How do trees grow support roots

Stability of trees and possibilities of static calculation

GÜNTER SENSE
(THE GARDEN OFFICE 32 (1983) September)

Anyone who deals with questions of the stability of trees must first keep the shape (habit) and the construction principle of the tree in mind. Roughly speaking, we distinguish, from bottom to top, the root system (which is largely hidden from view), the trunk and the crown.

Under the influence of wind, the inquiring tree shape acts like a lever on the root system, which as a rule, as it grows with you, provides stability through support and tension anchors. The tree is supported by the strong roots and is held by the rope-like coarse and fine roots Reaction force, namely the resistance of the soil surrounding the roots, which is composed of cohesive and frictional forces, against the wind force and prevents tipping.
For stability, the underground part of the tree and its functionality are crucial. The experts are well aware of what it looks like in many of our city streets.

A publication by KIERMEIER in DAS GARTENAMT 30 (1981) No. 2 should be mentioned as an example. Accordingly, the following interventions were identified as the main causes of oak death in an American city:
* Damage from construction work = 26%
* Over-paving of the root plate = 18%
* Excavations in the root area = 14%
* Changing groundwater level due to large construction pits = 8%
* Constant illumination of the crown (the tree is never in the dark at night) = 4%
* Improper use of weed killers = 3%
* Parking on the root plate = 3%
The relatively high proportion of excavations in the root area (14%) makes the importance of stability studies, especially in connection with traffic safety, clear.

Let us first deal with the undisturbed root system of the healthy tree. In the horticultural literature there is only sparse information. This results in blatant misjudgments and erroneous interpretations of the root performance and also the stability of the trees. In this context, reference is made to the text "The roots of forest trees "Referred to by KÖSTER, BRÜCKNER, BIEBELRIETHER (1968).

According to this, the majority of native tree species have relatively shallow roots; this also applies, for example, to the common oak, Quercus robur, which is often regarded as a deep-rooted oak, which only develops a taproot when it is young. From the age of 30 to 50, a heart-sinker root system forms. SCHOCH (1964) found maximum countersink depths of 1.2 to 1.4 m on alternately moist clay on oaks over one hundred years old. Similar root depths were also measured in the Munich gravel plain on pedunculate oaks of the same age.
The linden tree also reaches greater root depths in highly permeable soils. Investigations on 20 to 30 year old winter linden trees on sandy loam showed root depths of 1.2 to 1.3 m; on 65-year-old winter linden trees on loess loam, a maximum of 1.3 m. Similar results have been reported for hornbeam, ash and sycamore maple.

The genetic predisposition of the trees, their sociological position (in a dense association they will develop a different root system than in the free standing) and the location conditions, in particular the oxygen and nutrient supply, the mechanical resistance and the hydrological conditions of the tree, are decisive for the development of the roots The detailed examination of these factors is a prerequisite for a statement on stability. The schematic representation of some essential root and anchoring systems (there are still numerous intermediate stages) shows the natural construction principle, which can be compared with technical systems.

Figure 1 shows a so-called heart root system, characterized by obliquely growing strong roots and a hemispherical root zone. Far-reaching main lateral roots are missing (birch, linden, hornbeam).
Figure 2 shows what is known as a taproot system. A main root (fir, pine) that grows vertically down from the underside of the cane dominates.
Figure 3 shows what is known as a sinker root system. Anchors growing vertically downwards branch off from strong main lateral roots (spruce, ash).
Figure 4 shows board-like stiffeners between the trunk and side roots. This facility is very pronounced in various tropical trees, which under certain circumstances grow on shallow, oxygen- and humus-poor laterite soils and, due to their sometimes considerable height, are dependent on a wide supporting foundation.
Figure 5 shows stilt roots that provide stability due to their straddling position. There are examples of this in the mangrove forest, which is exposed to constant ocean currents (Rhizophora species).
Figure 6 would like to point out the formation of support roots, for example of the banyan tree, Ficus bengalensis. Under certain circumstances the support roots can even replace the central trunk.
The adaptability of the root system to the soil conditions is particularly evident in tropical trees.

But also the native tree species can develop completely different root systems in extreme locations.
It is striking that, for example, the robinia, which is generally characterized by deep roots, develops extensive lateral roots in shallow soils and forms a plate-shaped root system.
Figure 7 shows a plate root system. Information about the soil conditions is therefore of eminent importance for the assessment of the root system.

