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Dynamic characteristics and model updating of damaged slab
from ambient vibration measurements
Huzaifa Hashim, Zainah Ibrahim, Hashim Abdul Razak
⇑
Department of Civil Engineering, University of Malaya, LembahPantai, 50603 Kuala Lumpur, Malaysia
article info
Article history:
Received 14 May 2012
Received in revised form 14 November 2012
Accepted 23 November 2012
Available online 10 December 2012
Keywords:
Vibration testing
Output only response measurements
Full-scale slab structure
Modal parameters
abstract
This paper reports a field investigation using ambient vibration testing on a damaged floor
slab of a reinforced concrete frame building. Due to unexpected heavy rainfall, the hill
slope at the rear of building failed triggering a major landslide and causing major damage
to the perimeter beams and parts of the slab on the first floor. The modal parameters
namely natural frequencies and mode shapes were acquired using output only identifica-
tion technique and the results obtained from the undamaged and damaged floor slabs were
compared. It was observed that there was a 25–53% drop in natural frequencies of the dam-
aged slab compared to the undamaged slab, with a much bigger drop for the lower modes.
The irregularities in mode shapes identified correlates with the location of the cracks as
revealed from visual examination on the damaged slab. Two finite element models of
the slab were created using a finite element software package. The damaged slab was
updated manually so as to match the modal parameters obtained experimentally. The
results from this study further highlight the possibility and feasibility of using non-
destructive vibration testing for condition monitoring of structures over more conventional
testing techniques.
Ó2012 Elsevier Ltd. All rights reserved.
1. Introduction
Ambient vibration testing (AVT) is an output-only
dynamic test where the structure is excited by natural or
environmental excitations such as traffics and winds.
These excitation forces are not measured, thus an experi-
mental modal analysis procedure for AVT will need to base
itself on output only response measurement data. The
modal analysis involving output-only measurements pres-
ent a challenge that requires the use of special modal iden-
tification technique, which can deal with very small
amplitudes of ambient vibration that are usually contami-
nated by noise. The AVT is also known as Natural Input
Modal Analysis (NIMA), Operational Modal Analysis
(OMA) or Output-Only Modal Analysis. In civil engineering
applications the excitation force is often assumed to be
stochastic in nature, such as excitations by wind, traffic,
earthquakes, waves or human movements [1]. The ambi-
ent vibration tests describe the linear behavior of struc-
ture, since the amplitudes of vibration is small. They can
be used to describe the linear behavior of damaged struc-
tures and of their components, and can help on developing
time and amplitude dependent structural models and anal-
ysis algorithms, to be used in structural health monitoring
and in structural control studies [2]. Therefore the devel-
opment of experimental methods for in situ measurement
of full-scale partially damaged structure is of considerable
interest. An advantage of the ambient vibration over the
forced vibration surveys is that usually only light equip-
ment and smaller number of operators are required. The
sources of excitation are wind, micro tremors, microse-
isms, and various local random and periodic sources. Iva-
novic et al. [2] stated that the dynamic testing method of
full scale structure was first reported regularly around
the 1970s and has become more prolific in recent years.
0263-2241/$ - see front matter Ó2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.measurement.2012.11.043
⇑
Corresponding author. Tel./fax: +60 603 79675233.
E-mail address: hashim@um.edu.my (H.A. Razak).
Measurement 46 (2013) 1371–1378
Contents lists available at SciVerse ScienceDirect
Measurement
journal homepage: www.elsevier.com/locate/measurement
Various civil engineering structures were tested and stud-
ied using ambient vibration testing such as buildings [3,4],
dams [1] and bridges [5]. A complete process on the dy-
namic testing on a bridge revealed by Zivanovic et al. [6]
stated four important key phases in the updating process
of a civil engineering structure; initial FE modelling, modal
testing, manual model tuning and automatic updating con-
ducted using dedicated software.
