## 3 Numerical Simulation Process
### Model Preparation Using REV Calculations  
In order to simulate the rock splitting process in all types of rock using PFC\({}^{\text{2D}}\), the rock splitting models of size 6 m \(\times\) 6 m were prepared with fixed boundary conditions, as shown in Figure 11a. The particles at the model boundaries were fixed to control the displacements at the boundary. The microscopic parameters obtained for each rock type through REV calculations were used in simulating the rock splitting model for each case. In order to prepare a free surface, the particles at the top of the model as well as adjacent to the proposed borehole were removed up to 2 m, as shown in Figure 11b. Subsequently, a borehole of 76 mm diameter was excavated by removing the particles starting from the upper free surface of the model up to a depth of 1.4 m, as shown in Figure 11c. Finally, two walls were installed at both sides of the excavated borehole up to 1 m depth for simulating the counter-wedges, as shown in Figure 11d. The stiffness of both walls was kept as 200 GPa [31] in order to match the stiffness of structural steel used in fabricating the counter-wedges of the split-wedge system.  
In order to analyze rock splitting in soft rock, normal rock, and hard rock, the initial value of borehole spacing was kept as 0.5 m that was gradually increased until the crack propagation due to split-wedge action could not reach the adjacent free space. Borehole spacing can be defined as the horizontal distance from the center of the borehole to the free space created adjacent to it. The rock splitting analyses was performed by increasing the borehole spacing values in soft, normal and hard rocks. A series of rock splitting experiments were performed by using the splitting width of 20 mm. Splitting width is the horizontal distance between the two sides of  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Rock Type**} & \multicolumn{3}{c}{**Microscopic Parameters (\(\overline{\sigma}_{c}\) and \(\overline{\tau}_{c}\))**} \\ \cline{2-4}  & **Low Modulus Ratio** & **Average Modulus Ratio** & **High Modulus Ratio** \\ \hline Soft rock & 34.5 & 32 & 31 \\ Normal rock & 66 & 68 & 67.5 \\ Hard rock & 99.4 & 101 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Parallel bond normal and shear strength (\(\overline{\sigma}_{c}\) and \(\overline{\tau}_{c}\)).  
Figure 11: Steps involved in the formation of rock splitting model, (**a**) bonded particle model; (**b**) formation of free surface; (**c**) borehole excavation; (**d**) installation of counter-wedge walls.  
counter-wedges finish their splitting function. For achieving the splitting width in the rock splitting model, the two walls installed at both sides of the excavated borehole were moved apart and their displacements were monitored in both cases until the distance between both walls was obtained as 20 mm. The initial model was prepared with the borehole spacing of 0.5 m in all cases of rock strength. A number of models were generated by increasing the borehole spacing by 0.1 m at a time and rock splitting process was performed until the crack propagation failed to reach the free surface, as shown in Figure 12a,b.