iomac'15iomac.eu/iomac/2015/pdf/113_paper_soleimani.pdf · building code of canada (nbcc 2010)...

IOMAC'15

6th International Operational Modal Analysis Conference

2015 May12-14 Gijón - Spain

DETERMINATION OF FULL MODAL PROPERTIES

AND EFFECTS OF FOUNDATION ROCKING ON THE

DYNAMIC CHARACTERISTICS OF TWO HIGH-RISE

CONCRETE SHEAR WALL BUILDINGS

Salman Soleimani-Dashtaki1, Ferya Moayedi2, Carlos E. Ventura3

1 Ph.D. Candidate in Civil Engineering, University of British Columbia, Vancouver, BC, Canada, [email protected] 2 M.Eng. in Civil Engineering, University of British Columbia, Vancouver, BC, Canada, [email protected] 3 Professor of Civil Engineering, University of British Columbia, Vancouver, BC, Canada, [email protected]

ABSTRACT

In this study, two high-rise buildings with concrete shear wall cores have been tested. Both of the tested

buildings, shown in Figure 1 below, are thoroughly investigated for torsional modes as well as

foundation rocking, since torsional sensitivity is expected due to the structural irregularities present.

(a) 20-storey building (b) 30-storey tower

The first case study presents the results obtained from the ambient vibration measurements done on a

newly constructed, 20 stories high building, with reinforced concrete core, in Vancouver, British

Columbia, Canada, Figure 1 (a). The experimental results reveal the dynamic characteristics of the

investigated building by advanced system identification methods using enhanced signal processing

techniques and the fundamentals of frequency domain decomposition. The experimental results would

include the natural frequencies and the mode shapes of the buildings obtained from the vibration

measurements.

Figure 1. The tested buildings with their corresponding developed ARTeMIS models.

mailto:[email protected]



The second building tested using this unique technique is a newly constructed 30 stories tall reinforced

concrete building in Burnaby, British Columbia, Canada, Figure 1 (b). The experimental results reveal

the dynamic characteristics of this investigated building including the building rocking modes.

For the 20 storey building, a total of 12 modes of vibration, up to the 4th translational and torsional

modes, are identified. For the 30 storey building, a total of 15 natural periods of vibration are identified

including the translational and torsional modes (up to the 5th mode) along with the foundation rocking

component for each mode. Hence, the utilized testing approach and the analysis methodology would

work well for the tall buildings tested and the number of modes identified is beyond the expectation.

Keywords: System Identification, Experimental Techniques, Ambient Vibration Measurement, Modal

Estimation, Model Validation, Modal Parameter Identification, Foundation Rocking Modes, Tall

Buildings.

1. INTRODUCTION

The dynamic characteristics of a structure after its construction has been completed can be determined

using ambient vibration measurement techniques. The buildings chosen to be investigated are newly

constructed reinforced concrete core buildings in the Vancouver area.

In order to investigate the dynamics of the buildings, transducers used to record vibrations in terms of

velocity and acceleration at each floor level. The data are then analysed and the buildings are modelled

in order to extract the modal properties of the structure. These properties include the natural frequencies

of the building and their modes of vibration in the translational and torsional modes, as well as their

respective modal damping ratios. Depending on the type of the building and the quality of the obtained

data, the best attempts are done in order to identify as many modes of vibration as possible.

The results of the experimental ambient vibration studies are then compared to the analytical estimates

from the ETABS models of the buildings created at the time of the structural design.

2. EXPERIMENTAL PHASE

The modal characteristics of the structures investigated in this paper have been determined by different

methods. Initially, at the design stage, the buildings have been modeled in ETABS and the modal

properties are estimated. Later on, once the constructions of the buildings are near completion, the

building’s actual dynamic characteristics are investigated using output-only modal identification

methods. This section would elaborate on the experimental setup and the data acquisition techniques.

2.1. Buildings Tested

The first building tested, 20-storey tall, has two reinforced concrete cores, each one with a set of stairs

from the basement all the way up to the roof. Of the two concrete cores, one also contains an elevator

shaft which continues throughout the height of the building.

