Probabilistic integrity assessment of rehabilitated cracked polygonal tubes: Implications from FEA and multi-parameter sensitivity analysis

• A 3D XFEM model analyzes crack growth in polygonal cross-section steel tubes. • Surrogate regression models quantify SIFs across shape, load, and crack features. • Monte Carlo-based reliability analysis reveals higher fracture risk in triangular sections. • Crack orientation angle is the dominant parameter affecting structural integrity. • Composite sleeves with ±45° plies effectively reduce SIFs up to 70% in all shapes. The present study examines the fracture reliability and efficiency of reinforced cracked tubes, and provides a comprehensive probabilistic integrity assessment of cracked polygonal tubes, moving beyond traditional circular geometries. The most common of mechanical damages in pipes is dents, gouges, cracks and scratches, which severely threaten structural integrity. However, while these forms of mechanical damage are widely detected in polygonal pipes, there is a notable lack of research focusing on their behavior and repair in polygonal tube geometries. To this end, a three-dimensional finite element model (FEM), incorporating extended FEM (XFEM) for crack growth analysis, was developed to estimate stress intensity factors (SIFs) and analyze crack propagation in repaired metallic tubes with surface cracks. A novel integration of Monte Carlo simulations with surrogate modeling based on regression analysis enabled efficient and accurate evaluation of probabilistic failure scenarios and uncertainties. The sensitivity and impact of key parameters, including crack geometry, crack orientation angle, axial tensile pressure, stiffener thickness, and cross-sectional polygonality, were analyzed using Sobol-based global sensitivity analysis. Results indicated that circular cross-sections and thicker reinforcements significantly increased the fracture resistance, and crack orientation was the most influential uncertainty. In addition, composite sleeves demonstrated a sound reduction in SIFs from 1.05 (unrepaired) to 0.33 (repaired) for triangular tubes and from 0.98 (unrepaired) to 0.29 (repaired) for rectangular tubes, whereas the circular tubes showed a decrease from 0.89 to 0.28). from 1.05 to 0.33 in the triangular section. Concurrently, the probability of failure before repair was 8.9% for rectangular tubes, 6.2% for triangular tubes, and 3.7% for circular tubes; after composite repair, these values were substantially reduced to 1.1%, 0.7%, and 0.3%, respectively. These results clearly demonstrate a significant improvement in structural reliability across all tube geometries. The explicit investigation of polygonal cross-sectional effects on fracture mechanics and repair efficiency represents a significant advancement over prior works focused solely on cylindrical tubes. This research highlights the necessity of including axial load scenarios in future design codes and repair watermarks. Suggestions include prioritizing crack angle management, robust composite repairs, and targeting inspections on identified sensitivities to improve tube safety and reliability.