Abstract
This paper presents a methodology for the appropriate treatment of variability in the process of building vulnerability assessment. Material, geometric and mechanical properties of the assessed building typologies are simulated through a Monte-Carlo sampling procedure in which the statistical distribution of the latter parameters are taken into account. Record selection is performed in accordance with conditional hazard-consistent distributions of a comprehensive set of intensity measures, and matters of sufficiency, efficiency, predictability and scaling robustness are envisaged in the presented framework. Several intensity measures (IMs) are conjugated in the evaluation of building fragility and vulnerability, whereby fragility functions are established as the multivariate distribution of joint probability of being in a sequential set of damage states. Vulnerability Functions consequently determined provide not only a mean Damage Ratio per level of seismic intensity, but rather probabilistic distributions of Damage Ratio that reflect the ground motion variability expected as the interested site; as determined by the hazard-consistent conditional distribution of a set of sufficient intensity measures.
Highlights
The premise that sources of aleatory variability associated with groundmotion and structural response predictions cannot be neglected in loss assessment procedures has been demonstrated by several authors (e.g. Bazzurro and Luco, 2005)
According to Including multiple ground motion intensity measures in the derivation of Fragility Functions for Earthquake Loss estimation Luis Sousa, Vitor Silva,Mário Marques and Helen Crowley the latter, conditional distributions of a relevant set of IMs are determined taking into account all the rupture scenarios influencing seismic hazard at the interested site – Lisbon, Portugal – by means of the relative contribution established by disaggregation (Bazzurro and Cornell, 1999) of magnitude, distance and ground motion prediction models (GMPE), as formulated by Lin et al (2013a)
IMi is an intermediate variable that, representing the variability of seismic demand, allows separating the problem of determining the distribution of damage exceedance probabilities, as a conjunction of two uncertain variables: structural capacity represented by the conditional fragility function and seismic action characterised by the hazard consistent distribution of IMi, conditioned on the interested level of Sa(T1)
Summary
The premise that sources of aleatory variability (and its correlation) associated with groundmotion and structural response predictions cannot be neglected in loss assessment procedures has been demonstrated by several authors (e.g. Bazzurro and Luco, 2005). According to Including multiple ground motion intensity measures in the derivation of Fragility Functions for Earthquake Loss estimation Luis Sousa, Vitor Silva ,Mário Marques and Helen Crowley the latter, conditional distributions of a relevant set of IMs are determined taking into account all the rupture scenarios influencing seismic hazard at the interested site – Lisbon, Portugal – by means of the relative contribution established by disaggregation (Bazzurro and Cornell, 1999) of magnitude, distance and ground motion prediction models (GMPE), as formulated by Lin et al (2013a). It is proposed by the latter that for a given earthquake scenario, or rupture – Rup – any arbitrary vector of ground motion intensity measures – IM - has a multivariate lognormal distribution, to what follows that the distribution of IM given Rup (IM|Rup) conditioned on the occurrence of a particular level of a specific intensity parameter (IMj) ffIIIIII|RRRRRR,IIIIII iiiiII rrrrrrkk, iiiiII - presents identical statistical properties. From the assumption that the IM vector is characterized by a multivariate lognormal distribution, it follows that for each IMi in IM, ffIIIIII|RRRRRR,IIIIII iiiiII rrrrrrkk, iiiiII has a univariate lognormal distribution, which can be defined by its conditional mean and standard deviation parameters (Bradley, 2010a)
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