The shape of the building in plan view is a simple rectangle with some minor extrusions at some levels.

The size of the building in the three lower floors is approximately 36m by 30m and in the upper floors

it reduces to 30m by 20m. Typical storey height is approximately 3.7m.

The building is at the final stages of construction at the time of the study; hence, construction noises are

present within the recorded signals. The building floor plan is illustrated in Figure 2 (a).

The second building tested, a 30-storey concrete tower, sits on top of 4 levels of reinforced concrete

underground parking. The building has a huge central core with four elevator shafts and staircases all

the way from the parkade level up to the roof.

There are concrete reinforced columns of 60 inches in diameter extending from the foundations all the

way up to level 29. Columns get narrower with the height of the building, and at level 25 they reach a

diameter of 30 inches. The building in plan has a complex geometry with one round corner and straight

edges at all other corners. There are also some extrusions at different heights. The height of the parking

floors are 2.9m each, the height of the lobby is 4.9m, and the height of all the other floors is

approximately 3.7m.

The structure is under the final stages of construction at the time when measurements are made, so

construction noises are evident throughout the recorded signals. The floorplan of the building is

illustrated in Figure 2 (b).

2.2. Ambient Vibration Measurement

System identification of the selected buildings is performed by conducting ambient vibration tests to

analyze the dynamics of the structures and observe the structural modes of vibration. Ambient vibration

test is preferable to forced vibration measurement for different reasons. In order to obtain the modal

parameters of large structures, there is adequate excitation from wind, traffic, and human activity forces.

Hence, there would be no need for exciting devices to be used and the risk of damaging the structure

can be avoided.

Using a number of transducers, the velocity and accelerations of the structures are recorded in the time

domain. In order to capture the behavior of the structure, measurements are made in different setups. In

each setup one transducer is always kept at the highest floor of the building recording motions for the

entire duration of the test, as a reference sensor, and a number of transducers are moved around to

different floors. Typically, two sensors are placed at every single floor of each building at a time, usually

at opposing corners.

The durations of measurements for data recordings are usually predetermined by looking at the

structural drawings and ETABS models prior to the tests. The higher the fundamental period of the

building, the longer recording time is required in order to capture the low frequency content which

includes the lowest modes of vibration.

Figure 2. Building floor plans; 20-storey building (a), 30-storey tower (b)

(b) (a)

2.2.1. Sensor Locations

The vibration modes of the building are captured by setting up two TROMINO® transducers, each

recording data at 10-channels at 128Hz. They are placed at the opposite corners of each floor, recording

the movements in the X, Y, and Z directions. Such an arrangement is chosen prior to testing in order to

better capture the translational modes in the NS and EW directions as well as the torsional modes of the

building.

All the sensors are constantly acquiring date and time from the GPS, minimum of 3 satellites at a time,

throughout the entire measurements at one channel. The remaining 9 channels are recording high and

low gain velocity plus acceleration in three directions (X, Y, and Z).

The reference transducer is placed on the roof, close to the central core of the building. The schematic

layout of the sensor locations is shown below in Figure 3 for the 20-storey building (a) and the 30-

storey tower (b).

Ref. Transducer

Transducer

Transducer

Ref. Transducer

Transducer

Transducer

Figure 3. Sensor locations; 20-storey building (a) and 30-storey tower (b)

The recording duration and the sampling rate are set based on the estimated natural frequency of the

buildings. The natural frequency is once determined using the methodology suggested by the National

Building Code of Canada (NBCC 2010) and once by running the analysis on the ETABS model. In

order to capture the modal properties of a long period structure with TROMINO® transducers, it is

recommended to record data for longer durations of time; preferably not less than 1000 times the natural

period of the building in units of seconds, to be taken as a rule of thumb.

3. DATA PROCESSING

After testing, the recorded data need to be extracted from the TROMINO®s onto a computer using the

Grilla® Software. The same software is then used in order to convert the data to ASCII format and a

series of basic and preliminary signal processing is performed over the data in order to check the validity

of the recorded signals.

