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

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Abstract

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 ϕ at the stem base plays the major role. M(ϕ) describes the behavior of the root–soil system when subject to rotational moment, with the maximum M(ϕ) indicating the anchorage strength M a of the tree. We assessed M(ϕ) 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(ϕ) displayed a strong nonlinear behavior. M a was reached at a lower ϕ 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 ϕ 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 DBH2·H (0.80 < R 2 < 0.95), and ϕ at M a, ϕ 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 ϕ a. The 66 curves of M(ϕ), normalized (n) by M a in M-direction and by ϕ a in ϕ-direction, yielded one characteristic average curve: \(\overline{M} _{{\text{n}}} {\left( {\phi _{{\text{n}}} } \right)}\). Using \(\overline{M} _{{\text{n}}} {\left( {\phi _{{\text{n}}} } \right)}\) and the predictions of M a and ϕ a, it is shown that M(ϕ) and the curves associated with M(ϕ) can be predicted with a relative standard error ≤25%. The parameterization of M(ϕ) 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.

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Abbreviations

Notation:

Description (Unit)

b, α:

Regression coefficients

DBH:

Stem diameter on bark at breast height, i.e. 1.3 m (m)

ϕ :

Rotation at the base of the stem due to M (°)

ϕ a :

ϕ at M a (°)

ϕ n :

ϕ normalized with ϕ a

ϕ OT :

ϕ at which the tree overturns due to M g only (°)

H :

Total tree height (m)

HE, LE:

High-elevation site, low-elevation site

κ :

Average stem curvature between the stem base and the stem section initially at z g0 (m−1)

m :

Weight (kg)

M :

Resistive turning moment of the tree root–soil system (Nm)

M a :

Anchorage strength of the tree, i.e. the maximum M (Nm)

M F :

Contribution of the winching force to M. M F = M − M g (Nm)

M g :

Contribution of overhanging weight of stem and crown to M (Nm)

M n :

M normalized with M a

\( \overline{M} _{\rm n} \) :

The average M n(ϕ n)-curve

n :

Normalized value (as subscript)

p :

Predicted value (as subscript)

P :

Statistical P-value

R 2 :

R-squared value of a regression

SE:

Standard error, or after ± (mean value ± SE)

SEn :

Relative standard error = SE divided (normalized) by the estimate itself (-, %)

V :

Volume (m3)

X :

Explanatory variable

x, y, z :

Cartesian coordinates of the tree: origin at stem base; x = horizontal stem deflection; z = height above origin. (m)

z g0 :

Height of the tree’s centre of gravity.0 refers to the initial tree position (m)

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Acknowledgements

We thank the Board of the Swiss Federal Institutes of Technology for funding (Tree stability and natural hazards), all people involved in the tree stability project for field assistance, Pierre Vanomsen for valuable collaboration, and Silvia Dingwall for revision of the text.

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Authors and Affiliations

  1. WSL, Swiss Federal Institute for Snow and Avalanche Research SLF, CH-7260, Davos Dorf, Switzerland

    T. Lundström, M. J. Jonsson & M. Kalberer

  2. Laboratory of Dendrogeomorphology, University of Fribourg, 1700, Fribourg, Switzerland

    T. Lundström

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  1. T. Lundström
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  2. M. J. Jonsson
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  3. M. Kalberer
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Correspondence to T. Lundström.

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Responsible Editor: Peter J. Gregory.

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Lundström, T., Jonsson, M.J. & Kalberer, M. The root–soil system of Norway spruce subjected to turning moment: resistance as a function of rotation. Plant Soil 300, 35–49 (2007). https://doi.org/10.1007/s11104-007-9386-2

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