## 3 Results and Discussion
### Correlations between Physical and Mechanical Properties  
To provide a better understanding of the influence of high temperatures in the different properties of the mortars, correlations between physical and mechanical properties were established. For that purpose, individual values obtained from each sample were used in order to directly compare two properties (for example: the correlation between UPV and bulk density values for the same specimen, at a specific temperature, corresponds to a scatter point in Figure 8). It is possible to relate the values of UPV and bulk density in the hardened state, because both properties depend on the characteristics of the material, i.e., a material with weaker cohesion will also have lower UPV and vice versa [65, 66]. In Figure 8 it is possible to observe the relation between the UPV and bulk density of the various mortars for the different exposure temperatures. Acceptable linear tendencies were obtained, with correlation coefficients of Pearson ranging between 0.64 and 0.79 for mortars exposed to temperatures up to 200 \({}^{\circ}\)C, which decreased with the temperature increase; in the case of mortars exposed to a temperature of 250 \({}^{\circ}\)C, a lower correlation coefficient value was obtained (\(\sim\)0.51), which confirms the influence of temperature on the linearity of the relationship between these two variables. The values obtained for UPV value of expanded clay \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**Thermal Conductivity [W/(m.K)] [standard deviation]**} \\ \hline
**Mortar** & **A** & **B** & **C** & **D** & **E** \\ \hline \multirow{3}{*}{Temperature [\({}^{\circ}\)C]} & 20 & 0.202 (0.002) & 0.102 (0.005) & 0.074 (0.000) & 1.987 (0.009) & 1.326 (0.010) \\ \cline{1-1}  & 150 & 0.142 (0.001) & 0.078 (0.007) & 0.062 (0.001) & 1.338 (0.051) & 1.122 \\ \cline{1-1}  & 250 & 0.040\({}^{\star}\) & 0.075 & 0.060 & 1.247 & 0.956 (0.359) \\ \hline \hline \end{tabular}  
* This is a very low value for this mortar since the aggregate expanded clay exhibits a thermal conductivity around 0.1 W/(m.K) [16]. For this reason, this value was excluded from the remaining analysis.  
\end{table} 
Table 7: Thermal conductivity coefficient (average) vs. exposure temperature. Figure 7: Thermal conductivity coefficient (%) vs. exposure temperature. mortar are high for their bulk density (marked with a red circle); this should be due to the characteristics of this specific aggregate, which, despite having a reduced density, provides a high compactness and good bond between the aggregate and the matrix [67]. The Young's modulus and the bulk density can be related by a power law, as illustrated in Figure 9. Correlation coefficients between 0.86 and 0.92 were obtained for the different exposure temperatures, suggesting a high correlation between the two properties even after exposure to elevated temperatures; the more compact mortars (i.e., having a higher density) tend to be more rigid (less deformable) and vice versa. The Young's modulus can also be related to the UPV according to a power law, as shown in Figure 10. This figure indicates that for the studied mortars very high correlation coefficients were obtained between the two variables, between 0.92 and 0.98. It can also be concluded that the correlation coefficient between these two properties was insensitive to the exposure to elevated temperatures. As shown in Figure 11, there is also a good power correlation between the compressive strength and the bulk density in the hardened state, with correlation coefficients between 0.86 (100 \({}^{\circ}\)C) and 0.92 (150 \({}^{\circ}\)C). In addition, as shown in Figure 12, there is a very strong power correlation (R\({}^{2}\) ranging from 0.92 and 0.98) between the UPV and compressive strength for the different temperatures. This result is logical and was expected, since compressive strength was indirectly estimated from the Young' modulus, which was also shown to be strongly correlated with UPV.