(a) (b)

Data validation and pre-processing of the data is done using MATLAB at the preliminary stages.

MATLAB codes are generated in order to view the time history plots, take them into the frequency

domain, and verify the data. An extensive signal processing is performed in order to identify as many

modes of vibration as possible. The data is decimated in different ways and data filtering with different

orders is done to zoom into specific frequency bands in order to minimize the noise and distinguish the

structural modes of vibration at each frequency range.

The Frequency Domain Decomposition (FDD) technique which decomposes the spectral density matrix

at every frequency line using Singular Value Decomposition (SVD) is utilized in order to estimate the

mode shapes and the natural frequencies based on the set of single degree of freedom (SDOF) systems

for each mode. It is evident that the estimated modes can be grouped into the following types: structural

modes, harmonics, and noise modes [3]. Investigation is done on the Singular Value Decomposition

(SVD) graphs in order to identify the modes of the mentioned types and peak-picking method is

performed in order to distinguish and select only the structural modes of vibration from the rest of the

plotted frequency content.

4. SYSTEM IDENTIFICATION USING ARTEMIS MODAL

The ARTeMIS Modal is the main software used throughout the project for the purpose of enhanced

signal processing, modal estimation, and exploring the dynamics of the studied structures by

decomposing the recorded signals in domains of frequency.

4.1. Frequency Domain Decomposition (FDD)

This technique approximately decomposes the response into a set of independent single degrees of

freedom systems and performs singular value decomposition of the spectral density matrices. Table 1

Table 1 below summarizes the identified modal frequencies using this technique.

Table 1. Identified frequencies using the FDD technique

Mode No. Mode Descriptions

20-Storey Building

(FDD)

30-Storey Tower

(FDD)

Hz Hz

1 1st Translational Mode in the Y-Direction 1.08 0.50

2 1st Translational Mode in the X-Direction 1.27 0.53

3 1st Torsional Mode 1.83 0.94

4 2nd Translational Mode in the X-Direction 4.46 1.95

5 2nd Translational Mode in the Y-Direction 4.97 2.28

6 2nd Torsional 6.72 2.58

7 3rd Translational Mode in the X-Direction 9.68 3.73

8 3rd Torsional Mode 11.45 4.61

9 3rd Translational Mode in the Y-Direction 12.03 5.19

10 4th Translational Mode in the Y-Direction 15.01 5.61

11 4th Torsional Mode - 6.63

12 5th Translational Mode in the X-Direction - 7.29

13 4th Translational Mode in the Y-Direction - 8.20

14 6th Translational Mode in the X-Direction - 8.41

15 5th Torsional Mode - 10.04

4.2. Enhanced Frequency Domain Decomposition (EFDD)

The enhanced FDD adds a modal estimation layer which is divided into two steps. The first step is to

perform the FDD Peak Picking, and the second step is to use the FDD identified mode shapes to identify

the Single-Degree-Of-Freedom (SDOF) Spectral Bell functions and from these SDOF Spectral Bells

estimate both the frequency and damping ratio.

Table 2 below contains the calculated frequencies and the modal damping ratios for the identified modes

of vibration from peak-picking done using the EFDD technique.

Table 2. Identified frequencies using the EFDD technique

Mode

No. Mode Descriptions

20-Storey Building 30-Storey Tower

Frequency

(EFDD)

Damping

Ratio

Frequency

(EFDD)

