A CDF evolution approach for efficient time-dependent reliability analysis of aging RC structures

Evolution problems involving uncertain initial conditions naturally lead to stochastic formulations in which the state variable evolves as a random process. Classical Monte Carlo simulation (MCS) is commonly employed to track the time evolution of associated probability distributions. Still its accuracy requires a very large number of deterministic realizations, resulting in prohibitive computational costs for high-dimensional problems. In the present paper, an efficient method is presented to calculate the evolution of the cumulative distribution function (CDF), even in the presence of many random variables. This approach relies on a one-to-one mapping between the integration domain and a subset of the unit cube, enabling the use of good lattice point sets to evaluate the required integrals with substantially fewer deterministic analyses than MCS. The method is particularly suitable for structural reliability applications, where failure probabilities depend on multiple uncertain parameters. These probabilities may be very small and vary over time due to material degradation, evolving environmental conditions, and non-stationary loads that are sometimes modeled as stochastic processes. Its effectiveness is demonstrated in the context of durability assessment of aging reinforced concrete structures, with a specific focus on the evaluation of the time-dependent probability of corrosion damage under changing climate scenarios