Vibration assessment of the International Guadiana Bridge
Elsa Caetano
Assistant Professor, Faculty of Engineering of Porto (FEUP), Portugal
Álvaro Cunha
Associate Aggregate Professor, Faculty of Engineering of Porto (FEUP), Portugal
Filipe Magalhães
Assistant, Faculty of Engineering of Porto (FEUP), Portugal
ABSTRACT: The paper describes the development of a monitoring program for a cable-stayed bridge and resumes the major dynamic properties identified from a series of test campaigns conducted on the bridge, which are also correlated with results from a numerical analysis. Some aspects of the current dynamic behav-ior of the bridge under ambient excitation are discussed, considering in particular the large cable vibrations that are frequently observed.
1 INTRODUCTION
The International Guadiana Bridge (Fig. 1) is a con-crete cable-stayed bridge spanning the Guadiana River close to the border with Spain, at the southern part of Portugal. The bridge was designed by Câncio Martins (1992) and opened to traffic in 1991. Given the relatively severe wind and high seismic risk characteristics of the bridge site, extensive studies were developed prior, during and after construction (Branco, 1987; LNEC, 1992; Branco et al., 1991, 1993;). Despite the generally good performance un-der normal traffic and ambient conditions, the stay cables soon proved to be vulnerable to wind excita-tions, fact that is in a great deal associated with the absence of protection with a pipe of the individual parallel strands that form each stay cable, and that results in the occurrence of frequent oscillations of high amplitude, accompanied by a significant “rat-tling noise”. Furthermore, a study developed at commissioning stage by Pinto da Costa et al. (1994) pointed to some vulnerability of certain cables to the so-called phenomenon of parametric excitation.
Having the purpose of assessing the current condi-tion of the bridge in terms of the actual dynamic be-haviour, characterising in particular the possible dif-ferent sources of cable vibration and defining as a long-term objective the possible detection of dam-age, a monitoring program has been developed cen-tred on this bridge. This program includes the devel-opment of a series of test campaigns under normal traffic use, as well as the installation of a monitoring system, which will allow the continuous observation
of relevant physical quantities from a remote central located at the University.
The current paper describes the essential features of the monitoring system under development and systematises the most relevant dynamic parameters and characteristics of observed vibration that have been identified on the basis of several ambient vibra-tion test campaigns. The major dynamic parameters are correlated with results of a numerical analysis of the bridge.
Figure 1. View of Guadiana Bridge (Câncio Martins, 1992).
2 BRIDGE DESCRIPTION
The International Guadiana Bridge is a partial sus-pension cable-stayed bridge with a prestressed con-crete deck, formed by a central span of 324m, two lateral spans of 135m and two transition spans of 36m. The two A-shaped towers reach a height of 100m above the foundations and have a concrete box section. The 18m wide deck has a prestressed concrete box section with 2.5m depth and is partially suspended by the towers and by 64 pairs of cables arranged in a semi-fan. The stay cables are formed by bundles of 22 to 55 15mm monostrands, which
are clamped at mid-length or at the thirds of the length by collars.
3 VIBRATION ASSESSMENT
The installation of a monitoring system on a bridge requires a definition of objectives and the previous knowledge of the intervals of variation of the physi-cal quantities of interest.
In the current case, one of the major objectives is the identification of the major sources of cable vi-bration. Given that these oscillations are clearly as-sociated with the wind, the identification of the pat-terns of vibration requires a systematic observation of cable oscillation and wind velocity and direction. On another hand, considering the possibility of pa-rametric excitation, i.e., of cable oscillations trig-gered by the vibration of the deck, induced by wind and traffic, it is essential to measure deck accelera-tions too. An important issue in terms of the long-term behaviour of the bridge is the possibility of premature failures of some strands by fatigue, in consequence of repeated excessive vibration occur-rences. For this purpose, a direct measure of the lev-els of installed tension in cables is of interest. Addi-tional measures of temperature and strain at relevant sections of the bridge are devised for correlations with dynamic properties and for characterisation of traffic loads.
Having these aspects into consideration, the cur-rent Section presents a summary of measured prop-erties of the bridge, and discusses the major specifi-cations and characteristics traced for the monitoring system under development. Finally, some results of identification of modal parameters are presented, which are used to validate numerical models.
3.1 Vibration condition
The data analysed in this paper was collected in two measurement campaigns that took place in March 2003 and May 2004, under normal traffic use. The weather condition registered during measurements was generally considered good. Yet multiple events of large oscillation of the stay cables were regis-tered.
