Technical Papers
Jul 21, 2022

Experimental and Analytical Investigation into the Effect of Ballasted Track on the Dynamic Response of Railway Bridges under Moving Loads

Publication: Journal of Bridge Engineering
Volume 27, Issue 10

Abstract

Ballasted tracks are among the most widespread railway track typologies. The ballast possesses multiple functions. Among them, it significantly affects the dynamic interaction between a rail bridge and a moving load in terms of damping and load distribution. These effects entail accurate modeling of the track–ballast–bridge interaction. The paper presents a finite-difference formulation of the governing equations of the track and the bridge, modeled as Euler–Bernoulli (EB) beams, and coupled by a distributed layer of springs representing the ballast. The two equations are solved under a moving load excitation using a Runge–Kutta family algorithm and the finite-difference method for the temporal and spatial discretization, respectively. The authors validated the mathematical model against the displacement response of a rail bridge with a ballasted substructure. In a first step, the modal parameters of the bridge, obtained from ambient vibration measurements, are used to estimate the bending stiffness of an equivalent EB beam representative of the tested bridge. In a second step, the authors estimated the coupling effect of the ballast by assessing the model sensitivity to the modeling parameters and optimizing the agreement with the experimental data. Comparing the bridge’s experimental displacement responses highlights the ballast’s significant effect on the load distribution and damping. The considerable difference between the damping estimated from output-only identification and that determined from the displacement response under moving load proves the dominant role of the ballast in adsorbing the vibrations transmitted to the bridge under the train passage and the different damping sources under high-amplitude excitation. The authors discuss the tradeoff between model accuracy and computational effort for a reliable estimation of ballasted tracks response under moving loads.

