performance evaluation of a suspension bridge …...performance evaluation of a suspension bridge...

Performance evaluation of a suspension bridge excited by wind and trafficinduced action

Jónas SNÆBJÖRNSSON1, Etienne CHEYNET2 and Jasna BOGUNOVIC JAKOBSEN2

1School of Science and Engineering, Reykjavik University, ICELAND [email protected] of Mechanical and Structural Engineering and Materials Science, University of

Stavanger, NORWAY [email protected], [email protected]

Abstract

Wind and traffic induced vibrations of a 446 m long suspension bridge in a complex terrain

are studied, based on full-scale data. The full-scale data consists of wind velocity recorded by

sonic anemometers mounted above the bridge deck and acceleration records from accelerome-

ters placed on either side of four different sections of the steel bridge box-girder. In addition,

a GNSS base-rover system monitors the displacements at the center span. Ambient tempera-

ture data is also available. The analysis focuses on the identification of modal parameters and

the evaluation of the buffeting response. The modal parameters are affected by ambient tem-

perature, the magnitude of excitation and/or amplitude of response. Similarly, the response is

induced by either wind or traffic or both. For numerical modelling verification, it is necessary

to isolate the different sources of excitation. The variability in modal parameters and buffet-

ing response is investigated as such information is necessary for establishing the boundaries of

normal operations for the bridge.

Keywords: Suspension bridge, Wind, Traffic, Vibration, Full-scale, Response, Performance.

1 INTRODUCTION

Norway’s national road network along the west coast has been very dependent on ferry transportacross the many wide and deep fjords that cut through the Norwegian coastline. The NorwegianParliament has agreed on a transport plan to realize a ferry free road (E39) between Kristiansandin the south and Trondheim in the north by 2030 [1]. To achieve this goal, new standards needto be set in long span bridging and/or tunnelling, as the fjords that need crossing are between1.6 and 5 km long and up to 500 m deep. A development of this type requires research onmany levels. One part is to investigate the loading and response of suspension bridges. Forthis purpose, a full-scale monitoring program was initiated on the Lysefjord suspension Bridge,near Stavanger in Norway. The establishment of a full-scale suspension bridge laboratory isimportant for future development of fjord crossings, as relatively few studies of full-scale bridgein complex terrains such as fjords are available.

In traditional design of long span bridges, there are many sources of uncertainty. For in-stance:

• Simplified assumptions regarding terrain conditions, topography and local wind condi-tions.

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Snæbjörnsson et al. Performance evaluation of a suspension bridge

• Simplified loading and structural design assumptions.

• Simplified numerical modelling where possible Non-linear behaviour is often not ac-counted for.

• Simplified physical modelling in wind tunnels, using section models or full models atsmall scale.

Monitoring of real life structures is therefore important to assess the uncertainties in thedesign process through validation of structural modelling procedures and simplifications. Afull-scale laboratory of this type can also be utilized for testing of new monitoring equipmentand to develop information systems that can be used for facility management and road safetyprocedures.

For most of the strait crossings in question, wind loads will be among the governing de-sign factors. In relation to that, various research activities devoted to the assessment of windconditions and validation of the computational models for wind-induced vibrations have beeninitiated, in which the complex flow conditions at the Lysefjord inlet have been studied [2–4].The studies so far have focused on mean wind and turbulence statistics, wind spectra, coher-ence, co-coherence, and length scales of the flow. Which are all key parameters for wind loadmodelling.

In the following sections, the Lysefjord full-scale laboratory will be introduced, as well ason-going research and some current results. The emphasis will be on the identification andvariability of modal parameters, along with the buffeting response of the bridge.

