Engineering Structures 34 (2012) 483–494

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Engineering Structures

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Damage assessment of concrete structures through dynamic testing methods.Part 2: Bridge tests

Stefan Maas a,⇑, Arno Zürbes a, Danièle Waldmann a, Markus Waltering a, Volker Bungard a, G. De Roeck b

a University of Luxembourg, Research Unit Engineering Sciences, 6 rue Coudenhove Kalergi, L-1359 Luxembourg, Luxembourgb Catholic University Leuven, Department Civil Engineering, Kasteelpark Arenberg 40, Bus 2448 B-3001 Heverlee, Belgium

a r t i c l e i n f o a b s t r a c t

Article history:Received 13 July 2010Revised 23 August 2011Accepted 1 September 2011Available online 13 November 2011

Keywords:Damage assessmentBridge testsConcrete structuresModal propertiesLinear and non-linear characteristics

0141-0296/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.engstruct.2011.09.018

⇑ Corresponding author. Tel.: +352 466644 5222; faE-mail address: stefan.maas@uni.lu (S. Maas).

The present paper is split into two parts: in the first part the different dynamic damage indicators aredefined and applied to beam and slab structures under laboratory conditions, whereas the present secondpart deals with experiments carried out on two real post-tensioned bridges. The damage indicatorsdefined in part one are based on swept sine excitation and reveal the drop of the eigenfrequencies, thechanges in damping, the varying dependency range of the first eigenfrequency on excitation force ampli-tude and the occurrence of higher harmonics, which changed the Total Harmonic Distorsion (THD) and aspecial transfer-function called TF or FRFsmall. In the first part it was proved that the amount of nonlin-earities varies with damage and that harmonic excitation is favorable for good test conditions. In the lab-oratory this can easily be done using an electric or hydraulic shaker, but on real bridges this kind ofexcitation becomes more complicated due to the higher forces and the necessity to provide counter bear-ing for any shaker system.

That is why two machines were designed and used to excite big structures harmonically, e.g. realbridges in this part. The different indicators are applied to assess the state of two post-tensioned bridges,which had been in good order and condition before artificial damage in multiple steps was caused. Itturns out that the decrease in the eigenfrequencies is the most important damage indicator, providedtemperature and mass dependant effects can be eliminated. All other indicators may be used as supple-ments to give correct tendencies, but no strict limits.

� 2011 Elsevier Ltd. All rights reserved.

1. Mobile excitation systems

The development of two different mobile exciter systems is ex-plained, because a swept sine excitation with constant amplitudeis obligatory for the used non-linear methods.

A conventional shaker system may be used, but a support vs.ground in the case of large bridges is not evident as is highlightedin Fig. 1.

A big mass with a soft spring is used as dynamic support in spacefor the first exciter system. The soft-spring-mass system was de-signed with an eigenfrequency of fo = 1 Hz, so that approximatelyfrom above 2fo = 2 Hz on the mass serves as a ‘‘dynamic support inspace’’ for the shaker due to the high inertia, i.e. the shaker is work-ing against the resting mass pressing the three load cells against theground. Hence the system may be called ‘‘seismic exciter’’, and theprototype according to Fig. 1(right side) is shown in Fig. 2. There isa closed frame, and a big mass (a screwed package of steel plates)is oscillating in four soft springs.

ll rights reserved.

x +352 466644 5200.

As this seismic exciter system is limited to frequencies above2 Hz and relative low force amplitudes (here below 2.7 kN due tothe electric shaker used) a second system based on unbalance exci-tation was designed, using the soil compaction technology.

A pair of eccentric masses (m) rotating in opposite directions (Ref.to Fig. 3), a so-called vibrating box, is only generating a vertical forceas the horizontal components of the centrifugal forces sum up tozero. The resulting force amplitude of one box is 2meX2 withX = 2pf, where f is the rotational frequency of the shaft and e theeccentricity of the masses m with respect to the shaft. By combiningtwo of these boxes the total force amplitude Ftotal = 2meX2(1 + cosa)can also be controlled. The constructional parameters, i.e. the mass(m), the eccentricity (e) or the rotational speed (X), need not bechanged, only the phase angle (a) between the two boxes.

