observed dynamic characteristics of an overpass bridge during destructive test

8/6/2019 Observed Dynamic Characteristics of an Overpass Bridge During Destructive Test

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1 INTRODUCTION

Vibration measurement during progressive damagetest of a full-scale structure is a very rare and impor-tant learning opportunity. From such measurement,one can observe evolution of dynamic characteris-

tics, validate damage detection method, and formu-late the baseline criteria for typical structural dete-riorations. This paper describes such a study. Itincludes vibration measurement and destructive test,analyses the data and presents the results of vibra-tion analysis. Ambient vibration measurements wereconducted before, during and after introduction ofdamage. Sensitive features that can be utilized as in-dicators of damage were extracted from vibrationcharacteristics.

2 TESTED BRIDGE

The tested bridge is the S101 Overpass Bridge lo-

cated in Reibersdorf, Upper Austria, west side ofVienna, Austria. The bridge crossed over the na-tional highway A1 Westautobahn Austria. It is a

post-tensioned concrete bridge with the main span of32 m, side spans of 12 m, and the width of 6.6 m(Figure 1). The deck is continuous over the piers andis built into abutment. The bridge, built in 1960, wasa typical overpass in the national highway. Althoughthere were no known significant structural problems,

the bridge had to be demolished to allow a space foradditional lane of highway underneath. Before de-molition, series of vibration test was carried out bythe Vienna Consulting Engineers (VCE 2009). Theauthors participated in two-day measurement fromDecember 10 until 11, 2008.

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1200 12003200

470

120 360 12060

Cutting the pier

damaged pier

damaged pier

Figure 1. Destructive Test of S101 Bridge

Measurement system consists of six triaxial ac-celerometers. During two days measurement, ambi-ent vibration of bridge was measured and six sensor

Observed dynamic characteristics of an overpass bridge duringdestructive testing

D.M. Siringoringo, T. Nagayama, Y. Fujino, D.Su & C.Tandian

Department of Civil Engineering, The University of Tokyo, Tokyo, Japan

ABSTRACT: Vibration measurement and analysis of dynamic characteristics of an overpass bridge during afull-scale destructive test are described. Damage is introduced systematically by cutting one of bridge piers atthe footing level and inducing initial settlements. This type of damage is expected to simulate a conditionwhere a bridge suffers from non-uniform pier settlement. By applying time and frequency domain vibrationanalysis, as well as system identification, evolution of dynamic characteristics caused by damage is quanti-fied. The results show that changes of natural frequencies are clearly visible, thus can be used as indicator ofdamage presence, while the change in mode shapes can be used as the local damage indicator. In addition,application of novelty detection based on multivariate outlier analysis of the auto-spectra function is also dis-cussed.

Bridge Maintenance, Safety, Management and Life-Cycle Optimization Frangopol, Sause & Kusko (eds) 2010 Taylor & Francis G roup, London, ISBN 978-0-415-87786-2

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configurations were employed. Two sensors (i.e.node A and B) were kept at the same place through-out measurement to provide reference for time-synchronization. Four other sensors were the rovingsensors that moved from one end to the other end ofthe bridge (Figure 2). To measure the bridge in un-

damaged condition, three sensor arrangements wereutilized (sensor arrangement 1,2, and 3 in Figure 2).For damage cases sensor arrangement 4,5, and 6were employed. During the two-day measurement,temperature condition was relatively equal with av-erage temperature of -2

oC.

Figure 2. Sensor Arrangement

3 DAMAGE SCENARIOS

Damage was introduced to the structure by cuttingthe pier column just above the pier footing. The cutwas made twice each was approximately 5 cm layerof column. Damage 1 and Damage 2 is defined as astate where the first and second cut is made, respec-tively (Figure 3). During cutting process, a steel col-

umn was placed alongside the pier and tightened tothe pier with steel rods. A hydraulic jack was placedon bottom of the steel column to provide a tempo-rary support. Immediately after the cutting processwas completed, the temporary steel column was lo-wered gradually by releasing the pressure in hydrau-lic jack. This caused the vertical settlement of the

bridge at the location of pier column.To introduce the initial pier settlement, pressure in

hydraulic jack was released and the temporary steelcolumn was lowered 1 cm. This was followed by 1cm vertical settlement of pier (Damage 3). The set-tlement was further increased to 2 cm by further lo-wering the temporary steel column 1 cm (Damage4). Finally, at Damage 5, the steel column was low-ered until 3 cm but the total settlement of the bridgeis only 2.7 cm. From this point, no further verticalsettlement was observed. The pier column was sus-

pended completely; hence the hydraulic jack andtemporary steel column did not function anymore.During the process of damage and pier lowering,vertical settlement of the bridge at the pier locationwas recorded by geodetic leveling and laser system.

