title: Tree stability under wind: simulating uprooting with root breakage using a finite element method.
abstract: OBJECTIVE
  Windstorms are the major natural hazard affecting European forests, causing tree damage and timber losses. Modelling tree anchorage mechanisms has progressed with advances in plant architectural modelling, but it is still limited in terms of estimation of anchorage strength. This paper aims to provide a new model for root anchorage, including the successive breakage of roots during uprooting.
  
  
  METHODS
  The model was based on the finite element method. The breakage of individual roots was taken into account using a failure law derived from previous work carried out on fibre metal laminates. Soil mechanical plasticity was considered using the Mohr-Coulomb failure criterion. The mechanical model for roots was implemented in the numerical code ABAQUS using beam elements embedded in a soil block meshed with 3-D solid elements. The model was tested by simulating tree-pulling experiments previously carried out on a tree of Pinus pinaster (maritime pine). Soil mechanical parameters were obtained from laboratory tests. Root system architecture was digitized and imported into ABAQUS while root material properties were estimated from the literature.
  
  
  RESULTS
  Numerical simulations of tree-pulling tests exhibited realistic successive root breakages during uprooting, which could be seen in the resulting response curves. Broken roots could be visually located within the root system at any stage of the simulations. The model allowed estimation of anchorage strength in terms of the critical turning moment and accumulated energy, which were in good agreement with in situ measurements.
  
  
  CONCLUSIONS
  This study provides the first model of tree anchorage strength for P. pinaster derived from the mechanical strength of individual roots. The generic nature of the model permits its further application to other tree species and soil conditions.
authors.forename: Ming
authors.initials: M
authors.lastname: Yang
authors.forename: Pauline
authors.initials: P
authors.lastname: Défossez
authors.forename: Frédéric
authors.initials: F
authors.lastname: Danjon
authors.forename: Thierry
authors.initials: T
authors.lastname: Fourcaud
mesh_terms: D001696:Biomechanical Phenomena; D003198:Computer Simulation; D008954:Models, Biological; D028223:Pinus / Q000033:anatomy & histology / Q000502:physiology*; D018517:Plant Roots / Q000033:anatomy & histology / Q000502:physiology*; D018547:Plant Stems / Q000033:anatomy & histology / Q000502:physiology; D012987:Soil; D014197:Trees; D014919:Wind
chemical_list: D012987:Soil