## 3 Results and Discussion  
### Continuum Surfaces Properties  
The data used for machine learning are listed in Appendix A, Table A1. As shown in Figure 6, across all soil types, average shear strength, which is the mean of the peak and residual shear strength values, increases with normal stress. Stone surfaces consistently show the highest shear strength, followed by PVC and then steel, indicating that the stone's higher roughness and hardness provide greater resistance to shear forces. The considerable difference in shear strength observed for Sand-A when interfaced with the stone surface, as depicted in Figure 6a, can be attributed to several factors. The stone surface exhibited significantly higher roughness (Rt = 82.92 \(\upmu\)m) and hardness (HD = 795) compared to the steel and PVC surfaces, leading to a greater mechanical interlock with the sand particles and enhancing the shear resistance. This increased roughness allows for more substantial interlocking between the sand particles and the asperities of the stone surface, while the higher hardness provides greater resistance to deformation under shear stress. Additionally, Sand-A, characterized as quartz medium sand with a median particle size (D\({}_{50}\)) of 0.51 mm and a regularity index (RI) of 0.72, has particle shapes that are more conducive to interlocking with the asperities of rough surfaces like stone. The combination of angular to sub-angular particle shapes in Sand-A enhances the interlocking effect when sheared against a rough and hard surface, leading to significantly higher shear strength compared to smoother surfaces, like steel and PVC. Furthermore, the interaction mechanisms between the sand particles and the continuum surfaces differ significantly based on the surface characteristics. The stone surface, with its high roughness and hardness, promotes plowing and wedging actions, where sand particles dig into the surface and create additional resistance to shear. This phenomenon is less pronounced on smoother surfaces, like steel and PVC, leading to the observed differences in shear strength. Normalized roughness (R\({}_{\text{n}}\)), as proposed by [PERSON] and [PERSON] [9], is measured by dividing the R\({}_{\text{max}}\) by the D\({}_{50}\). Surface roughness measurements of continuum surfaces, as measured by a profilometer, are shown in Figure 7. The results in Figure 7 illustrate the initial roughness contours for the steel, PVC, and stone surfaces. These roughness measurements are critical in understanding the shear strength results. The pronounced fluctuation in the initial roughness contours of the stone surface, as shown in Figure 7c, is due to the inherent characteristics of the stone material, even when manufactured cut. The stone's natural composition and structure create a more heterogeneous surface texture compared to synthetic materials, like steel and PVC. These microscopic irregularities result in a more uneven surface profile. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sand Type** & **A** & **B** & **C** & **D** & **E** \\ \hline Loose state (g/cm\({}^{3}\)) & 1.65 & 1.64 & 1.74 & 2.22 & 1.66 \\ Dense state (g/cm\({}^{3}\)) & 1.72 & 1.83 & 2.03 & 2.42 & 1.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Sample initial density of A-Sand at loose and dense states during steel interface tests under 25 kPa. These fluctuations in roughness enhance the mechanical interlock between sand particles and the stone surface, increasing the interface shear strength. This variability in roughness leads to more effective particle interlocking, consistent with the higher shear strength values observed for stone surfaces, resulting in greater resistance to shear forces. Higher roughness leads to greater mechanical interlocking, which enhances shear resistance. This correlation shows that normalized roughness (R\({}_{\text{n}}\)) significantly influences the peak interface friction coefficient (\(\mu_{\text{p}}\)) for different sand types.