monitoring and analysis of wind and earthquake response of...

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Porto, Portugal, 30 June - 2 July 2014

A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.) ISSN: 2311-9020; ISBN: 978-972-752-165-4

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ABSTRACT: The purpose of this study is to utilize available wind and earthquake acceleration response data from three multi-story reinforced concrete buildings to examine structural behavior and system parameters. Having a realistic estimate of structural parameters such as natural frequency and critical damping ratio is important for design purposes. The dynamic properties of structures can also be used in connection with damage assessment associated with health monitoring. Therefore, improved understanding of possible “wandering” in natural frequencies and damping is important. The acceleration data has been sampled through “triggered” monitoring. The data stems from different two sources of excitation, i.e. wind and earthquakes, and is recorded for various excitation levels and environmental conditions. Structural analyses of the buildings are carried out based on the recorded data. The system parameters reflect structural changes directly, both short-term reaction to single events and long-term gradual alterations in material properties or structural settings. The findings support the thesis that the dynamic behavior of structures is determined by several external factors on very different timescales.

KEY WORDS: Building; Reinforced concrete; Dynamics; Earthquake; Wind; Acceleration response; Finite element analysis; Natural frequency; Damping.

1 INTRODUCTION The purpose of this study is to utilize available wind and earthquake acceleration response data from three multi-story reinforced concrete buildings to examine structural behavior and system parameters, their variability and their dependency on the source and amplitude of excitation as well as other environmental factors. The monitoring operations have been carried out by the Earthquake Engineering Research Centre of the University of Iceland.

Natural frequencies and damping of structural systems are known to vary depending on the level of excitation and environmental influences [5],[21]. Having a realistic estimate of structural parameters is important for design purposes. Also, the dynamic properties of structures are used in structural health-monitoring in association with damage assessment. Therefore, improved understanding of possible wandering in natural frequencies is important for the engineering community.

The buildings measurement systems are described and the recorded structural response data presented. The acceleration data has been sampled through “triggered” monitoring and the data extends over a period of twenty, six and one year, respectively for the three buildings, included in this study. The data stems from different two sources of excitation, i.e. wind and earthquake, and is recorded for various excitation levels and environmental conditions. Therefore, it is possible to investigate various relations that single event data or short term monitoring cannot resolve.

System identification analyses of the buildings are carried out applying previously verified parametric methods to the recorded data [15] as well as the MACEC toolbox [12]. Both short term and long-term dynamic behavior of concrete

buildings in a seismic and windy environment is studied through changes in the system parameters.

2 THE BUILDINGS AND DATA ACQUISITION This paper presents three case studies, involving analysis of recorded acceleration response data in 13, 14 and 20 story reinforced concrete buildings in Reykjavik, Iceland. Monitoring systems installed in these buildings have recorded building acceleration response in small to moderate earthquakes and storm events. The buildings and their monitoring systems will be introduced in the following.

2.1 Building A Building A, is a 13-storey, 41 meters high residential building built in 1992, see Figure 1. It is a cast in place reinforced concrete shear wall structure standing on a one story basement. The building has a 27.5 long and 15.5 m wide cross-section and is close to being symmetric in shape.

The building is founded on a 7 m thick compacted coarse basalt gravel cushion that needs to be included in any model of its dynamic behavior.

The monitoring system has been operating since fall 2007.

2.2 Building B Building B, is a 14 stories high (45 m) office building, shown in Figure 2. It is a reinforced cast-in place concrete structure, basically composed of shear walls and slabs. The geometry of the building is rather complex, as the floor plans vary, changing vertically.

The building was instrumented in January 1990. The instrumentation is composed of eight sensors (channels) located at three levels: the basement, the 8th floor and the

Monitoring and analysis of wind and earthquake response of three multi-story RC buildings

Jónas Thór Snaebjornsson1 1Department of Civil Eng., School of Science and Engineering, Reykjavik University, Menntavegi 1,101 Reykjavik, Iceland.

email: [email protected]

Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014

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14th floor. The data acquisition starts automatically when the acceleration on the 14th floor exceeds a specific trigger level. Basic wind and weather data is available from a meteorological site some 500 m away.

The measurement system has in the past 20 years, recorded over 100 earthquakes. The wind data catalogue contains over 600 sets of time series recorded in about 60 storm events.

Figure 1. Building A, seen from North-East.

Figure 2. Building B, seen from North-East.