2 THE BRIDGE SITE

The Lysefjord suspension Bridge is located at the inlet of a 40 km long Lysefjord in just inlandof the South-West part of the Norwegian coast. The fjord is less than 2 km wide and definedby steep cliffs reaching 1000 m in height. At the bridge location, the fjord narrows downto 500-600 m, so that the total bridge length is 600 m and the main span 446 m. At midspan, the bridge deck is 55 m above the sea level. It is oriented from North-West to South-East in a mountainous environment (Figure 1), where it is entrenched between two steep hills.The complex topography of Lysefjord with steep hills and high cliffs on either side of thebridge produces local wind conditions that are unique for the site. The channelling effect ofthe fjord is portrayed in two dominating wind directions: North-East for wind coming fromthe inside of the fjord, and South-West for wind coming from the outside of the fjord. As thetwo dominating wind directions lead to two distinct wind conditions with different spatial andtemporal characteristics, the response of the bridge is studied by using a case-by-case approach,i.e. by grouping data for wind from S-SW and N-NE.

3 THE INSTRUMENTATION

The wind conditions along the bridge are monitored using eight sonic anemometers mounted onhangers 8, 10, 16, 18, 20, 24 and 30, at the South-West side of the bridge. They are placed eitheron the hangers or on the main cables about 6 m above the deck, except at hanger 8 where thereare two anemometers mounted on the hanger at 6 and 10 m above the bridge deck respectively.The anemometer on hanger 10, is a Vaisala weather transmitter WXT520, providing ambienttemperature and barometric pressure as well as wind velocity and direction, while the others are3D WindMaster Pro sonic anemometers from Gill Instrument Ltd. The frequency resolution

2


Fig. 1. S-SW view of the bridge.

H-08

H-10

H-18

H-16North tower South tower

Accelerometer

Measuring GNSS

Reference GNSS

Sonic anemometer

H-09

H-20H-24

H-30

x

y z

Fig. 2. Sensors installed along the bridge deck. Anemometers are represented by grey triangles; GNSSsensors are visible as one blue and green dot; accelerometers are depicted as red rectangles.

for the WindMaster is 32 Hz and 4 Hz for the Vaisala weather station. The distance betweenhangers is 12 m, so the distance between anemometers varies from 24 m to 264 m.

The bridge response is monitored by four couples of tri-axial accelerometers located insidethe bridge deck, near hangers 9, 18, 24, 30, and one additional pair is placed at the top level ofthe North tower (figure 2). The accelerometers are placed on each side of the tower and the deckto be able to detect lateral, vertical and torsional motion. The dynamic displacement responseof the bridge is obtained based on the acceleration data through integration in the frequencydomain using discrete Fourier transform (DFT).

Real-Time Kinematic-Global Positioning System is installed at midspan on the deck of theLysefjord Bridge to measure directly the total displacement response of the bridge deck inthe East, North and vertical directions. The system is comprised of a set of Trimble BD930GNSS receivers coupled to Trimble AV33 GNSS antennas, in a base-rover setup. The individualsensors can handle data sampling at a frequency of 20 Hz with an accuracy of ± 8mm + 1ppmfor the horizontal displacement and ± 15mm + 1ppm for the vertical displacements. The base-rover combination will increase the measurement accuracy, as it is the relative displacementbetween the "fixed" base station and the "moving" rover station that is being recorded.

All sensors are linked to interconnected data acquisition units (CUSP-3/CUSP-M/CUSP-Me) from Canterbury Seismic Instruments. A GPS timestamp is used to synchronize the data.All data is sampled at 50 Hz and then decimated down to 20 Hz during data processing. A 3G

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router enables a wireless data access and transfer via a mobile net.

4 MODAL ANALYSIS AND SYSTEM IDENTIFICATION

A reliable knowledge of modal parameters describing the characteristics of structures is essen-tial for effective structural health management. The modal parameters of the Lysefjord Bridgehave been estimated based on the ambient vibration data from the lateral, vertical and torsionalacceleration response. The modal damping ratio of the structure can be expected to be lowerthan 1% because the bridge deck is a welded box-section. The modal identification procedureis further challenged by the non-availability of the impulse response function, the presence ofsignificant noise due to wind turbulence, and the evolution of the total modal damping ratiodue to aerodynamic damping contribution. Ambient modal identification of future ultra-longspan suspension bridge requires algorithm able to detect closely spaced modes of vibration atlow natural frequencies. Among them, Stochastic Subspace Identification (SSI) methods havebecome increasingly popular in the last twenty years. Surprisingly, few references describe theapplication of such a procedure to long-span suspension bridges, apart from e.g. [5, 6].

