Analysis of dynamic coupling between spans of two multi-span bridges usingambient vibration measurements

Leqia He1, Edwin Reynders1, Ting-Yu Hsu1,2, Guido De Roeck11Department of Civil Engineering, K.U.Leuven, KasteelparkArenberg 40, B-3001 Leuven, Belgium

2National Center for Research on Earthquake Engineering, No. 200, Sec. 3, XinHai Road, Taipei, Taiwanemail: Leqia.He@bwk.kuleuven.be, Edwin.Reynders@bwk.kuleuven.be, dysheu@ncree.narl.org.tw,

Guido.DeRoeck@bwk.kuleuven.be

ABSTRACT: Dynamic coupling in weakly coupled multi-span bridges usually is not considered in their design, since the couplingeffects normally leave the structure on the safe side by reducing the peak-peak deflection of each span under moving vehicles andtrains. Nonetheless in the framework of vibration monitoring, these coupling effects require further investigation,since some wellknown non-destructive damage identification technique relies on the fact that occurrence of damage leads to changes in structuraldynamic properties, which are very often also influenced by the coupling effects. In this study, ambient vibration measurementswere performed for two representative cases in order to investigate the dynamic coupling effects of these bridges. One is a three-span prestressed concrete highway bridge. And the other oneis a five-span steel-plate-girder railway bridge. The experimentalresults verify the influence of dynamic coupling between adjacent spans for these two bridges. From the first bridge, it isalso foundthat global modes of this weakly coupled multi-span bridge are very sensitive to the relative stiffness changes of an individual span,e.g., caused by localized damage.

KEY WORDS: Bridge dynamics; dynamic coupling; modal properties.

1 INTRODUCTION

With respect to structural condition assessments, the mea-surement of accurate dynamic characteristics of structures isimportant, since many damage-detection methods are basedon the observation that structural defects and damage changethe dynamic properties, e.g., mode shapes, modal statistics,natural frequencies and damping ratios of the structures. Thedynamics of highway and railway bridge structures, consideredas multi-span continuous beams under moving loads, havebeen extensively studied [1]. In practice, some multi-spanbridges with simply supported spans are weakly coupled via thecontinuous deck or the stringers. In [2], a numerical model hasbeen proposed to consider these structures as a number of beamscoupled together by means of rigid and/or non-rigid joints.Theirnumerical analysis shows that the dynamic coupling effect maybe significant to the vibration behaviour.

In this paper, we present the experimental results from tworepresentative case studies for investigation of the dynamiccoupling effects. The first bridge is a three-span prestressedconcrete highway bridge, which has a continuous concrete slab.The other one is a five-span steel-plate-girder railway bridge,in which the adjacent spans are weakly coupled via both thestringers and the bottom flanges of the main girders.

The tests were performed by using ambient vibrationmeasurements on the bridges. Wireless sensors, known asGMS-18 Netquakes Recorders from GeoSIG [3], were used forthese measurements. Advantages of using the wireless insteadof the traditional wired sensors are the easy configuration andrapid deployment of the wireless sensor network for vibrationmeasurements (Fig. 1).

The bridges and test setup are described in Section 2 andSection 3, respectively. Experimental results are given andcompared to the results of a Finite Element (FE) analysis. InSection 4 conclusions are made.

Figure 1. Wireless sensors in operation (left) and their masterunit with the GPS time synchronization module attached(right).

2 OPERATIONAL MODAL ANALYSIS OF THE BOIRSVIADUCT

2.1 Bridge description

The Boirs viaduct is a part of the E313 highway between thecities Antwerpen and Liege in Belgium. It is a concrete highwaybridge, as shown in Fig. 2. It consists of twenty-one spans madeof seven simply supported prestressed concrete main girders.Every three adjacent spans share the continuous concrete slabon top of these girders, as shown in Fig. 3 of Spans X, XI andXII. These three spans are of equal length, 26 meters. The maingirders were prefabricated with prestressed tendons. Afterwardsa post-tensioning was applied on site. Cross trusses between the

Figure 2. A south view of the Boirs viaduct, showing theseverely damaged side girder of span X.

