Dynamic behaviour of a 13-story reinforced concrete building under ambient vibration, forced vibration, and earthquake excitation

Journal Pre-proof Dynamic behaviour of a 13-story reinforced concrete building under ambient vibration, forced vibration, and earthquake excitation Sherif Beskhyroun, Niusha Navabian, Liam Wotherspoon, Quincy Ma PII:

S2352-7102(19)30995-7

DOI:

https://doi.org/10.1016/j.jobe.2019.101066

Reference:

JOBE 101066

To appear in:

Journal of Building Engineering

Received Date: 19 June 2019 Revised Date:

7 November 2019

Accepted Date: 9 November 2019

Please cite this article as: S. Beskhyroun, N. Navabian, L. Wotherspoon, Q. Ma, Dynamic behaviour of a 13-story reinforced concrete building under ambient vibration, forced vibration, and earthquake excitation, Journal of Building Engineering (2019), doi: https://doi.org/10.1016/j.jobe.2019.101066. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Dynamic Behaviour of a 13-Story Reinforced Concrete Building under Ambient Vibration, Forced Vibration, and Earthquake Excitation Sherif Beskhyroun1, Niusha Navabian1, Liam Wotherspoon2, Quincy Ma2

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Sherif Beskhyroun, Senior Lecturer at Auckland University of Technology

E-mail: [email protected] Telephone number: +64 22 647 2636 Postal address: Private Bag 92006, Room WS316D, WS Building, 34 St Paul Street, Auckland, New Zealand 1

Niusha Navabian, PhD student at Auckland University of Technology (*corresponding author)

E-mail: [email protected] Telephone number: +64 22 401 4284 Postal address: Room WZ816, WZ Building, 34 St Paul Street, Auckland, 1010, New Zealand. 2

Liam Wotherspoon, Senior Lecturer at University of Auckland

E-mail: [email protected] Telephone number: +64 9 923 4784 Postal address: Engineering block 1- Bldg. 401 Level 11, Room 1105, 20 Symonds ST AK CNTRL Auckland 1010, New Zealand. 2

Quincy Ma, Senior Lecturer at University of Auckland

E-mail: [email protected] Telephone number: +64 9 923 8 766 Postal address: Engineering block 1- Bldg. 401 Level 12, Room 1208, 20 Symonds ST AK CNTRL Auckland 1010, New Zealand.

ABSTRACT This paper presents a unique study of dynamic behaviour of a full-scale 13-story reinforced concrete building under forced vibration, ambient vibration, and distal earthquake-induced excitation. Initially, an eccentric mass shaker located on the upper floor of the building was used to excite the building while instrumented with eight accelerometers. Then, ambient vibrations induced by traffic and wind were recorded over a period of two weeks, utilizing over 40 tri-axial accelerometers. During the sampling period, the building was excited by a M6.5 earthquake and high-quality vibration data sets were recorded. Modal parameters of the building were identified with a range of frequency and time domain system identification (SI) methods, and the influence of excitation force characteristics on performance of various techniques was also investigated. A finite element model of the building was 1

developed using SAP2000 to compare modal properties to the identified counterparts from experiments. Results showed a strong correlation between modal parameters identified by different SI methods, and all techniques provided accurate estimation of modal parameters when used with output-only data. Modal parameters determined from ambient vibrations were comparable to their forced vibration counterparts, providing evidence that ambient vibration testing can be as effective as forced vibration testing in determining modal parameters for similar size structures. The near stationary vibration data can produce accurate estimation of modal parameters. However, further study is required to facilitate application of output-only SI techniques with non-stationary data. There was a good match between peak displacement amplitudes obtained by the numerical model and those experimentally measured at different excitation frequencies. This match demonstrated the accuracy of the finite element model to predict realistic dynamic behaviour of the building under various harmonic excitation forces. Keywords: Modal characteristics; ambient vibration; Forced vibration testing; Earthquake; Tall buildings.

1. Introduction The identification of the dynamic characteristics of structures (system identification) from vibration data is an important task in the course of seismic design of civil engineering structures [1]. In the literature, there are some studies that have been carried out to compare different system identification techniques for modal parameter estimation of civil structures [2-5]. To accomplish system identification for civil structures, ambient vibration data, forced and free vibration tests, as well as earthquake response measurements can be used. Among these tests, ambient vibration experiments are most common as they are economical, non-destructive, fast and easy to implement, and the test methodology does not affect the integrity and health of the structure [6, 7]. However, as the input force is unknown in ambient vibration measurements, the output-only modal identification techniques must be applied for modal parameter extraction. Additionally, as the input excitation in ambient vibration tests is usually weak, these tests are not effective in obtaining an accurate estimation of the dynamic characteristics related to higher modes, and uncertainties remain as to whether the modal information applies in the higher strain ranges. Forced vibration tests can overcome these issues as

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they provide higher input forces. However, they are substantially more expensive, time consuming to conduct, and often require special permissions as there is the potential for damage to the structure. Some researchers suggest that output-only analysis is superior with multiple-input data, and hence the distribution of the input forces across the structure will affect the quality of the identified modal parameters [8, 9]. Another important issue that needs further investigation is whether output-only analysis can work well in both the time and frequency domains. Research has also emphasized that for output-only analysis to be successful, it is important to have sufficient high-quality data with good signal-to-noise ratio [10]. To this end, due to high cost of traditional wired monitoring systems, micro-electro-mechanical systems (MEMS) have become a potential solution for

successful

implementation of large monitoring networks throughout large civil structures by limiting the high cost of installing and maintaining the extensive lengths of wiring [11]. These accelerometers can operate for an extended period of time powered only by a battery, as they generally have low power consumption. Moreover, some battery operated MEMS accelerometers have built-in analogue-todigital conversion and data recording capabilities, which can further simplify the set up and permit a higher number of locations across the structure to be monitored. Several ambient and forced vibration tests were conducted on large-scale structures to assess their dynamic behaviour for various applications. For instance, Rendon et al. [12] performed forced vibration testing on a large-scale building with many irregularities to measure the modal parameters of the building and compare with the results of a computational model of the structure. Ni et al. [13] performed a series of full-scale field vibration tests including ambient, forced and free vibration tests on a pedestrian bridge in Hong Kong. The modal parameters of the bridge were identified using the results of the tests to assess the bridge performance during its service life. Full-scale forced vibration tests presented by Salawu and Williams [14] investigated the dynamic characteristics of a concrete highway bridge before and after structural repairs, showing that the natural frequencies of the bridge were slightly reduced due to the repair works. Au et al. [8] carried out ambient vibration tests to identify the modal properties of two tall buildings including natural frequencies and damping ratios. The ambient data during the tests was collected due to the strong wind loading subjected to the buildings. Omenzetter et al. [15] carried out forced and ambient vibration testing on a full-scale bridge 3

