## 2 Numerical Model
### TBM Numerical Model  
Drawings of the 7.73 m EPB shield TBM from the Japanese company were used for the 3D TBM model. The TBM model was created with the 3D AUTO CAD software,  
Figure 1: 3D simulation of direct shear test showing (**a**) the numerical model and (**b**) the numerical results.  
Figure 2: Comparison of geotechnical design parameters and numerical simulation results based on the Mohr–Coulomb failure criteria.  
and comprises six parts--cutterhead, disc cutters, cutter bits, chamber, shield, and screw conveyor (Figure 3). The opening ratio of the cutterhead was \(\sim\)24.25%. Table 3 lists the specifications for each part. The interaction parameters between the TBM and the particles were not considered in this study. Each disc cutter on the cutterhead face was fixed without rotation during excavation.  
Eight plate geometries are created and placed in the form of a box to be filled with particles for the ground model. One of the plates located on the +x-axis was designed with a hole of the same diameter as the TBM. Once all plates were arranged, the TBM geometry was initially introduced into the hole by nearly 400 mm. About 400,000 particles were then randomly generated and stacked by gravity. A further 52,000 particles were generated in the chamber and screw conveyor to represent TBM excavation. The top and bottom of the ground boundaries were set as parallel boundaries. Once these works were complete, an additional, fixed, overburden load of 265 kPa was applied. It was also applied continuously to the top plate by the servo control during excavation. As a result, a rectangular parallel-piped ground model of size 1.5 m (width) \(\times\) 15.6 m (length) \(\times\) 14.6 m (height) was created over the stabilization time (Figure 4).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Information Type** & **Property** & **Description** \\ \hline \multirow{2}{*}{Disc cutter} & Size (diameter) & 483 mm \\  & Quantity & 51 pcs \\ \hline \multirow{2}{*}{Cutter bit} & Size (width \(\times\) height \(\times\) length) & 75 mm \(\times\)100 mm \(\times\)120 mm \\  & Quantity & 167 pcs \\ \hline \multirow{3}{*}{Cutterhead} & Size (diameter) & 7730 mm \\  & Length & 750 mm \\  & Opening ratio & 24.25\% \\ \hline \multirow{2}{*}{Chamber} & Size (diameter) & 7730 mm \\  & Length & 700 mm \\ \hline \multirow{2}{*}{Shield skin} & Size (diameter) & 7730 mm \\  & Length & 8500 mm \\ \hline \multirow{2}{*}{Screw conveyor} & Installation angle & 25.0\({}^{\circ}\) \\  & Pitch & 750 mm \\ \cline{1-1}  & Size (diameter) & 900 mm \\ \hline \hline \end{tabular}
\end{table}
Table 3: EPB Shield TBM model information.  
Figure 3: Front and side view of the 3D TBM model.  
Based on the EPB shield TBM's technical specifications, its advance (translational motion) was modeled under different rotational motion conditions. Excavation was simulated for 360 s under 12 combinations of conditions--four cutterhead RPMs and three screw conveyor RPMs. The TBM advance was simulated at \(\sim\)20 mm/min (Table 4). As there were no particles around the shield skin, the interaction between the shield skin and the particles was not considered in this study.