Back to stability and thus to the natural external influences to which the inquiring tree is exposed. First and foremost, it is wind power or wind load (we do not want to speak of the snow load here, as it usually does not play a major role in the deciduous tree species in our park and street trees).
The wind load is made up of pressure, suction and friction effects and is usually

W = cf x q x A (in kN)

Here, cf is the aerodynamic load coefficient, which is dependent on the shape and surface of the body and the direction of the flow. For different types of structures, for example for prismatic structures, circular cylindrical structures, frameworks, etc. there are corresponding cf values ​​in DIN 1055, "Load assumption for buildings", Part 45, the so-called collection of coefficients. If no analogy conclusions are possible, the coefficients must can be found in the wind tunnel.
q is the dynamic pressure in kN / m².
A is the reference area, in our case for example the crown area in the projection.

First of all we have to establish that the tree shape is generally adapted to the wind influences. The crown is more or less permeable. The narrowing branches, especially the twigs, are elastic. The conical knots indicate the adaptation to snow and wind loads. The leaves have aerodynamic shapes. The low cf value (drag coefficient), which is so much vaunted in the new car models, is, in my opinion, far undercut by many types of blades. The cylindrical trunk has enormous strength.

It is obvious that the wind speed plays a decisive role in the pressure on such a structure. And it is also evident that we have to start with maximum values ​​when considering stability. Here we can refer to the structural analysis tables, which indicate the wind speed and the dynamic pressure as a function of the altitude.

h = from 0 - 8 m, v = 28.3 m / s (101.88 km / h), q = 0.5
h = over 8-20 m, v = 35.8 m / s (128.88 km / h), q =. 0.8
h = over 20-100 m, v = 42.0 m / s (151.20 km / h), q = 1.1

h = height above ground
v = wind speed (m / s)
q = dynamic pressure (kN / m²)

Such wind speeds are only reached by hurricane-like storms. Storms with wind force 12, for example, have a wind speed of 120 km / h. Much higher wind speeds, namely up to approx. 370 km / h, are reached by tropical cyclones (known for example as hurricanes, typhoons, cyclones) that knock down trees like matches. A special form of these cyclones is the tornado, a thunderstorm that also occurs in Europe can occur.
In 1968 a so-called "tornado" raged in Pforzheim, in 1973 in Kiel, in 1978 in Recklinghausen and in Schechingen near Schwäbisch-Gmünd. The path of destruction is usually a few hundred meters wide and an average of 25 km long. In strong tornadoes, the vortex should travel at speeds of more than 500, even 800 to 1000 km / h. to reach. Other weather researchers speak of a maximum of 400 to 440 km / h.

The stability or risk of tipping, however you want, is still dependent on its own weight, the so-called dead load of the tree including the root foundation, which we want to refer to as the force N.
If we look at the lever arm of the weighty tree, which is blown on by a certain wind load, it becomes clear that the length of the lever arm plays a role for stability - we refer to this distance as distance 1 - and secondly the distance from the point of application of the force N, i.e. from the center of the trunk to the possible tilting edge. This line is called line a. The question now is: can we operate with these sizes?

According to the formula: Stability nk is given if the standing moment Ms, namely the product of the dead weight of the tree and the distance from the point of application of the force N to the tilting edge, is greater than the tilting moment MK, namely the product of the wind load and the distance the point of application of the wind load in the crown or trunk center of gravity to the lower edge of the bale.
All forces that threaten the body to tip over form the overturning moment MK, for example wind load and lever arm. All forces from the constantly existing dead loads counteract the overturning moment and form the standing moment Ms, for example dead weight of the tree and the standing area.

nk = Ms / Mk = (N x a) / (W x l)

n (Eta) is the safety factor in the foundation.

The answer is: We can calculate the stability exactly if we succeed
1. the actual dead weight of the living tree and
2. to quantify the wind pressure on the crown with trunk,
3. to delimit the statically effective root foundation.
The boundary lines here lie on the one hand in the demolition zone, on the other hand in the kink of the stressed root system.
We now want to carry out an example calculation according to the given formulas (diagram).

