IOMAC' May Guimarães - Portugal UPDATING AND VALIDATION OF THE FINITE ELEMENT MODEL OF A RAILWAY VIADUCT BASED ON DYNAMIC TESTS

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1 IOMAC'13 5 th Internatonal Operatonal Modal Analyss Conference 2013 May Gumarães - Portugal UPDATING AND VALIDATION OF THE FINITE ELEMENT MODEL OF A RAILWAY VIADUCT BASED ON DYNAMIC TESTS Joel Malvero 1, Dogo Rbero 2, Ru Calçada 3, Ramundo Delgado 4 ABSTRACT Ths paper descrbes the calbraton and expermental valdaton of the numercal model of a ralway vaduct wth precast deck located n the Portuguese ralway network. The three-dmensonal numercal model used to evaluate the dynamc behavor of the structure for the passage of Alfa Pendular trans s presented. The calbraton of the numercal model s performed by an optmzaton process based on the applcaton of a genetc algorthm. The dynamc test under ralway traffc allows obtanng the dynamc response n terms of dsplacements and acceleratons at dfferent deck locatons for the passage of Alfa Pendular tran. Ths dynamc test shows the exstence of a non-lnear behavour of the vaduct s supports. The calbrated model was valdated based on a comparson between numercal and expermental responses and a very good correlaton was obtaned. Keywords: ralway vaduct, dynamc test, ralway traffc, model updatng, valdaton 1. INTRODUCTION Ralway brdges and vaducts are structures subjected to hgh ntensty movng loads, where the dynamc effects can reach sgnfcant values. In the last decades, these effects have been great mportance due to the ncrease of the crculaton speed, not only n conventonal lnes but also n hgh speed lnes. In hgh speed ralway lnes the dynamc effects tend to ncrease consderably as a result of the resonance phenomena orgnated by the perodc loadng assocated wth the passage of regularly spaced axles groups of the trans [1]. The dynamc analyses are usually based on fnte element numercal models of the structure that nvolves assumptons and smplfcatons that may cause errors. These errors are bascally related to the naccuracy n the FE model dscretsaton, uncertantes n geometry and boundary condtons and varaton n the materal propertes. Due to these aspects, the mportance gven to the automatc calbraton process of the numercal models has been ncreased, especally takng nto account the 1 PhD Student, Faculty of Engneerng Unversty of Porto, jpmalvero@fe.up.pt 2 Assstant, School of Engneerng Polytechnc of Porto, drr@sep.pp.pt 3 Assocate Professor, Faculty of Engneerng Unversty of Porto, ruabc@fe.up.pt 4 Full Professor, Faculty of Engneerng Unversty of Porto, rdelgado@fe.up.pt

2 J. Malvero, D. Rbero, R. Calçada, R. Delgado modal parameters of the structure [2, 3]. However, the accuracy of the fnte element model n reproduce the dynamc behavour of the structure strongly depends on the expermental valdaton of the numercal results that s usually performed by means of dynamc tests. Ths paper descrbes the calbraton and expermental valdaton of the numercal model of a ralway vaduct wth precast deck. The calbraton of the three-dmensonal numercal model s performed by an optmzaton process based on the applcaton of a genetc algorthm. A dynamc test under ralway traffc enables to obtan records of dsplacements and acceleratons of the lower slab of the deck durng the passage of Alfa Pendular tran at dfferent speeds. Fnally, the expermental valdaton of the calbrated numercal model based on modal parameters s performed by the comparson between the numercal and the expermental responses. 2. ALVERCA RAILWAY VIADUCT Alverca ralway vaduct s a flyover structure on the Portuguese ralways Northern Lne that establshes the ral connecton between Lsbon and Porto. Its constructon allowed to separate the ral traffc flowng n the downstream and upstream drectons and also to mantan the maxmum speed of trans at 200 km/h. Fgure 1 shows a perspectve vew of the current zone of the vaduct (Fgure 1 a)) and a cross secton of the deck (Fgure 1 b)). a) b) Fgure 1 Alverca ralway vaduct: a) perspectve vew; b) cross secton The vaduct, that supports one sngle ralway track, has a total length of 1091 m dvded nto 47 smply supported spans: m m. Each span s composed by a prefabrcated and prestressed U shape beam connected by an upper slab cast n stu, formng a sngle-cell box-grder deck. The deck s drectly supported n the pers by elastomerc renforced bearngs. These bearngs are fxed n one extremty and longtudnally guded n the other extremty. The track s contnuous between successve spans and s composed by 30 cm of ballast, monoblock sleepers and UIC60 rals. 3. NUMERICAL MODELLING The dynamc analyss of the Alverca ralway vaduct was carred out usng a three-dmensonal numercal model developed n ANSYS software. The analyss focused on the three spans adjacent to the North abutment: one 16.5 m span and two 21 m spans. An extra extenson of the track, wth a length of 6 m, apart from the abutment, was modelled n order to smulate the effect of the track over the adjacent embankment. Fgure 2 shows an overvew of the numercal model wth a detal of the track components. 2