with frequency sweep tests and the effect of excitation force on modal frequencies and damping ratios was explored. Gomez et al. [16] used six earthquake-induced vibration data sets recorded by the monitoring system installed on a three-span highway bridge located in California to investigate and assess the dynamic characteristics of the bridge including vibration frequencies, damping ratios and mode shapes. Memari et al. [17] conducted full-scale ambient and forced vibration testing on a steel frame building to extract the dynamic characteristics of the building during construction. Chen et al. [18] investigated the effect of force and response amplitudes on the modal characteristics of an eleven-span motorway concrete bridge subjected to multiple dynamic tests with various excitation levels. Hogan et al. [19] performed forced vibration testing and system identification on a three-span precast concrete bridge to investigate the effect of different substructure components on the overall behaviour of the structure. Recently, Quaranta et al. [20] performed dynamic experimental tests on a prototype spatial truss beam in lab environment to measure the main modal characteristics of the new composite truss structures. Across all these studies, vibration testing of full-scale structures could provide the researchers with a reliable understanding of the structural characteristics at different phases of a structure’s lifetime. This paper presents the characterisation of the dynamic behaviour of a full-scale 13-story reinforced concrete building using various excitation sources. The details of the tall building and the instrumentation layout are first presented. Details of the ambient and forced vibration tests are then described, including forced vibration from an eccentric mass shaker, ambient vibration induced by wind, traffic and activity in the building and excitation from a M6.5 earthquake roughly 350 km away from the building that occurred during the ambient vibration recording period. Different system identification techniques are applied to each of the data sets recorded under various excitation sources. Correlation of mode shapes and variation in the natural frequencies and damping values are evaluated across each data set using these techniques and the effect of the excitation force characteristics on the performance of various system identification techniques is also investigated. Finally, a finite element model of the large-scale building is developed for comparison purposes and to predict the realistic dynamic behaviour of the building subjected to various harmonic excitation forces.

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The paper contribution to engineering application is to present a unique set of data on dynamic behaviour of a full-scale structure. The building, instrumented by large numbers of sensors, was subjected to various excitation sources, including stationary white noise, earthquake, and sine wave signals. This could provide a unique opportunity to investigate the effect of excitation force characteristics and amplitude on the identification and modal characteristics of the building. To summarize, the paper contributions in system identification and structural health monitoring fields are: a) Identification of the dynamic behaviour of the high-rise building under different excitation forces, including ambient vibration, forced vibration, and earthquake-induced vibration; b) Comparison of different output-only system identification techniques in time and frequency domains when used with low-amplitude ambient vibration; c) Comparison between the results of modal characteristics of the building using the ambient vibration testing and forced vibration testing carried out on the large-scale building; d) Investigation of the effect of the amplitude of input force during forced vibration testing on the modal characteristics of the building; e) Investigation of the application of output-only system identification techniques with nearstationary and non-stationary vibration; and f) Presentation of an accurate numerical model of the building to predict realistic dynamic behaviour of the building under various harmonic excitation forces. 2. Testbed Building Description The focus of this research is a 13-story pile-supported reinforced concrete office building, part of the School of Engineering in the University of Auckland, New Zealand (Fig. 1 (a)). This building was designed in 1964 based on New Zealand Standard 1900 for design of civil engineering structures. The tower block has a height of 40.54 m and is serviced by two elevators and stairwells located at its centre. The building has three floors under the ground level. Level 4 is used as a foyer and floors 5 to 12 are considered the office levels of the building, which are separated by interior plasterboard walls.

5

From level 6 to level 12, the building has a flat plate reinforced concrete slab with 18.28 m dimensions on either side as indicated in Fig. 1 (b). There is a machine room above the roof (level13), which is the location of the eccentric mass shaker described in the experimental procedure section. The machine room level has a smaller plan area than the levels below, as it sits above the central core of the building. 1

2

6.096 m

3

18.288 m 6.096 m

4

6.096 m 0.914 m

A

6.096 m B

18.288 m 6.096 m

Stairwell

N

Lifts C

6.096 m D

0.914 m

(a)

(b)

Fig. 1. (a) North and West faces, and (b) Plan view of levels 5 to 12 of engineering office building at the University of Auckland.

The building is supported by 12 reinforced concrete columns around its perimeter and pre-stressed shear walls at its core. The pre-stressed shear walls at the core provide the building with the majority of its lateral strength and stiffness [21], and are 305 mm thick throughout the entire structure. The thickness of all the floor slabs is 200 mm, except at the roof level where the slab is 120 mm thick. It is noteworthy that the structure is structurally separated from the adjoining buildings by a 400 mm seismic gap at the 2nd and 3rd stories, and above this level there are no other adjacent structures. The ground and 1st levels are connected to adjacent structures with part of the 1st level supported by the underlying soil. As a result, of most interest is the response of the building above the 1st level. 3. Experimental Procedure 3.1. Forced Vibration Testing Procedure

6

A forced vibration test was conducted on the building in 2002 using an eccentric mass shaker in the machine room installed on the fourteenth floor of the tower block in the 1980’s [22]. The eccentric mass shaker shown in Fig. 2 was installed 1.77 m from the geometric centre of the building perpendicular to the north-south excitation direction, meaning that both translational and torsional modes could be characterised. It produced a horizontal sinusoidal force in a north-south direction over a frequency range of 0.15-10 Hz, and to avoid any potential damage to the building a maximum force amplitude of 13 kN (26 kN peak to peak) was used. Three different sets of masses, 10, 20, and 40 kg, were attached to the shaker to excite the building with various forcing amplitudes.

Fig. 2. Original drawing of the eccentric mass exciter [22].

Three sets of forced vibration tests were performed, including frequency sweep tests, free vibration decay tests, and tests to obtain mode shapes; the two former for resonant frequency and damping ratio measurements and the latter for mode shape estimation in translational and torsional directions [22]. To perform free vibration decay tests, the eccentric mass shaker was used to create steady state motion at the resonant frequency of the building and then suddenly shut off. LCF-100-14.5 uniaxial servo accelerometers with an operating range of ±0.25 g were used during the forced vibration testing to measure the building accelerations with a sampling rate of 1000Hz. For the frequency sweep tests, six accelerometers were installed throughout the building to measure the modal parameters related to the first translational and torsional modes. For the second translational and torsional modes, one accelerometer was installed on level 13 and three installed on level 12. For the free vibration decay 7

test, two accelerometers were installed at levels 12 and 13 to measure the first translational mode and three were installed at level 12 for the first torsional mode. Similarly for the mode shape tests, five accelerometers were located on levels 13, 12, 9, 6 and 4 and one accelerometer at level 1 to measure the translational modes. For torsional modes, three accelerometers were installed on level 12 and two on level 6 of the building. It should be noted that the building was excited at its natural frequencies to obtain the mode shapes. The location of accelerometers for these setups are shown in Appendix A. 3.2. Ambient Vibration Testing Procedure Ambient vibration testing was conducted using 49 MEMS tri-axial accelerometers in 2012. The accelerometers were placed throughout the structure from floors 2 to 11 to measure ambient vibrations induced by wind, traffic and operational activities over a two week monitoring period. 38 accelerometers were placed in the four corners of each floor, apart from level 2 and level 3 where only three corners were accessible. The remaining 11 accelerometers were installed on the stairs running through the center of the building. USB X6-1A accelerometers produced by the Gulf Coast Data Concepts were selected to measure the ambient vibration of the building (Fig. 3).

