## 2 Methodology of the Tunneling Simulation
### Discrete Element Simulation  
The DEM is utilized to calibrate the stacking angle. The stacking angle is known as the repose angle, which is maintained by the conical material pile when granular materials are freely stacked on a plane. The maximum angle between the slope surface of the material and the plane is called the maximum stacking angle. For loose granular materials, the natural repose angle is approximately equal to the peak friction angle of the soil. Therefore, the internal friction angle of the particles can be estimated through the accumulation angle experiment. The process of staking angle measurement is shown in Figure 1.  
In order to reduce the errors caused by manual operation, when conducting the stacking angle experiments of the three types of particles above, the stacking angle experiments of each type of particle were repeated in three groups, and the average value of the measured stacking angles was taken as the stacking angles of each type of particle, as shown in Table 1. By consulting the geological exploration report and relevant materials, intrinsic parameters such as density, Poisson's ratio, and shear modulus of the three types of particles can be obtained, as shown in Table 2.  
The simulated experiments on the stacking angles of three types of particles involved sand, pebbles, and gravel. To eliminate the randomness of the simulation, after comparison and multiple simulation exercises, the stacking angles, recovery coefficients, static friction coefficients, and rolling friction coefficients of the three particle materials were finally determined, as shown in Table 3.  
Figure 2 is a schematic diagram of the speed of particles entering the soil chamber and the tunneling face of the cutterhead. The color changes in the figure reflect the speed changes in particles entering the soil chamber. When the cutter head system is being excavated, the particle movement at the face is relatively intense. In the later stage of the simulation, the particle movement is stable. It can be observed that the particle velocity is large in the part where the screw conveyor extends into the soil bunker. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Particle Type** & **Average Value of Stacking Angle** \\ \hline Sand & 32.6\({}^{\circ}\) \\ Pebble & 35.2\({}^{\circ}\) \\ Gravel & 34.5\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Particle stacking angle. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Particle Type** & **Density (kg/m\({}^{3}\))** & **Poisson’s Ratio** & **Shear Elasticity (Pa)** \\ \hline Sand & 1860 & 0.33 & 4.8 \(\times\) 10\({}^{6}\) \\ Pebble & 2400 & 0.25 & 4 \(\times\) 10\({}^{7}\) \\ Gravel & 2200 & 0.26 & 4.2 \(\times\) 10\({}^{7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Intrinsic parameters of three types of particles. Figure 1: Simulated and experimental determination of the stacking angle. Combining the simulation effect and calculation time, after adjustment, the selected particle diameter was 60 mm. The particle shape was circular particles. After the filling of each particle was completed, the particle wall was left to stand for 20 s. The tunneling speed of the cutter head system was set to 60 mm/min, the rotational speed of the cutter head to 1.6 r/min, and the rotational speed of the screw conveyor to 9 r/min; the step size was set to 20%. The simulation time for each group was set to 400 s, the data storage interval was set to 1 s, and the mesh particle size was set to 3R. Tunneling simulations were conducted in single-particle formation for three types of particles (sandy soil, gravel, and pebbles). Due to the discontinuous distribution of pebble layers in the formation, it was also necessary to conduct tunneling simulation of composite particle formation. The formations of sand--gravel, sand--pebbles, gravel--pebbles, and sand--gravel--pebbles were set up. The proportion of particles in the two types of formations was 50% each, and the proportion of particles in the three types of formations was 33.3% each.