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A Comparison of Ambient and Forced-Vibration Testing of a Full Scale Concrete Structure

Charles-Philippe Lamarche, Masters candidate Sébastien Mousseau, Ph.D. candidate Patrick Paultre, professor, and Jean Proulx, professor Civil engineering department, Faculty of engineering Université de Sherbrooke, Sherbrooke, QC, Canada (J1K 2R1) Contact: [email protected] ABSTRACT

This paper describes a unique research program on the behavior and damage detection of a full size two-story high-performance concrete (HPC) structure. The building was subjected to repeated pseudo-dynamic earthquake simulations, with increasing acceleration levels. After each test, the specimen was then subjected to both forced and ambient vibration tests. An eccentric mass shaker located on the upper floor of the building was used to excite the structure and obtain the "true" modal parameters. These parameters were used as a reference to evaluate the ambient vibration, output-only, tests results. The frequency domain decomposition (FDD) technique was used to extract frequencies, mode shapes, and damping ratios for the structure. Results for both methods, obtained for the damaged condition of the building are compared in the paper. Mode shape correlation is evaluated with the modal assurance criterion (MAC) and variation in damping values are statistically evaluated. Introduction Advances in earthquake engineering and building codes are made possible, in part, by the recent developments in large scale testing facilities throughout the world. In particular, the pseudo-dynamic testing method has been designed to allow very large or even real size models to be subjected to earthquake simulations in a laboratory. The Earthquake engineering and structural dynamics research center (CRGP) of the University of Sherbrooke has been involved in such tests, as well as in the development of laboratory and in-situ testing procedures for a number of years. These procedures were applied to civil engineering structures such as bridges, dams, and buildings [1-3]. An ongoing research project on the earthquake behavior of high-performance concrete (HPC) buildings has lead to the construction of a full-scale two-story specimen in our laboratory (shown in Figure 1 with a 7-m high reaction wall). The experimental program involves repeated pseudo-dynamic earthquake simulations, where increasing levels of damages are inflicted on the building. One of the objective of this project is to develop damage detection techniques that are based on the modifications in the dynamic properties of structure (other objectives are related to the earthquake behavior of HPC buildings [3]). These properties are evaluated by dynamic testing after each simulated earthquake to assess changes in frequencies, mode shape and damping. As both forced and ambient vibration tests are used to determine this "vibratory signature" of the building, their results can be compared and their performance can be evaluated.

Most ambient testing techniques are based on so called "output only" identification techniques, where the input is unknown. Dynamic characteristics are then evaluated with various methods, such as the recent frequency domain decomposition (FDD) technique [4, 5]. The performance of these methods is often assessed by comparing the extracted modal parameters with those obtained with other output only identification techniques. However, the research project described herein combines output-only methods with controlled-input methods (shaker-based, forced vibration tests). For large civil engineering structures, forced vibration tests are often too costly or practically difficult, and output-only methods are the only solutions. In a laboratory environment, these techniques can be evaluated by comparing them with forced-vibration tests, which lead to the "true" modal characteristics of the structure. This paper presents the HPC building specimen, the test setup, and the experimental results obtained with ambient and forced vibration tests after a design-level earthquake. Results obtained with both methods are then compared. Description of the building The two-story reinforced concrete building has a 5 m bay in the E-W direction and a 4-m bay in the N-S direction (Figure 1). The story height measured to top of slab is 3 m. The design forces used are in accordance with the National Building Code of Canada (NBCC 1995) [7] for a site located in Montreal, Canada. Plan and elevation views of the building are shown in Figure 2. Design and detailing of the structure are according to the special provisions for seismic design of the CSA A23.3-94 Design of Concrete Structures [8]. More details on the design and construction of the building can be found in reference [3].

