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# Recommended procedure for calculating thermal bridges of components in contact with the ground

In practice, very different methods are often used for calculating thermal bridges of components in contact with the ground (thermal bridges towards the ground). The ground especially is taken into account in the calculation in different ways:

- taking into account the ground as a material

- partial taking into account the ground with small layers of earth or with small blocks of earth in the calculation models

- no depiction of the ground, in a similar way to calculations of regular thermal bridges towards the air

- or the ground is depicted as an additional boundary condition for the temperature (see DIN 4108 Supplementray Sheet 2)

All methods constitute an estimation ultimately; nevertheless, the **procedure according to DIN EN ISO 10211** is recommended. Calculating the heat losses through the ground in the Ground worksheet of the PHPP corresponds for the most part with the method according to DIN EN ISO 13370. On the other hand, this requires that thermal bridges should be determined in accordance with DIN EN ISO 10211. The main advantage of this procedure is that the influence of the ground is also depicted. The effect of edge insulation or skirt insulation can also be depicted directly by the $\varPsi$-values in this way.

## Basic procedure according to DIN EN ISO 10211 (Option B)

In contrast to regular thermal bridges, conductances of the components in contact with the ground must be determined through an additional heat flow simulation. In doing so, exactly the same dimensions must be used in the models.

**For preparing the calculation models, attention must be given to the following points:**

- The ground must be depicted with the same length for the x and y directions in both calculation models with at least five or six times the floor slab length (see illustration).

- The external dimensional reference applies for the floor slab length (in contrast to the DIN EN ISO 10211). This is recommended for a length of 4 metres.

- For calculation of the additional conductances, it is recommended that the components in contact with the ground should be represented with a boundary condition corresponding with their heat transfer resistance R = 1/U, rather than with their build-up.

- The block of earth must exhibit adiabatic boundary conditions at the interfaces.

### Choosing the length and position of the floor slabs

The norm DIN EN ISO 10211 provides two options for calculating thermal bridges. As already described above, for **Option B** an additional numerical calculation is necessary for all components in contact with the ground so that the thermal resistance of the ground is included in the U-values and conductances, because this is already taken into account in the Ground worksheet of the PHPP. The PHPP does not use heat flow simulations for this and instead uses special analytical functions which provide almost the same values. However, these approximation functions assume that floor slabs are directly placed on the ground. For the Ψ-values to match the PHPP, in the additional calculation model it is also necessary that **the floor slab should be placed on the ground **.

Although the Ψ-values calculated thus are almost independent of the chosen length of the floor slab, these must be the same in both calculation models.
This norm recommends a floor slab length of 4 metres. **Note!** The reference dimensions have become mixed up in this norm! The exterior wall is taken into account with reference to the external dimension while the floor slab is taken into account with reference to the internal dimensions. **Because the PHPP uses the external dimensional reference everywhere for calculations the length of the floor slab should also be defined using the external dimensions!**

#### Option A

With Option A, the norm DIN EN ISO 10211 contains another possibility for calculating corresponding Ψ-values. The additional heat flow simulations for components in contact with the ground described above are not necessary. When calculating the Ψ-value, they must then be depicted using U-values which already include the influence of the ground. These values can be calculated using the approximation functions in the DIN EN ISO 13370, or taken directly from the Ground worksheet in the PHPP ($U_{bf}$ for floor slabs or $U_{bw}$ for basement walls, found in the rows 55-58 which are hidden).
These values can only be determined if the dimensions of the components in contact with the ground are known, because these specific U-values are not only dependent on their component build-up but also on their dimensions and position in the ground. For the same reason, in the two-dimensional calculation model (for calculating $L_{2d}$) it is not possible to choose the floor slab length freely and instead half of the **characteristic floor slab size ** must correspond with $B'$.

##### Characteristic floor slab size

With the aid of the characteristic floor slab size it is possible to reduce the actual three-dimensional heat flow issue (three-dimensional distribution of the soil around the building) to a two-dimensional heat flow issue as an approximation. The calculation of the corresponding conductances by means of heat flow simulations takes place additionally using an “infinitely” long analogous model (only two-dimensional heat flows). The previously mentioned approximation functions in the Ground worksheet are also based on $B'$. The use of $B'$ is not absolutely necessary for determining Ψ-values, but this is necessary for a two-dimensional dynamic calculation, otherwise three-dimensional transient calculation would be necessary.