# Numerical Simulation on Dynamic Response of Drilling Parameters in Loaded Rock Mass
## 3 Establishment of Numerical Model
### Reliability Analysis of Drilling Simulation  
Relevant research shows that [17] in the drilling construction of a coal mine roadway the trajectory of the drill bit in the hole shows a'step-up' change characteristic, accompanied by a rebound phenomenon. At the same time, the drilling rate is not uniform and stable but fluctuates, which is mainly due to the non-linear uniform growth relationship between the depth and load of the drill bit invading the rock. In the early stage of the load increase, the penetration depth increases in a certain proportion with the increase in load. When the load reaches a certain critical value, the penetration depth of the drill bit will increase suddenly. Therefore, the drilling rate and torque will also have a certain jump fluctuation due to the change in drilling depth. Through the field drilling data shown in Figure 2, it can be clearly observed that with the increase in drilling depth, the drilling rate and torque show a certain degree of fluctuation. In the numerical simulation study, in order to make the change in drilling parameters in the simulation results more in line with the actual drilling process, the following assumptions are made:  
1. During the drilling process, the drill bit is drilled in a manner perpendicular to the rock specimen, and the borehole does not deflect;
2. The stiffness and strength of the drill bit are much higher than that of the rock, so the drill bit is assumed to be a rigid body;
3. When the rock unit fails to drill, it is directly removed. Without considering the problem of repeated crushing, the broken rock unit will no longer affect the subsequent rock drilling work;
4. The rock in the numerical model is homogeneous and isotropic, without considering the existence of primary cracks in the rock and without considering the influence of tectonic stress and pore pressure in the rock [16; 18]. Based on the above assumptions, the drilling simulation experiment is carried out, and the obtained time-drilling rate and time-torque curves are shown in Figure 4. In the process of numerical simulation, it is assumed that the drill bit is a rigid body without deformation. This assumption simplifies the complex mechanical response of the drill bit itself in the simulation process, so that the research focuses on the relationship between the rock and drilling parameters. Secondly, the factor of bit wear is not considered for the time being. Bit wear cannot be ignored in practical engineering. However, the purpose of this simulation is to explore the influence of different initial characteristics of different rocks on drilling. If the influence is not included, the simulation conditions can be more idealized and controllable. Finally, the 'life and death unit' is used in the hypothesis. Its function is to remove the rock unit directly from the model when the rock unit fails to drill. This function makes the drilling rate curve more in line with the changes in the actual drilling process, as shown in Figure 4. After comparing the simulation curve in Figure 4 with the curve obtained from the field test shown in Figure 2, it is found that the change trend of the two is basically the same. It can be seen that the construction of this numerical simulation is reasonable and can provide a reliable basis for subsequent research. In the study of rock mechanics, there are many kinds of criteria to describe the yield behavior of rock. When it comes to the specific type of rock, the Drucker-Prager criterion and Mohr-Coulomb criterion are frequently used in related research and engineering practice. Mohr-Coulomb criterion, as a classical criterion for rock yield judgment, is based on the shear strength theory of rock and plays an important role in many rock mechanics analysis scenarios. The Drucker-Prager criterion [24; 25] is based on the theory of the Mohr-Coulomb criterion and [PERSON] criterion. Based on the expansion, under certain conditions, the Drucker-Prager criterion can achieve mutual transformation with the Mohr-Coulomb criterion.