## 3 Dynamic Cutting Model of the Cutterhead  
### Description of Model  
In order to study the mechanical properties of the cutterhead in composite strata, a dynamic cutting model including calculations of the thrust, torque, and power is developed. The program consists of five main modules. The data reading module reads the pre-stored coordinate data from excel into the memory of Python. The plotting module displays the contour of the excavation surface, the stratigraphic boundary, and the initial position of the cutters in Python. The dynamic cutting module converts the cutting process of the TBM  
Figure 6: Diagram of frontal and lateral forces on the cutterhead. cutterhead on the excavation surface into a circular rotation of each cutter with the center of the cutterhead. During this module, the cutter numbers in both strata are recorded in real time. The parameter calculation module is to obtain the change in each tunneling parameter during the advance of the TBM by inputting the machine, cutter, stratum, and working parameters and combining them with the theoretical calculation model in the previous section. The data statistics output module outputs the values of tunneling parameters obtained in the previous module and uses MATLAB version 2017 to draw the change curve of tunneling parameters, and it is observed that the trend of the curve can roughly reflect the running state of the machine in the process of tunneling. The schematic representation of the basic algorithm for the program is shown in Figure 7. The program, which can simulate the EPB TBM cutterhead cutting system, is created and runs smoothly using the Python version 3.8, as shown in Figure 8. The feature of this model is that it cannot only simulate the arrangement of each tool on the TBM cutterhead used in different actual projects but also change the position and proportion of each stratum according to the geological conditions. In this research, we investigate a cutterhead equipped with 64 drag cutters and 39 disc cutters in the RSI composite strata. The cutters and stratigraphic demarcation lines are placed at the appropriate locations, and each point is numbered. As shown in Figure 8a, the red line represents the dividing line between soft and hard strata (soft strata on the left and hard rock on the right), the green points indicate the disc cutters, and the blue points indicate the drag cutters. The locations of the cutters shift when the cutterhead rotates in the different geological conditions. Figure 8b shows the cutters' position after 10 degrees of cutterhead rotation, where the gray dots are the original positions of the cutters. The specifications of the EPB TBM and the parameters of the cutters are shown in Table 1, and the mechanical properties of the two geologies are shown in Table 2. During the program running, the system recognizes the numbers of the disc cutters and drag cutters in the soft and hard strata, respectively, and calculates the forces of all cutters during the cutting process using our theory. Combining with other partial forces (friction, chamber pressure, etc.) calculated by the system, the variation in thrust, torque, and power can be produced. The results of the model calculations are presented in the next section. Figure 7: The schematic representation of the basic algorithm for the program. (* represents different tunneling parameters).