# Prediction of Friction Coefficient Based on 3D Texture Characteristics of Road Surfaces
## 3 Results and Discussion
### Texture-Friction Relationship Analysis  
Following the evaluation of texture and friction, their relationships were investigated. The correlations were assessed for the primary surface and micro- and macrotexture surfaces. Although more than 80 parameters were calculated, this section highlights only the parameters with the highest impact on the friction prediction model, as determined by the multinomial regression analysis presented below. * Microtexture: As an example, the valley material portion (\(S_{m72,MIC}\)) parameter was selected. Initially, it was hypothesized that parameters like peak density (\(S_{pd}\)) representing the number of peaks per unit area, or kurtosis (\(R_{ku}\)) describing the sharpness of the surface profile peaks and valleys, would have the most significant influence on the friction coefficient. Nevertheless, the analysis demonstrated that the strongest relationship was achieved with \(S_{m72,MIC}\), which represents the areal material ratio separating the reduced valleys from the core surface. Figure 8 illustrates the obtained values, along with a comparison to the friction coefficient (\(\mu\)). The correlation between valley material portion \(S_{m72,MIC}\) and friction coefficient \(\mu\) is shown in Figure 9.  
Figure 8: Valley material portion \(S_{m72,MIC}\) and friction coefficient \(\mu\) (orange lines). Figure 7: Three-dimensional models of scanned pavement surfaces. As illustrated in Figure 9, there is a notable trend indicating a considerable correlation between the valley material portion (\(S_{m\times 2,MIC}\)) and the friction coefficient (\(\mu\)). The results suggest that the combination of surface peaks and the core roughness significantly influences the friction. Nevertheless, this relationship alone is insufficient to predict tire-road friction accurately. For this reason, it is necessary to combine this parameter with other relevant texture characteristics derived from primary or macrotexture surfaces, such as mean peak curvature (\(S_{pc}\)) or dale void volume (\(V_{vv}\)), to improve prediction accuracy. * Macrotexture: When considering the role of macrotexture in the interaction between the wheel and the road, it was hypothesized that the shape of surface irregularities would play a key role due to the interaction between rubber and surface grains. To investigate this, the arithmetic mean peak curvature (\(S_{pc,MAC}\)) calculated from waviness surfaces was analyzed. Figure 10 illustrates the obtained values, along with a comparison to the friction coefficient (\(\mu\)). There is a clear disparity between the \(S_{pc,MAC}\) and friction values across different measurement sections, as seen in Figure 10. For MS 6 and MS 7, with relatively large and rounded surface features, \(S_{pc,MAC}\) values are low, yet the friction coefficients are high, indicating good microtexture. In contrast, MS 11 to MS 13 exhibit significant irregularities with large and sharp grains. Here, although \(S_{pc,MAC}\) values are high, the friction coefficients are low due to the smoother surface of these grains. Overall, MS 6, MS 7, MS 12, and MS 13 show similar grain shapes, with the primary difference being in microtexture and its impact on friction. Figure 10: Arithmetic mean peak curvature \(S_{pc,MAC}\) and friction coefficient \(\mu\) (orange lines). Figure 9: Correlation between valley material portion \(S_{m\times 2,MIC}\) and friction coefficient \(\mu\). The correlation between the arithmetic mean peak curvature \(S_{pc,MAC}\) and friction coefficient \(\mu\) is shown in Figure 11.  
As illustrated in Figure 11, a visible trend demonstrates a moderate association between the arithmetic mean peak curvature and friction coefficient \(\mu\). This indicates that the hypothesis regarding the impact of aggregate particle shape on friction is valid. The graph shows a cluster of points on the left that appear to deviate from the main trend, seemingly acting as outliers.