Figure 1: View of test setup : HPC concrete building with reaction wall

Instrumentation After pseudo-dynamic earthquake simulation, forced and ambient vibration tests were carried out on the building to track the increasing damage. In the case of forced vibration tests, the accelerations of the building specimen are recorded while the structure was subjected to a sinusoidal horizontal harmonic load generated by an eccentric-mass shaker. The recorded acceleration responses were then used to extract various vibration properties, as discussed below. Figure 3 shows the experimental setup for the forced-vibration tests on the

building. Plan views of the top slab (roof) and bottom slab (first floor) are illustrated. Concrete blocks, used on each floor to simulate the added mass representing the combined dead and live loads, are shown on both floors and the building orientation is also indicated. The East/West axis was chosen for the pseudo-dynamic earthquake simulation as well as the forced-vibration tests. (horizontal axis in the figure)

Figure 2: Plan and elevation views of the building.

N BNWN BCNV BNEN BNEW TNWN TCNV TNEN TNEW W S Mass Mass BCEV Mass TCEV Mass E

ACCELEROMETER Arrow indicate horizontal positive direction

Mass

Mass Mass Mass

Vertical positive direction upward

BCSV

BSEW

TCSV

TSEW

PLAN VIEW - 1st FLOOR

PLAN VIEW - ROOF

Figure 3: Experimental setup for forced and ambient vibration tests.

The eccentric-mass shaker was placed on the roof in a position selected to put the excitation force (illustrated by a double-headed arrow in Figure 3) off-center by 430 mm. This position was chosen to excite both flexural and torsional modes of vibration. Inside the shaker, two sets of identical weights rotating about parallel vertical shafts generate a sinusoidal load. The amplitude of the resulting force, which is proportional to the square of the rotation frequency, can be adjusted by varying weight eccentricities. The tests on the building were carried out with a frequency range of 1 to 16 Hz, with loads varying from 0.04 to 11.4 kN. Because of the "high flexibility" of this structure, a smaller set of weights was used with a minimum eccentricity setting. The operation frequencies were remotely computer controlled. An optical pulse is emitted on each rotation of the masses to compute the exact rotating frequency for data processing, and hence to calculate the exact input force. The shaker was fastened to the upper slab with 12 anchor bolts (the base plate is shown on the top floor in Figure 3). This figure also shows the 50-Hp variable-frequency motor and the masses at full eccentricity.

