An improved approach for multiple support response spectral analysis of a long-span high-pier railway bridge

  • Li, Lanping ;
  • bu, Yizhi ;
  • Jia, Hongyu ;
  • Zheng, Shixiong ;
  • Zhang, Deyi ;
  • Bi, Kaiming
  • Published : 2017.08.25


To overcome the difficulty of performing multi-point response spectrum analysis for engineering structures under spatially varying ground motions (SVGM) using the general finite element code such as ANSYS, an approach has been developed by improving the modelling of the input ground motions in the spectral analysis. Based on the stochastic vibration analyses, the cross-power spectral density (c-PSD) matrix is adopted to model the stationary SVGM. The design response spectra are converted into the corresponding PSD model with appropriate coherency functions and apparent wave velocities. Then elements of c-PSD matrix are summarized in the row and the PSD matrix is transformed into the response spectra for a general spectral analysis. A long-span high-pier bridge under multiple support excitations is analyzed using the proposed approach considering the incoherence, wave-passage and site-response effects. The proposed approach is deemed to be an efficient numerical method that can be used for seismic analysis of large engineering structures under SVGM.


response spectral analysis;multiple support excitation;stochastic vibration analysis;high-pier railway bridge;seismic spatial variability


  1. Ates, S., Dumanoglu, A.A. and Bayraktar, A. (2005), "Stochastic response of seismically isolated highway bridges with friction pendulum systems to spatially varying earthquake ground motions", Eng. Struct., 27(13), 1843-1858.
  2. Berrah, M. and Kausel, E. (1992), "Response spectrum analysis of structures subjected to spatially varying motions", Earthq. Eng. Struct. D., 21(6), 461-470.
  3. Berrah, M.K. and Kausel, E. (1993), "A model combination rule for spatially varying seismic motions", Earthq. Eng. Struct. D., 22(9), 791-800.
  4. Bi, K.M., Hao, H. and Chouw, N. (2010), "Required separation distance between decks and at abutments of a bridge crossing a canyon site to avoid seismic pounding", Earthq. Eng. Struct. D., 39(3), 303-323.
  5. Chouw, N., Hao, H. and Su, H. (2006), "Multi-sided pounding response of bridge structures with non-linear bearings to spatially varying ground excitation", Adv. Struct. Eng., 9(1), 55-66.
  6. Cowan, D.R., Consolazio, G.R. and Davidson, M.T. (2015), "Response-spectrum analysis for barge impacts on bridge structures", J. Bridge Eng., 20(12), 04015017(1)-04015017(10).
  7. Dumanogluid, A.A. and Soyluk, K.A. (2003), "Stochastic analysis of long span structures subjected to spatially varying ground motions including the site-response effect", Eng. Struct., 25(10), 1301-1310.
  8. Hao, H. (1997), "Stability of simple beam subjected to multiple seismic excitations", J. Eng. Mech., 123(7), 739-742.
  9. Hao, H. (1998), "A parametric study of the required seating length for bridge decks during earthquake", Earthq. Eng. Struct. D., 27(1), 91-103.<91::AID-EQE722>3.0.CO;2-I
  10. Harichandran, R., Hawwari, A. and Sweidan, B. (1996), "Response of long-span bridges to spatially varying ground motion", J. Struct. Eng., 122(5), 476-484.
  11. Heredia, Z.E. and Vanmarcke, E.H. (1995), "Closure on the discussion on seismic random-vibration analysis of multisupport structural systems", J. Eng. Mech., 121(9), 1037-1038.
  12. Jankowski, R., Wilde, K. and Fujino, Y. (2000), "Reduction of pounding effects in elevated bridges during earthquakes", Earthq. Eng. Struct. D., 29(2), 195-212.<195::AID-EQE897>3.0.CO;2-3
  13. Jia, H.Y., Zhang, D.Y., Zheng, S.X., Xie, W.C. and Pandey, M.D. (2013), "Local site effects on a high-pier railway bridge under tridirectional spatial excitations: Nonstationary stochastic analysis", Soil Dyn. Earthq. Eng., 52, 55-69.
  14. Kahan, M. and Gibert, R.J. (1996), "Influence of seismic waves spatial variability on bridges: A sensitivity analysis", Earthq. Eng. Struct. D., 25(8), 795-814.<795::AID-EQE582>3.0.CO;2-X
  15. Kaul, M.K. (1978), "Stochastic characterization of earthquakes through their response spectrum", Earthq. Eng. Struct. D., 6(5), 497-509.
  16. Kawashima, K., Takahashi, Y. and Ge, H. (2009), "Reconnaissance report on damage of bridges in 2008 Wenchuan, China, Earthquake", J. Earthq. Eng., 13(7), 965-996.
  17. Kiureghian, A.D. (1981), "A response spectrum method for random vibration analysis of MDF systems", Earthq. Eng. Struct. D., 9(5), 419-435.
  18. Kiureghian, D.A. and Neuenhofer, A. (1992), "Response spectrum method for multi-support seismic excitations", Earthq. Eng. Struct. D., 21(8), 713-740.
  19. Konakli, K. and Kiureghian, A.D. (2011), "Extended MSRS rule for seismic analysis of bridges subjected to differential support motions", Earthq. Eng. Struct. D., 40(12), 1315-1335.
  20. Liu, G., Lian, J., Liang, C., Li, G. and Hu, J.J. (2016), "An improved complex multiple-support response spectrum method for the non-classically damped linear system with coupled damping", Bull. Earthq. Eng., 14(1), 161-184.
  21. Loh, C.H. and Yeh, Y.T. (1988), "Spatial variation and stochastic modeling of seismic differential ground movement", Earthq. Eng. Struct. D., 16(4), 583-596.
  22. Nazmy, A.S. and Abdelghaffar, A.M. (1992), "Effects of ground motion spatial variability on the response of cable-stayed bridge", Earthq. Eng. Struct. D., 21(1), 1-20.
  23. Soyluk, K. (2004), "Comparison of random vibration methods for multi-support seismic excitation analysis of long-span bridges", Eng. Struct., 26(11), 1573-1583.
  24. Wang, F., Zhou, Y. and Wang, S. (2010), "Investigation and assessment of seismic geologic hazard triggered by the Yushu earthquake using geo-spatial information technology", Disaster Adv., 3(4), 72-76.
  25. Wang, Z. and Kiureghian, A.D. (2014), "Multiple-support response spectrum analysis using load-dependent Ritz vectors", Earthq. Eng. Struct. D., 43(15), 2283-2297.
  26. Yau, J.D. and Fryba, L. (2007), "Response of suspended beams due to moving loads and vertical seismic ground excitations", Eng. Struct., 29(12), 3255-3262.
  27. Zanardo, G., Hao, H. and Modena, C. (2002), "Seismic response of multi-span simply supported bridges to a spatially varying earthquake ground motion", Earthq. Eng. Struct. D., 31(6), 1325-1345.
  28. Zhang, D.Y., Jia, H.Y., Zheng, S.X., Xie, W.C. and Pandey, M.D. (2014), "A highly efficient and accurate stochastic seismic analysis approach for structures under tridirectional nonstationary multiple excitations", Comput. Struct., 145, 23-35.


Supported by : National Science Foundation of China