Efficient Evaluation of Reliability for Slopes with Circular Slip Surfaces Using Importance Sampling

Evaluating the reliability of a slope is a challenging task because the possible slip surface is not known beforehand. Approximate methods via the first-order reliability method provide efficient ways of evaluating failure probability of the most probable failure surface. The tradeoff is that the failure probability estimates may be biased towards the unconservative side. The Monte Carlo simulation (MCS) is a viable unbiased way of estimating the failure probability of a slope, but MCS is inefficient for problems with small failure probabilities. This study proposes a novel way based on the importance sampling technique of estimating slope reliability that is unbiased and yet is much more efficient than MCS. In particular, the critical issue of the specification of the importance sampling probability density function will be addressed in detail. Three examples of slope reliability will be used to demonstrate the performance of the new method.