# Degradation Prediction Model for Friction of Road Pavements with Natural Aggregates and Steel Slags
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Period between Road** & **Road Identifier** & **Location** & **BPN** & **BPN\({}_{\text{s}}\)** & **Traffic *** \\ \cline{2-6}
**Rehabilitation and Test** & **(Designation)** & **(km + m)** & **BPN** & **BPN\({}_{\text{s}}\)** & **Traffic *** \\ \hline
4 y 6 m & S.P. 1 & 4 + 930 & 46.6 & 67.8 & 5,123,000 \\
1 y 0 m & S.P. 1 & 20 + 330 & 52.5 & 61.1 & 636,400 \\
2 y 0 m & S.P. 1 & 20 + 330 & 50.0 & 71.0 & 1,302,200 \\
2 y 11 m & S.P. 1 & 20 + 330 & 48.7 & 69.0 & 1,860,500 \\
0 y 5 m & S.P. 1 & 20 + 450 & 41.7 & 47.5 & 246,200 \\
6 y 11 m & S.P.5 & 1 + 260 & 48.0 & 75.4 & 1,713,000 \\
7 y 11 m & S.P. 5 & 1 + 260 & 47.0 & 73.0 & 1,956,900 \\
8 y 10 m & S.P. 5 & 1 + 260 & 46.3 & 72.5 & 2,186,000 \\
1 y 10 m & S.P. 6 & 0 + 720 & 50.2 & 71.5 & 1,218,000 \\
1 y 0 m & S.P. 6 & 0 + 720 & 52.8 & 73.4 & 654,500 \\
0 y 3 m & S.P. 9 & 2 + 050 & 56.7 & 65.9 & 580,000 \\
1 y 0 m & S.P. 10 & 1 + 950 & 50.8 & 73.7 & 1,074,300 \\
2 y 0 m & S.P. 10 & 1 + 950 & 50.6 & 74.0 & 2,134,300 \\
3 y 0 m & S.P. 10 & 1 + 950 & 48.2 & 73.1 & 3,103,500 \\
1 y 0 m & S.P. 14 & 9 + 200 & 49.4 & 61.9 & 736,000 \\
4 y 5 m & S.P. 35 & 4 + 320 & 48.6 & 53.1 & 742,600 \\ \hline \hline \end{tabular}  
* Cumulative traffic in equivalent passenger- cars since the last paving of wearing course.  
\end{table} 
Table 6: In-situ measurements. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of Sample** & **A** & **B** & **PSV** \\ \hline Slag 60\%, limestone 40\% & 365 & 0.910 & 48 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Laboratory model parameters. t is the polishing time expressed in minutes,
* v\({}_{\text{CLA}}\) is the speed in rounds per minute (360 RPM)
* T is the total traffic (number of vehicles)  
In this case, we can write Equation (2) as:  
\[\text{BPN}(\text{T})= \Big{(}\frac{\text{A}\text{-}\text{7-}\text{v}_{\text{CLA}}}{\text{ T}}\Big{)}^{4}+\frac{\text{B}\text{-}\text{PSV}}{\text{k}}, \tag{4}\]  
where k is a coefficient that takes into account a different behavior between the in-situ and in-laboratory test. The proposed model curve can be used to predict the decay of skid resistance of a wearing course due to traffic, calibrated with the models of the aggregates used. It will also be possible to compare the performance of different aggregates, evaluate the cost and provide assistance to maintenance operations. This result is valid for the road network covered by the measures, which is affected by the typical traffic level of a rural road of modest importance. The R2 value in Table 8, although obtained from a small sample size, was higher than that of similar in-situ experimentations. A variation in the traffic spectrum will not affect the shape of the monotonically decreasing curve, even though the time scale (the x-axis) will be modified. Obviously, decay will manifest more quickly for the same cumulative traffic in the curves. To complete this work, it will be necessary to establish the correspondence between the number of steps in the tangents and the curved road segments that produce the same degradation in terms of BPN reduction. The equivalence factor will depend on the radius of the curve. The measurements, which were carried out along the shoulder to examine the relative BPN differences in a road area unaffected by wearing, and performed at different times of the road rehabilitation, showed an increment of BPN values with time. This observation can be explained by the loss of binder from the surface of the aggregates. Figure 11: Comparison between degradation model in-situ and in laboratory. \begin{table}
\begin{tabular}{c c c c c} \hline  & **A** & **K** & **B-PSV** & **R2** \\ \hline Skid resistance BPN & 365 & 0.903 & 43.68 & 0.460 \\ \hline \end{tabular}
\end{table} 
Table 8: In-situ model parameters.