Non-stationary extreme value analysis applied to seismic fragility assessment for nuclear safety analysis

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.

Preface: Advances in extreme value analysis and application to natural hazards

“…The magnitude-frequency relation can also be established by using a probabilistic risk assessment approach. Rohmer et al (2020) present a "seismic probabilistic safety assessments" which was performed at the level of a nuclear power plant. This approach used non-stationary frequency estimations as boundary conditions of a dynamic model to compute hazard and fragility curves.…”

“…As was mentioned earlier, the special issue also aimed to promote probabilistic approaches useful in natural hazard characterization in a multi-hazard context and considering compounding effects. As shown in Table 1, several contributions in this special issue deal with probabilistic hazard approaches (e.g., Le Roux et al, 2020;Ben Daoued et al, 2020;Tilloy et al, 2020;Lu et al, 2020;Rohmer et al, 2020;Fu et al, 2020) and multi-hazard risk evaluation with compound effects (Stephens et al, 2020). Ben Daoued et al (2020) developed a new method for modeling dependence and coincidence of extreme storm surges with high tide, using the city of Le Havre in France as a case study.…”

“…In the contribution on compound effects and using tide gauge data from 1900 onwards, Stephens et al (2020) identify 85 extreme sea level events and 135 extreme skew surge events, which are then considered for a spatiotemporal analysis along the coastline of New Zealand. Their findings highlight that most extreme sea level events are the result of moderate skew surges and high perigean spring tides and that events are typically at least 10 d apart because of the spring-neap cycle.…”