Abstract
Abstract. Fragility curves (FCs) are key tools for seismic probabilistic safety assessments that are performed at the level of the nuclear power plant (NPP). These statistical methods relate the probabilistic seismic hazard loading at the given site to the required performance of the NPP safety functions. In the present study, we investigate how the tools of non-stationary extreme value analysis can be used to model in a flexible manner the tail behaviour of the engineering demand parameter as a function of the considered intensity measure. We focus the analysis on the dynamic response of an anchored steam line and of a supporting structure under seismic solicitations. The failure criterion is linked to the exceedance of the maximum equivalent stress at a given location of the steam line. A series of three-component ground-motion records (∼300) were applied at the base of the model to perform non-linear time history analyses. The set of numerical results was then used to derive a FC, which relates the failure probability to the variation in peak ground acceleration (PGA). The probabilistic model of the FC is selected via information criteria completed by diagnostics on the residuals, which support the choice of the generalised extreme value (GEV) distribution (instead of the widely used log-normal model). The GEV distribution is here non-stationary, and the relationships of the GEV parameters (location, scale and shape) are established with respect to PGA using smooth non-linear models. The procedure is data-driven, which avoids the introduction of any a priori assumption on the shape or form of these relationships. To account for the uncertainties in the mechanical and geometrical parameters of the structures (elastic stiffness, damping, pipeline thicknesses, etc.), the FC is further constructed by integrating these uncertain parameters. A penalisation procedure is proposed to set to zero the variables of little influence in the smooth non-linear models. This enables us to outline which of these parametric uncertainties have negligible influence on the failure probability as well as the nature of the influence (linear, non-linear, decreasing, increasing, etc.) with respect to each of the GEV parameters.
Highlights
A crucial step of any seismic probability risk assessment (PRA) is the vulnerability analysis of structures, systems and components (SSCs) with respect to the external loading induced by earthquakes
We focus on the analytical approach, which aims at deriving a parametric cumulative distribution function (CDF) from data collected from numerical structural analyses
Burnham and Anderson (2004) suggest an AIC difference of at least 10 to support the ranking between model candidates with confidence. If this criterion is not met, we propose complementing the analysis by the likelihood ratio test (LRT; e.g. Panagoulia et al, 2014: Sect. 2), which compares two hierarchically nested generalised extreme value (GEV) formulations using L = −2(l0 − l1), where l0 is the maximised log likelihood of the simpler model M0 and l1 is the one of the more complex model M1
Summary
A crucial step of any seismic probability risk assessment (PRA) is the vulnerability analysis of structures, systems and components (SSCs) with respect to the external loading induced by earthquakes. To this end, fragility curves (FCs), which relate the probability of an SSC to exceed a predefined damage state as a function of an intensity measure (IM) representing the hazard loading, are common tools. Gehl et al, 2013), nuclear power plants (Zentner et al, 2017), wind turbines (Quilligan et al, 2012), underground structures (Argyroudis and Pitilakis, 2012), etc Their probabilistic nature makes them well suited for PRA applications, at the interface between proba-. Rohmer et al.: Non-stationary extreme value analysis applied to seismic fragility assessment bilistic hazard assessments and event tree analyses, in order to estimate the occurrence rate of undesirable top events
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