What is a 'fragility curve' in the context of probabilistic seismic risk assessment, and what does it represent?

In the context of probabilistic seismic risk assessment, a 'fragility curve' is a graphical representation that shows the probability of a structure or component reaching or exceeding a specific damage state for a given level of ground motion intensity. It is a key component in quantifying seismic risk. A fragility curve plots ground motion intensity (e.g., peak ground acceleration, spectral acceleration) on the x-axis and the probability of exceeding a particular damage state (e.g., slight damage, moderate damage, extensive damage, collapse) on the y-axis. Each damage state represents a level of structural or non-structural damage. The curve typically has a sigmoidal shape, indicating that the probability of exceeding a damage state increases as the ground motion intensity increases. Fragility curves are developed based on structural analysis, expert opinion, or empirical data from past earthquakes. They account for uncertainties in the structural capacity and the seismic demand. These curves allow engineers to estimate the likelihood of different damage levels for a specific building under various earthquake scenarios, which is crucial for assessing seismic risk and making informed decisions about retrofitting or new construction. For instance, a fragility curve might show that a particular building has a 50% probability of reaching the 'moderate damage' state when subjected to a ground motion with a spectral acceleration of 0.5g at its fundamental period.