Safety estimation method for structures with cumulative damage

Considering progressive weakening under repetitive events of loading, the proposed method estimates the safety probability for structures with cumulative damage. The structural damage is represented by a finite number of discrete states. The time evolution of damage is described by a Markov chain where the collapse corresponds to an absorbing state. Structural loading is defined as a discrete stochastic process of random events. This stochastic model can describe the seismic phenomenon as well as other environmental loads. A homogeneous Poisson process is used to model the random occurrences of the loading. To illustrate this method, the safety estimation of a masonry structure under seismic loading was performed. The obtained results are checked by a numerical simulation and compared with those of the classical analysis, which did not consider cumulative damage. The main features of the damage time evolution, the safety assessment, and the hazard function are pointed out.