Structural Engineering and Mechanics

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Reliability-based fragility analysis of nonlinear structures under the actions of random earthquake loads

  • Received : 2017.08.19
  • Accepted : 2018.01.29
  • Published : 2018.04.10
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Abstract

This study presents the reliability-based analysis of nonlinear structures using the analytical fragility curves excited by random earthquake loads. The stochastic method of ground motion simulation is combined with the random vibration theory to compute structural failure probability. The formulation of structural failure probability using random vibration theory, based on only the frequency information of the excitation, provides an important basis for structural analysis in places where there is a lack of sufficient recorded ground motions. The importance of frequency content of ground motions on probability of structural failure is studied for different levels of the nonlinear behavior of structures. The set of simulated ground motion for this study is based on the results of probabilistic seismic hazard analysis. It is demonstrated that the scenario events identified by the seismic risk differ from those obtained by the disaggregation of seismic hazard. The validity of the presented procedure is evaluated by Monte-Carlo simulation.

Keywords

References

  1. Alibrandi, U. and Der Kiureghian, A. (2012), "A gradient-free method for determining the design point in nonlinear stochastic dynamic analysis", Prob. Eng. Mech., 28, 2-10. https://doi.org/10.1016/j.probengmech.2011.08.018
  2. Alibrandi, U. and Mosalam, K.M. (2017), "Equivalent linearization methods for stochastic dynamic analysis using linear response surfaces", J. Eng. Mech., 143(8), 04017055. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001264
  3. Atkinson, G.M. (1993), "Earthquake source spectra in Eastern North America", Bull. Seismol. Soc. Am. 83(6), 1778-1798.
  4. Atkinson, G.M. and Silva, W. (2000), "Stochastic modeling of California ground motions", Bull. Seismol. Soc. Am., 90(2), 255-274. https://doi.org/10.1785/0119990064
  5. Au, S.K. and Beck, J.L. (2003), "Subset simulation and its application to seismic risk based on dynamic analysis", J. Eng. Mech., 129(8), 901-917. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:8(901)
  6. Baker, J.W. and Cornell, C.A. (2006), Vector-Valued Ground Motion Intensity Measures for Probabilistic Seismic Demand Analysis, Pacific Earthquake Engineering Research Center, College of Engineering, University of California, Berkeley, U.S.A.
  7. Baker, J.W. and Lee, C. (2016), "An improved algorithm for selecting ground motions to match a conditional spectrum", J. Earthq. Eng., Accepted.
  8. Beresnev, I.A. and Atkinson, G.M. (1998), "Stochastic finite-fault modeling of ground motions from the 1994 Northridge, California, earth-quake, I. Validation on rock sites", Bull. Seismol. Soc. Am., 88(6), 1392-1401.
  9. Beresnev, I. and Atkinson, G. (1999), "Generic finite-fault model for ground motion prediction in eastern North America", Bull. Seismol. Soc. Am., 89(3), 608-625.
  10. Boatwright, J. and Choy, G.L. (1992), "Acceleration source spectra anticipated for large earthquakes in northeastern North America", Bull. Seismol. Soc. Am., 82(2), 660-682.
  11. Boore, D.M. (2003), "Prediction of ground motion using the stochastic method", Pure Appl. Geophys., 160, 635-676. https://doi.org/10.1007/PL00012553
  12. Boore, D.M. (2009), "Comparing stochastic point-source and finite-source ground-motion simulations", SMSIM and EXSIM, Bull. Seismol. Soc. Am., 99(6), 3202-3216. https://doi.org/10.1785/0120090056
  13. Boore, D.M. and Atkinson, G.M. (1987), "Stochastic prediction of ground motion and spectral response parameters at hard-rock sites in eastern North America", Bull. Seismol. Soc. Am., 77, 440-467.
