Structural Reliability Analysis of Reinforced Concrete: A Comparison of MCS, FORM, SORM, and Parallelized Subset Simulation in Julia

Resumo

In civil engineering, estimating the probability of rare events is essential for ensuring the safety and reliability of structural systems. Scenarios such as failures in reinforced concrete elements, progressive collapse, and performance-based design require accurate evaluation of low-probability events. Traditional methods like Monte Carlo Simulation (MCS), the First-Order Reliability Method (FORM), and the Second-Order Reliability Method (SORM) are widely used due to their theoretical foundation and practical simplicity. However, MCS becomes computationally prohibitive for rare events, while FORM and SORM may lose accuracy in nonlinear or non-Gaussian problems, common in structural analysis. Subset Simulation (SuS) overcomes these limitations by decomposing the rare event into a sequence of intermediate events, sampled efficiently through Markov Chain Monte Carlo (MCMC) techniques. To reduce computational time, SuS can be parallelized by distributing the sampling across multiple processors, this strategy enables faster analysis without compromising accuracy, making it suitable for large-scale models in civil engineering. This work explores the use of MCS, FORM, SORM, and SuS within the Julia programming environment, which offers high-performance computing capabilities. The methods are evaluated based on accuracy, computational cost, and robustness across a range of examples, including benchmark problems and structural models of reinforced concrete. Results indicate that SuS delivers accurate estimates with significantly fewer samples. When parallelized, it becomes a computationally efficient tool for reliability analysis in civil engineering, outperforming traditional methods in complex scenarios.