Low-frequency forced-balanced accelerometers were used to record horizontal acceleration in three orthogonal directions: (i) the East/West horizontal loading axis; (ii) the North/South perpendicular horizontal axis; and (iii) the vertical axis. The accelerometers act as low-pass filters with a 50-Hz cutoff frequency and have an output of 10 or 50 V/g. A total of 14 accelerometers positions were selected to describe flexural, torsional and vertical (slab) modes. These positions are identified in Figure 3 using a four-letter scheme. The first letter identifies the top (T) or bottom (B) slab (roof or first floor); the second and third letters indicate the accelerometer positions on the slab (NW = northwest, CN = center-north, SE = southeast, etc.); and the last letter indicates the direction of measurement (N = North, V = vertical, etc). Small arrows in Figure 4 indicate the direction of motion. The same setup was used for forced vibration and ambient tests. The acceleration responses and the optical pulse from the shaker were recorded with an HP data-acquisition system, which has an aggregate sampling rate of 100 000 Hz, and track-and-hold capabilities. Anti-aliasing hardware filters were used with a 20-Hz cutoff frequency. Forced vibration test : Rapid frequency sweeps were first carried out to obtain a preliminary estimate of the resonant frequencies, to select the mass eccentricities, and to select the operation range. A 1 to 16 Hz range was then selected for the tests to identify the first 8 resonances of the building. Complete frequency sweeps were carried out for each measurement configuration, with a frequency increment of 0.01 Hz. Up to 1500 frequency increments were necessary to cover the full range; samples were recorded during 4 to 8 s at 1000 Hz. This is a very high sampling frequency, considering the fact that the data was filtered at 20 Hz, but it was necessary to record the optical pulse, using an unfiltered channel. Ambient vibration test : Two series of tests were carried out with ambient vibrations. For the first four tests, vibrations were induced by a person walking randomly (with different pace and direction through time) on the first floor. For the next four tests, a person was still walking randomly but was also applying impacts randomly to the columns between the first floor and the roof. Accelerations were recorded at 100 Hz during 10 minutes. Forced vibration test results: The key parameters used to track changes in the dynamic behavior are the resonant frequencies, the mode shapes and the modal damping. Data is first reduced using a least-squares, curve-fitting algorithm to calculate the amplitude and phase of each recorded time history. The filtering characteristics of the accelerometers and the data-acquisition system are taken into account and the resulting amplitude and phase are corrected accordingly. The amplitudes are then normalized by the excitation force. This process leads to frequency responses for acceleration that can be used to extract the modal characteristics. Typical horizontal response curves are shown in Figure 4 for both undamaged and damaged conditions (after an earthquake simulation was applied to the building). The amplitudes recorded at position TNEW (top floor, northeast corner, horizontal axis parallel to the shaker force) and TNEN (top floor, northeast corner, horizontal axis perpendicular to the shaker force) are plotted in the graphs (a) and (b). The associated phase lags with respect to the excitation force are also shown for both positions. The building's resonant frequencies (flexion and torsion) can be readily identified from the peaks displayed in these response curves and are always associated with a substantial phase shift. The corresponding modal damping ratios are then obtained using the half-power bandwidth method and ranged from 1.28% of critical damping for the second torsional frequency to 2.05% for the second flexional frequency. The differences in amplitude at the resonances between both floors correspond to the relative deformations in each mode shape. Results for the damaged condition are given in Table 1. The torsional modes identified in the graphs (a) of Figure 4 have a relatively stronger perpendicular component in the N-S direction and exhibit larger resonant amplitudes in that direction (3.18 and 9.49 Hz). The two resonant flexional frequencies in the N-S direction that are barely visible in graphs (a) are clearly apparent in graphs (b) (2.20 and 6.50 Hz).

(a) Horizontal acceleration, East-West direction 0.100

Acceleration (g/kN)

(b) Horizontal acceleration, North-South direction 0.025

Acceleration (g/kN)

Accelerometer TNEW Undamaged Damaged (PGA = 0.18g)

Accelerometer TNEN

0.080 0.060 0.040 0.020 0 360 180 0

0.020 0.015 0.010 0.005 0 360 180 0

Phase (degrees)

Phase (degrees)

0

2

4

6 8 10 12 Frequency (Hz)

14

16

0

2

4

6 8 10 12 Frequency (Hz)

14

16

Figure 4: Typical acceleration frequency response function under forced-vibration tests (undamaged and damaged conditions) After the resonances have been identified, the vibration mode shapes are then plotted using the amplitude and phase information of each measurement position for a given resonant frequency. The relative steady-state displacements are computed and plotted for each point and for each resonance. Figure 5 illustrates the mode shapes corresponding to the four flexural and two torsional resonant frequencies that were identified from the horizontal measurements in the 1 to 16 Hz range. Two other vertical "slab modes" were also identified at 10.44 and 11.17 Hz, respectively. The properties for the damaged state were obtained after the building was subjected 7 times to the widely-used El-Centro ground motion record, scaled to 0.078 g; then 4 times to the same recording scaled to 0.129 g; and, finally, 2 times to the same recording at 0.18 g. The latter value is the design peak ground acceleration for the building. These properties were then used to apply different damage detection techniques based on model updating [3].

f = 1.83 Hz (East-West)

f = 5.67 Hz (East-West) Second Flexional mode shapes

f = 3.18 Hz (First mode)

First Flexional mode shapes

Torsional mode shapes

f = 2.20 Hz (North-South)

f = 6.50 Hz (North-South)

f = 9.49 Hz (Second mode)

Figure 5: Horizontal mode shapes obtained under forced-vibration tests.

