An analytical solution to the mapping relationship between bridge structures vertical deformation and rail deformation of high-speed railway

  • Feng, Yulin (School of Civil Engineering, Central South University) ;
  • Jiang, Lizhong (School of Civil Engineering, Central South University) ;
  • Zhou, Wangbao (School of Civil Engineering, Central South University) ;
  • Lai, Zhipeng (School of Civil Engineering, Central South University) ;
  • Chai, Xilin (School of Civil Engineering, Central South University)
  • Received : 2019.01.16
  • Accepted : 2019.10.14
  • Published : 2019.10.25


This paper describes a study of the mapping relationship between the vertical deformation of bridge structures and rail deformation of high-speed railway, taking the interlayer interactions of the bridge subgrade CRTS II ballastless slab track system (HSRBST) into account. The differential equations and natural boundary conditions of the mapping relationship between the vertical deformation of bridge structures and rail deformation were deduced according to the principle of stationary potential energy. Then an analytical model for such relationship was proposed. Both the analytical method proposed in this paper and the finite element numerical method were used to calculate the rail deformations under three typical deformations of bridge structures and the evolution of rail geometry under these circumstances was analyzed. It was shown that numerical and analytical calculation results are well agreed with each other, demonstrating the effectiveness of the analytical model proposed in this paper. The mapping coefficient between bridge structure deformation and rail deformation showed a nonlinear increase with increasing amplitude of the bridge structure deformation. The rail deformation showed an obvious "following feature"; with the increase of bridge span and fastener stiffness, the curve of rail deformation became gentler, the track irregularity wavelength became longer, and the performance of the rail at following the bridge structure deformation was stronger.


Supported by : Central South University, National Natural Science Foundations of China


