAC values for DS4 is reduced showing less match after the damage developed. This mismatch might have several sources including the damage which was introduced to the structure because of the shake tests © ASCE and ATC 2015 Improving the Seismic Performance of Existing Buildings and Other Structures 2015


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and could not be reflected in the linear model. It should be noted that because of the element removal due to the stiffness reduction factors in the model, the walls which were physically removed to introduce the DS2 and DS3 could not be modeled as they were severely damaged. As a result, the effect of these two damage states could not be determined in this study. CONCLUSIONS The system identification of the two-story building resulted from analyzing the ambient vibration recordings of the structure is discussed in this article. These results are compared with those obtained from a preliminary elastic FE model of the structure. Based on this comparison, the following observations can be made: Both fundamental modes of the structure include a combination of torsional and translational deformations because of the damaged walls at the three sides, as well as the existence of the stairway concrete shaft, which separated the center of the rigidity from the center of the mass. The reduction in the modal frequency was observed between the four damage states. Such a trend was expected as the stiffness was reduced due to the removal of the walls and the shake tests that pushed the structure in the nonlinear response. Excellent agreement was observed between the results of peak-picking and NExTERA method which confirms the system identification results of the structure. The modal frequencies between the model and system identification results are not in good agreement. The linear model still needs more modifications to be good representative of the structure and also, a nonlinear model is required to track the dynamic properties changes of the structure due to the wall removal and the shake tests. However, despite the simplifications of the preliminary model and the fact that the structure was already damaged and in the nonlinear range of its response, the linear FE model could predict the mode shapes with good accuracy. ACKNOWLEDGEMENTS The study is part of a project supported by the National Science Foundation (Grant No. 1430180). The collaboration of NEES@UCLA during the planning and execution stages of the experiments is gratefully acknowledged. The opinions expressed in this paper are those of the authors and do not necessarily represent those of the sponsor or the collaborators.

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