# Degradation Prediction Model for Friction of Road Pavements with Natural Aggregates and Steel Slags
## 3 Results and Discussion
where A and B are two regression parameters, PSV is the value determined by the test according to EN 1097-8 and t is the time in seconds. The second term in the previous equation (B-PSV) is the minimum asymptotic polishing value and the regression coefficients of the model are presented in Table 5 for the seven types of samples analyzed. The fitted value of the B parameter suggests that the BPN value varied between 86% and 91% of the corresponding PSV value, at the end of the polishing process. Figure 10 shows the interpolation curves obtained using the model shown in Equation (2). Table 6 summarizes the measurement results with the skid tester at various sites, where BPN is the representative value of the section, while BPN\({}_{\text{s}}\) is the value in the shoulder in the same section, that is not subject to wearing. Figure 10: Laboratory polishing curves. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type of Sample** & **A** & **B** & **PSV** & **R2** \\ \hline Slag & 344 & 0.910 & 54 & 0.937 \\ Mixture & 359 & 0.910 & 47 & 0.932 \\ Silica limestone & 379 & 0.910 & 38 & 0.949 \\ Basalt & 373 & 0.858 & 48 & 0.808 \\ Diabase & 335 & 0.880 & 51 & 0.752 \\ Limestone & 372 & 0.890 & 32 & 0.892 \\ Criggion stone & 344 & 0.880 & 60 & 0.905 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Laboratory model parameters. In situ measurements of BPN, performed on homogeneous sections, according to the traffic, show the same trend as the one of the model obtained in the laboratory. Specifically, the analyzed wearing coarse consisted of a mixture of aggregates with 60% slag and 40% limestone. Therefore, after observing a behavior directly proportional to quantities of this material, the following parameters could be found for this type of material (Table 7):  
The BPN decay curves in situ and in the laboratory can be represented by the same function. The independent variables of the two models are different: in the laboratory the polishing is linked to the number of revolutions of the PSV device wheel, on the road the polishing depends on the number of cumulative passages of equivalent cars. In order to be able to use the decay curve obtained in the laboratory to predict the behavior on site, it is necessary to determine a scale factor that links the two independent variables. The equivalent factor was determined by a non-linear regression technique using laboratory model and data measured on site. The equivalent value obtained was 2550: each minute of polishing with PSV device corresponds to 2520 passages of equivalent cars. Thus, when the type of aggregates used in situ, and degradation curves in laboratory are known, it will be possible to predict the in site behavior. In Figure 11, the continuous line features the degradation model of the aggregate mixture used in the wearing course, identified in the laboratory (Tables 4 and 5), with the addition of a coefficient k, which takes into account the different procedures of polishing at the site. The same graph, with a change of values on the x-axis, illustrates the values of the experimentally measured BPN as a function of traffic. Using an equivalence factor between the polishing time and the traffic, according to the following expression, an adequate interpolation of the experimental data was found (Table 8):  
\[\tt t\cong\left(\frac{T}{7\cdot v_{CLA}}\right)=\left(\frac{T}{2520}\right), \tag{3}\]  
where: