## 3 Analysis and Discussion of Results
### Thermal Conductivity
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**CRA-Valnor**} & \multicolumn{2}{c}{**FRA-Vimajas**} & \multicolumn{2}{c}{**FRA-Ambilei**} & \multicolumn{2}{c}{**CRA-Retria**} \\ \cline{2-9}  & \multicolumn{1}{c}{**\(\lambda\) (W/m.K)**} & \multicolumn{1}{c}{**Variation**} & \multicolumn{1}{c}{**\(\lambda\) (W/m.K)**} & \multicolumn{1}{c}{**Variation**} & \multicolumn{1}{c}{**\(\lambda\) (W/m.K)**} & \multicolumn{1}{c}{**Variation**} \\  & \multicolumn{1}{c}{**(\%)**} & \multicolumn{1}{c}{**(\%)**} & \multicolumn{1}{c}{**(\%)**} & \multicolumn{1}{c}{**(\%)**} & \multicolumn{1}{c}{**(\%)**} & \multicolumn{1}{c}{**(\%)**} & \multicolumn{1}{c}{**(\%)**} \\ \hline
0\% of RA & 2.08 \(\pm\) 0.02 & - & 2.08 \(\pm\) 0.02 & - & 2.08 \(\pm\) 0.02 & - & 2.08 \(\pm\) 0.02 & - \\
10\% of RA & 2.10 \(\pm\) 0.00 & 1.2 & 2.06 \(\pm\) 0.02 & \(-\)0.9 & 2.07 \(\pm\) 0.01 & \(-\)0.4 & 2.02 \(\pm\) 0.18 & \(-\)2.6 \\
25\% of RA & 2.05 \(\pm\) 0.00 & \(-\)1.2 & 1.94 \(\pm\) 0.02 & \(-\)6.8 & 2.02 \(\pm\) 0.03 & \(-\)2.8 & 2.01 \(\pm\) 0.00 & \(-\)3.3 \\
50\% of RA & 1.96 \(\pm\) 0.00 & \(-\)5.5 & 1.68 \(\pm\) 0.00 & \(-\)18.9 & 1.90 \(\pm\) 0.03 & \(-\)8.3 & 1.82 \(\pm\) 0.01 & \(-\)12.2 \\
100\% of RA & 1.72 \(\pm\) 0.00 & \(-\)16.7 & 1.21 \(\pm\) 0.02 & \(-\)41.9 & 1.63 \(\pm\) 0.00 & \(-\)21.7 & 1.60 \(\pm\) 0.14 & \(-\)22.8 \\ \hline \end{tabular}
\end{table} 
Table 11: Variation of the thermal conductibility (\(\lambda\)). Figure 8: Thermal conductivity of the concrete mixes studied. Figure 9: Variation of the thermal conductivity with the recycled aggregate replacement percentage. The thermal conductivity of concrete depends on several parameters: density, porosity, temperature, degree of hydration, water content and type of aggregates. Several works suggest that the thermal conductivity is directly proportional to the material's density [51]. Figure 10 shows the correlation between these two properties for the concrete mixes produced. The R\({}^{2}\) value obtained for the linear regression (R\({}^{2}\) = 0.70) shows that these two properties have a significant linear correlation. This comparative analysis allows concluding that the \(\lambda\)-values of concrete mixes with RA increases with increasing density. [PERSON] et al. [15] obtained a similar conclusion when evaluating the thermal conductivity of concrete mixes with RA (fine and coarse). These authors justify the results with the porosity increase stemming from rising RA contents in the concrete mixes. ACI 213R-03 [52] recommends an empirical equation (Equation (3)) that allows obtaining \(\lambda\) from the value of dry density (d) for lightweight concrete. Considering that the density of concrete with recycled aggregates, depending on the nature of the RA, can be approximated to the density of lightweight concrete, the exponential expression defined by ACI 213R-03 [52] is tested herein to evaluate whether it can be used in RAC. \[\lambda=0.0864e^{0.00125d} \tag{3}\]  
The values obtained in our study and represented in Figure 11 do not seem to fit well with the ACI 213R-03 [52] proposed equation, displaying an R\({}^{2}\) value of 0.57. Figure 11: Variation of the thermal conductivity with the dry density—proposal of regression. ACI 213R-03 was reported in the literature [52]. Figure 10: Variation of the thermal conductivity with the dry density. In order to better adapt the model established for lightweight concrete to the results obtained for RAC, a non-linear regression was performed. For this purpose, a model similar to that presented by ACI 213R-03 [52] was used, in which the thermal conductivity has an exponential relationship with the dry concrete mass \(\left(\lambda=ae^{hd}\right)\). The nonlinear regression performed has a R\({}^{2}\) = 0.71 and corresponds to Equation (4):  
\[\lambda=0.0157e^{0.00204d}. \tag{4}\]  
The other parameter that affects the thermal conductivity of concrete is porosity. In order to confirm this, the correlation between thermal conductivity and air content determined for fresh concrete was evaluated.