  14. Bouc, R. (1967), "Forced vibration of mechanical systems with hysteresis", Proceedings of the 4th Conference on Non-Linear Oscillation, Prague, Czechoslovakia.
  15. Broccardo, M. (2014), Further Development of the Tail-Equivalent Linearization Method for Nonlinear Stochastic Dynamics, University of California, Berkeley, U.S.A.
  16. Broccardo, M., Alibrandi, U., Wang, Z, and Garre, L. (2017), "The tail equivalent linearization method for nonlinear stochastic processes, genesis and developments", Risk Reliab. Analy.: Theor. Appl., 109-142.
  17. Broccardo, M. and Der Kiureghian, A. (2013), "Non-stationary stochastic dynamic analysis by tail-equivalent linearization", Proceedings of the 11th International Conference on Structural Safety and Reliability, New York, U.S.A.
  18. Broccardo, M. and Der Kiureghian, A. (2015), "Multicomponent nonlinear stochastic dynamic analysis by tail-equivalent linearization", J. Eng. Mech., 142(3), 04015100.
  19. Brune, J. (1971), "Correction: Tectonic stress and the spectra of seismic shear waves", J. Geophys. Res., 76, 5002. https://doi.org/10.1029/JB076i020p05002
  20. Brune, J.N. (1970), "Tectonic stress and the spectra of seismic shear waves from earthquakes", J. Geophys. Res., 75(26), 4997-5009. https://doi.org/10.1029/JB075i026p04997
  21. Burks, L.S., Zimmerman, R.B. and Baker, J.W. (2015), "Evaluation of hybrid broadband ground motion simulations for response history analysis and design", Earthq. Spectr., 31(3), 1691-1710. https://doi.org/10.1193/091113EQS248M
  22. Cimellaro, G.P., Reinhorn, A.M., D'Ambrisi, A. and De Stefano, M. (2009), "Fragility analysis and seismic record selection", J. Struct. Eng., 137(3), 379-390.
  23. Crandall, S.H. (2006), "A half-century of stochastic equivalent linearization", Struct. Contr. Health Monitor., 13(1), 27-40. https://doi.org/10.1002/stc.129
  24. Der Kiureghian, A. (2000), "The geometry of random vibrations and solutions by FORM and SORM", Prob. Eng. Mech., 15(1), 81-90. https://doi.org/10.1016/S0266-8920(99)00011-9
  25. Der Kiureghian, A. and Fujimura, K. (2009), "Nonlinear stochastic dynamic analysis for performance-based earthquake engineering", Earthq. Eng. Struct. Dyn., 38(5), 719-738. https://doi.org/10.1002/eqe.899
  26. Ellingwood, B.R., Celik, O.C. and Kinali, K. (2007), "Fragility assessment of building structural systems in mid-America", Earthq. Eng. Struct. Dyn., 36(13), 1935-1952. https://doi.org/10.1002/eqe.693
  27. Fujimura, K. and Der Kiureghian, A. (2007), "Tail-equivalent linearization method for nonlinear random vibration", Prob. Eng. Mech., 22(1), 63-76. https://doi.org/10.1016/j.probengmech.2006.08.001
  28. Garre, L. and Der Kiureghian, A. (2010), "Tail-equivalent linearization method in frequency domain and application to marine structures", Mar. Struct., 23(3), 322-338. https://doi.org/10.1016/j.marstruc.2010.07.006
  29. Hanks, T.C. and McGuire, R.K. (1981), "Character of high frequency ground motion", Bull. Seismol. Soc. Am., 71, 2071-2095.
  30. Haselton, C.B., Baker, J.W., Bozorgnia, Y., Goulet, C.A., Kalkan, E., Luco, N. and Watson-Lamprey, J. (2009), Evaluation of Ground Motion Selection and Modification Methods: Predicting Median Interstory Drift Response of Buildings, PEER Report 2009.
  31. Haukaas, T. and Der Kiureghian, A. (2004), Finite Element Reliability and Sensitivity Methods for Performance-Based Engineering, Rep. No. PEER 2003/14, Pacific Earthquake Engineering Research Center, University of California, Berkeley, California, U.S.A.
  32. Haukaas, T. and Der Kiureghian, A. (2006), "Strategies for zfinding the design point in nonlinear finite element reliability analysis", Prob. Eng. Mech., 21(2), 133-147. https://doi.org/10.1016/j.probengmech.2005.07.005
  33. He, J. (2015), "Karhunen-Loeve expansion for random earthquake excitations", Earthq. Eng. Eng. Vibr., 14(1), 77. https://doi.org/10.1007/s11803-015-0007-4
