Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article

Degree

Doctor of Philosophy

Program

Civil and Environmental Engineering

Supervisor

Tim Newson

Abstract

For urban planners, arborists and foresters, understanding tree stability under self-weight and applied loads from wind and snow is important when developing management strategies to reduce the risk of damage from these abiotic agents. Current predictive approaches are generally empirical and based on a posteriori surveys of failures. A more rigorous engineering approach to understanding response phenomenon in trees subjected to extreme winds has been attempted herein. The size of trees and their architecture (shape and structure) greatly influence their mechanical stability under dynamic loading. Considering trees as porous media, wind loads on them are affected by their resistance to through-flow, porosity, porosity distribution, and the overall geometry of their structure including the size, shape, and angle to the wind attack. When modelling the interaction between wind and trees we need to consider trees as dynamic structures and the most important parameters are the fundamental frequency and damping, which greatly affects their response. The dynamic behavior of trees can also be influenced by their geometric (e.g. mass distribution and cross-section along tree structures) and material (e.g. density, viscous damping and modulus of elasticity) properties.

The mechanical stability of trees is of interest to researchers studying the architecture and growth strategies of different genera and species across a wide variety of forest ecosystems. It is also relevant to forest managers due to the impacts on stand development and the loss of potential harvest revenue. The maximum height that a tree of a given diameter can attain has often been estimated on the basis of the avoidance of buckling. In the first part of the study, buckling analyses and methods to estimate the natural frequency of trees were developed for a non-prismatic elastic circular column of height H using the finite element method and taking self-weight into account. Various scenarios were considered: column taper, base rigidity, radial, and longitudinal stiffness, ellipticity, and crown weight. The results indicated that column taper, base fixity, ellipticity and E/ρ ratio are particularly important for buckling behavior and dynamic properties (natural frequency) of trees.

Considering the complexity of sub-critical and failure responses of trees, experiments and aerodynamic analysis were conducted from different viewpoints. Since a simple analog for a tree is an elevated porous plate, this type of model was used initially in a wind tunnel to try to better understand the behavior of vegetative structures under wind loading. Multimodal response of branches and tree’s ability to reconfigure and change porosity in wind fields were later considered using wind dependent flaps over plate holes. The results showed that increasing the wind angle of attack from 0° to 45° will decrease the drag coefficients of the designed systems. Moreover, when increasing the porosity, the drag coefficient, drag force and reduction factors will all decrease. Adding wind dependent flaps to the elevated porous plates alters the aerodynamic behavior and sway dynamics of the designed system, making it more similar to a real tree behavior and the resulting wind forces were proportional to the power of 1.7 of wind velocity.

To further study wind and tree interaction, a novel wind tunnel experimental technique was also used. Red Oak trees were chosen because of their ubiquity in North America and susceptibility to windthrow. The study was conducted in parallel with a field experiment carried out on a full-scale single oak tree at the Risø campus of the Technical University of Denmark and it aimed to understand the dynamic behavior of an open grown tree structure under incremental wind loading conditions, for different crown configurations (created by pruning the leaves and branches). The sheltering effect of the tree with different porosities was also investigated. The dynamic analysis conducted included the tree sapling sway response, natural frequency, damping, and admittance with increases in wind speed. The results showed that the wind force on the scaled sapling tree is proportional to a power exponent of approximately 1.3 and 2 for the tree with and without leaves respectively. In general, damping appears to increase with wind speed, but this trend was not fully clear especially for the oak with leaves. We observed similar behavior for the tree-like porous plate structures. The tree with leaves exhibited a much better sheltering effect, compared to the tree without leaves and a significant sheltered zone was formed behind the tree canopy. The wind tunnel results also showed that trees behave like fractal objects; increasing wind speed caused an increase in optical porosity and reductions in the fractal dimensions in trees with leaves.

Summary for Lay Audience

Trees have an important influence on society due to their sociological and environmental benefits. For urban planners, arborists and foresters, understanding tree stability under self-weight and applied loads from wind and snow is important when developing management strategies to reduce the risk of damage from these abiotic agents. Current predictive approaches are generally empirical and based on a posteriori surveys of failures. A more rigorous engineering approach to understanding response phenomenon in trees subjected to extreme winds has been attempted in this study.

To better understand wind and tree interaction, novel wind tunnel experimental techniques were used. Since a simple analog for a tree is an elevated porous plate, this type of model was used initially in a wind tunnel to try to better understand the behavior of vegetative structures under wind loading. Multimodal response of branches and tree’s ability to reconfigure and change porosity in wind fields were later considered using wind dependent flaps over plate holes. To further study wind and tree interaction, Red Oak trees were chosen because of their ubiquity in North America and susceptibility to windthrow. The study was conducted in parallel with a field experiment carried out on a full-scale single oak tree at the Risø campus of the Technical University of Denmark and it aimed to understand the dynamic behavior of a tree structure under incremental wind loading conditions, for different crown configurations, created by pruning the leaves and branches. The sheltering effect of the tree with different porosities was also investigated. Dynamic analysis conducted included the tree sapling sway response, natural frequency, damping, and admittance with increases in wind speed.

The results showed that the wind forces on various scaled trees is proportional to wind velocity to a power less than 2 for the tree with leaves. Thus, the tree with leaves behave quite differently to bluff bodies due to streamlining, flexibility and reduction in the projected frontal area with increasing wind speed. The trees with leaves exhibited a much better sheltering effect, compared to the trees without leaves and a better sheltered zone was formed behind the tree canopy.

Available for download on Wednesday, August 31, 2022

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