3 5 th Internatonal Operatonal Modal Analyss Conference, Gumarães May 2013 Fgure 2 Three-dmensonal numercal model The prefabrcated beam, the upper slab and the ballast retanng walls were modeled by shell fnte elements. The sleepers, the ral pads and the ballast layer were modeled by volume fnte elements. Each support was regarded as a sngle pont and modeled by a sprng element. The stffness of the supports was calculated takng nto account the confnement effect of the neoprene layers provded by varous metallc plates. The stffness of the support n the vertcal drecton (k v ), whch can be calculated consderng a system of seres-connected sprngs, each one smulatng an ndvdual neoprene layer, was ntally taken equal to 5200 MN/m. The longtudnal stffness of the support (k h ), whch consders the shear modulus of the neoprene, was also taken nto account and assumed equal 3.6 MN/m. The modulus of elastcty of the precast beam (E c ) and the upper slab of the deck (dfferent for the three spans E c1, E c2 and E c3 ) were consdered equal to 40.9 GPa and 35.4, respectvely, correspondng to the average value of ths parameter at 28 days wth the necessary adjustment to the age of the concrete at the expermental tests. The densty of the concrete (ρ c ) was assumed equal to kg/m 3. The modulus of elastcty of the ballast layer (E bal ) and ts densty (ρ bal ) were consdered equal to 145 MPa and 2039 kg/m 3, respectvely. Fgure 3 presents global vbraton modes of the deck (G) and local vbraton modes of the upper slab of the deck (L) obtaned from a modal analyss of the ntal numercal model of the vaduct. Mode 1G: f = 6.16 Hz Mode 1L: f = Hz Mode 2G: f = 6.07 Hz Mode 2L: f = Hz Mode 3G: f = 9.13 Hz Mode 3L: f = Hz 3

4 J. Malvero, D. Rbero, R. Calçada, R. Delgado Mode 4G: f = Hz Mode 4L: f = Hz Mode 5G: f = Hz Mode 5L: f = Hz a) b) Fgure 3 Numercal vbraton modes: a) global modes and b) local modes 4. MODEL UPDATING The ntal numercal model of the vaduct was calbrated takng nto account the modal parameters expermentally dentfed through the ambent vbraton test, namely ts natural frequences and modal confguratons for global and local vbraton modes. More detals about the ambent vbraton test can be found n Malvero et al. [4]. The calbraton process of the numercal model nvolved the defnton of an objectve functon and the applcaton of an optmzaton technque based on a genetc algorthm. The teratve calbraton process nvolves the use of three software packages: ANSYS, MATLAB and OptsLang [2]. The objectve functon ncludes two terms, one related to the natural frequences and other related to the MAC values, comprsng the global and local vbraton modes: f a nmod es 1 f exp f f exp num b nmod es 1 exp num MAC, 1 (1) where f exp and f num are the expermental and numercal frequences for mode, exp and num are the vectors contanng the expermental and numercal modal nformaton regardng mode, a and b are weghng factors of the objectve functon s terms, consdered equal to 1.0 n ths case, and nmodes s the total number of modes, equal to 6 (3 global and 3 local vbraton modes). Table 1 shows the parameter s values that orgnated the lowest resdual of the objectve functon, whch should be consdered n the numercal model n order to mnmze the dfferences between numercal and expermental responses. Table 1 Optmal numercal parameters Parameter Intal value Optmal value Unty Parameter Intal value Optmal value Unty E c GPa E c GPa E c GPa E c GPa c Kg/m 3 E bal MPa bal Kg/m 3 K h MN/m K h MN/m K h MN/m 4

5 5 th Internatonal Operatonal Modal Analyss Conference, Gumarães May 2013 Fgure 4 shows the comparson between expermental and numercal frequences and MAC values, before and after the calbraton process. a) b) Fgure 4 Modal parameter s values before and after calbraton: a) frequences; b) MAC After the calbraton, the average error of frequences decreased from 11.6 % to 6.5 % for global vbraton modes and from 7.3 % to 3.1 % for local vbraton modes. The average value of the MAC parameter slghtly ncreased from to n case of global vbraton modes and ncreased from to n case of local vbraton modes. 5. DYNAMIC TEST UNDER RAILWAY TRAFFIC The valdaton of the numercal model was based on the dynamc test under ralway traffc. Ths expermental test allowed the measurement of dsplacements and acceleratons on the lower slab of the deck, n the md-span secton of the span 2 and also the longtudnal dsplacements of the moble supports of the span 2. Fgure 5 shows some detals related to the locaton of these sensors n the deck. a) b) c) Fgure 5 Dynamc test under ralway traffc: a) accelerometer; b) LVDT on the lower slab of the deck; c) LVDT on the structural jont between spans 1 and 2, n the longtudnal drecton The dynamc response of the deck was measured for the passage of Alfa Pendular tran at 157 km/h and 185 km/h. Ths conventonal tran has a total length of approxmately 150 m and the axle loads vary between kn and kn. Fgure 6 shows the load scheme of the Alfa Pendular tran. 5

