Simplified closed-form expressions for the mean failure rate of structures considering structural deterioration

Two closed-form mathematical expressions are presented for the evaluation of the mean annual failure rate of deteriorating structures at the end of a given time interval. It is assumed that the structural capacity deteriorates linearly in time in both expressions. The assumption that the structural demand varies as a function of time is added to one of them. The approach is based on the probabilistic seismic demand hazard analysis used in SAC-FEMA project. The expressions are applied to a 10-storey building. The difference in expected number of failures after 150 years of constructing the building results about 16.3% higher with respect to the case when the structural deterioration is neglected. Attention is called to the importance of considering not only the time variation of the structural capacity, but also that of the structural demand in the evaluation of time-dependent failure probabilities of deteriorating structures.