4.2 Ventilated slab-on-ground structure under steady state conditions
4.2.2 Principles of the design
The moisture rate passing through the ventilation duct (Figure 4.16) with the dimensions height b, width d and length l is according to equation (4.1) /22/:
(
va va0)
R
G= ⋅ − [kg/s] (4.1)
where R= b d u = air flow [m3/s] and u = an average speed of air.
The moisture flow per width unit of a duct (d = 1 m) changes the formula into the equation (4.2) /22/:
( )
b ul(
va va0)
g = ⋅ ⋅ − [kg/m2 s] (4.2)
The current of air in the duct is 4.3 /22/:
l P A b
Qa = ∆
η 12
2
[m3/s] (4.3)
where A is the cross-sectional area of the duct (= b × d), b is the height, d is the width and l is the length of the duct. ∆P means the pressure difference and η the viscosity of the air [Ns/m2] (Figure 4.19).
Figure 4.16 Design of the ventilation duct. The dimensioning variables.
According to the measurements of Harderup /14/ the pressure decrease along the ventilation duct is ∆P = 1…2 Pa/m. Assuming that the air temperature in the duct remains constant the water vapor content of the ventilation air is (4.4) /22/.
v
a0v_
Z
u v
ab
l
x
(
a)
kxa v v v e
v = − − − − 0 − [g/m3] (4.4)
where va = water vapor content of the ventilation duct [g/m3]
v- = water vapor content of the subsoil (beneath the slab) [g/m3]
v0a = water vapor content of the incoming air [g/m3] (highest during the summer months)
k = 1/b u Z = d/Qa Z
u = average speed of the air (m/s) = Qa /A
Z = water vapor resistance of the slab structure [s/m]
x = distance from the inlet duct
The limit value for the relative humidity of the duct air is usually RH = 75% or less. The required current of air in a certain duct can be determined by the equation (4.5):
(
a) (
a)
a v vx dZ v v
Q = − − −
−
− ln
ln
) (
0 (4.5)
The required duct height with a certain current of air is (4.6):
3 12 d P
l
b Qa
= ∆η (4.6)
Equation 4.5 gives the design value for the required airflow of the ventilated slab-on- ground structure when the form and shape of the duct is known. As an example we could consider the situation of an uninsulated slab-on-ground structure where the relative humidity of the subsoil is RH = 100 %. The temperature of the ventilation duct is equal to the indoor temperature Ti = +20°C and the initial vapor content of the ventilating air is equal to the indoor air content v = 12 g/m3 (RH≈69%). The total distance of the floor duct is x = 20 m from the inlet to the outlet channel and the water vapor permeability of the concrete slab is δp = 6,76⋅ 10-7 kg/m·s·Pa. If the limit value for the ventilation air is RH = 75%, the subsoil temperature and thickness of the slab dictate the required volume of ventilation (Figure 4.17). The subsoil temperature under an uninsulated slab is usually equal to the temperature of the slab and indoor air T= 20°, and the required volume of ventilation air Q = 20 … 30 m3/h.
The capillary flow through a slab structure can be significantly higher than the diffusion flow. The equation (4.3) also applies in this case if the flow through the slab is determined by the equation (3.22). The maximum capillary flow values through the slab are presented in Figure 4.18.
Figure 4.17 The required ventilation flow of an uninsulated concrete slab structure in a 20 meter long duct as the thickness of the slab and temperature of the subsoil varies. Relative humidity of the subsoil RH = 100% and the temperature and vapor content of the duct and ventilation air are Ti=20°C, v = 12 g/m3
Figure 4.18 The maximum capillary flow values through the slab structure as the thickness and grade of concrete changes.
0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5
16 17 18 19 20 21 22
Subsoil temperature (oC)
Ventilation flow (m3 /h) 80 mm slab
100 mm slab 120 mm slab
Thickness of the concrete slab, mm Moisture flow, g/m2 s
50 100 150 200
0,25 0,20 0,15 0,10
0,05 0
X K20 K25 K30 K40
m d g B
= 2
X X X X X X X X X X
Maximum moisture flow in capillary rise through concrete slab
The relative humidity of the ventilation duct in a case where a hs = 80 mm thick concrete slab is connected to the free water table is shown in Figure 4.19. The figure shows that the duct height of 10 mm is sufficient with all grades of concrete except K20. With this grade the relative humidity of RH = 75% is achieved with the duct height of 13 mm.
Figure 4.19 Relative humidity of the air duct: 800 mm thick concrete slab with a direct capillary contact with water table
The effect of the grade of concrete and the thickness of the slab on the capillary flow through the slab structure is shown in Figure 4.20.
Figure 4.20 The effect of the grade of concrete and the thickness of the slab on the capillary flow through the slab structure.
Relative humidity of the air duct (%),
80 mm thich concrete slab with direct capillary contact with water table
65 70 75 80 85 90 95 100
2 3 4 5 6 7 8 9 10 111213 141516 1718 1920
Height of the air duct, mm Relative humidity of the air duct, RH (%)
K20 K25 K30 K40
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 100
95 90 85 80 75 70 65 Relatived humidity of the air duct, RH (%)
Height of the air duct ,mm
X
K20, slab 50 mm K40, slab 50 mm K20, slab 200 mm K40, slab 200 mm X
X
X X X
X Relative humidity of the air duct (%)
in various thicknesses of the concrete slab and grades of the concrete, 20 m long air duct
X X
X
5 IN SITU SURVEY OF SLAB-ON-GROUND STRUCTURES
Earlier in this report the moisture and temperature behavior of slab-on-ground structures were examined by moisture equilibrium characteristics of the structural materials determined by laboratory tests and theoretical calculations under different steady state conditions. However, the actual operating conditions and the true behavior of a structure under these conditions can only be verified by a long-term survey of a real structure under the true climatic conditions. Therefore this study included long-term surveys of three slab-on-ground structures of three different buildings in Tampere and Järvenpää regions in Southern Finland. These surveys performed during 2000 – 2002 measured the long term development in temperature and water content of the fill and drainage layers as well as changes in temperature and humidity of the structural layers: insulation and concrete slab.
The survey included a row building in Tampere region built during late fall and winter of 2001 –2002. The heating of the building started in February of 2002. Another case was a detached house in Järvenpää, built during summer and fall of 2001. This house has a massive concrete slab (hc = 190 mm) and a floor heating system including an exceptionally thick polystyrene insulation layer hi = 200 mm. The third case was an office building in Hervanta region near Tampere, built during winter of 2002. The heating season of this building started in late spring of 2002.
Instrumentations in all of these survey cases were similar. The measured variables were the temperature and water content of the fill layers and relative humidity and temperature of the slab and insulation layer. The unique instrumentation and conditions in each individual survey case are presented in Chapters 5.1 – 5.3.