S0211_A0533_Ribeiro et al

EXPERIMENTAL ASSESSMENT OF THE DYNAMIC BEHAVIOUR OF
SÃO LOURENÇO RAILWAY BRIDGE
Diogo Ribeiro
Instituto Superior de Engenharia do Porto
Porto, Portugal
[email protected]
Rui Calçada & Raimundo Delgado
Faculdade de Engenharia da Universidade do Porto
Porto, Portugal
[email protected]; [email protected]
ABSTRACT
This work concerns the experimental assessment of the dynamic behaviour of São Lourenço
railway bridge, located in the Northern line of the Portuguese railways. The experimental
work involves performing an ambient vibration test, a dynamic test for the passage of railway
traffic and a preliminary test on the track. The ambient vibration test allows the identification
of the dynamic properties of the structure, such as the natural frequencies, the modes of
vibration and the damping coefficients. The dynamic test for the passage of railway traffic
allows obtaining acceleration, displacement and deformation records at different locations of
the bridge. The preliminary test on the railway track allows the characterization of the track
geometrical irregularities and the identification of the track dynamic properties. The results of
these experimental tests will be used for the updating and validation of a Finite Element (FE)
numerical model of the bridge.
1 - INTRODUCTION
Railway bridges are structures subjected to high intensity moving loads, where the dynamic
effects can reach significant values. At present, these effects are being given greater
importance due to the increase of the circulation speed, not only in conventional lines but also
in new lines, such as the high speed railway lines.
In structures with complex behaviour, such as bowstring arch bridges, the evaluation of these
effects is usually performed by means of dynamic analyses using FE methodologies.
However, the success of the methods strongly depend on the experimental verification of the
results since simplified assumptions are made in the modeling and there are several
uncertainties concerning the material and geometric properties for establishing the FE models
of real structures.
In this context the implementation of in-situ dynamic testing of a structure provides an
accurate and reliable approach of its dynamic characteristics. These dynamic tests are
normally focused at the bridge and eventually extended to other subsystems, namely the track
and the railway vehicles. Concerning the bridge, the experimental modal analysis based on
ambient vibration tests is a usual procedure to identify the modal parameters based on
dynamic measurements. Tests carried out for the passage of railway traffic will also be a
valuable element in order to better understand the dynamic behavior of the structure.
In this paper, the results of the experimental works performed in a bowstring arch railway
bridge, the São Lourenço bridge, are presented. The experimental tests involved an ambient
vibration test, a dynamic test under railway traffic and a preliminary test performed on the
railway track. The ambient vibration test allows the identification of the modal parameters of
the bridge based on the application of two distinct output-only techniques, the Enhanced
Frequency Domain Decomposition (EFDD) and the Stochastic Subspace Identification (SSIDATA) methods. The dynamic test under railway traffic allows obtaining the accelerations,
displacements and deformations records in some locations of the bridge. Finally, the test
performed on the railway track consisted in the geometrical characterization of the track
irregularities and a dynamic test performed by means of an excitation hammer technique. The
results of these experimental tests will be used for the updating and validation of a numerical
model of the bridge.
2 - SÃO LOURENÇO RAILWAY BRIDGE
São Lourenço railway bridge is located at km +158.662 of the Northern line of the Portuguese
railways, in a recently upgraded section for the passage of the alfa pendular tilting train which
can travel at a speed of 220 km/h.
The bridge is a bowstring arch consisting of two half-decks with 42 m span, each one carrying
a single track [1]. Each deck consists of a 40 cm thick prestressed concrete slab suspended by
two lateral arches. The suspension is performed by means of metallic hangers and diagonals.
The height of the arches at the midspan of the bridge is approximately 8 m. The arches are
linked in the upper part by transversal girders with rectangular hollow section and diagonals
in double angles that assure the bracing of the arches.
The deck seats in each abutment by means of two pot bearing supports, one guided in the
longitudinal direction and other a multidirectional free sliding. The distance between the
supports is 38.4 m, and the extremities of the deck slab work as cantilevers with 1.8 m span.
