Structural Engineering and Mechanics

  • 제82권3호
  • /
  • Pages.325-341
  • /
  • 2022
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Effect of non-stationary spatially varying ground motions on the seismic responses of multi-support structures

  • Xu, Zhaoheng (School of Civil Engineering, Central South University) ;
  • Huang, Tian-Li (School of Civil Engineering, Central South University) ;
  • Bi, Kaiming (Centre for Infrastructure Monitoring and Protection, School of Civil and Mechanical Engineering, Curtin University)
  • 투고 : 2021.02.18
  • 심사 : 2022.02.11
  • 발행 : 2022.05.10
⟨ 이전 논문 다음 논문 ⟩

초록

Previous major earthquakes indicated that the earthquake induced ground motions are typical non-stationary processes, which are non-stationary in both amplification and frequency. For the convenience of aseismic design and analysis, it usually assumes that the ground motions at structural supports are stationary processes. The development of time-frequency analysis technique makes it possible to evaluate the non-stationary responses of engineering structures subjected to non-stationary inputs, which is more general and realistic than the analysis method commonly used in engineering. In this paper, the wavelet-based stochastic vibration analysis methodology is adopted to calculate the non-stationary responses of multi-support structures. For comparison, the stationary response based on the standard random vibration method is also investigated. A frame structure and a two-span bridge are analyzed. The effects of non-stationary spatial ground motion and local site conditions are considered, and the influence of structural property on the structural responses are also considered. The analytical results demonstrate that the non-stationary spatial ground motions have significant influence on the response of multi-support structures.

키워드

과제정보

The authors thank the financial support granted by the Natural Science Foundation of China (Grants No. 52078486, 50708113), the Natural Science Foundation of Hunan Province, China (Grant No. 2021JJ50145), the Scientific Research Fund of Hunan Provincial Education Department, China (Grant No. 19B106), and the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2020zzts635).