(a)

(b)

Fig. 3. (a) USB Accelerometer X6-1A [23], and (b) the attached D-cell battery for ambient vibration tests.

The heart of the X6-1A accelerometer is a low-noise 3-axis digital-output MEMS accelerometer chip by STMicroelectronics. The STMicroelectronics MEMS sensor incorporates oversampling and antialiasing filtering for a high quality signal and then real-time data is streamed digitally via an I2C bus. An 8-bit Silicon Labs 8051 microprocessor collects, processes and logs the data stream to the micro SD card. The advantage of this set up is that it requires no additional analogue-to-digital converter. A quantitative analysis for the accuracy of this accelerometer was summarised by Haritos [24] indicating its suitability and accuracy for structural health monitoring applications. In order to increase the 8

typical lifetime of the accelerometers to around three weeks, some modifications were made to enable D-cell batteries to be used. A sampling rate of 40 Hz was used, which was deemed appropriate for the measurement of first four modes of the building based on simple calculations. At this sampling rate the accelerometers could operate for a period of two weeks using a D-cell battery. For time synchronization between different accelerometers, the real time clock (RTC) integrated within each accelerometer was synchronized to a common computer prior to installation to ensure that each accelerometer had a similar timestamp. The post processing methodology outlined in Beskhyroun & Ma [25] was applied to the recorded vibration data to account for any possible drift in the RTC during the recording period. For ambient vibration tests, three data sets, including wind dominated ambient vibration, operational use dominated ambient vibration, and excitation from a distal earthquake were used. To find the most desirable time intervals for wind loading recordings, 10-min interval wind speed data for the region surrounding the test building was generated for the test period using data from the National Institute of Water and Atmospheric Research (NIWA) (www.niwa.co.nz). The time periods with maximum wind speed were utilized to analyse the response of the building to wind loading. Moreover, the peak operational use of the building was estimated as being between 4 to 5 pm each working day. During this period, there is heavy use of the lifts as the work day comes to an end. Additionally, there is heavy traffic on the road approximately 15 m from the edge of the building during this time. During the ambient vibration recording period, the building was also excited by a M6.5 earthquake on 3rd of July 2014 at 10:40 pm, with an epicentral distance of approximately 350 km. More information about the earthquake was obtained from GeoNet (http://www.geonet.org.nz). High quality acceleration data from this earthquake was recorded by accelerometers installed throughout the building. The earthquake- induced vibration data was used to identify the effect of a non-stationary signal on the outputs of system identification analysis. 4. Analysis Methodology Modal parameters of the building were identified using three frequency-domain based system identification methods; Peak Picking (PP) method, Frequency Domain Decomposition (FDD) method [26], and Enhanced Frequency Domain Decomposition (EFDD) method [27]. Also, a time-domain 9

system identification technique, the Stochastic Subspace Identification (SSI) method [28], was also utilized to estimate the modal parameters of the building. It should be mentioned that the data driven version of SSI method was considered in this study for modal parameter identification. In addition, to compare mode shapes extracted from various system identification methods, Modal Assurance Criterion (MAC) values were also calculated. The Modal Assurance Criterion (MAC) is generally used as a measure of the correlation between two mode shapes. The MAC value corresponding to the ith mode shape, ??ij and ??ij*, is defined by Eq. (1) as follows [21]: =

ϕ ϕ∗ ϕ

ϕ∗

(1)

where n is the number of elements in the mode shape vectors. A MAC value close to unity indicates perfect correlation between the two mode shapes and a value close to zero indicates mode shapes that are orthogonal. Two techniques were implemented to find stable poles in the SSI method. In both techniques, the algorithm starts with a high system order, which is then reduced by two on each iteration until the final iteration is run with a system order of two. Stable poles identified in each of these iterations are compared by two techniques. In the first technique (SSI1), the identified stable poles around the singular values, which are generated from the singular value decomposition of the power spectral density matrix, are compared [26]. If two consecutive poles within a predefined offset of the singular value have alteration in frequencies, change in damping and modal assurance criterion (MAC) within user defined values, both poles will be kept and averaged. If both poles do not meet these criteria, the first pole is discarded and the second pole is compared to the subsequent one. These series of comparisons continue until all stable poles in the frequency range are found and averaged. The resulting modal parameters, including mode shapes, natural frequencies and damping ratios are the combination of several stable poles and therefore provide a robust method of system identification. While the first technique (SS1) uses singular value decomposition of the power spectral density function (PSD) matrix to identify stable poles, the second technique (SSI2) breaks up the entire frequency range tested into bands. Those bands with the most poles are considered to contain true 10

modes and are used to find stable modes. Stable poles are found within each band and averaged using the same procedures as in the previous SSI1 technique. Further details regarding this method can be found in [29]. The dimension of the Hankel matrix in the SSI technique was set to 40. The frequency limit and MAC value were set to 10% and 0.80, respectively. Also, using the proposed stabilization method, the system order of the SSI method was selected in the range of 120 to 80, as it was observed that the most stable poles were included in this range. This flexible filtering range was selected due to the fact that the modal damping is very sensitive to the measurement noise, repeatability of the vibration tests and non-stationarity in the signals. 5. Experimental Results 5.1. Natural Frequencies The natural frequencies are defined by the peaks in any sort of frequency response curve obtained from structural vibrations [30]. This modal characteristic is a good indicator for structural condition assessment and can be obtained under different excitation sources. The first two natural frequencies of building measured using PP, FDD, EFDD and SSI methods are presented in Table 1 for different vibration data sets. Ambient vibration data induced by different types of excitation (wind, traffic, and earthquake) and forced vibration data induced by different levels of input force (10 kg, 20 kg, and 40 kg) were analysed for comparison purposes to evaluate the performance of various system identification techniques under different excitation sources. Another goal of this comparison was to show the efficiency of the low-amplitude ambient vibrations for modal parameter estimation of the full-scale building. Table 1 Natural Frequencies of the building obtained from forced and ambient vibration tests. Excitation source

PP

FDD

EFDD

SSI1

SSI2

Experimental [22]

1st Translational Mode Forced (10 kg)

1.89

1.92

1.92

1.90

1.90

1.91

Forced (20 kg)

1.89

1.89

1.89

1.89

1.89

1.90

Forced (40 kg)

1.89

1.89

1.89

1.88

1.88

1.88

Wind

1.88

1.84

1.84

1.85

1.85

_

Traffic

1.87

1.88

1.88

1.86

1.86

_

11

Earthquake

1.88

1.84

1.84

1.84

1.84

_

1st Torsional Mode Forced (10 kg)