At the last stage, a steel plate was inserted to closethe gap between pier and the footing. In this condi-tion the pier rested on the plate and the stage isnamed Retrofitted stage.

Figure 3. Damage scenarios

4 VIBRATION ANALYSIS

4.1 Spectrogram Analysis

The frequency content of response was observed inthe frequency range 1-50 Hz. The dominant fre-quencies at the girder in vertical direction appear inthe range of 1-15 Hz. Figure 4 shows the spectro-gram of Reference sensor A and B throughout the

measurement. The ordinate consists of two parts: theundamaged part (frame number 1-10), and damaged

part (frame number 11 onward). In the undamaged part, one can see four distinct vertical lines repre-senting four natural frequencies within the range of3 to 14 Hz. The first line is around 4 Hz, second lineis around 6 Hz, the third and the forth line is around9 Hz and 13 Hz, respectively. Despite the fact thatamplitude of ambient vibration was small, the fre-

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quency spectra show very clear peaks indicatingwell-separated modes and suggesting that the re-cords have high signal-to-noise ratio. The four verti-cal straight lines indicate constant peaks in frequen-cies plot and small variation of natural frequencyestimates.

Unlike the undamaged part, the damaged partshows distinct variation of frequencies. Startingfrom frame number 11 one can observe the leftwardshift of natural frequencies especially the forth mode(13 Hz). The other modes show apparent shift start-ing from frame 20 onward, which correspond to thetime when the bridge experienced 2cm of verticalsettlement. Leftward frequency shift of the first, sec-ond and third modes continue until frame number34. Largest shifts were observed at the time whenthe pier was completely suspended indicating thesignificant reduction of stiffness. Starting fromframe number 35 onward, we can observe rightwardshift of the natural frequencies. For the 1

stmode, the

frequency shifted back almost to its original posi-tion, while some residual frequency shifts were ob-served for the 2

nd, 3

rd, and 4

thmodes. Note that

frame 35 corresponds to the time when the steel-plate was inserted and the structure was in the Retro-fitted stage. This result indicates that the steel-plateinsertion reduces the vertical flexibility of the struc-ture as evident by the rightward shift of the 1

stand

3rd

mode (all are bending), but not in the same de-gree as it reduces the torsional flexibility, as evident

by residual frequency shift in 2nd

and 4th

mode (tor-sional modes). Results of spectrogram analysisclearly reveal the evolution of natural frequenciesduring damage stages and can be used as indicatorsof structural damage.

Figure 4. Spectrogram showing the evolution of natural fre-quencies with respect to damage level

4.2 Modal Analysis and Bootstrapping

Global modal parameters are derived from ambientacceleration response under the assumption of sta-tionary random excitation. To extract modal parame-ters, the Natural Excitation Technique (NExT)

(James et al. 1993) and Eigensystem Realization Al-gorithm (Juang and Pappa 1985) are employed inthis study. In the NExT, the cross-correlation func-tion (CCF) between reference and roving nodes arecomputed and treated as the free-vibration re-sponses. Considering sensor arrangement, the global

system identification is performed in two parts, oneis for undamaged stage where fourteen measurementnodes are used, and the other is for damaged stage,where only six measurement nodes are used.

To investigate the effect of variability and to es-timate the confidence bounds of identified modal pa-rameters, a statistical analysis is essential. By quan-tifying statistical properties we can interpret theresults with confidence. For this purpose, the Boot-strap method (Efron and Tibshirani 1993) is em-

ployed in this study. The Bootstrap method ran-domly selects and replicates the response fromlimited number of record to create ensemble averageof larger population of response. Statistical proper-ties of the ensemble average are computed to deter-mine the bounds of uncertainty.