4.1 Mode shapes

The first symmetric and the first anti-symmetric modes are presented in Figure 3. The figureshows the identified mode shape from a single day of record (26/10/2014) at all accelerometerstations, compared to the mode shapes calculated with two theoretical models, the Alvsat andthe benchmark model. A small standard deviation was obtained for each identified mode shape,and consequently, only the averaged values are displayed in Fig. 3. The "Alvsat model" comesfrom a Finite Element (FE) software, Alvsat, developed for the Norwegian Public Road Ad-ministration (NPRA). The "benchmark model", is based on Galerkin’s method and was appliedfirst by Sigbjornsson and Hjorth-Hansen [7] for the lateral motion of a suspension bridge. Itwas later expanded to the vertical and torsional motion by Strømmen [8].

4.2 Modal damping and the effect of excitation intensity

Full scale measurement of the modal damping ratio of wind-sensitive structures remains sparsein the literature. In this subsection, the total damping is considered for various wind conditionsand for a considerable amount of samples. A statistical representation of the evolution of themodal damping ratio with the wind velocity U is adopted here, where the mean damping ratiois superimposed to a shaded area representing its standard deviation (Fig. 4). The identifieddamping ratio is compared to a computed modal damping ratio obtained for a linear bridgemodel, assuming a fixed structural modal damping ratio of 0.005 for every mode, stationarywind conditions, no traffic induced vibrations and no temperature effects on the bridge modalproperties. The computed modal damping ratio is defined as the sum of the aerodynamic andstructural modal damping ratio and assumed to evolve linearly as a function of the mean windvelocity only.

For a mean wind velocity of 20 m/s, the measured modal damping ratio is found to be around1 % for TS1, 0.8 % for TA1 and 0.8 % for HA1, whereas for VA1 and VS1 it is equal to 2.5% and 1.9 % respectively. In general, the predicted structural modal damping ratio agreesrelatively well with the measured one, although some discrepancies are observed. The modaldamping ratio of the lateral modes of vibration is higher than predicted but follows the trend setby the theoretical predictions, exception for HS1 where the scatter of the model damping ratiois particularity large at low wind velocities, which may lead to an overestimation of the meanvalues. The evolution of the modal damping ratio with the mean wind velocity is particularlyimportant for the vertical motion. For the first modes of the vertical motion, the measured

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0 0.2 0.4 0.6 0.8 1−1

−0.50

0.51

HS1

measuredBenchmarkAlvsat

0 0.2 0.4 0.6 0.8 1−1

−0.50

0.51

HA1

0 0.2 0.4 0.6 0.8 1−1

−0.50

0.51

VA1

0 0.2 0.4 0.6 0.8 1−1

−0.50

0.51

VS1

0 0.2 0.4 0.6 0.8 1−1

−0.50

0.51

TS1

0 0.2 0.4 0.6 0.8 1−1

−0.50

0.51

TS2

Fig. 3. Identified mode shapes and natural frequencies for the first two lateral (top), vertical (middle)and torsional (bottom) modes of vibration.

structural damping is close to the predicted one. However, the evolution with the mean windvelocity is slightly non-linear and the measured damping is less than the predicted one. Thismay lead to a computed response larger than expected [4]. For larger suspension bridges, thenon-linearity of the vertical damping may be more important and less predictable, which wouldjustify the application of OMA to trace its evolution.

4.3 Effect of ambient temperature on the natural frequencies

Knowledge of temperature effects on modal parameters is of particular interest for structuralhealth monitoring (SHM) purposes, and studies of such effects have significantly increasedsince the 2000’s [9]. The role of temperature changes on bridge eigen-frequencies was stud-ied by e.g. [10, 11]. In the present study, the accuracy of an automated SSI-COV method isassessed by studying the influence of the daily and seasonal temperature fluctuations on the nat-ural frequencies of the Lysefjord Bridge, which offers unique features compared to previouslystudied suspension bridges. Firstly, it is located in Southern Norway, where sunlight variationsduring the year are particularly pronounced, which should have noticeable consequences on thefluctuations of the natural frequencies, according to Westgate et al. [12]. Secondly, the bridgeis located in a rural area, where the influence of traffic on the variation of natural frequencies isrelatively insignificant compared to previous studies [13].

