# Investigation of Rock-Breaking Mechanisms Based on the Adaptive Matching Method for Drilling Loads
## 2 Methodology
### Modeling of the PDC Cutter Cutting Rock  
To investigate the rock-breaking mechanism enabled by the proposed adaptive matching drilling load method in drilling operations, a discrete element method (DEM) numerical model was developed by means of the PFC3D platform, as shown in Figure 3. The radius of the particles ranges from 0.5 to 0.8 mm, and the total number of balls generated in the DEM model is 104313. The simulation framework incorporates a strongly heterogeneous rock, which is composed of a group of large-sized particles or particle clusters and the matrix. All of the large-sized particles or particle clusters are bonded by the matrix, with similar natural lithological characteristics. The micromechanical parameters of the simulated rock and the contact interaction parameters between the PDC cutter and the rock are referenced from several pieces from the existing literature, specifically those by [PERSON], [PERSON], [PERSON], and [PERSON] [20; 21; 22; 23; 24]. Table 1 summarizes the critical meso-parameters employed in the DEM model of the simulated heterogeneous  
Figure 3: The numerical model of a PDC cutter cutting strongly heterogeneous rock. Figure 2: The main components of the designed tool using adaptive matching method. rock, while Figure 4 demonstrates excellent agreement between experimental results and numerical predictions, thus validating the parameter selection process. In the rock breaking simulating model, a PDC cutter with a diameter of 16 mm and a certain back forward angle \(\beta\) (15\({}^{\circ}\)) is established, as shown in Figure 2(a). The axial load \(F_{\text{WOB}}\) and drive force \(F_{\text{t}}\) will be applied to the PDC cutter to replicate downhole drilling conditions. Under the action of axial load and drive force, the PDC cutter will execute rock cutting operations as schematically shown in Figure 2(a). There are no restrictions for the displacement and motion of the PDC cutter in the X, Y, and Z directions, and real-time monitoring of the three-dimensional displacement, _disp_x_, _disp_y_ and _disp_z_, and the reaction forces, _Fx_, _Fy_ and _Fz_, acting on the PDC cutter, is enabled while simulating. According to the simulation results, the relationship between the displacement of the PDC cutter in the X direction (cutting direction) and the applied axial force is shown in Figure 4(a), and the variation in the reaction force monitored in the PDC cutter and time while simulating are given in Figure 4(b). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Description** & **Parameter** & **Matrix** & **Particles** & **Bond** \\ \hline Ball density/kg\(\cdot\)m\({}^{-3}\) & \(\rho\) & 2500 & 2875 & / \\ Ball-ball contact & \(E_{c}\) & 11.4 & 25.2 & 12.6 \\ modulus/GPa & \(k_{n}/k_{s}\) & 2.21 & 1.52 & 0.76 \\ Ball stiffness ratio & \(k_{n}/k_{s}\) & 2.21 & 1.52 & 0.76 \\ Parallel bond Young’s & \(\overline{E_{c}}\) & 11.4 & 25.2 & 12.6 \\ modulus/GPa & \(\overline{k_{n}}/\overline{k_{s}}\) & 2.21 & 1.52 & 0.76 \\ Particle contact’s & & & & \\ normal to shear & \(\overline{k_{n}}/\overline{k_{s}}\) & 2.21 & 1.52 & 0.76 \\ stiffness ratio & & & & \\ Parallel bond normal & \(\overline{\sigma_{c}}\) & 31.1 & 45.4 & 22.7 \\ strength/MPa & \(\overline{c}\) & 31.1 & 45.4 & 22.7 \\ Conhesion/MPa & \(\overline{c}\) & 31.1 & 45.4 & 22.7 \\ Parallel bond & & & & \\ frictional angle/\({}^{\circ}\) & & 38 & 49 & 24.5 \\ Ball friction & & & & \\ coefficient & \(\mu\) & 0.31 & 0.24 & 0.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The meso-parameters of the simulated heterogeneous rock. Figure 4: Comparison of experimental and numerical simulation results. As shown in Figure 5, when the displacement in the X direction reached approximately 79.5 mm, the PDC cutter encountered a piece of a large particle, causing a significant reaction force and nearly halting the forward movement in the X direction.