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 that real decay cavities are eccentric, irregular, and frequently elongated.
How much uncertainty does relaxing this assumption inject into fatigue-life estimates?
Approach
- 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
- 10,000 geometry samples per scenario:
- Normalized eccentricity ~ Beta(2, 2)
- Cavity orientation ~ Uniform
- Anchored to absolute-life pipeline from prior paper
- Three wind-direction distributions compared (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 (under uniform orientation prior) | effectively collapses |
Implications
- Cavity eccentricity dominates fatigue-life uncertainty — far more than wind climate.
- Inspection resources should therefore prioritize higher-fidelity sonic-tomography (SoT) surveys.
- We propose risk-based inspection keyed to 5th-percentile lower bounds, tabulated for Korea's three wind regimes — instead of deterministic concentric estimates.
Related solutions
- Street-Tree Safety · Fatigue Diagnosis — this result directly informs inspection prioritization.