A comprehensive Bayesian methodology for developing probabilistic capacity and demand models for structural components and systems is formulated. The methodology is employed to develop probabilistic models for reinforced concrete (RC) columns and multi-bent bridges. The probabilistic models are used to objectively assess the seismic fragilities of RC structural components and systems, in particular, of highway bridge systems.
The approach seeks to properly account for both aleatory and epistemic uncertainties. The probabilistic models developed are similar to deterministic capacity models or demand procedures commonly used in practice, but have additional correction terms that explicitly describe the inherent systematic and random errors. Through the use of a set of “explanatory” functions, the terms that correct the bias in the existing models are identified. These functions provide means to gain insight into the underlying behavioral phenomena and to select ground motion parameters that are most relevant to the seismic demands. Systematic assessment of a measure of model quality can be made; thus, it is possible to differentiate between alternative candidate models. The approach takes in to account information gained from scientific/engineering laws, observational data from laboratory experiments or field investigations, and engineering experience and subjective judgment. Methods for assessing the model parameters on the basis of the available information are described.
The probabilistic capacity models are combined with the probabilistic demand models to construct limit-state functions that are used to construct point and interval estimates of the fragilities of structural components and systems, with special attention given to the treatment and quantification of aleatory and epistemic uncertainties. First, the probabilistic capacity models are used to estimate the fragilities of a typical bridge column in terms of maximum deformation and shear demands. Next, the probabilistic demand models are used in conjunction with the component capacity models to objectively assess the seismic fragilities of an example RC bridge bent for a given set of ground motion parameters. Finally, the analysis is extended to the fragility assessment of bridge systems. Two configurations of typical new California highway overpass bridges are considered. Fragility estimates are computed both at the component level and at the system level.
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