In order to indirectly evaluate the tension installed in stay cables, high sensitivity piezoelectric acceler-ometers were mounted on the deviator guides, at a height of around 2m from deck level. Using a port-able Fourier analyzer, average power spectral den-sity estimates (PSDs) of the ambient vibration re-sponse were collected, which allowed the identification of the fundamental vibration
frequen-cies and, consequently, of the installed cable ten-sions, based on the vibrating chord theory. Several of the cables that temporarily exhibited large vibra-tions were further investigated, by simultaneous measurement of ambient response at the deck an-chorage and at the deviator guide, accompanied by a registration of wind velocity and direction. Figure 2 shows some details of the instrumentation and an example of an obtained PSD estimate. Figure 3 shows PSD estimates obtained simultaneously at one stay cable of the central span and at the deck level, close to 1/3 span for the vertical plane measure-ments. Table 1 resumes the values and intervals of variation of global bridge and cable frequencies, ac-celerations and of average wind velocity observed during measurements. 0 5.0 10.0 -100.0 -90.0 -80.0 -70.0 -60.0 -50.0 -40.0 -30.0 -20.0 Hz dB M ag, g guadiana1.aps_Run00062_G1, 1sv00000 Harmonic #1 X: 0.90332 Y: -22.8987 F: 0.90332
Figure 2. Examples of cable, deck and wind measurements.
Figura 3. Simultaneous PSD estimates at deck and cable 4.
It can be noticed from that table that deck accel-erations are generally very low, the vertical compo-nent being one order of magnitude higher than the longitudinal component, and around five times the lateral component. On the contrary, cable accelera-tions measured at a distance of about 2.5m the deck anchorage present a wide range of values and can
0.90 4.54 3.64 2.72 1.82 1.29 1.45 1.82 1.92 2.72 4.54 1.10 0.95 0.87 0.81 0.72 0.56 0.39 1.00E-06 1.00E-04 1.00E-02 1.00E+00 1.00E+02 1.00E+04 0 1 2 3 4 5 Frequency (Hz) Amplitude PSD Cable 4, Vert. Deck, Vert.
reach around one hundred times the vertical deck acceleration, corresponding to maximum amplitudes of oscillation of around 0.50m (1.0m peak-to-peak). It should be noticed that these oscillations occurred for moderate average wind velocities no greater than 14m/s. As for the periodicity and patterns of cable vibration occurrences, various situations were identi-fied, which are clearly correlated with wind velocity and direction, involving different stay cables and presenting different characteristics. It could however be noticed that moderate oscillations occur almost systematically for moderate wind velocities in the range 10-15m/s, involving a significant number of cables. Particular situations were also detected in which one or a group of stay cables (normally, amongst the largest of the central span, or the mid-length cables of lateral spans) suddenly started vi-brating very strongly and kept oscillating for various hours after the wind velocity significantly reduced, or else modified the amplitude of oscillation with a slight modification of the wind direction. It is still relevant to notice that the range of fundamental fre-quencies of the stay cables clearly contains frequen-cies that are multiple or sub-multiple of global bridge frequencies, meaning that conditions for the occurrence of parametric excitations may be met for particular stay cables (Caetano & Cunha, 2003).
Table 1. Intervals of variation of some physical quantities.
Physical quantity Interval of variation
Deck acceleration (m/s2) 0.012-0.048(long.);
0.025-0.069 (lat.); 0.101-0.389 (vert.)
Cable acceleration (m/s2) 0.4-10
Average wind velocity ..- 14m/s
Fundamental cable frequencies (Hz) 0.72-2.97 Fundamental bridge frequencies (Hz) 0.391 (vert.); 0.537 (lat.); 1.445 (torsion) 3.2 Monitoring system
Considering the vibration characteristics systema-tised above, a monitoring system is being developed, following the instrumentation plan schematically represented in Fig. 4. Accordingly, the measurement system comprehends the following types of sensors: accelerometers, one anemometer, magneto-elastic sensors, one or more video cameras, temperature sensors and electric strain gages. A significant part of the sensors to employ are accelerometers, which constitute at the current state-of-art the motion sen-sors of highest sensitivity and lowest cost. Given the different amplitudes of vibration experienced by the deck and cables, different types of sensors are ex-pected: force balance type accelerometers are the most convenient sensors for deck motion measure-ments, due to the low frequency range of interest (0.39-5Hz) and the high sensitivity required. Piezo-electric accelerometers will be used for stay cable measurements, given that these sensors are less de-manding than the force balance sensors in terms of powering, and no site baseline correction is needed. Some of the cables instrumented with accelerome-ters will also have installed magneto-elastic sensors, which will provide a direct measure of cable tension, after convenient site calibration. These sensors have been developed at the Comenius University (Jarosevic & Chandoga, 1994).
