## 3 Experimental Process of the Cutterhead System
A relatively stable set of data was selected and analyzed for 60 s. Figure 9a-e shows the torque and thrust of the cutter heads in formations 1, 2, 3, 4, and 5. It can be seen from Figure 9f that the torque of the cutterhead increases gradually with the tunneling time. As the cutting depth increases, the contact of the front surface of the cutterhead with the soil layer becomes more thorough, the resistance in front of the cutterhead becomes greater, and the thrust of the cutterhead also increases accordingly. The torque of the cutterhead and the thrust of the cutterhead have the same trend. It is clear that there is a strong correlation between the torque and the thrust of the cutterhead. The torque of the cutterhead measured in the experiment was compared with that obtained from the discrete element simulation. Formation 1 and formation 2 in the formation category were selected, and the simulation data were proportionally reduced through a similar ratio. The comparison results are shown in Figure 10. Due to the stability of the operation on the experimental bench, there are slight differences in the values. It can be found that the torque variation trend of the cutter head is the same, which proves the validity of the discrete element simulation model. It can be seen from the simulation experiment results of the cutterhead excavation that the variation trends of the cutterhead torque and thrust have a certain correlation. To understand the relationship among the operating parameters of the cutter head, the correlation analysis method was used to explore the correlation among the data collected in the tunneling simulation experiment. Among the tunneling parameters, such as the torque of the cutterhead, the thrust of the cutterhead, and the rotational speed of the cutterhead,do not meet the conditions of a normal distribution. Therefore, the Spearman correlation coefficient is adopted. Figure 10: Torque and thrust differences between the experiment and simulation. (**a**) Cutterhead torque; (**b**) cutterhead thrust. Figure 9: Torque and thrust of the cutterhead in five tunneling formations. (**a**) Formation 1; (**b**) formation 2; (**c**) formation 3; (**d**) formation 4; and (**e**) formation 5. (**f**) The average value of five formations. The Spearman correlation coefficient is applicable to measure the relationship between two sequential variables and is suitable for nonlinear or non-normal data types. Since this method is not sensitive to outliers, the magnitude of the difference between the actual values has little impact on the calculation results. It is expressed as follows:  
\[\rho=1-\frac{6\Sigma d_{i}^{2}}{n(n^{2}-1)} \tag{1}\]  
where \(\rho\) is the Spearman correlation coefficient, \(d_{i}\) is the rank difference between variables \(x\) and \(y\) after sorting, and \(n\) is the sample size. A total of 1200 samples from the collected experimental data were selected, and correlation analysis was conducted. The results obtained are shown in Table 6. A correlation coefficient greater than 0.5 indicates a significant correlation. It can be seen from the table that there is a strong correlation between the torque of the cutterhead and the thrust of the cutterhead, the rotational speed of the cutterhead, and the propulsion speed.