# Prediction of Friction Coefficient Based on 3D Texture Characteristics of Road Surfaces
## 3 Results and Discussion
### Development of a Friction Prediction Model Using Texture Parameters
In comparison with [29], which explores the correlation between morphology parameters and skid resistance on asphalt pavements, our research advances this field by incorporating a more diverse set of 3D texture parameters for predicting friction coefficients on rural road surfaces. While both studies emphasize the importance of texture in determining skid resistance, our approach uniquely integrates microtexture and macrotexture measurements, resulting in a more comprehensive prediction model with higher accuracy, as indicated by our \(R^{2}\) values. The study in [29] found that increased texture depth and fractal dimension significantly improve skid resistance, with notable contributions from \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Coefficients**} & \multicolumn{2}{c}{**Standard Error**} & \(p\)**-Value** & \(\mathbf{r}\) & \(R^{2}\) & \(R^{2}_{adjusted}\) & \(F\)**-Value** & **Ftab**tab \\ \hline Intercept & \(a_{0}\) & \(-11.362\) & 0.540 & 8.44 \(\times\) 10\({}^{-46}\) & & & & \\ \hline \(V_{vv,PS}\) & \(a_{1}\) & \(-0.568\) & 0.167 & 8.41 \(\times\) 10\({}^{-4}\) & & & & \\ \hline \(S_{m2,MIC}\) & \(a_{2}\) & 0.136 & 0.006 & 4.69 \(\times\) 10\({}^{-46}\) & & & & \\ \hline \(S_{pc,MAC}\) & \(a_{3}\) & 0.192 & 0.023 & 9.07 \(\times\) 10\({}^{-14}\) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Model statistical significance and regression coefficients for texture parameters \(S_{m2,MIC}\), \(S_{pc,MAC}\), \(V_{vv,PS}\). Figure 13: Correlation of measured and predicted friction coefficients \(\mu\) vs. \(\mu_{p}\)_-_  
macrotexture. Similarly, our study investigates skid resistance using 3D texture parameters across different road sections. The key difference lies in our prediction model, which integrates multiple texture parameters, including the valley material portion (\(S_{m\text{2,MIC}}\)), arithmetic mean peak curvature (\(S_{pc,\text{MIC}}\)), and dale void volume (\(V_{vc,PS}\)), for a more accurate prediction of friction. This contrast highlights our study's novelty in combining these parameters within a regression model to enhance prediction accuracy. The study in [30] evaluates the correlation between the Pendulum test value (PTV) and mean texture depth (MTD) using the Sand Patch Test for porous asphalt pavements, highlighting the challenges in achieving a strong correlation between these parameters. Our research advances this discussion by employing a more sophisticated approach using 3D texture parameters to predict friction coefficients across various road surfaces. Unlike the stationary Pendulum test, our study utilized a continuously operating device, the Traction Watcher One (TWO), providing a more dynamic and comprehensive assessment of friction over extended road sections. While the study in [30] focuses on porous asphalt and its initial performance, our work integrates a broader set of texture parameters, offering a comprehensive prediction model applicable to different road surface types. The inclusion of both microtexture and macrotexture parameters in our regression model provides a more detailed understanding of the surface interactions, ultimately leading to more accurate and reliable friction predictions. The study in [31] focuses on the impact of macrotexture on the skid resistance of asphalt pavements, using a handy laser scanner and a dynamic friction tester. It identifies peak density and arithmetic mean peak curvature as significant factors influencing the friction coefficient, though these effects are speed-dependent. In contrast, our study not only examines macrotexture but also integrates microtexture parameters using a more comprehensive set of 3D texture data. We employed a continuously operating device, the Traction Watcher One (TWO), for dynamic friction measurements across different road surfaces, offering a broader analysis of friction coefficients.