Risks involved in engineering projects need to be quantified objectively. Therefore, a keystone to this process is the quantification of the probabilities of failure of the single and combined failure modes. In geotechnical engineering, the most common technique used to calculate the probability of failure of an engineering system is the Monte Carlo simulation MCS. This technique leads to the exact answer when the number of realizations tends to infinite. This condition can be a handicap. To overcome this handicap, the direct coupling surge as novel technique that can lead with complex scenarios in an efficient way. Thus, this paper presents an application of the direct coupling method to estimate the probabilities of failure of a rock slope analyzed by Hoek (2007). Hoek (2007) performed MCS to obtain the probability of failure of that slope. The direct coupling was implemented in a Mathematica 9.0 version of the StRAnD. Also, the analytical formulation of the problem was written in a Mathematica notebook and coupled to StRAnD. The probability of failure was approximated using FORM and SORM. The results obtained by using SORM are very close to those obtained by Hoek using MCS. MCS performed in this study showed that both FORM and SORM approximations are good estimators of the probability of failure. This similarity between FORM and SORM suggest that the limit state surface was reasonably linear. Our results show that precise estimates of the probability of failure can be obtained by using a small number of callings of the performance with FORM or SORM approximations. With this, the used of advanced reliability techniques can be used to quantify the risk involved in engineering project in a more efficient fashion by the use of the direct coupling approach.

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