## 3 Results and Discussion
### Specific Energy  
This study also aimed to compare the SE from the numerical simulation with that from the LCM test. As mentioned previously, the SE is a representative index of cutting efficiency. As described in Equation (1), it is calculated by the cutting force and cut volume of the rock during the rock cutting process. Therefore, the result of specific energy is important for assessing the applicability of the numerical simulation. For comparison, Table 5 summarizes the results of the numerical simulations and the LCM tests. Figure 17 compares the specific energy values that were obtained from the LCM test and the numerical simulations for all cutting conditions. The results showed that the optimum cut spacings at each penetration depth were 20, 21, 28, and 22 mm, respectively. The optimum cut spacings obtained from the numerical simulations were consistent with the experimental values. However, at 11 mm, the optimum cut spacing in the numerical simulation was 22 mm, whereas the optimum cut spacing was 33 mm is in the LCM test. As shown in Figure 17, in the LCM test, the optimum cut spacing was 33 mm if the optimum cut spacing was defined as the minimum point of specific energy. However, in the LCM test, because the specific energy tended to converge after the cut spacing exceeded 22 mm, the minimum point was not clear. Despite the lack of observations, the difference in specific energy between cut spacings of 22 mm and 33 mm was not significant. Therefore, the optimum cut spacing obtained from the numerical simulation was considered to be reasonable. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Penetration Depth, \(p\) (mm)**} & \multirow{2}{*}{**Cut Spacing, \(s\) (mm)**} & \multicolumn{2}{c}{**Specific Energy (MJ/m\({}^{3}\))**} \\ \cline{3-5}  & & & **LCM \({}^{*}\)** & **Numerical** \\ \hline \hline \multirow{8}{*}{5} & 5 & 82.96 & 57.89 \\  & 10 & 77.65 & 60.45 \\  & 15 & 77.86 & 53.08 \\  & 20 & 67.57 & 41.05 \\  & 25 & 85.81 & 50.66 \\ \hline \multirow{8}{*}{7} & 7 & 54.74 & 53.00 \\  & 14 & 48.94 & 45.67 \\  & 21 & 42.17 & 40.99 \\  & 28 & 44.94 & 49.00 \\  & 35 & - & 52.42 \\ \hline \multirow{8}{*}{9} & 9 & 49.73 & 57.94 \\  & 18 & 37.69 & 49.88 \\ \cline{1-1}  & 27 & 33.12 & 42.80 \\ \cline{1-1}  & 36 & 39.70 & 53.76 \\ \cline{1-1}  & 45 & - & 52.86 \\ \hline \multirow{8}{*}{11} & 11 & 46.30 & 55.46 \\  & 22 & 34.39 & 43.10 \\ \cline{1-1}  & 33 & 31.10 & 46.32 \\ \cline{1-1}  & 44 & 32.71 & 45.40 \\ \hline \hline \end{tabular} \({}^{*}\) The results of LCM tests were obtained from [8].  
\end{table} 
Table 5: The results of specific energy in LCM test and numerical simulation. Overall, the optimum cut spacings of the numerical simulations were generally consistent with the experimental values. However, in quantitative comparisons, the specific energy of the numerical analysis was somewhat different from that of the experimental results. Compared to the LCM test results, the numerical simulations underestimated the specific energy at a penetration depth of 5 mm, and overestimated the specific energy at penetration depths of 9 mm and 11 mm. In contrast, at a penetration depth of 7 mm, the specific energy of the numerical analysis was in good agreement with those of the LCM test. The difference in the specific energy was due to the difference in the cutting force. Table 4 shows that the differences between the LCM test and numerical results for specific energy were similar to the differences in the cutting force, indicating that, in spite of the fact that the numerical simulation had an error in estimating the cutter forces, it accurately identified the fragmentation patterns and the cut volume of the rock. In addition, although they produced different values of specific energy, the numerical simulation and the LCM test showed the same trend in the changes in specific energy for all of the cutting conditions. In the numerical simulation, the behavior of rock depended on the predetermined EOS, constitutive equation, conservation law, and failure and yield functions.