## 3 Results and Discussion
### Marshall Parameters  
Figures 2 and 3 give the results of apparent density, air voids (Vh), and voids in the mineral aggregate (VMA) obtained according to the norms noted in Section 2.3.1, which in turn may be used to determine the optimal percentage of the bituminous binder. The figures give the mean values of each parameter corresponding to each studied percentage of bitumen, along with error bars that represent the standard deviation. Additionally, the equation of the best second-order polynomial fit and the associated value of R\({}^{2}\) have also been included. In accordance with the results and in order to comply with the PG-3 Spanish norm for bituminous AC16S mixes made for wearing courses, the air void content in the mix, (Vh), should be between 4-6% and the voids in the mineral aggregate, (VMA), should be greater than 15%. Furthermore, Table 5 includes the percentage of binder necessary to obtain the 4% and the 6% Vh obtained through the polynomial fit and the percentage of bitumen to obtain the minimum VMA, attained by setting the derivative of the VMA polynomial to zero to find the appropriate local minimum for each aggregate. Figure 2: Apparent density as a function of bitumen content for the AC-PA, AC-WC, and AC-MT mixes. The error bars represent \(\pm 1\) standard deviation. The best second-order polynomial fit and the square of the multiple correlation coefficient, R\({}^{2}\), are also shown. As may be observed in Figure 2, the apparent density of the AC-WC and AC-MT mixes is less than that of the control AC-PA aggregate. This is principally due to the lower density of the mine wastes, as indicated by Table 3.  
Figure 3 gives the mean Vh and VMA as a function of bitumen content for each of the aggregate mixes. As may be observed (Figure 3a), the data and fitting polynomials for Vh decrease with increasing bitumen in the mix. This tendency is consistent with the idea that increasing the amount of bitumen in the mix allows a greater filling of the pore volume. The AC-PA and AC-WC aggregates show similar behavior; that is, the same quantity of bitumen gave similar values to the air voids, Vh. However, the AC-MT mixes needed a greater amount of bitumen to obtain the same air void content. This is due to the higher absorption of the MT aggregate that produces a drop in the effective bitumen volume, so that a greater quantity of bitumen was necessary to cover the aggregate and to reduce the air void content to the necessary value, as shown in Table 3. The percentage of bitumen necessary for the AC-PA and AC-WC to comply with Spanish technical specifications was similar in these two mixes, as shown in Table 5 and in Figure 3.  
Figure 3b also shows the mean values of the VMA quantity as a function of bitumen content for each aggregate mix. The best second-order polynomial fit in this case has a convex form and the recommended bitumen dosage corresponds to the descending part of the curve, as the mix is more compactable in that region. If a bitumen dose is chosen that corresponds to the rising part of the curve, the bitumen displaces the aggregates, which could result in plastic flow within the mix. In Figure 3, it is apparent that all of the mixes have a VMA value larger than 15% over the entire range of bitumen  
Figure 3: (**a**) Air void content (Vh) and (**b**) voids in the mineral aggregate (VMA) of the AC-PA, AC-WC, and AC-MT mixes. The error bars represent \(\pm 1\) standard deviation. Included are the equations of the best fit second-order polynomials and their R\({}^{2}\) value. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**AC 16 Surf 35/50 S**} & \multicolumn{3}{c}{**Percentage of Bitumen Necessary**} \\ \cline{2-4}  & **AC-PA** & **AC-WC** & **AC-MT** \\ \hline
4\% Vh & 4.54 & 4.72 & 5.89 \\
6\% Vh & 3.68 & 4.11 & 5.11 \\ Minimum VMA & 3.91 (15.05\%) & 5.02 (15.00\%) & 5.53 (17.58\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Percentage of bitumen necessary to obtain 4–6% air void content in AC-PA, AC-WC, and AC-MT mixes.