In Figure 1 two general views of São Lourenço bridge are presented.
Figure 1 - General views of São Lourenço bridge
3 – AMBIENT VIBRATION TEST
The ambient vibration test allows for the identification of the dynamic properties of the
structure, namely its natural frequencies, mode shapes and damping coefficients. These
experimental data will be used for the updating of the numerical model developed for the
bridge [2].
3.1 – Measurement setup
The ambient vibration test was implemented using a technique that considers fixed reference
points and involves the use of 12 piezoelectric accelerometers PCB® model 393A03. The
ambient response was evaluated in the vertical and transversal directions, in successive
setups. Four fixed reference points and 28 mobile measurement points were considered,
located in the axes of the main girders of the deck (Figure 2 a)). Acceleration series with
duration of 10 minutes and a sampling frequency of 100 Hz were recorded for each setup. The
acquisition of the data was performed by means of a NI CDAQ-9172® system equipped with
IEPE analog input modules and controlled by a laptop (Figure 2 b)).
Attending to the reduced acceleration levels of the bridge under ambient conditions, a scatter
external excitation, through an impact hammer in several locations of the main girders of the
deck, was provided (Figure 2 c)). This technique guarantees higher signal-to-noise ratios and
consequently an increase of the coherence between the measured signals.
1/3 span
1/3 span
1/4 span
1/4 span
REF
REF
Fixed reference point
Mobile measurement point
a)
b)
c)
Figure 2 - Measurement setup: a) measurement points; b) data acquisition system; c) excitation with an impact
hammer on the main girder of the deck
3.2 – Modal parameter identification
The identification of the modal parameters of the bridge was performed using two different
output-only techniques: the Enhanced Frequency Domain Decomposition (EFDD) method, in
the frequency domain, and the Stochastic Subspace Identification (SSI-DATA) method, in the
time domain. The refereed methodologies are available in the software ARTeMIS [3].
3.2.1 - Enhanced Frequency Domain Decomposition method (EFDD)
The EFDD technique involves the Singular Value Decomposition (SVD) of the spectral
matrix at each frequency and the inspection of the curves representing the singular values to
identify the resonant frequencies and estimate the corresponding mode shape using the
information contained in the singular vectors of the SVD [4].
In Figure 3 are presented the average of normalized singular values of the spectral matrices of
all data sets using the EFDD technique. An inspection of these plots shows that the majority
of the 12 modes of the bridge are well represented. This technique allows identifying closely
spaced modes, as it occurs with the frequencies of 7.111 and 7.400 Hz, and 9.936 and
9.895 Hz. For the second case the identification was based on the first and second singular
value curves respectively.
11.300
6.016
4.437
7.111
9.936
15.720
22.050
7.400
2.340
9.895
23.040
15.210
Figure 3 - EFDD method: average of normalized singular values of the spectral matrices of all data sets
In Figure 4 are illustrated the mode shapes in correspondence with the identified frequencies.
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Mode 6
Mode 7
Mode 8
Mode 9
Mode 10
Mode 11
Mode 12
Figure 4 - Experimental mode shapes
3.2.2 - Stochastic subspace identification method (SSI-DATA)
The Stochastic Subspace Identification is a time-domain method that directly works with time
data, without the need to convert them to correlations or spectra. The SSI algorithm identifies
the system matrix of the state space model based on the measurements by using robust
numerical techniques. The advantage of the method is related to the possibility to skip
unstable and noisy modes [4].
For all measured data sets, proper state space models with order from 90 to 170 were
identified by the SSI method. The search for the best models was based on the construction of
stabilization diagrams. Figure 5 shows, as an example, the stabilization diagram associated to
a particular data set where the identified frequencies can be determined from the stabilized
poles.
Figure 5 - SSI-DATA method: stabilization diagram
3.2.3 - Comparison between EFDD and SSI-DATA modal estimates
Table 1 resumes the values of natural frequencies identified on the basis of the EFDD and
SSI-DATA methods. As shown in this table, the application of EFDD and SSI-DATA
methods led to very close estimates of the natural frequencies of the bridge.