This principle of Fig. 3 was realized using special electric motorsdesigned for unbalanced excitation. Two of these exciters were builtas prototypes and mounted in piggyback style as shown in Fig. 4. Thesmall one on top is used for frequencies from 20 to 50 Hz and the big-ger one beneath for frequencies from 0 to 25 Hz, without them run-ning at the same time.

Both of the presented exciters are able to change the excitation-frequency finer than 0.1 Hz from the controller side. Due to the

Fig. 1. On the left we explain why a simple frame cannot be used as support. On theright side a closed frame with a spring-mass-element is used as ‘‘dynamic supportin space’’ for this ‘‘seismic exciter’’.

484 S. Maas et al. / Engineering Structures 34 (2012) 483–494

inertia effects of the real machines, there is always a gliding tran-sition from a distinct frequency to the next. So a resolution of0.1 Hz of the reference signal does not guarantee this resolutionfor the actual signal. Anyway, the force is measured at the excita-tion point and this resolution depends only on the data acquisitionsystem. Here all data were sampled at 2000 Hz and then post-processed off-line.

Fig. 2. The prototype of the ‘‘seismic exciter’’ we designed, its ke

All measurements presented in this paper were done with asweep rate of 0.02 Hz/s and sampled at 2000 Hz and then post-pro-cessed. The duration of the measurements varied from 2 up to25 min. The FRFs were calculated using time intervals of 40 s, and80% were overlapping. They were Fourier-transformed and thenaveraged. The final resolution in the frequency range was 0.025 Hz.

As shown in Figs. 2 and 4, these machines make a controlledexcitement of large structures with swept sine force at constantamplitude possible, including a precise measurement of the excita-tion force.

2. Tests on the bridge ‘‘Deutsche Bank’’

The first tests we performed were on the ‘‘Deutsche Bank’’bridge, a three-span concrete bridge with a total length of 51 m,post-tensioned by 29 tendons with subsequent grouting (Fig. 5).This bridge was an ideal test object regarding artificial ageingand simulated corrosion as it was to be demolished due to changesin urban planning.

First a visual inspection was done which revealed no damage,followed by static load tests with trucks to assess the structurein a traditional way. The bridge was successively loaded with 37-ton semitrailers. Four different load cases (LC) were defined for 6different damage scenarios.

LC-1 = 37 tons (1 semitrailer), LC-2 = 111 tons (3 semitrailers),LC-3 = 148 tons (4 semitrailers) and LC-4 = 222 tons (6 semitrailers).

y characteristics and a sample of one measured force signal.

Fig. 3. The principle of a controllable harmonic unbalance-exciter.

Characteristics

• frequency range 0 to 50 Hz

• forces of 10 kN and more

• amplitude et frequency adjustable

• framework ≈ 1m x 1m x 2 m

• weight ≈ 3 t

force sensor

eccentric mass (cap dismounted)

sinus,f=const.

sinus, f=variable« swept sine »

Sample of measured force signal (f= 6Hz, = 11 kN)^F

Fig. 4. The second prototype: two unbalanced exciters mounted in piggyback style and a sample of one measured force signal.

S. Maas et al. / Engineering Structures 34 (2012) 483–494 485

Fig. 5. The investigated bridge and the cross-section.

Fig. 6. Position of the 4 semitrailers for LC-3: four trucks with total load of 148 tons.

Fig. 7. The 9 tendons, which were cut at location C and later at locations B and D.

