# Experimental Test of Non-Destructive Methods to Assess the Anchorage of Trees

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### Data Analysis

## 3. Results

#### 3.1. Indicators of Anchorage Strength

#### 3.1.1. Tree Size

#### 3.1.2. Soil–Root Rotational Stiffness ${k}_{r}$

#### 3.2. Testing the Estimations of Anchorage Strength

#### 3.2.1. Linear Extrapolation of Rotational Stiffness (Equation (1))

#### 3.2.2. Non-Linear Extrapolation (Equation (3))

#### 3.2.3. Comparison between Predictors

#### 3.3. Species Effect on Anchorage Strength

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

M | Bending moment |

${M}_{a}$ | Anchorage strength |

${k}_{r}$ | Root–soil rotational stiffness |

$\varphi $ | Root plate rotation |

d | Stem diameter in m |

h | Tree height in m |

## Appendix A

**Table A1.**ANOVA of a linear model $ln{\left({M}_{a}\right)}_{i}={\beta}_{0}+{\beta}_{1}\times {\mathrm{Species}}_{i}+{\beta}_{2}\times ln{\left(\mathrm{Size}\right)}_{i}+{\beta}_{3}\times {\mathrm{Species}}_{i}\times ln{\left(\mathrm{Size}\right)}_{i}+{\u03f5}_{i}$.

DF | Sum Sq | Mean Sq | F-Value | Pr (>F) | |
---|---|---|---|---|---|

Species | 7 | 22.38 | 3.20 | 28.93 | 0.0000 |

Size | 1 | 100.90 | 100.90 | 913.03 | 0.0000 |

Species:Size | 7 | 1.14 | 0.16 | 1.47 | 0.1771 |

Residuals | 267 | 29.51 | 0.11 |

**Table A2.**ANOVA of a linear model $ln{\left({M}_{a}\right)}_{i}={\beta}_{0}+{\beta}_{1}\times {\mathrm{Species}}_{i}+{\beta}_{2}\times ln{\left({k}_{r}\right)}_{i}+{\beta}_{3}\times {\mathrm{Species}}_{i}\times ln{\left({k}_{r}\right)}_{i}+{\u03f5}_{i}$.

DF | Sum Sq | Mean Sq | F-Value | Pr (>F) | |
---|---|---|---|---|---|

Species | 7 | 22.4 | 3.2 | 59.9 | 0.00 |

$ln\left({k}_{r}\right)$ | 1 | 116.4 | 116.4 | 2178.4 | 0.00 |

Species:$ln\left({k}_{r}\right)$ | 7 | 0.9 | 0.1 | 2.5 | 0.02 |

Residuals | 267 | 14.3 | 0.1 |

**Table A3.**ANOVA of model $ln\left(\frac{2.5{k}_{r}}{{M}_{a}}\right)={\beta}_{0}+{\beta}_{1}\mathrm{Species}+{\beta}_{2}ln\left(\mathrm{Size}\right)+{\beta}_{3}\mathrm{Species}\times log\left(\mathrm{Size}\right)+{\u03f5}_{i}$.

DF | Sum Sq | Mean Sq | F-Value | Pr (>F) | |
---|---|---|---|---|---|

fSpecies | 7 | 5.36 | 0.77 | 9.08 | 0.000 |

logSize | 1 | 6.29 | 6.29 | 74.57 | 0.000 |

fSpecies:logSize | 7 | 1.08 | 0.15 | 1.83 | 0.081 |

Residuals | 267 | 22.53 | 0.08 |

**Table A4.**ANOVA of a linear mixed-effects model ${M}_{{a}_{ij}}={\beta}_{0}+{\beta}_{1}\times {k}_{{r}_{ij}}+{\beta}_{2}\times {\mathrm{Site}}_{ij}+{\gamma}_{0i}+{\gamma}_{1i}\times {\mathrm{Site}}_{ij}+{\u03f5}_{ij}$ with ${\u03f5}_{ij}$ modeled as a power function of ${k}_{r}$.

DF | F-Value | Pr (>F) | |
---|---|---|---|

(Intercept) | 68 | 297.73 | 0.00 |

${k}_{r}$ | 68 | 157.16 | 0.00 |

Site | 7 | 0.34 | 0.58 |

**Table A5.**ANOVA of model $log\left(\frac{{M}_{\mathrm{est}}}{{M}_{a}}\right)=\mathrm{Species}\times log\left(\mathrm{Size}\right)$.

