The paper reports on the results of the modal identification of several small to medium span railway viaducts. The identification was based mainly on the free vibration of each structure immediately after the train passages. The non-linear behavior of some components, namely the ballast and the aged bearing supports, conditioned the evolution of the free vibration signals, which showed increasing values for the eigenfrequencies and lower values for the damping as far as the vibration amplitude decreased. An estimate for the ballast shear stiffness and for the influence of the superstructure (track plus ballast) in the overall dynamic behaviour could also be obtained from the measurements evaluation

Rebelo, Carlos

Rigueiro, Constança

Silva, Luís Simões da

Repositório do Instituto Politécnico de Castelo Branco

MODAL IDENTIFICATION OF SINGLE-SPAN RAILWAY VIADUCTS   Carlos Rebelo, Civil Eng. Dept, University of Coimbra  Portugal Cosntança Rigueiro,  Polytechnic Institute of Castelo Branco Portugal Luís Simões da Silva Civil Eng. Dept, University of Coimbra Portugal crebelo@dec.uc.pt Abstract The paper reports on the results of the modal identification of several small to medium span railway viaducts. The identification was based mainly on the free vibration of each structure immediately after the train passages. The non-linear behavior of some components, namely the ballast and the aged bearing supports, conditioned the evolution of the free vibration signals, which showed increasing values for the eigenfrequencies and lower values for the damping as far as the vibration amplitude decreased. An estimate for the ballast shear stiffness and for the influence of the superstructure (track plus ballast) in the overall dynamic behaviour could also be obtained from the measurements evaluation.  1 Introduction Due to the rapid increase of train speeds and/or transported loads, existing railway bridges and viaducts have to be structurally re-evaluated in order to maintain adequate safety levels under the new traffic conditions. This re-evaluation must be done according to standards (for instance Eurocode 1) whose clauses apply mainly to new structures. Therefore, for existing bridges, this poses an additional difficulty, since very often they exhibit a dynamic behavior concerning eigenfrequencies and structural damping different from those assumed in the original project, and this may decisively condition the need for strengthening/replacing of the structure. The response of railway bridges to the passage of trains depends on one side on the type of train and on its traveling speed and on the other side on the type of bridge, specially its dynamic characteristics expressed through the eigenfrequencies and respective damping. As it is well known, the situation of resonance imposed by the dynamic loads generated during the periodic passage of the wheels or groups of wheels over the bridge can induce very high accelerations in the structure.  Recently, several existing small to medium span bridges in the track Linz-Wels (Austria) were reevaluated in order to permit the increase of train speeds. In a preliminary numerical evaluation, considering conservative values for the dynamic parameters, very high vertical accelerations were computed for some of those structures. Resonance under train speeds between 200km/h and 240 km/h lead to maximum accelerations of up to 20 m/s2 in some cases. An experimental program was thus carried out in order to get a better estimation of the dynamic behavior of the bridges, concerning mainly the first vertical eigenfrequency and the corresponding viscous damping. However, the amount of measurements and the different structural types of the bridges allowed some further conclusions about the contribution of the rails and the ballast to the overall dynamic behaviour of the bridges. 2 Measurement setup 2.1 Structural layout Two types of structures were to be measured. One set was composed by several reinforced small span monolithic frames and another set contained several reinforced, prestressed and mixed single-span simply supported slabs, whith spans from 5.75 meters to 23.5 meters. Only results for this last set are here presented and discussed.  The viaducts, built in the 1970’s (see Figures 1 and 2) are composed of two twin decks laying side by side, one for each track. The ballast depth has an average of 0.60 m, varying between 0.55 m and 0.65 m depending on the slab thickness, and spans over the entire width of the two decks.  The structural layout of the prestressed concrete decks (Bridges 1, 3, 8 and 12) corresponds to one-span simply supported slab with slightly variable depth. In the case of Bridge 7 the simply supported slab is made of HEB360 steel bars filled with concrete. Bridge 11 is also simply supported and made of reinforced concrete.  