Table 1 - Experimental natural frequencies according to EFDD and SSI-DATA methods
Mode
1
2
3
4
5
6
7
8
9
10
11
12
Frequency (Hz)
EFDD
SSI-DATA
2.340
2.327
4.437
4.439
6.016
6.015
7.111
7.104
7.400
7.430
9.895
9.766
9.936
9.885
11.300
11.310
15.210
15.160
15.720
15.810
22.050
22.030
23.040
23.050
To evaluate the correlation between the identified mode shapes using EFDD and SSI-DATA
methods the Modal Assurance Criterion (MAC) is used [5]. The MAC correlation matrix is
shown in Figure 6. It can be seen high values of MAC, i.e. above 90%, for all the modes, with
exception of modes 6, 9 and 12, which demonstrates a good correlation between the identified
mode shapes despite the use of distinct techniques. Furthermore, modes 6 and 9 that have
very close frequencies to modes 7 and 10, present the lowest values of MAC with 0.84 and
0.66 respectively. The off-diagonal MAC values between modes 4 and 8, and modes 1 and 5,
revealed the existence of a high correlation between these modes.
Figure 6 - MAC correlation matrix between EFDD and SSI-DATA methods
Figure 7 presents the values of the damping coefficients obtained for all modes by the
application of the EFDD and SSI-DATA methods and considering the results obtained from
the different experimental data sets.
3
EFDD
SSI-DATA
Damping coefficient (%)
2.5
2
1.5
1
0.5
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Mode number
Figure 7 – Damping coefficient estimates by EFDD and SSI-DATA methods
The observation of the figure enables to conclude that the damping coefficient estimates
provided by SSI-DATA method are similar to those obtained by EFDD method for modes 2,
4, 6, 7, 8 and 10. For the other modes the estimates provided by SSI-DATA method are
generally higher compared with the estimated obtained from EFDD method. Furthermore,
SSI-DATA method revealed to have a high level of uncertainty, as shown by the large
intervals of variation of the damping coefficient, and in some particular cases, such as for
modes 5 and 9, tends to clearly overestimate the estimated values for this parameter.
4 – DYNAMIC TEST UNDER RAILWAY TRAFFIC
The dynamic test under railway traffic enables to obtain acceleration, displacement and
deformation records in different locations of the bridge. The results of this test will be used
for the validation of the updated numerical model of the bridge [2].
4.1 – Measurement setup
The accelerations were measured using piezoelectric accelerometers PCB® model 393A03,
located in the main girders of the bridge deck, as illustrated in Figure 8 a). The accelerometers
were fixed to metallic plates directly glued to the girder.
The vertical displacements were measured at the reference section of the bridge deck, in the
main girder (D1) and slab (D2), and at the support (D3), as shown in Figure 8 b).
The evaluation of the vertical displacements of the bridge deck was performed using two
LVDT’s RDP® model ACT500. The body of the displacement sensors was supported by
means of a metallic tripod, fixed on the ground, and the armature, manually guided into the
body, was suspended on a L shaped bar directly connected to the bridge deck (Figure 8 c)).
Supports
1/4 span
a)
1/3 span
b)
c)
Figure 8 - Dynamic test under railway traffic: a) accelerometers; b) location of the displacements measurement
points; c) detail of the metallic tripod and the LVDT
The relative displacement at the support was measured by means of a non-contact laser
system OMRON® model ZX-LD100 (Figure 9 a)). The laser system consists in a sensor head,
which transmits and receives a spot beam laser, and an amplifier unit. The sensor head should
be positioned at a distance of 100 mm of the target and approximately in the perpendicular
direction (90°±10°) to the target surface. The target consists of a high reflective metallic plate
glued to the deck slab nearby the pot bearing. The measurement range is ±40 mm and the
resolution can easily achieve 0.01 mm.