Figure 3. Elevation, top view and cross-section A-A of theBoirs viaduct (units in meter).

main girders are also connected by means of post-tensioningtendons. Severe deterioration of post-tensioned concretedueto corrosion of post-tensioning strands had been found in thesouth outer girder during inspection of the bridge. The corrosionis related to penetration of rainwater in the non-fully injectedducts of the post-tensioning. As shown in Fig. 2, part of theconcrete covers was peeled off the web of the south outer girder,which is especially evident in the middle of Span X. Moreover,it was found that some tendons were even broken. There areless visible damage on the surface of the main girders of theother two spans XI and XII. Since the damage was so severe thatno repair and replacement of the post-tensioning cables werepossible, the whole structure has to be demolished and replaced.

2.2 Finite element analysis

Figure 4. FE model of the Boirs viaduct, built of solidelements (a south view). The arrows indicate the boundaryconditions.

In order to investigate the modal properties of the bridge, anANSYS model built of solid45 elements [4] is used. In theFE model, damage was simulated by a stiffness decrease of anindividual finite element. An uniform decrease of the stiffnessmatrix of the whole element is assumed. A damage index∆ae

is chosen to present the fractional change in stiffness of theelement [5], which is defined by

∆ke = ke− ke = ∆aeke. (1)

in which ke and ke are, respectively, theeth element stiffnessmatrices of the undamaged and damaged structure.∆ke isthe reduction of the stiffness. The higher value of∆ae ∈

[0,1] represents the higher severity of damage. Following thedefinition of ∆ae, a reduced Young’s modulus is assigned tothe elements of the south outer girder where damage was morevisible in comparison to the other parts, indicated by differentcolours in Fig. 4.

Table 1. Natural frequencies extracted for the two globalcoupled modes from the FEM analysis.∆ fi = ( fi − f0)/ f0for i=1,2 and 3.

Damage scenario 1st global mode 2nd global modeD0(undamaged) 5.206 5.459

fi D1 (∆ae = 25%) 5.134 5.458[Hz] D2 (∆ae = 50%) 4.966 5.458

D3 (∆ae = 75%) 4.630 5.458D1 -1.39 -0.01

∆ fi D2 -4.61 -0.01[%] D3 -11.07 -0.01

The natural frequencies of the simulated structure with threedifferent damage severities and the undamaged case are listedfor the first and second global coupled modes in Table 1. Thecorresponding mode shapes are plotted in Fig. 5 and Fig.6, respectively. All modes have been normalized to unity.Simulated damage scenarios are shown to have a significantinfluence on the 1st coupled mode and an insignificant influenceon the 2nd coupled mode. As described in [5], the explanationis that the damaged elements are located at the zone where themaximum curvature occurs of the 1st mode, but with almost zerocurvature of the 2nd mode. Moreover, the simulated damagescenario causes the first frequency to reduce up to 11%, whileonly 0.01% decrease is found for the 2nd frequency. Especially,the symmetry across the three spans of the 1st coupled modeis gradually lost when the damage severity increases. In other

words, the increased damage level gradually amplifies the modaldisplacements of the damaged span in comparison to the otherspans.

For a similar weakly coupled multi-span bridge the previousobservation can be used as a damage indicator for an individualspan, if each span is not going to undergo a similar damagescenario with the same severity. Moreover, the difference ofthe maximum modal displacement among the spans can be usedto quantify the relative damage severities between the spans.

(a) undamaged structure

(b) damaged structure of D3

(c) FEM mode shapes of the simulated structure with differentdamage severities (plotted along the south outer girder and

normalized to unity).

Figure 5. First coupled bending mode of the FEM.

2.3 Experimental verification

Ambient vibration measurements were performed by theStructural Mechanics division of K.U. Leuven on the Boirs

(a) undamaged structure

(b) damaged structure of D3

(c) FEM mode shapes of the simulated structure with differentdamage severities (plotted along the north outer girder and

normalized to unity).

Figure 6. Second coupled bending mode of the FEM.

viaduct. The excitation was introduced from wind and vehiclespassing on the parallel highway bridge just near to the northofthe tested structure. Modal parameters are extracted from themeasured ambient accelerations by using the reference basedStochastic Subspace Identification (SSI) algorithm [6]. Dataprocessing and system identification were performed using theModal Analysis of Civil Engineering Constructions (MACEC)software package [7]. In the application of SSI algorithm, asystem order must be specified for the linear model realization.In this work, the identification is performed sequentially forstate-space system orders of 2 to 250 (numbers of modes from 1

to 125). The stabilization criteria for the modal parameters are:1% for frequencies, 5% for damping ratios and 1% for ModalAssurance Criteria (MAC) of the mode shape vectors [7].

1020

3040

5060

70

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−1012

X

Y

Z

(North)

(South)

(a) isometric view.

