3D fractal modeling of non-uniform corrosion in steel pipes: Failure behavior analysis and structural integrity assessment

To address the limitations of conventional idealized geometric assumptions in evaluating the failure pressure of corroded steel pipes, this study proposes an integrated methodology combining three-dimensional (3D) fractal theory with finite element (FE) modeling to characterize the mechanical behavior of random non-uniform corrosion defects. A random non-uniform corrosion pipe model was developed by reconstructing corrosion morphologies using the Weierstrass-Mandelbrot (W-M) fractal function within a Python-ABAQUS collaborative framework, incorporating fractal dimension (Dn), spatial frequency (γ), and scale coefficient (Cn). The model's reliability was validated through full-scale burst tests. Systematic quantification revealed the correlation between geometric parameters of single-point defects, spacing of double-point defects, and failure behavior. The results demonstrate that under single-point corrosion conditions, increasing the defect length to 180 mm and depth to 0.8t reduces failure pressure by 15.99 % and 23.66 %, respectively. Conversely, widening the corrosion angle to 40° reduces failure pressure by only 7.85 % through stress dispersion effects. For double-point corrosion interaction, longitudinal spacing exerts a significantly stronger influence on defect coupling than circumferential spacing. Critical spacings (1.5Dt for longitudinal alignment and 0.16πD for circumferential alignment) effectively isolate interaction effects. This study establishes a systematic correlation framework between fractal characteristics and mechanical responses, advancing a theoretical paradigm for the reliability assessment of corroded pipelines.