Seismic reliability assessment

Let us consider the seismic reliability assessment of a structure and assume that the site seismic hazard is described by the earthquake magnitude M and the source-to-site distance R. The probability of structural failure P(F), that is, the probability of exceeding a threshold response level, can be expressed by the Theorem of Total Probability as ... 

Sibilio, E., Ciampoli, M., Beck, J.L. 2006. Seismic reliability assessment of structures via Subset Simulation and Bayesian updating. 3rd International Conference on Advances in Mechanical Engineering and Mechanics, Hammamet, Tunisia, CDRom. 

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This entry introduces the main sources of uncertainty in demand and capacity, as well as their treatments through alternative reliability methods. In this regard, three general families of methods are briefly summarized in this entry the second-moment reliability methods, the simulation-based reliability approaches, and finally the probabilistic performance-based methodology developed within the joint efforts of Pacific Earthquake Engineering Research Center (PEER). The closing section provides a brief discussion about future challenges in seismic reliability assessment. 

Seismic Reliability Assessment, Alternative Methods for, Fig. 1 Reliability problems for the special case of only two uncertain parameters xi and X2 (a) Component,... 

Seismic Reliability Assessment, a Time Variant Nonlinear Problem... 

If the limit state function reveals time-dependent properties, then the reliability problem can be referred to as time variant. Hence, given the stochastic nature of the seismic excitation, the seismic reliability assessment can be classified as a... 

The main drawback of the standard MC simulation methods is that it is not computationally efficient for problems dealing with small probabilities of failure (i.e., Pp < 10 ). The main reason is due to the fact that the number of samples and hence the number of structural analyses, which are required to achieve a given accuracy, is inversely proportional to Pp. It requires information from rare samples that lead to failure, and on average, many samples are required before one such failure sample occurs. For instance, in case of achieving the Pp in order of lO"" (which is typical in seismic reliability assessment) with a coefficient of variation around 10 %, nearly 10 simulations are required. Essentially, for rare events, the chance of generating samples from /x(x) for which l/r(x) equals one is extremely small (i.e., success rate is slow) therefore, many samples are needed to fulfill this requirement. 

Seismic Reliability Assessment, Alternative Methods for. Fig. 5 Typical fragility curve... 

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