## 3 Analysis of Numerical Simulation Result  
The TBM performance indicators of compressive force, pressure, torque, wear, and mass flow rate were evaluated from the simulation.  
The compressive force was determined from the sum of the normal contact force magnitudes (Figure 5a). This sum was calculated from the product of the average normal contact force and the contact frequency at data write-out points. The normal contact force was obtained from two bodies in direct contact and acted perpendicular to each body. The pressure was determined from the compressive force and the geometry's surface area, which was composed of structured meshes [31].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Part**} & \multicolumn{2}{c}{**Translational Motion**} & \multicolumn{2}{c}{**Rotational Motion**} & \multirow{2}{*}{**Operating Time [s]**} \\ \cline{2-2} \cline{4-6}  & **Direction** & **Velocity** & & **Velocity** & **Vine \\  & **[mm/min]** & **Direction** & & **[rev/min]** & \\ \hline Disc cutter & & & & 1.0 & 0–90 \\ Cutter bit & \(-x\) axis & 20 & \multirow{2}{*}{Clockwise} & 1.5 & 90–180 \\ Cutterhead & & & & 2.0 & 180–270 \\ \hline Chamber & & & & 3.0 & 270–360 \\ Shield skin & \(-x\) axis & 20 & - & - & 0–360 \\ \hline Screw auger & \(-x\) axis & 20 & \multirow{2}{*}{Clockwise} & 12.0 & 0–30, 90–120, 180–210, 270–300 \\  & & & & 9.0 & 30–60, 120–150, 210-240, 300–330 \\  & & & & 6.0 & 60–90, 150–180, 240–270, 330–360 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Operating conditions for simulated advance of the TBM.  
Figure 4: Side and rear views of the simulation model. 3. Simulation model.  
Wear is defined as the gradual loss of mass from the movement of a body's surface, arising from its relative motion [32]. Relative wear of the cutterhead, cutting tools, and screw conveyor was analyzed using a relative wear model based on energy. Although there are various kinds of wear, impact wear (defined as the normal force on each element of the geometry) was selected for wear evaluation. Based on the energetic approach, the total normal contact energy was derived as follows:  
\[E_{n}=\sum\lvert F_{n}V_{n}\delta_{t}\rvert \tag{1}\]  
where \(E_{n}\) is the normal cumulative contact energy, \(F_{n}\) is the normal contact force, \(V_{n}\) is the normal relative velocity, and \(\delta_{t}\) represents each time interval.  
The energy approach shows that the disc cutter's impact damage could accumulate as energy and gradually increase over time [33]. The variation of the normal cumulative contact energy of the geometry (from the beginning of excavation) was used to indicate the impact wear.  
The muck discharge rate was defined as the mass flow (kg/s), owing to the rotation of the screw conveyor--it was the total mass of particles per unit time measured and recorded by a mass-flow sensor (Figure 6). The sensor's domain in the x-direction was set at 770 mm and fixed relative to the TBM shield geometry.  
The torque on the geometry was the product of the tangential contact force between two bodies and the distance from the center of mass to the contact point (Figure 5b). The tangential force was the force from the tangential overlap. The total torque was calculated from the torque and moment around each geometry element. The sum of the torque from each element was converted to the total torque on the entire geometry about the center of mass, and was plotted along the selected axis [31].  
Figure 5: Definition of attributes on the performance indicator, showing (**a**) compressive force and (**b**) torque.