Modelling and mechanical analysis of large displacement of windward lateral roots of trees under horizontal loads

Windward lateral roots have been shown to play a significant role in the resistance of trees to overturning under typhoons. However, there is a paucity of research focusing on their behaviours under large displacements. Through physical model tests and finite element simulations, the force-displacement curves of root elements under large displacements were obtained. Subsequently, the bilinear softening assumption incorporating the Winkler foundation beam method was used to analyze the response of single windward lateral roots under horizontal loads. Effects of root diameter and length on the peak bending moment and rotational stiffness were investigated. The findings demonstrated that when the root length was less than the critical length, the peak bending moment increased with an increase in diameter and length, and exhibited heightened sensitivity to diameter. Additionally, the overall rotational stiffness and initial rotational stiffness both increased with the increase in diameter; however, the overall rotational stiffness decreased with the increase in length, while the initial rotational stiffness basically remained unchanged. When the root was longer than the critical length, the moment-rotation curve generally no longer changed, so the above indexes were unchanged. The critical length was fitted with root diameter and elastic modulus, which can satisfty the estimation of the critical length of thick roots in engineering.