## 2 Materials and Methods
### Data Presentation
Although CT and UCS exhibited a strong Pearson correlation (0.84), both were retained as input variables due to their distinct physical significance. CT represents the duration of curing, while UCS quantifies the mechanical behaviour of the grout. Eliminating either variable would result in a loss of valuable information. Furthermore, XGBoost's decision-tree-based architecture effectively handles multicollinearity, ensuring both variables contribute meaningfully to the model's predictive accuracy. Additionally, UCS exhibited a strong positive correlation with PL values, with a coefficient of 0.57, indicating that higher UCS values enhance the maximum pull-out capacity of fully grouted rock bolts. Overall, the study emphasises the significant influence of UCS, CT, and DC on increasing PL values and the performance of fully grouted rock bolting systems. Conversely, increasing W/G ratios and FA contents could negatively impact axial load bearing capacity. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameter** & **Unit** & **Mean** & **Median** & **SD** & **Kurtosis** & **Skewness** & **Min** & **Max** \\ \hline W/G & \% & 35 & 35 & 4.11 & \(-1.52\) & 0 & 30 & 40 \\ Curing time & Day & 14.75 & 14 & 9.49 & \(-1.30\) & 0.006 & 1 & 28 \\ Diameter confinement & mm & 33.13 & 23 & 13.16 & \(-1.77\) & 0.52 & 23 & 50 \\ Grout & \% & 99.38 & 100 & 0.813 & \(-1.01\) & \(-0.80\) & 98 & 100 \\ Fly ash content & \% & 0.63 & 0 & 0.813 & \(-1.01\) & 0.80 & 0 & 2 \\ Uniaxial compressive & MPa & 48.42 & 53.17 & 16.98 & 0.11 & \(-0.77\) & 9.41 & 82.50 \\ strength & Peak load & kN & 35.44 & 37.95 & 13.00 & 0.08 & \(-0.0459\) & 8.05 & 68.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptive statistics of all parameters. Figure 4: Violin plot of parameters. Along with the violin diagram and Pearson matrix, the Kernel density estimation (KDE), which represents the distribution or density of multiple variables over a specific gradient or parameter, was also employed to show the distribution of all parameters, such as UCS, (W/G) ratio, CT, DC, grout percentage, FA contents, and peak load values along a specific dimension or index (Figure 6). Different coloured curves were used in this diagram to show the distribution/influence of each mentioned parameter. The height and width of the curves along the \(x\)-axis indicate the density/intensity of the parameter across the observed gradient. The blue colour, the W/G ratio, covered a moderate and relatively wide range, suggesting diversity in the (W/G) ratios utilised. The CT (red) distribution was more intricate, showing multiple peak values that suggested irregular curing periods. The green area within the DC demonstrated a gentle and even expansion, indicating a largely uniform spread of values. Figure 5: Heatmap plot of parameters to analyse their Pearson correlations. Figure 6: Density of parameters and their Kernel smooth. On the other hand, the grout percentage (yellow) experienced a sudden increase, suggesting that the grout content stayed relatively consistent across most samples, with slight fluctuation. The curve representing the FA content (coloured in black) was narrow with a low peak, indicating minimal changes in FA contents throughout the dataset. The cyan-coloured UCS demonstrated a more comprehensive range of UCS values in the dataset with a more extensive and smoother distribution. Eventually, the peak loads (purple colour) displayed a broad, slightly asymmetrical distribution, indicating variations in the highest loads recorded, with some data skewness. Moreover, a rug plot is located at the bottom of the figure, with short lines representing the dataset's actual values for each parameter, further illustrating the density distribution of the data points. The overlapping of curves suggests interactions or comparative influences among different parameters.