DF | Sum Sq | Mean Sq | F-Value | Pr (>F) | |
---|---|---|---|---|---|

Species | 7 | 5.36 | 0.77 | 9.08 | 0.000 |

log(Size) | 1 | 6.29 | 6.29 | 74.57 | 0.000 |

Species:log(Size) | 7 | 1.08 | 0.15 | 1.83 | 0.081 |

Residuals | 267 | 22.53 | 0.08 |

**Table A6.**ANOVA of model $log\left({\varphi}_{a}\right)=\mathrm{Species}\times log\left(\mathrm{Size}\right)$.

DF | F-Value | Pr (>F) | |
---|---|---|---|

(Intercept) | 1 | 2108.16 | 0.00 |

Species | 5 | 2.40 | 0.04 |

log(Size) | 1 | 46.95 | 0.00 |

Species:log(Size) | 5 | 3.19 | 0.01 |

DF | F-Value | Pr (>F) | |
---|---|---|---|

(Intercept) | 1 | 3482.60 | 0.00 |

Species | 8 | 21.81 | 0.00 |

## References

- Smiley, E.T.; Holmes, L.; Fraedrich, B.R. Pruning of Buttress Roots and Stability Changes of Red Maple (Acer Rubrum). Arboric. Urban For.
**2014**, 40, 230–236. [Google Scholar] [CrossRef] - Ghani, M.A.; Stokes, A.; Fourcaud, T. The Effect of Root Architecture and Root Loss through Trenching on the Anchorage of Tropical Urban Trees (Eugenia Grandis Wight). Trees-Struct. Funct.
**2009**, 23, 197–209. [Google Scholar] [CrossRef] - Schmidlin, T.W. Human Fatalities from Wind-Related Tree Failures in the United States, 1995-2007. Nat. Hazards
**2009**, 50, 13–25. [Google Scholar] [CrossRef] - Heneka, P.; Hofherr, T.; Ruck, B.; Kottmeier, C. Winter Storm Risk of Residential Structures–Model Development and Application to the German State of Baden-Württemberg. Nat. Hazards Earth Syst. Sci.
**2006**, 6, 721–733. [Google Scholar] [CrossRef] [Green Version] - Pomnitz, M. Mangelnde Standsicherheit von Bäumen nach Baumaßnahmen—Gründe für einen sinnvollen Baumschutz. In Proceedings of the Jahrbuch der Baumpflege; Dujesiefken, D., Ed.; Haymarket Media GmbH: Augsburg, Germany, 2016; pp. 183–190. [Google Scholar]
- Smiley, E.T.; Matheny, N.P.; Lilly, S. Tree Risk Assessment; Best Management Practices, International Society of Arboriculture: Champaign, IL, USA, 2011. [Google Scholar]
- Kim, D.; Jin, J. Does Happiness Data Say Urban Parks Are Worth It? Landsc. Urban Plan.
**2018**, 178, 1–11. [Google Scholar] [CrossRef] - Kuo, M. The Role of Arboriculture in a Healthy Social Ecology. J. Arboric.
**2003**, 29, 148–155. [Google Scholar] - Na, H.R.; Heisler, G.M.; Nowak, D.J.; Grant, R.H. Modeling of Urban Trees’ Effects on Reducing Human Exposure to UV Radiation in Seoul, Korea. Urban For. Urban Green.
**2014**, 13, 785–792. [Google Scholar] [CrossRef] - Price, C. Putting a Value on Trees: An Economist’s Perspective. Arboric. J.
**2007**, 30, 7–19. [Google Scholar] [CrossRef] - Bratman, G.N.; Anderson, C.B.; Berman, M.G.; Cochran, B.; de Vries, S.; Flanders, J.; Folke, C.; Frumkin, H.; Gross, J.J.; Hartig, T.; et al. Nature and Mental Health: An Ecosystem Service Perspective. Sci. Adv.
**2019**, 5, eaax0903. [Google Scholar] [CrossRef] [Green Version] - Bridge, M. Risk and Hazard Assement for Arborists. In Trees in Tune, Proceedings of the ISA 2005 Annual Conference and Trade Show; International Society of Arboriculture: Nashville, TN, USA, 2005. [Google Scholar]
- Detter, A.; Cowell, C.; McKeown, L.; Howard, P. Evaluation of Current Rigging and Dismantling Practices Used in Arboriculture; HSE Books: Norwich, UK, 2008. [Google Scholar]
- Mazzocchi, F.; Cecchini, M.; Monarca, D.; Colantoni, A.; Caruso, L.; Colopardi, F.; Cipollari, G.; Rapiti, R. An Overview of Risk Assessment for Tree Climber Arborists. Contemp. Eng. Sci.