486 S. Maas et al. / Engineering Structures 34 (2012) 483–494

After an initial test several tendons were cut locally at differentpositions to simulate damage due to corrosion. The different dam-age scenarios #1 to #6 are defined as follows:

#1. initial state without damage,#2. initial state after removal of asphalt which weight was about

170t,

Fig. 9. Detail of tendon cut from bottom (C).

Fig. 8. The tendons cut at location C from the bottom side.

Fig. 10. Cutting at locations B and D from top.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

#1 #2 #3 #4 #5 #6scenario

defo

rmat

ion

[mm

]

Increasing damagewith asphalt

withoutasphalt

Fig. 11. Vertical static deformation in the center of the mid-span (location C) for alldamage scenarios. Loading with four trailers (LC3).

0.0

20.0

40.0

60.0

80.0

100.0

#1 #2 #3 #4 #5 #6scenario

stra

in [

µm

/m]

Increasing damagewith asphalt

without asphalt

Fig. 12. Strain in passive reinforcement in the center of the bridge (bottom side) forall damage scenarios, approximately 1.50 m beyond the center line (location C) fordamage scenarios #1 to #6.

Fig. 13. Experimentally identified modes (with Global Polynomial Method) forscenario #2 using swept sine excitation. In total, there were 68 measuring points oneach side of the bridge (in sum 136) equally spaced at a distance of 0.75 m.

S. Maas et al. / Engineering Structures 34 (2012) 483–494 487

#3. cutting of one tendon (No. 15, Figs. 5 and 7) in the middle atlocation C (Fig. 7) from bottom side (Fig. 9),

#4. cutting of five tendons (No. 7, 13, 15, 17, 23) at location C(Fig. 7) from bottom side,

#5. cutting of nine tendons (No. 5, 7, 9, 13, 15, 17, 21, 23, 25) atlocation C (bottom side),

#6. cutting of nine tendons (No. 5, 7, 9, 13, 15, 17, 21, 23, 25) atlocations B from top side and C from bottom side and D fromtop side (Fig. 8).

Due to the time restrictions and the safety regulations for allpeople involved, no further damage was possible before demolition.

Fig. 6 presents the arrangement of the semitrailers and Figs. 8–10 the cutting of tendons in the middle of the mid span (location C)and above the intermediate supports (locations B and D).

It can be noticed that the static deformations for damage sce-nario ‘‘#1 – initial state’’ and damage scenario ‘‘#2 – without as-phalt’’ are approximately the same (Figs. 11 and 12). This meansthat the stiffness of the bridge with and without asphalt, respec-tively, is nearly the same. This is an important fact proving thatthe asphalt shows nearly no static stiffness/influence, contrary tothe dynamic tests, as is shown subsequently in Fig. 15.

mode 1-B1 4.5 Hz

mode 2-T15.1 Hz

mode 3-T2 11.0 Hz

mode 4-B2 12.3 Hz

Fig. 14. Calculated modes for scenario #2 (finite element-model).

0200400600800

100012001400160018002000

0 20 40 60 80

Tens

ile s

tres

s [M

Pa]

Percentage of cut tendons [%]

Calculated stresses in the tendons

Pont Dt. Bank

Slab element#4#3#2

#5 #6

#7

3/29 6/29 9/29

stop

Cracking start #6

Fig. 16. Calculated stresses in the tendons for the ‘‘Deutsche Bank’’ bridge and forthe slab element (see part 1) vs. percentage of cut reinforcement.

488 S. Maas et al. / Engineering Structures 34 (2012) 483–494

Although no cracks occurred, Figs. 11 and 12 show an increaseby about 15% in the vertical deformation compared to damage sce-nario #1 to #5 and an increase by about 35% in the longitudinalstrain of the passive reinforcement at position C. These tendencies

Fig. 15. Transfer functions for different damage scenari

towards increasing deformation indicate damage; however, theyare very small compared to the measurement accuracy and the le-vel of damage. Supposing that damage was unknown and measure-ments were done over a long period of time, i.e. #6 many years

os and two force amplitudes of 900 N and 9900 N.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

#1 #2 #3 #4 #5 #6scenario

[%]

900N9900N

Increasing damagewithasphalt

without asphalt

Fig. 17. Damping values for mode 1 for different excitation force amplitudes vs.damage scenario.