(b) Comparison of FEM results with the experimentallyidentified mode shape (plotted along the south outer girder and

normalized to unity).

Figure 7. The identified first global mode (f = 4.99 Hz,ξ =0.84 %).

The results of the identified first global mode are given inFig. 7. It is observed that the damage localized on Span Xchanges the symmetry of the coupled mode shapes. Thoughthe identified mode shape is not as smooth as predicted bythe FE analysis, the amplification of the modal displacementsof the damaged span in comparison to the other spans is stillsignificant. Note that all mode shapes have been normalized tounity.

The modal properties of the identified second global mode aregiven in Fig. 8. It is found that the modal displacements of SpanX are larger than those of Span XI and XII, being maximumvalues 0.8 and 0.6, respectively. The difference suggests apossibly similar damage due to corrosion on the north outergirder of Span X as had been found on the south outer girderof the same span. Visual inspection on the north side is moredifficult due to the limited accessibility by the parallel bridge,which is still open to traffic. In order to quantify the damageonthe north side, another damage scenario D4 was simulated byFE analysis (Fig. 9). It is based on D3 by considering additionaldamaged elements on the north outer girder located on a similarzone as those of the south outer girder and with∆ae= 10%. It isfound that the FE mode shape of D4 corresponds better with the

1020

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−1012

X

Y

Z

(South)

(North)

(a) isometric view.

(b) Comparison of FEM results with the experimentallyidentified mode shape (plotted along the north outer girder and

normalized to unity).

Figure 8. The identified second global mode (f = 5.62 Hz,ξ = 1.23 %).

Figure 9. FE model of the Boirs viaduct with the damagescenario D4 (a south view). The damaged parts areindicated by the different colours in comparison to theremaining parts.

experimental results. Note that the identified first global modeof D4 is similar to that of D3, shown in Fig. 7(b).

In contrast to these two global modes, the other identifiedmodes are mainly local modes of an individual span. Therefore,their results are omitted here.

Figure 10. An east view of the Saaletalbrucke bridge.

Figure 11. Top views and cross-section A-A of theSaaletalbrucke bridge (units in meter).

3 OPERATIONAL MODAL ANALYSIS OF THE SAALE-TALBRUCKE BRIDGE

3.1 Bridge description

In the framework of RFCS research project RFCS-CT-2009-00027 FAtigue Damage controL and assESSment for railwaybridges (FADLESS), operational modal analysis was appliedto a steel-plate-girder railway bridge in Germany in order todetermine the modal properties of the bridge superstructure. Thecase study bridge is the Saaletalbrucke bridge in Großheringen,Germany, connecting Berlin and Munich. It consists of fivespans with similar length of about 35 meters (Fig. 10). Therearetwo similar lines in parallel, accommodating, respectively, thetwo tracks where trains move in opposite directions. The firstspan of the western line at the north end of the Saaletalbruckebridge, shown as Span I in Fig. 11, was chosen for experimentalanalysis. Some cracks have been discovered at the connectionof the cross girder to the south side of the western main girder

over the pier. The adjacent spans are weakly coupled via boththe stringers, the rails and the lower flanges of the main girders.

3.2 Test setup

Figure 12. Measurements on the upper flanges (left) and bottomflanges of the main girders(right), showing one commonreference node (left).

Within the FADLESS project, vibration measurements havebeen performed by the Structural Mechanics division of K.U.Leuven and the Institute of Structural Mechanics of theBauhaus-University Weimar on 27th and 28th of May 2010.Seven 3D wireless sensors were used to measure the top flangesof the main girders, while several 2D wired accelerometers wereused to measure the bottom flanges of the main girders (Fig.12). In order to combine the model shapes identified from thetwo systems, both wireless and wired reference sensors wereplaced at two common locations on the upper flanges of themain girders. In addition to the measurements on Span I, theadjacent Span II and one of the two main girders of Span IIIwere also measured on the top flanges with the wireless sensors.The sensor locations are numbered 1 to 45 (Fig. 11), which havebeen measured by 10 wireless setups and 6 wired setups.

Table 2. Identified natural frequencies and damping ratios ofthe Saaletalbrucke bridge.

