It is widely recognized that there are various uncertainties in the analysis of rock slope stability owing to inadequate information for site characterization and inherent variability and measurement errors in geological and corresponding parameters. Therefore, reliability-based approaches that allow the systematic and quantitative treatment of these uncertainties have become a topic of increasing interest in rock slope engineering. There has been extensive reliability analysis of rock slope stability in the literature. However, all of these analyses are based on the First-Order Reliability Method (FORM). The probability of failure of a rock slope in the First-Order Reliability Method is provided by a linear approximation of the failure function. The FORM is most commonly used because it is efficient; its accuracy, however, deteriorates when the nonlinearity of limit-state function increases. A better approximation of the failure function can establish a more accurate value of the probability of failure. The Second-Order Reliability Method (SORM) overcomes this drawback with a cost of lower efficiency in terms of the number of function calls and computation expenses. Despite considerable studies of the application of the SORM in other engineering fields, a few attempts have been made in the slope stability studies. In this study, a recently published Second-Order Reliability Method with First-Order Efficiency (SORM-FOE) is implemented on a selected rock slope in Amasya, Turkey. The SORM-FOE overcomes the low efficiency of the SORM by decreasing the number of function calls. The probability of failure of both FORM and SORM-FOE are obtained and the results are compared. It is shown that, in high value of failure probability, SORM's do not significantly affect the analysis and design. However, in very low failure probability, the discrepancy between FORM and SORM-FOE becomes pronounced. It is also shown that, where the second order methods are required, the SORM-FOE is more efficient than the conventional curvature fitting methods in terms of computational costs.

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