Probabilistic characterisation of an analytical fuzzy-random model for seismic fragility computation

There is a high degree of uncertainty in the assessment of seismic performance of civil structures, and in the estimate of risk and loss, insomuch that the probabilistic approach is essential. Recently, the cognitive source of uncertainty, i.e. fuzziness, has been stressed as an aspect beside randomness. Consistent with the classical time-invariant first-order second-moment reliability method, the author proposed a simple analytical model to incorporate fuzziness into the fragility computation, being capacity and demand lognormal random variables independent of each other. In the present study, such a fuzzy-random model is fully characterised in terms of probabilistic moments, distribution, and percentiles, in comparison with the classical reliability model. Above all, the fuzziness causes the fragility dispersion to decrease in most cases. Since the fuzziness makes the distribution partly continuous, the fragility percentiles can be considered. Application is presented referring to the fragility curve of seismic non-structural damage to masonry-infilled reinforced-concrete frames. Basic techniques for parameter estimation are tested. Coupled identification of the randomness and fuzziness parameters would be advisable, as opposed to independent identification. Referring to the whole frame as a series system, the fragility curve according to the proposed fuzzy-random model with coupled identification of the parameter values is lower than the curve according to the classical model. The former curve is similar to the curve according to the fuzzy-deterministic model. The proposed model appears to be suitable for practical fuzzy-random estimate of seismic fragility.