No. f [Hz] σ f [Hz] ξ [%] σξ [%] Mode Type1 3.62 0.02 0.38 0.17 Lateral bending2 4.20 0.03 0.56 0.29 Lateral bending3 5.28 0.04 0.36 0.14 Vertical bending4 5.93 0.07 0.71 0.24 Vertical bending5 7.90 0.01 0.53 0.15 Torsion6 8.58 0.10 0.82 0.49 Torsion

The experimental eigenfrequencies, damping ratios and theirrespective standard deviations for the first six modes aresummarized in Table 2. Their type is also given. Dataprocessing and system identification is performed by thestochastic subspace identification method for ambient vibrationdata [6]. In this work, the identification is performedsequentially for state-space system orders of 2 to 500 (numbersof modes from 1 to 250). The stabilization criteria for the modalparameters are: 1% for frequencies, 5% for damping ratios and1% for mode shape vectors (MAC) [7].

The first four identified mode shapes are plotted in Fig. 13 toFig. 16. These four modes are coupled global modes, whereasthe fifth and sixth modes are mainly local modes of torsion onSpan I and II, respectively. Moreover, the identified damping

ratios are generally very low, less than 1 percent, though with arelatively large variation.

Fig. 17 and Fig. 18 show the modal displacements inboth lateral and vertical directions on the upper flanges ofthe main girders of Span I for the first and second modes,respectively. The smooth-looking mode shapes reflect the goodaccuracy of the experimental results. The experimental curvesare overlaid with the numerical mode shapes extracted from theFE model built of ANSYS shell63 elements [4] by the Instituteof Structural Mechanics of the Bauhaus-University Weimar[8]. The numerical mode shapes correspond very well withthe experimental results. The relative differenceδ f betweenthe numericalfc and experimental frequenciesfe, defined byδ f = ( fc− fe)/ fe, is less than 3%. The MAC values are alsohigh, exceeding 0.96. All mode shapes have been normalized tounity.

Figure 13. The identified first mode - lateral bending (f = 3.62Hz, ξ = 0.38 %) - isometric, top and side views.

Figure 14. The identified second mode - lateral bending (f =4.20 Hz,ξ = 0.56 %) - isometric, top and side views.

4 CONCLUSIONS

The experimental results obtained from the Boirs viaduct showthat global coupled modes of the weakly coupled multi-span

Figure 15. The identified third mode - vertical bending (f =5.28 Hz,ξ = 0.36 %) - isometric, top and side views.

Figure 16. The identified fourth mode - vertical bending (f =5.93 Hz,ξ = 0.71 %) - isometric, top and side views.

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Figure 17. Comparison between the experimental and FEMresults of the first mode (δ f = 3%, MAC = 0.97).

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Figure 18. Comparison between the experimental and FEMresults of the third mode (δ f = 2%, MAC = 0.96).

bridge are very sensitive to the relative stiffness changesofindividual spans. It can be used for damage detection andquantification of similar structures. This observation canbe used for damage assessment methods like [9]. For theSaaletalbrucke bridge, dynamic coupling effects on this type ofstructure were verified experimentally. The dynamic responsesof the bridge during train passages are now being investigated toestimate the fatigue life.

Both examples show that spans which are considered asstatically uncoupled behave differently when addressing theirdynamic behaviour. Therefore, the results of the operationalmodal analysis of an individual span shall be interpreted byconsidering the coupling effects.

ACKNOWLEDGMENTS

The research of the Saaletalbrucke bridge has been carriedout inthe framework of the RFCS-CT-2009-00027 project FADLESSwith a financial contribution of the Commission. The authorsare also very thankful for the cooperative support of this workby the project partner, the Institute of Structural Mechanics ofthe Bauhaus-University Weimar.

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[3] GeoSIG Ltd, GMS-xx GSR-IAX user manual, 07 edition, 2010,http://www.geosig.com/.

[4] ANSYS Inc., Elements Reference, ANSYS Release 11.0, January 2007.[5] W.-X. Ren and G. De Roeck, “Structural damage identification using modal

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[7] E. Reynders, M. Schevenels, and G. De Roeck, “Macec 3.1: amatlabtoolbox for experimental and operational modal analysis, report bwm-2010-05,” Tech. Rep., Department of Civil Engineering, K.U.Leuven, February2010.

[8] Leqia He, Edwin Reynders, Guido De Roeck, Volkmar Zabel,Maik Brehm,and Sofyan Ahmad, “Case study Saaletalbrucke bridge Großheringen,Germany: Report of the modal tests on 27th and 28th May 2010,”Tech.

Rep., Institute of Structural Mechanics, Bauhaus-University Weimar andDepartment of Civil Engineering, K.U.Leuven, September 2010, RFCSproject FADLESS.

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