Another innovative component of the monitoring system consists in the use of video cameras as sen-sors. The use of these cameras can be made at two levels: (i) at a first level, the image will be used for remote contact with the structure, allowing for the long distance activation of the acquisition system whenever large oscillations are observed at particu-lar stay cables; (ii) at a second level, and using im-age processing techniques developed at FEUP, the amplitudes of oscillation of certain cables will be quantified.
Figure 4. Monitoring plan. 17 SPAIN S3 1 S2 S1 S4 16 32 PORTUGAL
Uniaxial accelerometer, I channels Sonic/propeller anemometer Magneto-elastic sensor Bi-axial accelerometer Video cameras Temperature sensors Strain gages Data acquisition system
An anemometer will be installed at the top of one tower. The system will be complemented with a set of temperature sensors and strain gages. A to-tal of 64 measurement channels are expected.
The data acquisition system presently under de-velopment incorporates a few innovative compo-nents, which will allow an increased efficiency at reduced implantation costs. The multi-sensorial system incorporates a technology that allows the replacement of individual electric cables associated with each sensor or set of sensors, by one only electrical cable. This cable links together all the system sensors and connects to a central station, located inside the deck, close to one of the towers, and will be used to provide electrical current to all or part of the sensors, to develop a synchronised sampling and to transmit the measured signals. These signals will be conditioned and digitised close by the sensors, in order to guaranty a high signal/ noise ratio. The measurement chain will be complemented with the development of a computa-tional platform where the control and programming of measurements will be performed. This system will communicate remotely with FEUP for trans-mission of data and modification of the parameters of acquisition.
3.3 Dynamic properties
The most relevant dynamic parameters of the bridge were identified on the basis of an ambient vibration test. Given the low level of signals, the frequency range of interest and the closeness be-tween some relevant natural frequencies, a detailed analysis was required. For this purpose a set of four tri-axial 18-bit strong motion recorders were used. These sensors operate in a synchronised form through GPS units, after initial programming by a laptop, therefore providing an efficient form of de-veloping measurements at many sections along the bridge.
The test scheme adopted was based on the consideration of two reference recorders located close to the third of the central span, at section 17 (Fig. 5), the other two records being successively positioned at the upstream and downstream sides of the deck, at each of the sections 1 to 27 along the deck, and at two levels at each of the towers (sections 28 and 29).
For each setup, time series of 21 minutes were col-lected, at a sampling frequency of 100Hz. The full test was developed in two and a half days. During this period, the wind velocity at deck level was
monitored, using a propeller anemometer. Average wind velocities of 2-14m/s were recorded.
The identification of modal parameters was per-formed using the classical peak-picking method, after combination of upstream and downstream signals, to separate bending and torsional compo-nents. Figure 6 presents Average Normalised Power Spectral Density (ANPSD) functions that were used for identification of natural frequencies.
Portugal Spain 1J 9J 10J 2J 28E 8J 3J 4J 5J 6J 7J 12J 11J 29E 13J 19J 20J 21J 22J 23J 24J 25J 26J 27J 14J 15J 16J 17J 18J 9M 10M 2M 28P 8M 3M 4M 5M 6M 7M 12M 11M 29P 13M 19M 20M 21M 22M 23M 24M 25M 26M 27M 14M 15M16M 17M 18M 1M
Figure 5. Measurement sections for ambient vibration test.
ANPSD - half-sum of vertical acceleration
0.391 0.566 0.952 1.660 1.880 1.035 1.299 2.251 2.783 0.845 1.812 1E-05 1E-04 1E-03 1E-02 1E-01 1E+00 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Frequency (Hz) Amplitude
ANPSD - half-difference of vertical acceleration 1.445 2.578 1E-07 1E-06 1E-05 1E-04 1E-03 1E-02 1E-01 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 Frequency (Hz) Amplitude
ANPSD - half-sum of transversal acceleration
0.537 1.450 1E-07 1E-06 1E-05 1E-04 1E-03 1E-02 1E-01 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 Frequency (Hz) Amplitude
Figure 6. Average Normalised Power Spectral Density func-tions for vertical and lateral direcfunc-tions.
