Safety criteria for geotechnical design based on generalized reliability ratio of safety margin

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 F-S 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 F-S. The generalized RRSM is applicable to design situations with F-S 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 F-S and RRSM guarantees the equivalence between safety criteria of deterministic design and reliability-based design (i.e., identical feasible design domains) when F-S follows normal and/or lognormal distributions. Similarly, it is also proved that equality between RSM of F-S and generalized RRSM guarantees the equivalence between safety criteria of deterministic design and reliability-based design when F-S follows arbitrary probability distributions. Calibration of allowable F-S 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.