## 3 Analysis of Numerical Simulation Result
### Analysis of TBM Disc Cutter Model  
#### 3.4.1 Compressive Force Acting on the Disc Cutter  
The cutterhead face could be divided into three zones--center, face, and gauge area. The compressive force acting on a disc cutter depended on its position on the cutterhead. Figure 17 shows the estimated compressive forces acting on all disc cutters to be \(<\)311 kN, the amount allowable on a 19-inch disc cutter. Table 8 shows that the higher compressive forces acted on a few disc cutters (19, 30, 43, 50, and 51) close to the center of the cutterhead, while the lower compressive forces acted on certain other cutters (7, 24, 31, 32, and 49). The five central disc cutters, thus, appeared vulnerable to impact damage during excavation, a trend confirmed by analysis of TBM wear during excavation in the field [3]. To protect the disc cutters from impact damage, those at the center were generally twin- or double- types, with a higher maximum load capacity instead of single disc cutter types.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Case**} & **Operating Condition** & **Average and Standard Deviation of** \\  & **(Cutterhead RPM/Screw RPM)** & **Ratio Per Simulation Time** \\ \hline
1 & 1.0/12.0 & 3.64/0.32 \\
2 & 1.0/9.0 & 3.74/0.27 \\
3 & 1.0/6.0 & 3.71/0.27 \\
4 & 1.5/12.0 & 3.72/0.26 \\
5 & 1.5/9.0 & 3.55/0.20 \\
6 & 1.5/6.0 & 3.44/0.23 \\
7 & 2.0/12.0 & 3.50/0.27 \\
8 & 2.0/9.0 & 3.30/0.21 \\
9 & 2.0/6.0 & 3.23/0.20 \\
10 & 3.0/12.0 & 3.08/0.20 \\
11 & 3.0/9.0 & 3.08/0.19 \\
12 & 3.0/6.0 & 3.02/0.23 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Average and standard deviation of the ratio of compressive force to torque for different operating conditions.  
Figure 17: Average compressive force on each numbered disc cutter.  
Similar to the results for the cutterhead (Figure 13b), the average compressive force on all disc cutters increased as the cutterhead RPM increased, and was estimated to be 16-17% of the compressive force acting on the cutterhead. Furthermore, the total compressive force acting on the disc cutters and cutterhead were estimated to be 37-43% of the actual TBM's maximum thrust (Figure 18).  
Figure 19 shows the dependence of the average compressive force acting on each disc cutter on the cutter's distance from the cutterhead center. The force tended to decrease as the distance increased to ~1750 mm. Moving farther outward from 1750 mm to the gauge area, it increased, remained constant, and then decreased. As there was no opening at the center of the cutterhead, a localized high pressure could emerge that decreased the fluidity of the surrounding soil particles [34]. The high pressure could also greatly affect any centrally placed disc cutter. As the radius from the center increased, the radial opening ratio and the fluidity of the soil particle also increased. The pressure on the disc cutter therefore decreased. However, as the radius from the center increased to 2240 mm, close to the connection between the main spoke and two auxiliary spokes, this connection acted as a barrier to decrease the flow rate. Hence, the compressive force acting on the disc cutter  
Figure 18: Average compressive force acting on all disc cutters with respect to cutterhead RPM.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Rank** & **Disc Cutter Number** & **Location Zone** \\ \hline
1 & 43 & Face \\
2 & 51 & Center \\
3 & 19 & Face \\
4 & 30 & Face \\
5 & 50 & Center \\
47 & 32 & Face \\
48 & 49 & Gauge \\
49 & 24 & Gauge \\
50 & 7 & Face \\
51 & 31 & Face \\ \hline \hline \end{tabular}
\end{table}
Table 8: Disc cutters ranked highest and lowest for compressive force.  
increased abruptly, and the fitted trend line of force with respect to the radius from the center also changed.