  34. Hong, H.P. and Goda, K. (2006), "A comparison of seismichazard and risk deaggregation", Bullet. Seismol. Soc. Am., 96(6), 2021-2039. https://doi.org/10.1785/0120050238
  35. Ju, B.S., Jung, W.Y. and Ryu, Y.H. (2013), "Seismic fragility evaluation of piping system installed in critical structures", Struct. Eng. Mech., 46(3), 337-352. https://doi.org/10.12989/sem.2013.46.3.337
  36. Kafali, C. and Grigoriu, M. (2007), "Seismic fragility analysis: Application to simple linear and nonlinear systems", Earthq. Eng. Struct. Dyn., 36(13), 1885-1900. https://doi.org/10.1002/eqe.726
  37. Kanai, K. (1957), "Semiempirical formula for the seismic characteristics of the ground motion", Bull. Earth. Res. Inst., 35(2), 308-325.
  38. Katsanos, E.I., Sextos, A.G. and Manolis, G.D. (2010), "Selection of earthquake ground motion records: A state-of-the-art review from a structural engineering perspective", Soil Dyn. Earthq. Eng., 30(4), 157-169. https://doi.org/10.1016/j.soildyn.2009.10.005
  39. Key, D. (1988), The Calculation of Structure Response. Earthquake Design Practice for Buildings, Thomas Telford, London, U.K.
  40. Khorami, M., Motahar, H., Alvansazyazdi, M., Shariati, M., Jalali, A. and Tahir, M.M. (2017) "Evaluation of the seismic performance of special moment frames using incremental nonlinear dynamic analysis", Struct. Eng. Mech., 63(2), 259-268. https://doi.org/10.12989/SEM.2017.63.2.259
  41. Kohrangi, M., Vamvatsikos, D. and Bazzurro, P. (2017), "Site dependence and record selection schemes for building fragility and regional loss assessment", Earthq. Eng. Struct. Dyn.
  42. Koo, H. and Der Kiureghian, A. (2003), FORM, SORM and Simulation Techniques for Nonlinear Random Vibrations, Rep. No. UCB/SEMM-2003/1, Dept. of Civil and Environmental Engineering, University of California, Berkeley, California, U.S.A.
  43. Koo, H., Der Kiureghian, A. and Fujimura, K. (2005), "Designpoint excitation for non-linear random vibration", Probab. Eng. Mech., 20(2), 136-147. https://doi.org/10.1016/j.probengmech.2005.04.001
  44. Kwon, O.S. and Elnashai, A. (2006), "The effect of material and ground motion uncertainty on the seismic vulnerability curves of RC structure", Eng. Struct., 28(2), 289-303. https://doi.org/10.1016/j.engstruct.2005.07.010
  45. Lallemant, D., Kiremidjian, A. and Burton, H. (2015), "Statistical procedures for developing earthquake damage fragility curves". Earthq. Eng. Struct. Dyn., 44(9), 1373-1389. https://doi.org/10.1002/eqe.2522
  46. Lee, T.H. and Mosalam, K.M. (2005), "Seismic demand sensitivity of reinforced concrete shear-wall building using FOSM method", Earthq. Eng. Struct. Dyn., 34(14), 1719-1736. https://doi.org/10.1002/eqe.506
  47. Li, C.C. and Der Kiureghian, A. (1993), "Optimal discretization of random fields", J. Eng. Mech., 119(6), 1136-1154. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:6(1136)
  48. Lin, T., Harmsen, S.C., Baker, J.W. and Luco, N. (2013), "Conditional spectrum computation incorporating multiple causal earthquakes and ground-motion prediction models", Bullet. Seismol. Soc. Am., 103(2A), 1103-1116. https://doi.org/10.1785/0120110293
  49. Liu, J., Liu, Y. and Liu, H. (2010), "Seismic fragility analysis of composite frame structure based on performance", Earthq. Sci., 23(1), 45-52. https://doi.org/10.1007/s11589-009-0049-7
  50. Liu, Z., Liu, Z. and Peng, Y. (2017), "Dimension reduction of Karhunen-Loeve expansion for simulation of stochastic processes", J. Sound Vibr., 408, 168-189. https://doi.org/10.1016/j.jsv.2017.07.016
  51. Mandal, T.K., Ghosh, S. and Pujari, N.N. (2016), "Seismic fragility analysis of a typical Indian PHWR containment: Comparison of fragility models", Struct. Safety, 58, 11-19. https://doi.org/10.1016/j.strusafe.2015.08.003