2.3 Building C Building C, is a 21 story office and retail building (see Fig. 3) built in 2007. It is a reinforced cast-in place concrete structure composed of slabs supported by concrete columns at the outer perimeter and a shear-wall core in the middle. The height of the tower is 76.3 m from street level. The building also has a 2

story basement of 7.6 m from street level down, making the total height of the structure 83.9 m, from the foundation and up. A parking structure is placed next to the building and reaches up to the third floor of the tower; a dilatation separates the parking structure from the building.

The monitoring system was installed in March 2008 and in operation until fall 2009. The instrumentation was composed of two tri-axial accelerometers, one located in a utility building on the roof (21st floor) and the other placed next to the shear core on the 13th floor. The acceleration data catalogue from this 18 month campaign contains about 168 storm events and 28 earthquake events[19].

In addition to this monitoring campaign, the buildings ambient excitation was systematically recorded in July 2011 [4]. The equipment’s used were one tri-axial acceleration sensor and three uni-axial sensors. Systematic recordings were done on each floor of the building for both the strong- and the weak axis of the building.

Figure 3. Building C, seen from North-East.

3 SYSTEM IDENTIFICATION AND FE MODELLING Recorded data from all three buildings has been analyzed, and a Finite element model constructed based on design drawings and site inspections. The elasticity modulus of the buildings has been measured on site using ultrasonic techniques, to support the modeling process and validate the designer specified concrete quality. In the following the analysis procedures and results will be presented for each building.

3.1 Building A All recorded time series from 2008 – 2012 were reviewed. About 100 recordings were evaluated as earthquake induced. The recorded earthquakes were of magnitude between 3 and 6.3. The highest measured peak response acceleration was 180.5 cm/s2 during the Olfus 2008 earthquake, of magnitude


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6.3 [15]. Unfortunately that event was only recorded at the roof floor.

The geographic epicentres of observed earthquakes are shown on Figure 4 in relation to the location of the building. Sixteen earthquakes were picked out of the database for further processing.

Figure 4. A map showing south-west Iceland, the location of the observed building (blue square) and epicenters of recorded earthquakes (red circles) within 65 km with magnitude > 3. The spacing of the green circles is 10 km.

The recorded acceleration data was used for system identification of the building. The aim of the system identification was to estimate the natural frequencies and critical damping ratios for the main modes of vibration. The

The recorded acceleration data was used for system identification. The SI analysis was done using the Matlab toolbox MACEC [12]. The basement records were defined as an input and the top floor records as an output in a multi input-multi output (MIMO) system.

Frequencies and critical damping ratios for first 6 modes of vibration, evaluated with system identification and using 12 earthquake recordings, are listed in Table 1.

Table 1. Natural frequencies and critical damping ratios for the first 6 modes evaluated from 12 earthquake data seris.

Mode Natural frequency Critical damping ratio no. average median std.dev average median std.dev1 1,81 1,83 0,04 1,11 1,05 0,67 2 2,14 2,15 0,06 1,61 1,46 0,77 3 2,50 2,50 0,04 0,83 0,79 0,42 4 6,05 6,04 0,10 0,93 0,92 0,48 5 6,59 6,57 0,17 1,33 1,12 1,03 6 7,21 7,14 0,30 1,28 0,98 1,23 The building is founded on an approximately 7 meter thick

filling made of compact pillow lava, which was found to affect the response of the building, due to soil-structure interaction effects [22]. This was demonstrated through FE modeling in SAP2000 [14] using both fixed base supports and spring supports. Modal analyses were performed for both cases. Calibration of FE-model to fit natural frequencies evaluated by SI of the recorded data was found to be

unachievable without introducing spring supports to account for the finite stiffness of the lava cushion.

Figure 5. Fourier spectra of measured response of the building (blue lines) and of time history analysis (red lines) for damping ratios as evaluated by system identification based on recorded data [7].

Figure 6. Fourier spectra of measured response of the building (blue lines) and response evaluated through modal frequency analysis (red lines) for the critical damping ratio determined by iteration [7].

The frequency characteristics of the gravel cushion were estimated using H/V spectral ratio studies [8] and the EERA software [3]. A one-dimensional wave transformation was used to transfer the basement acceleration through the cushion to create a rock-type base acceleration to use for time history analysis on a model including the lava cushion.