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References

Aloisio, A., R. Alaggio, and M. Fragiacomo. 2020a. “Dynamic identification and model updating of full-scale concrete box girders based on the experimental torsional response.” Constr. Build Mater. 264: 120146. https://doi.org/10.1016/j.conbuildmat.2020.120146.
Aloisio, A., R. Alaggio, and M. Fragiacomo. 2020b. “Time-domain identification of elastic modulus of simply supported box girders under moving loads: Method and full-scale validation.” Eng. Struct. 215: 110619. https://doi.org/10.1016/j.engstruct.2020.110619.
Aloisio, A., R. Alaggio, and M. Fragiacomo. 2021a. “Bending stiffness identification of simply supported girders using an instrumented vehicle: Full scale tests, sensitivity analysis, and discussion.” J. Bridge Eng. 26 (1): 04020115. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001654.
Aloisio, A., R. Alaggio, and M. Fragiacomo. 2021b. “Equivalent viscous damping of cross-laminated timber structural archetypes.” J. Struct. Eng. 147 (4): 04021012. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002947.
Aloisio, A., D. P. Pasca, R. Alaggio, and M. Fragiacomo. 2021c. “Bayesian estimate of the elastic modulus of concrete box girders from dynamic identification: A statistical framework for the A24 motorway in Italy.” Struct. Infrastruct. Eng. 17 (12): 1626–1638. https://doi.org/10.1080/15732479.2020.1819343.
Åström, K. J., and B. Wittenmark. 2013. Computer-controlled systems: Theory and design. Chelmsford, MA: Courier Corporation.
Au, F., Y. Cheng, and Y. Cheung. 2001. “Vibration analysis of bridges under moving vehicles and trains: An overview.” Prog. Struct. Eng. Mater. 3 (3): 299–304. https://doi.org/10.1002/(ISSN)1528-2716.
Cheng, Y., F. Au, and Y. Cheung. 2001. “Vibration of railway bridges under a moving train by using bridge-track-vehicle element.” Eng. Struct. 23 (12): 1597–1606. https://doi.org/10.1016/S0141-0296(01)00058-X.
Craig, R. R., Jr., and A. J. Kurdila. 2006. Fundamentals of structural dynamics. Hoboken, NJ: John Wiley & Sons.
Das, B. M., and Z. Luo. 2016. Principles of soil dynamics. Boston, MA: Cengage Learning.
Di Lorenzo, S., M. Di Paola, G. Failla, and A. Pirrotta. 2017. “On the moving load problem in Euler–Bernoulli uniform beams with viscoelastic supports and joints.” Acta Mech. 228 (3): 805–821. https://doi.org/10.1007/s00707-016-1739-6.
Dormand, J. R., and P. J. Prince. 1980. “A family of embedded Runge–Kutta formulae.” J. Comput. Appl. Math. 6 (1): 19–26. https://doi.org/10.1016/0771-050X(80)90013-3.
Feng, D., and M. Q. Feng. 2015. “Model updating of railway bridge using in situ dynamic displacement measurement under trainloads.” J. Bridge Eng. 20 (12): 04015019. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000765.
Frỳba, L. 2013. Vol. 1 of Vibration of solids and structures under moving loads. Berlin: Springer Science & Business Media.
Gibbons, J. 1985. Nonparametric statistical inference. 2nd ed. New York: Marcel Dekker.
He, L., C. Castoro, A. Aloisio, Z. Zhang, G. C. Marano, A. Gregori, C. Deng, and B. Briseghella. 2022. “Dynamic assessment, FE modelling and parametric updating of a butterfly-arch stress-ribbon pedestrian bridge.” Struct. Infrastruct. Eng.: 18 (7): 1064–1075. https://doi.org/10.1080/15732479.2021.1995444.
Hirzinger, B., C. Adam, and P. Salcher. 2020. “Dynamic response of a non-classically damped beam with general boundary conditions subjected to a moving mass–spring–damper system.” Int. J. Mech. Sci. 185: 105877. https://doi.org/10.1016/j.ijmecsci.2020.105877.
Ichikawa, M., Y. Miyakawa, and A. Matsuda. 2000. “Vibration analysis of the continuous beam subjected to a moving mass.” J. Sound Vib. 230 (3): 493–506. https://doi.org/10.1006/jsvi.1999.2625.
Ju, S.-H., H.-T. Lin, and J.-Y. Huang. 2009. “Dominant frequencies of train-induced vibrations.” J. Sound Vib. 319 (1–2): 247–259. https://doi.org/10.1016/j.jsv.2008.05.029.
Kathnelson, A. 1992. “High eigenfrequencies of non-uniform Bernoulli-Euler beams.” Int. J. Mech. Sci. 34 (10): 805–808. https://doi.org/10.1016/0020-7403(92)90043-G.
