Utilising fragility functions in assessing damage to structures due to accidental actions

Abstract

An application of fragility functions to an assessment of damage to structures from rare and difficult-to-predict accidental actions is analysed. The problem of damage assessment is formulated in the Bayesian format. The specific damage is characterised by a probability of foreseeable damage event (damage probability). This is expressed as a mean value of a fragility function developed for the damage event. An estimate of the damage probability is formulated in terms of a Bayesian prior or posterior distribution. It is used to express the epistemic uncertainty in the damage probability. Formally, the prior or posterior distribution is specified for the mean of a fictitious population consisting of fragility function values. The prior distribution is derived by transforming prior knowledge through the fragility function and “mapping” it on the scale of probability values. It is assumed that this knowledge is only partially relevant to the situation of exposure to a specific accidental action. The technique of the Bayesian bootstrap resampling is applied to update the prior distribution. The new information used to updating is also obtained by applying the fragility function. This is done by transforming experimental observations of accidental action characteristics into a fictitious statistical sample of fragility function values. Updating is first applied to a fragility function which is free of any epistemic uncertainty. Thereafter a heuristic procedure is proposed to introduce the epistemic uncertainty related to the fragility function into the updating process. The procedure is based on discretising continuous distributions of the epistemic uncertainty appearing in the fragility function.