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And State-Dependent Seismic Risk Over Urban Scales

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And State-Dependent Seismic Risk Over Urban Scales Towards time- and state-dependent seismic risk over urban scales vorgelegt von M.Sc. Michael Haas geb. in München von der Fakultät VI- Planen Bauen Umwelt der Technischen Universität Berlin zur Erlangung des akademischen Grades Doktor der Naturwissenschaften - Dr.rer.nat. - genehmigte Dissertation Promotionsausschuss: Vorsitzender: Prof. Dr. Frank Rackwitz Gutachter: Prof. Dr. Paolo Bazzurro Gutachter: Prof. Dr. Stefano Parolai Gutachter: Prof. Dr. Yuri Petryna Tag der wissenschaftlichen Aussprache: 22. November 2018 Berlin 2019 Abstract 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 se- quences 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 mod- eled assuming a Poisson process with constant average rates. This is convenient from a mathematical point of view, as the connected probability distribution is sim- ple, 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 afected, might take several years. As a consequence, buildings are likely to be still damaged when sub- sequent events occur. For aftershocks, which commonly occur within hours or days after the main event, this is defnitely the case. Furthermore, a building’s response is not identical for its intact and damaged states. If these efects 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 re- search questions are: 1) if this results in loss estimates that are signifcantly diferent from those of a classical model, 2) which components of the model have the strongest infuence, and 3) if simplifcations can be made to model the complex process. The approach developed here employs a simulation framework that models full seis- mic 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 identifed building types, a simplifed analysis is performed to obtain state-dependent fragility models, while the many simplifca- tions applied don’t yield reliable absolute losses, they permit the identifcation of tendencies and answer the formulated research questions. The results show that a time- and state-dependent model yields signifcantly higher losses than a classical model, reaching a diference of up to 58% in the examples presented in this work. It is shown that considering the problem only partially is not sufcient. 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 infuence the losses signifcantly, at least for the demonstrated case of Nablus. It can be concluded that despite the greater eforts required to develop time- and state-dependent models over urban scales, the efects 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 sufcient to approximate more complex time-variant repair models. Many addi- tional questions have emerged from the fndings 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 feld of cascad- ing efects. These may include the consideration of multiple hazards, dynamically evolving exposure models, and interactions between them. iv Zusammenfassung Eine probabilistische Erdbebenrisikoanalyse beinhaltet die Bewertung dreier Kom- ponenten: der aus Bodenbewegungen resultierenden seismischen Gefährdung, dem Exposure, sprich Werte, die der Gefährdung ausgesetzt sind und der Vulnerabili- tät dieser im Hinblick auf die Gefährdung. Erdbeben ereignen sich als Folgen und sind das Ergebnis eines zeitabhängigen Prozesses, dessen wahrscheinlichkeitstheore- tische Berücksichtigung kompliziert ist. Deshalb ist es üblich die Erdbebensequenz auf deren größtes Erdbeben, sogenannte Hauptbeben zu reduzieren. Das Auftreten dieser Hauptbeben kann als Realisierungen eines Poissonprozesses mit konstanten Raten simuliert werden. Dies ist aus mathematischer Sicht günstig, da die damit verknüpfte Wahrscheinlichkeitsverteilung einfach zu handhaben ist, allerdings wird durch die Reduktion ein großer