Seismic fragility curves for structures using non-parametric representations

Abstract

Fragility curves are commonly used in civil engineering to assess the vulnerability of structures to earthquakes. The probability of failure associated with a prescribed criterion (e.g. the maximal inter-storey drift of a building exceeding a certain threshold) is represented as a function of the intensity of the earthquake ground motion (e.g. peak ground acceleration or spectral acceleration). The classical approach relies on assuming a lognormal shape of the fragility curves;it is thus parametric. In this paper, we introduce two non-parametric approaches to establish the fragility curves without employing the above assumption, namely binned Monte Carlo simulation and kernel density estimation. As an illustration, we compute the fragility curves for a three-storey steel frame using a large number of synthetic ground motions. The curves obtained with the non-parametric approaches are compared with respective curves based on the lognormal assumption. A similar comparison is presented for a case when a limited number of recorded ground motions is available. It is found that the accuracy of the lognormal curves depends on the ground motion intensity measure, the failure criterion and most importantly, on the employed method for estimating the parameters of the lognormal shape.

Seismic Vulnerability Assessment of a Shallow Two-Story Underground RC Box Structure

“…After calculating the probability of exceedance of the limit states for each PGA, the vulnerability curve can be constructed by plotting the calculated data versus PGA. There are parametric (e.g., log-normal function) and non-parametric method (e.g., binned Monte Carlo simulation and Kernel density estimation [28]) to establish fragility curve. In this study, the log-normal cumulative distribution function is used to define the fragility function [29][30][31][32][33].…”

Dimensionless fragility analysis of seismic acceleration demands through low-order building models

“…The intensity measure, IM, is linked to the ground motion characteristics, and (IM) denotes the annual frequency of exceedance of the IM. The estimation of the conditional probability P(EDP ≥ edp|IM) , where edp represents a rational demand threshold, is a major challenge for the earthquake engineer (Mai et al 2017). Is this conditional probability which is usually provided via fragility functions (Miranda and Akkar 2006;Mai et al 2017).…”

Gaussian mixture–based equivalent linearization method (GM‐ELM) for fragility analysis of structures under nonstationary excitations

“…This approach is systematic, well‐established, and practically convenient, but the selection and scaling of ground motions still remain a source of debate . An alternative fragility analysis strategy is to evaluate seismic reliability of the system by nonlinear stochastic dynamic analysis employing a site‐specific stochastic ground motion model . Instead of fitting a few simulated response samples to a predefined distribution model, this approach aims to estimate the conditional probability of exceeding limit states through nonlinear stochastic dynamic analysis employing the models representing the structure and stochastic ground motions.…”

“…4,5 An alternative fragility analysis strategy is to evaluate seismic reliability of the system by nonlinear stochastic dynamic analysis employing a site-specific stochastic ground motion model. [4][5][6][7][8][9] Instead of fitting a few simulated response samples to a predefined distribution model, this approach aims to estimate the conditional probability of exceeding limit states through nonlinear stochastic dynamic analysis employing the models representing the structure and stochastic ground motions. Therefore, when such models are available, the seismic reliability approach could accurately capture the probability of rare but far-reaching extreme failure events that are related to the tail region of response distribution.…”