Annex E

(informative)

# Worked examples

The procedures given in the standard are illustrated for a building 12 m long and 8 m wide in the following climate:

– design freezing index *F*_{50} = 47 000 K·h,

– annual mean external temperature = 1,5 °C.

## E.1 No frost insulation

The foundation depth is to be at least the maximum frost depth, according to clause 7. Using equation (1),

m

The foundation depth is therefore 2,34 m (all round the building). This depth applies irrespective of any insulation of the floor. It is valid for both heated and unheated buildings, and for both slab-on-ground floors and suspended floors (although, in the case of a slab-on-ground floor below an unheated building, the slab itself would not be protected against frost heave damage).

## E.2 Slab-on-ground floor using frost insulation

The floor will be insulated with all-over insulation of thermal resistance *R*_{f} = 3,0 m^{2}·K/W.

a) Using vertical edge insulation only

Using Table 2, the thermal resistance of the vertical edge insulation will be at least 1,9 m^{2}·K/W (interpolating between 1,7 m^{2}·K/W and 2,0 m^{2}·K/W), extending to at least 0,6 m below ground level.

The minimum foundation depth is then found using Table 3:

- along the walls, 0,75 m;
- for a distance of 1,5 m from each corner, 1,30 m.

b) Ground insulation at corners

Vertical edge insulation, of resistance at least 1,9 m^{2}·K/W, is applied all round the building, extending to at least 0,6 m below ground level, as in a). From Table 4, the foundation depth is 0,75 m all round the building, and ground insulation 0,6 m wide of thermal resistance 1,0 m^{2}·K/W is applied over a distance of 1,5 m from each corner.

c) Ground insulation all round the building

Using 8.6.3, the foundation depth can be 0,4 m all round the building, provided that:

- vertical edge insulation of thermal resistance not less that 1,9 m
^{2}·K/W is applied all round the building, as in a) and b), but in this case extending to the lower surface of the ground insulation (typically 0,3 m to 0,4 m); - along the walls, ground insulation is applied: to use Figure 5, either the thermal resistance of the ground insulation or its width is chosen (within the limits indicated on Figure 5), and the other parameter is determined from the Figure; suppose that ground insulation of thermal resistance 1,4 m
^{2}·K/W will be used: in that case using Figure 5 its width is to be at least 650 mm; - near the corners additional ground insulation is needed: again, either its thermal resistance or its width can be chosen; suppose that ground insulation of thermal resistance 2,0 m
^{2}·K/W will be used near the corners: then using Figure 4 its width is to be at least 800 mm, and from Table 5 the corner insulation is to be continued for 1,5 m from each corner.

Figure E.1 Illustrates the design for this case.

## E.3 Suspended floor

a) Using vertical edge insulation only

From Table 6, the thermal resistance of the foundation walls above ground, and of vertical edge insulation below ground, is to be at least 1,2 m^{2}·K/W, extending to at least 0,6 m below ground. The length of the building is less than three times its width, so it is regarded as short. From Table 8 the foundation depth is:

- 1,10 m for
*R*_{f}=2 m^{2}·K/W - 1,65 m for
*R*_{f}=4 m^{2}·K/W

and interpolation between these values for *R*_{f} =3 m^{2}·K/W gives a minimum foundation depth of 1,40 m all round the building.

b) Using ground insulation

Vertical edge insulation, of thermal resistance at least 1,2 m^{2}·K/W, is applied all round the building, as in a), but in this case extending to the lower surface of the ground insulation. Different possibilities can then be deduced from Table 9:

- for a foundation depth of 1,25 m (all round the building), the ground insulation is 1,0 m wide and its thermal resistance is at least 1,0 m
^{2}·K/W along the walls and 1,4 m^{2}·K/W within 1,5 m from each corner; - for a foundation depth of 0,50 m (all round the building), the ground insulation is 1,0 m wide and its thermal resistance is at least 2,5 m
^{2}·K/W along the walls and 3,5 m^{2}·K/W within 1,5 m from each corner.

## E.4 Unheated building using frost insulation

If the building may be unheated during the winter, the design of the foundation is in accordance with the data in clause 10.

From Table 10, the width of the ground insulation needs to be at least 2,28 m (interpolating between 2,00 m and 2,40 m).

The annual mean external air temperature is 1,5°C: the column for 1°C in Tables 11 and 12 will be used to provide a safety margin.

For a foundation depth of *H*_{f} = 0,4 m, *R*_{g} = 5,3 m^{2}·K/W by interpolation between freezing indexes of 40 000 and 50 000 in Table 11.

For a foundation depth of *H*_{f} = 1,0 m, *R*_{g} = 2,9 m^{2}·K/W by interpolation between freezing indexes of 40 000 and 50 000 in Table 12.

The necessary thermal resistance of ground insulation for intermediate foundation depths can be obtained by linear interpolation between the values of 5,3 m^{2}·K/W and 2,9 m^{2}·K/W. Thus, for a foundation depth of 0,6 m, *R*_{g} will be at least 4,5 m^{2}·K/W.

For unheated buildings, the same ground insulation (in terms of both width and thermal resistance) is placed all round the building.

# Bibliography

[1] E J Gumbel. *Statistics of extremes*. Columbia University Press, New York, 1958. (In English).

[2] R S Heiersted. *Statistisk bestemmelse av klimapåkjenninger* (Statistical treatment of climatic loads on constructions), Frost i jord, 19, December 1977. (In Norwegian).

[3] ENV 1997-2. *Eurocode 7: Geotechnical design – Part 2: Design assisted by laboratory testing*.

[4] *Report of ISSMFE Technical Committee on Frost (TC-8)*, International Society of Soil mechanics and Foundation Engineering, 1989. (In English).

[5] *Pohjarakennusohjeet* (Instructions for ground construction), publication RIL 121-1988, Finnish Union of Civil Engineers, Helsinki, 1988. (In Finnish).

[6] *Talonrakennuksen Routasuojausohjeet* (Instructions for frost protection in building construction), Technical Research Centre of Finland, Helsinki, 1987. (In Finnish).