Background
The fatigue-life pipeline of our earlier work (Trees submission) uses Mattheck & Breloer (1994)'s concentric hollow-cylinder model. But field sonic-tomography surveys show real decay cavities are eccentric, irregular, and frequently elongated.
This study quantifies how uncertainty in cavity geometry propagates into uncertainty on fatigue life.
Method
- Derived closed-form section properties for circular and elliptical cavities of arbitrary eccentricity
- Verified a vectorisable stress-amplification function that reproduces the Mattheck formula to machine precision in the concentric limit
- Per scenario, sampled 10,000 cavity geometries: eccentricity ~ Beta(2,2), orientation ~ Uniform
- Anchored to absolute-life pipeline from prior paper
- Compared three wind-direction distributions (isotropic, Seoul empirical, Jeju empirical)
- First-order Sobol decomposition for variance attribution
Key Results
| Metric | Value | |---|---| | Median fatigue life at Mattheck threshold | 25% of concentric estimate | | 5th-percentile lower bound shortening factor | 47× | | Variance contribution — normalized eccentricity | 99.6% | | Effect of wind direction (uniform-orientation prior) | ~0 |
Significance
Statistically proves that cavity eccentricity dominates fatigue-life uncertainty — far above wind climate. Therefore sonic-tomography (SoT) precision is the top priority for inspection-resource investment. We propose risk-based inspection keyed to 5th-percentile lower bounds, tabulated for three Korean wind regimes — replacing deterministic concentric estimates.