## 3 Results  
### Experimental Results  
#### 3.1.1 Packing Density  
The structure of a sand sample (skeleton) plays a crucial role in determining the mechanical behaviour, which can be controlled by density and anisotropy. The packing density of sand can depend on multiple factors, such as the particle shape, size, and gradation along with the arrangement of particles. A sample consisting of particles with high regularity has a higher density and low void ratio compared to a sample with low regularity particles [2]. Sand gradation can be poorly graded, well graded, or gap graded. A poorly graded sand represents sand that has similar grain sizes; in contrast, the well-graded sand has a percentage of each size when the \(\mathrm{C_{u}}\) is greater than 6 and when the \(\mathrm{C_{c}}\) lies between 1 and 3. The gap-graded sand represents sand that has two different mixed sizes, in other words, two different poorly graded sands mixed together [9]. A well-graded sample will have a high density and a lower void ratio compared to a poorly graded sample. According to [PERSON] [54], when the particle size range is coarser, the density increases and the void ratios decrease. In the poorly graded sand used, it was shown that as the mean particle size increases, the density also increases, and the coefficient of volume compressibility decreases, as demonstrated in Figure 8. These findings are consistent with the works of [PERSON] [54] and [PERSON] [1]. In terms of shape, there is a strong correlation between particle shape and packing density. A complete sphere shape has the densest possible structure compared to other shapes [1]. Spherical shapes require less compressive force to achieve a dense state because they are easier to reorient compared to less spherical shapes [1]. However, further studies [55] have shown that for particles of similar sizes, the optimal shape for achieving maximum packing fraction is not necessarily a perfect sphere. A comparison between a marble-ball model and M&M candies (which have an elongated and flattened shape) showed that the M&M candy shape has a higher packing fraction of C = 71% compared to a sphere shape with C = 64%. When examining the relationship between particle shape and void ratio, [PERSON], [PERSON] and [PERSON] [2] found that as particle roundness, sphericity, and regularity approach one (indicating complete rounded and spherical shape), the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Phase** & **Parameter** & **Value** \\ \hline \multirow{2}{*}{Train and Test Sets} & test\_size & 0.2 \\  & random\_state & 0 \\ \hline \multirow{3}{*}{K-Fold Cross-Validation} & n\_splits & 10 \\  & random\_state & 0 \\  & shuffle & True \\ \hline \multirow{2}{*}{Model} & n\_estimators & 100 \\  & random\_state & 0 \\ \hline \multirow{2}{*}{Visualisation} & start\_point & 0 \\  & boundary\_shift & 20\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Numerical hyperparameters for the random forest regressor code, including parameters for both with and without the application of 10-fold CV. difference between the maximum and minimum void ratio decreases. Similar results were found by [PERSON] et al. [56], where the void ratio decreased as regularity increased. The mineral composition of a soil is one of its essential characteristics. Mineralogy influences properties such as specific gravity, Young's modulus, shear modulus, and the Poisson ratio [12; 57]. The dry unit weight and specific gravity of sand are important, as they can influence the sample's void ratio, as shown in the following equation:  
\[e=\frac{G_{\mathrm{s}}\,\gamma_{w}}{\gamma_{d}}-1 \tag{6}\]  
where \(G_{\mathrm{s}}\) represents the specific gravity, \(\gamma_{w}\) indicates the unit weight of water, and \(\gamma_{d}\) represents the dry unit weight of the sample. According to the equation, when the specific gravity increases, the void ratio also increases. Similarly, when the dry unit weight decreases, the void ratio increases.