  52. Mehani, Y., Bechtoula, H., Kibboua, A. and Naili, M. (2013), "Assessment of seismic fragility curves for existing RC buildings in Algiers after the 2003 Boumerdes earthquake", Struct. Eng. Mech, 46(6), 791-808. https://doi.org/10.12989/sem.2013.46.6.791
  53. Mitropoulou, C. C., and Papadrakakis, M. (2011), "Developing fragility curves based on neural network IDA predictions", Eng. Struct., 33(12), 3409-3421. https://doi.org/10.1016/j.engstruct.2011.07.005
  54. Motazedian, D. and Atkinson, G.M. (2005), "Stochastic finitefault modeling based on a dynamic corner frequency", Bull. Seismol. Soc. Am., 95(3), 995-1010. https://doi.org/10.1785/0120030207
  55. Radu, A. and Grigoriu, M. (2014), "A comparative study on fragility analyses in earthquake engineering", In A. Cunha, E. Caetano, P. Ribeiro, & G. Muller (Eds.), Proceedings of the 9th International Conference on Structural Dynamics, Porto, Portugal,
  56. Raoufi, R. and Ghafory-Ashtiany, M. (2016), "Nonlinear biaxial structural vibration under bidirectional random excitation with incident angle ${\theta}$ by tail-equivalent linearization method", J. Eng. Mech., 142(8), 04016050. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001103
  57. Schotanus, M.I.J., Franchin, P., Lupoi, A. and Pinto, P.E. (2004), "Seismic fragility analysis of 3D structures", Struct. Safety, 26(4), 421-441. https://doi.org/10.1016/j.strusafe.2004.03.001
  58. Seyedi, D.M., Gehl, P., John Douglas, L., Davenne, N.M. and Ghavamian, S. (2010), "Development of seismic fragility surfaces for reinforced concrete buildings by means of nonlinear time-history analysis", Earthq. Eng. Struct. Dyn., 39(1), 91-108. https://doi.org/10.1002/eqe.939
  59. Silva, V., Crowley, H. and Bazzurro, P. (2016), "Exploring risktargeted hazard maps for Europe", Earthq. Spectr., 32(2), 1165-1186. https://doi.org/10.1193/112514EQS198M
  60. Sudret, B. and Der Kiureghian, A. (2000), Stochastic Finite Element Methods and Reliability: A State-of-the-Art Report, Berkeley: Department of Civil and Environmental Engineering, University of California, U.S.A.
  61. Tajimi, H. (1960), "A statistical method of determining the maximum response of a building structure during an earthquake", Proceedings of the 2nd World Conference on Earthquake Engineering, Tokyo.
  62. Vamvatsikos, D. and Cornell, C.A. (2002), "Incremental dynamic analysis", Earthq. Eng. Struct. Dyn., 31(3), 491-514. https://doi.org/10.1002/eqe.141
  63. Vanmarcke, E. (1975), "On the distribution of the first-passage time for normal stationary random processes", J. Appl. Mech., 42(1), 215-220. https://doi.org/10.1115/1.3423521
  64. Wang, Z. and Der Kiureghian, A. (2016), "Tail-equivalent linearization of inelastic multisupport structures subjected to spatially varying stochastic ground motion", J. Eng. Mech., 142(8), 4016053. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001106
  65. Wen, Y.K. (1976), "Method for random vibration of hysteretic systems", J. Eng. Mech. Div., 102(2), 249-263.
  66. Yazdani, A. and Eftekhari, S.N. (2012), "Variance decomposition of the seismic response of structures", Sci. Iran., 19(1), 84-90. https://doi.org/10.1016/j.scient.2011.12.003
  67. Yazdani, A. and Salimi, M.R. (2015), "Earthquake response spectra estimation of bilinear hysteretic systems using randomvibration theory method", Earthq. Struct., 8(5), 1055-1067. https://doi.org/10.12989/eas.2015.8.5.1055
  68. Yazdani, A. and Takada, T. (2011), "Probabilistic study of the effect of the influence of ground motion variables on the response spectra", Struct. Eng. Mech., 39, 877-893. https://doi.org/10.12989/sem.2011.39.6.877
  69. Zhang, J. and Ellingwood, B. (1994), "Orthogonal series expansions of random fields in reliability analysis", J. Eng. Mech., 120(12), 2660-2677. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:12(2660)

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