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We present a method for a probabilistic estimation of the time variation during aftershock sequences of the vulnerability of reinforced concrete structures which deteriorate as they accumulate damage and become more vulnerable. First we describe the steps of the proposed method and then we apply it in the case of two building models and two aftershock sequences. The degradation of the structural elements of the buildings is assumed to be stochastic and computed with time-history analyses using a hysteretic model of bending response. Then the engineering demand parameter of maximum drift is associated with the elongation of the fundamental period of the structure and we define limit damage states using as thresholds values of the period elongation ratio. The numerical models of the buildings that correspond to the defined damage states are defined and analyzed, in order to calculate their fragility curves and the probability of the damaged building models transitioning to higher damage states. The cumulative probability of exceeding a damage state for the selected aftershock sequences is calculated with a Markov chain whose transition matrices are a function of the intensity of the aftershocks. This results to the variation of the probability of exceedance of period elongation thresholds due to damage accumulation as a function of time during the selected aftershock sequences.

APPLICATION OF A DAMAGE STATE METHOD BASED ON PERIOD ELONGATION FOR TIME VARIANT VULNERABILITY OF DEGRADING REINFORCED CONCRETE BUILDINGS