0

0.5

1

1.5

2

2.5

3

#1 #2 #3 #4 #5 #6Varia

tion

of th

e am

plitu

de d

epen

denc

yra

nge

from

900

to

10 0

00N

[%]

Damage scenario

Fig. 18. Amplitude dependency range (Ref. to Figs. 4 and 7, part 1) vs. damagescenario.

Fig. 19. Total Harmonic Distorsion (THD) for two different force amplitudes and all6 damage scenarios.

S. Maas et al. / Engineering Structures 34 (2012) 483–494 489

after #2, than an increase by 15% in vertical deformation would notreveal that 9 tendons out of 29 (�1/3) have failed. The straingauges are more sensitive, but only if they are located near thedamaged area.

Fig. 13 shows experimentally identified modes based on FRFmeasurements at 136 points equally spaced on both sides of thebridge. The excitation was done with the electric shaker shownin Fig. 2 at a force of 2700 N. The calculations for the modes inFig. 14 were done ad hoc with a linear finite element model andwithout any special up-dating procedure to match the measure-ments. The largest variation between measurement and calcula-tion in the eigenfrequencies are in mode 3-T2 with 7.5%. Thisdeviation between measurement and calculation is not acceptableas the variations due to damage are in the same order of magnitudeand, therefore, precise measurements of the undamaged state arehighly recommended as reference. Ad hoc calculations which aredone afterwards to describe the undamaged state do not seem tobe sufficient. Of course, these measurements – if available – mayalso be used for a precise calibration of finite element models.

Fig. 15 shows the transfer-functions and hence the change inthe eigenfrequencies for damage scenarios #1 to #6. In scenario#1, the eigenfrequency is lower because the asphalt adds moremass than stiffness, so that the removal of the asphalt from #1to #2 has nothing to do with damage and consequently shouldnot be considered here. As already stated (Ref. to Fig. 11), it isimportant to note that the asphalt changed the dynamic thoughnot the static characteristics of the bridge. A very slight decreaseby 1% in the eigenfrequencies from scenario #2 to #5 is visible,showing a very small amount of stiffness reduction. However, anincrease by 2% from #5 to #6 followed, a trend which corresponds

to the results from the static tests (Ref. to Figs. 11 and 12) andwhich cannot be explained yet. Other researchers observed thesame phenomenon, for instance on the I-40 Bridge in NewMexico [6], for which all data can be downloaded [7]. In chapter4 of this article the temperature influence is briefly discussed.Though all tests on the ‘‘Deutsche Bank’’ bridge were carriedout during 10 days in autumn and with no significant weatherchanges, the exact air and structure temperature was notmonitored, unfortunately.

As no cracks appeared in the bridge although approximatelyone third of the tendons were cut, these small differences in theeigenfrequencies cannot be used as damage indicator. The sectionremained uncracked as the removal of the asphalt (170t)discharged this bridge sufficiently so that stresses did not exceedtensile strength of concrete, despite the local reduction of prestressforce.

Fig. 16 shows the results of a calculation of the tensile stress onthe remaining middle-part tendons. These calculations were doneboth for the ‘‘Deutsche Bank’’ bridge and the slab-elements pre-sented in the first part of this paper. At least for the slab elementthis calculation has proved to be correct as the slab failed after84% of the tendons has been cut in scenario #8 and the calculatedstress had exceeded the given tensile strength of the tendons(1800 MPa). Now, when we look at the point when 9 out of 29 ten-dons (=31%) were cut, we note a less than 2% reduction of theeigenfrequencies for the slabs (#4) in part one (Fig. 17) and areduction by approximately 1% for the ‘‘Deutsche Bank’’ bridgehere in part two (Fig. 15). There is a correlation in the shape ofthe two curves in Fig. 16, though the absolute stress level dependson the amount of prestress and type of construction.