The presence of a significant number of peaks in the spectral estimates evidences, not only the closeness between successive global mode fre-quencies (marked and labelled in Fig. 6), but also the contribution of cable vibration, that was very
significant for the highest levels of wind velocity. This effect is well evidenced in Fig. 7, where PSD estimates were obtained at the reference section us-ing records collected at average wind velocities of 2m/s, 10m/s and 14m/s.
Power Spectral Density functions at reference section (half-sum of vertical acceleration)
1E-06 1E-05 1E-04 1E-03 1E-02 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 Frequency (Hz) Amplitude
wind - 2 m/s wind - 10 m/s wind - 14 m/s
Power Sepctral Density functions at reference section (half-difference of vertical acceleration)
1E-08 1E-07 1E-06 1E-05 1E-04 1E-03 1E-02 1E-01 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 Frequency (Hz) Amplitude
wind - 2 m/s wind - 10 m/s wind - 14 m/s
Power Sepctral Density functions at reference section (half-sum of transversal acceleration)
1E-07 1E-06 1E-05 1E-04 1E-03 1E-02 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 Frequency (Hz) Amplitude
wind - 2 m/s wind - 10 m/s wind - 14 m/s
Figure 7. Power Spectral Density functions at reference sec-tion at three wind velocity levels.
Figures 8 to 10 represent some of the identified modal configurations associated with the most relevant natural frequencies. In those figures the symbols • define the position of the towers and in-termediate supports. Due to the significant interac-tion observed between some global vibrainterac-tion modes and with cable vibrations, more sophisti-cated algorithms were explored to provide a better identification of modes, namely the Enhanced Fre-quency Domain Decomposition (EFDD) and the data driven Stochastic Subspace Identification (SSI) methods. These methods provided also esti-mates of damping ratios (Magalhães, 2004).
Comparing natural frequencies and modal shapes identified based on the three different methods, no significant differences were found, provided that particular care was taken in the ap-plication procedures. As for estimates of damping, Table 2 systematises the values obtained using the EFDD method, which show a certain dispersion. This dispersion is however expected, not only due to the intrinsic nature of damping and to the sto-chastic character of the identification algorithms,
but also due to the variation of certain parameters, like wind or temperature, that strongly affect its value. In fact, the simple analysis of the PSD func-tions represented in Figure 7 for three different wind velocities, shows a progressive enlargement of the curves with the wind velocity increase at some resonances, corresponding to increasing damping ratio estimates of the corresponding modes. The variation with wind velocity of damp-ing ratio estimates is shown in Table 3 for the first vertical, lateral and torsional modes.
f = 0.391 Hz -2 -1.5 -1 -0.5 0 0.5 0 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360 378 396 414 432 450 468 486 504 522 540 558 576 594 612 630 648 666 m f=0.566Hz -1.5-1 -0.5 0 0.5 1 1.5 0 18 36 54 72 90 10 8 12 6 14 4 16 2 18 0 19 8 21 6 23 4 25 2 27 0 28 8 30 6 32 4 34 2 36 0 37 8 39 6 41 4 43 2 45 0 46 8 48 6 50 4 52 2 54 0 55 8 57 6 59 4 61 2 63 0 64 8 66 6 m f = 0.845 Hz -10 -5 0 5 10 0 18 36 54 72 90 10 8 12 6 14 4 16 2 18 0 19 8 21 6 23 4 25 2 27 0 28 8 30 6 32 4 34 2 36 0 37 8 39 6 41 4 43 2 45 0 46 8 48 6 50 4 52 2 54 0 55 8 57 6 59 4 61 2 63 0 64 8 66 6 m f=0.952Hz -3 -2 -1 0 1 2 0 18 36 54 72 90 108 12 6 14 4 16 2 18 0 19 8 21 6 23 4 25 2 27 0 28 8 30 6 32 4 34 2 36 0 37 8 39 6 41 4 43 2 45 0 46 8 48 6 50 4 52 2 54 0 55 8 57 6 59 4 61 2 63 0 64 8 66 6 m f = 1.035 Hz -3 -2 -1 0 1 2 0 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360 378 396 414 432 450 468 486 504 522 540 558 576 594 612 630 648 666m f=1.299Hz -4 -2 0 2 4 0 18 36 54 72 90 10 8 12 6 14 4 16 2 18 0 19 8 21 6 23 4 25 2 27 0 28 8 30 6 32 4 34 2 36 0 37 8 39 6 41 4 43 2 45 0 46 8 48 6 50 4 52 2 54 0 55 8 57 6 59 4 61 2 63 0 64 8 66 6 m