The objective of this investigation is to verify the feasi-
bility of using operational modal analysis to acquire the
modal parameters of a damage structural element in a
building for purpose of condition assessment. By compar-
ing the modal parameters from the undamaged and dam-
aged structural elements, the percentage of severity can
be calculated. In the past, there have been very few studies
on the use of modal analysis for condition and damage
assessment on full scale civil engineering structures and
the outcome of this investigation will further enhance
the awareness and understanding of this non-conventional
approach in non-destructive structural testing. Several
comparative studies were made on the results from exper-
imental works. The results from this study is anticipated to
further investigation of other types of civil structures that
is exposed to natural disaster mainly for the interest of
professionals and researchers involved with design of civil
engineering structures.
2. Test structure
The structure considered in this investigation com-
prised of a three storey reinforced concrete frame building
which housed the administrative offices and library of one
of the faculties in the main campus of University of Malaya.
The building was built in 1999 and located at the toe of a
hill. Due to abnormal heavy rainfall in October 2008, a slip
failure of the soil on the slope occurred triggering a land-
slide and burying some parts of the ground and first floor
at the rear of the building. Fig. 1 shows the landslide area
while clearing works was in progress. The impact on the
structural frame resulting from the movement of soil dur-
ing the landslide caused severe damage on the perimeter
beams. In addition the massive amount of soil into the
building resulted in excessive loading on the first floor
causing some parts of the floor slab to crack. However,
the main columns, beams and slab of the second floor
remain unaffected and intact. The total amount of soil
removed from the site during the clearing work amounted
to about 16,000 m
3
. Consequently the building was va-
cated and rendered unsafe to occupy until full structural
investigation was carried out and repair work on the build-
ing completed. Fig. 2 illustrates the condition of the perim-
eter beams and slab of the affected floor while Fig. 3 shows
the overall extent of damage to the affected building.
The severely damaged zone was confined to two bays of
the first floor slab measuring approximately 7.6 m by
15.4 m. The slabs with a thickness of 150 mm were sup-
ported on three internal primary beams and four perimeter
beams measuring 460 mm by 300 mm deep and 150 mm
by 600 mm deep respectively. In addition two secondary
beams having cross sectional dimensions of 300 mm by
300 mm deep, spanning between the internal primary
beams and perimeter beams were provided. The structural
configuration and detailing for the undamaged slab on the
second floor were identical. The load was transferred to the
foundation via six main columns measuring 600 mm by
600 mm as shown in Fig. 4. The external walls were unre-
inforced masonry while dry board panels made up the
internal partitioning.
3. Ambient vibration testing
The ambient vibration test (AVT) was conducted upon
completion of the clearing works, visual inspection and
in situ testing to ascertain the structural integrity of the
building. The damage zone at each floor level was subdi-
vided into 5 by 12 rectangular grids and the response
measurements obtained from 78 test points as shown in
Fig. 5. The time signals were recorded using a 24 bit PC-
based data acquisition system on recorder mode with
40 kHz bandwidth and maximum sampling frequency of
102.4 kS/s. It is equipped with 24 dynamic input channels
with 4 DSP’s for gap free recording. Single axis force feed-
back accelerometer capable of measuring static accelera-
tion or low-level, low-frequency vibration were used in
this investigation. The accelerometer has a frequency re-
sponse of 0–500 Hz, sensitivity of 1200 mV/g and measur-
ing range of ±3 g with 1.3
l
g resolution. The data recorder
and accelerometer are shown in Fig. 6.
Time signal records for all the 78 test points were
acquired using seven accelerometers. In order to cover all
the test points, 19 measurement setups were configured
with the data acquisition parameters as shown in Table 1.
Fig. 1. Landslide area and clearing works in progress.
1372 H. Hashim et al. / Measurement 46 (2013) 1371–1378
Three accelerometers were placed permanently at test
points 14, 35 and 64 during the entire test period and acted
as references. The remaining four accelerometers were
roved so as to cover all the test points. A sample of the re-
Fig. 2. Condition of the perimeter beams and slab of the affected floor.