This underlines that the amount of damage in the DeutscheBank bridge was relatively low due to the asphalt discharge.Cracking of concrete and a reduction of stiffness would have ap-peared at higher levels of damage and shortly before the bridge’scollapse, which is indeed a serious problem with this type of con-struction with its post-tensioning and grouting.

Figs. 17–20 show the damage indicators defined in part one andapplied to this bridge. The damping values in Fig. 17 do not showsignificant variations.

In Fig. 18, the amplitude dependency ranges are shown, i.e. therelative variations in percent of the eigenfrequencies with excita-tion force amplitude (Ref. to part one of this article, especiallyFigs. 4, 7 and 20). As it can be easily seen, these variations donot show a clear tendency.

Fig. 19 shows the Total Harmonic Distorsion (THD) as definedin Eq. (2) of the first part. It is the ratio of the first higherharmonic to the fundamental frequency, considering only thesystem output.

Fig. 20. Analysis of higher harmonics; excitation from 3 to 5.8 Hz with 2700 N force amplitude.

490 S. Maas et al. / Engineering Structures 34 (2012) 483–494

The THD is below 0.6%, which corresponds approximately tothe level measured in the laboratory tests when cracking started(Figs. 9 and 21 in part one). Thus, no cracking occurred, and,when falling below this level, the THD cannot separate and allo-cate the damage scenarios.

Fig. 20 presents measurements concerning the special trans-fer-function, trying to reveal the higher harmonics with the func-tion TF = FRFsmall (Ref. to Eq. (3) and Figs. 11 and 22 in part one).The yellow area in Fig. 20 shows the frequency range outsidenoise, where the first higher harmonic of the first eigenfrequencycould occur.

The variation of the damping, the amplitude dependency range,the THD and the transfer-function method presented in Figs. 17–20do not show a clear direction and underline that it was unlikelythat the bridge would crack, i.e. undergo severe and detectabledamage.

Fig. 21. ‘‘JFK’’ bridge – one-span prestressed concrete box girder bridge.

Fig. 22. Photo with damage of tendons and main concrete girders.

Fig. 23. Sketch showing the damaged areas at both sides.

Fig. 24. Laid bare tendons.

Fig. 25. Damage of concrete & tendons.

0

0,5

1

1,5

2

2,5

3

3,5

#1 #2 #3 #4 #5

Def

lect

ion

z[m

m]

Damage scenario

Fig. 26. Vertical deformations of the bridge for all damage scenarios under ownweight.

S. Maas et al. / Engineering Structures 34 (2012) 483–494 491

3. Tests on the bridge ‘‘Avenue John F. Kenedy (JFK)’’

We were given the opportunity to investigate another pre-stressed concrete bridge (post-tensioning with grouting) onAvenue John F. Kennedy (JFK) in Luxembourg (Fig. 21).

As shown in Figs. 22–25, the one-span box girder bridge (9 ver-tical webs, each one containing 5 tendons = 45 tendons in total) of29-m length was gradually damaged in 4 steps by demolishingconcrete and tendons on both sides of the superstructure.

The following damage scenarios had been accomplished:

#1. initial case (without asphalt ayer),#1a. initial case with a two excavators on the bridge (100t of

additional mass),

#2. cutting of 2 tendons at both sides,#3. cutting of 5 tendons at both sides,#4. cutting of 10 tendons and 2 concrete main girders at both

sides,#5. cutting of 4 concrete main girders at both sides with 10 ten-

dons cut at one side and 18 tendons cut at the other side. Inscenario #5, nearly half of the bridge width was destroyedover a distance of 3 m from both ends. This substantial dam-age led to cracking though there was only own weight!