**2015**, 8, 1171–1177. [Google Scholar] [CrossRef] - Gardiner, B. Wind Damage to Forests and Trees: A Review with an Emphasis on Planted and Managed Forests. J. For. Res.
**2021**, 26, 248–266. [Google Scholar] [CrossRef] - Stokes, A.; Salin, F.; Kokutse, A.D.; Berthier, S.; Jeannin, H.; Mochan, S.; Dorren, L.; Kokutse, N.; Abd Ghani, M.; Fourcaud, T. Mechanical Resistance of Different Tree Species to Rockfall in the French Alps. Plant Soil
**2005**, 278, 107–117. [Google Scholar] [CrossRef] - Jonsson, M.J.; Volkwein, A.; Ammann, W. Quantification of Energy Absorption Capacity of Trees against Rockfall Using Finite Elements; Technical Report; WSL Swiss Federal Institute for Snow and Avalanche Research SLF: Davos, Switzerland, 2006. [Google Scholar]
- Chandelier, A.; Gerarts, F.; San Martin, G.; Herman, M.; Delahaye, L. Temporal Evolution of Collar Lesions Associated with Ash Dieback and the Occurrence of Armillaria in Belgian Forests. Forest Pathol.
**2016**, 46, 289–297. [Google Scholar] [CrossRef] - Kehr, R. Eschentriebsterben—Aktuelles zur Schadensdynamik. In Jahrbuch der Baumpflege; Dujesiefken, D., Ed.; Haymarket Media: Braunschweig, Germany, 2018; pp. 192–201. [Google Scholar]
- Tamate, S.; Kashiyama, T.; Sasanuma, T. A Trial of Pulling down Standing Trees. J. Jpn. For. Res.
**1965**, 47, 210–213. [Google Scholar] [CrossRef] - Fraser, A.I. The Soil and Roots as Factors in Tree Stability. Forestry
**1962**, 35, 117–127. [Google Scholar] [CrossRef] - Coutts, M.P. Root Architecture and Tree Stability. Plant Soil
**1983**, 71, 171–188. [Google Scholar] [CrossRef] - Ylinen, A. Über die mechanische Schaftformtheorie der Bäume; Technical Report 76; Technische Hochschule in Finnland: Helsinki, Finland, 1952. [Google Scholar]
- Stubbs, C.J.; Cook, D.D.; Niklas, K.J. A General Review of the Biomechanics of Root Anchorage. J. Exp. Bot.
**2019**, 70, 3439–3451. [Google Scholar] [CrossRef] [PubMed] - Dahle, G.A.; James, K.R.; Kane, B.; Grabosky, J.C.; Detter, A. A Review of Factors That Affect the Static Load-Bearing Capacity of Urban Trees. Arboric. Urban For.
**2017**, 43, 89–106. [Google Scholar] [CrossRef] - Danjon, F.; Fourcaud, T.; Bert, D. Root Architecture and Wind-Firmness of Mature Pinus Pinaster. New Phytol.
**2005**, 168, 387–400. [Google Scholar] [CrossRef] - Weber, K.; Mattheck, C. Die Doppelnatur der Wurzelplatte. Allg. Forst Jagdztg.
**2005**, 176, 77–85. [Google Scholar] - Gruber, F. Die VTA-Rw/R-Grenzregel zum Baumwurf, ein weiteres wissenschaftlich nicht nachvollziehbares und praktisch inadäquates Versagenskriterium der Standsicherheit. Agrar Umweltr.
**2007**, 3, 74–79. [Google Scholar] - Vanomsen, P. Der Einfluss der Durchforstung auf die Verankerung der Fichte Hinsichtlich ihrer Sturmresistenz. Ph.D. Thesis, ETH Zürich, Zürich, Switzerland, 2006. [Google Scholar] [CrossRef]
- Comin, S.; Vigevani, I.; Fini, A. Non-Invasive Methods for the Investigation of Trees’ Root System in the Urban Environment. Italus Hortus
**2021**, 28, 37–57. [Google Scholar] [CrossRef] - Sinn, G.; Wessolly, L. A Contribution to the Proper Assessment of the Strength and Stability of Trees. Arboric. J.
**1989**, 13, 45–65. [Google Scholar] [CrossRef] - Sinn, G. Baumstatik; Thalacker Medien: Braunschweig, Germany, 2003. [Google Scholar]
- Brudi, E.; van Wassenaer, P. Trees and Statics: Nondestructive Failure Analysis. In How Trees Stand up and Fall Down Proceedings of the Tree Structure and Mechanics Conference; Smiley, E.T., Coder, K.D., Eds.; International Society of Arboriculture: Savannah, GA, USA, 2002; pp. 53–70. [Google Scholar]
