A simple model to include fuzziness in the seismic fragility curve and relevant effect compared with randomness

Damage has to be quantified in civil structures to assess their seismic performance and risk and loss on a regional scale. Fragility curves have proved to be suitable for coping with randomness inherent in such an issue. Recently, the cognitive source of uncertainty has been stressed. Because the seismic limit states are defined descriptively more than analytically, fuzziness is inherent as well. In this study, a model to include fuzziness in the seismic fragility curve is implemented and appraised. First, several methods to compute seismic fragility are briefly reviewed. Consistent with the first-order second-moment reliability method, a simple extension is proposed and the explicit formulation of the probability measure is derived. Conclusions about the effect of fuzziness are drawn based on this analytical formulation. Above all, fragility increases at lower seismic intensity, whereas it decreases at higher intensity. Steepness of the fragility curve, that is, sensitivity to the ground motion, decreases with increase of fuzziness. This effect is shown to be similar to the effect of randomness. However, the greater the randomness, the smaller is the importance of fuzziness. Fuzziness aside, deterministic capacity may give excessive overestimation of fragility. A numerical example is presented. The fuzzy random fragility curves of a masonry infilled reinforced concrete frame are compared with the curves with fuzziness neglected and with different degrees of randomness. All results by the proposed model are reasonable. Copyright © 2011 John Wiley & Sons, Ltd.