The deformations were measured in the hanger located at the midspan, and in the arch, close
to the connection with the support block, using bounded electrical resistance strain gages
(Figure 9 b)). Each strain gage was mounted in a three-wire quarter-bridge circuit [6]. The
location of the strain gages was conditioned by safety reasons due to the proximity of the
catenary.
a)
b)
Figure 9 - Dynamic test under railway traffic: a) non-contact laser system; b) strain gage at the arch
4.2 – Results
The results concerning accelerations and displacements are referred to the passage of the alfa
pendular train at a speed of 184 km/h.
Figure 10 a) shows, as an example, the vertical acceleration record at the reference point. The
vertical peak acceleration is approximately 0.035g. The amplitude of the power spectrum
density estimate of the acceleration record, during the passage of the train and in free
vibration, is presented in Figure 10 b). The figure enables to verify that during the passage of
the train several frequencies are participating in the dynamic response, namely in
correspondence with the frequency of passage of regularly spaced groups of axles with
25.9 m spacing (f = v/d = 184/3.6/25.9 = 1.97 Hz) and the frequency of mode 2. Concerning
the free vibration, the response is essentially dominated by the frequencies of modes 2 and 3.
0.04
8
5.95
Train passage
0.03
Free vibration
6
0.01
Amplitude
Acceleration [g]
0.02
0
2.05
4
6.05
-0.01
-0.02
2
4.40
-0.03
-0.04
0
8
9
10
11
12
13
14
15
0
5
10
Time [s]
15
20
25
30
Frequency [Hz]
a)
b)
Figure 10 - Dynamic test under railway traffic: a) acceleration record; b) power spectrum density estimate of the
acceleration, corresponding to the passage of the alfa pendular train at 184 km/h
The modal damping coefficients were determined through the logarithmic decrement method,
using part of the acceleration records corresponding to the free vibration response [4].
Figure 11 illustrates the application of the refereed method for the evaluation of the damping
coefficients of modes 2 and 3, considering 15 cycles in an initial zone or in an intermediate
zone of the free vibration response.
0.008
0.002
15 cycles - initial zone
15 cycles - intermediate zone
y = 0.5443e -0.3286x
0.006
2
R = 0.9927
R2 = 0.9893
0.001
y = 0.2808e-0.3003x
R 2 = 0.915
0.002
Acceleration (g)
Acceleration (g)
0.004
0.000
-0.002
-0.004
15 cycles - initial zone
15 cycles - intermediate zone
a = 0.0364e-0.3145t
a = 0.0134e-0.2414t
R2 = 0.9232
0.000
-0.001
-0.006
-0.008
-0.002
13
15
17
Time (s)
a)
19
21
13
14
15
16
17
18
19
20
21
Time (s)
b)
Figure 11 – Application of the logarithmic decrement method for the evaluation of the damping coefficients of:
a) Mode 2; b) Mode 3
The values of the modal damping coefficients obtained for modes 2 and 3 are equal to 1.19 %
and 0.83 % for the initial zone, and 1.08 % and 0.64 % for the intermediate zone respectively.
The results evidence that the damping coefficients calculated considering the initial zone of
the free vibration response are higher than those calculated considering an intermediate zone.
This result corroborates the trend of growth of the damping with the increase of the level of
vibration. It should also be pointed that the values of the damping coefficients obtained by the
logarithmic decrement method are inside the interval of values estimated by the EFDD and
SSI-DATA methods (see Figure 7).
The vertical displacements records in the main girder and in the slab of the bridge deck are
presented in Figure 12 a). The results show that the maximum vertical displacement at the
slab, equal to 3.17 mm, is higher than the maximum vertical displacement measured at the
main girder equal to 2.81 mm. Furthermore both records are clearly dominated by a frequency
in correspondence with the frequency of passage of regularly spaced groups of alfa pendular
train. Figure 12 b) shows the vertical displacement record at the support. In this record the
maximum vertical displacement is approximately 0.22 mm. The frequency in correspondence
with the passage of the axles of the successive bogies with 2.7 m spacing (f = v/d =
184/3.6/2.7 = 18.93 Hz) revealed to be preponderant for the characterization of the dynamic
response.
