Efficient reliability method for implicit limit state surface with correlated non-Gaussian variables

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In contrast to the traditional approach that computes the reliability index in the uncorrelated standard normal space (u-space), the reliability analysis that is simply realized in the original space (x-space, non-Gaussian type) would be more efficient for practical use, for example, with the Low and Tang’s constrained optimization approach. On the other hand, a variant of Hasofer, Lind, Rackwits and Fiessler algorithm for firstorder reliability method is derived in this paper. Also, the new algorithm is simply formulated in x-space and requires neither transformation of the random variables nor optimization tools. The algorithm is particularly useful for reliability analysis involving correlated non-Gaussian random variables subjected to implicit limit state function. The algorithm is first verified using a simple example with closed-form solution. With the aid of numerical differentiation analysis in x-space, it is then illustrated for a strut with complex support and for an earth slope with multiple failure modes, both cases involving implicit limit state surfaces.
Original languageEnglish
Pages (from-to)1898 - 1911
Number of pages14
JournalInternational Journal for Numerical and Analytical Methods in Geomechanics
Issue number17
Publication statusPublished - 2015


  • FORM
  • HL–RF variant
  • Correlated non-Gaussian variables
  • Implicit limit state surface
  • Numerical differentiation
  • Slope reliability

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