The root-soil system of Norway spruce subjected to turning moment: resistance as a function of rotation

The reactions of trees to wind, rockfall, and snow and debris flow depend largely on how strong and deformable their anchorage in the soil is. Here, the resistive turning moment M of the root-soil system as a function of the rotation [Greek Phi symbol] at the stem base plays the major role. M([Greek Phi symbol]) describes the behavior of the root-soil system when subject to rotational moment, with the maximum M([Greek Phi symbol]) indicating the anchorage strength M a of the tree. We assessed M([Greek Phi symbol]) of 66 Norway spruce (Picea abies L. Karst) by pulling them over with a winch. These 45- to 170-year-old trees grew at sites of low and high elevation, with a diameter at breast height DBH = 14-69 cm and a height H = 9-42 m. M([Greek Phi symbol]) displayed a strong nonlinear behavior. M a was reached at a lower [Greek Phi symbol] for large trees than for small trees. Thus overhanging tree weight contributed less to M a for the large trees. Overturning also occurred at a lower [Greek Phi symbol] for the large trees. These observations show that the rotational ductility of the root-soil system is higher for small trees. M a could be described by four monovariate linear regression equations of tree weight, stem weight, stem volume and DBH ² ·H (0.80 < R ² < 0.95), and [Greek Phi symbol] at M a, [Greek Phi symbol] a, by a power law of DBH²·H (R ² = 0.85). We found significantly higher M a for the low-elevation spruces than for the high-elevation spruces, which were more shallowly anchored, but no significant difference in [Greek Phi symbol] a. The 66 curves of M([Greek Phi symbol]), normalized (n) by M a in M-direction and by [Greek Phi symbol] a in [Greek Phi symbol]-direction, yielded one characteristic average curve: [graphic removed] . Using [graphic removed] and the predictions of M a and [Greek Phi symbol] a, it is shown that M([Greek Phi symbol]) and the curves associated with M([Greek Phi symbol]) can be predicted with a relative standard error <=25%. The parameterization of M([Greek Phi symbol]) by tree size and weight is novel and provides useful information for predicting with finite-element computer models how trees will react to natural hazards.