- Wessolly, L.; Erb, M. Handbuch der Baumstatik und Baumkontrolle; Patzer Verlag: Berlin, Germany, 1998. [Google Scholar]
- Esche, D.; Schumacher, P.; Detter, A.; Rust, S. Experimentelle Überprüfung der Windlastanalyse für statische Zugversuche. In Proceedings of the Jahrbuch der Baumpflege; Dujesiefken, D., Ed.; Haymarket Media: Augsburg, Germany, 2018; pp. 229–236. [Google Scholar]
- Dupuy, L.; Fourcaud, T.; Stokes, A.; Danjon, F. A Density-Based Approach for the Modelling of Root Architecture: Application to Maritime Pine (Pinus Pinaster Ait.) Root Systems. J. Theor. Biol.
**2005**, 236, 323–334. [Google Scholar] [CrossRef] - Dupuy, L.X.; Fourcaud, T.; Lac, P.; Stokes, A. A Generic 3d Finite Element Model of Tree Anchorage Integrating Soil Mechanics and Real Root System Architecture. Am. J. Bot.
**2007**, 94, 1506–1514. [Google Scholar] [CrossRef] [PubMed] - Rahardjo, H.; Harnas, F.R.; Indrawan, I.G.B.; Leong, E.C.; Tan, P.Y.; Fong, Y.K.; Owc, L.F. Understanding the Stability of Samanea Saman Trees through Tree Pulling, Analytical Calculations and Numerical Models. Urban For. Urban Green.
**2014**, 13, 355–364. [Google Scholar] [CrossRef] - Osullivan, M.; Ritchie, R. Tree Stability in Relation to Cyclic Loading. Forestry
**1993**, 66, 69–82. [Google Scholar] [CrossRef] - Jonsson, M.J.; Foetzki, A.; Kalberer, M.; Lundström, T.; Ammann, W.; Stöckli, V. Root-Soil Rotation Stiffness of Norway Spruce (Picea Abies (L.) Karst) Growing on Subalpine Forested Slopes. Plant Soil
**2006**, 285, 267–277. [Google Scholar] [CrossRef] [Green Version] - Lundström, T.; Jonas, T.; Stöckli, V.; Ammann, W. Anchorage of Mature Conifers: Resistive Turning Moment, Root–Soil Plate Geometry and Root Growth Orientation. Tree Physiol.
**2007**, 27, 1217–1227. [Google Scholar] [CrossRef] [Green Version] - James, K.; Hallam, C.; Spencer, C. Measuring Tilt of Tree Structural Root Zones under Static and Wind Loading. Agric. For. Meteorol.
**2013**, 168, 160–167. [Google Scholar] [CrossRef] - Marchi, L.; Mologni, O.; Trutalli, D.; Scotta, R.; Cavalli, R.; Montecchio, L.; Grigolato, S. Safety Assessment of Trees Used as Anchors in Cable-Supported Tree Harvesting Based on Experimental Observations. Biosyst. Eng.
**2019**, 186, 71–82. [Google Scholar] [CrossRef] - Wessolly, L. Standsicherheit von Bäumen. Der Kippvorgang ist geklärt. Stadt Grün
**1996**, 4, 268–272. [Google Scholar] - Buza, Á.K.; Divós, F.; Divos, F. Root Stability Evaluation with Non-Destructive Techniques. ActaSilv Lign Hung
**2016**, 12, 125–134. [Google Scholar] [CrossRef] [Green Version] - Detter, A.; van Wassenaer, P.; Rust, S. Stability Recovery in London Plane Trees Eight Years After Primary Anchorage Failure. Arboric. Urban For.
**2019**, 45, 279–288. [Google Scholar] [CrossRef] - Detter, A.; Rust, S. Experimental Test of Non-Destructive Methods to Assess the Anchorage of Urban Trees. In Proceedings of the 21st International Non-Destructive Testing and Evaluation of Wood Symposium; Wang, X., Sauter, U., Ross, R.J., Eds.; Forest Products Laboratory: Madison, WI, USA, 2019; General Technical Report FPL-GTR-272; pp. 417–421. [Google Scholar]
- R Core Team R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2021.
- Urata, T.; Shibuya, M.; Koizumi, A.; Torita, H.; Cha, J. Both Stem and Crown Mass Affect Tree Resistance to Uprooting. J. For. Res.