Ambient vibration tests results: The resonant frequencies, mode shapes and modal damping ratios were estimated using the FDD (frequency domain decomposition) technique using the Artemis Extractor software [8]. Samples of 8192 data point were used to compute the FFTs. A Hanning window was used to simulate periodicity over the whole interval, thus minimizing the bias error introduced by leakage. Overlap averaging of 60% was also used to obtain smoother spectra. Details on the FDD method can be found in references [4, 5]. The first six horizontal modes described above were identified with this method. Figure 6 shows the responses on a linear scale for both methods for comparison. The ambient results on this figure represent the average of the 8 Power Spectral Density (PSD) obtained from the 8 accelerometers placed at different key location on the structure. The two types of random loading that were used during the ambient vibration tests lead to very similar estimates of the modal parameters.

1 Normalized Amplitude 0.8

Ambient vibration tests

0.6 0.4 0.2 0 0 1 2 4 6 Frequency (Hz) 8 10

Normalized Amplitude

0.8 0.6 0.4 0.2 0 0 2

Forced vibration tests

N/S accelerometer E/W accelerometer

4 6 Frequency (Hz)

8

10

Figure 6: Comparison of ambient and forced-vibration results. Comparison between modal parameters calculated by both techniques: The quality of the results calculated using the FDD technique can be evaluated comparing them to the forced vibration tests (FVT) results, as they are considered as the most reliable technique to evaluate modal parameters experimentally (resonant frequencies, mode shapes and modal damping). Table 1 shows that the resonant frequencies for both techniques are the same for the first three modes. The slight differences in frequencies between the results of both techniques for the fourth, fifth and sixth mode may be caused by the high loading level induced by the shaker. It is recalled that the building was subjected to several pseudo-dynamic tests prior to these measurements. These earthquake simulations induced damage to the structure to the point where cracking of the concrete occurred at several locations in the beams, columns and slab. When the frequency of the shaker increases, the building has to carry relatively high oscillatory forces

creating crack opening in the damaged areas. It is believed that this slight nonlinear behavior leads to a loss of effective rigidity thus reducing the resonant frequencies of those three modes. During the ambient vibration test, this phenomenon does not occur, as the random forces applied to the structure are much lower. Table 1: Ambient and forced-vibration tests results Frequency (Hz) Damping Forced Ambient Forced Rand. Walk Rand. Impacts 1.83 2.20 3.18 5.67 6.50 9.49 10.44 11.17 1.87 2.14 3.16 6.07 6.64 9.93 10.53 11.30 1.92% 1.70% 1.69% 2.05% 1.51% 1.28% 0.84% 0.67% 2.12% 1.96% 1.72% 1.58% 1.54% 1.85% 1.84% 2.02% 1.68% 1.58% 1.32% 1.74% 0.67% 0.50%

Mode Shapes 1st flexional (E-W) 1 flexional (N-S) 1 torsional 2 flexional (E-W) 2 flexional (N-S) 2 torsional 1 vertical 2 vertical

nd st nd nd nd st st

Another means of comparing the correlation of the ambient and forced vibration data is to compute the Modal Assurance Criterion (MAC). These values are given in Table 2, and the agreement between modes shapes obtained with both methods is graphically depicted in Figure 7 for the first six horizontal mode shapes. The very high diagonal values indicate a high level of correlation between both sets of mode shapes. The maximum coupling value (5%) occurs between the third and the sixth mode witch is both torsional modes. All the other coupling indices are under 1%.