Teil der Seismizität vernachlässigt. Da die Zeit zwi- schen zwei dieser Hauptbeben eines solchen Poissonmodelles verhältnismäßig lang ist, wird für gewöhnlich angenommen, dass die möglicherweise in einem Beben be- schädigten Gebäude bis zum nächsten Beben wieder repariert sind. In Wirklichkeit kann die Reparatur von Gebäuden unter Umständen mehrere Jahre dauern, ins- besondere wenn eine große Anzahl beschädigt wurde. Daraus folgt, dass im Falle weiterer Beben einige Gebäude wahrscheinlich noch beschädigt sind. Für Nachbe- ben, die auch innerhalb von Stunden oder Tagen nach dem Beben auftreten können, ist dies mit hoher Wahrscheinlichkeit der Fall. Des Weiteren ist die Antwort eines Gebäudes auf eine Bodenbewegung im beschädigten Zustand nicht identisch zu der eines intakten Gebäudes. Falls diese Efekte im Rahmen einer Erdbebenrisikoanalyse nicht berücksichtigt werden, ist es möglich, dass die resultierenden Abschätzungen daran scheitern akkurate Vorhersagen trefen zu wollen. Um herauszufnden ob dies über urbane Skalen der Fall ist, wird im Rahmen die- ser Arbeit ein Ansatz entwickelt, implementiert und getestet, der beide klassischen Annahmen in Frage stellt, und hin zur Entwicklung von zeit- und zustandsabhän- gigen Erdbebenrisikomodellen führt. Die damit einhergehenden wissenschaftlichen Fragestellungen sind: 1) ob solch ein Modell Verlustabschätzungen zur Folge hat, die signifkant verschieden von denen eines Modells unter klassischen Annahmen ist, 2) welche Komponenten des Modells den stärksten Einfuss darauf haben und 3) ob zu einem gewissen Grad Vereinfachungen für das komplexe Modell möglich sind. Der hier entwickelte Ansatz baut auf eine Simulationsumgebung die vollständige Erdbebensequenzen mit Hilfe eines epidemischen Nachbebenmodelles simuliert, ei- nen Markov-Ketten Schadensprozess nutzt und zustandsabhängige Fragilitätsmo- delle sowie verschiedene Wahrscheinlichkeitsfunktionen für die Reparatur berück- sichtigt. Der Ansatz wird anhand der Stadt Nablus im Westjordanland (Palästina) getestet. Zu diesem Zweck wird ein vollständig probabilistisches Erdbebengefähr- dungsmodell entwickelt. Zudem wird eine Satellitenbild- und Mobile-Mapping ge- stützte Bildanalyse multipler Quellen durchgeführt, um mit Hilfe von rascher visu- eller Gebäudefernerkundung Exposureinformationen zu Gebäuden zu sammeln. Für die so bestimmten Gebäudetypen wird eine einfach gehaltene Analyse durchgeführt, um zustandsabhängige Fragilitätsmodelle zu erhalten. Obwohl die zahlreichen Ver- einfachungen dabei keine verlässlichen Modelle liefern, erlauben diese es Trends zu identifzieren, um die genannten wissenschaftlichen Fragestellungen zu beantwor- ten. Die Ergebnisse zeigen, dass ein zeit- und zustandsabhängiges Modell signifkant hö- here Verlustabschätzungen als ein klassischer Ansatz liefert, der Unterschied erreicht dabei bis zu 58% in den in dieser Arbeit präsentierten Beispielen. Des Weiteren kann gezeigt werden, dass eine nur teilweise Berücksichtigung der Problematik nicht aus- reicht. Während ein Ansatz, der nur Vor- und Nachbeben, aber keine zeitverzögerte Reparatur berücksichtigt, Verluste am unteren Ende der Wahrscheinlichkeiten mög- licherweise stark überschätzt, führt eine Vernachlässigung der Zustandsabhängigkeit der Gebäudefragilität dazu, dass die Verluste für alle Wahrscheinlichkeiten unter- schätzt werden. Außerdem konnte festgestellt werden, dass die Berücksichtigung von zeit- und zustandsabhängigen Komponenten in Poissonmodellen, zumindest für den Fall von Nablus, die Verlusteinschätzungen nicht signifkant beeinfusst. Es lässt sich schlussfolgern, dass trotz des größeren Aufwandes, der nötig ist um zeit- und zustandsabhängige Modelle über urbane Skalen zu entwickeln, die beob- achteten Efekte stark genug sind, um die Entwicklungskosten zu rechtfertigen, wenn akkurate Risikoeinschätzungen gewünscht sind. Für kurze
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