**2012**, 17, 65–71. [Google Scholar] [CrossRef] [Green Version] - Ribeiro, G.H.P.M.; Chambers, J.Q.; Peterson, C.J.; Trumbore, S.E.; Magnabosco Marra, D.; Wirth, C.; Cannon, J.B.; Negron-Juarez, R.I.; Lima, A.J.N.; de Paula, E.V.C.M.; et al. Mechanical Vulnerability and Resistance to Snapping and Uprooting for Central Amazon Tree Species. For. Ecol. Manag.
**2016**, 380, 1–10. [Google Scholar] [CrossRef] [Green Version] - Bergeron, C.; Ruel, J.C.; Elie, J.G.; Mitchell, S.J. Root Anchorage and Stem Strength of Black Spruce (Picea Mariana) Trees in Regular and Irregular Stands. Forestry
**2009**, 82, 29–41. [Google Scholar] [CrossRef] [Green Version] - Sun, H.L.; Li, S.C.; Xiong, W.L.; Yang, Z.R.; Cui, B.S. Influence of Slope on Root System Anchorage of Pinus Yunnanensis. Ecol. Eng.
**2008**, 32, 60–67. [Google Scholar] [CrossRef] - Nicoll, B.C.; Gardiner, B.A.; Rayner, B.; Peace, A.J. Anchorage of Coniferous Trees in Relation to Species, Soil Type, and Rooting Depth. Can. J. For.-Res.-Rev. Can. Rech. For.
**2006**, 36, 1871–1883. [Google Scholar] [CrossRef] - Fraser, A.I.; Gardiner, J.B.H. Rooting and Stability in Sitka Spruce; Technical Report 40; Forestry Commision: London, UK, 1967. [Google Scholar]
- Cucchi, V.; Meredieu, C.; Stokes, A.; Berthier, S.; Bert, D.; Najar, M.; Denis, A.; Lastennet, R. Root Anchorage of Inner and Edge Trees in Stands of Maritime Pine (Pinus pinasterAit.) Growing in Different Podzolic Soil Conditions. Trees
**2004**, 18, 460–466. [Google Scholar] [CrossRef] - Peterson, C.J.; Claassen, V. An Evaluation of the Stability of Quercus Lobata and Populus Fremontii on River Levees Assessed Using Static Winching Tests. Forestry
**2013**, 86, 201–209. [Google Scholar] [CrossRef] [Green Version] - Detter, A.; Rust, S.; Böttcher, J.; Bouillon, J. Ambient Influences on the Results of Non-Destructive Pulling Tests. In Proceedings of the 21st International Nondestructive Testing and Evaluation of Wood Symposium; General Technical Report; Wang, X., Sauter, U.H., Ross, R.J., Eds.; U.S. Department of Agriculture, Forest Service, Forest Products Laboratory: Madison, WI, USA, 2019; Volume 272, pp. 422–436. [Google Scholar]
- Coutts, M.P. Components of Tree Stability in Sitka Spruce on Peaty Gley Soil. Forestry
**1986**, 59, 173–197. [Google Scholar] [CrossRef] - Mergen, F. Mechanical Aspects of Wind-Breakage and Windfirmness. J. For.
**1954**, 52, 119–125. [Google Scholar] - England, A.H.; Baker, C.J.; Saunderson, S.E.T. A Dynamic Analysis of Windthrow of Trees. Forestry
**2000**, 73, 225–237. [Google Scholar] [CrossRef] - Mattheck, C.; Bethge, K. Wind Breakage of Trees Initiated by Root Delamination. Trees-Struct. Funct.
**1990**, 4, 2–4. [Google Scholar] [CrossRef] - Fritzsche, K. Sturmgefahr und Anpassung: (Physiologische und technische Fragen des Sturmschutzes); Parey: Berlin, Germany, 1933; p. 94. [Google Scholar]
- Crook, M.J.J.; Ennos, A.R.R. The Anchorage Mechanics of Deep Rooted Larch, Larix Europea× L. Japonica. J. Exp. Bot.
**1996**, 47, 1509–1517. [Google Scholar] [CrossRef] [Green Version] - Day, S.D.; Wiseman, P.E.; Dickinson, S.B.; Harris, J.R. Contemporary Concepts of Root System Architecture of Urban Trees. Arboric. Urban For.
**2010**, 36, 149–159. [Google Scholar] [CrossRef] - Stokes, A. Strain Distribution during Anchorage Failure of Pinus Pinaster Ait. at Different Ages and Tree Growth Response to Wind-Induced Root Movement. Plant Soil
**1999**, 217, 17–27. [Google Scholar] [CrossRef] - Saint Cast, C.; Meredieu, C.; Défossez, P.; Pagès, L.; Danjon, F. Correction to: Modelling Root System Development for Anchorage of Forest Trees up to the Mature Stage, Including Acclimation to Soil Constraints: The Case of Pinus Pinaster. Plant Soil
**2019**, 444, 537–538. [Google Scholar] [CrossRef] [Green Version] - Yang, M.; Defossez, P.; Danjon, F.; Fourcaud, T. Analyzing Key Factors of Roots and Soil Contributing to Tree Anchorage of Pinus Species. Trees-Struct. Funct.
