Probabilistic analysis and fragility quantification of RC containment structures under seismic excitations using the probability density evolution method

Containment structures play an influential role in protecting the environment/society against releasing radioactive material from nuclear power plants. Thus, the continuous worldwide threat of seismic hazards to these structures makes studying their response to seismic events an urgent necessity. Additionally, several uncertainty sources, which significantly influence the structural response, are neglected in a deterministic analysis, and thus, the probability of failure under such events cannot be quantified. Consequently, the current study aims to develop a framework to explore the stochastic response and quantify the probability of failure for an existing reinforced concrete containment structure (RCCS) excited by a strong earthquake based on the probability density evolution method (PDEM) combined with the equivalent extreme value event. The finite element method (FEM) for simulation and analysis of the RCCS comprise the multi-layered shell element and multi-axial concrete plasticity damage constitutive model, which is employed through the VUMAT subroutine. Since an RCCS is highly sensitive to tensile damage and cracking under seismic events, a new formula is proposed for defining the crack-width failure criterion. The stochastic response and the instantaneous probability density function are attained through the developed framework. The results reveal that, when considering the uncertainty sources, the maximum crack width increases in some cases to roughly eight times its value coming from the deterministic analysis. Besides, in contrast to the deterministic analysis results, where the structure exhibits only functional failure, the probabilistic analysis demonstrates that the structure exhibits functional and structural failure with a probability of 81.5% and 31%, respectively. Finally, this study highlights the importance of fragility analysis in ensuring the safety of containment structures and help mitigate risks associated with natural disasters.