Time history and frequency response analysis were performed in order to check the evaluated critical damping ratios and to adjust the damping to get a modal parametric model that would give a good fit to the recorded response at the top floor of the building. It was found (see Figure 5 and


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Figure 6) that the SI seemed to underestimate the damping for mode 1, but overestimate the damping for mode 2 and 3. The underestimation of the damping for the first mode may be traced to the added damping from the lava cushion, not accounted for in the SI analysis. The overestimation of damping for mode 2 and 3, is more difficult to explain but may be related to lack of excitation of these modes. Although, the iterative optimization of the frequency response was restricted by the fact that the high frequency content was somewhat filtered out by the transformation process through the cushion, the importance of taking the soil-interaction effects into account was clearly demonstrated.

3.2 Building B Over the course of the last 24 years the monitoring system has recorded a considerable amount of earthquake induced acceleration records, such as the events shown on Figure 4, as well as wind induced acceleration. A sample of those earthquakes were used for analysis in the study reported here as well as all major wind storms during the past 15 years. t

The natural frequencies and critical damping ratios of the building were evaluated by a power spectral density analysis. The power spectral density was determined in two different ways. On the one hand using an autoregressive analysis [11] and on the other hand with a fast Fourier transform analysis [20]. An example of the two spectral densities are shown in Figure 7.

In the fast Fourier transform the power spectral density is estimated with the Welch method where the each time-series is divided into segments with an overlap of 50%. A power spectral density is evaluated from 8192 sample points of each segment and then averaged to get the final power spectral density of the time-series [1].

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Figure 7. Power spectral density from an AR analysis and a FFT analysis for (a) X component and (b) Y component [9].

The natural frequencies are taken at the maximum value of resonance and the critical damping ratio is evaluated with the half-power bandwidth method [6].

An important factor in the autoregressive analysis is the autoregressive model order. To find an appropriate model order, the evaluated natural frequencies and damping ratios were evaluated for test records using the Burg algorithm [20] and different model order (see Figure 8).

1.68 1.7 1.72 1.74 1.760

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The power spectral densities representing the different

models were plotted up and compared. After some consideration, it was decided that a model order of 500 provided an acceptable accuracy, as it identifies the higher natural frequencies without showing unreal peaks.

Figure 9, shows the natural frequency and critical damping ratios evaluated from wind induced acceleration data using an autoregressive model order of 500 as well as the average values of natural frequency and critical damping ratios determined with the autoregressive model of order varying from 200 to 1000. It can also be seen from Figure 9 how the first natural frequency is steadily decreasing during observation period. The great variability of the critical damping ratio is also noticeable.

A comparison of the results from the two methods shows extremely similar results for the average natural frequencies but the average critical damping ratio varies considerably as The difference of the critical damping ratios is largest for the first mode of vibration and then decreases gradually for the higher modes of vibration.

A comparison of the results from the wind data and the earthquake data shows only a slight difference in the natural frequencies but quite a big difference in the critical damping ratios as shown in Table 2. The biggest difference in the critical damping ratios occur in the first three modes of vibration, while there is much less difference in the higher three modes. This could indicate different behaviour of the structure in earthquake induced excitation than, which excites all the lower modes of the structure, than in wind induced excitation when only the first three modes are excited and the vibration is predominently in the top-tower.

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Figure 9. Comparison of (a) natural frequencies and (b) critical damping ratios for the first mode of vibration [9].

Table 2. Natural frequencies (fi) and critical damping ratios (ζi) evaluated from earthquake and wind induced response.

Type of data

Mode 1 Mode 2 Mode 3 Mode 4 f1 (Hz) ζ1 (%) f1 (Hz) ζ1 (%) f1 (Hz) ζ1 (%) f1 (Hz) ζ1 (%)

EQ data 1,64 1,92 2,20 2,40 3,22 4,71 4,01 1,08

Wind data 1,68 1,37 2,29 1,36 3,11 1,41 4,16 1,47

Diff. 2,6% 40,8% 3,6% 77,0% 3,5% 235,3% 3,6% 26,6%

The finite element modelling of the building is carried out using the finite element software SAP2000, [14]. The software is a practical general purpose structural analysis program that can perform various analyses, from a simple static 2D frame analysis to a complicated 3D non-linear dynamic analysis.

The finite element model of the building is shown in Figure 10. It is based on the available architectural and structural drawings, along with on-site measurements to verify the dimensions of structural elements and the modulus of elasticity of the concrete. It is important to make appropriate assumptions in the construction of a model like this to achieve good correspondence between the natural frequencies of the model and the natural frequencies from the recorded full-scale data. Therefore it is important to take into account the true characteristics of the floor slabs, the core wall openings, possible stiffness contribution from non-structural elements as well as applying realistic material properties [10].

