Distribution of structural collapses and optimum reliability for infrequent environmental loads

Structures located in a particular zone of interest may be subjected to the same environmental events or the same natural phenomena that occur infrequently. That is, the structures are subjected to the same environmental loading parameters such as the peak ground acceleration, the reference wind velocity pressure, and the total ice accumulation. Therefore, the structural collapses are dependent or correlated. The correlation may affect the probability distribution of the number of structural collapses and the optimum reliability level for upgrading the exiting structures and infrastructures. This is investigated in this paper. It is shown that the coefficient of variation of the number of structural collapses is an increasing function of the correlation coefficient. This increase can be important to the selection of optimum reliability level for retrofitting of existing structures and infrastructures when the risk aversion factor is considered. An approach by taking the correlation among structural collapses into account in selecting the optimum upgrading level of a group of existing structures is presented and illustrated by a numerical example.