To implement Bootstrap analysis, large numberof CCF data set was randomly selected from theavailable time-normalized CCF data, and the CCFensembles were formed. On each ensemble, the CCFensemble average was computed, and then treated asMarkov parameter in the Hankel matrix of ERA.This procedure was repeated for large number oftimes to form a histogram of the identified modal pa-rameters. The confidence bounds of modal parame-ters are calculated by the percentile interval methodthat computes the 95% confidence limit by sortingthe modal parameters in an ordered list and definingthe value of upper and lower 2.5% percentile.

4.3 Result of Modal Analysis on Damage Stages

Table 1. Identified natural frequencies and damping ratios (val-ue in brackets denotes 95% confidence interval by Bootstrap)

_______________________________________________Mode Frequencies (Hz)

____________________________________Damage 3-4 Damage 5 Retrofitted_______________________________________________

1st Bending 3.90 (0.13) 3.65 (0.05) 3.94 (0.07)1st Torsion 5.84 (0.08) 5.22 (0.20) 5.76 (0.05)2ndBending 9.21 (0.13) 8.16 (0.39) 9.04 (0.06)2

ndTorsion 11.76 (0.31) 10.28 (0.16) 11.06 (0.44)_________________________________________________________________________________________________

_____________________________________________Mode Damping Ratio (%)

____________________________________Damage 3-4 Damage 5 Retrofitted_______________________________________________

1st Bending 1.98 (3.19) 2.10 (1.31) 2.76 (2.62)1st Torsion 2.14 (1.23) 2.72 (2.54) 1.93 (1.05)2ndBending 2.12 (1.25) 1.93 (3.91) 2.13 (0.63)2ndTorsion 1.49 (3.07) 1.23 (2.29) 1.48 (3.65)________________________________________________________________________________________________

The first four mode shapes are shown in Figure 5.Results of identification for damage stages are listedin Table 1. In this table the results are divided into

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three groups: 1) Damage 3 and 4 (frame number 16-29), 2) Damage 5 (frame 30-33) and 3) Retrofittedstage (frame 34-36).

Table 2. Changes in frequencies due to damage______________________________________________

Mode Frequency Changes (%)____________________________________Damage 3-4 Damage 5 Retrofitted_______________________________________________

1st Bending -3.01 -9.23 -2.011st Torsion -7.49 -17.31 -8.762ndBending -4.51 -15.40 -6.272ndTorsion -12.02 -23.09 -17.26________________________________________________________________________________________________

Figure 6 shows the comparisons of 95% confi-dence bound estimated by Bootstrap method andTable 2 lists the identified change of frequencies asa result of damage. It can be seen in the figure andtable that for Damage 3 and 4, natural frequencies ofthe second, third and forth modes experience signifi-cant changes as denoted by frequency changes that

are larger than the 95% confidence bound. Thesechanges despite small can be considered statisticallysignificant and be used with confidence as damageindicators. On contrary, frequency change of thefirst mode is statistically insignificant because itsvalue is smaller than the 95% confidence boundsand thus cannot be used as damage indicator. DuringDamage 5, the changes in natural frequencies of allmodes become more significant. All frequencychanges are now larger than the 95% confidence

bounds.

Figure 5. Identified mode shapes for undamaged case

Figure 6. Confidence bound of identified natural frequency

For damping ratio (Table 1), there is slight in-crease in the mean value as a result of damage. Theaveraged values of damping for all four modes were

between 1.2 to 1.5 % for undamaged structure withsmall bound of 95% confidence. These values in-crease slightly up to 2% for Damage 3, 4, and 5; andup to 2.7% for Retrofitted condition. Note, however,

that in damage condition the 95% confidence boundwere significantly larger than that during undam-aged. These large bounds indicate large variation orscatternes in damping estimates. Therefore, eventhough damage created damping change (i.e. in-creased the damping), they are statistically insignifi-cant and cannot be used with confidence as damageindicator.

4.4 Mode Shapes Local Change

Another important aspect is the effect of damage onthe mode shape. Simulation using FEM suggestedthat when damage altered the support condition, sig-nificant change in mode shapes were resulted. Oneof the two stationary points on the mode shape thatinitially located at the pier-girder connections movesvertically as the results of pier damage. This changeis understandable because vertical movement thatwas restrained by pier on footing level is now re-leased due to damage.