Fig. 3. Overall extent of damage to the affected building.
Key:
Damaged slab
Undamaged slab
Fig. 4. Plan view and building elements of the affected floor.
H. Hashim et al. / Measurement 46 (2013) 1371–1378 1373
corded acceleration-time data for a typical test setup is
shown in Fig. 7.
4. Modal results
The modal identification of both slabs for the damaged
and undamaged conditions respectively was identified
using the ambient response identification software, ARTe-
MIS. An output-only modal identification method namely
the non parametric technique based Enhanced Frequency
Domain Decomposition (EFDD) method in frequency
domain as implemented in ARTeMIS is used in the estima-
tion of the modal parameters of both slab structure. The
detailed procedure for FDD/EFDD is available in several
publications [3,7–9].
4.1. Natural frequencies
Table 2 presents the first four natural frequencies ob-
tained from the ambient vibration testing on the slabs.
The range of natural frequency for the undamaged and
damaged slab is between 12 Hz and 24 Hz and from 6 Hz
to 18 Hz respectively as identified from the output-only
identification technique. It was found out that the natural
frequencies dropped drastically for every mode in the
damaged floor and the observed decrease was expected.
The highest percentage difference was found in the first
mode with a 53% drop. The changes in natural frequencies
according to Rytter [10] corresponds to Level 1 damage
identification i.e. determination that damage is present in
the structure. Doebling et al. [11] stated that the observed
changes in structural properties cause changes in vibration
frequencies. From the damage assessment of the building,
it was found that excessive damage on perimeter beam 1
and 2 is the main contributing factor to the structural
change causing a big reduction in stiffness. This can be
observed from the mode shapes in Fig. 8 which indicates
high amplitude of motion in the damaged slab.
4.2. Mode shapes
Fig. 8 presents an overview of the vibration behavior
obtained from the undamaged and damaged slab. It was
found that the first mode of vibration in Fig. 8 indicates
high amplitude of motion at a specific location i.e. at the
middle part of the first bay of the slab. The second, third
and fourth mode also indicated similar pattern in that high
amplitudes were observed at a specific location where the
damage is located. By observing the mode’s motion, the
damage location can be located. In this study it was found
Fig. 5. Grid layout and test points on damaged slab.
Fig. 6. (a) 24 channel data recorder. (b) Capacitive accelerometer.
Table 1
Data acquisition parameters adopted for AVT.
Parameter description Parameter value
Data acquisition time 600 s
Frequency span 60 Hz
Sampling frequency 102.4 samples/s
Recorded signal Random
1374 H. Hashim et al. / Measurement 46 (2013) 1371–1378
that the location of damage was at perimeter beam 1 and 2
of the slab structure as shown in Fig. 4. By computing and
comparing the MAC values it was found that the correla-
tion between undamaged and damaged slab was greatly
reduced. The MAC values were in the range of 0.5–0.75
for all the modes and these low values indicate the severity
of the damage induced.
5. Analytical study
The mathematical model of the slab was created using a
finite element (FE) software package, DIANA in order to ob-
tain as reliable as possible estimates of modal properties of
the slabs in the damaged building. The objective is to come
up with a mathematical model that has the same dynamic
characteristics as the actual slab namely the frequencies,
mode shapes and mass. The frequencies and mode shapes
of the first four modes of vibration obtained from the finite
element analysis are presented in Table 3 and Fig. 9,
respectively.
