Approach for redefining the damping factor of railway bridges with ballast superstructure: model calibration and guidelines for practical application

Abstract

To ensure the compatibility between rolling stock and infrastructure when dynamically assessing railway bridges under high-speed traffic, the damping properties considered in the calculation model significantly influence the predicted acceleration amplitude at resonance. However, due to the normative specifications of EN 1991-2, which are considered to be overly conservative, damping factors that are far below the actual damping have to be used when predicting vibrations of railway bridges, which means that accelerations at resonance tend to be overestimated to an uneconomical extent. Comparisons between damping factors prescribed by the standard and those identified based on in situ structure measurements always reveal a large discrepancy between reality and regulation. Given this background, this contribution presents a novel approach for defining the damping factor of railway bridges with ballasted tracks, where the damping factor for bridges is mathematically determined based on three different two-dimensional mechanical models. The basic principle of the approach for mathematically determining the damping factor is to separately define and superimpose the dissipative contributions of the supporting structure (including the substructure) and the superstructure. Using the results of a measurement campaign on 15 existing steel railway bridges in the Austrian rail network, the presented mechanical models are calibrated, and by analysing the energy dissipation in the ballasted track, guiding principles for practical application are defined. This guideline is intended to establish an alternative to the currently valid specifications of EN 1991-2, enabling the damping factor of railway bridges to be assessed in a realistic range by mathematical calculation and thus without the need for extensive in situ measurements on the individual structure. In this way, the existing potential of the infrastructure with regard to the damping properties of bridges can be utilised. This contribution focuses on steel bridges, but the mathematical approach for determining the damping factor applies equally to other bridge types (concrete, composite, or filler beam).

Keywords

Railway bridges / Bridge dynamics / Damping / Track–bridge interaction / Structural health monitoring / Condition assessment

References

[1.] European Committee for Standardization EN 1990/A1:2013 03 15 Eurocode—basis of structural design—amendment 1: application for bridges (consolidated version), 2013 Vienna Austrian Standards International

[2.] YangB, YauJD, WU YS, Vehicle–bridge interaction dynamics with applications to high-speed railways, 2004 Taipei World Scientific

[3.] ZhangY, MiyamoriY, KadotaT, et al.. Long-term investigations of dynamic behavior of a pre-stressed concrete ballasted railway bridge. Structures, 2023, 53: 822-832

[4.] ZhaiW, HanZ, ChenZ, et al.. Train–track–bridge dynamic interaction: a state-of-the-art review. Veh Syst Dyn, 2019, 57(7): 984-1027

[5.] ArvidssonT, KaroumiR. Train–bridge interaction—a review and discussion of key model parameters. Int J Rail Transp, 2014, 2(3): 147-186

[6.] CanteroD, ArvidssonT, OBrien E, , et al.. Train–track–bridge modelling and review of parameters. Struct Infrastruct Eng, 2016, 12(9): 1051-1064

[7.] TahiriM, KhamlichiA, DkiouakR, et al.. Combined effect of track–bridge interaction on the dynamic response of a simply supported railway bridge. Structures, 2024, 68: 107071

[8.] TahiriM, KhamlichiA, BezzaziM. Nonlinear analysis of the ballast influence on the train–bridge resonance of a simply supported railway bridge. Structures, 2022, 35: 303-313

[9.] TiconaMeloLR, RibeiroD, CalçadaR, et al.. Validation of a vertical train–track–bridge dynamic interaction model based on limited experimental data. Struct Infrastruct Eng, 2020, 16(1): 181-201

[10.] BornetL, AnderssonA, ZwolskiJ, et al.. Influence of the ballasted track on the dynamic properties of a truss railway bridge. Struct Infrastruct Eng, 2015, 11(6): 796-803

[11.] MalveiroJ, RibeiroD, CalçadaR, et al.. Updating and validation of the dynamic model of a railway viaduct with precast deck. Struct Infrastruct Eng, 2014, 10(11): 1484-1509