Damping

Ratio

Hz % Hz %

1 1st Translational Mode in the Y-Direction 1.08 1.49 0.50 1.84

2 1st Translational Mode in the X-Direction 1.27 1.43 0.53 0.00

3 1st Torsional Mode 1.83 1.07 0.94 1.08

4 2nd Translational Mode in the X-Direction 4.46 1.28 1.95 1.37

5 2nd Translational Mode in the Y-Direction 4.96 1.34 2.28 1.13

6 2nd Torsional 6.73 1.28 2.57 0.74

7 3rd Translational Mode in the X-Direction 9.63 0.00 3.74 1.27

8 3rd Torsional Mode 10.90 0.00 4.61 1.32

9 3rd Translational Mode in the Y-Direction 12.04 0.00 5.18 1.15

10 4th Translational Mode in the Y-Direction 15.01 0.00 5.60 1.13

11 4th Torsional Mode - - 6.61 0.00

12 5th Translational Mode in the X-Direction - - 7.28 0.82

13 4th Translational Mode in the Y-Direction - - 8.31 0.00



4.3. Curve-fit Frequency Domain Decomposition (CFDD)

The curve-fit FDD is similar to the EFDD estimation. The natural frequency and the damping ratio of

the mode are estimated by curve fitting the SDOF Spectral Bell using frequency domain least-squares

estimation, shown graphically in Figure 4. Since the SDOF spectral bell is free of influence of other

modes there is only a single eigenvalue and residue to fit. The natural frequency as well as the damping

ratios are then extracted from the eigenvalues and are presented in Table 3.

Table 3. Identified frequencies using the CFDD technique

Mode



Frequency

(CFDD)

Damping

Ratio

Frequency

(CFDD)

Damping

Ratio

Hz % Hz %






6 2nd Torsional 6.724 0.837 2.57 0.46










For illustration of the technique, the singular values of the spectral density matrices of all the test setups

using the Curve-fit Frequency Domain Decomposition (CFDD), for the 20-storey building, are shown

in the plot represented in Figure 4.

Figure 4. Singular values of spectral density matrices, using CFDD technique, for the 20-storey building

4.4. Frequency Domain Operational Deflection Shapes (ODS)

An Operating Deflection Shape or ODS is the deflection of a structure at a particular frequency relative

to a specific point, also known as the driving point, on the structure. Before any modal estimation and

after each modal identification the ODS is done to confirm the validity of the deflected shape at the

identified frequency. A summary of the frequencies identified by the FDODS technique is presented in

Table 4 below.

Table 4. Identified frequencies using the frequency ODS shape technique

Mode



Freq.

(ODS)

Mode

Complexity

Freq.

(ODS)

Mode

Complexity

Hz % Hz %






6 2nd Torsional 6.75 28.10 2.58 12.03










4.5. Detecting Foundation Rocking at the Base of the 30-Storey Tower

An enhanced modal estimation is performed, on the 30-storey tower, using the frequency domain

decomposition technique identifying the frequencies at which the rocking component is evident in the

vibration modes. Since considerable rocking components are expected to be detected in the very first

fundamental modes at lower frequency ranges, a different filtering and decimation approach is utilized

in order to identify these specific mode shapes.

For this purpose, only one of the measured test setups for this tall building is considered. Indeed, the

only setup considered in this part of the study is a modified version of the test of “Setup 8” which was

recorded by 8 transducers all sitting on top of different foundations at the lowest parking level of the

building plus a reference sensor at the roof level. The locations of the main foundations are determined

prior to the test, from the structural drawing sets.

The FDD plot presented in Figure 5 shows all of the identified modes using the FDD method, presented

in the preceding sections. This plot can be obtained by passing a series of low, high, and band pass type

Butterworth filters, in increasing orders, over the data, initially with no decimations. Then the peak-

picking method is performed to identify the modal frequencies, also tabulated in Table 1.

Figure 5. Singular values of spectral density matrices of the rocking test setup

In order to identify the rocking component of the previously identified mode shapes, the equations

driving the building model in the ARTeMIS Modal Pro software had to be modified such that a rigid

body motion can be assumed throughout the height of the building. With this new condition, all of the

predetermined frequencies, listed in Table 1, are revisited in order to detect the rocking component of

each mode. It is worth mentioning that at the higher frequency ranges the data needs to be filtered in

different orders to minimize the noise content. Table 5 indicates if a rocking component is detected for

each associated mode of vibration, for the first 10 natural frequencies.