2.00
Displacement (mm)
1.00
0.00
-1.00
-2.00
D1
D2
-3.00
-4.00
0
1
2
3
4
5
6
7
Time (s)
a)
0.10
Displacement (mm)
0.05
0.00
-0.05
-0.10
-0.15
Series1
D3
-0.20
-0.25
0
1
2
3
4
5
6
7
Time (s)
b)
Figure 12 – Displacement records for the passage of alfa pendular train at 184 km/h at the: a) main girder and
slab; b) supports
Figure 12 shows the deformation records in the hanger (E1) and in the arch (E2) for the
passage of intercity train at a speed of 160 km/h. The figure shows that during the train
passage the hanger is subjected to tensile deformations and the arch is subjected to
compressive deformations, with maximum values of 63.4 µm/m and -46.8 µm/m respectively.
In both cases the maximum values occur for the entrance of BS5600 locomotive in the bridge.
This vehicle, with a load of 21.3 t per axle, is clearly heavier comparing with the five Corail
carriages with a load of 11.8 t per axle.
70
Deformation ( m/m)
50
30
10
-10
-30
E2
E1
-50
-70
11
12
13
14
15
16
Time (s)
17
18
19
20
21
Figure 12 – Deformation records in the hanger and arch for the passage of intercity train at 160 km/h
Figure 13 shows the power spectral density estimates in correspondence with the deformation
records in the hanger and arch presented in Figure 12 and considering the train passage. The
peaks with higher amplitudes are related to local modes of vibration that mainly involve the
vibration of the diagonals (5.27 and 12.11 Hz) and out-of-plane vibrations of the non-braced
elements of the arches (13.28 and 13.48 Hz). The peaks with frequencies of 1.56 and 1.78 Hz
are related with the frequency of passage of regularly spaced groups of axles with 26.4 m
spacing (f = v/d = 160/3.6/26.4 = 1.68 Hz). There are also some peaks associated to global
modes of the bridge, namely with frequencies of 2.34, 4.10, 5.86 and 7.03 Hz, in
correspondence with modes 1 to 4.
0.0015
13.28
E1_Train passage [12-16]s
E2_Train passage [12-16]s
13.48
0.0010
Amplitude
1.56
5.86
12.11
1.76
3.52
0.0005
2.34
5.27
4.10
2.73
7.03
0.0000
0
5
10
15
20
25
Frequency [Hz]
Figure 13 – Power spectral density estimate for the deformation records in the hanger and arch during the train
passage
5 – PRELIMINARY TESTS ON THE RAILWAY TRACK
The preliminary tests performed on the railway track consisted in the measurement of the
geometry of the track and a dynamic test for the identification of modal parameters of the
track, namely natural frequencies and damping coefficients.
The evaluation of the track irregularities, namely in terms of longitudinal level, is crucial to
characterize the excitation that the vehicles are subjected for an adequate evaluation of the
passengers comfort. Concerning the dynamic test performed on the track, the results will be
used for the updating of the numerical model of the track subsystem that includes the rails,
rail pads, sleepers and ballast layer.
5.1 – Track geometry measurement
In the Portuguese railway network the infrastructure diagnosis for the acceptance and
maintenance of the track is provided by the track inspection vehicle EM 120 (Figure 14 a)).
This vehicle allows for the track geometry measurement, in what concerns the gauge,
alignment, cant, twist and longitudinal level, the rail profile and rail corrugation
measurements, the inspection of the rail fastenings and running surfaces, sleepers, ballast bed,
track signalling, etc., at speeds up to 120 km/h.
The measurement of the longitudinal level of the track is performed by means of an inertial
measuring system formed by a laser beam and an accelerometer installed on the bogie frame.
This system provides high accuracy results in the identification of irregularities with short and
large wavelengths [7].