The natural frequencies are displayed as a function of the temperature in Fig. 5, where aroughly linear increase in natural frequency values for decreasing temperatures is easily visible.For temperatures below 4 ◦C, the mode TA1 shows variations that are actually measurementerrors due to the low amount of data for that temperature range. The scatter observed in Fig.5 is most likely due to the influence of other parameters such as traffic and wind load on thebridge.

The evolution of the natural frequency with time can be studied at different time scales, i.e.

5


0 5 10 15 200

2

4

ζ(%

)HS1

0 5 10 15 200

2

4

HA1

0 5 10 15 200

2

4

ζ(%

)

VA1

0 5 10 15 200

2

4

VS1

0 5 10 15 200

2

4

U (m/s)

ζ(%

)

TS1

ζ + σζ

ζ

Computed

0 5 10 15 200

2

4

U (m/s)

TA1

Fig. 4. The modal damping ratio as a function of the mean wind velocity for the first two lateral (top),vertical (middle) and torsional (bottom) modes of vibration.

long term fluctuations (several years), seasonal fluctuations (several months) or daily fluctua-tions (several days). For the Lysefjord Bridge, the seasonal periodicity and the daily periodicityhave been investigated.

The influence of seasonal temperature variations on the modal parameters of a suspensionbridge is not well documented, although such analysis have been carried out for a concretearch bridge [14, 15] where significantly higher eigenfrequencies were recorded during wintertime. The Lysefjord study suggests that the first lateral, veritcal and torsional eigen-modesclearly display a temperature dependent "seasonal trend" in line with the temperature depen-dancy demonstrated in Fig. 5.

The daily fluctuations of the natural frequencies were studied for a period of ten days, usingdata recorded in September 2015 (Fig. 6). The natural frequency of the first horizontal symmet-ric lateral mode of vibration, HS1, fluctuates between 0.135 Hz for diurnal data and 0.14 Hz fornocturnal data. These frequency fluctuations are relatively small compared to those for VA1,where the natural frequency ranges from 0.217 at day time to almost 0.23 during the night. Forthe first symmetric torsional mode of vibration, TS1, the natural frequency fluctuates between1.225 and 1.25 Hz. As indicated by Kim et al. [16], the natural frequency variations may bemagnified by the influence of traffic. At night time, the lower temperatures and the reducedtraffic load leads to higher natural frequencies, whereas during the day time, the increased tem-perature and traffic load leads to lower natural frequencies. The relative importance of the trafficload is however surely much less than the temperature effects.

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0 5 10 15 200.13

0.135

0.14

0.145H

S1

(Hz) mean + RMS value

mean value

0 5 10 15 200.43

0.44

0.45

0.46

HA

1(H

z)

0 5 10 15 200.215

0.22

0.225

0.23

VA

1(H

z)

0 5 10 15 200.29

0.295

0.3

VS

1(H

z)

0 5 10 15 201.22

1.24

1.26

T (◦)

TS

1(H

z)

0 5 10 15 202.16

2.18

2.2

T (◦)

TA1(

Hz)

Fig. 5. Evolution of the first two lateral (top), vertical (middle) and torsional (bottom) naturalfrequencies as a function of temperature.

0.13

0.135

0.14

0.145

HS

1(H

z)

0.215

0.22

0.225

0.23

VA

1(H

z)

20/09 22/09 24/09 26/09 28/09 30/091.22

1.23

1.24

1.25

time (DD/MM)

TS

1(H

z)

Fig. 6. Evolution of the natural frequency for the first lateral (top), vertical (middle) and torsional(bottom) mode of vibration for a period of 10 days and nights in September 2015.

