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Structural reliability approach to analysis of probabilistic seismic hazard and its sensitivities

  • Hossein Rahimi
  • Mojtaba Mahsuli
Original Research
  • 22 Downloads

Abstract

This paper presents a new probabilistic framework for seismic hazard assessment and hazard sensitivity analysis. Hazard in this context means the probability of exceeding a measure of ground shaking intensity, such as peak ground acceleration and spectral acceleration. The main components of the proposed framework include structural reliability methods to estimate exceedance probabilities and their sensitivities, and multiple probabilistic models for earthquake occurrence, magnitude, location, and ground motion. This paper presents two analysis approaches. The first approach utilizes the first- and second-order reliability methods and importance sampling. This approach efficiently yields the hazard exceedance probabilities at a single site. The second approach employs the Monte Carlo sampling reliability method and yields the hazard exceedance probabilities at a multitude of sites in a single analysis, which is suited for large-scale seismic zonation. This paper also presents the probabilistic models that are suited for such analyses with an emphasis on characterization of epistemic uncertainties. Finally, novel sensitivity measures are proposed for hazard sensitivity analysis. These measures provide a framework to identify the most important uncertainties and guide the research to reduce these uncertainties over time. The proposed approach is validated and showcased by an illustrative example. The companion paper presents a comprehensive application to hazard analysis of Iran.

Keywords

Probabilistic seismic hazard analysis Reliability method Probabilistic model Sensitivity analysis FORM SORM Monte Carlo sampling 

Notes

Acknowledgements

Grant No. 96013800 from Iran National Science Foundation (INSF) is gratefully acknowledged. The authors thank Dr. Jack Baker from Stanford University and Dr. Laurentiu Danciu from Swiss Seismological Service at ETH Zurich for insightful comments that improved the quality of this paper.