2.47

2.47

2.47

2.47

2.48

2.48

Forced (20 kg)

2.44

2.47

2.47

2.46

2.46

2.46

Forced (40 kg)

2.44

2.44

2.44

2.44

2.45

2.45

Wind

2.34

2.42

2.42

2.45

2.45

_

Traffic

2.42

2.46

2.46

2.44

2.44

_

Earthquake

2.48

2.46

2.46

2.44

2.44

_

As is apparent, all natural frequencies extracted from the ambient and forced vibration data sets were very well correlated, and only small differences between the results can be observed. The natural frequencies calculated using both frequency and time domain system identification techniques matched very well for the various vibration data sets. The small variation in these values, which was approximately below 4% and 8% for the first translational and first torsional modes respectively, can be attributed to mathematical errors and different levels of measurement noise associated with the vibration data. The first two natural frequencies measured during frequency sweep test are presented in last column of Table 1 for each excitation amplitude. The vibration data recorded during forced vibration testing was processed in MATLAB during several steps to identify the modal frequencies from displacement frequency response curves. These steps can be found in [22]. The time histories of structural response recorded from top of the building due to three different levels of excitation force (10 kg, 20 kg, and 40 kg) are shown in Figure 4 to compare different levels of the input excitation force.

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Fig. 4. Time histories of structural response (m/s2) recorded due to various excitation forces.

As is clear, the frequency of the first translational mode was between 1.88-1.91 Hz and the frequency of the first torsional mode was between 2.45-2.48 Hz. The natural frequencies of the building measured during forced vibration testing decreased as the input force applied by the eccentric mass shaker increased. This suggests that in force vibration testing, the level of input force could affect the dynamic characteristics of the system. It can be concluded that the resonant frequencies might be amplitude dependent, even if the structure behaves within elastic behaviour limits. There are several factors in real behaviour of the structure, which could result such variations in natural frequencies of the structure once it is subjected to different amplitudes of input force. Some of these factors are crack opening in concrete structural elements, friction in structural connections, soil-structure interaction, and the behaviour of non-structural elements. By increasing the amplitude of input excitation, these factors start to affect the dynamic behaviour of the structure. The stabilization diagrams obtained during analysis procedure for the SSI1 and SSI2 techniques are shown in Fig. 5 (a) and (b), respectively, for the traffic-induced ambient vibration.

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System Order

System Order

(a)

(b)

Fig. 5. Stabilization diagrams for: (a) SSI1 technique, and (b) SSI2 technique.

It can be observed from the results that there was a good match between the natural frequencies obtained during forced vibration testing and those obtained by various output-only system identification methods using three sets of ambient vibration, evidence that ambient vibration testing can be used for an accurate estimation of modal characteristics of the large-scale building. 5.2. Mode Shapes The mode shapes of the building extracted from different excitation sources, including traffic-induced ambient vibration, earthquake-induced vibration and forced vibration were presented and compared. Also, to compare the performance of different system identification techniques, the MAC values for the first two mode shapes of the building identified using different techniques were obtained using the vibration induced in the building by traffic.

5.2.1. Ambient Vibration Data Figure 6 shows the first four mode shapes of the building as estimated by the PP method using 20 minutes of vibration data induced by operational activities in the building and nearby traffic. The high quality acceleration data captured by the accelerometers resulted in a very clear identification of mode shapes. This was also true for the higher modes of vibration, despite the fact that ambient vibration tests are traditionally not as effective in obtaining an accurate estimation of the higher modes due to providing a low signal to noise ratio.

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Mode Shape at Freq. 2.4218

35

35

30

30

25

25 Z dimension

Z dimension

Mode Shape at Freq. 1.8749

20 15

20 15

10

10

5

5

0

0

15

15

20 10 5

5 0

15

10

0 X dimension

Y dimension

-5

0 X dimension

Y dimension

(a) First translational mode NS (North-South)

(b) First torsional mode

Mode Shape at Freq. 6.4841

Mode Shape at Freq. 8.2809

35

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25 Z dimension

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10

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5 X dimension

Y dimension

20

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10

10

0 0

Y dimension

(c) Second torsional mode

10

-5 X dimension

(d) Second translational mode (NS)

Fig. 6. First four mode shapes developed with operational uses and traffic-induced ambient vibrations.

The first four modes of the building, including the first two translational modes and the first two torsional modes, were well excited by the vibration data induced by traffic and operational activities, which can be attributed to the good distribution of input forces across the structure during ambient vibration testing. In addition, the input force resembled a white noise signal and the drift in the accelerometers RTC was negligible shortly after the start of the test period (no time synchronization error between the sensors). Figure 7 shows MAC values for the first two mode shapes of the building identified by PP, FDD, EFDD, SSI1 and SSI2 methods. Each bar in the figure represents the MAC value when comparing a 15

specific mode extracted from a pair of system identification methods. Traffic-induced ambient vibration recorded from levels 9 to 13 was used here to compare the performance of different system identification techniques.

(a) 1st translational mode (NS)

(b) 1st torsional mode

Fig. 7. MAC values for the first two mode shapes extracted from traffic-induced ambient vibration.

MAC values ranged from 0.95 to 1.00 for the first translational mode shape and from 0.80 to 1.00 for the first torsional mode shape. The values indicated a very high correlation between mode shapes identified by time-domain and frequency-domain identification techniques used in this study. A near perfect correlation was shown for the first translational mode and the first torsional mode, showing that both system identification techniques can be highly efficient for modal parameter estimation using output- only data. 5.2.2. Earthquake Excitation Data In operational modal analysis and output-only modal identification, it is assumed that the excitation is unknown and can be modelled by a Gaussian white noise. This assumption can be accepted with confidence in the case of using ambient vibration data produced by wind, nearby traffic or operational uses, as the response is typically stationary and we can assume that the excitation signal is a Gaussian white noise. However, this assumption is not valid for earthquake-induced excitation, especially in case of strong earthquakes. In order to investigate the influence of non-stationary vibration on the identified modal parameters using output-only system identification methods, the earthquake-induced

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vibration data recorded by accelerometer 51 located at floor 11 of the building during the subjected earthquake was analysed. To do so, the time- history response was divided into three sections as shown in Fig. 8. The second section (T2) in the time interval between 60 and 125 seconds includes the most non-stationary vibration, while section T3 in the time interval between 125 and 220 seconds was considered the closest to a stationary signal. It should be mentioned that the signal was filtered using a band-pass Butterworth filter of order 4 with cut-off frequencies at 0.2 and 5 Hz presenting a frequency range that contains all the vibration modes contributing to the building response. The first translational and the first torsional mode shapes identified by time-domain SSI method using the traffic-induced vibration and non- stationary (T2) and near stationary (T3) parts of the earthquake-

Acceleration at Ch. 51

induced signal are shown and compared in Fig. 9.

Fig. 8. Acceleration response (m/s2) recorded at top of the building due to earthquake excitation.