When investigating the vertical deformation of the structure bycutting the tendons and demolishing the concrete, it was obviousthat the deflections increased significantly with the degree of dam-age, especially when cracks occurred, as presented in scenario #5.Fig. 26 shows the vertical deflections in the middle of the structurefor all damage scenarios under dead load.

In scenario #3, a reading error of the mechanical dial gauges(resolution of 1/100 mm) obviously occurred, but it was impossibleto redo the measuring due to restrictions at site. In parallel thebridge was excited harmonically in order to investigate the dropof the eigenfrequencies, the amplitude dependency of the modalparameters and the occurrence of higher harmonics. Frequency re-sponse functions in the range of the first eigenfrequency measuredfor different force amplitudes are shown plotted for the differentdamage states in Fig. 27.

The Fig. 27 shows that there are nonlinearities and considerablereductions (�15%) with damage. At first glance, this observationseems to be banal. However, discovering that an additional 100-ton load (two excavators) has a stronger influence on the modes(�17%) than any damage makes it quite important. As a conse-quence static or dynamic tests have to be evaluated under definedconditions, including traffic loading.

Fig. 28 shows that, with increasing damage, the first eigenfre-quency decreases by about 15% (Fig. 27) and leaves no doubt thatstiffness was reduced already from scenario #2 on. This is of coursea consequence of this type of destruction of concrete and reinforce-ment, which is not equivalent to corrosion.

Damping values in Fig. 29 do not vary considerably, but here inthis special case, where concrete and reinforcement were de-stroyed, this is likely as micro-cracking of concrete has an increas-ing effect while the removal of material affects the bridge in theopposite way. From scenario #5 onwards, severe cracking startsand damping rises slightly.

The same applies to the variation of the amplitude dependencyrange, shown in Fig. 30. Severe cracking starts scenario #5 and be-comes visible.

THD in Fig. 31 (corresponding to Fig. 19) is only capable of sep-arating the cracked scenario #5 from the uncracked (#1 to #4). Thetransfer-function method in Fig. 32 reveals an increase in the firsthigher harmonic in scenarios #4 and #5.

4. Temperature dependency of the tests

Several researchers [1–4] mention an enormous dependency ofthe eigenfrequencies of bridges on air temperature, ranging be-tween 0.1% and 0.6% per �C. We analyzed a bridge in Luxembourgwith even above 1% per �C [5]. One origin is a strong dependency ofYOUNGs modulus of asphalt on temperature, but also boundaryand soil effects play an important role as they are independent ofdamage. It needs to be highlighted that, due to the temperature’sstrong influence, measuring the air and structure temperature ismandatory. Adjustments have to be made if temperature cannotbe maintained for all comparisons. This can only be done if mea-surements at different temperatures have been made and the sen-sitivities for the corresponding modes are known. Long and cloudy

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

#1A #1 #2 #3 #4 #5scenario

[%]

Fig. 29. Damping values [%] for the first mode measured with an excitation force of900 N.

Fig. 27. FRFs in the range of the first eigenfrequency measured for different force amplitudes (inducing the max. calculated stress amplitudes in the concrete) and differentdamage scenarios.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

#1A #1 #2 #3 #4 #5scenario

[%]

Fig. 28. Relative decrease in the first eigenfrequency related to the undamagedstate #1, 900 N excitation force.

1.4

1.6

1.8

epen

denc

y0

N [%

]

492 S. Maas et al. / Engineering Structures 34 (2012) 483–494

time periods with low day/night variations are optimal for a homo-geneous temperature distribution over the structure to overcomegradients due to the high inertia of concrete and steel, for instancesuccessive cloudy days in autumn [5].

0

0.2

0.4

0.6

0.8

1

1.2

#1A #1 #2 #3 #4 #5

Varia

tion

of th

e am

plitu

de d

rang

e fr

om 9

00 to

10

00

Damage scenario

Fig. 30. Amplitude dependency range (corresponding to Fig. 18) vs. damagescenario.

