*6.1. Thermophysical Properties of C 60*/*75 Concrete*

The tests were carried out with Portland cement CEM I 52,5N SR3/NA (Table 1), [32]. The composition of the concrete for 1 m<sup>3</sup> is as follows: Cement, 440 kg; water, 143 kg; sand 0/2, 632 kg; basalt aggregate 2/8, 498 kg; basalt aggregate 8/16, 785 kg and plasticizers, 8.49 kg.


**Table 1.** Chemical and physical properties of the cement.

The used cement characterizes by a normal (N) initial strength gain, low content of alkali (NA: Na2Oeq < 0.6%) and very high corrosion resistance, especially sulphate (SR3: C3A < 3%) and chloride [33]. The considered cement is indicated for applications where a high initial and final strength is required, primarily in communication engineering and for the rapid stripping of prefabricated elements. The composition of the aggregate affects on the final strength of concrete and on the modulus of elasticity, which for concrete with basalt aggregate is about 15%–20% greater, than with granite or pebble aggregate. In the analyzed mixture, three types of admixtures: Liquefying, plasticizing and aerating were also used. The composition of the mixture was a complex process, which included selecting ingredients, performing a series of laboratory experiments and technological trials. The designed concrete had to meet the strength requirements of class C 60/75 and reach a minimum 47 MPa after 48 h. Other mix requirements were as follows: Water–cement ratio *w*/*c* < 0.34, exposure class XC4 (carbonation of concrete), XD1 (chloride other than sea water) and XF2 (freeze), consistency S4 (slump range 160–210 mm) according to [34], air content 4.0%–6.0% in place, good pumpability and workability.

In order to determine the activation energy divided by the gas constant (*Ea*/*R*), tests on 50 mm mortar samples (acc. to ASTM C1074 [2]) were carried out. Three sets of 18 specimens were prepared and placed in a water bath at constant temperatures: *Tw*<sup>1</sup> = 5 oC, *Tw*<sup>2</sup> = 24 oC and *Tw*<sup>3</sup> = 35 oC. A detailed scope of testing mortar samples is described in [3]. The rate constants *k* for strength development and curing temperatures were determined on the basis of approximation of strength

data (Figure 10a) using non-linear regression according to the equation proposed by Freiesleben Hansen et al. [35]:

$$S = S\_{\mu} \cdot \exp\left(-\left(\tau/t\right)^{\beta}\right),\tag{21}$$

where *S* means compressive strength at time *t*, *Su* is the ultimate strength, τ is the time constant and β is the shape constant. The values of τ and β were determined using approximation by the least squares method. For temperature *Tw*<sup>1</sup> : τ = 3.658 day, β = 1.338 (−), for *Tw*<sup>2</sup> : τ = 1.335 day, β = 1.549 (−) and for *Tw*<sup>3</sup> : τ = 0.716 day, β = 0.715 (−). The *k*-values for temperature 5, 24 and 35 ◦C equaled respectively 0.273, 0.749 and 1.397 (1/day). The results of the presented studies were *Ea*/*R* = 4620 K (Figure 10b).

**Figure 10.** (**a**) The average compressive strength for mortar cubes and the (**b**) determination of *Ea*/*R* [3].

The cement content per cubic meter of concrete *C*, density ρ and water–cement ratio *w*/*c*based on the composition of the mixture, was assumed. The parameters such as: ξmax, *c* and λ using literature formulas were calculated.

The final hydration degree ξmax for *w*/*c* = 0.325 can be obtained from the Mills' (4):

$$
\zeta\_{\text{max}} = (1.031 \cdot 0.325) / (0.194 + 0.325) = 0.65,\tag{22}
$$

and Waller's (5) formula, where the parameter δ is equal to zero due to the absence of fly ash and silica fume:

$$
\zeta\_{\text{max}} = 1 - 1/\exp\left(3.38\left(0.325 - 0\right)\right) = 0.67.\tag{23}
$$

Similar values of ξmax were obtained, however, the calculations according to Mills' proposal [13] were adopted.