The support conditions, although defined generally as simple supports, are of two types. In Bridges 1, 3, 8 and 12, the bearing supports (Figure 3), two at each extremity of the deck, are made of steel pots filled with elastomeer and can be considered free to rotate. For the other structures no specific apparatus have been used and the slab lies directly on the abutment top. There is no continuity of the slab over the supports to the abutments, except the one materialized by the superstructure composed of ballast, sleepers and rails. It is also to stress the fact that in Bridges 1, 3 and 8 the line of supports is not collinear when considering both decks as illustrated in Figure 4 and that the line of supports in Bridge 12 is skew relatively to the axis of the bridge. Table 1 in conjunction with Figure 5 summarizes the structural characteristics of the bridges. 2.2 Measurement procedures Two methods were considered for the identification of eigenfrequencies, eigenforms and damping: i) free vibration after train passages  ii) natural ambient vibration Since the traffic is intense during the daylight the second method could not be used with all its potentialities, that is, we could not use a set of reference sensors and move the other set of sensors across the structure. As a consequence the number of measurement points was limited to the number of channels available. It was decided to capture and record the signal during enough time in order to obtain a significant number of train passages, corresponding to two to five hours of continuous signal recording with at least 10 train passages.      Figure 1 – Bridge 12 (skew): general view Figure 2–Bridge7 (filled beam): general view    Figure 3 – Bearing supports Figure 4 – Bridge 8: view of the abutments area   spanwidthα=90°HL H HR Figure 5 –Structural layout  Table 1 – geometrical characteristics of the bridges according to the structural layout Bridge Span [m] Width [m] HL [m] H [m] HR [m] α [º] Type 1 23.50 5.14 0.92 1.14 0.91 90º Prestressed 3 19.50 6.49 0.97 1.10 0.84 90º Prestressed 7 9.00 4.52 0.43 0.43 0.43 90º Mixed 8 21.00 4.23 1.05 1.15 1.05 90º Prestressed 11 5.75 4.44 0.40 0.40 0.40 90º Reinforced 12 11.44 4.54 0.7 0.90 0.70 63.9º Reinforced Table 2 – Measurement points MP Bridge 1 Bridge 3 Bridge 7 Bridge 8 Bridge 11 Bridge 12 1  ●  ● ● ● 2 ● ● ● ● ● ● 3  ●  ●   4 ● ● ● ● ● ● 5 ● ●  ● ●  6 ● ● ● ● ● ● 7  ●     8 ● ●  ● ●  Figure 6 – General scheme of the measurement locations ed eigenforms and to the symmetry conditions only one half-side of each LSE® multi analyser platform and  such a way that the power ridge,  ion during the interval iii)  to each train passage. Since the m for the expected maximum acceleration her hand, the free vibration immediately after the train passages showed to be very useful. 3 Measurement results 3.1 Free vibration analysis  h  length were considered, starting from the instant when each train widt BM span MP1 ½ span ¼  spanMP2 MP3 MP4 MP5MP6MP7MP8w/2 w/4 w/4 According to the expectdeck was instrumented. Although a maximum of eight channels were available only a number of them were used to capture the vertical accelerations of the deck at mid-span and at ¼ of the span (see Figure 6 and Table 2). Nevertheless, the setup used in each bridge allowed the lower eigenforms, either flexural or torsional, to be clearly identified. The response data was acquired using the Brüel & Kjær PUrecorded for post processing. In addition, observation files were manually filled with the type of train, number of carriages and velocity, measured with a speedometer. During the post processing the signal was inspected and analyzed inspectra corresponding to the following situations could be obtained: i) the free vibration immediately after the train leaves the bii) the ambient free vibration caused by unidentified natural excitatof train passages and  the individual responseaximum signal peak input had to be set up during the train passages, the signal to noise ratio for the ambient free vibration was poor and, in addition to relatively short time histories, conditioned the results obtained from this identification method. On the otHowever, attention must be paid to the effective time after which there is no more excitation on the bridge in order to prevent the distortion of the results. In the present research the visual inspection of the time records was usually sufficient to ensure this, since the signal always became smoother after the train left the bridge.   