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C. Gasser:
"Contributions to reliability assessment of engineering structures with special consideration of the seismic safety of an arch dam";
Betreuer/in(nen), Begutachter/in(nen): C. Bucher, C. Adam, D. Kisliakov; Institut für Hochbau, Baudynamik und Gebäudetechnik, 2018; Rigorosum: 18.02.2019.

The safety of structures depends on loads and resistances which both eventually have to be regarded as random by nature. The conventional approach to handle uncertainties in engineering is to use safety factors. Although this approach has proven its worth in practice, it is rather inappropriate for designing a real structure such as to match a target reliability level, in the sense of a damage/failure probability referring to a given period of time. This is because, in a real situation, the interaction of all kinds of resistances and prospective loads is much more complicated than any situation that can be covered by a general framework of design rules. These considerations will be easy to understand for any civil engineer who has ever been asked, e.g. by a non-expert person, under which load a bridge provided with a load limitation is eventually going to collapse. To get one step closer to the aim of having the exact failure probability (respectively, the exact bearing capacity), one may adopt a (full) probabilistic analysis. Hereby, the probability distributions of loads and resistances enter the structural calculations directly. Since, nowadays, structural calculations are primarily performed by numerical methods, also the actual probabilistic analysis is performed numerically. The according technique is Monte-Carlo Simulation (MCS). Thereby, a sample with different parameter sets is analysed. The distributions of the resulting response quantities - especially the number of limit state exceedances - give information about the damage and failure probabilities, respectively about the exact bearing capacity. This thesis starts with a presentation of reliability theory. The background of the semiprobabilistic safety concept is explained using a simple example. Based in this, transition takes places to ever more general and complicated systems, whereas the resulting limitations are elaborated. This leads to MCS, which is the most universal method of reliability calculations. The topic of the subsequent chapter is the estimation of small failure probabilities. In that case, conventional MCS may become unaffordable since the high number of necessary simulation runs increases the computational effort substantially. The problem may be addressed by the asymptotic sampling technique. Thereby, first, the reliability problem, i.e. the multivariate probability distribution and the limit state condition, is transformed to standard normal space. Then, some Monte-Carlo estimates are performed for the failure probabilities of some artificially stretched (scaled) systems. The computational effort is thereby much smaller because the failure probabilities are higher. The failure probability of the original system is obtained by extrapolation of the results for the stretched systems. This can be accomplished by exploiting some asymptotic properties in standard normal space, which are explained in detail in this work. Strategies to optimize the asymptotic sampling technique are presented. In particular, a method is developed which yields better results in cases where the number of random variables is very high. Furthermore, recommendations concerning the optimal number of scale levels and simulation runs are provided. Moreover, the technique is extend such that it yields exceedance probabilities for a range of values of the response quantities. By means of three examples, the advantages of the methods developed or refined are shown. In the next chapter, the seismic safety of an arch dam is analysed. The associated challenges arise not only from the extension to the complicated earthquake load case, but also from the fact that a finite element model of a realistic structure is analysed. Four damage mechanisms as well 8 as failure of the dam are analysed. Since failure occurs as a consequence of progressive concrete deterioration, the implementation of a specific material model for concrete is necessary. At the centre of the analyses of damage and failure is the development of respective fragility curves, which indicate the occurrence probabilities as functions of the seismic intensity. Since this is accomplished by means of MCSs (involving, furthermore, a complex nonlinear finite element model), one is particularly interested in a reduction of the computational effort. In this regard, two approaches are successfully tested and refined, which are based on the assumption of a lognormal distribution of the fragility curves. Finally, the fragility curves are combined with the seismic risk of three selected locations. As a result of that, it can be shown that an additional investigation of smaller earthquakes in greater detail is expendable, and that MCS for a single intensity level is inappropriate for seismic safety analysis.

Contributions, Reliability Assessment, Seismic Safety, Arch Dam