## 3 Results of Statistical Analyses and Discussion  
The total number of triaxial compression tests used in the analysis is 70. For all selected soil parameters, a Shapiro-Wilk analysis of distribution was conducted. The dependent variables, namely the internal friction angle (\(\phi^{\prime}\)) and cohesion (\(\mathrm{c^{\prime}}\)), obtained a \"W statistic value\" for the Shapiro-Wilk test greater than the critical value of 0.957 (for 70 samples). This indicates that the data distribution is normal (Figure 9). Figure 8: Diffraction image of the analysed soil sample [22]. Figure 7: Grain size range for limestone waste [22]. As indicated by the Shapiro-Wilk test, the independent variables, namely the corrected cone resistance (q\({}_{t}\)) and the normalised friction coefficient (Fr), do not follow a normal distribution (Figure 8). To determine if the variables are dependent, the Spearman correlation coefficient was calculated for two sets of data separately: the corrected cone resistance (q\({}_{t}\)) and the laboratory-determined internal friction angle (\(\Phi^{\prime}\)) (Table 1). Table 2 shows the Spearman correlation coefficient values for the normalised friction coefficient (Fr)--a variable derived from field studies--and the laboratory-determined internal friction angle (\(\Phi^{\prime}\)). The significance level was set at 0.05, indicating a 95% probability of dependence between the variables. The calculations reveal that, at the specified significance level of 0.05, both q\({}_{t}\) and Fr are dependent on the variable \(\phi^{\prime}\). The significance of the correlation coefficient was tested using hypothesis testing, yielding positive results. However, the Spearman correlation coefficient for q\({}_{t}\) and \(\phi^{\prime}\) is higher, at 0.91, indicating that the internal friction angle \(\phi^{\prime}\) is more dependent on q\({}_{t}\) than on Fr. Figure 10: Histogram of the analysed data: (**a**) corrected cone resistance q\({}_{t}\) and (**b**) normalised friction ratio Fr [22]. Figure 9: Histogram of the analysed data: (**a**) effective friction angle and (**b**) effective cohesion [22]. Utilising the corrected qt parameter from the CPTUs, which incorporates the pore water pressure value, enabled the establishment of a relationship as depicted in Figure 13 with a high degree of agreement and a coefficient of determination R\({}^{2}\) = 0.81. Finally, based on linear regression analysis, the functional relationship result can be represented by Equation (5):  
\[\varphi^{\prime}=3.49\cdot\log_{10}(q_{t})+30.61\ \ \left(\text{R}^{2}=0.81\right) \tag{5}\]  
Furthermore, the calculation of the effective friction angle, due to small differences in the R\({}^{2}\) parameter, can be determined for simplicity using the linear formula shown in Figure 11 (Equation (6)). \[\varphi t=0.84\ (qt)+29.83\ \ \ \ \left(R^{2}=0.79\right) \tag{6}\]  
Prediction of the effective friction angle (\(\phi^{\prime}\)) based on the normalised friction coefficient Fr will be inaccurate due to the low degree of agreement with the data. Below are the functional relationship results, which demonstrated the coefficient of determination R\({}^{2}\) in the regression analysis, as shown in Figures 15-18. Figure 14: The exponential relationship between the effective friction angle (\(\phi^{\prime}\)) and corrected cone resistance (qt). Figure 13: The logarithmic relationship between the effective friction angle (\(\phi^{\prime}\)) and corrected cone resistance (qt). Figure 16: The polynomial relationship between the effective friction angle (\(\phi^{\prime}\)) and the normalised friction coefficient \(\mathrm{Fr}\). Figure 17: The logarithmic relationship between the effective friction angle (\(\phi^{\prime}\)) and the normalised friction coefficient \(\mathrm{Fr}\). Figure 7:0 The linear relationship between the effective friction angle (\(\phi^{\prime}\)) and the normalised friction coefficient \(\mathrm{Fr}\).