We assume that it is a detached street tree that is 15 m high and has a circular crown outline with a diameter of 12 m. The trunk height under the crown and the trunk diameter are irrelevant in our calculation example stand at a distance of 4 m on a row of houses. In addition to earlier excavations through pipes and cables to the houses, which were carried out on both sides at a distance of 2 m from the center of the trunk, the root foundation is now severely damaged by a canal trench 1.25 m from the center of the trunk, at a depth of 1.20 m a compression layer that is not rooted through. A very realistic simulation. In the course of the traffic safety obligation, the stability must be examined.

Stability (security against tipping)

nk = Ms / Mk = (N x a) / (W x l)

The weight of the above-ground part of the tree is 4 t. We now have to convert the weight into a measure of force. The unit of force is the Newton. The mass of one gram at the point of normal acceleration weighs 0.00981 Newton (= 1 pond). One ton therefore weighs 9810 Newtons or 9.81 kN (Kilonewtons).
In structural engineering, the conversion factor is rounded up to 10 kN. 4 t is therefore 40.00 kN.

In our case, the volume weight of the roots results from the formula L x W x H x volume weight of the soil with 5.25 x 4.00 x 1.20 m assumed 1.8 = 18 kN / m³ = 453.60 kN, force N together so 493.60 kN.

The distance a from the center of the trunk to the excavation at the tipping edge is 1.25 m.

The wind load on the trunk is minimal and is not taken into account.

The wind load on the crown is calculated using the formula
W cf x q x A in kN
Assumption of the coefficient cf = 0.6
Dynamic pressure q simplified = 0.65 kN / m²

Crown area A in the projection according to the formula:
r x r = pi = 6.00 x 6.00 x 3.14 m = 113.04 m²
W = 0.6 x 0.65 kN / m² x 113.4 m² = 44.09 kN

Distance 1 from the area where the wind load acts in the center of gravity of the crown to the lower edge of the root foundation = 10.20 m

We now insert the values ​​in the stability formula:
nk = (493.60 kN x 1.25 m) / (44.09 kN x 10.20 m) = 617.00 kNm / 449.72 kNm

nk = factor 1.372

The tree no longer has the 1.5-fold safety required by statics for buildings, as there is a risk of tipping over due to hurricane-like storms.
In the present case, only the principle of static calculation should be made clear.
I repeat and expressly emphasize that it is crucial to quantify the dead weight of the tree as well as the wind load, i.e. in particular the cf value (load coefficient) and the tree parts actually hit by the wind and the statically effective root volume possible due to static calculation.

literature
* BRÜNNING, E .: The tropical rainforest. Springer-Verlag, 1956.
* DIN 1055, Part 4: Load assumptions for buildings, traffic loads for buildings that are not susceptible to vibration, May 1977.
* DIN 1055, Part 45: Load assumptions for buildings, traffic loads, aerodynamic shape coefficients for buildings, draft May 1977.
* GÖTZ, Karl-Heinz, Dieter HOOR, Karl MÖHLER, Julius NATTERER: Timber Construction Atlas, Institute for International Architecture Documentation, 1980.
* KIERMEIER, Peter: Development of new street tree varieties in the USA. Das Gartenamt 309 (1981) H. 2, pp. 96-106.
* KÖSTLPR, J. N., E. BROCKNER and H. BIEBELRIETHER: The roots of forest trees, Paul Parey, 1968.
* KUCHLING, Horst: Physics, formulas and laws, Buch- und Zeit-Verlagsgesellschaft, 1979.
* LAUSCH, Erwin: Cyclones, Whips from Heaven, Geo No. 5, May 1979, pp. 36-62.
* LOHMEYER, G .: Baustatik. Publishing house B. G. Teubner, 1980.
* NEIZEL, Ernst: Tables for the building trade, Ernst Klett Publishing House, 6th ed.
* OTTO, Frei: Natural Constructions, Deutsche Verlagsanstalt, 1982.
* SINN, Günter: Calculations for the statics of park trees. Taxationspraxis series. Booklet G 4. Expert Board for Agriculture, Forestry, Horticulture.
* SINN, Günter: Stability of park trees. The garden office 32 (1983) H. 3, S. 161-164.
* WENDEHORST and MUTH: Building technical number tables, Publishing House B. G. Teubner, 1981.