## 2 Materials and Methods
### Specim Preparation and Testing Procedure  
Mine tailings that come from the ore-processing plant are in a slurry, which passes through a filter to reduce the water content to approximately 17 to 23%. For this reason, this work intended to simulate the wet tailings as they come from the filter plant. Therefore, 15 mL of water was added to the oven-dried tailings for each mixture combination. With the water incorporated into the tailings, fly ash was added and mixed until full homogenization. This process is not only more realistic but has also the advantage of releasing less dust during mixing. Then, sodium hydroxide solution (activator) \begin{table}
\begin{tabular}{c c c} \hline \hline \(\mathbf{t_{FA}}\) & \(\mathbf{t_{L}}\) & \(\mathbf{c_{SH}}\) (mol/kg) \\ \hline
0.1–0.3 & 0.14–0.17 & 5.00–11.76 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Range of values used for each variable in the DOE. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{3}{c}{**Factorial and Central Runs**} & \multicolumn{3}{c}{**Axial Runs**} & \multicolumn{3}{c}{**Middle Plane Runs**} \\ \hline
**Id** & \(\mathbf{t_{FA}}\) & \(\mathbf{t_{L}  
was added with further homogenization before transferring the final mixture to a sealed plastic container to minimize liquid loss. This mixture preparation methodology is shown in Figure 10.  
Due to the initial added water, the concentration of sodium hydroxide in the solution was diluted, with the actual concentration (\(c_{A}\)) being calculated using Equation (1):  
\[c_{A}=[(m_{SH_{s}}\times 1000)/(m_{w}+m_{wSH})]/40 \tag{1}\]  
where \(m_{SH_{s}}\) is the mass of solid sodium hydroxide in the activator, \(m_{w}\) is the initial mass of water added, and \(m_{wSH}\) is the mass of water present in the activator. The specimens were prepared in models of 36 mm in diameter and 66 mm in height by static compaction in three layers targeting a dry unit weight, \(\gamma_{d}\), equal to 17.2 kN/m\({}^{3}\), which corresponds to 95% compaction degree compared to the optimum unit weight presented in Figure 8. As noted by [26; 27], dry stackings are usually constructed with different compaction levels in order to optimize the execution and follow the production rate, so in most cases, a 100% Proctor density is not achieved. Demolding was carried out on the same day, using an extractor, and the specimens were subsequently stored in an insulated box for 7 days, before being tested in unconfined compression. To evaluate if this preparation procedure was providing repeatable specimens, the porosity (\(\eta\)) of the specimens on the molding day was calculated using Equation (2):  
\[\eta=100-100\Bigg{\{}\left[\frac{\gamma_{d_{m}}}{\frac{w_{5}}{w_{T}}+\frac{w_ {FM}}{w_{T}}+\frac{w_{SH_{s}}}{w_{T}}}\right]\left[\frac{\frac{w_{5}}{w_{T}}}{  
where \(\gamma_{dm}\) is the dry unit weight of the mixture, given by Equation (3); \(w_{S}\), \(w_{FA}\), and \(w_{SHs}\) are the dry masses of soil, fly ash, and solid sodium hydroxide in the mixture, respectively; \(w_{T}\) is the total mass of the specimen on the molding day; \(\gamma_{SS}\), \(\gamma_{SFA}\), and \(\gamma_{SSHs}\) are the particles unit weight of soil, fly ash, and solid sodium hydroxide; V is the volume of the specimen; and \(t_{L}\) is the liquid content.  
The unconfined compression strength test (UCS) performed was based on ASTM D2166-06 [28] using a 20 kN load cell with a ball joint to ensure vertical load application, and a linear variable differential transformer (LVDT) for vertical strain measurement.  
From the UCS test, the stress-strain curve of the specimens was obtained, as well as the values for the maximum peak strength (\(q_{u}\)), given by Equation (4):  
\[q_{u}=\frac{F_{mix}}{A_{corr}} \tag{4}\]  
where \(F_{mix}\) is the peak load registered, and \(A_{corr}\) is the corrected area due to the radial deformation of the specimen during the compression.