Analytical solution to mapping rail deformation under bridge transverse deformation using energy variational principle

Abstract

The track geometry is a critical factor that affects the running safety and riding comfort of trains moving on a high-speed railway bridge. This study addresses the mapping relationship between the track deformation and lateral deformations of bridges. Equilibrium equations and natural boundary conditions of the track-bridge system are established based on the energy variational principle, and an analytical solution is derived for the track deformation accounting for lateral bridge deformations. A five-span simply-supported bridge with continuous welded rail has been selected as the case study. The mapping rail deformations are compared to the finite element results, and both results agree well with each other, validating the analytical method proposed in this paper. The influence factors on the mapping rail deformation are further evaluated. Results show that the mapping rail deformation is consistent with the girder displacement at the area that is away from the girder ends when the flexural stiffness ratio between the track and the bridge girder is low. The interlayer stiffness has a significant effect on the mapping rail deformation when the track flexural stiffness is of a high value.

Keywords

energy variational principle / simply-supported beam bridge / high-speed railway / continuous welded rail / mapping rail deformation

References

[1] SuM, DaiG-L, MarxS, et al.. A brief review of developments and challenges for high-speed rail bridges in China and Germany [J]. Structural Engineering International, 2019, 29(1): 160-166

[2] ShaoG-Q, JiangL-Z, ChouwN. Experimental investigations of the seismic performance of bridge piers with rounded rectangular cross-sections [J]. Earthquakes and Structures, 2014, 7(4): 463-484

[3] HeX-H, LiH. Review of aerodynamics of high-speed train-bridge system in crosswinds [J]. Journal of Central South University, 2020, 27(4): 1054-1073

[4] HeX-H, WuT, ZouY-F, et al.. Recent developments of high-speed railway bridges in China [J]. Structure and Infrastructure Engineering, 2017, 13(12): 1584-1595

[5] LiossatouE, FardisM N. Near-fault effects on residual displacements of RC structures [J]. Earthquake Engineering & Structural Dynamics, 2016, 45(9): 1391-1409

[6] ChengH, LiH-N, WangD-S, et al.. Research on the influencing factors for residual displacements of RC bridge columns subjected to earthquake loading [J]. Bulletin of Earthquake Engineering, 2016, 14(8): 2229-2257

[7] JiangL-Z, KangX, LiC-Q, et al.. Earthquake response of continuous girder bridge for highspeed railway: A shaking table test study [J]. Engineering Structures, 2019, 180: 249-263

[8] KangX, JiangL-Z, BaiY, et al.. Seismic damage evaluation of high-speed railway bridge components under different intensities of earthquake excitations [J]. Engineering Structures, 2017, 152: 116-128

[9] GongX, LiZ. Bridge pier settlement prediction in highspeed railway via autoregressive model based on robust weighted total least-squares [J]. Survey Review, 2018, 50(9): 147-154

[10] WangZ-C, XingJ-F, ChenG-D, et al.. Differential settlement effect on reliability of bridge superstructure and implementation in load and resistance factor design specification [J]. Advances in Structural Engineering, 2016, 19(10): 1533-1546

[11] LaiM-H, HanzicL, HoJ C M. Fillers to improve passing ability of concrete [J]. Structural Concrete, 2019, 20(1): 185-197

[12] WuW-Q, ShanH-W, YangS, et al.. Key assumption to evaluate the mechanical performance of widened voided-slab bridge due to foundation settlement [J]. KSCE Journal of Civil Engineering, 2018, 22(4): 1225-1234

[13] KarttunenK, KaboE, EkbergA. A numerical study of the influence of lateral geometry irregularities on mechanical deterioration of freight tracks [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2012, 226(6): 575-586

[14] ZengZ-P, ZhaoY-G, XuW-T, et al.. Random vibration analysis of train-bridge under track irregularities and traveling seismic waves using train-slab track-bridge interaction model [J]. Journal of Sound and Vibration, 2015, 342: 22-43