**2018**, 32, 703–712. [Google Scholar] [CrossRef] [Green Version] - Wessolly, L. Verfahren zur Bestimmung der Stand- und Bruchsicherheit von Bäumen. Holz Roh-Werkst.
**1991**, 49, 99–104. [Google Scholar] [CrossRef] - Kubler, H. Growth Stresses in Trees and Related Wood Properties. For. Prod. Abstr.
**1987**, 10, 61–119. [Google Scholar] - Gril, J.; Jullien, D.; Bardet, S.; Yamamoto, H. Tree Growth Stress and Related Problems. J. Wood Sci.
**2017**, 63, 411–432. [Google Scholar] [CrossRef] - Brudi, E. Longitudinal Prestresses in Tilia Cordata and Acer Pseudoplatanus. Master Thesis, University of Aberdeen, UK. 2001.
- Wessolly, L. Die natürliche Konstruktion Baum als intelligentes statisch-dynamisches System. In Proceedings of the Beiträge zum Internationalen Symposium des SFB 230-Natürliche Konstruktionen, Leichtbau in Architektur und Natur; Mitteilungen des SFB 230; Universität Stuttgart: Stuttgart, Germany, 1988; Volume 2, pp. 203–212. [Google Scholar]
- Wessolly, L. Baumdiagnose – Eingehende Untersuchung mittels Zugversuch – Ergebnisse. ProBaum
**2004**, 1, 2–3. [Google Scholar] - Gartner, B.L. Trees Have Higher Longitudinal Growth Strains in Their Stems Than in Their Roots. Int. J. Plant Sci.
**1997**, 158, 418–423. [Google Scholar] [CrossRef] - Young, W.C.; Budynas, R.G. Roark’s Formulas for Stress and Strain, 7th ed.; McGraw-Hill: New York, NY, USA, 2002. [Google Scholar]
- Ray, D.; Nicoll, B.C.C. The Effect of Soil Water-Table Depth on Root-Plate Development and Stability of Sitka Spruce. Forestry
**1998**, 71, 169–182. [Google Scholar] [CrossRef] [Green Version] - 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
**2007**, 300, 35–49. [Google Scholar] [CrossRef] - Dorval, A.D.; Meredieu, C.; Danjon, F. Anchorage Failure of Young Trees in Sandy Soils Is Prevented by a Rigid Central Part of the Root System with Various Designs. Annals Botany
**2016**, 118, 747–762. [Google Scholar] [CrossRef] [Green Version] - Saint Cast, C.; Meredieu, C.; Defossez, P.; Pages, L.; Danjon, F. Clustering of Pinus Pinaster Coarse Roots, from Juvenile to Mature Stage. Plant Soil
**2020**, 457, 185–205. [Google Scholar] [CrossRef] - Schindler, D.; Mohr, M. Non-Oscillatory Response to Wind Loading Dominates Movement of Scots Pine Trees. Agric. For. Meteorol.
**2018**, 250, 209–216. [Google Scholar] [CrossRef] - Rodgers, M.; Casey, A.; McMenamin, C.; Hendrick, E. An Experimental Investigation of the Effects of Dynamic Loading on Coniferous Trees Planted on Wet Mineral Soils. In Wind and Trees; Coutts, M.P., Grace, J., Eds.; Cambridge University Press: Cambridge, UK, 1995; pp. 204–219. [Google Scholar]
- Göcke, L.; Rust, S.; Ruhl, F. Assessing the Anchorage and Critical Wind Speed of Urban Trees Using Root-Plate Inclination in High Winds. Arboric. Urban For.
**2018**, 44, 1–11. [Google Scholar] [CrossRef] - Fathi, S.; Bejo, L.; Divos, F. Investigating the Effect of Weather and Seasonal Factors on Root Stability Using Dynamic Measurements. Open J. For.
**2020**, 10, 124–134. [Google Scholar] [CrossRef] [Green Version] - Smiley, E.T. Root Pruning and Stability of Young Willow Oak. Arboric. Urban For.
**2008**, 34, 123–128. [Google Scholar] [CrossRef]