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0 5 10 15 200.13

0.135

0.14H

S1

(Hz) Mean + RMS value

Mean value

0 5 10 15 200.43

0.44

0.45

HA

1(H

z)

0 5 10 15 200.215

0.22

0.225

0.23

VA

1(H

z)

0 5 10 15 200.29

0.295

0.3

VS

1(H

z)

0 5 10 15 20

1.22

1.24

1.26

U (m/s)

TS

1(H

z)

0 5 10 15 202.16

2.19

2.22

U (m/s)

TA1

(Hz)

Fig. 7. Evolution of the first two lateral (top), vertical (middle) and torsional (bottom) naturalfrequencies as a function of wind velocity.

4.4 Effect of excitation intensity on natural frequency

It is well established that natural frequency values are influenced by the excitation level. Theevolution of the eigen-frequencies with the mean wind velocity was studied using accelerationdata recorded between July and December 2015 (Fig. 7). It is seen that the variations of thelateral eigen-frequencies with U are larger than expected, whereas the vertical and torsionaleigen-frequencies hardly fluctuate. The study is however, partly inconclusive as the wind ve-locity and temperature can not be considered as fully independent variables for the study period,as larger wind velocities are generally recorded in the latter part of the autumn when the tem-peratures are low.

5 BUFFETING RESPONSE ESTIMATION

In addition to the structural characteristcs reflected by the modal parameters, the structuralresponse can be utilised to evaluate the structural performance. To have a verified model thatreliably predicts the buffeting response of a suspension bridge is of great value for the purposeof structural health management.

The response of the bridge to the buffeting load is evaluated numerically based on the quasisteady theory developed by [17, 18]. It is compared to the measured response obtained from144 samples of 10-minutes duration recorded on 26/10/2014 and on 07/10/2014 [4]. The modeshapes applied are idealized in terms of Fourier series, and the first symmetric and the firstasymmetric modes of vibration are considered for the lateral, vertical and torsional motion ofthe bridge. The aerodynamic damping and the torsional aerodynamic stiffness are approximatedby the quasi-steady terms. A description of the bridge properties can be found in [4]. The

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6 8 10 12 14 160

0.20.40.60.8

σx/I u(m

)computed

measured

6 8 10 12 14 160

0.20.40.60.8

σz/I w

(m)

6 8 10 12 14 160

1

2

·10−3

V x (m/s)

σt/I w

(◦)

6 8 10 12 14 160

0.20.40.60.8

σx/I u(m

)

6 8 10 12 14 160

0.20.40.60.8

σz/I w

(m)

6 8 10 12 14 160

1

2

·10−3

V x (m/s)

σt/I w

(◦)

Fig. 8. RMS of the bridge deck response for a N-NE wind (left panels) and a S-SW-wind (right panels)as a function of the mean wind velocity normal to the deck V x.

wind field is assumed stationary and homogeneous along the bridge deck. The modal couplinginduced by the wind load as well as the non-symmetry of the structure about the centre of thebridge span is neglected. The wind load is calculated using a co-coherence function which isfitted to measured data. The PSD of the buffeting response is computed for the resonant partonly since the accelerometers are not designed to measure accurately the background response,and the lowest frequency measured is consequently set to 0.08 Hz.

The standard deviation of the measured bridge displacement at mid-span is compared to thecomputed one in Fig. 8. The RMS of the displacement has been normalized by the corre-sponding turbulence intensity to reduce the spreading of the data. A good overall agreement isfound between the measured and computed RMS values for S-SW wind. However, the com-puted response underestimates the bridge displacements for N-NE exposure, which is generallycharacterized by a larger turbulence intensity and a larger yaw angle. The mountainous envi-ronment affects particularly the yaw angle that fluctuates between 20◦ and 45◦. For large yawangles, larger bridge displacement are recorded than predicted by the "cosine rule" [19] whichis applied in the present study.

For the data studied, the RMS of the measured bridge displacement does not display anysudden variations at low wind speeds, which indicates that the traffic induced vibrations werenot strongly present during the period studied.