Time istories with a fixed timeleaves the bridge. Considering the longest eigenperiod expected for the structures, that time length should be enough for the free response to decay significantly as it can be seen in Figure 7, where typical free response time histories are shown. Considering the sampling time interval used, a frequency definition of 0.125Hz was achieved.  Taking into account for each structure the entire sequence of all the time histories described above, it is possible to use a method for the parameter identification in the frequency domain such as the Peak Picking Method. The Enhanced Peak Picking Such methods implemented in the software ARTeMIS® were here used to extract the eigenmodes, frequencies and damping.  -0.4-0.20.00.20.40.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Time [seconds]Acceleration [ms-2 ] Bridge 8 Figure 7 – Typical free vibration decay at the mid-span of the bridges To assess the c k, ballast and able 3 –Eigenfrequencies and damping considering non-shifted and shifted time series ontribution of probable non-linear effects provided mainly by the tracsupports, time shifts of up to 1,5 seconds were introduced in the starting point of the time histories, maintaining the same total time length.  In this way significantly lower signal amplitudes are considered in those shifted time series when compared to the initial time considered before. In Table 3 the results from both shifted and non-shifted time series are presented.   TNon-shifted time series Shifted time series Bridge Mode F  Fre ng Mode type requency Damping[Hz] Ratio [%] quency Dampi[Hz] Ratio [%] 1st 1st  Bending 4.8 7.8 5.2 5.3 2nd 13.3 4.9 14.9 2.8 2nd Bending 3rd 16.9 2.0 17.0 1.3 1st Torsion 1  4th 27.7 1.9 30.1 0.7 3rd Bending1st 6.4 9.3 8.5 7.2 1st Bending 2nd 14.7 4.5 16.0 2.6 1st Torsion 3rd 18.5 2.5 22.2 1.9 2nd Bending 3 4th 33.7 2.8 n.a. n.a. 3rd Bending 1st 16.9 4.7 n.a. n.a. 1st Bending 2nd 25.5 0.9 n.a. n.a. 1st Torsion 7   3rd 49.0 0.7 n.a. n.a. 2nd Bending1st 5.4 6.1 5.8 5.2 1st Bending 2nd 18.8 2.8 18.7 0.8 2nd Bending 3rd 19.2 1.8 19.7 1.3 1st Torsion 8  4th 37.4 1.2 n.a. n.a. 3rd Bending1st 15.0 2.0 n.a. n.a. 1st Bending 11 2nd 13. .5 7.7 7  13. .9 6. 6  2nd 36.4 1.4 n.a. n.a. 1st Torsion 1st– 7 – 16  – 4. 2 – 16 4 – 3. Bending 3rd–4th 26.2 – 29.4 3.0 – 1.5  26.3 – 31.8  2.3 – 2.1 Torsion 5th–6th 41.4 – 43.6 2.1 – 2.2  41.6 – 44.4  1.0 – 1.6 Bending  12 7th–8th 50.7 – 51.8 0.2 – 0.2  50.7 – 51.8 0.2 – 0.3 Bending When the  pa aine m spon s a ed with 2 is skew and, therefore, the influence of the interaction between both twin plates is shown e s are based on the assumption that all the dynamic excitation in the re summarized in Table 4. Because of the insufficient total measuring time and the fact ing ambient vibration  modal rameters obt d from the ti e shifted re se historie re comparthose from the non-shifted histories two tendencies can be recognized: (i) the frequency increases and (ii) the damping factor decreases. These results are more evident in the lower modes and must be, therefore, related to the amplitudes of vibration. In fact the higher amplitudes in the lower modes mobilize mechanisms of energy dissipation related to friction in the supports and internal friction in the ballast in a stronger way than they are mobilized in the higher modes, for which the amplitudes of vibration are much lower. This also stresses the idea that the friction forces, probably mainly inside the ballast, become more important for lower amplitudes having an effect of increasing the overall stiffness of the structure. Again, this effect is less important for the higher modes. Bridge 1in the duplication of the frequency peaks corresponding to symmetrical and non-symmetrical shapes with reference to the contact plan between the plates. This effect allows the quantification of the ballast shear stiffness and is further exploited in the item concerning parameter identification. 3.2 Ambient vibration Ambi nt vibration methodstructure is of such a random type that all modes in the relevant range are excited in the same way. Although this is not a typical problem for the application of such methods, the length of the time histories corresponding to the free vibration considered before can be extended for several minutes, depending on the railway traffic, so that the effect of the free vibration induced by the train passage is dimmed.  The results athat the maximum signal peak input had to be set up for the expected maximum acceleration during the train passages, conditioning the goodness of the signal, the results are limited to the first natural frequency and to the longer span bridges. Comparing these results with those given in Table 3, the difference is to be found in the damping, resulting from the ambient vibration much lower damping values. The frequencies coincide with those given in Table 3, as expected.  