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Mode Shape at Freq. 1.847

Mode Shape at Freq. 1.8749

Mode Shape at Freq. 1.8414

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(b) First translational mode (NS) identified using non-stationary vibrations (T2)

Mode Shape at Freq. 2.4218

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(a) First translational mode (NS) identified using ambient data

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-5

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(c) First translational mode (NS) identified using near stationary vibrations (T3) Mode Shape at Freq. 2.4227

Mode Shape at Freq. 2.379

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(d) First torsional mode (NS) identified using ambient data

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20 15

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(e) First torsional mode (NS) identified using non-stationary vibrations (T2)

(f) First torsional mode (NS) identified using near stationary vibrations (T3)

Fig. 9. Comparison of the mode shape derived from ambient vibration and earthquake excitation data.

As is apparent from the figures, the near stationary earthquake-induced vibration data can produce an accurate estimation of first translational and first torsional mode shapes of the building, similar to the traffic-induced vibration data. However, the non-stationary part of the signal resulted in a poor representation of the first two mode shapes of the building despite the fact that the first mode was strongly excited during this interval. The results could validate the aforementioned assumption for earthquake-induced excitation and also indicate that further study is required to estimate the level of

18

non-stationarity in the signals required to facilitate the application of output-only system identification techniques with non-stationary vibration data. 5.2.3. Comparison of Forced and Ambient Vibration Data As is shown in Appendix A, during the forced vibration tests conducted to obtain mode shapes, five horizontal accelerometers were installed at levels 4, 6, 9, 12, and 13 and one accelerometer at level 1 as the reference channel to measure the first translational mode. For the first torsional mode, two accelerometers were placed at level 6, three at level 12 and similarly one at level 1 as the reference channel. In order to compare the mode shapes extracted in forced vibration tests and ambient vibration tests, the elevation mode shapes of the building were presented in this section for the first two modes. The data recorded by accelerometers installed at four corners of the building was used to measure the elevation mode shapes due to the ambient vibrations. The average of the four mode shapes obtained for each corner of the building was considered as the total elevation mode shape of the building for the first two natural modes. The modal amplitudes were computed at the corresponding accelerometer locations in the forced vibration test. It should be mentioned that due to the different accelerometer configuration used for the forced and ambient vibration testing, the building levels used to extract the elevation mode shapes are different for each test. The normalised mode shapes obtained from the forced and ambient vibration tests are shown in Fig. 10 for the first translational and first torsional modes of vibration. 12 11 10 9

Floor number

8 7 6 5 4 3

Ambient vibration data @ 1.87 Hz- PP method Ambient vibration data @ 1.88 Hz- FDD method Ambient vibration data @ 1.88 Hz- EFDD method Forced vibration data (10 kg) @ 1.91 Hz Forced vibration data (20 kg) @ 1.90 Hz Forced vibration data (40 kg) @ 1.88 Hz

2 1

st

0

0.5

1 st

(a) 1 translational mode shape

1.5

2

2.5

(b) 1 torsional mode shape

19

3

Fig. 10. First two elevation mode shapes of the building measured from forced and ambient vibrations.

For the forced vibration data, the first two mode shapes were presented for different levels of excitation (10 kg, 20 kg, and 40 kg) at different frequencies [22]. Also, three frequency domain system identification techniques, including PP, FDD, and EFDD methods were used to extract the mode shapes from ambient vibrations induced by traffic in the building. To perform an accurate comparison, the translational and torsional mode shapes obtained from both sets of data were normalised with respect to the mode shape obtained in floor 9 and floor 6, respectively. The first two mode shapes obtained from forced vibration testing under different excitation levels were identical regardless of magnitude of input force. Moreover, the first translational and torsional mode shapes extracted from low-amplitude ambient vibrations presented a relatively close results with the mode shapes measured using forced vibration data sets. Due to the different accelerometer configurations in each test setup and the measurement noises, a good match between the results cannot be presented. The source of the noise could be due to the use of different type of accelerometers with various resolution, different sampling frequency, and different amplitudes of excitation force during the ambient and forced vibration tests. It can be concluded that although forced vibration testing could precisely measure the natural deflected shapes of the large-scale structure, the ambient vibration testing could also provide relatively close results for modal parameter estimation. In addition, the frequency-domain output-only system identification techniques could roughly estimate modal parameters from low-amplitude ambient vibration. It is noteworthy that the accuracy of the results obtained using ambient vibration tests could be improved by enhancing the precision of vibration measurement to decrease the effect of measurement noise. 5.3. Damping Unlike the mass and stiffness, damping is the most difficult dynamic characteristic of a structure to predict from the physical properties of a structure’s components. During the frequency sweep forced vibration testing carried out in [22], the modal damping ratios were estimated using four different methods; half power bandwidth, logarithmic decrement, a hybrid method and least squares exponential using the forced vibration measurements. The results for modal damping ratios using the

20

half power bandwidth method are presented in Table 2. It is clear that the damping ratios increased from 1.525% to 1.707% for the first translational mode and from 1.394% to 1.640% for the first torsional mode of the building as the amplitude of excitation increased from 10 kg to 40 kg. It can be concluded that damping of the structure is force amplitude dependent, that higher damping occurs in higher amplitude of excitation force. The results from the forced vibration testing were used here to compare with the modal damping values derived using other excitation sources. Table 2 Modal damping ratios in percent, as extracted from full-scale forced vibration testing [22]. Mode No.

10kg

20kg

40kg

1st Translational

1.525

1.556

1.707

1.394

1.466

1.640

st

1 Torsional

To measure the modal damping from ambient vibration data, the time domain SSI method described previously was used. The modal damping at different system orders versus the natural frequency are shown in Fig. 11 for three sets of ambient vibrations, including wind, traffic and earthquake-induced vibration data. During the SSI analysis method, the frequency ranges were considered 1.8-2 Hz and 2.3- 2.5 Hz for the first translational and first torsional modes, respectively. The limits with the most concentrated poles were considered to contain true modes and were then used to find stable modes. Stable poles were found within each band and averaged to find the modal damping of the specific mode of vibration. The damping values obtained for the first two modes are shown in Table 3. The modal damping values extracted from ambient and forced vibration data are relatively close. The small differences between the results can be due to the noise associated with the low-amplitude ambient vibrations. The noise can originate from different resolution of accelerometers used for the ambient and forced vibration tests resulting in various signal to noise ratios, difference in sensor installation and orientation, and the effect of excitation amplitude during the vibration tests.

21

(a) Wind data

(b) Traffic data

(c) Earthquake data

Fig. 11. Modal damping values extracted from ambient vibrations using SSI method. Table 3 Modal damping extracted from ambient vibration testing. Mode No.

