Seismic Structural Reliability by Time‐Variant Fragility Functions

The seismic vulnerability of aging structures is often represented in the form of fragility curves that vary with time. On one hand, each of these functions is intended to apply if the earthquake hits at the time the fragility refers to. On the other hand, performance‐based earthquake engineering (PBEE) resources to classical probabilistic seismic hazard analysis (PSHA), according to which earthquakes occur according to a homogeneous Poisson (HPP) process and, in addition, the ground motion intensities in these earthquakes are independent and identically distributed random variables. This short communication shows that, consequently, the occurrence of earthquakes causing structural failure is regulated by a non‐homogeneous Poisson process (NHPP), the rate function of which is obtained multiplying the time‐invariant rate of earthquakes and the time‐variant failure probability in one event. The latter is given by the integral of the fragility's time‐function and the distribution of the intensity in a generic event. The NHPP, consistent with PBEE, leads to a closed‐form for the failure probability via time‐variant fragility.