König, P., P. Salcher, C. Adam, and B. Hirzinger. 2021. “Dynamic analysis of railway bridges exposed to high-speed trains considering the vehicle–track–bridge–soil interaction.” Acta Mech. 232 (11): 4583–4608. https://doi.org/10.1007/s00707-021-03079-1.
Kumar, C. S., C. Sujatha, and K. Shankar. 2015. “Vibration of simply supported beams under a single moving load: A detailed study of cancellation phenomenon.” Int. J. Mech. Sci. 99: 40–47. https://doi.org/10.1016/j.ijmecsci.2015.05.001.
Liu, K., G. De Roeck, and G. Lombaert. 2009. “The effect of dynamic train–bridge interaction on the bridge response during a train passage.” J. Sound Vib. 325 (1): 240–251. https://doi.org/10.1016/j.jsv.2009.03.021.
Majka, M., and M. Hartnett. 2008. “Effects of speed, load and damping on the dynamic response of railway bridges and vehicles.” Comput. Struct. 86 (6): 556–572. https://doi.org/10.1016/j.compstruc.2007.05.002.
Mao, L., and Y. Lu. 2013. “Critical speed and resonance criteria of railway bridge response to moving trains.” J. Bridge Eng. 18 (2): 131–141. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000336.
Mottershead, J. E., M. Link, and M. I. Friswell. 2011. “The sensitivity method in finite element model updating: A tutorial.” Mech. Syst. Sig. Process. 25 (7): 2275–2296. https://doi.org/10.1016/j.ymssp.2010.10.012.
Museros, P., E. Moliner, and M. D. Martínez-Rodrigo. 2013. “Free vibrations of simply-supported beam bridges under moving loads: Maximum resonance, cancellation and resonant vertical acceleration.” J. Sound Vib. 332 (2): 326–345. https://doi.org/10.1016/j.jsv.2012.08.008.
Ouyang, H. 2011. “Moving-load dynamic problems: A tutorial (with a brief overview).” Mech. Syst. Sig. Process. 25 (6): 2039–2060. https://doi.org/10.1016/j.ymssp.2010.12.010.
Pasca, D. P., A. Aloisio, M. Fragiacomo, and R. Tomasi. 2021. “Dynamic characterization of timber floor subassemblies: Sensitivity analysis and modeling issues.” J. Struct. Eng. 147 (12): 05021008. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003179.
Peeters, B., and G. De Roeck. 2001. “Stochastic system identification for operational modal analysis: A review.” J. Dyn. Syst. Meas. Contr. 123 (4): 659–667. https://doi.org/10.1115/1.1410370.
Pelliciari, M., G. C. Marano, T. Cuoghi, B. Briseghella, D. Lavorato, and A. M. Tarantino. 2018. “Parameter identification of degrading and pinched hysteretic systems using a modified Bouc–Wen model.” Struct. Infrastruct. Eng. 14 (12): 1573–1585. https://doi.org/10.1080/15732479.2018.1469652.
Pesterev, A., B. Yang, L. Bergman, and C. Tan. 2003. “Revisiting the moving force problem.” J. Sound Vib. 261 (1): 75–91. https://doi.org/10.1016/S0022-460X(02)00942-2.
Rebelo, C., L. S. da Silva, C. Rigueiro, and M. Pircher. 2008. “Dynamic behaviour of twin single-span ballasted railway viaducts—field measurements and modal identification.” Eng. Struct. 30 (9): 2460–2469. https://doi.org/10.1016/j.engstruct.2008.01.023.
Rebelo, C., M. Heiden, M. Pircher, and L. Simões da Silva. 2005. “Vibration measurements on existing single-span concrete railway viaducts in Austria.” In Vol. 1637 of Proc. of 6th Int. Conf. on Structural Dynamics EURODYN, edited by G. I. Schuëller, and C. Soize, 1642. Rotterdam: Millpress.
Reynders, E., R. Pintelon, and G. De Roeck. 2008. “Uncertainty bounds on modal parameters obtained from stochastic subspace identification.” Mech. Syst. Sig. Process. 22 (4): 948–969. https://doi.org/10.1016/j.ymssp.2007.10.009.
Ribeiro, D., R. Calçada, R. Delgado, M. Brehm, and V. Zabel. 2012. “Finite element model updating of a bowstring-arch railway bridge based on experimental modal parameters.” Eng. Struct. 40: 413–435. https://doi.org/10.1016/j.engstruct.2012.03.013.
Robnett, Q., M. Thompson, W. Hay, S. Tayabji, and R. Knutson. 1975. Technical data bases report. Ballast and foundation materials research program. Technical Rep. FRA/OR&D-76-138. Washington, DC: US Dept. of Transportation.
Salcher, P., and C. Adam. 2015. “Modeling of dynamic train–bridge interaction in high-speed railways.” Acta Mech. 226 (8): 2473–2495. https://doi.org/10.1007/s00707-015-1314-6.
Saltelli, A., and I. M. Sobol’. 1995. “Sensitivity analysis for nonlinear mathematical models: Numerical experience.” Matematicheskoe Modelirovanie 7 (11): 16–28.
