Equivalence between Safety Factor-Based and Reliability-Based Design Requirements for Gravity Retaining Wall Design

Traditional deterministic design approaches, e.g., safety factor-based design (SFBD), were prevailing in retaining wall design practice due to its simplicity. With SFBD, the safety factors (FS) is taken as the measure of safety margin that does not explicitly consider uncertainties. However, there are inevitably many uncertainties in the process of retaining wall, such as inherent variability, model uncertainty, etc. The reliability level of feasible designs with the same FS values can vary significantly using SFBD. As a result, SFBD results might be unsatisfactory from a perspective of reliability-based design (RBD). RBD can reasonably consider various uncertainties, for which the probability of failure (P_f) is taken as the measure of safety margin. Although a number of RBD codes of retaining wall design have been developed, the reliability level corresponding to the allowable factor of safety (FS_a) used in SFBD is unknown, and the final design obtained using RBD may be significantly different from that obtained using SFBD. This poses a question that whether the equivalence between SFBD and RBD can be achieved for retaining wall design. If that is the case, RBD gives the feasible design domain similar to that obtained using SFBD. In general, the equivalence between SFBD and RBD does not always exist. This study discussed sufficient conditions for the equivalence between SFBD and RBD and their application to retaining wall design. When the sufficient conditions are satisfied, the target probability of failure (P_T) can be calibrated from FS_a adopted in SFBD. The proposed approach is illustrated using a gravity retaining wall design example. Results show that the gravity retaining wall design example satisfies the sufficient conditions, and the feasible design domain of RBD based on the calibrated PT is consistent with that of the SFBD based on the FS_a adopted in design codes.

Keywords: target probability of failure, allowable factor of safety, equivalence, feasible designs, retaining wall.