## 3 Results and Discussion
### Cutter Force
Even though the rocks beneath the cutter tip are crushed, they can still bear cutter loads in a condensed state. However, in this study, the cutter forces in numerical simulations resulted in fluctuations based on a certain value rather than zero. As described Figure 8, under compressive stress, the rock particle remains with a certain level of residual strength rather than being deleted as in traditional FEM, even if it reaches the maximum damage. This characteristic of CD failure function is thought to have contributed to the results of realistic cutter forces. Regarding the described characteristics, the proposed numerical model shows an improvement on the traditional FEM models in terms of simulating realistic behavior of rock in cutting process and providing quantitative results in cutter forces. Figure 16 shows that the results of the cutter forces estimated by LCM with the numerical simulations for all of the cutting conditions considered in this study. Similar to the results obtained from the LCM test, the numerical analysis identified the tendency of the cutting and normal forces to increase with both penetration depth and cut spacing. On average, the relative errors of the cutting force and normal force between the LCM test and numerical simulations were 25.7% (5.6-69.0%) and 15.5% (2.3-33.8%), respectively. The relative error (\(\varepsilon\)) is calculated by Equation (9). \[\varepsilon\ (\%)=\frac{|F_{num}-F_{LCM}|}{F_{LCM}}\times 100 \tag{9}\]  
where \(\varepsilon\) is the relative error and \(F_{num}\) and \(F_{LCM}\) are the cutter forces obtained from the numerical simulation and LCM test, respectively. The relative errors in the cutter forces differed with the penetration depth. At 5 mm, the numerical simulation slightly underestimated both the cutting force and the normal force compared with the LCM test. The relative errors in the cutting force and normal force between the LCM and numerical simulation were 13.5% (7.5-21.5%) and 21.3% (16.7-31.1%). As the penetration depth increased to 7 mm, the numerical simulation slightly overestimated the cutting force and underestimated the normal force compared with the LCM test. The relative errors of the cutting force and normal force between the LCM test and numerical simulation were 15.7% (5.6-36.0%) and 20.0% (5.7-33.8%), respectively. At 9 mm, the numerical simulation overestimated the cutting force of a pick cutter. The maximum relative error of the cutting force was 76.4% when the cut spacing was 9 mm. The relative errors of the cutting force and normal force between the LCM test and numerical simulation were 38.9%  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Penetration Depth**, \(p\) (mm)} & \multirow{2}{*}{**Cut Spacing**, \(s\) (mm)} & \multicolumn{3}{c}{**Mean Cutting Force**} & \multicolumn{3}{c}{**Mean Normal Force**} \\ \cline{3-8}  & & & **LCM \({}^{*}\)** & **Numerical** & **Relative** & **LCM \({}^{*}\)** & **Numerical** & **Relative** \\  & & **(kN)** & **(kN)** & **Error (\%)** & **(kN)** & **(kN)** & **Error (\%)** \\ \hline \multirow{4}{*}{9} & 9 & 5.00 & 8.82 & 76.4 & 5.68 & 4.12 & 27.5 \\  & 18 & 6.66 & 9.21 & 38.3 & 7. (16.4-76.4%) and 11.7% (4.5-27.5%). At 11 mm, the numerical simulation significantly overestimated the cutting force at cut spacings of 11 mm and 22 mm. The relative errors at these cut spacings were 69.0% and 54.3%, respectively. However, the normal force of the numerical simulation showed good agreement with the LCM test results for all cut spacings. Overall, the results showed that the numerical simulation, compared with the LCM test, overestimated the cutting force and underestimated the normal force. It was presumed that this occurred because of the geometric shape of the cutter model. As shown in Figure 9, the shape of the modeled pick cutter was simplified in the modeling process. The contact surface between the pick and the rock was affected by the geometries of the pick.