## 3 Results and Discussion
### Definition of a Mixture Index
\[q_{u}=10^{3.687}\times\left(wb_{c}^{0.211}\right)^{2.009} \tag{15}\]  
Its curve is shown in Figure 19.  
Model 6 provides the worst fit when compared to previous models. This is expressed by low values of \(R^{2}\) and \(R^{2}_{adj}\). (see Table 8). From these results, it can be concluded that, even when the liquid content/water content varies, the index proposed [15] remains valid and capable of providing a better explanation for strength prediction than other input variables that are based on water content or liquid content. This may be explained by \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & \(R^{2}\) & \(R^{2}_{adj}\) \\ \hline
**3** & 0.765 & 0.757 \\ \hline
**4** & 0.780 & 0.764 \\ \hline
**5** & 0.790 & 0.783 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Coefficient of determination of Models 3, 4, and 5.  
indicate the best tailing-binder mixture for a required strength considering both the mixture components (tailings, fly ash, and sodium hydroxide) and the tailings' in situ water content. For that purpose, an experimental plan set by a response surface method was conducted which served for a further statistical analysis, leading to the following conclusions:  
* The most influencing factor on the unconfined compression strength was the fly ash content, although the sodium hydroxide concentration and the mixture liquid content were also significant;
* Two statistical models were initially proposed based on those three factors. Although they provide a similar performance, the second model provides a slightly better fit, having the additional advantage of requiring just two variables;
* Higher strengths were obtained when the input variables were on the upper values of their range, but when tests were performed outside this range, the strength decreased, suggesting a nonlinear relation outside the initial interval;
* Towards the definition of a mixture index that could represent the mixture components, other statistical models depending on different indexes were proposed. The best-performing model was based on the porosity/cement ratio proposed by [34], even when the mixture's liquid content varies. These conclusions are very important since they highlight the relevance of the porosity/cement ratio, even when other parameters besides porosity or cement content vary. However, further tests are required to evaluate whether these same trends are observed in other AAB-tailing mixtures made by other types of mine tailings (from gold, bauxite, copper, etc.) or other AAB precursors and activators. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app14188116/s1](https://www.mdpi.com/article/10.3390/app14188116/s1)]([https://www.mdpi.com/article/10.3390/app14188116/s1](https://www.mdpi.com/article/10.3390/app14188116/s1)). Conceptualization, S.R. ; Methodology, P.M.-O. ; Validation, P.M.-O. ; Formal analysis, I.C. ; Investigation, I.C. ; Writing--original draft, I.C. ; Writing--review & editing, S.R. and P.M.-O. ; Supervision, S.R. ; Funding acquisition, S.R. All authors have read and agreed to the published version of the manuscript. This work was financially supported by Base Funding--UIDB/04/08/2020 of the CONSTRUCT--Instituto de I&D em Estruturas e Construcoes ([[https://doi.org/10.54499/UIDP/04708/2020](https://doi.org/10.54499/UIDP/04708/2020)]([https://doi.org/10.54499/UIDP/04708/2020](https://doi.org/10.54499/UIDP/04708/2020))), by the project INPROVE-2022.02638.PTDC ([[http://doi.org/10.54499/2022.02638.PTDC](http://doi.org/10.54499/2022.02638.PTDC)]([http://doi.org/10.54499/2022.02638.PTDC](http://doi.org/10.54499/2022.02638.PTDC))), by scholarship 2022.13858.BD to the first author, and by CEECIND/04583/2017 grant to the second author ([[https://doi.org/10.54499/CEECIND/04583/2017/CPI399/CT0003](https://doi.org/10.54499/CEECIND/04583/2017/CPI399/CT0003)]([https://doi.org/10.54499/CEECIND/04583/2017/CPI399/CT0003](https://doi.org/10.54499/CEECIND/04583/2017/CPI399/CT0003))), all funded by national funds through the RCT/MCTES (PIDDAC).