5.1 Effects of traffic induced vibrations on the buffeting response

Analysis of acceleration records from the Lysefjord Bridge shows that heavy vehicles are re-sponsible for non-negligible vibrations. The buffeting analysis of long-span suspension bridgesis likely to be affected by such parasitic phenomena, especially at low and moderate wind ve-locities. To eliminate or at least reduce this source of uncertainty in the validation of numericalmethods, such as the buffeting theory, three simple approaches to remove samples dominatedby traffic-induced vibrations were proposed [20]:

1. The separation of diurnal and nocturnal records. Assuming that traffic on the bridgeduring the night is minimal compared to the daytime.

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0 2 4 6 8 10 120

2

4

6

·10−2

U (m/s)

σz

(m/s

2)

with trafficwithout traffic

0 2 4 6 8 10 120

2

4

6

·10−2

U (m/s)

σz

(m/s

2)

Fig. 9. RMS of vertical bridge acceleration at mid span for S-SW wind using the criteria τ (left) andcriteria λ (right).

2. The application of a criterion (τ ) based on the time varying standard deviation of thevertical bridge acceleration response as a ratio of the RMS of vertical wind velocity.

3. The application of a criterion (λ) based on the relative importance of the high frequencycomponents of the acceleration response, evaluated as a ratio of the RMS of verticalresponse at 4 to 10 Hz and 0 to 4 Hz respectively.

The selection of nocturnal records is straightforward, but may be too harsh. The analysis ofseveral samples showed that buffeting response from nocturnal and diurnal samples did notshow strong differences when the wind velocity was above 12 m/s. The proposed criterion τ ,may efficiently detect variation of the acceleration response due to heavy vehicles, but is bestsuited for low and moderated wind speeds. Criterion λ, tends to overestimate the number ofsamples dominated by traffic-induced vibration at low wind speed. The two criterions τ andλ are compared on Fig. 9. For criterion τ , some samples displaying a high RMS at low windspeed are not counted as dominated by traffic-induced vibration. One reason may be that thethreshold value for τ is too low. For strong winds, criterion λ detects almost no traffic-inducedvibration, as is to be expected. The criterion τ may be more adapted for low wind speeds, whileλ seems more reliable for high wind speeds. Alternative forms of these criteria will be furtherexplored.

6 CONCLUSIONS

Wind and traffic induced vibrations of a 446 m long suspension bridge in a complex terrain havebeen studied in full scale.The focus has been on modal parameter characterization of a full-scale suspension bridge by the use of an automated SSI-COV procedure. This step is central toproperly study the buffeting response of a full-scale bridge.

One of the challenges in the data analyzing is to differentiate between the two main excitationsources, wind and traffic. Because traffic-induced vibrations affect every mode of vibrationof the bridge, direct filtering cannot be applied. A simple approach, based on evaluating therelative importance of the high frequency part of the acceleration bridge response over the low-frequency part, has been proposed to isolate records dominated by wind-induced vibrationsfrom those dominated by traffic.

Environmental effects were observed, such as the daily and seasonal fluctuations of theeigen-frequencies. The large data scatter obtained, especially at low wind speed, may be due toinfluence from traffic-induced vibrations.

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If a sufficient amount of acceleration data is accumulated, a statistical description of theinfluence of the mean wind velocity on the modal parameters can be established. Further anal-ysis could aim to characterize probability distributions for the modal damping ratio and theeigen-frequency, so that they can be considered as "random parameters". A sensitivity analysismay provide precious information on the influence of such randomness on the bridge respone.If these effects are non-negligible, a Monte Carlo simulation of the buffeting response with"randomized" modal parameters may provide results that accounts for the randomness of thestructural parameters.

As the monitoring is continuously ongoing it will be possible to evaluate probability distri-butions for excitation-, system- and response parameters. These can subsequently be used todevelop performance indicators or criteria’s for structural health management purposes.

7 ACKNOWLEDGEMENTS

The authors would like to gratefully acknowledge the support of the Norwegian Public RoadsAdministration to the measurement campaign, as well as the installation and maintenance ofthe monitoring system.

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