Sufficient conditions for equivalence between safety factor-based deterministic design and reliability-based design of slope stability

Design of stability of soil slopes inevitably involves many uncertainties, but the deterministic design method is difficult to properly consider various uncertainties. In contrast, the reliability-based design (RBD) can quantitatively consider the uncertainties in geotechnical design. Different safety criteria are adopted in the deterministic design and RBD, and possible designs with the same safety factor may have different levels of reliability and resulting in the inconsistency of feasible design domains of the two design methods (i.e., the safety criterion is not equivalent), hampering the applications of RBD in practice. The ratio of safety margin and the generalized reliability ratio of safety margin provide a useful tool to bridge the design criterion of the deterministic design method and the RBD. The generalized reliability ratio of safety margin is applied to RBD of slope stability, and the sufficient conditions for the equivalence between the deterministic design and RBD of slope stability are proposed. Based on different random field models, the equivalence between the deterministic design and RBD for two soil slope examples with one layer and two layers is studied, respectively. The results indicate that the one-layer slope satisfies the sufficient conditions when considering spatial variability, and the same feasible design domain can be obtained by the deterministic design and RBD. On the contrary, the sufficient conditions are not satisfied for the two-layer slope. The equivalence between the safety criterion of the two design methods for the two-layer slope example considering the spatial variability cannot be held.