## 3 Correlation Analysis of the Discing Core Section and the Drilling Parameters  
The cores obtained from the five sets of tests are shown in Figure 6. The diameter of the cores was about 24 mm. The drilling rate of test 1 and test 2 was set to 5 and 10 mm/min, respectively. The core was intact, and there was no core discing phenomenon. The drilling rate of test 3, test 4, and test 5 was set to 15, 20, and 25 mm/min, respectively. Core discing occurred in all three tests. The core discs of each test were numbered along the drilling direction. For example, no. 3-1 represents the first core disc of test 3, and so on. Figure 4: Drilling test. Figure 5: The phenomenon of granite core discing. The drilling pressure at the drill bit was derived by the drill bit propulsion force according to the contact area between the diamond particles on the drill bit and the rock (Equation (1)). \[P=\frac{4F}{\alpha(1-\beta)\pi(D_{e}^{2}-D_{i}^{2})} \tag{1}\]  
where \(P\) represents the drilling pressure exerted by the drill bit on the rock sample, \(F\) represents the drill bit propulsion force exerted by the rig while drilling, \(\alpha\) is the concentration percentage of impregnated diamond particles, \(\beta\) is the ratio of cooling water port to borehole area, \(D_{e}\) is the external diameter of the drill bit, and \(D_{i}\) is the internal diameter of the drill bit. [PERSON] [28] proposed the theory of rock breaking energy, which can calculate the energy required by rock breaking per unit volume of rock according to drilling parameters. This energy is called drilling specific energy, \(u_{\text{m}}\)(Unit of \(u_{\text{m}}\) is MPa or mJ/mm\({}^{3}\)), which can be calculated by Equation (2) [28]:  
\[u_{m}=P+\frac{480\pi MNF}{P} \tag{2}\]  
\(M\) is the bit torque; \(N\) is the bit rotation speed. \(F\) and \(P\) have the same meaning as Equation (1). The drilling pressure and bit torque of the tests are shown in Figure 7. It is observed that the drilling pressure of test 1 and test 2, with complete coring, changes slightly along the core. The drilling pressure curve shows fluctuation characteristics, but the fluctuation range is basically within \(\pm\) 2.0 MPa. The torque curve also shows fluctuation characteristics, but the fluctuation range is basically within \(\pm\) 0.1 N\(\cdot\)m.  
Figure 6: Cores of test 1-5. The drilling pressure data curves of test 3, test 4, and test 5 can be divided into two sections. As shown in Figure 7, the complete core section and the discing core section of the test 3, test 4, and test 5 data are marked. The drilling pressure, torque, and drilling specific energy data of the complete core section is less volatile and has similar characteristics to test 1 and test 2; the drilling pressure of the discing core section increases significantly, and the data fluctuates wildly. The fluctuation range of drilling pressure is \(\pm\) 10 MPa, the fluctuation range of torque is \(\pm\) 7.5 N\(\cdot\)m, and the fluctuation range of drilling specific energy is \(\pm\) 45000 mJ/mm\({}^{3}\). The results of tests 3, test 4, and test 5 show that, without the confining pressure, under the conditions of drilling parameters set in this study, core discing occurred. Drilling parameters reflected the interaction process between the drill bit and the rock sample. With the increase of drilling rate, the drilling pressure, torque, and drilling specific energy also gradually increased. To explore the relationship between drilling parameters and drilling rate, the drilling parameters' average value of test 1 and test 2 and the drilling parameters' average value of the complete core sections of test 3, test 4, and test 5 are plotted in Figure 8 against the drilling rate. Drilling pressure, torque, and drilling specific energy are all linearly and positively correlated with drilling rate. The data points are all within the 95% confidence interval of the linear fitting curve (the gray shaded area in Figure 8). The faster the drilling rate, the more rocks will be broken per unit time when the rotation speed is constant.