The model consists of all the elements of the building that contribute to stiffness, such as the reinforced concrete walls, beams, columns and slabs. The foundation is included in the model in the form of shell elements that reach down to about 1,0 m below the bottom slab. The boundary conditions of the foundations, both walls and columns, allow rotation but no translation.

Figure 10. 3D view of the FE-model [9].

Calibration of the FE-model for the case at hand, primarily involves modifications of the modulus of elasticity. The initial model showed somewhat less stiffness than the recorded data and by increasing the modulus of elasticity the results of the modal analysis corresponded reasonably well with the results from the system identification of the full-scale data. As the measurements of the modulus of elasticity of the concrete indicates higher modulus of elasticity at the basement and lower at higher floors, the modulus of elasticity used in the calibration process of the model was set accordingly, although at slightly higher values to account for added stiffness from nonstructural elements, such as internal wall partitions.

To validate the quality of the model, a time history analysis was performed to get a modal response that could be compared to a recorded time series. The time history used was acceleration recorded at the building during a 6,4 magnitude


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earthquake, located about 60 km south-east of the building, from June 21, 2000 [16]. The computed acceleration time history and recorded time history at the 14th floor are plotted together and shown in Figure 11. A comparison of the Fourier amplitude spectra is shown in Figure 12.

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Figure 11. Computed and recorded time history acceleration at

14th floor.[9]

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Figure 12. Fourier amplitude spectra of the acceleration time history of the 14th floor. Vibration in the E-W direction.[9]

Table 3. Comparison of the natural frequencies from a calibrated FE model and system identification.

Data type/ Analysis

Mode of vibration 1 (Hz) 2 (Hz) 3 (Hz) 4 (Hz) 5 (Hz) 6 (Hz)

FEM 1,69 2,25 2,88 4,17 6,96 7,82 Wind/AR 1,68 2,29 3,11 4,16 6,97 7,81 Wind/FFT 1,69 2,29 3,11 4,16 6,99 7,82

EQ/AR 1,64 2,20 3,22 4,01 7,07 7,68

A comparison of the natural frequencies of the finite element model and the average values of natural frequencies evaluated by the system identification is shown in Table 3. It shows how the model resembles the wind data very closely except for the third mode of vibration which is the only clear torsional mode. All the modes are however influenced by torsion to some extent due to the asymmetry of the cores and the complexity of the geometry of the structure.

3.3 Building C Overview of storm related acceleration recordings is shown in Figure 13, in the form of peak acceleration values as a function of recording date and time. As can be seen from Figure 13, the largest wind related acceleration measured during the measuring period was approximately 6.5 cm/s2 (0.7% g), during a storm with a maximum 10 minute mean wind velocity of 19.6 m/s on December 11, 2008.

The wind induced acceleration response of the structure is very dependent on the gustiness of the wind. When a gust captures the building a build-up in the acceleration response is produced that can be described as nodes of acceleration bursts each of approximately 30 seconds duration or less. During a storm that may last for six hours or more, many such gusts may shake the building and trigger a recording, each time the acceleration level exceeds the threshold level. Therefore multiple time series are usually collected in each storm, when triggered recording scheme is applied. This is seen in Figure 10, where several peak acceleration values are usually plotted for each windy day.

The behavior and response of Building C, has been studied using various methods of analysis [19].

Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr0

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Figure 13. Storm induced peak acceleration values as a function of recording date and time on floor 21.

An example of wind induced acceleration time series

recorded at the 21st floor is shown in Figure 14(a), which shows all three components of acceleration recorded.

Looking at Figure 14(b), which shows an example of the energy distribution of the recorded wind induced response, it is clear that the response is dominated by the first lateral modes of vibration, i.e. the energy in the wind induced response is exclusively contained at the first two natural frequencies of the building.

The time series of acceleration recorded in the largest earthquake event (see Figure 15(a)), shows that the peak acceleration was 146 cm/s2 at the roof level or about 15% g


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(where g is the acceleration of gravity). The acceleration in the same direction at the 13th floor was 94 cm/s2 (or 9.5% g). The acceleration in the longitudinal direction of the building, was much less, or 47 cm/s2 (4.8 g%) at the roof level and 34 cm/s2 (3.5 g%) at the 13th floor. Vertical acceleration was 42 cm/s2 (4.3 g%) and 28 cm/s2 (2.9%, g) at the respective locations. This was by far the largest acceleration values recorded during the monitoring period. The peak acceleration values from the smaller earthquakes were all below 4 cm/s2 (~0.4% g).

