natural frequencies of bridge structures from ambient vibration measurements

148 Pages·2010·12.6 MB·French

FIELD INVESTIGATION OF FUNDAMENTAL FREQUENCY OF
BRIDGES USING AMBIENT VIBRATION MEASUREMENTS

by
Arden Reisham Pradeep Heerah

Department of Civil Engineering and Applied Mechanics
McGill University
Montréal, Canada
August 2009

A thesis submitted to McGill University
in partial fulfillment of the requirements of the degree of
MASTER OF ENGINEERING.

© Arden Reisham Pradeep Heerah, 2009. All Rights Reserved.
ABSTRACT

The transient nature of forces induced in structures during
earthquakes requires the use of dynamic analyses to fully characterise
their behaviour. A modal analysis describes the dynamic response of the
structural system through modal descriptors: natural frequencies, mode
shapes and damping ratios. Efficiently estimating these modal parameters
for bridges allows for better structural integrity assessments and structural
health monitoring of these structures. Using ambient vibration
measurements to estimate modal parameters is time-saving and efficient.
This research reviews the literature on the application of ambient vibration
testing to the modal characterisation of bridges. Natural frequencies from
ambient vibration measurements are obtained for a typical bridge in the
City of Montréal in Canada.
The MATLAB computing platform is used to execute spectral
analyses of the field measurements. Linear, analytical models of the
bridges are constructed with the SAP2000 structural analysis programme
and Eigenvalue analyses are performed. The experimental and analytical
results are compared and discussed, followed by recommendations for the
application of this procedure to other bridges in the Montréal region.

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RÉSUMÉ

Du fait de la nature transitoire des forces se créant au sein des
structures lors des tremblements de terre, la caractérisation complète de
leur comportement nécessite l’utilisation d’analyses dynamiques. Une
analyse modale décrit la réponse dynamique de la structure à travers ses
modes de vibration : les fréquences naturelles, la forme des modes et le
facteur d’amortissement. Une estimation efficace des paramètres modaux
des ponts permet alors une meilleure évaluation, et donc un meilleur suivi,
de leur intégrité structurale. L’utilisation des mesures de vibrations
ambiantes pour estimer les paramètres modaux est donc une méthode
efficace et économique. Cette étude passe en revue la littérature sur
l’application de l’analyse des mesures de vibrations ambiantes pour la
caractérisation modale des ponts.
Les fréquences naturelles ont été obtenues sur un pont typique de
la ville de Montréal. La plate-forme informatique MATLAB a été utilisée
pour effectuer des analyses spectrales de ces mesures. Des modèles
analytiques linéaires ont ensuite été construits avec le programme
d’analyse structurel SAP2000 pour effectuer des analyses d’Eigenvalue.
Les résultats expérimentaux et analytiques sont ensuite comparés et
discutés, et des recommandations énoncées, pour appliquer ce procédé à
d’autres ponts de la région de Montréal.

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ACKNOWLEDGEMENTS

I extend sincere appreciation to the following, among others:

My supervisor, Professor Luc E. Chouinard, for his invariable and
multifaceted support and guidance throughout our research activities at
McGill University and my stay in the City of Montreal.

Salman Saeed, Dr. Myriam Belvaux, Dr. Alejandro de la Puente Altez, Dr.
Philippe Rosset, Damien Gilles, Kuei-hua Rebecca Huang and Wendy
Itagawa; their assistance throughout my research has been consequential.

The Ministère des Transports du Québec, for assisting our research
efforts.

Lennartz electronic and LEAS électronique, manufacturers of the
equipment used in this research, for their guidance and clarification.

Fédon Honoré, for translating the abstract into French.

Professors Saeed Mirza, Ghyslaine McClure and Colin Rogers, for their
invaluable contributions toward my development throughout graduate
studies.

C.E.P. Ltd, to whom I am timelessly grateful.

Peter and Michelle Santlal, for their friendship and limitless generosity.

Staff of the Department of Civil Engineering and Applied Mechanics:
Franca Della-Rovere, Anna Tzagournis, Sandy Shewchuk-Boyd, Dr.
William Cook, Jorge Sayat and Ronald Sheppard, among others; and staff
of the Schulich Library of Science and Engineering.

My colleagues at McGill University, for their stimulating, earnest and
sometimes inebriated discussions: Adriana Parada, Ali Ghafari, Hilary
Ingram, Joe Mattar, John-Edward Franquet, Lai Wai Tan, Li Li, Ling
Zhang, Miguel Nunes, Nabil Elias Saliba, Nicolas Desramaut, Nisreen
Balh, Reza Erfani, Tatiana Tobar Valencia, Stephane Villemain, among
others.

I also convey gratitude to my friends and their families for their thoughts
and involvement; especially to Andre Bagoo, Anuradha Gobin, Beena
John, Binta Trotter, Charline Augustine, Dwayne Dubarry, Fadil Sahajad,
Fédon Honoré, Navin Seebaran, Shalu Bujun, Suzette Parillon, Suzanne
Seepersad, Vijay Mohan, Vince Ramlochan, Xue Zeng.

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ACKNOWLEDGEMENTS

My mum, Gemma, and my brother, Arundel, to whom I am grateful for
their unwavering support, patience and encouragement during my
research efforts and for fostering the resolve within me to strive for more
than only what seems possible.

”Be the change you want to see in the world.”
- from Mahatma Gandhi

“The art of directing the great sources of power in Nature for the use and
convenience of man.”
- from Institution of Civil Engineers’ Royal Charter of 1828.

“Plagiarize, Let no one else’s work evade your eyes.”
- from the song Lobachevsky by Tom Lehrer, Harvard Mathematics
lecturer.

