S0211_A0533_Ribeiro et al
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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. REFERENCES [1] REFER, E.P (2003): Substituição da ponte de S.Lourenço ao km 158,662. Projecto de execução – Memória descritiva e justificativa, Lisboa (in portuguese). [2] Ribeiro, D., Almeida, P., Calçada, R. and Delgado, R. (2008): Experimental analysis and model updating of a bowstring arch railway bridge. In Proceedings of Conference Eurodyn2008, Southampton, UK. [3] ARTeMIS (2009): ARTeMIS Extractor Pro - Academic Licence. User’s Manual, Structural Vibration Solutions ApS, Aalborg, Denmark. [4] Magalhães F. (2003): Identificação modal estocástica para validação experimental de modelos numéricos, MSc. Thesis, FEUP, Porto (in portuguese). [5] Allemang, R. J. and Brown, D. L. (1982): A Correlation Coefficient for Modal Vector Analysis. In Proceedings of 1st International Modal Analysis Conference, pp. 110–116. [6] M.T. Restivo, F.G de Almeida, M.F. Chouzal, J.G. Mendes and A.M. Lopes (2007): Laboratories of instrumentation for measurement. University of Porto Edition. [7] M.M. Maynar (2008): Apuntes de introduccíon a la Dinâmica vertical de la vía y a las Señales digitales en ferrocarriles. Escuela de Ingenieros de Caminos, Canales y Puertos de la Universidad Politecnica de Madrid (in spanish) [8] De Man, A.P. (2002): DYNATRACK – A survey of dynamic railway track properties and their quality. PhD Thesis, Technical University Delft, DUP Science, Delft University Press, Netherlands.