Root-soil rotation stiffness of Norway spruce ( Picea abies (L.) Karst) growing on subalpine forested slopes

Trees bend and break when exposed to external forces such as wind, rockfall, and avalanches. A common simplification when modelling the tree response to these forces is to simplify the system as a clamped beam which means that the stem deflection is related to the stem flexibility only. However, a certain part of the stem deflection originates from rotation of the root-soil plate. In this paper, we investigate this contribution to the overall stem deflection. Norway spruce (Picea abies (L.) Karst) trees were subjected to winching tests to analyse the anchorage mechanics of the tree. The tests were performed at two experimental sites with an average slope of 32 and 34° and one site with a nearly flat ground in subalpine forests near Davos, Switzerland, during the vegetation periods of 2003 and 2004. The trees were pulled downslope with a winch and the applied force, stem base rotation, and the angle of the applied force relative to the stem were recorded. After the tree had fallen over, stem diameter and branch mass were measured for every meter segment. These data were used to model the tree in the finite element software ANSYS®, which was used for calculating the rotational stem base moment as a␣function of stem base rotation. The root-soil rotation stiffness k root was defined as the secant stiffness calculated at 0.5° root-soil plate rotation. Young's modulus of elasticity E of the stem was iteratively changed until the correct stem rotation was obtained. The best correlation between k root and different tree characteristics was the squared diameter at breast height, DBH2. Not incorporating the normal forces due to weight of the overhanging masses from crown and stem resulted in a maximum underestimation for k root of approximately 14%. Thus, also the acting moment on the stem base will be underestimated causing the safety factor against uprooting to be overestimate