Fragility Increment Functions for Deteriorating Reinforced Concrete Bridge Columns

The increased deformation and shear fragilities of corroding RC bridge columns subject to seismic excitations are modeled as functions of time using fragility increment functions. These functions can be applied to various environmental and material conditions by means of controlling parameters that correspond to the specific condition. For each mode of failure, the fragility of a deteriorated column at any given time is obtained by simply multiplying the initial fragility of the pristine/nondeteriorated column by the corresponding function developed in this paper. The developed increment functions account for the effects of the time-dependent uncertainties that are present in the corrosion model as well as in the structural capacity models. The proposed formulation is a useful tool for engineering practice because the fragility of deteriorated columns is obtained without any extra reliability analysis once the fragility of the pristine column is known. The fragility increment functions are expressed as functions of time $t$ and a given deformation or shear demand. Unknown parameters involved in the models are estimated using a Bayesian updating framework. A model selection is conducted during the assessment of the unknown parameters using the Akaike information criterion and the Bayesian information criterion. For the estimation of the parameters, a set of data are obtained by first-order reliability method analysis using existing probabilistic capacity models for corroding RC bridge columns. Example fragilities of a deteriorated bridge column typical of current California’s practice are presented to demonstrate the developed methodology. The increment functions suggested in this paper can be used to assess the time-variant fragility for application to life cycle cost analysis and risk analysis.