Table 4 – Eigenfrequencies, eigenmodes and damping for Bridges 1, 3, 8 usBridge Mode Frequency [Hz] Damping Ratio [%] Mode type 1 1st st5.2 2.0 1  Bending 3 1stst 8.6 1.9 1  Bending stst8 1 5.8 2.7 1  Bending 4 Modal identification  de ffness distribution simple structural models were considered for each of only the rails over an extension corresponding to about the interval length of the sleepers (0.60 meters). The stiffness ks is unknown and have to be 4.1 Structural models In or r to identify the stithe bridges. The discretization was made using common plate finite elements and the supports were considered free to rotate but not free to slip, where a spring of stiffness ks was considered (see Figure 8). The continuity of the superstructure (ballast+sleepers+rails) was modeled using a single spring at the rails level with stiffness kr. In the case of the skew slab the shear stiffness Gb of the ballast is modeled through elastic springs kb. The stiffness kr can be estimated taking into account estimated by comparison with the measured frequencies. The shear stiffness of the ballast Gb is obtained directly from the comparison of the measured pairs of eigenfrequencies with those computed in the model for Bridge 12. The mass was estimated according to the mean values for the density of the concrete (2,5 ton/m3) and of the superstructure (1,53 ton/m2) RailsFigure 8 – Model for the support area and for interaction between twin skew plates 4.2 Ptat mber of parameters were considered for identification. Table 5 a ncies and the values considered for those parameters.  arameter identification As s ed before only a small nusumm rizes the computed eigenfrequeTable 5 – Results from FE models and parameter values used  Bridge Mode Frequency [Hz] Mode type Parameters 1st 4.9 1st  Bending Ec=39 GPa 2 2  Be   nd 14.0 nd nding Ks=2.6 GN/m3rd 18.4 1st Torsion Kr=2.6 GN/m1 4th 28.0 3rd Bending  1st 5.8 1st Bending Ec=39 GPa 2nd 14.9 1st Torsion Ks=2.6 GN/m  3  3rd 16.1 2nd Bending Kr=2.6 GN/m4th 32.0 3rd Bending  1st 16.1 1st Bending Ec=30 GPa 2nd 28.0 1st Torsion Es=200 GPa  7  3rd 45.3 2nd Bending  Ks=2.6 GN/m   Kr=2.6 GN/m1st 5.5 1st Bending Ec=39 GPa 2nd 15 st Torsion  8  .8 1 Ks=2.6 GN/m 3rd 22.2 2nd Bending  Kr=2.6 GN/m4th 32.3 3rd Bending  1st 14.9 1st Bending Ec=30 GPa 2nd 30.1 1st Torsion Ks=0.25 GN/m 11 /m  2nd 14. .5    Kr=0.25 GN1st – 0 – 16 Bending Ec=39 GPa 3rd – 4th 26.3 0.8 ending + Torsion  Torsion  n – 3 B Ks=2.6 GN/m 5th – 6th 37.4 – 44.0 Bending + Kr=2.6 GN/m12 Twiplates 7th – 8th 57.0 – 59.0 Bending + Torsion Gb=35 MPa kb SupportBallastSlabkr ks Ec ; Es 5 Fina rks se lway bridges were measured in order to characterize their dynamic a tion after train passages showed to be very effective for the model  those models the main parameters were the modulus of elasticity of the materials ween pairs of eigenfrequencies, which depends only on that stiffness. A   Austrian railway authorities ÖBB for the technical support and the ent setup, as well as Eng. Helena Gervásio and TDV-Austria for L I.(2003) New Eurocode Requirements for the igh Speed Railway Bridges, IABSE Symposium, [2] h, ort 002 (Conversion of ENV-1991-3 into 1991-2) (final [4] ements and system identification of plate and frame , [5] ate & Frame Bridges between Linz and Wels , [6] eraction phenomena between train, track, [7] ail s   l remaA t of single span raibeh viour. The free vibraidentification. In order to identify the stiffness distribution simple structural models were considered for each of the Bridges. In(concrete or mixed concrete-steel), and the slab end-restriction at the supports. The stiffness of those springs showed to be much similar to the axial stiffness of the rails, considering the length of the sleeper interval. Since a skew slab was also measured, it was possible to estimate the shear stiffness of the ballast analyzing the difference betvalue of Gb=35 MPa for the shear modulus was found. 6 Aknowledgements The authors would like to thankfacilities needed for the measuremthe experimental support. 7 References [1] BUCKNALDesign of HAntwerp ERRI D 214/RP9 (1999) Rail bridges for speeds over 200Km/Final Rep[3] prEN 1991- EUROCODE 1 – Part 2 (2002) Traffic loads on bridges, July 2draft) Rebelo, C & Gervásio, H (2004) Final report on the dynamic measurrailway bridges between Linz and Wels, Austria, ACIV/GIPACCoimbra, Portugal TDV-Austria (2004) Final Report of the Rolling Stock Investigations of PlMay 2004, Austria UIC leaflet: UIC 776-2R(2002) Design requirements for rail-bridges based on intbridge and in particular speed. (July 2002) Zacher M. (2000) Dynamic of Railway Bridges, 5th ADAMS/RUsers' Conference Haarlem, The Netherland

