## 2 Materials and Methods
### Data Presentation  
A descriptive statistical analysis, including mean, median, standard deviation (SD), skewness, and minimum (Min) and maximum (Max) values of all parameters, is presented in Table 1. These statistics provide a comprehensive understanding of the dataset by highlighting measures such as mean, median, standard deviation, skewness, and kurtosis. The variability and distribution of the parameters inform the model selection process and ensure that the machine learning models are applied to appropriately characterised data. Furthermore, these descriptive statistics are essential for identifying the influence of each parameter on the performance of fully grouted rock bolts and justifying the use of advanced optimisation techniques in the prediction models. Indeed, seven parameters were considered: W/G ratio, curing time (CT), diameter confinement (DC), grout percentage, fly ash (FA) content, uniaxial compressive strength (UCS), and peak load (PL) values. The W/G ratio exhibited a mean and median of 35%, with a moderate SD of 4.11%, suggesting some variability. Its distribution was symmetric but leptokurtic (kurtosis = \(-\)1.52). CT averaged 14.75 days, with a higher degree of variability reflected by a standard deviation of 9.49 days. Figure 3: A view of a fully grouted rock bolting sample in the tensile machine. The distribution was nearly symmetric but also leptokurtic. DC demonstrated significant variability, with a mean of 33.13 mm and an SD of 13.16 mm. The distribution was slightly positively skewed and leptokurtic. Grout percentages remained relatively constant, with a mean of 99.38% and very low variability due to replacing grout with varying amounts of FA contents. The distribution was slightly negatively skewed and leptokurtic. Also, FA contents had a low mean of 0.625%, with minimal variability and a somewhat positive skew. UCS exhibited a mean value of 48.423 MPa, with a median of 53.168 MPa and a higher SD of 16.977 MPa, indicating substantial variability. Its distribution was slightly negatively skewed with a kurtosis of 0.112, signifying a near-normal distribution. Peak load values averaged 35.44 kN, with moderate variability and an SD of 13 kN. The distribution was nearly symmetric, with a kurtosis close to zero, indicating a near-normal distribution. The violin plot presented in Figure 4 visually illustrates the distribution of peak load values across different parameters. In this figure, the \"Range within 1.5 IQR\" indicates the extent of the data distribution, excluding outliers. The interquartile range (IQR) represents the spread of the middle 50% of the data, defined as the difference between the third quartile (Q3) and the first quartile (Q1). The whiskers of the plot extend up to 1.5 times the IQR from the lower and upper quartiles, encompassing most of the dataset while treating any points beyond this range as potential outliers. The direct and indirect relationships between the parameters using a Pearson correlation coefficient matrix, are shown in Figure 5. The W/G ratio exhibited a moderate negative correlation with peak load values, with a coefficient of \(-0.43\), suggesting that higher water contents in the grout mixtures may lead to decreased maximum pull-out capacity of the fully grouted system. Conversely, the CT factor positively affected peak load values with a coefficient of approximately 0.35, emphasising that longer curing periods triggered increased peak load values. DC, with a coefficient of 0.44, also positively correlated with PL measurements, suggesting that larger confinement diameters could improve the axial bearing load capacity. Grout percentages also positively influenced peak load, with a coefficient of 0.30, though the impact was less noticeable than that of CT or DC. However, a higher fraction of FA with a coefficient of around \(-0.30\) negatively correlated with PL values, indicating that increased FA contents could decrease grout strengths and obtain lower PL values.