5.1. Finite element model updating
The main purpose of finite element (FE) model updating
is to calibrate and ensure sufficient correlation with results
obtain form measurements on the actual structure. This is
achieved by matching as many pairs of analytical and
experimental modes of vibration in terms of the natural
frequencies and mode shapes. Consequently a more
accurate finite element model can be obtained and would
facilitate further studies on the behavior of the undamaged
and damaged slab without conducting further physical
tests on the actual structure. Pavic and Reynolds [12] and
Ramos et al. [13] presented FE model updating procedures
applicable for actual structures whereby correlation analy-
ses were carried out using Modal assurance criterion
(MAC) between two sets of vibration mode shapes. The
MAC values were computed to indicate the degree of
Time
Acceleration (g)
Sensor 1
Sensor 2
Sensor 3
Sensor 4
Sensor 5
Sensor 6
Sensor 7
Fig. 7. Time history signals of slab during measurement.
Table 2
Natural frequencies from AVT.
Mode Ambient vibration testing on slab
condition
% Difference in
natural frequencies
Undamaged (Hz) Damaged (Hz)
1 12.59 6.00 53.34
2 13.15 6.63 49.58
3 20.49 15.20 21.60
4 23.39 17.23 26.34
Mode 1
MAC = 0.5795
Mode 2
MAC = 0.7356
Mode 3
MAC = 0.5635
Mode 4
MAC = 0.5039
High amplitude of motion on
damaged slab (indicate by red
marking)
High amplitude of motion on
damaged slab (indicate by red
marking)
High amplitude of motion on
damaged slab (indicate by red
marking)
High amplitude of motion on
damaged slab (indicate by red
marking)
DAMAGE SLAB
Fig. 8. Overview of first four mode shapes of both damaged and
undamaged slabs.
H. Hashim et al. / Measurement 46 (2013) 1371–1378 1375
correlation between the experimental and computed finite
element mode shapes. In this study, the two sets of data for
correlation purposes were obtained from ambient vibra-
tion testing and the finite element results. The MAC values
derived from the first four modes of vibration for the
undamaged slab are presented in Fig. 10 and shows good
correlation since the values are more than 0.8.
Fig. 11 presents the results obtained from AVT and FE
modeling data for the first four modes. The finite element
results yield lower values of natural frequencies for Modes
1 and 2 compared to the values obtained from vibration
testing, whilst the values were higher for the remaining
modes. It is apparent that that there is good agreement
for the first and second modes with differences of less than
5%. However for higher modes the difference tends to be
much higher at less than 20%. A study conducted by
Ibrahim [14] on FE refinement and manual updating pro-
cess reported errors in frequencies of less than 10% by
modifying values of the beam stiffnesses to achieve the de-
sired level of refinement and accuracy.
Subsequently in order to obtain the mathematical mod-
el of the damaged slab, manual updating was performed on
the FE model of the undamaged slab such that it gives the
closest match to the results obtained from the ambient
vibration testing. Doebling et al. [11] reported that the
changes in the physical properties, such as reductions in
stiffness resulting from the onset of cracks or loosening
of a connection, will cause detectable changes in the modal
parameters notably frequencies, mode shapes and modal
damping.
The approach adopted in this study is by directly
removing portions of the structural element which were
damaged, through trial and error. The modeling configura-
tion for updating the FE model of the undamaged slab to
simulate the behavior of the damaged slab is outlined in
Table 4. The process of refinement and manual updating
was carried out in sequence from configurations 1 to 5
and each configuration presents the cumulative reduction
in the number of elements based on the damage assess-
ment report and observations on site of the damage
location. It is apparent that by removing the damage
elements there is reduction in natural frequencies until it
converges to a reasonably close value to the results ob-
tained from actual measurements.
Figs. 12a and 12b presents the first four mode shapes of
the resulting updated FE model for the damaged structure.
The first mode obtained at 6.61 Hz appeared to be a simple
bending mode with higher amplitude at one bay compared
to the adjacent bay. The perimeter beams situated on the
rear side of the building facing the failed slope was re-
moved in the finite element model since from observations
this part of the structure was severely damaged as evident
from Fig. 2.
Fig. 13 compares the values of natural frequencies for
the first four bending modes obtained from the updated
Table 3
Natural frequencies calculated in pre-test FE model.
