Probability-based cumulative damage assessment of structures subjected to non-stationary repeated loads

In-service civil structures are often subjected to repeated external loads (shock events), which may lead to an accumulation of structural damage and further an increase in the probability of structural failure. The shock actions are by nature stochastic with randomness arising from their intensities and occurrence times. A varying trend in future intensity and/or occurrence rate of many types of shock action has been projected in the literature, such as cyclone actions due to the potential impact of climate change. This article proposes a method to assess the structural reliability in the presence of uncertainty and non-stationarity in external shock events, with a limit state that the cumulative damage exceeds the permissible level. The mean value and variance of the cumulative damage are estimated with proposed closed-form solutions, and the gamma distribution is suggested to describe the probabilistic characteristics of the cumulative damage, whose accuracy is verified through a comparison with Monte Carlo simulation. Furthermore, the cumulative density function of structural service life is derived explicitly. Parametric studies are conducted to investigate the impact of non-stationarity in shock actions on structural reliability.