Application of the First-Order Reliability Method to Probabilistic Failure Assessment Based on the Two-Parameter Approach -A Quantitative Study Using Numerical Examples-
Tetsuya SASAKI
Abstract:Recent fitness-for-service standards for pressure vessels and pipes tend to adopt the two-parameter approach to evaluate structural integrity of components with crack-like flaws. Some probabilistic methods have also been developed to make quantitative assessments of structural reliability based on the two-parameter approach because there exist a large amount of uncertainties in the assessment parameters. However, most of them employ restricted numerical integration or tedious Monte Carlo simulation methods to calculate failure probabilities, and sufficient sensitivity studies have not yet been carried out. In this paper, making use of the first-order reliability method (FORM) is suggested to efficiently and generally compute failure probabilities based on the two-parameter approach. To confirm adequacy of employing FORM, the failure probabilities of a plate with a center through-wall crack subject to uniform tension are computed by FORM and Monte Carlo simulation methods considering uncertainties in crack size, tensional stress, yield stress and fracture toughness. The results show that FORM provides satisfactory estimates for the wide range of fracture mechanics parameters. Furthermore, the effect of a correlation of yield stress and fracture toughness on the failure probability is also investigated. It is revealed that a positive correlation between yield stress and fracture toughness results in the increase of the failure probability as long as the limit-state surface may be approximated by a hyper-plane near the design point in the standard normal space. Key Words:Structural Reliability, Failure Probability, Two-Parameter Approach, Failure Assessment Diagram, First-Order Reliability Method, Monte Carlo Simulation, Importance Sampling