Figure 8. Identified vertical vibration modes. f=0.537Hz -1.5 -1 -0.5 0 0.5 0 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360 378 396 414 432 450 468 486 504 522 540 558 576 594 612 630 648 666 m f=1.450Hz -1.5 -1 -0.5 0 0.5 1 0 18 36 54 72 90 10 8 12 6 14 4 16 2 18 0 19 8 21 6 23 4 25 2 27 0 28 8 30 6 32 4 34 2 36 0 37 8 39 6 41 4 43 2 45 0 46 8 48 6 50 4 52 2 54 0 55 8 57 6 59 4 61 2 63 0 64 8 66 6 m
Figure 9. Identified lateral vibration modes. f=1.445Hz -1.5 -1 -0.5 0 0.5 1 1.5 0 18 36 54 72 90 10 8 12 6 14 4 16 2 18 0 19 8 21 6 23 4 25 2 27 0 28 8 30 6 32 4 34 2 36 0 37 8 39 6 41 4 43 2 45 0 46 8 48 6 50 4 52 2 54 0 55 8 57 6 59 4 61 2 63 0 64 8 66 6 m f=2.578Hz -1.5 -1 -0.5 0 0.5 1 1.5 0 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360 378 396 414 432 450 468 486 504 522 540 558 576 594 612 630 648 666 m
Table 2. Calculated and identified natural frequencies.
Frequency (Hz) Damping ratio
(EFDD) (%) Mode number Calc. Ident.(P.P) ξ σξ Type of mode* 1 0.377 0.391 1.37 0.41 1st VS 2 0.508 0.537 2.23 0.79 1st LS 3 0.521 0.566 1.2 0.45 1st VAS 4 0.778 0.845 - - 2nd VS 5 0.884 0.952 0.69 0.25 2nd VAS 6 0.963 1.035 0.51 0.12 3rdVS 7 1.193 1.299 0.54 0.11 3rd VAS 8 1.222 1.450 - - 1st LAS 11 1.493 1.445 0.47 0.16 1st T 12 1.506 1.660 0.63 0.28 4th VS 14 1.684 1.812 - - 4th VAS 15 1.786 1.880 0.65 0.25 5th VS 20 2.140 2.251 0.59 0.22 5th VAS 23 2.644 2.783 0.46 0.53 6th VS 24 2.682 2.578 1.48 0.19 2nd T
* V: Vertical; S: Symmetric; AS: Anti-symmetric; L: Lateral; T: Torsional f = 0.377 Hz f = 0.521 Hz f = 0.778 Hz f = 0.884 Hz f = 0.963 Hz f = 1.193 Hz f = 1.222 Hz f = 1.493 Hz f = 1.506 Hz f = 1.684 Hz f = 1.7858 Hz f = 2.140 Hz f = 2.644 Hz f = 2.682 Hz
Figure 11. Calculated modal shapes. Table 3. Variation of ξ with wind velocity.
Wind vel. 1st vertical
mode 1 st lateral mode 1 st torsional mode 2m/s 0.95% 1.84% 0.37% 9m/s 1.43% 2.28% 0.51% 14m/s 1.95% 2.43% 0.47%
Table 2 and Figure 11 summarise the modal pa-rameters obtained from the numerical modelling of the bridge and provide a comparison with experi-mental data, which shows a good agreement. The identified natural frequencies of in-plane bending and lateral modes are generally slightly higher than the corresponding numerical values. The contrary occurs for the two torsional modes, fact that is
pos-sibly associated with insufficient restriction of ro-tation over the tower supports.
4 CONCLUSIONS
The paper describes the studies developed on a ca-ble-stayed bridge with the purpose of assessing the corresponding dynamic behavior. These compre-hend the development of a monitoring system for systematic observation of vibration events and fu-ture detection of damage, and a full characteriza-tion of the current dynamic properties, to be used as reference. These properties, identified on the ba-sis of an ambient vibration test, are used to validate a numerical model. It is shown that some vibration modes have an increased damping ratio for higher wind velocities.
ACKNOWLEDGEMENTS
The present research has been developed in the context of the Project POCTI/ECM/46475/2002, Vibrations in Cable-stayed Bridges”. The authors acknowledge the support of this project, funded by the Portuguese Sci-ence Foundation (FCT).
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