6 J. Malvero, D. Rbero, R. Calçada, R. Delgado Fgure 6 Load scheme of the Alfa Pendular tran Fgure 7 shows the records of acceleratons, n the tme and frequency doman, n the md-span secton of the span 2, expermentally obtaned for the passage of Alfa Pendular tran at speeds (v) of 157 km/h and 185 km/h. The dynamc response s domnated by frequences related to the tran acton, as can be seen by the peak of 6.71 Hz, correspondng to the passage of boges of dfferent carrages (d = 6.5 m) for a speed of 157 km/h (f = v/d = 6.71 Hz). Ths frequency s very close to the frequency of the expermentally dentfed mode 1G, equal to 6.76 Hz, amplfyng the dynamc response and assumng a preponderant contrbuton towards the remanng frequences. The same effect s not vsble at the speed of 185 km/h due to the dfference between the frequences values. Fgure 7 Acceleratons records for the passage of Alfa Pendular tran: a) tme and b) frequency doman 6

7 5 th Internatonal Operatonal Modal Analyss Conference, Gumarães May VALIDATION OF THE NUMERICAL MODEL The valdaton of the numercal model was performed accordng to the results of the dynamc test under ralway traffc. The numercal analyses were performed usng the modal superposton method, consderng the Alfa Pendular tran as a set of movng loads, vbraton modes wth frequences up to 30 Hz and an ntegraton tme ncrement equal to s. The modal dampng coeffcents were consdered equal to those obtaned n the ambent vbraton test [4]. As descrbed before, the ntal numercal model was calbrated based on modal parameters dentfed n the ambent vbraton test, known as Model 1. However, a new model, known as Model 2 was consdered, whch was obtaned by reducng the longtudnal stffness of the supports from Model 1. Ths model was consdered n order to obtan a moblty effect of the supports closer to the one shown n the dynamc test under ralway traffc. Fgure 8 shows the comparson between the expermental and numercal responses based on numercal models 1 and 2, n terms of dsplacements and acceleratons n the md-span secton of the lower slab for the passage of Alfa Pendular tran at 185 km/h and also the longtudnal dsplacements of the moble support for a passage at 157 km/h. a) b) c) Fgure 8 Expermental and numercal responses from models 1 and 2: a) dsplacement of the deck; b) acceleraton of the deck; c) longtudnal dsplacement of the moble support of the span 2 7

8 J. Malvero, D. Rbero, R. Calçada, R. Delgado In order to mnmze the dfferences between numercal and expermental responses, a value of 4.40 MN/m was consdered for the support s longtudnal stffness. Ths value s slghtly hgher than the one adopted n the ntal numercal model, whch was equal to 3.6 MN/m. Takng ths aspect nto account, t s possble to note a better agreement between expermental and numercal results wth the numercal model 2. Ths result seems to show a non-lnear behavour of the supports that act as fxed supports under ambent actons and act as moble supports under ralway traffc. 7. CONCLUSIONS Ths paper descrbes the calbraton and valdaton of the numercal model of a ralway vaduct wth precast deck, composed by several smply supported spans. In the calbraton process, based on the applcaton of a genetc algorthm, the optmal parameters of the numercal model are obtaned. The average error between numercal and expermental frequences decreased consderably after the calbraton, whle the average value of the MAC parameter ncreased, especally consderng the local vbraton modes. Dynamc responses regardng to vertcal dsplacements and acceleratons of the deck and longtudnal dsplacements of the supports for two tran speeds (157 km/h and 185 km/h) of Alfa Pendular tran are obtaned, based on a dynamc test under ralway traffc. It s possble to note that the response s clearly domnated by frequences assocated to the acton. For a speed of 157 km/h t s clear a hgh amplfcaton on the frequency of mode 1G due to the proxmty of one of the tran acton frequences. The expermental valdaton of the calbrated model based on modal parameters s performed by the comparson between the numercal and the expermental responses measured n a dynamc test under ralway traffc. The modfed numercal model, wth the reducton of the longtudnal stffness of the supports showed a better agreement between numercal and expermental results, whch can be assocated to ts non-lnear behavour that operate lke rgd supports under envronmental actons, whle operate as moble supports under the acton of ralway traffc. ACKNOWLEDGEMENTS The present work was funded by the Portuguese Foundaton for Scence and Technology (FCT), n the context of the research project «PTDC/ECM/68430/2006», and also by the agency AdI Agênca da Inovação, n the context of the research project «SI-IDT-3440/2008». The authors would also lke to thank to REFER, for all the nformaton provded about the vaduct and for all the support gven durng the expermental tests. REFERENCES [1] ERRI D214/RP9. (2001) Ralway brdges for speeds >200 km/h. Fnal Report. Utrecht, Netherlands. European Ral Research Insttute (ERRI) [2] Rbero D, Calçada R, Delgado R, Brehm M, Zabel V. (2012) Fnte element model updatng of a bowstrng-arch ralway brdge based on expermental modal parameters. Engneerng Structures 40: [3] Jash B, Ren W. (2005) Structural fnte element model updatng usng ambent vbraton test results. Journal of Structural Engneerng 45: [4] Malvero J, Rbero D, Calçada R. (2011) Dynamc montorng of a ralway vaduct wth precast deck. In: Proceedngs of the Internatonal Conference EVACES 11 Varenna, Italy 8