Observation on identified mode shapes revealssimilar outcome. Unfortunately, due to limited num-

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ber of sensor, only half-span of mode shapes can beanalyzed. To compare these half-span mode shapesof damaged bridge with the complete span modeshape of undamaged bridge, the first and secondmodes (i.e. bending and torsion) are normalized tothe maximum value that occurred in the midpoint of

the span. Mode shapes comparisons are shown inFigure 7.a and b. In both modes, we can observe lar-ger relative modal displacement at the pier-girderconnection during damage stages. The largest modaldisplacement was observed in Damage 5, when the

pier is completely suspended. In addition, duringDamage 5, node that has the highest modal dis-

placement in the torsion mode shifts toward dam-aged pier as suggested by FEM.

Figure 7.a. Effect of damage on (a) 1st Bending mode, (b) 1st

Torsional Mode

To quantify the significance of the change in mo-dal displacement, the 95% confidence bounds ofidentified mode shapes were computed for all dam-age stages. For comparison, the modal displace-ments at pier-girder connection in the first and sec-ond mode generated by FEM were also computedfor undamaged and damaged stages. For undamagedstage, their values are 0.017 and 0.03 for the first

and second mode, respectively. And for Damage 5case, the value becomes 0.47 and 0.93, respectively.A comparison of the change in modal displacementdue to damage and the 95% confidence bounds is

presented in Figure 8. For mode 1, the changes inmean values are 0.03, 0.26 and 0.07 for Damage 3

and 4, Damage 5, and retrofitted stage respectively.These changes are significantly larger than the 95%confidence bounds. For mode 2, the changes inmean values are even larger: 0.2, 0.5 and 0.29 forDamage 3 and 4, Damage 5 and retrofitted stage re-spectively. These changes are also significantly lar-ger than the 95% confidence bounds indicating thatin both modes, the changes of modal displacementon the pier-girder connection are statistically signifi-cant and can be used as damage indicator.

Figure 8. Quantification of modal displacement change causedby pier settlement

5 DAMAGE DETECTION USING

MULTIVARIATE OUTLIER ANALYSIS

The use of multivariate outlier analysis in detectingdamage has gained an increased attention recently.The main idea of this approach is to combine the useof damage-sensitive features and statistical noveltydetection such as outlier detection. Outlier is an ele-ment of data set that appears inconsistent with therest of data and thus perceived to be governed byother mechanisms. The advantage of this approachover modal-based damage detection is that it re-quires only data from undamaged structure. Basedon this data, the statistical pattern of undamagedstructure is formulated and utilized as a baseline forevaluation of future data. When the statistical prop-erty of future data is inconsistent with that of base-line, they will be considered as possible outliers.

In this study we investigate the feasibility ofauto-spectra of acceleration as damage sensitive fea-ture. The auto-spectra contain at least two basic in-formation of structure that is sensitive to damage:natural frequency indicated by spectra peaks, anddamping indicated by the sharpness or the width of

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are beneath the frequency peaks. It is a simple fea-ture that can be derived directly from ambient meas-urement and it captures changes in natural frequencyand damping simultaneously.

To implement the method, a number of data point(m) within the frequency range of interest is selected

from spectra plot and treated as a multivariate fea-ture vector. The procedure is repeated for several da-ta sets under the same undamaged condition. In or-der to provide a clear distinction between inliers andoutliers there needs to be some threshold value. Inthis study we follow closely the method by (Wordenet.al. 2000), in which the threshold value is set byMonte Carlo simulation using the following steps:

1. Create a bank of data for undamaged cond-tion. For this purpose, 100 equally-sampled data

points (m = 100) are selected as feature vector fromauto-spectra of reference A and B during undamagedstage. Data in the feature vector are within the fre-quency range of 3-7 Hz. Since there are only 10 dataframe for undamaged condition, only 20 number ofobservation (n) are available. This was consideredinsufficient. To provide appropriate mean and co-variance matrix for undamaged condition largernumber of observation is required. For this purpose,the feature vectors were randomly copied 500 times,and for each copy, Gaussian random vectors with therms of 1% of the maximum value were added tosimulate noise.

2. Compute the largest Mahalanobis squared dis-tances. The largest values of Mahalanobis distancewere calculated exclusively for each observation.This procedure was repeated for large number of tri-als (e.g. 10.000 trials in this study) and all the largestvalues are ordered. The threshold is then defined as

99.99 percentile value of the largest Mahalanobissquared distance in all trials.After defining the threshold, Mahalanobis dis-

tances for all feature vectors in each damage stagewere computed and their status as outliers or inlierswere conformed.