Modal identification of single-span railway viaducts

Repositório Científico do Instituto Politécnico de Castelo Branco

MODAL IDENTIFICATION 
OF 
SINGLE-SPAN RAILWAY VIADUCTS  
 
Carlos Rebelo, Civil Eng. Dept, University of Coimbra  Portugal 
Cosntança Rigueiro,  Polytechnic Institute of Castelo Branco Portugal 
Luís Simões da Silva Civil Eng. Dept, University of Coimbra Portugal 
crebelo@dec.uc.pt 
Abstract 
The paper reports on the results of the modal identification of several small to medium span 
railway viaducts. The identification was based mainly on the free vibration of each structure 
immediately after the train passages. The non-linear behavior of some components, namely the 
ballast and the aged bearing supports, conditioned the evolution of the free vibration signals, which 
showed increasing values for the eigenfrequencies and lower values for the damping as far as the 
vibration amplitude decreased. An estimate for the ballast shear stiffness and for the influence of 
the superstructure (track plus ballast) in the overall dynamic behaviour could also be obtained from 
the measurements evaluation. 
 
1 Introduction 
Due to the rapid increase of train speeds and/or transported loads, existing railway bridges and 
viaducts have to be structurally re-evaluated in order to maintain adequate safety levels under the 
new traffic conditions. This re-evaluation must be done according to standards (for instance 
Eurocode 1) whose clauses apply mainly to new structures. Therefore, for existing bridges, this 
poses an additional difficulty, since very often they exhibit a dynamic behavior concerning 
eigenfrequencies and structural damping different from those assumed in the original project, and 
this may decisively condition the need for strengthening/replacing of the structure. 
The response of railway bridges to the passage of trains depends on one side on the type of train 
and on its traveling speed and on the other side on the type of bridge, specially its dynamic 
characteristics expressed through the eigenfrequencies and respective damping. As it is well 
known, the situation of resonance imposed by the dynamic loads generated during the periodic 
passage of the wheels or groups of wheels over the bridge can induce very high accelerations in the 
structure.  
Recently, several existing small to medium span bridges in the track Linz-Wels (Austria) were 
reevaluated in order to permit the increase of train speeds. In a preliminary numerical evaluation, 
considering conservative values for the dynamic parameters, very high vertical accelerations were 
computed for some of those structures. Resonance under train speeds between 200km/h and 240 
km/h lead to maximum accelerations of up to 20 m/s2 in some cases. 
An experimental program was thus carried out in order to get a better estimation of the dynamic 
behavior of the bridges, concerning mainly the first vertical eigenfrequency and the corresponding 
viscous damping. However, the amount of measurements and the different structural types of the 
bridges allowed some further conclusions about the contribution of the rails and the ballast to the 
overall dynamic behaviour of the bridges. 
2 Measurement setup 
2.1 Structural layout 
Two types of structures were to be measured. One set was composed by several reinforced small 
span monolithic frames and another set contained several reinforced, prestressed and mixed single-
span simply supported slabs, whith spans from 5.75 meters to 23.5 meters. Only results for this last 
set are here presented and discussed.  
The viaducts, built in the 1970’s (see Figures 1 and 2) are composed of two twin decks laying side 
by side, one for each track. The ballast depth has an average of 0.60 m, varying between 0.55 m 
and 0.65 m depending on the slab thickness, and spans over the entire width of the two decks.  
The structural layout of the prestressed concrete decks (Bridges 1, 3, 8 and 12) corresponds to one-
span simply supported slab with slightly variable depth. In the case of Bridge 7 the simply 
supported slab is made of HEB360 steel bars filled with concrete. Bridge 11 is also simply 
supported and made of reinforced concrete.  
The support conditions, although defined generally as simple supports, are of two types. In Bridges 
1, 3, 8 and 12, the bearing supports (Figure 3), two at each extremity of the deck, are made of steel 
pots filled with elastomeer and can be considered free to rotate. For the other structures no specific 
apparatus have been used and the slab lies directly on the abutment top. 
There is no continuity of the slab over the supports to the abutments, except the one materialized by 
the superstructure composed of ballast, sleepers and rails. It is also to stress the fact that in Bridges 
1, 3 and 8 the line of supports is not collinear when considering both decks as illustrated in Figure 4 
and that the line of supports in Bridge 12 is skew relatively to the axis of the bridge. Table 1 in 
conjunction with Figure 5 summarizes the structural characteristics of the bridges. 
2.2 Measurement procedures 
Two methods were considered for the identification of eigenfrequencies, eigenforms and damping: 
i) free vibration after train passages  
ii) natural ambient vibration 
Since the traffic is intense during the daylight the second method could not be used with all its 
potentialities, that is, we could not use a set of reference sensors and move the other set of sensors 
across the structure. As a consequence the number of measurement points was limited to the 
number of channels available. It was decided to capture and record the signal during enough time in 
order to obtain a significant number of train passages, corresponding to two to five hours of 
continuous signal recording with at least 10 train passages. 
 
