Towards Time- and State-Dependent Seismic Risk over Urban Scales

Probabilistic seismic risk assessment involves the appraisal of three components: the seismic hazard due to expected ground motions, the exposure, i.e., assets exposed to the hazard, and their vulnerability with respect to the hazard. Earthquake sequences are a result of a time dependent process, which is complex to consider in a probabilistic framework. It is thus common to reduce sequences to their largest event, the so-called main shock. The occurrence of these main shocks can be modeled assuming a Poisson process with constant average rates. This is convenient from a mathematical point of view, as the connected probability distribution is simple, but of course, a large portion of the seismicity is neglected. As a result of the long inter-event times in such a Poissonian model, it is commonly assumed that potentially damaged buildings are repaired before the next strong event. In reality, the repair of buildings, especially if a large number have been affected, might take several years. As a consequence, buildings are likely to be still damaged when subsequent events occur. For aftershocks, which commonly occur within hours or days after the main event, this is definitely the case. Furthermore, a building’s response is not identical for its intact and damaged states. If these effects are not considered within a seismic risk assessment, then the resulting estimates will most likely fail to predict accurate results. In order to determine if this is the case over urban scales, this thesis sets out to design, develop and test an approach to relax the two assumptions with the aim of developing time- and state-dependent seismic risk models. The accompanying research questions are: 1) if this results in loss estimates that are significantly different from those of a classical model, 2) which components of the model have the strongest influence, and 3) if simplifications can be made to model the complex process. The approach developed here employs a simulation framework that models full seismic sequences using an epidemic type aftershock model, a Markov-chain damage process, state-dependent fragility models, and various probabilistic repair functions. The approach is tested for the city of Nablus in the West Bank, Palestine. For this purpose, a fully probabilistic seismic hazard model is developed for the region. A multi-source imaging analysis is employed to collect exposure data using remote rapid visual screening. For the identified building types, a simplified analysis is performed to obtain state-dependent fragility models, while the many simplifications applied don’t yield reliable absolute losses, they permit the identification of tendencies and answer the formulated research questions. The results show that a time- and state-dependent model yields significantly higher losses than a classical model, reaching a difference of up to 58% in the examples presented in this work. It is shown that considering the problem only partially is not sufficient. While including fore- and aftershocks, but no time-delayed repair and state-dependency, yields a potentially strong overestimate of losses at low exceedance probabilities, disregarding the state-dependency underestimates the losses over the whole range of probabilities. Furthermore, considering time- and state-dependency in Poissonian models does not influence the losses significantly, at least for the demonstrated case of Nablus. It can be concluded that despite the greater efforts required to develop time- and state-dependent models over urban scales, the effects are strong enough to justify the development cost if accurate risk models are intended. However, for observation periods of a single year, it was found that a constant daily repair probability may be sufficient to approximate more complex time-variant repair models. Many additional questions have emerged from the findings of this thesis. These concern the issue of more detailed analyses using more sophisticated components, mainly for the hazard and fragility models. In addition, the framework developed within this thesis can form the basis for a multitude of new research directions in the field of cascading effects. These may include the consideration of multiple hazards, dynamically evolving exposure models, and interactions between them