Analysis of the probability of failure for open-grown trees during wind storms

• Random wind time history samples were generated using a modified Ochi–Shin spectrum.
• Two example trees in both summer and winter were modeled with Finite Element method.
• Fragility curves of the trees were estimated for both winter and summer seasons.
• Fragility curves of the trees were estimated for various decay cases in tree sections.
• The relationship between max-bending moments for winter and summer seasons was shown.

Although trees convey important environmental, economic, and sociological benefits on humans and society, they can also cause significant economic and societal disruptions, especially when subjected to wind storms in urban environments. Tools for proper assessment of the risk of these disruptions can be of significant benefit to society. In this research an approach to quantifying the failure probability for trees subject to wind storms is presented and illustrated by application to two specific maple trees in Massachusetts, USA. The approach entails four specific steps: (1) Random wind time history samples were generated using a modified Ochi–Shin spectrum, (2) these wind time histories were used as loading time histories on finite element models of the example trees in both summer (in-leaf) and winter (leafless), (3) maximum bending moments generated by the random wind time histories were compared to the failure (yield) moment of the tree at 1.4 m above ground, (4) the failure/fragility curves of the trees were estimated by Monte Carlo simulation for a range of average wind speeds and for 1000 independent wind time histories at each wind speed.