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Abstract This paper aims at proposing a stochastic response surface method(SRSM) for reliability analysis involving correlated random variables. The Nataf transformation is adopted to effectively transform the correlated nonnormal random variables into the independent standard normal variables，which facilitates the collocation points associated with the correlated random variables and reliability computation using the SRSM. Explicit polynomials are derived for fourth-order to sixth-order Hermite polynomial chaos expansions of any number of random variables. A C#-language based computer program WHUSRSM (Wuhan University SRSM) is developed. An example of reliability analysis of rock slope stability with plane failure is presented to demonstrate the validity and capability of the proposed SRSM. The results indicate that the proposed SRSM can evaluate the reliability of rock slope stability involving correlated random variables efficiently. The proposed SRSM has a higher accuracy than the conventional first-order reliability method；and its efficiency is higher than Monte Carlo simulations. Moreover，the convergence in Hilbert space of the SRSM can be ensured in any case. The mean of factor of safety for slope stability can be accurately estimated by the proposed SRSM with different orders. However，the orders of the SRSM should be selected carefully to accurately estimate the probability of rock slope failure. The calculation of factor of safety and the reliability analysis can be conducted separately within the framework of the SRSM based on reliability analysis. Slope stability analysis would be investigated systematically with the results associated with factor of safety as well as probability of failure. These results can provide a basis for extending the application of the SRSM to reliability analysis of rock slope stability.
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Received: 31 January 2010
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