This exercise can be very helpful when looking at higher modes of vibration, and more specifically,

when looking at the rocking component present in the torsional modes. In fact, isolating the dedicated

rocking test setup and modifying the driving equations of the model would magnify the rocking motion

and makes them easier to be perceived. However, the rocking motion should be clearly visible from the

mode shapes when there is significant rocking component associated with a translational or torsional

mode of vibration. In this 30-storey tower, there is significant rocking components associated with the

first mode of vibration, both in X and Y directions. Also, the rocking motion is fairly visible in the first

torsional mode of vibration of the tower, but not very clear in higher torsional modes.

Table 5. Foundation rocking components of the 30-storey tower modes of vibration

Mode No. Mode Description

Frequency

(FDD)

Rocking

Component

Detected

Hz Y/N

1 1st Translational Mode in the Y-Direction 0.50 Yes (strong)

2 1st Translational Mode in the X-Direction 0.53 Yes (strong)

3 1st Torsional Mode 0.94 Yes

4 2nd Translational Mode in the X-Direction 1.95 Yes

5 2nd Translational Mode in the Y-Direction 2.28 Yes

6 2nd Torsional 2.58 No

7 3rd Translational Mode in the X-Direction 3.73 Yes (weak)

8 3rd Torsional Mode 4.61 No

9 3rd Translational Mode in the Y-Direction 5.19 Yes (weak)

10 4th Translational Mode in the Y-Direction 5.61 No

Two of the typical rocking mode shapes of Table 5 are presented in Figure 6 below, obtained by the

aforementioned exercise. Also, all of the mode shapes from the identified frequencies are presented

in the appendix of this paper.

(a) (b)

Figure 6. Rocking Mode No. 16 (a) and rocking Mode No. 18 (b)

5. CONCLUSION AND RESULT SUMMARY

The summarized values in Table 6 present the natural frequencies of the two tested buildings, using

different decomposition methods. As observed from the table, the results from the different modal

analysis techniques are very similar, so there is a good degree of consistency amongst the methods used.

Table 6. Summary of the results

Mode

No.


Frequency (Hz)

Frequency (Hz)

(FDD) (EFDD) (CFDD) (ODS) (FDD) (EFDD) (CFDD) (ODS)

1 1.08 1.08 1.08 1.08 0.50 0.50 0.50 0.50

2 1.27 1.27 1.27 1.27 0.53 0.53 0.53 0.53

3 1.83 1.83 1.83 1.83 0.94 0.94 0.94 0.94

4 4.46 4.46 4.45 4.46 1.95 1.95 1.95 1.95

5 4.97 4.96 4.96 4.98 2.28 2.28 2.28 2.28

6 6.72 6.73 6.72 6.75 2.58 2.57 2.57 2.58

7 9.68 9.63 9.63 9.67 3.73 3.74 3.74 3.72

8 11.45 10.90 11.64 11.46 4.61 4.61 4.61 4.61

9 12.03 12.04 11.96 12.08 5.19 5.18 5.16 5.17

10 15.01 15.01 15.00 13.17 5.61 5.60 5.60 5.63

11 - - - - 6.63 6.61 6.61 6.61

12 - - - - 7.29 7.28 7.28 7.30

13 - - - - 8.20 8.31 8.31 8.31

14 - - - - 8.41 8.44 8.44 8.44

15 - - - - 10.04 10.14 10.14 10.14

The estimated natural frequencies of the structures identified using the FDD technique are compared

against the values obtained from the ETABS model of the buildings, developed at the structural design

phase. As an illustration, Figure 7 shows the 30-storey tower along with its ETABS model and the

ARTeMIS model developed for it. Also, Table 7 summarizes the measured and the ETABS mode

frequencies, before performing any model updating on the ETABS model.