**Figure 1.**Species effect on anchoring strength (fitted lines: ${M}_{a}={y}_{0}(1-{e}^{-a\mathrm{Size}})$, ANOVA: Table A1).

**Figure 2.**Robust correlation of bending moments at a root plate inclination of 0.25° ${k}_{r}$ and at failure ${M}_{a}$. The blue line illustrates Equation (1).

**Figure 4.**Depending on the degree of non-linearity in the relationship between rotational stiffness and anchorage strength, the ratio between predicted (Equation (1)) and measured anchorage strength approaches 1 (red line) for larger trees. Fitted lines: $\frac{2.5{k}_{r}}{{M}_{a}}={y}_{0}{e}^{-a\mathrm{Size}}+b$, ANOVA: Table A3.

**Figure 5.**Estimated (Equation (3)) and measured anchorage strength (with four outliers beyond 1000 kNm removed). The blue line illustrates 1:1.

**Figure 8.**Species effect on anchoring strength. ANOVA: Table A7.

Species | n | d in cm | h in m |
---|---|---|---|

Betula pendula | 78 | 33 | 24 |

Picea abies | 65 | 32 | 25 |

Fraxinus excelsior | 48 | 34 | 25 |

Pinus sylvestris | 48 | 31 | 25 |

Fagus sylvatica | 21 | 33 | 26 |

Populus sp. | 18 | 44 | 30 |

Platanus acerifolia | 12 | 28 | 18 |

Acer saccharinum | 7 | 28 | 17 |

Acer pseudoplatanus | 5 | 22 | 23 |

Prunus sp. | 3 | 33 | 13 |

Quercus robur | 3 | 54 | 19 |

Tilia sp. | 3 | 32 | 14 |

Robinia pseudoaccacia | 2 | 48 | 19 |

Alnus glutinosa | 1 | 72 | 21 |

Acer platanoides | 1 | 34 | 10 |

Pseudotsuga menziesii | 1 | 31 | 22 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Detter, A.; Rust, S.; Krišāns, O.
Experimental Test of Non-Destructive Methods to Assess the Anchorage of Trees. *Forests* **2023**, *14*, 533.
https://doi.org/10.3390/f14030533

**AMA Style**

Detter A, Rust S, Krišāns O.
Experimental Test of Non-Destructive Methods to Assess the Anchorage of Trees. *Forests*. 2023; 14(3):533.
https://doi.org/10.3390/f14030533

**Chicago/Turabian Style**

Detter, Andreas, Steffen Rust, and Oskars Krišāns.
2023. "Experimental Test of Non-Destructive Methods to Assess the Anchorage of Trees" *Forests* 14, no. 3: 533.
https://doi.org/10.3390/f14030533