Probabilistic modeling of degree of bending in FRP-strengthened offshore tubular X-joints

A probabilistic framework is developed to quantify the Degree of Bending (DoB) behavior in fiber-reinforced polymer (FRP)-strengthened tubular X-joints subjected to axial and in-plane bending loads. Despite extensive research on FRP retrofitting, the probabilistic modeling of DoB behavior in strengthened joints-across different joint types, composite systems, and loading conditions-has not been addressed. The proposed framework, therefore, represents the first systematic attempt to statistically characterize DoB in FRP-retrofitted tubular joints. The proposed model considers multiple FRP types (SFRP, GFRP, AFRP, and CFRP) and is validated against seventeen existed experimental and analytical benchmarks to ensure predictive reliability. A total of 296 finite element simulations were performed on 148 unique joint configurations, incorporating detailed weld geometry and explicit contact interactions between the FRP layers and the steel substrate. Simulation outputs were compiled into a statistical database, to which 25 candidate probability distributions were fitted. Goodness-of-fit was evaluated using Chi-squared, Anderson-Darling, and Kolmogorov-Smirnov tests. Among the tested models, the three-parameter Fatigue Life distribution demonstrated the best agreement with the simulated DoB data under both axial and bending loads. In contrast to deterministic approaches that usually give conservative results because of fixed input assumptions, the proposed probabilistic model reflects the actual variability in joint behavior. This makes it possible to carry out more realistic reliability assessments and to adjust safety factors in design practice. In engineering applications, the proposed identified distributions can be used in reliability analyses of jacket-type offshore platforms, where tubular connections are often the most vulnerable parts, helping engineers move toward performance-based design and a clearer understanding of failure probability.