    
Figure 1 – Bridge 12 (skew): general view Figure 2–Bridge7 (filled beam): general view 
   
Figure 3 – Bearing supports Figure 4 – Bridge 8: view of the abutments area 
 
 
span
width
α=90°
HL H HR
 
Figure 5 –Structural layout 
 
Table 1 – geometrical characteristics of the bridges according to the structural layout 
Bridge Span 
[m] 
Width 
[m] 
HL 
[m] 
H 
[m] 
HR 
[m] 
α 
[º] 
Type 
1 23.50 5.14 0.92 1.14 0.91 90º Prestressed 
3 19.50 6.49 0.97 1.10 0.84 90º Prestressed 
7 9.00 4.52 0.43 0.43 0.43 90º Mixed 
8 21.00 4.23 1.05 1.15 1.05 90º Prestressed 
11 5.75 4.44 0.40 0.40 0.40 90º Reinforced 
12 11.44 4.54 0.7 0.90 0.70 63.9º Reinforced 
Table 2 – Measurement points 
MP 
B
ri
dg
e 
1 
B
ri
dg
e 
3 
B
ri
dg
e 
7 
B
ri
dg
e 
8 
B
ri
dg
e 
11
 
B
ri
dg
e 
12
 
1  ●  ● ● ● 
2 ● ● ● ● ● ● 
3  ●  ●   
4 ● ● ● ● ● ● 
5 ● ●  ● ●  
6 ● ● ● ● ● ● 
7  ●     
8 ● ●  ● ●  
Figure 6 – General scheme of the measurement locations 
ed eigenforms and to the symmetry conditions only one half-side of each 
LSE® multi analyser platform and 
 such a way that the power 
ridge,  
ion during the interval 
iii)  to each train passage. 
Since the m for the expected maximum acceleration 
her hand, the free vibration immediately after the train passages showed to be very useful. 
3 Measurement results 
3.1 Free vibration analysis 
 h  length were considered, starting from the instant when each train 
w
id
t BM 
span 
MP1 
½ span 
¼  span
MP2 
MP3 
MP4 
MP5
MP6
MP7
MP8
w
/2
 
w
/4
 
w
/4
 
According to the expect
deck was instrumented. Although a maximum of eight channels were available only a number of 
them were used to capture the vertical accelerations of the deck at mid-span and at ¼ of the span 
(see Figure 6 and Table 2). Nevertheless, the setup used in each bridge allowed the lower 
eigenforms, either flexural or torsional, to be clearly identified. 
The response data was acquired using the Brüel & Kjær PU
recorded for post processing. In addition, observation files were manually filled with the type of 
train, number of carriages and velocity, measured with a speedometer. 
During the post processing the signal was inspected and analyzed in
spectra corresponding to the following situations could be obtained: 
i) the free vibration immediately after the train leaves the b
ii) the ambient free vibration caused by unidentified natural excitat
of train passages and  
the individual response
aximum signal peak input had to be set up 
during the train passages, the signal to noise ratio for the ambient free vibration was poor and, in 
addition to relatively short time histories, conditioned the results obtained from this identification 
method. 
On the ot
However, attention must be paid to the effective time after which there is no more excitation on the 
bridge in order to prevent the distortion of the results. In the present research the visual inspection 
of the time records was usually sufficient to ensure this, since the signal always became smoother 
after the train left the bridge.  
 
Time istories with a fixed time
leaves the bridge. Considering the longest eigenperiod expected for the structures, that time length 
should be enough for the free response to decay significantly as it can be seen in Figure 7, where 
typical free response time histories are shown. Considering the sampling time interval used, a 
frequency definition of 0.125Hz was achieved.  
Taking into account for each structure the entire sequence of all the time histories described above, 
it is possible to use a method for the parameter identification in the frequency domain such as the 
Peak Picking Method. The Enhanced Peak Picking Such methods implemented in the software 
ARTeMIS® were here used to extract the eigenmodes, frequencies and damping.  
-0.4
-0.2
0.0
0.2
0.4
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Time [seconds]
A
cc
el
er
at
io
n 
[m
s-
2 ] Bridge 8
 
Figure 7 – Typical free vibration decay at the mid-span of the bridges 
To assess the c k, ballast and 
able 3 –Eigenfrequencies and damping considering non-shifted and shifted time series 
ontribution of probable non-linear effects provided mainly by the trac
supports, time shifts of up to 1,5 seconds were introduced in the starting point of the time histories, 
maintaining the same total time length.  In this way significantly lower signal amplitudes are 
considered in those shifted time series when compared to the initial time considered before. In 
Table 3 the results from both shifted and non-shifted time series are presented.  
 