(a) (b) (c)

Figure 7: The 30-storey tower street photo (a), its ETABS model (b), and its ARTeMIS Modal Pro model (c)

The comparison reveals that there is a significant difference between the natural frequencies obtained

from the ETABS model and from the experiment; by a factor of two in some cases. The potential

reasoning behind the major difference can be explained through two main points of discussion. First of

all, the ETABS models are over-simplified and are only considering the main shear wall central cores

of the buildings, which is not truly reflecting the reality. In fact, a significant portion of the building’s

overall stiffness is coming from the building cladding and the long columns of the gravity load carrying

systems around the structures. These two major stiffness contributing factors have been ignored in the

analytical model, resulting in underestimation of the building’s lateral stiffness; and so the frequencies.

Secondly, the “cracked values” are used in the ETABS models, in order to account for the material

nonlinearity within the concrete elements. However, this would also result in higher estimations for the

building’s fundamental vibration period, compared to the measured values. Updating the ETABS

models of both buildings is highly suggested as part of possible future investigations on these buildings.

Table 7. Comparison of the building frequencies, ARTeMIS model vs. FEM model

Mode



FDD

Freq.

FEM Model

Freq.

FDD

Freq.

FEM Model

Freq.

Hz Hz Hz Hz






6 2nd Torsional 6.72 5.17 2.58 1.32








14 6th Translational Mode in the X-Direction - - 8.44 -

15 5th Torsional Mode - - 10.14 -

This paper would like to conclude that the utilized testing strategy would work very well for both of the

tested buildings. The number of modes identified is beyond the expectation. This study would like to

highlight considerable rocking components in the first two translational modes of vibration (X and Y).

Moreover, MAC values have been utilized in order to bring assurance in the mode shape identification

process, but they are not discussed in this paper for simplicity. Also, it is realized that recording data at

higher sampling rates, i.e. above 256Hz, would increase the resolution of the data in order to facilitate

looking for specific information at higher frequency ranges.

Also, taller buildings need to be recorded for longer durations of time in order to capture the low

frequency contents with higher resolutions. Longer signals are usually handled and processed with

greater efforts [2], but they reveal much more distinct information about the dynamics of the structure,

especially when dealing with tall buildings.

ACKNOWLEDGEMENTS

The authors of this paper would like to acknowledge the help and support of Mr. Grant Newfield and

Dr. Ron DeVall of RJC, Read Jones Christoffersen Consulting Engineers, in Vancouver, BC, Canada.

We would also like to thank Dr. Palle Andersen of Structural Vibration Solutions.

REFERENCES

[1] Carlos E. Ventura, R. B. (2001). FEM Updating of the Heritage Court Building Structure. 19th

International Modal Analysis Conference (IMAC), (pp. pp.324-330). Kissimmee, Florida.

[2] Jean-François Lord, C. E. V. (2003). FEM Updating Using Ambient Vibration Data from a 48-

storey Building in Vancouver. 32nd International Congress and Exposition on Noise Control

Engineering (InterNoise). Seogwipo, Korea.

[3] Rune Brincker, P. A., N. M. (2000). An Indicator for Seperation of Structural and Harmonic Modes

in Output-Only Modal Testing. Structural Vibration Solutions, www.svibs.com.

Appendix

In this appendix, the deflected translational mode shapes, the torsional mode shapes, and the foundation

rocking modes have been shown, using the building model in the ARTeMIS Modal Pro software. In

fact, Figure 8Figure 8 to Figure 13 show the mode shapes of the 30-storey tower, while Figure 14 to

Figure 17 show the deflected mode shapes of the 20-storey building.

Figure 8. Mode 1 - X and Y directions



Figure 11. Mode 4 - X and Y direction (top) & mode 5 and 6 - X directions (bottom)

Figure 12. Torsional mode 1, 2, 3, and 4 (top left, top right, bottom left, and bottom right)

Figure 13: Foundation rocking (left) and rocking coupled with the X-Y translational mode (right)

(a) (b)

Figure 14. Mode 1 – X direction (a) and Y direction (b)

(a) (b)

Figure 15. Mode 2 - X direction (a) and Y direction (b)

(a) (b)

Figure 16. Mode 3 - X direction (a) and Y direction (b)

Figure 17. Torsional modes – 1 (a), 2 (b), 3 (c) and 4 (d)

(a) (b)

(c) (d)

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