Ntime-Dependent Reliability Analysis of Pipelines Integrating Burst Pressure Modeling, Fatigue Crack Growth, and Stochastic Operational Loading

Fatigue crack growth driven by cyclic pressure loading in oil and gas pipelines remains a critical concern for structural integrity. This study implements a time-dependent reliability analysis of fatigue crack propagation in pressurized pipelines by integrating Paris law–based crack growth modeling with empirically derived operational pressure statistics and fracture-mechanics-based burst pressure assessment. A limit state function is defined by comparing, over time, the predicted burst pressure of the cracked pipe with operational pressure, where pressure ranges are modeled as independent stochastic variables sampled from empirically calibrated probability distributions based on field measurements. As a preliminary step, different burst pressure formulations (Ln-Sec, CorLas and BS 7910) are evaluated against experimental burst test data to quantify predictive accuracy, model bias, and computational efficiency. Based on this assessment, the Ln-Sec model is selected for subsequent reliability analysis. Large-scale Monte Carlo simulations with 10⁵ realizations are performed to quantify mean time to failure, crack shape evolution, and time-dependent failure probabilities for different initial crack depth ratios ( a 0 /t ) over approximately 97 years. The results demonstrate strong sensitivity to the initial crack depth. For the example considered, the peak annual failure probability occurs in the first year for a t / t = 0.8, in year 7 for 0.7 and in year 42 for 0.5. The findings highlight the combined influence of initial defect size and stochastic operational loading on long-term pipeline reliability and underline the role of burst pressure model selection in reliability-oriented fatigue assessments.