References

  1. Abrahamson NA (2006) Seismic hazard assessment: problems with current practice and future developments. In: First European conference on earthquake engineering and seismology. Geneva, SwitzerlandGoogle Scholar
  2. Abrahamson NA, Silva WJ, Kamai R (2014) Summary of the ASK14 ground motion relation for active crustal regions. Earthq Spectra 30:1025–1055CrossRefGoogle Scholar
  3. Akkar S, Cheng Y (2015) Application of a Monte-Carlo simulation approach for the probabilistic assessment of seismic hazard for geographically distributed portfolio. Earthq Eng Struct Dyn 45:525–541.  https://doi.org/10.1002/eqe.2667 CrossRefGoogle Scholar
  4. Akkar S, Sandıkkaya MA, Ay BÖ (2014a) Compatible ground-motion prediction equations for damping scaling factors and vertical-to-horizontal spectral amplitude ratios for the broader Europe region. Bull Earthq Eng 12:517–547CrossRefGoogle Scholar
  5. Akkar S, Sandıkkaya MA, Ay BÖ (2014b) Erratum to: compatible ground-motion prediction equations for damping scaling factors and vertical-to-horizontal spectral amplitude ratios for the broader Europe region. Bull Earthq Eng 12:1429–1430CrossRefGoogle Scholar
  6. Anagnos T, Kiremidjian AS (1988) A review of earthquake occurrence models for seismic hazard analysis. Probab Eng Mech 3:3–11.  https://doi.org/10.1016/0266-8920(88)90002-1 CrossRefGoogle Scholar
  7. Ang AHS, Tang WH (2007) Probability concepts in engineering: emphasis on applications to civil and environmental engineering, vol 1. Wiley, New YorkGoogle Scholar
  8. Ansari A, Firuzi E, Etemadsaeed L (2015) Delineation of seismic sources in probabilistic seismic-hazard analysis using fuzzy cluster analysis and Monte Carlo simulation. Bull Seismol Soc Am 105:2174–2191CrossRefGoogle Scholar
  9. ASCE (2005) Minimum design loads for buildings and other structures. ASCE/SEI 7-05, Reston, VAGoogle Scholar
  10. ASCE (2010) Minimum design loads for buildings and other structures. ASCE/SEI 7-10, Reston, VAGoogle Scholar
  11. Assatourians K, Atkinson GM (2013) EqHaz: an open-source probabilistic seismic-hazard code based on the Monte Carlo simulation approach. Seismol Res Lett 84:516–524CrossRefGoogle Scholar
  12. Atkinson GM, Bommer JJ, Abrahamson NA (2014) Alternative approaches to modeling epistemic uncertainty in ground motions in probabilistic seismic-hazard analysis. Seismol Res Lett 85:1141–1144CrossRefGoogle Scholar
  13. Boore DM, Stewart JP, Seyhan E, Atkinson GM (2014) NGA-West2 equations for predicting PGA, PGV, and 5% damped PSA for shallow crustal earthquakes. Earthq Spectra 30:1057–1085CrossRefGoogle Scholar
  14. Box GEP, Tiao GC (1992) Bayesian inference in statistical analysis. Wiley, New JerseyCrossRefGoogle Scholar
  15. Bozorgnia Y, Abrahamson NA, Atik LA et al (2014) NGA-West2 research project. Earthq Spectra 30:973–987CrossRefGoogle Scholar
  16. Bradley BA (2012) Empirical correlations between cumulative absolute velocity and amplitude-based ground motion intensity measures. Earthq Spectra 28:37–54CrossRefGoogle Scholar
  17. Breitung K (1984) Asymptotic approximations for multinormal integrals. J Eng Mech 110:357–366CrossRefGoogle Scholar
  18. Campbell KW, Bozorgnia Y (2012) Cumulative absolute velocity (CAV) and seismic intensity based on the PEER-NGA database. Earthq Spectra 28:457–485CrossRefGoogle Scholar
  19. Campbell KW, Bozorgnia Y (2014) NGA-West2 ground motion model for the average horizontal components of PGA, PGV, and 5% damped linear acceleration response spectra. Earthq Spectra 30:1087–1115CrossRefGoogle Scholar
  20. Cheng Y, Akkar S (2016) Probabilistic permanent fault displacement hazard via Monte Carlo simulation and its consideration for the probabilistic risk assessment of buried continuous steel pipelines. Earthq Eng Struct Dyn 46:605–620CrossRefGoogle Scholar
  21. Chiou BSJ, Youngs RR (2014) Update of the Chiou and Youngs NGA model for the average horizontal component of peak ground motion and response spectra. Earthq Spectra 30:1117–1153.  https://doi.org/10.1193/072813EQS219M CrossRefGoogle Scholar
  22. Christensen K, Olami Z (1992) Variation of the Gutenberg–Richter b values and nontrivial temporal correlations in a spring-block Model for earthquakes. J Geophys Res Solid Earth 97:8729–8735.  https://doi.org/10.1029/92JB00427 CrossRefGoogle Scholar
  23. Cornell CA (1967) Bounds on reliability of structural systems. Am Soc Civ Eng Pro J Struct Div 93:171–200Google Scholar
  24. Cornell CA (1968) Engineering seismic risk analysis. Bull Seismol Soc Am 58:1583–1606.  https://doi.org/10.1016/0167-6105(83)90143-5 CrossRefGoogle Scholar