It should be noted, that when the earthquake response of the building is inspected it can be seen that the building response is controlled by the second lateral modes of vibration. This can for instance be seen in Figure 15(b) which shows the relative distribution of energy over the frequency range from 0 to 5 Hz. The implications of this is that the acceleration levels of the lower floor will be relatively higher during earthquake induced motion compared to the wind induced response which is dominated by the first lateral modes of vibration (see Fig. 14(b) for comparison).

The system identification of the structure is based on two separate studies, using two different analysis programs and two different data sets. The results are given in Table 4.

The acceleration time series recorded in 2008 and 2009, were analysed using the MACEC-Toolbox[16] applying the Stochastic Subspace Identification method (SSI) to extract the buildings natural frequency and the critical damping ratio.

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Figure 15. Earthquake induced acceleration (a) Time series (b) Power spectral density and model order.

Bjarnason and Hafsteinsson [4] applied the modal identification software, ARTeMis Extractor [2], which also uses the SSI method, to evaluate the dynamic properties of the structure using ambient vibration data from each floor of the building.

The results from the two studies are given in Table 4 for the first three modes of vibration. It should be noted that due to the location of the accelerometers at the central core of the building, the rotational modes of vibrations are not well presented by the data analyzed with the MACEC toolbox.

Table 4. Dynamic parameters determined using forced (MACEC ) and ambient vibrations (ARTeMis).

Mode of vibration

Natural frequency (Hz) Critical damping ratio (%) MACEC ARTeMis MACEC ARTeMis

mean std mean std 1 0.61 0.62 0.029 1.1 1.6 0.75 2 0.80 0.78 0.005 2.2 1.3 0.72 3 - 0.91 0.007 - 2.0 0.89

It is noteworthy, that using the commonly used estimation

formula of n = 46/H [6], for buildings above 50 m tall, gives an estimate of 0.60 for the natural frequency if using H=76.3 m, i.e. the height above ground level.

A finite element model gave similar results for the natural frequencies of the first few modes after an appropriate choice of the modulus of elasticity [5].


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4 DISCUSSION AND RESULTS Recorded acceleration data, both ground motion and response, has been studied for three reinforced concrete buildings in Reykjavik. In each case the natural frequencies and critical damping ratios have been evaluated using different system identification approaches. A FE model has been built for each of the buildings and calibrated using an iterative time-series and frequency response analysis based on ground motion and comparing the evaluated response with recorded response.

The following key results can be learned from the three cases studied:

Foundation-Building interactions are important for the overall behavior of the building. If built on a relatively thick gravel cushion, the cushion should be included in the overall building model, to represent the correct natural frequency and damping values.

The dynamic parameters of buildings are not constant, but vary with the amplitude and direction of the excitation action, as well as through other environmental conditions at the time of recordings.

The long term observations in Building B, indicate that the stiffness of concrete buildings can be expected to diminish somewhat with time. The results show about 11% decrease in stiffness over a 15 year period for building B. This is probably at least partly due to creep and shrinkage effects, that may differ from building to building depending on the quality of concrete.

Building C, that has lowest natural frequency of 0.6 Hz, demonstrates well how the modes of vibration participate in different ways to different excitation, such as earthquakes and wind.

In general different system identification methods resulted in very similar results for the natural frequencies of the buildings, but the critical damping ratios were seen to vary considerably, both between SI methods and between each recorded event using the same SI approach.

Comparing wind and earthquake induced response revealed the dependence of stiffness, and thereby the natural frequencies, on the amplitude of motion as the earthquakes generally induce considerably higher response than the wind. Similar dependence has partly been seen for the damping, but the inherent variability of the damping parameter makes the relation unclear.

These studies show that a calibration procedure is needed for all FE-models in order for them to simulate adequately the true dynamic response of the real structure. A frequency response analysis using recorded earthquake data was found to be a good calibration approach.

ACKNOWLEDGMENTS The discussion and results presented herein are partly based on the work of [7], [8] and [4]. The contribution of the staff at EERC of the University of Iceland on the instrumentation of the buildings and data acquisition is acknowledged.

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