Simplified state‐dependent seismic fragility assessment

Earthquakes are clustered in time and space; therefore, structures may be subjected to multiple consecutive instances of potentially damaging shaking, with insufficient in‐between time for repair operations to take place. Methodologies to evaluate the risk dynamics in this situation require vulnerability models that are able to capture the transitions between damage states, from the intact conditions to failure, due to multiple damaging earthquakes, that is, state‐dependent fragility curves. One of the state‐of‐the‐art methods for the assessment of structure‐specific state‐dependent fragility curves relies on a variant of incremental dynamic analysis (IDA), which is often termed back‐to‐back or B2B‐IDA. The computational costs typically involved in B2B‐IDA motivate attempts to simplify the evaluation of state‐dependent fragility curves. This paper presents a simplified method for multi‐story moment‐resisting frame structures, based on pushover analysis in conjunction with a predictive model for the main features of a damaged structural system, such as residual deformations and loss of stiffness and/or strength. The predictive model enables the probabilistic definition of the post‐earthquake pushover curve of a damaged structural system, given the displacement demand imposed by a preceding damaging shock. The state‐dependent fragility curves are then evaluated via IDA of single‐degree‐of‐freedom oscillators based on these pushover curves. Illustrative applications validate the ability of the proposed methodology to provide state‐dependent fragilities with reduced computational costs compared to the back‐to‐back IDA method.