The hydration heat of CEM I 52,5 N SR3/NA marked in the semi-adiabatic calorimetry test given by the cement producer after 48 h was about 302 kJ/kg. In Figure 11 the extrapolated value of the total heat *Q*max = 330 kJ/kg was highlighted. For one cubic meter of concrete, the *Q*max value had to multiply by the cement content. It is also worth remarking that the considered cement was sulphate resistant (SR) and the amount of tricalcium aluminate (C3A) was restricted to lower than 3%, which affected the relatively low heat of cement hydration.

**Figure 11.** Hydration heat of CEM I 52, 5 N SR3/NA.

Prediction formulas also exist for specific heat of concrete, for instance, in the work of Lura and Breugel [36] the value of *c* is based on the mass component per cubic meter (*W*) and specific heat of each fraction of the mix (cement *ccem*, basalt aggregate *cbas*, quartz aggregate *cquar* and water *cw*). For the degree of hydration ξ = 0, the specific heat expressed in J/(kg·K) is given by relation:

$$\begin{split} \mathbf{c} &= \frac{\mathbf{W}\_{\text{carw}} \mathbf{c}\_{\text{cam}} + \mathbf{W}\_{\text{bus}} \mathbf{c}\_{\text{bus}} + \mathbf{W}\_{\text{qurr}} \mathbf{c}\_{\text{qurr}} + \mathbf{W}\_{\text{vv}} \mathbf{c}\_{\text{us}} - 0.2 \cdot \mathbf{W}\_{\text{cvar}} \cdot \mathbf{c}\_{\text{cs}}}{\mathbf{W}\_{\text{cvar}} + \mathbf{W}\_{\text{bas}} + \mathbf{W}\_{\text{qurr}} + \mathbf{W}\_{\text{uv}}} = \\ &= \frac{440 \cdot 456 + 1283.766 + 632.699 + 143 \cdot 4187}{440 + 1283 + 632 + 143} = 890.23 \end{split} \tag{24}$$

and for ξ = ξmax = 0.65 the specific heat is equal to 794.41 J/(kg·K). The high value of *c* reduces the extremum temperature of concrete and for a low value of specific heat, the temperature peak increases. Generally, the specific heat of concrete depends not only on the composition of the concrete mixture, but also on the temperature and humidity, which change during the hardening process. However, the models described in the literature often omit this relation and the constant specific heat estimated on the basis of the mixture composition is applied. Therefore, based on the above calculations, the model adopted the average specific heat value equals 840 J/(kg·K) = 0.84 kJ/(kg·K).

The heat conduction coefficient of concrete, expressed in W/(m·K), was estimated based on the thermal conductivities of the mix components using the following equation [36]:

$$\lambda = \frac{\mathcal{W}\_{\text{form}} \cdot \lambda\_{\text{form}} + \mathcal{W}\_{\text{has}} \cdot \lambda\_{\text{bias}} + \mathcal{W}\_{\text{qart}} \cdot \lambda\_{\text{qart}} + \mathcal{W}\_{\text{lb}} \cdot \lambda\_{\text{lb}}}{\mathcal{W}\_{\text{ctru}} + \mathcal{W}\_{\text{has}} + \mathcal{W}\_{\text{qart}} + \mathcal{W}\_{\text{lb}}} = \frac{440 \cdot 1.23 + 1283 \cdot 1.91 + 632 \cdot 3.09 + 143 \cdot 0.6}{440 + 1283 + 632 + 143} = 2.01 \tag{25}$$

According to Neville [37], for concrete with basalt aggregates, this coefficient equals 2.0 W/(m·K). A similar approach has been reported by Breugel [38], which says, that the value of λ ranges between 1.9 and 2.2 W/(m·K). Thus, the computed value of the thermal conductivity is consistent with the literature proposals and for further calculations λ = 2.0 W/(m·K) was assumed.

Table 2 summarizes all thermophysical parameters, fixed for the C 60/75 high-performance concrete analyzed in this paper.

**Table 2.** Thermophysical properties of concrete C 60/75 class.