Figure 9 shows the values of Mahalanobis dis-tance for four damage cases. The figure consists oftwo parts, one is training set, which represent un-damaged stage, and the other is the testing sets, ob-tained from auto-spectra of reference sensors indamage stages. In the training set, the mean vectorand covariance matrix are estimated by followingthe procedure in Section 4.6 for 1000 trial. One cansee from this figure that all points in the undamaged

stage fall well below the threshold line. There is nofalse negatives observed, indicating that the thresh-old line clearly separates the condition of damageand undamaged.

For Damage 1and 2, and Damage 3 most of thepoints are detected as outliers. False positives, how-ever, are obtained from two points in each damagestages. These two points are from data sets with thefrequencies of 3.8 and 3.9 for mode 1, and frequen-

cies of 6.1 and 5.9 for mode 2, respectively. The twofalse positives data sets that are from frame 11 and12 that correspond to the time when damage is stillin progress. Therefore, it is understandable that thedamage has not changed the structure significantly.When damage has significantly changed the charac-

teristics of structure such as the case of Damage 4and Damage 5, all points are unambiguously de-tected as outliers. Note that the distance betweenundamaged points and that of damage points ofDamage 4 and Damage 5 increase as damage in-creases. This is rather expected result since the lar-ger the damage is the more auto-spectra deviatefrom the undamaged pattern. In these two cases, thedistance between outliers and threshold line can beused as indicator of damage severity.

Figure 9. Mahalanobis distance plot for each damage stage

6 CONCLUSIONS

The study has described the process of vibrationmeasurement and presented the results of vibrationanalysis. Important results of the study are summa-rized as follow:

1. A non-uniform pier settlement simulated asdamage in this study, affects global stiffnessof structure significantly. This is evident bythe significant change in frequency of low-order modes. The effects are more obvious intorsional modes than in bending modes, asindicated by larger changes in frequencies oftorsional modes than that of bending modes.

This finding can be used as an indicator ofthe presence of a non-uniform pier settle-ment.

2. Damage in the form of pier settlement alsoalters the mode shapes locally. Modal dis-

placements at the pier-girder node for dam-age cases increase significantly suggestingimmediate effect of constraint-losing at the

boundary condition. The changes are evident

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from bending and torsional low-order modesand are well predicted by FEM. Effects ofdamage on mode shapes are more obvious intorsional modes than in bending modes asindicated by larger changes in modal dis-

placement of pier-girder node of torsional

modes than that of bending modes.3. In general damping increases as the damage

level increases. Estimations from ERA indi-cate that damping in damage stages increaseup to 2.5-3% from previously 1.5% in un-damaged stage.

4. Feasibility of multivariate outlier detectionusing auto-spectra as damage features has

been investigated in this study. The resultsshow that the use of Mahalanobis distancecan detect the presence of damage at the ear-liest stage (i.e. Damage 1). When damagehas significantly changed the characteristicsof structure such as the case of Damage 4and Damage 5, all points are unambiguouslydetected as outliers indicating the clear pres-ence of damage. The distance between thre-shold line and damage points in outlier de-tection are increasing as damage becomeslarger. This distance can be used further asindicator of damage severity.

7 ACKNOWLEDGEMENT

The authors wish to express their sincere gratitude toDr. Helmut Wenzel, Robert Veit-Egerer, MonikaWidmann from Vienna Consulting Engineers (VCE)for this precious test opportunity, and acknowledge

their fruitful discussions and assistance during theauthors technical visits.

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Efron B., and Tibshirani R.J. 1993. An Introduction to theBootstrap, volume 57 of Monographs on Statistics and Ap-

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tation Technique (NExT) for Modal Parameter Extractionfrom Operation Wind Turbines, Sandia Report SAND92-1666.UC-261.

Juang JN, Pappa RS,1985. An Eigensystem Realization Algo-rithm For Modal Parameter Identification And Model Re-duction, Journal of Guidance, Control, and Dynamics, Vol.8(5): 620-627

VCE 2009. Progressive damage test S101 Flyover Reibesdorf,Vienna Consulting Engineers (VCE) Internal Report, Re-

port Nr.08/2308, Vienna Austria, May 2009Worden K., Manson G., and Fieller N.R.J. 2000. Damage De-

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observed dynamic characteristics of an overpass bridge during destructive test

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