## 4 Numerical Simulation Results and Discussion  
### Design of Numerical Model  
The numerical simulation model of rock breaking using a disc cutter performed in this study was established using the LS-DYNA module in ANSYS. Figure 6 shows the model of rock breaking using a disc cutter. The simulation uses a disc cutter with a diameter of 457.2 mm (18 inches). To be closer to the actual rock-breaking behaviour of the disc cutter, the cutter model is divided into two parts, one is the cutter ring, and the other is the cutter body. In this study, the cutter ring is an elastic body, and the cutter body is a rigid body. The two are in contact with each other, but not fixed to ensure that the outer cutter ring can be rotated during the rock-breaking process, as shown in Figure 7. The rotation depends on the friction between the disc cutter and the rock, which is more in line with the actual behaviour of the disc cutter. The disc cutter model parameters are shown in Table 2.  
Figure 4: Description of data processing method for the values of \(K1\), \(K2\), \(K3\). Figure 5: Technique for obtaining the value of \(EF_{min}\). In this study, the rock mass is designed as a rectangle with length, width and height of 500 mm, 300 mm and 150 mm, respectively, as shown in Figure 8. The constitutive relation selected for the rock in the numerical simulation of rock breaking using a disc cutter is the HJC model of the diorite of the Jinan region, and the characteristic parameters of the HJC model are shown in Table 3. The contact between the cutter ring and the rock mass corresponds to eroding contact. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Category** & **Density (kg/m3)** & **Young’s Modulus (GPa)** & **Poisson’s Ratio** \\ \hline Cutter ring & 7850 & 209 & 0.3 \\ \hline Cutter body & 7830 & 207 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Disc cutter material characteristic parameters. Figure 6: Model of rock breaking by disc cutter. Figure 7: Cutter ring and cutter body. In terms of boundary conditions, the displacement in the x direction of the two sides of the rock is limited, and the bottom surface restricts the displacement and rotation in all directions, as shown in Figure 9a,b. Non-reflective boundaries are set on two sides, the bottom face and the face in front of the disc cutter forward direction, as shown in Figure 9c. For the disc cutter, translational and rotational constraints in two directions (x, y) other than the forward direction are set, so that the disc cutter can maintain its penetration and avoid deviating from the predetermined trajectory. In terms of rock breaking, an additional keyword (MAT_ADD_EROSION) is set for the HJC model, which allows each unit of the rock to be deleted after its maximum principal strain reaches a predetermined value. The  
Figure 8: Schematic diagram of rock materials. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters Type** & **Symbol** & **Value** & **Unit** \\ \hline \multirow{4}{*}{Basic parameters} & \(\rho\) & 3013 & kg/m\({}^{3}\) \\  & \(G\) & 43.3 & GPa \\  & \(T\) & 12.26 & MPa \\  & \(f_{c}\) & 195.5 & MPa \\ \hline \multirow{2}{*}{Strain rate constants} & \(C\) & 0.00103 & \\  & \(ESPO\) & 1.0 & \\ \hline \multirow{4}{*}{Limit surface parameters} & \(A\) & 0.254 & \\  & \(B\) & 1.695 & \\  & \(N\) & 0.742 & \\  & \(S_{FMAX}\) & 1.42 & \\ \hline \multirow{4}{*}{State equation parameters} & \(P_{crash}\) & 65.169 & MPa \\  & \(P_{lock}\) & 2.2 & GPa \\  & \(\mu_{crash}\) & 0.000831 & \\  & \(\mu_{lock}\) & 0.00204 & \\  & \(K1\) & 94.7 & GPa \\  & \(K2\) & 632.4 & GPa \\  & \(K3\) & 938.1 & GPa \\ \hline \multirow{2}{*}{Damage model constant} & \(D1\) & 0.0312 & \\  & \(D2\) & 1 & \\ \cline{1-1}  & \(EF_{min}\) & 0.00977 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: [PERSON]’s HJC model characteristic parameters. parameter settings are shown in Figure 10. In addition, the standard crack initiation and crack growth model are not considered in the present work, and will be discussed in depth in follow-up studies.