Table 2. MAC Values (Forced vs. Ambient) Forced Vibrations

Mode

Ambient Vibrations

1

0.999 0.000 0.001 0.000 0.000 0.001

2

0.010 0.988 0.000 0.000 0.000 0.000

3

0.002 0.000 0.992 0.001 0.001 0.000

4

0.007 0.001 0.002 0.985 0.007 0.000

5

0.000 0.000 0.000 0.010 0.987 0.004

6

0.000 0.000 0.050 0.000 0.001 0.941 Figure 7: MAC values

1 2 3 4 5 6

Damping values calculated from the ambient vibrations are also shown in Table 1. The average values obtained for each mode with both methods are quite similar and within 0.5%. A statistical analysis was performed on damping results obtained from each type of loading : (i) forced vibration; (ii) ambient (random walk); (iii) ambient (random walk & impacts). Intervals of the mean damping values were calculated with a 90% confidence level and are shown in Figure 8 for each identified mode. For the first five horizontal modes, the damping interval from ambient data is close to or overlaps the probabilistic range of the forced vibration test (which is our reference). The modal dampings of the sixth mode estimated with ambient data are slightly out of the probabilistic range but still in a 0.5% damping ratio range.

Forced Vibrations 3.00 % Damping Ratio Ambient Vibrations Ambient + Impact Vibrations

2.00 %

1.00 %

0.00 %

Mode 1

(f =1.83 Hz)

Mode 2

(f =2.20 Hz)

Mode 3

(f =3.18 Hz)

Mode 4

(f =5.67 Hz)

Mode 5

(f =6.50 Hz)

Mode 6

(f =9.49 Hz)

Figure 8: Damping variation ­ 90% confidence level Conclusions A full-scale 2-story high-performance building specimen was tested under ambient and forced vibration in a controlled laboratory environment. The building was subjected to repeated and increasing levels of simulated earthquake damage. After each damage increment, ambient and forced vibration tests were carried out on the structure and the results obtained from both methods were compared. The performance of the ouput-only ambient method, using the frequency domain decomposition technique (FDD), was evaluated by using force-vibration results as a reference. Resonant frequencies and damping ratios were found to be in close agreement, and MAC coupling values mostly below 1%, indicating a high level of correlation between both methods. As ambient vibration testing techniques are more often used in field applications, it is of utmost importance to assess there reliability by comparing them to controlled-input methods. Acknowledgements The authors gratefully acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada. They would also like to thank Sébastien Gauthier, Claude Aubé, and Laurent Thibodeau, technicians at the Department of Civil Engineering at the University of Sherbrooke. References [1] [2] [3] [4] [5] [6] [7] [8] Paultre, P. and Proulx, J., Dynamic Testing of Large Scale Structures, International Association for Bridges and Structural Engineering (IABSE), V. 7, No. 1, 29­34, 1997. Proulx, J. and Paultre, P., Experimental and Numerical Investigation of Dam-Reservoir-Foundation Interaction for a Large Gravity Dam, Canadian Journal of Civil Engineering, V. 24, No. 1, 90­105, 1997. Paultre, P., Proulx, J., Mousseau, S., Prévost, T. et Savard, C. (2003) : "Pseudo-Dynamic and Forced Vibration Tests of a Full-Size Two-Story Reinforced High-Performance Concrete Building", American Concrete Institute, SP-211-7, 135­160. R. Brincker, L. Zhang, P. Andersen, Output-Only Modal Analysis by Frequency Domain Decomposition. ISMA25 Noise And Vibration Engineering Volume 11., Leuven,Belgium, pp.717-723, Sept. 13-15, 2000. R. Brincker, P. Andersen, L. Zhang. ,Modal Identification From Ambient Responses Using Frequency Domain Decomposition. IMAC 18, San Antonio,Texas, pp.625-630, 2000. NBCC 1995, "National building code of Canada 1995 and supplement to the national building code of Canada," National Research Council of Canada, Ottawa, Ontario. 8 CSA Technical Committee, "Design of Concrete Structures for Buildings," CAN3-A23.3-M94, Canadian Standards Association, Rexdale, Ontario, 1994, 199 pp. Structural Vibration Solutions. ARTeMIS Extractor, release 3.2, 2002 (www.svibs.com).

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