참고문헌

  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. https://doi.org/10.1016/j.engstruct.2005.05.016.
  2. Basu, B. and Gupta, V.K. (1997), "Non-stationary seismic response of MDOF systems by wavelet transform", Earthq. Eng. Struct. Dyn., 26(12), 1243-1258. https://doi.org/10.1002/(SICI)1096-9845(199712)26:12<1243::AID-EQE708>3.0.CO;2-P.
  3. Basu, B. and Gupta, V.K. (1998), "Seismic response of SDOF systems by wavelet modeling of nonstationary processes", J. Eng. Mech., 124(10), 1142-1150. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:10(1142).
  4. Basu, B. and Gupta, V.K. (1999), "Wavelet-based analysis of the non-stationary response of a slipping foundation", J. Sound Vib., 222(4), 547-563. https://doi.org/10.1006/jsvi.1998.2122.
  5. Basu, B. and Gupta, V.K. (2000), "Stochastic seismic response of single-degree-of-freedom systems through wavelets", Eng. Struct., 22(12), 1714-1722. https://doi.org/10.1016/S0141-0296(99)00109-1.
  6. Bi, K., 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. Dyn., 39(3), 303-323. https://doi.org/10.1002/eqe.943.
  7. Bi, K., Hao, H. and Ren, W. (2010), "Response of a frame structure on a canyon site to spatially varying ground motions", Struct. Eng. Mech., 36(1), 111-127. https://doi.org/10.12989/sem.2010.36.1.111.
  8. Bolt, A.B., Loh, C.H., Penzien, J., Tsai, Y.B. and Yeh, Y.T. (1982), "Preliminary report on the SMART-1 strong motion array in Taiwan", Report No. UCB/EERC-82-13, Earthquake Engineering Research Center, University of California.
  9. Chakraborty, A. and Basu, B. (2008), "Nonstationary response analysis of long span bridges under spatially varying differential support motions using continuous wavelet transform", J. Eng. Mech., 134(2), 155-162. https://doi.org/10.1061/(ASCE)0733-9399(2008)134:2(155).
  10. Chouw, N. and Hao, H. (2008), "Significance of SSI and nonuniform near-fault ground motions in bridge response II: Effect on response with modular expansion joint", Eng. Struct., 30(1), 154-162. https://doi.org/10.1016/j.engstruct.2007.02.020.
  11. Chouw, N. and Hao, H. (2008), "Significance of SSI and nonuniform near-fault ground motions in bridge response I: Effect on response with conventional expansion joint", Eng. Struct., 30(1), 141-153. https://doi.org/10.1016/j.engstruct.2007.03.002.
  12. Clough, R.W. and Penzien, J. (2003), Dynamics of Structures, McGraw-Hill, New York, USA.
  13. Conte, J.P. (1992), "Effects of earthquake frequency nonstationarity on inelastic structural response", Proc. of the 10th World Conference on Earthquake Engineering, 3645-3651.
  14. Conte, J.P. and Peng, B.F. (1997), "Fully nonstationary analytical earthquake ground motion model", J. Eng. Mech., 123(1), 15-16. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:1(15).
  15. Daubechies, I. (1992), Ten Lectures on Wavelets, Society for Industrial and Applied and Mathematics, Philadephia, USA.
  16. Deodatis, G. (1996), "Non-stationary stochastic vector processes: Seismic ground motion applications", Prob. Eng. Mech., 11(3), 149-167. https://doi.org/10.1016/0266-8920(96)00007-0.
  17. Dinh, V.N., Basu, B. and Brinkgreve, R.B.J. (2014), "Wavelet-based evolutionary response of multispan structures including wave-passage and site-response effects", J. Eng. Mech., 140(8), 04014056. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000708.
  18. Failla, G., Pappatico, M. and Cundari, G.A. (2011), "A wavelet-based spectrum for non-stationary processes", Mech. Res. Commun., 38(5), 361-367. https://doi.org/10.1016/j.mechrescom.2011.04.010.
  19. Grigoriu, M., Sonia, E.R. and Rosenblueth, E. (1988), "The Mexico earthquake of September 19, 1985-Nonstationary models of seismic ground acceleration", Earthq. Spectra, 4(3), 551-568. https://doi.org/10.1193/1.1585490.
  20. Hammond, J. (1968), "On the response of single and multidegree of freedom systems to non-stationary random excitations", J. Sound Vib., 7(3), 393-416. https://doi.org/10.1016/0022-460X(68)90138-7.
  21. Hammond, J. (1973), "Evolutionary spectra in random vibrations", J. Roy. Stat. Soc.: Ser. B (Methodological), 35(2), 167-179. https://doi.org/10.1111/j.2517-6161.1973.tb00950.x.
  22. Hao, H. (1993), "Arch responses to correlated multiple excitations", Earthq. Eng. Struct. Dyn., 22(5), 389-404. https://doi.org/10.1002/eqe.4290220503.
  23. Hao, H. (1994), "Ground-motion spatial variation effects on circular arch responses", J. Eng. Mech., 120(11), 2326-2341. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:11(2326).
  24. Hao, H. (1998), "A parametric study of the required seating length for bridge decks during earthquake", Earthq. Eng. Struct. Dyn., 27(1), 91-103. https://doi.org/10.1002/(SICI)1096-9845(199801)27:1<91::AID-EQE722>3.0.CO;2-I.
  25. Hao, H. and Duan, X. (1995), "Seismic response of asymmetric structures to multiple ground motions", J. Struct. Eng., 121(11), 1557-1564. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:11(1557).
  26. Hao, H. and Duan, X. (1996), "Multiple excitation effects on response of symmetric buildings", Eng. Struct., 18(9), 732-740. https://doi.org/10.1016/0141-0296(95)00217-0
  27. Hao, H. and Zhang, S.R. (1999), "Spatial ground motion effect on relative displacement of adjacent building structures", Earthq. Eng. Struct. Dyn., 28(4), 333-349. https://doi.org/10.1002/(SICI)1096-9845(199904)28:4<333::AID-EQE820>3.0.CO;2-R.