Selig, E. T., and J. M. Waters. 1994. Track geotechnology and substructure management. London: Thomas Telford.
Sirotti, S., M. Pelliciari, F. Di Trapani, B., Briseghella, G. Carlo Marano, C. Nuti, and A. M. Tarantino. 2021. “Development and validation of new Bouc–Wen data-driven hysteresis model for masonry infilled RC frames.” J. Eng. Mech. 147 (11): 04021092. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002001.
Svedholm, C., A. Zangeneh, C. Pacoste, S. François, and R. Karoumi. 2016. “Vibration of damped uniform beams with general end conditions under moving loads.” Eng. Struct. 126: 40–52. https://doi.org/10.1016/j.engstruct.2016.07.037.
Valle, J., D. Fernández, and J. Madrenas. 2019. “Closed-form equation for natural frequencies of beams under full range of axial loads modeled with a spring-mass system.” Int. J. Mech. Sci. 153: 380–390. https://doi.org/10.1016/j.ijmecsci.2019.02.014.
Wu, Y.-S., Y.-B. Yang, and J.-D. Yau. 2001. “Three-dimensional analysis of train-rail-bridge interaction problems.” Veh. Syst. Dyn. 36 (1): 1–35. https://doi.org/10.1076/vesd.36.1.1.3567.
Xia, H., H. Li, W. Guo, and G. De Roeck. 2014. “Vibration resonance and cancellation of simply supported bridges under moving train loads.” J. Eng. Mech. 140 (5): 04014015. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000714.
Xia, H., and N. Zhang. 2005. “Dynamic analysis of railway bridge under high-speed trains.” Comput. Struct. 83 (23–24): 1891–1901. https://doi.org/10.1016/j.compstruc.2005.02.014.
Xia, H., N. Zhang, and G. De Roeck. 2003. “Dynamic analysis of high speed railway bridge under articulated trains.” Comput. Struct. 81 (26–27): 2467–2478. https://doi.org/10.1016/S0045-7949(03)00309-2.
Xia, H., N. Zhang, and W. Guo. 2018. “Dynamic interaction of train–bridge systems in high-speed railways. Berlin, HL: Springer.
Xu, Y. L., N. Zhang, and H. Xia. 2004. “Vibration of coupled train and cable-stayed bridge systems in cross winds.” Eng. Struct. 26 (10): 1389–1406. https://doi.org/10.1016/j.engstruct.2004.05.005.
Yang, Y.-B., J.-D. Yau, and L.-C. Hsu. 1997. “Vibration of simple beams due to trains moving at high speeds.” Eng. Struct. 19 (11): 936–944. https://doi.org/10.1016/S0141-0296(97)00001-1.
Yang, Y.-B., J. Yau, Z. Yao, and Y. Wu. 2004. Vehicle-bridge interaction dynamics: With applications to high-speed railways. Singapore: World Scientific.
Zhai, W., S. Wang, N. Zhang, M. Gao, H. Xia, C. Cai, and C. Zhao. 2013. “High-speed train–track–bridge dynamic interactions—Part II: Experimental validation and engineering application.” Int. J. Rail Transp. 1 (1–2): 25–41. https://doi.org/10.1080/23248378.2013.791497.
Zhang, N., H. Xia, W. Guo, and G. De Roeck. 2010. “A vehicle–bridge linear interaction model and its validation.” Int. J. Struct. Stab. Dyn. 10 (2): 335–361. https://doi.org/10.1142/S0219455410003464.
Zhang, Q.-L., A. Vrouwenvelder, and J. Wardenier. 2001. “Numerical simulation of train–bridge interactive dynamics.” Comput. Struct. 79 (10): 1059–1075. https://doi.org/10.1016/S0045-7949(00)00181-4.
Zhu, Z., W. Gong, L. Wang, Q. Li, Y. Bai, Z. Yu, and I. E. Harik. 2018. “An efficient multi-time-step method for train-track-bridge interaction.” Comput. Struct. 196: 36–48. https://doi.org/10.1016/j.compstruc.2017.11.004.

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Go to Journal of Bridge Engineering
Journal of Bridge Engineering
Volume 27Issue 10October 2022

History

Received: Jan 3, 2022
Accepted: May 23, 2022
Published online: Jul 21, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 21, 2022

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Univ. degli Studi dell’Aquila, via Giovanni Gronchi n.18, 67100 L’Aquila, Italy (corresponding author). ORCID: https://orcid.org/0000-0002-6190-0139. Email: [email protected]
Dipartimento di Ingegneria Strutturale, Edile e Geotecnica (DISEG), Politecnico di Torino, 10129 Torino, Italy. ORCID: https://orcid.org/0000-0002-9098-4132. Email: [email protected]
Rocco Alaggio [email protected]
Univ. degli Studi dell’Aquila, via Giovanni Gronchi n.18, 67100 L’Aquila, Italy. Email: [email protected]

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