A fragility curve is a probabilistic function that gives the likelihood of a structure or component reaching or exceeding a specific damage state as a function of a ground motion intensity measure. It is a fundamental tool in performance-based earthquake engineering and seismic risk assessment.
A fragility curve is a probabilistic relationship between a ground motion intensity measure (IM) β typically spectral acceleration at the structure's fundamental period, Sa(Tβ), or peak ground acceleration (PGA) β and the probability that a structure, component, or system will reach or exceed a specified damage state. The curve is typically expressed as a lognormal cumulative distribution function, defined by two parameters: the median capacity (the IM value at which there is a 50% probability of exceeding the damage state) and the dispersion (a measure of the uncertainty in the capacity, often denoted Ξ²). Fragility curves are developed from empirical data (post-earthquake damage surveys), analytical models (nonlinear response history analysis with many ground motions), expert judgment, or a combination of these approaches.
Fragility curves are central to modern performance-based earthquake engineering (PBEE). In the PEER PBEE framework, the seismic performance of a structure is computed through a four-step process: hazard analysis (defining the IM distribution), structural analysis (computing the engineering demand parameters, EDPs, such as drift or acceleration), damage analysis (using fragility curves to convert EDPs to damage states), and loss analysis (converting damage states to repair cost, downtime, and casualties). The fragility curve is the bridge between structural response and damage β it encodes the physical vulnerability of the component or system in probabilistic terms. Fragility curves are typically defined for multiple damage states β slight, moderate, extensive, and complete β allowing for a full probabilistic characterization of damage.
Fragility curves are developed through several methods, each with its own assumptions and limitations. Empirical fragility curves are derived from observed damage in past earthquakes, using statistical regression on damage survey data. These have the advantage of reflecting real-world performance, including construction quality and aging effects, but are limited to the earthquake characteristics and building types represented in the available data. Analytical fragility curves are developed from nonlinear response history analyses of representative structural models subjected to suites of ground motions. These allow systematic exploration of parameter uncertainty but depend on the accuracy of the analytical models and the ground motion selection. Expert-judgment fragility curves β such as those in HAZUS and GEM β are based on the collective judgment of engineers and are used for regional risk assessment where empirical data is unavailable. In Iran, fragility curves have been developed for common building types β including masonry, steel moment frames, and reinforced concrete frames β and are used in seismic risk assessment and retrofit prioritization at both the building and regional scale. The accuracy of fragility curves is limited by the inevitable simplifications in the models and the uncertainty in the damage state definitions; their interpretation requires understanding of these limitations.