Computationally efficient fragility assessment using equivalent elastic limit state and Bayesian updating

Abstract

Conventionally, the seismic response of primary structures such as buildings and secondary systems such as piping is evaluated through uncoupled analyses. Many studies have illustrated that the two systems interact in many different ways (mass interaction, non-classical damping, phasing, etc.). An analysis of the coupled system is not only rational but also eliminates the excessive conservatism that exists in an uncoupled analysis. Consequently, fragility assessments based on uncoupled analysis are also incorrect and a coupled analysis must be conducted in such evaluations. However, nonlinear analyses of such complex systems particularly in the context of fragility assessment, which requires a large number of nonlinear analyses, becomes computationally prohibitive. Tadinada and Gupta (2017) presented an equivalent elastic limit state concept with an intent to reduce the computational effort needed in these assessments and yet evaluate the seismic fragility with sufficient accuracy. This paper outlines some of the limitations that have been experienced in the use of originally proposed equivalent limit-state formulation and presents valuable enhancements. The novel contribution of this study is focused on accounting for the effect of uncertainty in nonlinear characteristics and the effect of non-classical damping. Unlike the originally proposed formulation, the proposed formulation also considers the asymmetric variation of the equivalent limit state with respect to tuning ratio. Furthermore, a Bayesian approach is incorporated into the proposed methodology for increasing the accuracy of seismic fragilities in the case of tuned or nearly tuned primary-secondary systems. Numerical examples are used to illustrate that the modified form improves the accuracy for both the tuned and the detuned systems. In summary, the proposed approach provides an efficient framework of seismic fragility assessment and risk evaluation for coupled systems.