[12.] GattulliV, LofranoE, PaoloneA, et al.. Measured properties of structural damping in railway bridges. J Civ Struct Health Monit, 2019, 9(5): 639-653

[13.] MalveiroJ, SousaC, RibeiroD, et al.. Impact of track irregularities and damping on the fatigue damage of a railway bridge deck slab. Struct Infrastruct Eng, 2018, 14(9): 1257-1268

[14.] RibeiroD, CalçadaR, DelgadoR, et al.. Finite element model updating of a bowstring-arch railway bridge based on experimental modal parameters. Eng Struct, 2012, 40: 413-435

[15.] Castellanos-ToroS, MarmolejoM, MarulandaJ, et al.. Frequencies and damping ratios of bridges through Operational Modal Analysis using smartphones. Constr Build Mater, 2018, 188: 490-504

[16.] López-AragónJA, PucholV, AstizMA. Influence of the modal damping ratio calculation method in the analysis of dynamic events obtained in structural health monitoring of bridges. J Civ Struct Health Monit, 2024, 14(5): 1191-1213

[17.] European Committee for Standardization EN 1991-2:2012 03 01 Eurocode 1: actions on structures—part 2: traffic loads on bridges (consolidated version), 2012 Vienna Austrian Standard International

[18.] Specialists’ Committee D214 (1999) Railway bridges for speeds > 200 km/h, RP1–RP9. European Rail Research Institute, Utrecht

[19.] ReitererM, LachingerS, FinkJ, et al.. Ermittlung der dynamischen Kennwerte von Eisenbahnbrücken unter Anwendung von unterschiedlichen Schwingungsanregungsmethoden. Bauingenieur, 2017, 92(10): 2-13

[20.] ReitererM, LachingerS, FinkJ, Bruschetini-AmbroSZ. In-situ experimental modal testing of railway bridges. Proceedings, 2018, 2(8): 413

[21.] SilvaA, RibeiroD, MontenegroPA, et al.. New contributions for damping assessment on filler-beam railway bridges framed on In2Track EU projects. Appl Sci, 2023, 13(4): 2636

[22.] BrunettiM, CiambellaJ, EvangelistaL, et al.. Experimental results in damping evaluation of a high-speed railway bridge. Procedia Eng, 2017, 199: 3015-3020

[23.] GalvínP, RomeroA, MolinerE, et al.. On the dynamic characterisation of railway bridges through experimental testing. Eng Struct, 2021, 226: 111261

[24.] Montenegro PA, Silva R, Pimenta F et al (2024) Damping assessment on railway bridges based on an extensive experimental database framed on the InBridge4EU project. In: Civil-comp conferences, Prague, Czech Republic, 1–5 September, 2024. Civil-Comp Press, pp 1–14

[25.] MalveiroJ, RibeiroD, SousaC, et al.. Model updating of a dynamic model of a composite steel-concrete railway viaduct based on experimental tests. Eng Struct, 2018, 164: 40-52

[26.] RibeiroD, CalçadaR, BrehmM, et al.. Calibration of the numerical model of a track section over a railway bridge based on dynamic tests. Structures, 2021, 34: 4124-4141

[27.] Stollwitzer A (2021) Developing an approach for the mathematical calculation of the damping value of railway bridges with ballasted track. Dissertation, TU Wien

[28.] Stollwitzer A, Bettinelli L, Loidl S et al (2025) Novel evaluation methods for data-based determination of damping factors in the frequency and time domain with application to railway bridges. Railw Eng Sci. https://doi.org/10.1007/s40534-024-00373-1

[29.] StollwitzerA, FinkJ. Mathematical calculation of the damping value of steel railway bridges—part II: verification on the basis of existing bridges. Stahlbau, 2021, 90(6): 449-462

