## 3 Results and Discussion
### Site-Specific Correlation  
To date, several correlations have been published between the parameters of residual shear strength and the physical parameters of soil (percentage of clay fractions and  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Comparison** & **Absolute Difference** & **Critical Range** & **Result** \\ \hline \(\varphi_{\text{R}}\) DS vs. \(\varphi_{\text{R}}\) DS & 1.5 & 0.441 & Means significantly different \\ \(\varphi_{\text{R}}\) RS vs. \(\varphi_{\text{R}}\) RS & 2.03 & 1.210 & Means significantly different \\ \(\varphi_{\text{R}}\) RS vs. \(\varphi_{\text{R}}\) DS & 1.77 & 1.560 & Means significantly different \\ \hline \hline \end{tabular}
\end{table}
Table 1: Statistical differences of the residual angle of internal friction of the selected groups of samples.  
Figure 10: Values of the residual shear strength parameters depending on the testing method.  
plasticity index) across different soil types using various types of direct and ring shear apparatuses [29, 40, 43, 45, 52].  
For a relatively small number of soil samples from the open pit mine Drmno (six samples), a correlation analysis was performed on the obtained values of residual angles of internal friction from the DS and RS apparatuses and the percentage of fractions d < 0.002 mm, as well as the plasticity index (I\({}_{\rm p}\)).  
Figure 11 shows the correlation of the values of the residual angle of internal friction obtained from six soil samples in the DS and RS apparatuses.  
The correlation between the angle values measured in the two shear apparatuses can be expressed by a linear relationship:  
\[\varphi_{R}^{\prime}RS=1.347\varphi_{R}^{\prime}DS+6.5206 \tag{3}\]  
where \(\varphi_{R}^{\prime}\)\(RS\) is the angle obtained in the \(RS\) apparatus, and \(\varphi^{\prime}\)\(DS\) is the angle value obtained from the \(DS\) apparatus.  
A correlation has also been established between the plasticity index and the residual angles of internal friction obtained from the DS and RS apparatuses, as shown in Figure 12. The values of the coefficients of determination for the relationships between the parameters Ip-\(\varphi^{\prime}\) RS and Ip-\(\varphi^{\prime}\) RS are 0.91 and 0.92, respectively.  
Figure 11: Correlation values of the residual angle of internal friction obtained from the DS and RS apparatuses.  
Figure 12: Correlation values between the plasticity index (I\({}_{\rm p}\)) and the residual angle of internal friction obtained from the DS (**right**) and RS (**left**) apparatuses.  
Figure 13 shows the correlation between the values of the residual angle of internal friction and the clay fractions (less than 0.002 mm). The correlation between these values is expressed by a linear relationship, with the coefficients of determination for d < 0.002 mm-\(\varphi\)\({}^{\prime}\)\({}_{\text{R}}\) RS and d < 0.002 mm-\(\varphi\)\({}^{\prime}\)\({}_{\text{R}}\) DS being 0.86 and 0.88, respectively.  
All the presented correlations confirmed a negative correlation between the residual angle of internal friction and the physical parameters of the soil (Figures 12 and 13) and are useful for estimating trends at the studied location. However, they cannot be applied in a general sense in geotechnical practice. [PERSON] et al., 1989 [53] emphasized that similar correlations with a larger number of samples (from different locations) can yield more significant variability in the variables.