  25. Cramer CH, Petersen MD, Reichle MS (1996) A Monte Carlo approach in estimating uncertainty for a seismic hazard assessment of Los Angeles, Ventura, and Orange Counties, California. Bull Seismol Soc Am 86:1681–1691Google Scholar
  26. Danciu L, Kale Ö, Akkar S (2018a) The 2014 earthquake model of the middle east: ground motion model and uncertainties. Bull Earthq Eng 16:3497–3533.  https://doi.org/10.1007/s10518-016-9989-1 CrossRefGoogle Scholar
  27. Danciu L, Şeşetyan K, Demircioglu M et al (2018b) The 2014 earthquake model of the middle east: seismogenic sources. Bull Earthq Eng 16:3465–3496.  https://doi.org/10.1007/s10518-017-0096-8 CrossRefGoogle Scholar
  28. Der Kiureghian A (2005) First-and second-order reliability methods. In: Nikolaidis E, Ghiocel DM, Singhal S (eds) Engineering design reliability handbook. CRC Press, Boca RatonGoogle Scholar
  29. Der Kiureghian A, Ang AHS (1977) A fault-rupture model for seismic risk analysis. Bull Seismol Soc Am 67:1173–1194Google Scholar
  30. Ditlevsen O, Madsen HO (1996) Structural reliability methods, 2nd edn. Wiley, ChichesterGoogle Scholar
  31. Du W, Wang G (2013a) A simple ground-motion prediction model for cumulative absolute velocity and model validation. Earthq Eng Struct Dyn 42:1189–1202.  https://doi.org/10.1002/eqe.2266 CrossRefGoogle Scholar
  32. Du W, Wang G (2013b) Intra-event spatial correlations for cumulative absolute velocity, Arias intensity, and spectral accelerations based on regional site conditions. Bull Seismol Soc Am 103:1117–1129CrossRefGoogle Scholar
  33. Ebel JE, Kafka AL (1999) A Monte Carlo approach to seismic hazard analysis. Bull Seismol Soc Am 89:854–866Google Scholar
  34. Giardini D, Danciu L, Erdik M et al (2018) Seismic hazard map of the Middle East. Bull Earthq Eng 16:3567–3570.  https://doi.org/10.1007/s10518-018-0347-3 CrossRefGoogle Scholar
  35. Goda K, Atkinson GM (2009) Probabilistic characterization of spatially correlated response spectra for earthquakes in Japan. Bull Seismol Soc Am 99:3003–3020CrossRefGoogle Scholar
  36. Goda K, Hong HP (2008) Spatial correlation of peak ground motions and response spectra. Bull Seismol Soc Am 98:354–365CrossRefGoogle Scholar
  37. Green RA, Hall WJ (1994) An overview of selected seismic hazard analysis methodologies. Report No. UILU-ENG-94-2011, Department of Civil Engineering, University of Illinois at Urbana-Champaign, Urbana-Champaign, ILGoogle Scholar
  38. Gutenberg B, Richter CF (1944) Frequency of earthquakes in California. Bull Seismol Soc Am 34:185–188Google Scholar
  39. Halchuk S, Allen T, Adams J, Rogers G (2014) Fifth generation seismic hazard model input files as proposed to produce values for the 2015 National Building Code of Canada. Open File 7576, Geological Survey Canada, Ottawa, ON, CanadaGoogle Scholar
  40. Han S-W, Choi Y-S (2008) Seismic hazard analysis in low and moderate seismic region-Korean peninsula. Struct Saf 30:543–558CrossRefGoogle Scholar
  41. Hasofer AM, Lind NC (1974) Exact and invariant second-moment code format. J Eng Mech Div 100:111–121Google Scholar
  42. Hohenbichler M, Rackwitz R (1988) Improvement of second-order reliability estimates by importance sampling. J Eng Mech 114:2195–2199CrossRefGoogle Scholar
  43. Hong HP, Goda K, Davenport AG (2006) Seismic hazard analysis: a comparative study. Can J Civ Eng 33:1156–1171CrossRefGoogle Scholar
  44. Idriss IM (2014) An NGA-West2 empirical model for estimating the horizontal spectral values generated by shallow crustal earthquakes. Earthq Spectra 30:1155–1177CrossRefGoogle Scholar
  45. Jayaram N, Baker JW (2009) Correlation model for spatially distributed ground-motion intensities. Earthq Eng Struct Dyn 38:1687–1708CrossRefGoogle Scholar
  46. Karimiparidari S, Zaré M, Zare M et al (2013) Iranian earthquakes, a uniform catalog with moment magnitudes. J Seismol 17:897–911.  https://doi.org/10.1007/s10950-013-9360-9 CrossRefGoogle Scholar
  47. Kleiber M, Hien TD, Antúnez H, Kowalczyk P (1997) Parameter sensitivity in nonlinear mechanics: theory and finite element computations. Wiley, West SussexGoogle Scholar
  48. Kohrangi M, Danciu L, Bazzurro P (2018) Comparison between outcomes of the 2014 Earthquake Hazard Model of the Middle East (EMME14) and national seismic design codes: the case of Iran. Soil Dyn Earthq Eng 114:348–361.  https://doi.org/10.1016/j.soildyn.2018.07.022 CrossRefGoogle Scholar
  49. Kramer SL (1996) Geotechnical earthquake engineering. Prentice Hall, Upper Saddle RiverGoogle Scholar
  50. Liu P-L, Der Kiureghian A (1986) Multivariate distribution models with prescribed marginals and covariances. Probab Eng Mech 1:105–112CrossRefGoogle Scholar