“If we do not maintain our infrastructure, do not upgrade it, we’ll continue
to have spectacular collapses.”
- from Professor Saeed Mirza, McGill University.

“One shall have to undergo suffering to reach truth. That is why it is said
that truth is eternally victorious.”
- from Rig Veda.

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TABLE OF CONTENTS

Section Page

ABSTRACT i
RÉSUMÉ ii
ACKNOWLEDGEMENTS iii
LIST OF FIGURES viii
LIST OF TABLES xii
LIST OF APPENDICES xiii

CHAPTER 1 - INTRODUCTION 1
1.1 Developments 3
1.2 Objectives 4
1.3 Organisation of the thesis 5

CHAPTER 2 - LITERATURE REVIEW 7
2.1 Dynamical behaviour of structures 7
2.2 Experimental modal analysis 12
2.2.1 Frequency response function (FRF) 14
2.2.2 Impulse response function (IRF) 15
2.2.3 Vibration tests 18
2.2.4 Modal testing of civil engineering structures 21
2.2.5 Ambient vibration testing of bridges 22
2.3 Modal parameter estimation 24
2.3.1 Fourier spectral analysis (FSA) 25
2.3.2 Power Spectral Density (PSD) and Cross-power 28
Spectral Density (CSD) Analysis
2.3.3 Auto-regressive moving-average (ARMA) method 30
2.4 Signal processing issues in AVT 32
2.4.1 Sampling 32
2.4.2 Averaging 33

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TABLE OF CONTENTS

Section Page

2.4.3 Spectral leakage 33
2.4.4 Resolution 38

CHAPTER 3 - CASE STUDY 40
3.1 Bridge structure 40
3.2 Construction materials 47
3.3 Equipment 49
3.3.1 Testing 52
3.3.2 Test locations 55
3.3.3 Sampling parameters 55
3.3.4 Tests 57
3.3.5 Synchronisation 57
3.4 Analysis of experimental results 60
3.4.1 Fourier method 60
3.4.2 Welch’s PSD method 61
3.4.3 Welch’s CSD method 61
3.4.4 Auto-regressive, Modified Covariance method 62
3.5 Analysis of analytical models 62
3.5.1 Models 63

CHAPTER 4 - DISCUSSION AND RECOMMENDATIONS 69
4.1 Notes on the experimental analysis 69
4.2 Notes on the analytical analysis 79
4.3 Fundamental frequency estimates 80
4.4 Reviewing the analysis 83
4.5 Recommendations for ambient vibration testing of bridges 84

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TABLE OF CONTENTS

Section Page

CHAPTER 5 - CONCLUSIONS AND FUTURE 88
RECOMMENDATIONS
5.1 Conclusions 88
5.2 Reviewing the analysis 90
5.3 Recommendations for ambient vibration testing of bridges 90
5.4 Proposal for future research 91
5.5 Fulfillment of objectives 93

REFERENCES

APPENDICES

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LIST OF FIGURES

Figure Content Page

1-1 Approximate distribution of seismic risk across Canada’s 2
urban population. (Adams et al., 2002)
1-2 Map of Canada showing delimitation of the eastern and 2
western seismic regions and the stable central region.
(Adams and Halchuk, 2007)
2-1 Mechanical models of a multi-story building structure. 10
(Tedesco et al., 1999)
2-2 Mechanical model for a SDOF system. (Tedesco et al., 10
1999)
2-3 Coupling theoretically and experimentally derived 13
dynamic modelling. (Maia and Silva, 1997)
2-4 Definition of the unit impulse forcing function. (Maia and 17
Silva, 1997)
2-5 Definition of an arbitrary, non-periodic forcing function. 17
(Maia and Silva, 1997)
2-6 Devices used in FVT. (Cunha and Caetano, 2006) 19
2-7 Shaker devices used to excite. (Cunha and Caetano, 19
2006)
2-8 Random signals. (Ewins, 2000) 28
2-9 Description of Welch PSD analysis. (Trauth, 2007) 30
2-10 Interpretations of multi-sample averaging. (Ewins, 2000) 35
2-11 Finite-length sample and spectral leakage. (Ewins, 2000) 35
2-12 Window functions used frequently in spectral analysis. 36
(Stoica and Moses, 1997)
2-13 The effect of the window functions from Figure 2-15 in 37
the frequency domain. (Stoica and Moses, 1997)
2-14 Demonstration of how original time histories are treated 38
with select windows. (Ewins, 2000)
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LIST OF FIGURES

Figure Content Page

3-1 Views of the monitored bridge. 41
3-2 Sketch views of the bridge deck framing system. 43
3-3 Sketch view of the bridge deck framing system: plan 44
view.
3-4 Sketch views of the moment-resisting, reinforced 44
concrete frame. (De La Puente Altez, 2005)
3-5 Sketch sections through a typical column in the moment- 45
resisting, reinforced concrete frame. (De La Puente
Altez, 2005)
3-6 Sketch views of the girders’ connection to the top of the 46
moment-resisting, reinforced concrete frame.(De La
Puente Altez, 2005)
3-7 Profile view (transverse direction) sketch of the beam 46
connected to the top of the abutment. (Ministry of
Transport of Quebec)
3-8 Assumed stress-strain plots for the steel and concrete at 48
the time of construction of the bridge. (De La Puente
Altez, 2005)
3-9 (a) Experimental equipment: seismometer and DAS. 49
3-9 (b) Experimental equipment: RCS antenna attached to DAS 50
and GPS sensor mounted on railing.
3-10 Extract from a data file indicating record details followed 50
by five rows of data points.
3-11 Typical measurement time history describing motion in 53
each orthogonal direction (Record 6: File 27 from DAS
28 on November 30th 2007).

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