[15] MaoJ-F, YuZ-W, XiaoY-J, et al.. Random dynamic analysis of a train-bridge coupled system involving random system parameters based on probability density evolution method [J]. Probabilistic Engineering Mechanics, 2016, 46: 48-61

[16] YanW-J, ZhaoM-Y, SunQ, et al.. Transmissibility-based system identification for structural health monitoring: Fundamentals, approaches, and applications [J]. Mechanical Systems and Signal Processing, 2019, 117: 453-482

[17] XuP, SunQ-X, LiuR-K, et al.. Key equipment identification model for correcting milepost errors of track geometry data from track inspection cars [J]. Transportation Research Part C: Emerging Technologies, 2013, 35: 85-103

[18] SadeghiJ, AskarinejadH. An investigation into the effects of track structural conditions on railway track geometry deviations [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2009, 223(4): 415-425

[19] KraftS, CausseJ, CoudertF. Vehicle response-based track geometry assessment using multi-body simulation [J]. Vehicle System Dynamics, 2018, 56(2): 190-220

[20] GulerH. Prediction of railway track geometry deterioration using artificial neural networks: A case study for Turkish state railways [J]. Structure and Infrastructure Engineering, 2014, 10(5): 614-626

[21] AndradeA R, TeixeiraP F. Statistical modelling of railway track geometry degradation using Hierarchical Bayesian models [J]. Reliability Engineering & System Safety, 2015, 142: 169-183

[22] AhmariS, YangM-J, ZhongH. Dynamic interaction between vehicle and bridge deck subjected to support settlement [J]. Engineering Structures, 2015, 84: 172-183

[23] FengY-L, JiangL-Z, ZhouW-B, et al.. An analytical solution to the mapping relationship between bridge structures vertical deformation and rail deformation of high-speed railway [J]. Steel and Composite Structures, 2019, 33: 209-224

[24] LiuX, JiangL-Z, XiangP, et al.. Dynamic response limit of high-speed railway bridge under earthquake considering running safety performance of train [J]. Journal of Central South University, 2021, 28(3): 968-980

[25] LAI Zhi-peng, JIANG Li-zhong, ZHOU Wang-bao, et al. Lateral girder displacement effect on the safety and comfortability of the high-speed rail train operation [J]. Vehicle System Dynamics, 2021: 1–25. DOI: https://doi.org/10.1080/00423114.2021.1942507.

[26] GouH-Y, YangL-C, LengD, et al.. Effect of bridge lateral deformation on track geometry of highspeed railway [J]. Steel and Composite Structures, 2018, 29(2): 219-229

[27] LaiZ-P, JiangL-Z, LiuX, et al.. Analytical investigation on the geometry of longitudinal continuous track in high-speed rail corresponding to lateral bridge deformation [J]. Construction and Building Materials, 2021, 268121064

[28] LaiZ-P, JiangL-Z, ZhouW-B, et al.. Improved finite beam element method to analyze the natural vibration of steel-concrete composite truss beam [J]. Shock and Vibration, 2017, 20175323246

[29] UIC 774-3Track/bridge Interaction: Recommendations for Calculations [S], 2001, Paris, International Union of Railways

[30] LAI Zhi-peng, JIANG Li-zhong, ZHOU Wang-bao. An analytical study on dynamic response of multiple simply supported beam system subjected to moving loads [J]. Shock and Vibration, 2018: 2149251. DOI: https://doi.org/10.1155/2018/2149251.

[31] YanB, LiuS, PuH, et al.. Elastic-plastic seismic response of CRTS II slab ballastless track system on highspeed railway bridges [J]. Science China Technological Sciences, 2017, 60(6): 865-871

[32] ZhaiW-M, ChenZ-W, SunY. Mapping relationship between pier settlement and rail deformation of high-speed railways-part (II): The longitudinal connected ballastless track system [J]. Scientia Sinica Technologica, 2014, 44(7): 778-785 in Chinese)