Equivalence between reliability and factor of safety

Traditionally, geotechnical engineers have been practicing design approaches based on safety factors to account for uncertainties due to their simplicity. More recently, reliability-based design approaches emerge as a more reasonable and rigorous way of handling uncertainties. This research raises a fundamental question: “Are reliability and safety factor equivalent?” or “Does there exist a one-to-one functional relationship between reliability and safety factor?”. This paper presents research that proves a sufficient condition for the existence of such a relationship. Moreover, a theorem is derived to determine the functional relationship between reliability and safety factor with stochastic simulations. The proposed framework is so general that it is applicable to arbitrarily complex geotechnical systems with arbitrarily high-dimensional uncertainties. Several simulated examples are used to verify the proposed approach. The results show that the proposed approach is quite promising.