## 2 Materials and Methods
### Test Methods  
Thermal conductivity of the four candidate FTB mixtures was evaluated in accordance to ASTM D5334 [45] by making use of a thermal needle probe (60 mm long and 3.9 mm in diameter), which was successfully used in previous investigations carried out by the authors [13; 14]. Tests were performed by drilling three holes on the top surface of cured cylindrical specimens (diameter 100 mm, height 200 mm), in which the needle probe could be inserted. To avoid any misreading in measurements, drilled holes were preventively filled with a ceramic-based polysynthetic compound that provided the needle probe \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**FTB Mixture**} & **Cement** & \multirow{2}{*}{**W/P [–]**} & \multirow{2}{*}{**Superplasticizer**} & \multicolumn{3}{c}{**Composition of Aggregate Skeleton [\%]**} \\ \cline{4-9}  & [kg/m\({}^{3}\)] & & & **[\%]** & **Sludge A** & **Sludge B** & **Quartzite** & **Quartzite** \\ \hline A-C50-0.85 & 50 & 0.85 & 0.25 & 18 & - & 71 & 11 \\ A-C100-0.75 & 100 & 0.75 & 0.50 & 18 & - & 71 & 11 \\ B-C50-0.75 & 50 & 0.75 & 0.25 & - & 19 & 69 & 12 \\ B-C100-0.75 & 100 & 0.75 & 0.50 & - & 19 & 69 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Composition of investigated Fluidized Thermal Backfills (FTB) mixtures. with the necessary continuous contact with the surrounding mixture. Thermal conductivity was calculated by means of the following expression (Equation (2)):  
\[\mathrm{k}\ =\frac{\mathrm{q}}{4\cdot\mathrm{r}\cdot\mathrm{a}} \tag{2}\]  
where k is the thermal conductivity (in W/(m\(\cdot\)K)), q represents the heating power of the needle, and a indicates the slope of the linear function that describes temperature as a function of the logarithm of time. Thermal conductivity was measured after 18 days of curing at room temperature, when it was considered that the FTB mixtures would reach conditions that are representative of those ordinarily met in the field. After carrying out the above-described tests, specimens were oven-dried at 60 \({}^{\circ}\)C for 48 h in order to reach low-moisture conditions, hereinafter referred to as \"lab-dried\", that mimic those that may occur in service as a consequence of possible drying phenomena due to the heat generated by buried cables. Thermal conductivity tests were repeated on all specimens in lab-dried conditions. Resilient modulus (M\({}_{\mathrm{r}}\)) tests were carried out on slender cylindrical specimens (diameter 100 mm, height 200 mm) after 7 days of curing. Given the low cement contents adopted for the preparation of the FTB mixtures, such a curing period was considered to be sufficient for the development of most of the time-dependent hardening phenomena occurring in service and therefore adequate for the assessment of the long-term bearing capacity of these materials. The M\({}_{\mathrm{r}}\) test is commonly employed for the evaluation of the stress-strain response of granular materials under the effects of traffic loading [46; 47; 48; 49; 50; 51; 52]. However, it has also been used successfully for the assessment of the mechanical behavior of cement-treated and cold-recycled bituminous mixtures [51; 52; 53; 54]. As prescribed by AASHTO T307-99 [55], M\({}_{\mathrm{r}}\) tests were carried out by means of a triaxial apparatus that allows the simultaneous control of confining pressure (\(\sigma_{3}\)), which is kept constant, and of deviatoric stress applied in the vertical direction (\(\sigma_{\mathrm{d}}\)), which has a haversine-shaped form. Resulting vertical strains (\(\varepsilon_{1}\)), of a reversible and permanent nature (\(\varepsilon_{1\mathrm{r}}\) and \(\varepsilon_{1\mathrm{p}}\), respectively), were measured by means of a pair of LVDTs (Linear Variable Displacement Transducer). According to the adopted standard, test specimens were subjected to 15 loading sequences composed of 100 cycles with various combinations of \(\sigma_{3}\) and \(\sigma_{\mathrm{d}}\).