Figure 14 b) shows the longitudinal level of the left and right rails in the descendent track,
between km +158.600 and +158.750 that includes São Lourenço bridge. The results
incorporate the wavelengths of the track irregularities between 3 and 70 m.
Amplitude (mm)
a)
20
Left rail
15
Right rail
Series3
10
Bridge
5
0
-5
-10
-15
158.600
158.620
158.640
158.660
158.680
158.700
158.720
158.740
Distance (km)
b)
Figure 14 - Measurement of the track irregularities: a) track inspection vehicle EM120; b) record of the vertical
profile for the left and right rails between km +158.600 and +158.750
The results show a good agreement between the longitudinal profile of the left and right rails.
The maximum amplitude of the vertical irregularities is approximately 11.9 mm, for the right
rail, and occurred approximately at the midspan of the bridge. The measured profile is
sensitive to the deformability length of the bridge, approximately equal to the span, and also
to the transition zones.
5.2 – Dynamic test
The in-situ dynamic test of the railway track was carried out by means of an excitation
hammer testing. This test consisted in the application of successive impulses on the rail head
with a hammer, and the measurement of the accelerations at the rail, sleeper and bridge deck
according to the details of Figure 19 a).
The evaluation of the dynamic properties of the track was performed by the application of an
output-only technique, as an alternative to the classical input-output techniques based on the
receptance function [8]. The applied technique assumes the excitation source as white noise,
therefore with a constant power spectrum density function, and consequently the amplitude of
the frequency response function of a one degree-of-freedom system can be considered as
proportional to the amplitude of the power spectrum density function of the response [4].
In Figure 14 b) the amplitude of the power spectrum density functions for the accelerations
measured on the rail and sleeper are presented. The figure enables to identify several natural
frequencies common to the rail and the sleeper, namely at 88.9 Hz, 270 Hz and 613 Hz, and a
frequency at 823 Hz that is exclusive of the rail and associated to the pin-pin resonance.
a)
b)
Figure 15 - Dynamic test: a) impact hammer and accelerometers; b) amplitude of the power spectrum density
function on the rail and sleeper
Figure 16 shows the average normalized power spectrum density (ANPSD) function of the
two measurement records. The identification of the damping coefficients associated to each
mode was performed by curve fitting in order to minimize the differences to the ANPSD
function. The identified damping coefficients are equal to 9.5%, 15.3%, 3.3% and 0.50% for
the first four identified mode shapes respectively. The differences observed between the
ANPSD function and the adjusted curve for the second and third peaks, namely in the
intervals [300-400] (Hz) and [450-600] (Hz) respectively, may indicate the presence of high
damped non-identified mode shapes or non-linearities in the behaviour of the system. Some
residual peaks, identified at frequencies of 693 and 739 Hz are probably related to high
damped modes or low participative modes in the measured points.
Figure 16 - ANPSD and curve fitting
6 - CONCLUSIONS
This paper describes the experimental campaign carried out on the São Lourenço railway
bridge. The results of this campaign allowed the characterization of the bridge dynamic
properties, namely its natural frequencies, mode shapes and damping coefficients, and the
corresponding dynamic response due to passage of the railway traffic. The preliminary tests
performed on the railway track enable the characterization of the track irregularities and the
identification of the track frequencies and corresponding damping coefficients.
The experimental informations will be used to update and validate the numerical models
developed for the bridge, track and vehicle that include their dynamic interaction. The
numerical models will be updated by the application of advanced optimization techniques
based on Genetic Algorithms (GA) and Adaptative Response Surface Methods (ARSM).
ACKNOWLEDGEMENTS
The present work has been funded by the Portuguese Foundation for Science and Technology
(FCT), in the context of the Research Project with reference PTDC/ECM/69697/2006. The
first author, Ph.D. student, acknowledges the support provided by the European Social Fund,
Programa Operacional da Ciência e Inovação 2010. The authors would also like to thank all
the collaboration and information provided by engineers Ana Isabel Silva, Hugo Patrício and
Marco Baldeiras from REFER.
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