Fatigue life assessment of urban street trees under wind loading: effects of decay progression and soil conditions

Urban street trees are susceptible to windthrow and branch failure during storms, yet existing risk frameworks focus on static ultimate-load criteria and neglect cumulative fatigue damage under repeated wind loading. This study presents an integrated, screening-level engineering–biology framework — explicitly adapted from structural-fatigue methodology to the biological realities of living trees — coupling ABAQUS finite element dynamic analysis (with documented mesh convergence), Kaimal-spectrum biaxial wind time series, rainflow cycle counting, Miner’s damage rule, a concentric-hollow decay stress amplification model, and regional Weibull wind-speed distributions. Six tree geometries (H = 6 and 8 m; DBH = 15, 20, and 25 cm) were modelled as tapered B31 beams with biaxial wind loading (longitudinal mean-plus-turbulence and lateral turbulence at σ_v = 0.75σ_u) and Rayleigh damping (ζ = 2%). Wind-induced stem oscillation is treated as fully reversed bending ( R = − 1); the use of $$\:R=0$$ -derived S-N coefficients is recognised as a non-conservative simplification and is partially compensated by lower-bound S-N parameters. The maximum dynamic amplification factor (DAF) was 7.71 for H = 8 m, DBH = 15 cm, with a peak stress of 138.7 MPa exceeding the ginkgo modulus of rupture (MOR), indicating that static failure precedes fatigue in slender trees. For a decayed reference tree (r_d/ R = 0.8) under Jeju typhoon-regime winds (Weibull scale parameter c = 9.0 m/s), lower-bound S-N fatigue life was approximately 1.4 years. Sound-tree fatigue life differed by up to several hundred thousand times across five Korean street tree species due to MOR differences alone, with species-specific elastic-modulus variation contributing only ± 6% to peak base bending moment. A Winkler rotational spring model showed that soft-clay soils reduce basal stress by up to 64.5% relative to a fully fixed base, but at the cost of increased overturning risk under extreme loads. Independent corroboration from Korea Forest Service typhoon damage statistics, Korean post-typhoon field surveys, and Hurricane Sandy and Hurricane Irma urban-tree damage records is qualitatively consistent with the framework’s central prediction that the dominant failure mode is decay-accelerated low-cycle fatigue. The results establish that decay detection and species selection are the primary determinants of fatigue safety for urban trees, that delayed post-storm failures can be interpreted as the joint product of accumulated fatigue damage and post-storm soil-stiffness loss, and that regionally differentiated inspection standards are warranted.