  28. Hao, H., Oliveira, C.S. and Penzien, J. (1989), "Multiple-station ground motion processing and simulation based on SMART-1 array data", Nucl. Eng. Des., 111(3), 293-310. https://doi.org/10.1016/0029-5493(89)90241-0.
  29. Harichandran, R.S. and Wang, W. (1988), "Response of simple beam to spatially varying earthquake excitation", J. Eng. Mech., 114(9), 1526-1541. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:9(1526).
  30. Harichandran, R.S. and Wang, W. (1990), "Response of indeterminate two-pan beam to spatially varying seismic excitation", Earthq. Eng. Struct. Dyn., 19(2), 173-187. https://doi.org/10.1002/eqe.4290190203.
  31. Kijewski-Correa, T. and Kareem, A. (2006), "Efficacy of Hilbert and wavelet transforms for time-frequency analysis", J. Eng. Mech., 132(10), 1037-1049. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:10(1037).
  32. Kiureghian, A. (1980), "Structural response to stationary excitation", J. Eng. Mech. Div., 106(6), 1195-1213. https://doi.org/10.1061/JMCEA3.0002659.
  33. Kiureghian, A. (1996), "A coherency model for spatially varying ground motions", Earthq. Eng. Struct. Dyn., 25(1), 99-111. https://doi.org/10.1002/(SICI)1096-9845(199601)25:1<99::AID-EQE540>3.0.CO;2-C.
  34. Kiureghian, A.D. and Neuenhofer, A. (1992), "Response spectrum method for multi-support seismic excitations", Earthq. Eng. Struct. Dyn., 21(8), 713-740. https://doi.org/10.1002/eqe.4290210805.
  35. Kong, F., Kougioumtzoglou I.A., Spanos, P.D. and Li, S.J. (2016), "Nonlinear system response evolutionary power spectral density determination via a harmonic wavelets based Galerkin technique", Int. J. Multis. Comput. Eng., 14(3), 255-272. https://doi.org/10.1615/IntJMultCompEng.2016016464.
  36. Mallat, S.G. (1989), "Multiresolution approximations and wavelet orthonormal bases of L2(R)", Tran. Am. Math. Soc., 315(1), 69-87. https://doi.org/10.1090/S0002-9947-1989-1008470-5.
  37. Newland, D.E. (1994), "Wavelet analysis of vibration: Part 1-theory", J. Vib. Acoust., 116(4), 21-37. https://doi.org/10.1115/1.2930443.
  38. Pasparakis, G.D., Fragkoulis, V.C. and Beer M. (2021), "Harmonic wavelets based response evolutionary power spectrum determination of linear and nonlinear structural systems with singular matrices", Mech. Syst. Signal Pr., 149, 107203. https://doi.org/10.1016/j.ymssp.2020.107203.
  39. Peng, B.F. and Conte, J.P. (1998), "Closed-form solutions for the response of linear systems to fully nonstationary earthquake excitation", J. Eng. Mech., 124(6), 684-694. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:6(684).
  40. Priestley, M.B. (1965), "Evolutionary spectra and non-stationary processes", J. Roy. Stat. Soc.: Ser. B (Methodological), 27(2), 204-229. https://doi.org/10.1111/j.2517-6161.1965.tb01488.x.
  41. Priestley, M.B. (1967), "Power spectral analysis of non-stationary random processes", J. Sound Vib., 6(1), 86-97. https://doi.org/10.1016/0022-460X(67)90160-5.
  42. Priestley, M.B. (1981), Spectral Analysis and Time Series: Probability and Mathematical Statistics, Academic Press, New York, USA.
  43. Qiao, D., Zhi, X.D., Fan, F. and Hong, H.P. (2020), "Estimation of wavelet coherence of seismic ground motions", Bull. Seismol. Soc. Am., 110(2), 613-628. https://doi.org/10.1785/0120190160.
  44. Richards, P.G. and Aki, K. (1980), Quantitative Seismology Theory and Methods, W.H. Freeman and Company, San Francisco.
  45. Roesset, J.M. (1977), Soil Amplification of Earthquakes, Numerical Methods in Geotechnical Engineering, McGraw-Hill, New York.
  46. Ruiz, P. (1969), "Probabilistic study of the behavior of structures during earthquakes", Report No. UCB/EERC-69-03, University of California at Berkeley, Berkeley, CA.
  47. Safak, E. (1995), "Discrete-time analysis of seismic site amplification", J. Eng. Mech., 121(7), 801-809. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:7(801).
  48. Shinozuka, M. and Sata, Y. (1967), "Simulation of nonstationary random process", J. Eng. Mech. Div., 93(1), 11-40. https://doi.org/10.1061/JMCEA3.0000822
  49. Spanos, P.D. (1978), "Non-stationary random vibration of a linear structure", Int. J. Solid. Struct., 14(10), 861-867. https://doi.org/10.1016/0020-7683(78)90076-8.
  50. Spanos, P.D. and Failla, G. (2004), "Evolutionary spectra estimation using wavelets", J. Eng. Mech., 130(8), 952-960. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:8(952).
  51. Spanos, P.D., Kong, F., Li, J. and Kougioumtzoglou I.A. (2016), "Harmonic wavelets based excitation-response relationships for linear systems: A critical perspective", Prob. Eng. Mech., 44, 163-173. https://doi.org/10.1016/j.probengmech.2015.09.021.
  52. Sun, W.J. and Kareem, A. (1989), "Response of MDOF systems to nonstationary random excitation", Eng. Struct., 11(2), 83-91. https://doi.org/10.1016/0141-0296(89)90017-5.
  53. Tajimi, H. (1960), "A statistical method of determining the maximum response of a building during earthquake", Proceeding of 2nd World Conference on Earthquake Engineering, Tokyo.
  54. Zerva, A. (1990), "Response of multi-span beams to spatially incoherent seismic ground motions", Earthq. Eng. Struct. Dyn., 19(6), 819-832. https://doi.org/10.1002/eqe.4290190604
  55. Zerva, A. and Zervas, V. (2002), "Spatial variation of seismic ground motions: an overview", Appl. Mech. Rev., 55(3), 271-297. https://doi.org/10.1115/1.1458013.
  56. Zhang, C. and Wolf, J.P. (1998), "Dynamic soil-structure interaction: Current research in China and Switzerland", Developments in Geotechinical Engineering, Elsevier Science & Technology.