Wind

Traffic

Earthquake

1st Translational

1.52

1.41

1.27

1st Torsional

1.46

1.25

1.55

The experimental results presented in this study confirm the previous investigations carried out on dynamic characteristics estimation of different types of large-scale civil structures [13, 18, 31]. In summary, the results obtained from vibration tests showed that the output-only linear dynamic identification techniques can be effectively used for dynamic characterization of the building subjected to small-to-large excitation forces. In addition, general decreasing and increasing trends in natural frequencies and modal damping of the first translational and torsional modes were respectively observed as the excitation amplitude increased, showing the amplitude dependency of the modal characteristics of the reinforced concrete building. 6. Finite Element Model of the Building This part of the paper describes a finite element model of the building that was developed using SAP2000 to evaluate the modal properties of the structure, including natural frequencies and the associated mode shapes, and to predict time-history responses of the building under various excitation forces. A summary of structural specifications used for finite element modelling and numerical results are provided in the following sections. 6.1. Specifications of the numerical Model An initial SAP model of the building was created based on New Zealand Standard for design of concrete structures (NZS 3101: Part 1, 1982) considering rigid floor diagrams and fixed boundary conditions at the support level. In addition, the mass of each floor diagram was assumed to be the geometric centre of the building. Using this simplified numerical model, very useful information about dynamic characteristics of the building, such as natural frequencies, was estimated and used for

22

preliminary forced vibration tests. In the next stage, the SAP model was refined to simulate more accurate dynamic behaviour of the structure. A summary of the structural specifications used for finite element modelling is provided in the following [22]. 1.

Different dimensions of the columns and beams were modelled using frame elements. Levels 5 to 13 of the building were modelled with no floor beams. However, for levels 3 and 4 relatively deep foundation beams and peripheral beams rigidly connected to the columns were used, respectively.

2. Shell elements were used for modelling the shear walls and the floor slabs of the building. The thickness of the shear walls and the slabs of all floors were 305 mm and 200 mm, respectively. The thickness was considered to be 120 mm for the slab of floor 14. 3. The elastic modulus of concrete is E = 4700

, where fc is the concrete 28-day compressive

strength, which was considered 27 MPa for the numerical modelling. Here, the elastic modulus was increased by 10% for the increase in modulus under dynamic conditions. 4. For all beam, column and shear wall properties, an uncracked concrete cross-section was used. 5. The specific weight of concrete was considered 24 kN/m3. The Poisson’s ratio (υ) was assumed to be 0.2 for concrete and also the shear modulus of concrete was calculated by =

(

)

.

The boundary conditions of the building were modelled using one-joint link elements. As mentioned before, the building is supported on 24 piles with various shaft diameters and lengths. All piles have expanded base diameters and act as end bearing piles, where the pile shaft passes through a soil profile and the tip bears on rock which is much stiffer. Based on this condition, the vertical stiffness of the pile is very high and was considered as a rigid vertical support. Another factor that was considered in calculating the foundation stiffness was the effects of the relatively deep foundation beams that extend right down to the top of the piles. These deep beams were assumed to operate as stiff walls hence having an effect on the foundation stiffness. The foundation stiffness at the base of

23

each column were calculated using the pile foundation and the shallow foundation system based on the elastic homogeneous half-space. Therefore, the stiffness of the foundation in the X and Y directions was estimated by combination of these two stiffness values based on the square-root-ofsum-of-squared rule [22]. These values of foundation stiffness were used in this study to model the linear links with three deformational degrees-of-freedoms considering rigid in the vertical direction. The 2-dimensional and 3-dimensional views of the building developed using the aforementioned specifications are shown in Fig. 12.

Fig. 12. 2-dimensional and 3-dimensional views of the finite element model of the building.

6.2. Natural frequencies and mode shapes of the numerical Model The dynamic characteristics of the building obtained using the finite element model are presented here for different modes of vibration. Also, in order to validate the numerical model, the results were compared with the identified counterparts measured using traffic-induced ambient vibration. Table 4. Natural frequencies obtained from ambient vibration testing and numerical model. Mode No.

Mode description

Measured natural frequency (Hz)

Numerical natural frequency (Hz)

Error (%)

1

1st E-W translation

1.71

1.70

0.58

2

1st N-S translation

1.88

1.93

2.65

3

1st torsion

2.42

2.24

7.43

4

2nd torsion

6.48

6.28

3.08

5

2nd E-W translation

7.61

7.34

3.54

6

2nd N-S translation

8.28

8.06

2.65

24

Table 4 shows the first six natural frequencies obtained using the numerical model and the ambient vibration testing. As is clear from the table, the theoretically obtained frequencies were approximately 1-10% lower than the measured ones, except for the first N-S translational mode at which the measured frequency was lower than its numerical counterpart. In general, there was a very good agreement between the natural frequencies obtained using finite element model and the experimental tests. For more validation, the elevation mode shapes of the building obtained using the finite element model are presented here and compared with the elevation mode shapes obtained using the trafficinduced ambient vibration. The first translational and torsional mode shapes are shown in Fig. 13. As is clear, the first translational and torsional modal amplitudes of the building obtained using the finite element model and the experiments matched good. The results presented in this section can validate the accuracy of the finite element model to correctly predict the dynamic characteristics of the building. Experiment

SAP model 36

33

33

30

30

27

27

Height of building (m)

Height of building (m)

Experiment 36

24 21 18 15 12 9

SAP model

24 21 18 15 12 9

6

6

3

3

0 0

0

1

0

Modal Displacement

1

Modal Displacement

st

st

(a) 1 translational mode shape

(b) 1 torsional mode shape

Fig. 13. First two Elevation mode shapes obtained from numerical model and experimental testing.

6.3. Response of the numerical Model to Harmonic Excitation Force After validation of the finite element model using the modal characteristics of the building, the model was used to predict the time-history response of the building under various harmonic force excitations. The excitation forces were generated using different eccentric masses (10 kg, 20 kg, and 25

40 kg) at the natural frequency of interest. Three different harmonic excitation forces were applied to the finite element model at the desired frequencies. These applied forces were calculated by following equation: =

ω cos ωt

(2)

where ω is the frequency at which the harmonic excitation force is applied to the numerical model and e is the eccentricity with a value of 0.325 m. Here, the first N-S modal frequencies measured from forced vibration testing were used to create the different harmonic excitation forces and me defines the eccentric mass of the exciter (10 kg, 20 kg and 40 kg) that creates excitation forces with different amplitudes at desired frequencies. The excitation forces, which were estimated using the measured natural frequencies, provided near to real behaviour of the building subjected to different amplitudes of excitation force. Table 5 shows the harmonic excitation forces calculated using Eq. 2 at three different excitation frequencies. Table 5 Peak Amplitude of forces generated at different levels of excitation frequency. Eccentric weight (kg) 10

Excitation Frequency (Hz) 1.91

Peak Amplitude (kN) 0.47

20

1.90

0.93

40

1.88

1.81

These excitation forces were applied to the numerical model in N-S direction at a node on top floor of the building with a time step of 0.02 second. The model was analysed using linear time history analysis under three defined harmonic excitation forces. The modal damping ratios measured during forced vibration testing were used in the analysis process. These ratios for the first six modes of vibration are presented in Table 6 for different excitation amplitudes. The time-history responses of the building in terms of translational displacement (N-S) were obtained at a node on the 14th floor of the building. Table 6 Modal damping ratios used for finite element modelling [22]. Mode No.

