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SUMMARYState-of-the-art methods for the assessment of building fragility consider the structural capacity and seismic demand variability in the estimation of the probability of exceeding different damage states. However, questions remain regarding the appropriate treatment of such sources of uncertainty from a statistical significance perspective. In this study, material, geometrical and mechanical properties of a number of building classes are simulated by means of a Monte Carlo sampling process in which the statistical distribution of the aforementioned parameters is taken into consideration. Record selection is performed in accordance with hazard-consistent distributions of a comprehensive set of intensity measures, and issues related with sufficiency, efficiency, predictability and scaling robustness are addressed. Based on the appraised minimum number of ground motion records required to achieve statistically meaningful estimates of response variability conditioned on different levels of seismic intensity, the concept of conditional fragility functions is presented. These functions translate the probability of exceeding a set of damage states as a function of a secondary sufficient intensity measure, when records are selected and scaled for a particular level of primary seismic intensity parameter. It is demonstrated that this process allows a hazard-consistent and statistically meaningful representation of uncertainty and correlation in the estimation of intensity-dependent damage exceedance probabilities.

SUMMARYThe assessment of earthquake loss often requires the definition of a relation between a measure of damage and a quantity of loss, usually achieved through the employment of a damage-to-loss model. These models are frequently characterized by a large variability, which inevitably increases the uncertainty in the vulnerability assessment and earthquake loss estimation. This study provides an insight on the development of damage-to-loss functions for moment-frame reinforced concrete buildings through an analytical methodology. Tri-dimensional finite element models of existing reinforced concrete buildings were subjected to a number of ground motion records compatible with the seismicity in the region of interest, through nonlinear dynamic analysis. These results were used to assess, for a number of damage states, the probability distribution of loss ratio, taking into consideration member damage and different repair techniques, as well as to derive sets of fragility functions. Then, a vulnerability model (in terms of the ratio of cost of repair to cost of replacement, conditional on the level of ground shaking intensity) was derived and compared with the vulnerability functions obtained through the combination of various damage-to-loss models with the set of fragility functions developed herein. In order to provide realistic estimates of economic losses due to seismic action, a comprehensive study on repair costs using current Portuguese market values was also carried out. The results of this study highlight important issues in the derivation of vulnerability functions, which are a fundamental component for an adequate seismic risk assessment.

In recent years a number of nonlinear static procedures (NSPs) have been developed and proposed. Such pushover-based seismic assessment procedures are relatively straightforward to employ and are generally chosen over nonlinear dynamic analysis, especially within the realm of design office application. Parametric comparisons between the different NSPs available, however, are still somewhat sparse. In this work, five commonly employed NSPs (the N2 method, capacity spectrum method, modal pushover analysis, adaptive modal combination procedure, and the adaptive capacity spectrum method) are applied in the assessment of 16 frames subjected to a large number of input motions with a view to assess the accuracy level of such approaches through comparison with nonlinear dynamic analysis results. The evaluation shows that all the NSPs are able to accurately predict displacements and to produce reasonable estimates for other response parameters, with limited dispersion. Even though no single NSP tested led to consistently superior results, modal pushover analysis and the adaptive capacity spectrum method seemed to perform slightly better.

Summary The recent concerns regarding the seismic safety of the existing building stock have highlighted the need for an improvement of current seismic assessment procedures. Alongside with the development of more advanced commercial software tools and computational capacities, nonlinear dynamic analysis is progressively becoming a common and preferable procedure in the seismic assessment of buildings. Besides the complexity associated with the formulation of the mathematical model, major issues arise related with the definition of the seismic action, which can lead to different levels of uncertainty in terms of local and global building response. Aiming to address this issue, a comparative study of different code‐based record selection methods proposed by Eurocode 8, ASCE41‐13 and NZS1170.5:2004 is presented herein. The various methods are employed in the seismic assessment of four steel buildings, designed according to different criteria, and the obtained results are compared and discussed. Special attention is devoted to the influence of the number of real ground motion records selected on the estimation of the mean seismic response and, importantly, to the efficiency that is achieved when an additional selection criteria, based on the control of the spectral mismatch of each individual record with respect to the reference response spectrum, is adopted. The sufficiency of the methods with respect to the pairs of M–R of the selected group of records and the robustness of the scaling procedure are also examined. The paper closes with a study which demonstrates the suitability of a simplified probability‐based approach recently proposed for estimating mean seismic demands. Copyright © 2015 John Wiley & Sons, Ltd.

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SummaryIn a related study developed by the authors, building fragility is represented by intensity-specific distributions of damage exceedance probability of various damage states. The contribution of the latter has been demonstrated in the context of loss estimation of building portfolios, where it is shown that the proposed concept of conditional fragility functions provides the link between seismic intensity and the uncertainty in damage exceedance probabilities. In the present study, this methodology is extended to the definition of building vulnerability, whereby vulnerability functions are characterized by hazard-consistent distributions of damage ratio per level of primary seismic intensity parameter-Sa(T 1 ). The latter is further included in a loss assessment framework, in which the impact of variability and spatial correlation of damage ratio in the probabilistic evaluation of seismic loss is accounted for, using test-bed portfolios of 2, 5, and 8-story precode reinforced concrete buildings located in the district of Lisbon, Portugal. This methodology is evaluated in comparison with current state-of-the-art methods of vulnerability and loss calculation, highlighting the discrepancies that can arise in loss estimates when the variability and spatial distributions of damage ratio, influenced by ground motion properties other than the considered primary intensity measure, are not taken into account. KEYWORDS damage ratio uncertainty and spatial correlation, event-based seismic loss estimation, hazard-consistent fragility and vulnerability | INTRODUCTIONIn the process of risk computations, several studies have demonstrated the importance of accounting for spatial cross correlation of ground motion residuals in the evaluation of portfolio losses (eg, Park et al, Weatherill et al, Silva, and Yoshikawa and Goda 1-4 ). However, when the correlation of uncertainty in vulnerability (ie, in the damage ratio residuals across a class of buildings) is incorporated in loss estimation procedures (eg, Silva et al 5 ), it is done such that when sampling the uncertainty in the vulnerability of 2 assets with the same building class (and same level of seismic intensity measure), the residuals are assumed to be either uncorrelated of perfectly correlated. 6 Furthermore, as demonstrated by Bradley 7 and Silva et al 8 in the context of component and building fragility, respectively, the propagation of uncertainty from fragility to vulnerability is related to the scatter of results to which a parametric (usually lognormal) fragility curve is fitted (ie, uncertainty associated with the regression; Figure 1A).Typically used parametric relationships such as the lognormal or beta probabilistic functions provide a good approximation to the vulnerability uncertainty that results from the scatter of possible fragilities ( Figure 1B; eg, Silva et al 5 ). For a given level of

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