## 3 Results
### Correlations Analysis between Friction and Micro-Roughness  
According to the above considerations, the correlation coefficients between friction (BPN, BPN *, and \(\Delta\)BPN) and \(R_{i}\) (R\({}_{A}\), R\({}_{Q}\), R\({}_{Z}\)) were carried out, Table 7 shows all correlation coefficients in term of R\({}^{2}\)  
Figure 8: Schematization of fragmentation phenomenon of the aggregate surfaces under polishing procedure.  
Figure 9: Examples of profile segments from the examined aggregates before and after polishing process: (**a**) basalt; (**b**) EAF Slags; (**c**) kinginzite; (**d**) limestone.  
In particular, for Table 7 it is possible to observe that roughness descriptors show high correlation coefficients between themselves in accordance with Qian and Meng [29]. R\({}^{2}\) values obtained by correlating BPN to roughness descriptors are always lower 0.6525 for BPN * vs. R\({}_{Q}\); on the contrary, very high R\({}^{2}\) values are registered for BPN correlation to \(\Delta Ri\) parameters, thus highlighting that both testing procedures (British pendulum and surface profilometric analysis) record the morphological change of aggregates characteristics due to the polishing effect (see, submatrix 3 \(\times\) 3 top right in Table 7). The most significant correlations are shown in Figure 10a-c; from Figure 10d, it can be seen that the linear correlation between R\({}_{Q}\) and BPN data for both polishing conditions (before, R\({}_{Q}\) * and BPN */after, R\({}_{Q}\) and BPN) has the same trend highlighted in previous studies [26,38], despite the R\({}^{2}\) value is lower than 0.6.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline  & **BPN * & **BPN** & \(\Delta\)**BPN** & \(\mathbf{R_{A}}\) * & \(\mathbf{R_{Q}}\) * & \(\mathbf{R_{Z}}\) * & \(\mathbf{R_{A}}\) & \(\mathbf{R_{Q}}\) & \(\mathbf{R_{Z}}\) & \(\Delta\mathbf{R_{A}}\) & \(\Delta\mathbf{R_{Q}}\) & \(\Delta\mathbf{R_{Z}}\) \\ \hline
**BPN** & 1 & 0.9341 & 0.7312 & 0.4102 & 0.4497 & 0.3722 & 0.5998 & 0.6525 & 0.5659 & 0.8102 & 0.7983 & 0.8421 \\
**BPN** & 1 & 0.9190 & 0.2895 & 0.3205 & 0.2502 & 0.4898 & 0.5395 & 0.4546 & 0.9066 & 0.9057 & 0.9539 \\ \(\Delta\)**BPN** & & 1 & 0.1668 & 0.1857 & 0.1357 & 0.3442 & 0.3822 & 0.3147 & 0.8941 & 0.8997 & 0.9453 \\ \(\mathbf{R_{A}}\) * & & & 1 & 0.9963 & 0.9702 & 0.9514 & 0.9285 & 0.9399 & 0.2397 & 0.2050 & 0.2885 \\ \(\mathbf{R_{Q}}\) * & & & & 1 & 0.9695 & 0.9609 & 0.9449 & 0.9519 & 0.2651 & 0.2286 & 0.3164 \\ \(\mathbf{R_{Z}}\) * & & & & & 1 & 0.9230 & 0.9012 & 0.9512 & 0.2328 & 0.1965 & 0.2616 \\ \(\mathbf{R_{A}}\) & & & & & & 1 & 0.9944 & 0.9845 & 0.4481 & 0.4020 & 0.4979 \\ \(\mathbf{R_{Q}}\) & & & & & & & 1 & 0.9803 & 0.4890 & 0.4498 & 0.5415 \\ \(\mathbf{R_{Z}}\) & & & & & & & & 1 & 0.4341 & 0.3879 & 0.4737 \\ \(\Delta\mathbf{R_{A}}\) & & & & & & & & & 1 & 0.9777 & 0.9650 \\ \(\Delta\mathbf{R_{Q}}\) & & & & & & & & & & 1 & 0.9471 \\ \(\Delta\mathbf{R_{Z}}\) & & & & & & & & & & & 1 \\ \hline \end{tabular} The performance indicators marked with (*) refer to the measurements performed before polishing test.  
\end{table}
Table 7: Correlation coefficient R\({}^{2}\) between superficial friction and roughness parameters.