## 3 Numerical Simulation Process  
### UCS Tests Based on Modulus Ratio Concept  
The DEM (Discrete Element Method) modeling of non-vibrational rock splitting method was performed using PFC and the optimum borehole spacing for soft rock, normal rock, and hard rock was proposed. In order to simulate the mechanical behavior of the rock material, a typical PFC2D model requires some microscopic parameters to be determined such as; particle radius, particle and parallel bond stiffness ratios, particle friction coefficient, and parallel bond normal and shear strengths. Since these microscopic parameters cannot be measured directly through the laboratory experiments, back calculation needs to be performed by a numerical calibration process. The microscopic parameters used in the UCS tests in PFC2D were calibrated so that the required intact rock properties, such as Young's modulus, Poisson's ratio and UCS were obtained. The rock materials to be used for numerical analysis in this study were classified into three types; soft rock, normal rock, and hard rock, and the UCS of these rocks was selected as 50, 100 and 150 MPa, respectively. Based on the modulus ratio concept, these rock types were further classified into three categories, presented in Table 3. In this study, the ratio of Young's modulus to unconfined compressive strength for high modulus ratio, average modulus ratio, and low modulus ratio was used as 550:1, 300:1 and 150:1, respectively.  
Using PFC2D, the UCS tests were performed to obtain the microscopic parameters of soft rock, normal rock, and hard rock in all three categories of modulus ratios. A lot of careful iterations performed for the calibrations of the microscopic parameters so that the calibration results could match with the index properties of the intact rock types used in this study. As the size of PFC models prepared to simulate the rock fracturing phenomenon was 6 m \(\times\) 6 m, the minimum particle size used in the  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Rock Type** & **UCS (MPa)** & **Borehole Spacing (m)** \\ \hline Soft rock & 50 & 0.7 \\ Normal rock & 100 & 0.6 \\ Hard rock & 150 & 0.6 \\ \hline \hline \end{tabular}  
* UCS, unconfined compressive strength.  
\end{table}
Table 2: Borehole spacing values typically used according to intact rock strength 1.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Rock Type**} & \multicolumn{3}{c}{**Young’s Modulus (GPa)**} \\ \cline{2-4}  & **Low Modulus Ratio** & **Average Modulus Ratio** & **High Modulus Ratio** \\ \hline Soft rock & 8 & 15 & 27.5 \\ Normal rock & 15 & 30 & 55 \\ Hard rock & 23 & 45 & 82.5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Young’s modulus values of soft, normal, and hard rock based on modulus ratio concept.  
model was 6 mm due to the computational limitations. That is why, the minimum particle size used for UCS tests was also 6 mm. The microscopic parameters related to all three types of rocks obtained by the calibration process are given in Table 4. Four microscopic parameters namely; particle-particle contact Young's modulus (\(E_{c}\)), [PERSON]'s modulus of parallel bond (\(E_{c}\)), parallel bond normal and shear strength (\(\overline{\sigma}_{c}\) and \(\overline{\tau}_{c}\)) depend on the respective modulus ratio of the rock and were obtained for each intact rock type in all three categories of modulus ratios by using REV concept which will be discussed in the later sections.