  51. Lombardi AM, Akinci A, Malagnini L, Mueller CS (2005) Uncertainty analysis for seismic hazard in Northern and Central Italy. Ann Geophys 48:853–865Google Scholar
  52. Mahsuli M (2012) Probabilistic models, methods, and software for evaluating risk to civil infrastructure. Ph.D. Dissertation, Department of Civil Engineering, University of British Columbia, Vancouver, CanadaGoogle Scholar
  53. Mahsuli M, Haukaas T (2013a) Computer program for multimodel reliability and optimization analysis. J Comput Civ Eng 27:87–98CrossRefGoogle Scholar
  54. Mahsuli M, Haukaas T (2013b) Seismic risk analysis with reliability methods, part I: models. Struct Saf 42:54–62.  https://doi.org/10.1016/j.strusafe.2013.01.003 CrossRefGoogle Scholar
  55. Mahsuli M, Haukaas T (2013c) Seismic risk analysis with reliability methods, part II: analysis. Struct Saf 42:63–74.  https://doi.org/10.1016/j.strusafe.2013.01.004 CrossRefGoogle Scholar
  56. Mahsuli M, Haukaas T (2013d) Sensitivity measures for optimal mitigation of risk and reduction of model uncertainty. Reliab Eng Syst Saf 117:9–20CrossRefGoogle Scholar
  57. Mahsuli M, Rahimi H, Bakhshi A (2018) Probabilistic seismic hazard analysis of Iran using reliability methods. Bull Earthq Eng.  https://doi.org/10.1007/s10518-018-0498-2 CrossRefGoogle Scholar
  58. Marzocchi W, Taroni M, Selva J (2015) Accounting for epistemic uncertainty in PSHA: logic tree and ensemble modeling. Bull Seismol Soc Am 105:2151.  https://doi.org/10.1785/0120140131 CrossRefGoogle Scholar
  59. McGuire RK (1974) Seismic structural response risk analysis incorporating peak response regressions on earthquake magnitude and distance. Department of Civil Engineering, Massachusetts Institute of Technology, Boston, MAGoogle Scholar
  60. McGuire RK (2004) Seismic hazard and risk analysis. Earthquake Engineering Research Institute, BerkeleyGoogle Scholar
  61. McGuire RK (2008) Probabilistic seismic hazard analysis: early history. Earthq Eng Struct Dyn 37:329–338.  https://doi.org/10.1002/eqe.765 CrossRefGoogle Scholar
  62. Musson RMW (1999) Determination of design earthquakes in seismic hazard analysis through Monte Carlo simulation. J Earthq Eng 3:463–474Google Scholar
  63. Musson RMW (2000) The use of Monte Carlo simulations for seismic hazard assessment in the UK. Ann Di Geofis 43:1–9Google Scholar
  64. Pagani M, Monelli D, Weatherill G et al (2014) OpenQuake engine: an open hazard (and risk) software for the global earthquake model. Seismol Res Lett 85:692–702CrossRefGoogle Scholar
  65. Rackwitz R, Fiessler B (1978) Structural reliability under combined random load sequences. Comput Struct 9:489–494CrossRefGoogle Scholar
  66. Scherbaum F, Bommer JJ, Bungum H et al (2005) Composite ground-motion models and logic trees: methodology, sensitivities, and uncertainties. Bull Seismol Soc Am 95:1575–1593.  https://doi.org/10.1785/0120040229 CrossRefGoogle Scholar
  67. Şeşetyan K, Danciu L, Demircioğlu Tümsa MB et al (2018) The 2014 seismic hazard model of the Middle East: overview and results. Bull Earthq Eng 16:3535–3566.  https://doi.org/10.1007/s10518-018-0346-4 CrossRefGoogle Scholar
  68. Sokolov V, Wenzel F (2015) On the relation between point-wise and multiple-location probabilistic seismic hazard assessments. Bull Earthq Eng 13:1281–1301.  https://doi.org/10.1007/s10518-014-9661-6 CrossRefGoogle Scholar
  69. Sokolov V, Zahran HM, Youssef SE-H et al (2017) Probabilistic seismic hazard assessment for Saudi Arabia using spatially smoothed seismicity and analysis of hazard uncertainty. Bull Earthq Eng 15:2695–2735.  https://doi.org/10.1007/s10518-016-0075-5 CrossRefGoogle Scholar
  70. Wen Y-K (1990) Structural load modeling and combination for performance and safety evaluation. Elsevier, AmsterdamGoogle Scholar
  71. Zahran HM, Sokolov V, Youssef SE-H, Alraddadi WW (2015) Preliminary probabilistic seismic hazard assessment for the Kingdom of Saudi Arabia based on combined areal source model: Monte Carlo approach and sensitivity analyses. Soil Dyn Earthq Eng 77:453–468CrossRefGoogle Scholar
  72. Zare M, Amini H, Yazdi P et al (2014) Recent developments of the Middle East catalog. J Seismol 18:749–772.  https://doi.org/10.1007/s10950-014-9444-1 CrossRefGoogle Scholar
  73. Zhang Y, Der Kiureghian A (1995) Two improved algorithms for reliability analysis. In: Proceedings of the 1994 6th IFIP WG7.5 working conference on reliability and optimization of structural systems. p 297CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Center for Infrastructure Sustainability and Resilience Research, Department of Civil EngineeringSharif University of TechnologyTehranIran

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