Mode no. Natural frequencies (Hz)
1 12.20
2 12.60
3 24.90
4 26.50
Mode 1
Frequeny = 1 2.20 Hz
Mode 2
Frequeny = 12.60 Hz
Mode 3
Frequeny = 24.90 Hz
Mode 4
Frequeny = 26.50 Hz
UNDAMAGED SLAB
DAMAGE SLAB
Fig. 9. Results of pre-test FE model.
Fig. 10. Modal assurance criterion (MAC) of AVT and FEA undamaged
floor.
1376 H. Hashim et al. / Measurement 46 (2013) 1371–1378
FE model and measurements. Results obtained from the FE
modeling gave consistently higher values compared to the
values obtained from vibration testing. The first three
modes gave good agreement with differences of less than
10% whilst for the fourth mode the difference is much
higher.
6. Conclusions
The ambient vibration test on the undamaged and dam-
aged slabs of the building affected by the landslide pro-
vided details on the changes of modal parameters due to
the damage induced. The natural frequencies of the
damaged slab showed a reduction within the range of
25–53%, with a higher drop for the first two lower modes.
Even though the damage appeared severe, there was no
imminent danger of a total collapse of the first floor slab
structure. However due to permanent deformation of the
slab and excessive twisting and concrete spalling of the
perimeter beams, it is rendered unserviceable and has to
be demolished and rebuilt. A comparison of the mode
Mode 1
Frequency = 6.61 Hz
Mode 2
Frequency = 7.11 Hz
Fig. 12a. Mode shape of updated FE model for the damaged structure
(Mode 1 and Mode 2).
Mode 3
Frequency = 16.80 Hz
Mode 4
Frequency = 20.70 Hz
Fig. 12b. Mode shape of updated FE model for the damaged structure
(Mode 3 and Mode 4).
Mode 1 Mode 2 Mode 3 Mode 4
AVT 12.59 13.15 20.49 23.39
FE 12.20 12.60 24.90 26.50
0
5
10
15
20
25
30
Frequency (Hz)
Undamaged Slab
Fig. 11. Experimental and theoretical results of the undamaged slab.
Table 4
Modeling configuration for the updating of the damaged floor slab.
Configuration Model refinement and updating of damaged slab
Natural frequencies
of first mode of
vibration (Hz)
Description
1 12.20 Basic model from
undamaged floor slab
2 7.50 2 secondary beams
removed
3 7.15 2 secondary beams + 2
portions of slab removed
4 7.10 2 secondary beams + 4
portions of slab removed
5 6.61 2 secondary beams + 6
portions of slab removed
Mode 1 Mode 2 Mode 3 Mode 4
AVT 6.00 6.63 15.20 17.23
FE 6.61 7.11 16.80 20.70
0.00
5.00
10.00
15.00
20.00
25.00
Frequency (Hz)
Damaged Slab
Fig. 13. Experimental and theoretical results of the damaged slab.
H. Hashim et al. / Measurement 46 (2013) 1371–1378 1377
shapes revealed higher amplitudes of vibration at certain
parts of the damaged slab as compared to the undamaged
slab and these correlated with the severity and location of
the damage.
Finite element updating based on measured modal
parameters as employed in this study is a useful approach
and technique for accurately modeling structures which
experienced some degree of deterioration or damage. A
simplified approach was adopted for updating the finite
element model to simulate the behavior of the damaged
slab by removing parts of the structural components and
this was verified and concurred with the observation of
severity and location of the damage in the actual slab.
Acknowledgements
The authors would like to acknowledge the financial
assistance provided by the Institute of Research Manage-
ment and Monitoring, University of Malaya (IPPP) through
a research grant entitled ‘‘Development of Algorithms for
Structural Health Monitoring using Modal Parameters’’
(RG090/10AET). The authors would also like to thank all
the people who have contributed either directly and indi-
rectly, in making this research possible.
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