Abstract
Recent catastrophic seismic events, such as the events that struck L'Aquila in Italy and Port-au-Prince in Haiti, have highlighted once again the urgent need for effective mitigation plans for the building stocks. The effectiveness of these plans should be based on a well-informed assessment of the associated risk. The main challenge in this assessment involves the incorporation of the uncertainty associated with its main components, namely, the ground shaking hazard, the building's vulnerability and its associated exposure to damage. A significant contribution for better understanding and communication of the examined risk to any interested parties is the distinct treatment of uncertainties inherent in the model (aleatory) from those that could be, theoretically at least, reduced (epistemic). Following these principles, the aforementioned sources of uncertainty are treated, in this thesis, rigorously and explicitly through a novel two-stage Monte Carlo methodology, which is superior to existing simplified and/or approximate and potentially inaccurate procedures. The developed methodology can be applied under general conditions and results in the estimation of seismic damage and subsequent direct financial loss for a single building. In particular, the proposed procedure is based on fragility curves which may be obtained by any of the generally accepted vulnerability assessment methodologies. Moreover, it accounts for all possible seismic events likely to cause damage to any given building in a single year but can also deals with single events. In the first stage of the Monte Carlo procedure, the aleatory uncertainty in the three risk assessment components is introduced. This results in a point estimate for the annual failure probability for the building and the cumulative distribution of the scenario and annual loss. The degree of confidence in these results is obtained by the introduction of the epistemic uncertainty in the second stage of the proposed Monte Carlo methodology. This source of uncertainty is investigated here with respect to the building's vulnerability and the exposure, both of which have received limited attention in the literature compared to the epistemic uncertainty associated with the hazard. The overall uncertainty in the damage and loss of a low-rise steel moment resisting frame is quantified through the proposed methodology and conclusions are drawn on' the significance of the two types of uncertainty and the role of the components of risk on each type. In this case study, the aleatory uncertainty in the vulnerability is associated with structural parameters and performance level thresholds, while the epistemic component is represented by the record-to-record variability. With regard to the exposure, the aleatory uncertainty in the repair cost due to the random extent of damage, as well as the modelling uncertainty in the damage-to-loss relationship, is considered. Finally, uncertainty in the hazard is expressed via the randomness in the characteristics of the seismic events. It is shown that for this case study epistemic uncertainty plays a significant role in the annual failure probability. With regard to the scenario loss, the epistemic uncertainty dominated when small events were considered, while the aleatory uncertainty was the most influential uncertainty type for large events. It was also shown that the vulnerability dominated both the aleatory and epistemic component of uncertainty in loss for small events, while its role was substantially reduced for high intensities. The introduction of hazard, i.e. when annual loss is considered, showed that the epistemic uncertainty was as influential as the aleatory uncertainty. Finally, the dominant role of hazard for this loss was highlighted. Although the above conclusions are linked to the specific building considered, it is shown that the proposed methodology can produce risk estimates, together with the confidence levels associated with these estimates. This is an important contribution to the development of loss estimation tools, which are increasingly being used by the insurance industry and civic authorities in their attempt to quantify and mitigate seismic risk.