Probabilistic assessment of structures considering the effect of cumulative damage under seismic sequences

An approach to describe the evolution of damage that a structure could accumulate by the action of seismic sequences at the end of a time interval is proposed. The cumulative damage is quantified by means of a damage index that considers both the demanded drift and ultimate drift. The damage index at the end of a time interval is expressed in terms of: (a) the distribution function of damage and (b) the distribution function to the first failure. Based on the above, the structural reliability is obtained, and it is expressed in terms of reliability functions. The proposed criterion considers the stochastic variability of the seismic occurrence that affects the structural performance under seismic loads. Distribution functions and reliability functions are obtained for a reinforced concrete bridge located in transition soil (type 2) in Mexico City. Such bridge was designed for three different drift thresholds. The different study cases are subjected to seismic sequences during a time interval. Acceptable reliability levels were found up to 50 years after the bridge construction.