## 3 Results and Discussion
### Mechanical Properties  
Results obtained from M\({}_{\rm r}\) tests performed on the FTB mixtures after 7 days of curing are reported in Figure 2, where they are plotted as a function of the first stress invariant (\(\Theta\)). Such a parameter provides a quantification of the global level of stress to which materials are subjected during testing, and it has been found to greatly affect recorded values of M\({}_{\rm r}\)[46]. In Figure 2, experimental data are also compared to the typical variation range indicated by [PERSON] for standard granular sub-bases [58].  
\begin{table}
\begin{tabular}{c c c} \hline \multirow{2}{*}{**FTB Mixture**} & \multicolumn{2}{c}{**Thermal Conductivity, k**} \\ \cline{2-3}  & \multicolumn{2}{c}{**[W/(m\(\cdot\)K)]**} \\ \cline{2-3}  & **18 Days of Curing** & **Lab-Dried** \\ \hline A-C50-0.85 & 0.97 & 0.51 \\ A-C100-0.75 & 1.57 & 1.04 \\ B-C50-0.75 & 1.16 & 0.84 \\ B-C100-0.75 & 1.70 & 1.15 \\ \hline \end{tabular}
\end{table}
Table 8: Thermal conductivity of FTB mixtures.  
Experimental data plotted in Figure 2 indicate that all the investigated FTB mixtures exhibited a stress-stiffening behavior, with M\({}_{\rm r}\) values increasing as a function of increasing values of \(\theta\). As expected, the FTB mixtures with the higher cement content (100 kg/m\({}^{3}\)) displayed a higher stiffness than those with the lower cement content (50 kg/m\({}^{3}\)). Recorded M\({}_{\rm r}\) values were significantly higher than those normally reported for pavement subgrades (of the order of 100-200 MPa). It was also observed that with the exception of one of the mixtures with the lower cement content (mixture AC-C50-0.85), most of the displayed M\({}_{\rm r}\) were close to the upper limit of the reference variation range. This finding confirms that the considered FTB mixtures possess mechanical properties that are adequate with respect to their intended use, and they are in fact superior to most of the commonly employed subgrade and sub-base materials.  
A comparison between FTB mixtures containing different types of sludge (A and B) is provided in Figure 3, in which M\({}_{\rm r}\) values are plotted as a function of \(\theta\) on a log-log scale. The two displayed charts separately refer to mixtures prepared with the same cement content (equal to either 50 or to 100 kg/m\({}^{3}\)).  
From the analysis of Figure 3, it can be observed that the FTB mixtures prepared by employing sludge B exhibited at all stress levels a higher stiffness (i.e., a higher M\({}_{\rm r}\) value) than those containing sludge A. It was also found that greater differences were recorded at the lower cement dosage (50 kg/m\({}^{3}\)). Such an outcome can be explained by referring to the high quartz content and specific mineralogical composition of sludge B, which probably had a non-negligible influence on cement hydration processes  
Figure 3: Results of M\({}_{\rm r}\) tests performed after 7 days of curing: **(a)** FTB mixtures with cement content 50 kg/m\({}^{3}\); **(b)** FTB mixtures with cement content 100 kg/m\({}^{3}\).  
Figure 2: Results of M\({}_{\rm r}\) tests performed after 7 days of curing (all FTB mixtures).  
and on the resulting calcium-silicate hydrates. Furthermore, it can be postulated that these effects were of reduced intensity when considering a higher cement content (100 kg/m\({}^{3}\)), since in this case, cement paste hydration became predominant with respect to other interfering phenomena or reactions.