## 2 Materials and Methods
### Experimental
#### 2.2.1 Direct Shear Apparatus  
A Mateset direct shear apparatus was used to conduct the experiments, which were carried out according to the Australian standard [48]. The dimensions of the mould in the direct shear box were 60 \(\times\) 60 mm. In each test, different amounts of normal stresses, 25, 50, 100, and 200 kPa, were applied to the sample. Each test was conducted on a dry sample at a shear rate of 1 mm/min, which is the maximum allowable speed according to the standard.  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline
**Material** & **Range (mm)** & **Grade** & **C\({}_{\mathbf{u}}\)** & **C\({}_{\mathbf{c}}\)** & **D\({}_{\mathbf{50\,(mm)}}\)** & **G\({}_{\mathbf{s}}\)** & **R** & **S** & \(\rho_{\mathbf{r}}\) \\ \hline B6-Sand & 2.36 to 1.18 & PG & 1.45 & 0.96 & 1.77 & 2.66 & - & - & - \\ B5-Sand & 1.18 to 0.6 & PG & 1.44 & 0.96 & 0.89 & 2.67 & 0.263 & 0.557 & 0.410 \\ B4-Sand & 0.6 to 0.425 & PG & 1.20 & 0.97 & 0.51 & 2.66 & 0.246 & 0.538 & 0.392 \\ B3-Sand & 0.425 to 0.3 & PG & 1.20 & 0.97 & 0.36 & 2.69 & 0.279 & 0.584 & 0.432 \\ B2-Sand & 0.3 to 0.15 & PG & 1.45 & 0.96 & 0.23 & 2.69 & 0.270 & 0.583 & 0.427 \\ B1-Sand & 0.15 to 0.075 & PG & 1.45 & 0.96 & 0.11 & 2.70 & 0.328 & 0.580 & 0.454 \\ M5-Sand & 1.18 to 0.6 & PG & 1.44 & 0.96 & 0.89 & 2.68 & 0.189 & 0.551 & 0.370 \\ M4-Sand & 0.6 to 0.425 & PG & 1.20 & 0.97 & 0.51 & 2.69 & 0.206 & 0.565 & 0.386 \\ M3-Sand & 0.425 to 0.3 & PG & 1.20 & 0.97 & 0.36 & 2.67 & 0.327 & 0.597 & 0.462 \\ M2-Sand & 0.3 to 0.15 & PG & 1.45 & 0.96 & 0.23 & 2.72 & 0.299 & 0.542 & 0.421 \\ M1-Sand & 0.15 to 0.075 & PG & 1.45 & 0.96 & 0.11 & - & 0.389 & 0.499 & 0.444 \\ P5-Sand & 1.18 to 0.6 & PG & 1.44 & 0.96 & 0.89 & 2.66 & 0.246 & 0.559 & 0.403 \\ P4-Sand & 0.6 to 0.425 & PG & 1.20 & 0.97 & 0.51 & 2.68 & 0.203 & 0.575 & 0.389 \\ P3-Sand & 0.425 to 0.3 & PG & 1.20 & 0.97 & 0.36 & 2.69 & 0.233 & 0.523 & 0.378 \\ P2-Sand & 0.3 to 0.15 & PG & 1.45 & 0.96 & 0.23 & 2.67 & 0.286 & 0.565 & 0.426 \\ P1-Sand & 0.15 to 0.075 & PG & 1.45 & 0.96 & 0.11 & - & 0.330 & 0.508 & 0.419 \\ GB6 * & 2.36 to 1.18 & PG & 1.45 & 0.96 & 1.77 & 2.45 & 1 & 1 & 1 \\ GB5 & 1.18 to 0.6 & PG & 1.44 & 0.96 & 0.89 & 2.45 & 1 & 1 & 1 \\ \hline \end{tabular} *  
\end{table}
Table 1: _Cont._  
Figure 2: Sieve analysis of the used particulate materials, with (**a**) displaying the sieve analysis for sand, and (**b**) showing the sieve analysis for glass beads.  
The pluviation technique, sometimes called the rainfall method, is employed in the preparation of granular soil samples, specifically sands, with differing relative densities. Figure 3 provides a schematic diagram of the pluviation technique. By adjusting the height from which the sand particles are dropped, the method allows for the creation of samples with the required density.  
The relationship between drop height versus void ratio and relative density is shown in Figure 4, with the void ratio decreasing as drop height increases. A loose sample is achieved by dropping the soil from a low distance between the cone and mould, reducing the particles' kinetic energy and enabling them to loosely pack. Conversely, a dense sample is formed by dropping the particles from a high distance, increasing their kinetic energy, and causing them to efficiently rearrange and pack densely. Upon dropping the particles from the selected height, the mould is removed, and the sample can be used for shearing testing.  
Figure 4: Drop height versus void ratio and relative density of L-Sand.  
Figure 3: Schematic view of the pluviation technique.  
In the study, two different densities were considered when preparing the sample: the loose and dense density states. In the loose density state, the sand was spooned and dropped from a very low height (zero height). Conversely, in the dense state, the sample was dropped from a cone with a 5.2 mm opening at a height of 83 cm.