T
Non-shifted time series Shifted time series 
Bridge Mode F  Fre ng Mode type requency Damping
[Hz] Ratio [%] 
quency Dampi
[Hz] Ratio [%] 
1st 1st  Bending 4.8 7.8 5.2 5.3 
2nd 13.3 4.9 14.9 2.8 2nd Bending 
3rd 16.9 2.0 17.0 1.3 1st Torsion 1 
 4th 27.7 1.9 30.1 0.7 3rd Bending
1st 6.4 9.3 8.5 7.2 1st Bending 
2nd 14.7 4.5 16.0 2.6 1st Torsion 
3rd 18.5 2.5 22.2 1.9 2nd Bending 3 
4th 33.7 2.8 n.a. n.a. 3rd Bending 
1st 16.9 4.7 n.a. n.a. 1st Bending 
2nd 25.5 0.9 n.a. n.a. 1st Torsion 7 
  3rd 49.0 0.7 n.a. n.a. 2nd Bending
1st 5.4 6.1 5.8 5.2 1st Bending 
2nd 18.8 2.8 18.7 0.8 2nd Bending 
3rd 19.2 1.8 19.7 1.3 1st Torsion 8 
 4th 37.4 1.2 n.a. n.a. 3rd Bending
1st 15.0 2.0 n.a. n.a. 1st Bending 11 
2nd 13. .5 7.7 7  13. .9 6. 6  
2nd 36.4 1.4 n.a. n.a. 1st Torsion 
1st– 7 – 16  – 4. 2 – 16 4 – 3. Bending 
3rd–4th 26.2 – 29.4 3.0 – 1.5  26.3 – 31.8  2.3 – 2.1 Torsion 
5th–6th 41.4 – 43.6 2.1 – 2.2  41.6 – 44.4  1.0 – 1.6 Bending  12 
7th–8th 50.7 – 51.8 0.2 – 0.2  50.7 – 51.8 0.2 – 0.3 Bending 
When the  pa aine m spon s a ed with 
2 is skew and, therefore, the influence of the interaction between both twin plates is shown 
e s are based on the assumption that all the dynamic excitation in the 
re summarized in Table 4. Because of the insufficient total measuring time and the fact 
ing ambient vibration 
 modal rameters obt d from the ti e shifted re se historie re compar
those from the non-shifted histories two tendencies can be recognized: (i) the frequency increases 
and (ii) the damping factor decreases. These results are more evident in the lower modes and must 
be, therefore, related to the amplitudes of vibration. In fact the higher amplitudes in the lower 
modes mobilize mechanisms of energy dissipation related to friction in the supports and internal 
friction in the ballast in a stronger way than they are mobilized in the higher modes, for which the 
amplitudes of vibration are much lower. This also stresses the idea that the friction forces, probably 
mainly inside the ballast, become more important for lower amplitudes having an effect of 
increasing the overall stiffness of the structure. Again, this effect is less important for the higher 
modes. 
Bridge 1
in the duplication of the frequency peaks corresponding to symmetrical and non-symmetrical 
shapes with reference to the contact plan between the plates. This effect allows the quantification of 
the ballast shear stiffness and is further exploited in the item concerning parameter identification. 
3.2 Ambient vibration 
Ambi nt vibration method
structure is of such a random type that all modes in the relevant range are excited in the same way. 
Although this is not a typical problem for the application of such methods, the length of the time 
histories corresponding to the free vibration considered before can be extended for several minutes, 
depending on the railway traffic, so that the effect of the free vibration induced by the train passage 
is dimmed.  
The results a
that the maximum signal peak input had to be set up for the expected maximum acceleration during 
the train passages, conditioning the goodness of the signal, the results are limited to the first natural 
frequency and to the longer span bridges. Comparing these results with those given in Table 3, the 
difference is to be found in the damping, resulting from the ambient vibration much lower damping 
values. The frequencies coincide with those given in Table 3, as expected.  
Table 4 – Eigenfrequencies, eigenmodes and damping for Bridges 1, 3, 8 us
Bridge Mode Frequency [Hz] Damping Ratio [%] Mode type 
1 1st st5.2 2.0 1  Bending 
3 1
st
st 8.6 1.9 1  Bending 
st
st
8 1 5.8 2.7 1  Bending 
4 Modal identification 
 
de ffness distribution simple structural models were considered for each of 
only the rails over an extension corresponding 
to about the interval length of the sleepers (0.60 meters). The stiffness ks is unknown and have to be 
4.1 Structural models 
In or r to identify the sti
the bridges. The discretization was made using common plate finite elements and the supports were 
considered free to rotate but not free to slip, where a spring of stiffness ks was considered (see 
Figure 8). The continuity of the superstructure (ballast+sleepers+rails) was modeled using a single 
spring at the rails level with stiffness kr. In the case of the skew slab the shear stiffness Gb of the 
ballast is modeled through elastic springs kb. 
The stiffness kr can be estimated taking into account 
estimated by comparison with the measured frequencies. The shear stiffness of the ballast Gb is 
obtained directly from the comparison of the measured pairs of eigenfrequencies with those 
computed in the model for Bridge 12. The mass was estimated according to the mean values for the 
density of the concrete (2,5 ton/m3) and of the superstructure (1,53 ton/m2) 
Rails
Figure 8 – Model for the support area and for interaction between twin skew plates 
4.2 P
tat mber of parameters were considered for identification. Table 5 
a ncies and the values considered for those parameters.  
arameter identification 
As s ed before only a small nu
summ rizes the computed eigenfreque
Table 5 – Results from FE models and parameter values used  
Bridge Mode Frequency [Hz] Mode type Parameters 
1st 4.9 1st  Bending Ec=39 GPa 
2 2  Be  
 
