## 4 Conclusions  
This study utilized a ring shear apparatus to measure both peak and residual interface shear strength between five different types of sand and three various continuum surfaces (steel, PVC, and stone) under varying normal stresses (25, 50, 100 kPa) at an interface shear rate of 0.5 mm/min. The key findings from this experiment are as follows:  
* Coarse sand exhibited higher \(\mu_{\text{p}}\) with steel and PVC surfaces, while medium sand showed higher \(\mu_{\text{p}}\) with stone. * Well-graded sand showed a higher \(\mu_{\text{p}}\) compared to poorly graded sand. * As the sample density increases, the \(\mu_{\text{p}}\) also increases. * Due to its high roughness and hardness, stone consistently provided the highest interface shear strength values across different sand types, followed by PVC and then steel. * The machine learning models (MLR and RFR) demonstrated high accuracy for both peak and residual shear strength. For peak shear strength, the MLR model achieved an R\({}^{2}\) of 0.92 during training and 0.90 during testing, while the RFR model achieved an R\({}^{2}\) of 0.98 during training and 0.88 during testing. For residual shear strength, the MLR model achieved an R\({}^{2}\) of 0.89 during both training and testing, while the RFR model achieved an R\({}^{2}\) of 0.97 during training and 0.88 during testing. * In the 10-fold cross-validation, the models continued to demonstrate high accuracy. For peak shear strength, both models achieved an R\({}^{2}\) of 0.90. For residual shear strength, the MLR model achieved an R\({}^{2}\) of 0.90, while the RFR model attained an R\({}^{2}\) of 0.87. * Among the eight input parameters, particle regularity was identified as the most influential factor for both peak and residual shear strength, followed by mean particle size and porosity. Figure 16: Feature importance analysis in 10-fold cross-validation: (**a**) MLR for peak interface friction, (**b**) RFR for peak interface friction, (**c**) MLR for residual interface friction, and (**d**) RFR for residual interface friction. **Author Contributions:** Methodology, R.A. and H.A.-N.; writing--original draft preparation, R.A. and F.D. ; writing--review and editing, R.A., F.D. and H.A.-N.; supervision, H.A.-N. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data presented in this study are available in the article. **Conflicts of Interest:** The authors declare no conflicts of interest. **Nomenclature**  
\(\mu_{\text{p}}\) & Peak interface friction \(\delta_{\text{p}}\) & Peak interface friction angle \(\text{RI}\) & Particle regularity \(\text{D}_{\text{S0}}\) & Median particle size \(\text{n}\) & Porosity \(\text{C}_{\text{u}}\) & Coefficient of uniformity \(\text{C}_{\text{c}}\) & Coefficient of curvature \(\text{R}_{\text{t}}\) & Surface roughness \(\text{HD}\) & Surface hardness \(\text{\sigma}\) & Normal stress \(\text{\tau}_{\text{p}}\) & Peak interface shear strength \(\text{\tau}_{\text{r}}\) & Residual interface shear stress \(\text{MLR}\) & Multiple linear regression \(\text{RFR}\) & Random Forest regression \(\text{\bf A}\)  
**Table A1. ** The ring shear experiment data on interface shear strength employed for machine learning analysis.