[30.] StollwitzerA, FinkJ, MohamedE. Verfahren zur Reduktion der Ergebnisstreuung zur Ermittlung realistischer Lehr’scher Dämpfungsmaße von Eisenbahnbrücken-Teil 1: Methoden im Frequenzbereich (Methods for reducing the output scatter of results for determining realistic damping factors of railway bridges—PART 1: methods in the frequency range). Bauingenieur, 2022, 97(5): 153-164

[31.] StollwitzerA, FinkJ. Mathematical calculation of the damping value of steel railway bridges—part I: theoretical background. Stahlbau, 2021, 90(4): 305-315

[32.] StollwitzerA, FinkJ, MalikT. Experimental analysis of damping mechanisms in ballasted track on single-track railway bridges. Eng Struct, 2020, 220: 110982

[33.] StollwitzerA, FinkJ. Bestimmung modellabhängiger Steifigkeits- und Dämpfungskennwerte des Schotteroberbaues zur dynamischen Berechnung von Eisenbahnbrücken (Determination of model-dependent stiffness and damping values of ballasted track for dynamic analyses of railway bridges). Bauingenieur, 2020, 95(9): 345-356

[34.] StollwitzerA, BettinelliL, FinkJ. The longitudinal track–bridge interaction of ballasted track in railway bridges: experimental determination of dynamic stiffness and damping characteristics. Eng Struct, 2023, 274: 115115

[35.] PetersenC, WerkleH Dynamik der Baukonstruktionen, 2018 Wiesbaden Springer

[36.] ChopraAK Dynamics of structures: theory and application to earthquake engineering, 2020 London Pearson Education Limited

[37.] KönigP, SalcherP, AdamC. An efficient model for the dynamic vehicle–track–bridge–soil interaction system. Eng Struct, 2022, 253: 113769

[38.] RomeroA, SolísM, DomínguezJ, et al.. Soil–structure interaction in resonant railway bridges. Soil Dyn Earthq Eng, 2013, 47: 108-116

[39.] ZangenehA, SvedholmC, AnderssonA, et al.. Identification of soil–structure interaction effect in a portal frame railway bridge through full-scale dynamic testing. Eng Struct, 2018, 159: 299-309

[40.] HeilandT, AjiHDB, WuttkeF, et al.. Influence of soil–structure interaction on the dynamic characteristics of railroad frame bridges. Soil Dyn Earthq Eng, 2023, 167: 107800

[41.] Hackl K (2017) Development and application of a testing facility for studying the dynamic behaviour of ballasted track at railway bridges. Dissertation, TU Wien

[42.] Stollwitzer A, Bettinelli L, Fink J (2024) Vertical track–bridge interaction in railway bridges with ballast superstructure: experimental analysis of dynamic stiffness and damping behavior. Int J Str Stab Dyn:2540008

[43.] StollwitzerA, FinkJ. Dämpfungskennwerte des Schotteroberbaus auf Eisenbahnbrücken—Teil 2: Energiedissipation im Schotteroberbau und zugehöriges Rechenmodell (Damping parameters of ballasted track on railway bridges—part II: energy dissipation in the ballasted track and related calculation model). Bautechnik, 2021, 98(8): 552-562

[44.] MolinerE, Martínez-RodrigoMD, GalvínP, et al.. On the vertical coupling effect of ballasted tracks in multi–span simply–supported railway bridges under operating conditions. Struct Infrastruct Eng, 2023, 19(11): 1633-1655

[45.] BettinelliL, StollwitzerA, FinkJ. Numerical study on the influence of coupling beam modeling on structural accelerations during high-speed train crossings. Appl Sci, 2023, 13(15): 8746

[46.] HeQ, LiS, YangY, et al.. A novel modelling method for heavy-haul train–track–long-span bridge interaction considering an improved track–bridge relationship. Mech Syst Signal Process, 2024, 220: 111691

[47.] ÖBB Infrastruktur AG (2022) Regelwerk 08.01.05 Dynamische Berechnung von Eisenbahnbrücken. Austrian Federal Railways, Vienna