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A scalar damage measure (DM) for probabilistic performance assessment of structures can be expressed as the critical demand-to-capacity ratio corresponding to the component or mechanism that leads the structure closest to failure at the onset of which, the DM assumes the value of one. This DM can be employed to make probabilistic performance assessments taking into account the uncertainty in the ground motion, in the structural modelling parameters, and also in the model(s) used for determining components capacity. Nonlinear dynamic analysis methods can be used to estimate this DM in two ways: (a) applying a (small-size) set of un-scaled ground motion records to the structure and (b) using incremental dynamic analysis. Case (a) is suitable for making performance assessments based on demand and capacity factor design format and case (b) is suitable for estimating directly the probability of failure using numerical integration. Performance assessments using this DM are described in a case study of a RC frame in which the critical demand-to-capacity ratio is determined by taking into account various modes of failure for the limit state of collapse, such as weak storey mechanisms, shear failure in the columns, and ultimate deformations in the columns. Copyright (C) 2007 John Wiley & Sons, Ltd

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This study focuses on the evaluation of the seismic vulnerability of the Italian roadway bridge stock, within the framework of a Civil Protection sponsored project. A comprehensive database of existing bridges (17,000 bridges with different level of knowledge) was implemented. At the core of the study stands a procedure for automatically carrying out state-of-the-art analytical evaluation of fragility curves for two performance levels—damage and collapse—on an individual bridge basis. A WebGIS was developed to handle data and results. The main outputs are maps of bridge seismic risk (from the fragilities and the hazard maps) at the national level and real-time scenario damage-probability maps (from the fragilities and the scenario shake maps). In the latter case, the WebGIS also performs network analysis to identify routes to be followed by rescue teams. Consistency of the fragility derivation over the entire bridge stock is regarded as a major advantage of the adopted approach.

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A method is presented for the evaluation of the seismic fragility function of realistic structural systems. The method is based on a preliminary, limited, simulation involving nonlinear dynamic analyses performed to establish the probabilistic characterization of the demands on the structure, followed by the solution of a general system reliability problem with correlated demands and capacities. The results compare favorably with the fragility obtained by plain Monte Carlo simulation, while the associated computational effort is orders of magnitude lower. The method is demonstrated with two applications, a steel-concrete box girder viaduct with RC piers subjected to both uniform and nonuniform excitations, and a three-dimensional RC building structure subjected to bidirectional excitation

Eurocode 8 Part 3 (EC8-3) is devoted to assessment and retrofitting of existing buildings. In order to take into account the uncertainty in the knowledge of structural properties, EC8-3 defines, analogously to the ordinary material partial factors, an adjustment factor, called oconfidence factor (CF),o whose value depends on the level of knowledge (KL) of properties such as geometry, reinforcement layout and detailing, and materials. This solution is plausible from a logical point of view but it cannot yet profit from the experience of its use in practice, hence it needs to be substantiated by a higher level probabilistic analysis accounting for and propagating epistemic uncertainty (i.e., incomplete knowledge of a structure) throughout the seismic assessment procedure. This article investigates the soundness of the format proposed in EC8-3. The approach taken rests on the simulation of the entire assessment procedure and the evaluation of the distribution of the assessment results (distance from the limit state of interest) conditional on the acquired knowledge. Based on this distribution, a criterion is employed to calibrate the CF values. The obtained values are then critically examined and compared with code-specified ones. The results pinpoint a number of deficiencies that appear to somewhat invalidate the approach. The methodological significance of the work extends beyond the assessment procedure in EC8-3, since similar factors appear in other international guidelines (e.g., the knowledge factor of FEMA356)

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