  1. Arisoy, B. and Erol, O. (2018), "Finite element model calibration of a steel railway bridge via ambient vibration test", Steel Compos. Struct., Int. J., 27(3), 327-335.
  2. Biondi, B., Muscolino, G. and Sofi, A. (2005), "A substructure approach for the dynamic analysis of train- track-bridge system", Comput. Struct., 83(28-30), 2271-2281.
  3. Cai, X., Liu W., Wang. P. and Ning. X. (2014), "Effect of land subsidence on regularity of double-block ballastless track", Eng. Mech., 31(9), 160-165. [In Chinese]
  4. Chen, Z., Zhai, W., Cai, C. and Sun, Y. (2015), "Safety threshold of high-speed railway pier settlement based on train-track-bridge dynamic interaction", Sci. China: Technol. Sci., 58(2), 202-210.
  5. Chen, Z., Zhai, W. and Tian, G. (2018), "Study on the safe value of multi-pier settlement for simply supported girder bridges in high-speed railways", Struct. Infrastruct. E, 14(3), 400-410.
  6. Cheng, H., Li, H., Wang, D., Sun, Z., Li, G. and Jin, J. (2016), "Research on the influencing factors for residual displacements of RC bridge columns subjected to earthquake loading", B Earthq. Eng., 14(8), 2229-2257.
  7. Feng, Y., Jiang, L., Zhou, W. and Han, J. (2019), "Lateral-torsional buckling of box beam with corrugated steel webs", J. Central South Univ., 26(7), 1946-1957.
  8. Gou, H., Yang, L., Leng, D., Bao, Y. and Pu, Q. (2018a), "Effect of bridge lateral deformation on track geometry of high-speed railway", Steel Compos. Struct., Int. J., 29(2), 219-229.
  9. Gou, H., Zhou, W., Bao, Y., Li, X. and Pu, Q. (2018b), "Experimental study on dynamic effects of a long- span railway continuous beam bridge", Appl. Sci., 8(5), 669.
  10. Gou, H., Yang, L., Mo, Z., Guo, W., Shi, X. and Bao, Y. (2019), "Effect of long-term bridge deformations on safe operation of high-speed railway and vibration of vehicle-bridge coupled system", Int. J. Struct. Stab. Dyn., 19(9), 1950111.
  11. He, X., Wu, T., Zou, Y., Chen, Y. F., Guo, H. and Yu, Z. (2017), "Recent developments of high-speed railway bridges in China", Struct. Infrastruct. E, 13(12), 1584-1595.
  12. He, C., Chen, Z. and He, Q. (2018), "Dynamic Behaviors of High Speed Train Running through Subgrade Bridge Transition Section", In: ICRT 2017: Railway Development, Operations, and Maintenance, Reston, VA, USA: American Society of Civil Engineers, pp. 197-206.
  13. Jahangiri, M. and Zakeri, J. (2017), "Dynamic analysis of trainbridge system under one-way and two-way high-speed train passing", Struct. Eng. Mech., Int. J., 64(1), 33-44.
  14. Jiang, L., Feng, Y., Zhou, W. and He, B. (2018), "Analysis on natural vibration characteristics of steel- concrete composite truss beam", Steel Compos. Struct., Int. J., 26(1), 79-87.
  15. Jiang, L., Yu, J., Zhou, W., Feng, Y. and Chai, X. (2019a), "Analysis of flexural natural vibrations of thin-walled box beams using higher order beam theory", Struct. Des. Tall Spec., 28(14), 1-15.
  16. Jiang, L., Feng, Y., Zhou, W. and He, B. (2019b), "Vibration characteristic analysis of high-speed railway simply supported beam bridge-track structure system", Steel Compos. Struct., Int. J., 31(6), 591-600.
  17. Ju, S.H. (2013), "3D analysis of high-speed trains moving on bridges with foundation settlements", Arch. Appl. Mech., 83(2), 281-291.
  18. Kang, X., Jiang, L., Bai, Y. and Caprani, C.C. (2017), "Seismic damage evaluation of high-speed railway bridge components under different intensities of earthquake excitations", Eng. Struct., 152, 116-128.
  19. Kun, C., Yang, Z. and Chouw, N. (2018), "Seismic response of skewed bridges including pounding effects", Earthq. Struct., Int. J., 14(5), 467-476.
  20. Lai, M., Hanzic, L. and Ho, J.C.M. (2018), "Fillers to improve passing ability of concrete", Struct. Concrete, 20(1), 1-13.
  21. Lee, J.S., Choi, S., Kim, S.S., Kim, Y.G., Kim, S.W. and Park, C. (2012), "Waveband analysis of track irregularities in high -speed railway from on board acceleration measurement", J. Solid Mech. Mater. Eng., 6(6), 750-759.
  22. Li, X., Liang, L. and Wang, D. (2018), "Vibration and noise characteristics of an elevated box girder paved with different track structures", J. Sound Vib., 425, 21-40.
  23. Ministry of Railways (2014), Code for design high speed railway; China Railway Press, Beijing, China.
  24. Podworna, M. (2017), "Dynamic response of steel-concrete composite bridges loaded by high-speed train", Struct. Eng. Mech., Int. J., 62(2), 179-196.
  25. Qiao, H., Xia, H. and Du, X. (2018), "Dynamic analysis of an integrated train-bridge-foundation-soil system by the substructure method", Int. J. Struct. Stab. Dyn., 18(5), 1850069.
  26. Shi, R.X. (2013), "Influence of pier differential settlement on the track vertical profle irregularity", Sichuan Architect., 1, 94-99. [In Chinese]
  27. Sun, L., Hayashikawa, T., He, X. and Xie, W. (2015), "Influential parameter analysis on vibration responses of rigid-frame viaducts induced by running high-speed trains", Int. J. Steel Struct., 15(4), 809-826.
  28. Sun, L.M., Xie, W.P., He, X.W. and Hayashikawa, T. (2016), "Prediction and mitigation analysis of ground vibration caused by running high-speed trains on rigid-frame viaducts", Earthq. Eng. Eng. Vib., 15(1), 31-47.
  29. Toydemir, B., Kocak, A., Sevim, B. and Zengin, B. (2017), "Ambient vibration testing and seismic performance of precast I beam bridges on a high speed railway line", Steel Compos. Struct., Int. J., 23(5), 557-570.
  30. Toyooka, A., Ikeda, M., Yanagawa, H., Kataoka, H., Iemura, H. and Murata, K. (2005), "Effects of track structure on seismic behavior of isolation system bridges", Quarterly Report of RTRI, 46(4), 238-243.
  31. Wang, K., Liu, P., Zhai, W., Huang, C., Chen, Z. and Gao, J. (2015), "Wheel/rail dynamic interaction due to excitation of rail corrugation in high-speed railway", Sci. China: Technol. Sci., 58(2), 226-235.
  32. Wei, Y., Xu, H. and Niu, B. (2010), "Laboratory test and numerical analysis on the mechanical behaviors of the slab track fastener due to the beam-ending deformation", China Railway Sci., 31(6), 43-49.
  33. Wei, Y., Xu, H. and Niu, B. (2011), "Model test and numerical analysis of the influence of ballastless track bridge beam end deformation on fastener", Railway Eng., 3, 99-102. [In Chinese]
  34. Xu, H. (2017), "Quantitative study on mapping relationship between bridge deformation and track geometry of high-speed railway", Southwest Jiaotong University, Chengdu, China.
  35. Yau, J.D. (2009), "Response of a maglev vehicle moving on a series of guideways with differential settlement", J. Sound Vib., 324(3-5), 816-831.
  36. Zhai, W., Zhao, C., Xia, H., Xie, Y., Li, G., Cai, C., Luo, Q. and Song, X. (2014), "Basic scientific issues on dynamic performance evolution of the high-speed railway infrastructure and its service safety", Sci. China: Technol. Sci., 44(7), 645-660.
  37. Zhou, W. and Jiang, L. (2017), "Distortional buckling of coldformed lipped channel columns subjected to axial compression", Steel Compos. Struct., Int. J., 23(3), 331-338.
  38. Zhou, W.B., Jiang, L.Z. and Yu, Z.W. (2013), "Analysis of free vibration characteristic of steel-concrete composite box girder considering shear lag and slip", J. Central South Univ., 20(9), 2570-2577.