nd 14.0 nd nding Ks=2.6 GN/m
3rd 18.4 1st Torsion Kr=2.6 GN/m
1 
4th 28.0 3rd Bending  
1st 5.8 1st Bending Ec=39 GPa 
2nd 14.9 1st Torsion Ks=2.6 GN/m 
 3 
 
3rd 16.1 2nd Bending Kr=2.6 GN/m
4th 32.0 3rd Bending  
1st 16.1 1st Bending Ec=30 GPa 
2nd 28.0 1st Torsion Es=200 GPa 
 7 
 
3rd 45.3 2nd Bending  Ks=2.6 GN/m
   Kr=2.6 GN/m
1st 5.5 1st Bending Ec=39 GPa 
2nd 15 st Torsion 
 8 
 
.8 1 Ks=2.6 GN/m 
3rd 22.2 2nd Bending  Kr=2.6 GN/m
4th 32.3 3rd Bending  
1st 14.9 1st Bending Ec=30 GPa 
2nd 30.1 1st Torsion Ks=0.25 GN/m 11 
/m 
 2nd 14. .5 
   Kr=0.25 GN
1st – 0 – 16 Bending Ec=39 GPa 
3rd – 4th 26.3 0.8 ending + Torsion 
 Torsion  n 
– 3 B Ks=2.6 GN/m 
5th – 6th 37.4 – 44.0 Bending + Kr=2.6 GN/m
12 
Twi
plates 
7th – 8th 57.0 – 59.0 Bending + Torsion Gb=35 MPa 
kb 
Support
BallastSlab
kr 
ks 
Ec ; Es 
5 Fina rks 
se lway bridges were measured in order to characterize their dynamic 
a tion after train passages showed to be very effective for the model 
 those models the main parameters were the modulus of elasticity of the materials 
ween pairs of eigenfrequencies, which depends only on that stiffness. A 
  Austrian railway authorities ÖBB for the technical support and the 
ent setup, as well as Eng. Helena Gervásio and TDV-Austria for 
L I.(2003) New Eurocode Requirements for the 
igh Speed Railway Bridges, IABSE Symposium, 
[2] h, 
ort 
002 (Conversion of ENV-1991-3 into 1991-2) (final 
[4] 
ements and system identification of plate and frame 
, 
[5] 
ate & Frame Bridges between Linz and Wels , 
[6] 
eraction phenomena between train, track, 
[7] ail 
s 
 
 l rema
A t of single span rai
beh viour. The free vibra
identification. 
In order to identify the stiffness distribution simple structural models were considered for each of 
the Bridges. In
(concrete or mixed concrete-steel), and the slab end-restriction at the supports. The stiffness of 
those springs showed to be much similar to the axial stiffness of the rails, considering the length of 
the sleeper interval. 
Since a skew slab was also measured, it was possible to estimate the shear stiffness of the ballast 
analyzing the difference bet
value of Gb=35 MPa for the shear modulus was found. 
6 Aknowledgements 
The authors would like to thank
facilities needed for the measurem
the experimental support. 
7 References 
[1] BUCKNAL
Design of H
Antwerp 
ERRI D 214/RP9 (1999) Rail bridges for speeds over 200Km/
Final Rep
[3] prEN 1991- EUROCODE 1 – Part 2 (2002) Traffic loads on 
bridges, July 2
draft) 
Rebelo, C & Gervásio, H (2004) Final report on the dynamic 
measur
railway bridges between Linz and Wels, Austria, ACIV/GIPAC
Coimbra, Portugal 
TDV-Austria (2004) Final Report of the Rolling Stock 
Investigations of Pl
May 2004, Austria 
UIC leaflet: UIC 776-2R(2002) Design requirements for rail-
bridges based on int
bridge and in particular speed. (July 2002) 
Zacher M. (2000) Dynamic of Railway Bridges, 5th ADAMS/R
Users' Conference Haarlem, The Netherland


English

https://repositorio.ipcb.pt/bitstream/10400.11/1347/1/2005_IOMAC_CRigueiro.pdf

Modal identification of single-span railway viaducts

Abstract

Similar works

Full text

Available Versions

Repositório do Instituto Politécnico de Castelo Branco

Repositório Científico do Instituto Politécnico de Castelo Branco