5. Practical experience and comments of the authors

In order to detect damage dynamic testing of concrete struc-tures is a quick and easy-to-apply method, which may be used asan alternative or addendum to visual or static testing or any othermethod. However, the interpretation of the results has to be donecarefully and a number of requirements have to be fulfilled.

The mass-loading has a very big impact, e.g. for bridges traffic,rain or snow and the thickness of the asphalt layer. Fig. 27 shows,this trivial yet important fact. In chapter 4, temperature effects are

Fig. 31. Total Harmonic Distortion (THD) for 3 force amplitudes and all damagescenarios.

S. Maas et al. / Engineering Structures 34 (2012) 483–494 493

cited due to their importance for any practical application. Theinfluence of these two disturbing parameters has to be eliminated,by either maintaining them or by correcting the measured data,which is not always trivial.

We recommend inspections with dynamic tests in arbitrarytime intervals and compare the actual results with the referencevalues with known mass-loading, temperature and excitation forceamplitude.

If the analysis of the dynamic parameters shows significantchanges from test to test, a more detailed inspection becomes

Fig. 32. Analysis of Higher Harmonics with the transfer-function method for the fir

necessary. This could be either an extended visual control, poten-tially with magnifying class or an optical crack width ruler, or astatic or a more extended dynamic one boasting many measure-ment points for the determination of the exact mode-shapes.

Finally, and this is independent of the type of inspection, itshould be highlighted again that the behavior of passively rein-forced concrete is different from strongly prestressed concrete.For the latter, the surest criterion are the cracks, which appear verylate though, i.e. shortly before collapse. Therefore, some countriesrenounce from using the cementitious grouting of the tendons incase of post-tensioning, in order to have the option of a laterinspection and replacement, a clever approach according to us.

6. Conclusions

In the first part of this paper some damage indicators were de-fined and tested on laboratory structures, whereas in this secondpart they were applied to two real bridges.

An important conclusion of this article is the considerable non-linearities and boundary conditions, which influence the measuredmodal properties.

There is a dependence on the excitation force amplitude whichreached 3% of the eigenfrequency here and, therefore, is quite impor-tant for damage assessment. A precise swept sine excitation withforce amplitude control is recommended and special designed mo-bile exciters are presented here to overcome this problem by main-taining the excitation force at a constant level. These exciters may beused on any old and new object. Compared to monitoring systems

st eigenfrequency. Excitation with a swept sine force of 2700 N from 3 to 6 Hz.

494 S. Maas et al. / Engineering Structures 34 (2012) 483–494

triggered by ambient excitation, the advantages are lower costs anda precise control and measurement of the excitation force. Measuredreference values from the undamaged situation are highly recom-mended, because the precision of ad hoc numerical finite elementsimulations without precise up-dating is insufficient, though calcu-lations are very helpful for many other analyses.

In this case the most sensitive and easiest damage indicator wasthe eigenfrequencies, however, the analyses should not be limitedto them. From the measured data of a few points (DOFs) modaldamping, THD and the transfer-function method may also be di-rectly extracted. By repeating the measurement for several forceamplitudes, which takes only a few more minutes if the systemis already installed on the site, it is possible to calculate the varia-tion of the amplitude dependency, an additional nonlinear damageindicator. All these additional indicators show tendencies but nosharp limits.

On the ‘‘Deutsche Bank’’ bridge none of these indicators re-vealed the important artificial damage as the prestressed concretedid not crack at all. In the laboratory tests, only the cracking chan-ged the damping and stiffness characteristics of the structure andso the measured dynamic and static indicators. On this bridge,there was no cracking detected, which confirms the observationsdescribed above.

On the second bridge, the first eigenfrequency decreased by 15%and while the static deflection increased also considerably. Thecracking occurred in the last damage scenario and these twoparameters were the most sensitive damage indicators.

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