5.3 Summary and conclusions
6.1.3 Effect of temperature changes
With the formulations presented in the past subsections, the relative humidity of con- crete can be calculated for variable conditions of relative humidity of the environment at different but steady conditions of temperature. In order to develop a model capable of integrally calculating the drying and wetting process of concrete, the effect of vari- able temperature conditions must be taken into account. As it was briefly explained in Chapter 2.1.2.2, at constant moisture content, a change in the concrete temperature causes a variation of the relative humidity of the concrete pores. When the tempera- ture raises, the water molecules within the concrete microstructure gain energy and the internal surfaces of the concrete microstructure cannot hold them anymore, causing a migration of the water molecules from small pores into larger pores. The consequences of this behaviour are described by the hygrothermic coefficient of concrete, which de- notes the increment of the relative humidity in the concrete pores due to an increment in the temperature at constant moisture content.
Using the measurements presented in Chapter 4.1.3, a formulation for the hygrothermic coefficient of concreteK was developed. Eq. 6.11 describes a dome-shaped curve tilted to the right towards high relative humidities. The equation is calibrated with the para- metersa,bandc, dependent on the concrete microstructure (see Eqs. 6.12 to 6.14).
K(h) = dh
dT =a·(1−h)b·exp[c·(1−h)] (6.11)
6.1 Modelling the transport of moisture in concrete
Eq. 6.11 must satisfy three important conditions. In first place, it has to be always posi- tive because the relative humidity in the concrete pores always increases with increasing temperature as depicted by the comparison of the sorption isotherms of porous mate- rials at different temperatures (see Chapter 2.1.2.2). The second and third conditions are given by the extreme values of relative humidity. If the vapour pressure of the con- crete pores already equals the saturation pressure, any additional water coming from the smaller pores will condensate without elevating the relative humidity because it cannot be higher than 100 %. On the other hand, at relative humidities close to 0 %, no moisture is available to migrate from the small pores to the large pores and the value ofK must be very close to zero. Eqs. 6.12 to 6.14 were derived to take into account the influence of the w/c-ratio on the hygrothermic coefficient of concrete.
a=400·(w/c)14.3+0.15 (6.12) b=12·(w/c)6.5+1.15 (6.13)
c=−900·(w/c)11−7.0 (6.14)
Eq. 6.11 in combination with Eqs. 6.12 to 6.14 allows to calculate the hygrothermic coef- ficient of concrete satisfying the conditions mentioned before and delivering plausible results for a range of w/c-ratios between 0.2 and 0.7. The comparisons of the calcu- lated hygrothermic coefficient of concrete with the measurements conducted on sealed samples from the concretes MLC, MRC and MHC are presented in Fig. 6.5.
0 . 5 0 0 . 5 5 0 . 6 0 0 . 6 5 0 . 7 0 0 . 7 5 0 . 8 0 0 . 8 5 0 . 9 0 0 . 9 5 1 . 0 0
0 . 0 0 0 0 . 0 0 1 0 . 0 0 2 0 . 0 0 3 0 . 0 0 4 0 . 0 0 5 0 . 0 0 6 0 . 0 0 7 0 . 0 0 8
w / c = 0 . 7 w / c = 0 . 2
w / c = 0 . 4 ( M L C )
w / c = 0 . 6 ( M H C ) Hygrothermic coefficient,K [K-1 ]
R e l a t i v e h u m i d i t y , h [ - ]
M L C M R C M H C M o d e l
w / c = 0 . 5 ( M R C ) a c c o r d i n g t o
B a z a n t a n d N a j j a r [ 1 1 ]
Figure 6.5: Changes of the relative humidity in the concrete pores due to a temperature change. Compar- isons between calculated values and measurements
In Fig. 6.5 the calculations according to Eq. 6.11 are represented by the continuous lines, for which the corresponding w/c-ratios are indicated in the diagram. The dashed line represents the values ofKcalculated according to the formulation from Bažant and Najjar [11]. Following the tendencies shown by the measurements, the influence of a temperature change on the relative humidity of the concrete pores gain in importance as the relative humidity decreases from 100 % and reaches a maximum value by relative humidities around 85 %. The formulation from Bažant and Najjar assumes that this peak occurs at relative humidities around 70 %. Both formulations deliver values of the same order of magnitude, the difference lies on the inclination to the right that the present formulation assumes in order to fit the measured data in a better way.
The influence of the microstructure on the hygrothermic coefficient of concrete can be understood by means of the following considerations. As the gel pores are assumed to be completely filled with water while the capillary pores also contain air and water vapour, the relative humidity of the concrete corresponds to the relative humidity of the capillary pores. When temperature increases, the water molecules stored in the gel pores migrate to the capillary pores increasing their relative humidity. At low w/c-ratios, the amount of gel pores increases and the amount of capillary pores is reduced. The larger the amount of gel pores, the larger the amount of water molecules willing to migrate from the gel pores into the capillary pores, and moreover, the smaller the amount of capillary pores capable of storing these new water molecules. Therefore the hygrothermic coefficient of concrete has to be higher at lower w/c-ratios. This was verified by the measurements and taken into account in the formulation of the parameters from Eq. 6.11. In Fig. 6.5 besides the curves representing the w/c-ratios used for the concrete mixtures, two extreme values of the equation (w/c = 0.2 and w/c = 0.7) are plotted as well. At w/c-ratios lower than 0.4, the presence of capillary pores in the concrete microstructure can be neglected. Hence, the formulation forK assumes similar behaviours of the concretes with w/c-ratio lower or equal than 0.4. For concretes with w/c-ratio larger than 0.6, the amount of capillary pores increases in such a way that any increment in the relative humidity of these pores would need a considerable large amount of water molecules. As temperature raises, the water molecules coming from the gel pores will not be able to increase the relative humidity of the capillary pores in the same manner as concretes with lower w/c-ratios, because the amount of gel pores at such high w/c-ratios is restricted.
The presented formulation of the hygrothermic coefficient of concrete does not include any time influence and therefore it assumes that the changes in the relative humidity of the concrete pores occurs instantaneously after the variation of temperature takes place.
As it was mentioned before, these changes obey a moisture exchange between gel and capillary pores which requires time to develop. In case of a temperature increase the water molecules gain energy which allow those located in the gel pores to abandon the surface at which they were bonded and head for zones of lower energy that can be found in the capillary pores. This moisture exchange between water molecules from the gel into the capillary pores takes place within a couple hours and therefore assuming an