General partial safety factor theory for the assessment of the reliability of nonlinear structural systems

Abstract

The paper develops a novel and general theory for characterizing the nonlinearity of structural systems and for applying partial safety factors to these systems. The theory establishes a key relationship between the partial safety factor concept and the reliability theory of nonlinear structural systems, using the degree of homogeneity as a measure of nonlinearity at the design point. This measure allows for an efficient mathematical decoupling of the reliability index into nonlinearity-invariant partial reliability indexes. This formulation enables the identification of critical safety situations in extreme cases of nonlinearities in complex nonlinear structural systems. The theory leads to two main outcomes based on the asymptotic behavior of the reliability index. First, the reliability index of any nonlinear structural system is always bounded between an upper and lower bound, which can be determined using the concept of nonlinearity-invariant partial reliability indexes. Second, nonlinearity-invariant critical partial safety factors ensure that the reliability index is greater than the target reliability index. The proposed theory provides a simple and easy-to-implement method for assessing the safety of nonlinear structural systems, which can be used in conjunction with existing codes and standards. The theory can be applied to a wide range of nonlinear systems in engineering practice, including structural and geotechnical problems. It is designed primarily to provide code writers with the necessary procedure for calibrating partial safety factors for nonlinear structural systems and to identify the over-safe or under-safe cases.