Reliability of structures to earthquake clusters

Recent literature about life-cycle models for earthquake resistant structures considers that damage accumulation and failure are possibly due to subsequent shocks occurring during the time period of interest. In fact, most of these models only consider the effect of mainshocks. On the other hand, it is well known that earthquakes occur in clusters in which the mainshock represents only the principal (e.g., prominent magnitude) event. Because there is a chance that aftershocks can also cause deterioration of structural conditions, it may be appropriate to include this effect in the life-cycle assessment. Recently, stochastic processes describing the occurrences of aftershocks and their effect on cumulative structural damage have been formalized. These can be employed to develop stochastic damage accumulation models for earthquake resistant structures, accounting for the cluster effect. In the paper, such a model is formulated with reference to simple elastic-perfectly-plastic single degree of freedom systems. Temporal distribution of mainshocks is modeled via a homogeneous Poisson process. Occurrence of aftershocks is modeled by means of non-homogeneous Poisson processes conditional to the characteristics of the triggering mainshock. Approximate closed-form solutions are derived for the reliability assessment under the two hypotheses that total damages produced by events pertaining to different clusters can be assumed to be independent and identically distributed gamma or inverse-Gaussian random variables. An application illustrates the implications of the model on the life-cycle assessment when compared to the case where the effect of damaging aftershocks is ignored.