10 kg

20 kg

40 kg

1st E-W translation

1.53

1.56

1.71

1st N-S translation

1.53

1.56

1.71

1st torsion

1.40

1.47

1.64

26

2nd torsion

1.34

1.34

1.34

2nd E-W translation

5.00

5.00

5.00

2nd N-S translation

6.84

6.84

6.84

The time-history responses of the finite element model obtained at various excitation frequencies are shown in Fig. 14. It can be seen that a steady state response was established after approximately 20 seconds at all excitation frequencies, so the peak amplitude for each excitation was estimated from the response from 20-60 sec.

(a) Response at excitation frequency, 1.911 Hz

(b) Response at excitation frequency, 1.900 Hz

(c) Response at excitation frequency, 1.880 Hz Fig. 14. Time history responses of the numerical model excited by: (a) 10 kg, (b) 20 kg, (c) 40 kg.

27

Table 7 shows a comparison between the modal displacements measured from forced vibration testing and those obtained numerically. It is evident that, the modal displacements measured from the forced vibration testing were smaller than those obtained from the finite element model. The discrepancies between the experimental modal displacements and those obtained using the finite element model were 5%, 11%, and 8%, respectively for the three eccentric weights. The peak amplitudes of the time history response obtained by the finite element model were very close to the experimentally obtained modal displacements at different excitation frequencies. This match shows the high accuracy of the finite element model to predict the realistic dynamic behaviour of the building under various harmonic excitation forces. It is noteworthy that the finite element model was first calibrated using the lowest excitation amplitude and then the model was used to predict structural response due to higher amplitudes of the excitation force. In total, there are some limitations for comparison between numerical and experimental analysis results. The small differences between the numerical and experimental results can be due to the nonlinear effects observed experimentally, which cannot be modelled using elastic linear time history analysis. No variation of natural frequency or damping ratio with different levels of excitation force was considered in the numerical modelling, which could increase the discrepancy between the measured and predicted responses as the excitation amplitude increased. It should be mentioned that the observed discrepancy between the results can be decreased by taking into account factors, such as the nonlinear effects and the soil-structure interaction consequences on the overall behaviour of the building. Table 7 Comparison of modal displacements obtained from experiment and the numerical model. Eccentric weight (kg) 10

Measured displacement (m) 8.790E-05

Numerical displacement (m) 9.255E-05

Error (%)

20

1.630E-04

1.815E-04

11%

40

2.900E-04

3.158E-04

8%

7. Conclusions

28

5%

In this study, the dynamic behaviour of a full-scale 13-story reinforced concrete building was measured using different excitation sources, including forced vibration and ambient vibration. During the monitoring period, the building was subjected to a 6.5M earthquake roughly 350 km away from the building. Dynamic characteristics of the building were identified with a range of time and frequency domain system identification techniques using the vibration measurements recorded from each excitation sources. A finite element model of the building was also developed using SAP2000 to compare the modal properties of the building to the identified counterparts measured from experiments. The following results on dynamic behaviour of the large-scale structure were extracted. 1. The results obtained from the forced vibration tests indicate that the amplitude of input force affects the dynamic characteristics of the structure, as the natural frequencies and the modal damping ratios respectively decreased and increased as the magnitude of excitation increased. 2. Good agreement between the modal parameters of the building, including natural frequencies and modal damping ratios, was obtained from different sets of low-amplitude ambient vibration induced by various excitation sources. Also, the ambient data recorded from traffic and earthquake produced satisfactory estimations of the mode shapes of the building when considering the first four modes of the structure. 3. The natural frequency, mode shape and modal damping values extracted using ambient vibrations were comparable with those measured during forced vibration testing, providing substantial evidence that ambient vibration testing can be as effective as forced vibration testing in determining modal parameters of the full-scale building. At this level of ambient vibration, it is guaranteed that the structure response is in linear range. Therefore, the identified modal parameters from ambient vibration can be used to establish baseline details for future monitoring of the structure. 4. In addition, good agreement between the modal parameters obtained by different system identification methods was found. Both conventional time and frequency domain system identification techniques provided very consistent and accurate estimations of the modal characteristics of the building when used with output-only data. Therefore, these techniques

29

can extract the building dynamic characteristics from low-amplitude ambient vibrations as baseline information to be used for condition assessment of the large-scale building. 5. The results obtained from the earthquake excitation data indicate that although near-stationary vibration data can produce accurate estimates of the modal characteristics of the system, nonstationary part, of the signal resulted in a poor representation of all mode shapes. Therefore, further study is required to estimate the level of non-stationarity in the signal to facilitate the application of output-only modal parameter identification techniques with non-stationary data. 6. A very good agreement was observed between the first six natural frequencies obtained using finite element analysis and the experiments. Also, the first translational and torsional mode shapes of the building obtained numerically and using ambient vibration testing matched very well. The results show high accuracy of the finite element model to simulate realistic modal displacement of the building under various harmonic excitation forces. ACKNOWLEDGEMENTS The financial support of the New Zealand Earthquake Commission (EQC) is gratefully acknowledged. The authors would like to thank Annabelle Hale (Dean’s assistant) for her help in the setting up of the accelerometers throughout the building. Also, special thanks to Bharat Popli and Morgan Wang, final year project students, for their assistance in instrumenting the building and preparing the recorded data. At the end, the authors would like to sincerely appreciate Jenny Lee and Dr John W. Butterworth for providing the vibration data collected during the forced vibration testing on the building. REFERENCES 1. 2. 3.

4.

Farrar, C. and G. James III, System identification from ambient vibration measurements on a bridge. Journal of Sound and Vibration, 1997. 205(1): p. 1-18. Andersen, P., et al. Comparison of system identification methods using ambient bridge test data. in Proc. of the 17th International Modal Analysis Conference, Kissimee, Florida. 1999. Peeters, B., et al. Comparison of system identification methods using operational data of a bridge test. in PROCEEDINGS OF THE INTERNATIONAL SEMINAR ON MODAL ANALYSIS. 1999. KATHOLIEKE UNIVERSITEIT LEUVEN. Rahman, M.S. and D. Lau. Comparison of system identification techniques with field vibration data for structural health monitoring of bridges. in Masters Abstracts International. 2012. 30

