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W. R. Gilks, S. Richardson and D. J. Spiegelhalter, “In troducing Markov chain Monte Carlo,” In: W. R. Gilks, S. Richardson and D. J. Spiegelhalter, Eds., Markov Chain Monte Carlo in Practice, CRC Press, 1996, pp. 1-19.

has been cited by the following article:

• TITLE: Seismic Damage Estimation of an Actual Reinforced Concrete Structure Using Subset MCMC

  AUTHORS: Shigeru Kushiyama

  KEYWORDS: Failure Probability; Nonlinear Dynamic Response Analysis; Subset Simulation; Markov Chain Monte Carlo

  JOURNAL NAME: Open Journal of Civil Engineering, Vol.3 No.3, August 23, 2013

  ABSTRACT: To estimate seismic damage of structures under strong motions is very important to know true safety of structures. However, we have to deal with very small failure probability issue to investigate quantitatively. If we use standard MCS (Monte Calro Simulation) to discuss failure probability, e.g., 1 × 10-6 order, since we have to execute nonlinear dynamic response analyses of approximate 107 times, it is not realistic. Recently, a subset simulation, which reduces the computation time by replacing small failure probability into the product of conditional failure probabilities, was proposed. In this study, the subset simulation is applied to estimate failure probability of an actual reinforced concrete building with 11 stories, and discuss the safety of the structure by checking with design criteria.