Formulating, fitting and fusing fragility functions (F5)

Fragility functions derived from nonlinear dynamic analysis are a central ingredient in seismic performance assessment and risk analysis of structural systems. This technical report revisits fragility functions from a unified perspective that addresses their formulation, fitting, uncertainty propagation, and fusion across multiple modeling assumptions. The report reviews a range of analytical and semi-/non-parametric fitting strategies, including maximum likelihood, generalized linear models, minimum-distance estimators, generalized additive models, and kernel-based approaches. The report further examines how fragility estimates are affected by key modeling decisions, including the definition of failure, the treatment of limit states, the choice of intensity measure, and the incorporation of multiple uncertainty sources. Particular emphasis is placed on the propagation of ground motion record-to-record variability, material randomness, and modeling uncertainty using a benchmark reinforced concrete bridge-column case study. The results show that, for the benchmark problem considered herein, modeling uncertainty produces substantially larger changes in fragility estimates than material uncertainty, especially at higher limit-state levels. Beyond the derivation of individual fragility functions, the report evaluates several approaches for combining multiple candidate fragility functions, including decision-trees election, uniform and non-uniform weighting, mixed-EDP strategies, and variance–bias based fusion. Additional topics such as intensity-measure transformation, smoothing of non-smoothed fragility functions, and treatment of crossing fragility curves are also discussed. Overall, the report provides a practical framework for developing, comparing, and unifying fragility functions, with the goal of improving transparency, consistency, and risk relevance in fragility-based seismic assessment