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Chen, G., S. Beskhyroun, and P. Omenzetter. A comparison of operational modal parameter identification methods for a multi-span concrete motorway bridge. in Proceedings of the New Zealand Society for Earthquake Engineering Annual Conference. 2015. Endrun, B., M. Ohrnberger, and A. Savvaidis, On the repeatability and consistency of threecomponent ambient vibration array measurements. Bulletin of Earthquake Engineering, 2010. 8(3): p. 535-570. Çelebi, M., Comparison of recorded dynamic characteristics of structures and ground during strong and weak shaking. Increasing Seismic Safety by Combining Engineering Technologies and Seismological Data, 2009: p. 99-115. Au, S.-K., F.-L. Zhang, and P. To, Field observations on modal properties of two tall buildings under strong wind. Journal of Wind Engineering and Industrial Aerodynamics, 2012. 101: p. 12-23. Brownjohn, J., Ambient vibration studies for system identification of tall buildings. Earthquake engineering & structural dynamics, 2003. 32(1): p. 71-95. Brincker, R., C. Ventura, and P. Andersen. Why output-only modal testing is a desirable tool for a wide range of practical applications. in Proc. Of the International Modal Analysis Conference (IMAC) XXI, paper. 2003. Çelebi, M., Seismic instrumentation of buildings. 2000: US Department of the Interior, US Geological Survey. Rendon, A.R., G.C. Archer, and C.C. McDaniel. Ultra-Low Forced-Vibration Testing of a Large Building. in 15th World Conference on Earthquake Engineering, Lisbon. 2012. Ni, Y., F. Zhang, and H. Lam, Series of full-scale field vibration tests and Bayesian modal identification of a pedestrian bridge. Journal of Bridge Engineering, 2016. 21(8): p. C4016002. Salawu, O.S. and C. Williams, Bridge assessment using forced-vibration testing. Journal of structural engineering, 1995. 121(2): p. 161-173. Omenzetter, P., et al., Forced and Ambient Vibration Testing of Full Scale Bridges. A report submitted to Earthquake Commission Research Foundation (Project No. UNI/578), 2013. Gomez, H.C., H.S. Ulusoy, and M.Q. Feng, Variation of modal parameters of a highway bridge extracted from six earthquake records. Earthquake Engineering & Structural Dynamics, 2013. 42(4): p. 565-579. Memari, A., et al., Full-scale dynamic testing of a steel frame building during construction. Engineering Structures, 1999. 21(12): p. 1115-1127. Chen, G.-W., S. Beskhyroun, and P. Omenzetter, Experimental investigation into amplitudedependent modal properties of an eleven-span motorway bridge. Engineering Structures, 2016. 107: p. 80-100. Hogan, L.S., et al., Dynamic Field Testing of a Three-Span Precast-Concrete Bridge. Journal of Bridge Engineering, 2016. 21(12): p. 06016007. Quaranta, G., C. Demartino, and Y. Xiao, Experimental dynamic characterization of a new composite glubam-steel truss structure. Journal of Building Engineering, 2019. 25: p. 100773. Ewins, D., Modal testing: theory, practice and application. 2000, Baldock. Research Studies Press. XIII. Lee, J.H., Assessment of modal damping from full scale structural testing. 2003, University of Auckland. USB AccelerometerModel X16-1C. Gulf Coast Data Concepts, 2012 Haritos, N. Low cost accelerometer sensors-applications and challenges. in Australian Earthquake Engineering Society Conference. 2009. Beskhyroun, S. and T.M.Q. Ma. Low-cost accelerometers for experimental modal analysis. in 15th World Conference on Earthquake Engineering. 2012. Brincker, R., L. Zhang, and P. Andersen. Modal identification from ambient responses using frequency domain decomposition. in Proc. of the 18*‘International Modal Analysis Conference (IMAC), San Antonio, Texas. 2000. Jacobsen, N.-J., P. Andersen, and R. Brincker. Using EFDD as a robust technique for deterministic excitation in operational modal analysis. in International Operational Modal Analysis Conference. 2007. 31

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Van Overschee, P. and B. De Moor, Subspace identification for linear systems: Theory— Implementation—Applications. 2012: Springer Science & Business Media. Beskhyroun, S. Graphical interface toolbox for modal analysis. in Ninth Pacific Conference on Earthquake Engineering. 2011. Chopra Anil, K., Dynamics of structures. Theory and Application to Earthquake Engineering. Prentice Hall, New Jersey, 1995. Ceravolo, R., et al., Amplitude dependence of equivalent modal parameters in monitored buildings during earthquake swarms. Earthquake Engineering & Structural Dynamics, 2017. 46(14): p. 2399-2417.

Appendix A:

Accelerometers at level 13 for first translational and torsional modes

Accelerometers at level 12 for first translational and torsional modes

32

Accelerometer at level 13 for second translational mode

Accelerometers at level 12 for second torsional mode

Fig. A1. Position of accelerometers for the frequency sweep setup during forced vibration test.

Accelerometer at levels 12 and 13 for first translational mode

Accelerometers at level 12 for first torsional mode

Fig. 2A. Position of accelerometers for the free vibration decay setup during forced vibration test.

Accelerometer at levels 13, 12, 9, 6 and 4 for translational

Accelerometer at level 1 (ground level) for translational modes

33

modes

Accelerometers at level 12 for torsional modes

Accelerometers at level 6 for torsional modes

Accelerometer at level 1 (ground level) for torsional modes Fig. 3A. Position of accelerometers for the mode shape setup during forced vibration test.

34

1. The results obtained from the forced vibration tests indicate that the amplitude of input force affects the dynamic characteristics of the structure, as the natural frequencies and the modal damping ratios respectively decreased and increased as the magnitude of excitation increased. 2. Good agreement between the modal parameters of the building, including natural frequencies and modal damping ratios, was obtained from different sets of low-amplitude ambient vibration induced by various excitation sources. Also, the ambient data recorded from traffic and earthquake produced satisfactory estimations of the mode shapes of the building when considering the first four modes of the structure. 3. The natural frequency, mode shape and modal damping values extracted using ambient vibrations were comparable with those measured during forced vibration testing, providing substantial evidence that ambient vibration testing can be as effective as forced vibration testing in determining modal parameters of the full-scale building. At this level of ambient vibration, it is guaranteed that the structure response is in linear range. Therefore, the identified modal parameters from ambient vibration can be used to establish baseline details for future monitoring of the structure. 4. In addition, good agreement between the modal parameters obtained by different system identification methods was found. Both conventional time and frequency domain system identification techniques provided very consistent and accurate estimations of the modal characteristics of the building when used with output-only data. Therefore, these techniques can extract the building dynamic characteristics from low-amplitude ambient vibrations as baseline information to be used for condition assessment of the large-scale building. 5. The results obtained from the earthquake excitation data indicate that although near-stationary vibration data can produce accurate estimates of the modal characteristics of the system, nonstationary part, of the signal resulted in a poor representation of all mode shapes. Therefore, further study is required to estimate the level of non-stationarity in the signal to facilitate the application of output-only modal parameter identification techniques with non-stationary data.

6. A very good agreement was observed between the first six natural frequencies obtained using finite element analysis and the experiments. Also, the first translational and torsional mode shapes of the building obtained numerically and using ambient vibration testing matched very well. The results show high accuracy of the finite element model to simulate realistic modal displacement of the building under various harmonic excitation forces.

Conflict of Interest Form:

o

This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue.

o

The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript