Multi-risk analysis of wind and rain on trees in urban environments

Understanding and mitigating the failure of urban trees under extreme weather conditions has become a critical issue in the face of increasing climate variability. Urban trees offer invaluable ecosystem services, yet they pose a threat to public safety and infrastructure when subjected to severe climate-related hazards. This thesis presents an integrated methodology that combines mechanistic modeling of the tree and root systems into a multi-risk framework to analyze the performance of trees under environmental loading. The approach is based on the principles of Performance-Based Wind Engineering (PBWE), applied to trees, and enhanced to account for the combined effects of wind and rainfall hazards. The core contribution of this research is the development of two complementary models representing the below-ground and above-ground parts of the tree. A novel modeling framework is introduced to capture the geometric and mechanical complexity of root–soil interaction systems. To generate root geometries, a Space Colonization Algorithm (SCA) is employed, which stochastically simulates root growth within a soil domain, accounting for both natural variability and site-specific constraints, such as urban infrastructure. These synthetic root structures are then imported into a three-dimensional Finite Element Model (FEM) built in Plaxis 3D software, where the roots are represented as elastoplastic embedded beams and the soil is modeled using an elastoplastic Mohr–Coulomb model. This mechanical framework allows for the simulation of failure mechanisms, including root yielding and soil slippage, and helps identify critical paths for failure under lateral wind-induced loading. A simplified Above-Ground Model (AGM) is also developed to evaluate the dynamic response of the tree under wind excitation. This model uses the Power Spectral Density (PSD) functions of wind turbulence to calculate the tree's base rotation. The AGM represents the tree as a flexible vertical cantilever with a distributed mass along the stem and a concentrated mass at the top, representing the canopy. At its base, the stem is connected to a rotational spring that simulates the root–soil rotational stiffness. This spring is defined using the nonlinear moment–rotation curve obtained from the Below-Ground Model (BGM). This integrated analysis enables the evaluation of two primary failure modes: uprooting, driven by root–soil interaction under lateral wind loading, and stem breakage, caused by excessive bending stresses in the stem. Building on the Performance-Based Wind Engineering (PBWE) methodology, this thesis extends the framework to a multi-risk context by incorporating wind and rainfall as two effective hazards. Rainfall alters soil strength and pore water pressure, reducing root anchorage and increasing the likelihood of failure. Fragility analyses are conducted for combined wind and rainfall scenarios using Monte Carlo simulations to estimate the probability of failure across a population of trees. Fragility curves are then integrated with hazard scenarios and a simplified loss model to estimate the total risk, outlining a workflow for conducting multi-risk analysis of urban trees under compound environmental loads. The results show that rainfall increases the risk of tree failure by reducing soil strength and increasing the likelihood of uprooting, especially when combined with wind loads. By linking mechanical modeling with probabilistic risk analysis, the methodology offers a tool for understanding failure mechanisms and estimating potential impacts. This integrated framework supports risk-informed decision-making for urban planners, arborists, and policymakers, providing quantitative insights essential for sustainable urban management. The primary objective of this research is to present a structured modeling and analysis framework rather than to validate the procedure. The models developed in this study can be further improved and calibrated using field data, while the probabilistic analysis can be enhanced with more detailed representations of uncertainties and failure scenarios.