Abstract: Ratio of safety margin (RSM) provides a rational tool for establishing the quantitative relationship between the safety criteria of deterministic design and reliability-based design and for verifying the universality of safety criteria. However, the existing definition of RSM is only applicable to design situations, where the response (e.g., safety factor FS of stability against sliding of retaining wall) follows normal and/or lognormal distributions. This paper proposed a generalized reliability RSM (RRSM) based on the cumulative probability distribution function of FS. The generalized RRSM is applicable to design situations with FS following arbitrary probability distributions and overcomes the limitation resulted from the normal and/or lognormal assumption. This makes the RSM principle feasible in general design situations. Based on the generalized RRSM, it is proved that equality between RSM of FS and RRSM guarantees the equivalence between safety criteria of deterministic design and reliability-based design (i.e., identical feasible design domains) when FS follows normal and/or lognormal distributions. Similarly, it is also proved that equality between RSM of FS and generalized RRSM guarantees the equivalence between safety criteria of deterministic design and reliability-based design when FS follows arbitrary probability distributions. Calibration of allowable FS based on generalized RRSM is illustrated through a gravity earth retaining wall example. Results obtained from RRSM and generalized RRSM are compared for validating the calibration results based on generalized RRSM.

Key words: reliability-based design, factor of safety, reliability index, ratio of safety margin, safety criteria