## 5 Engineering Cases and Comparative Analyses
### Hard-Rock Cutting Cases and Analyses
The project overview is shown in Table 1.  
Cutters for tunnelling projects are often sampled in 17-inch and 19-inch sizes, and the cutters are of homogeneous H13 hot-worked abrasive steel material [40]. The cutter body material has good wear and impact resistance, and the performance parameters of the cutter material are shown in Table 2.  
For the same shield distance, the wear varies with the installation radius of the cutter, and the fitting study of the data is shown in Figure 20. And Figure 20a shows the wear depth with an increasing radius for different-strength rock types, but the growth rate \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{3}{c}{**Project Cases**} \\ \cline{2-4}  & **NTNU Case** & **SJTU Case** & **TUM and BJU Cases** \\ \hline Project location & North-central Europe & South Asia & Central Europe and East Asia \\ Approximate tunnel length (km) & 7.0 & 4.3 & 2.4 \\ Rock samples & Granite & Basalt and breccia & Marble and granite \\ Rock strength range & High–extremely high & Medium–very high & Medium \\ UCS (MPa) & \(\geq\)120 & 80–120 & 40–80 \\ Rock density (g/m\({}^{3}\)) & 2.6–2.7 & 2.8–3.0 & 2.6–3.3 \\ Tunnel diameter (m) & 7.2 & 6.6 & 6.5 \\ Disc cutter diameter (mm) & 483 & 483 & 483 \\ Cutter head rotation speed (rpm) & 0–8.7 & 0–7.0 & 5.5–8.0 \\ Cutter thrust (kN) & 1400 & 1070 & 214 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: TBM boring parameters and hard-rock geological characteristics of shield engineering [8; 26]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Disc Cutter Ring Material Properties** & **Value** \\ \hline Density (kg/m\({}^{3}\)) & 7850 \\ Young’s modulus (GPa) & 210 \\ Poisson’s ratio & 0.3 \\ Hardness HRC & 57 \\ Uniaxial compressive (MPa) & 2560 \\ Angle of the disc cutter ring (\({}^{\circ}\)) & 26 \\ Ultimate load (MPa) & 250 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Calculated parameters for disc cutter ring materials. decreases gradually. The strength of cutting hard rock is 40-80 MPa, the actual maximum wear depth reaches 23.7 mm, the error between the theoretical value and the actual value is 10.3%, and the error of the theoretical prediction model of wear considering the thermal effect is about 5.4%. Figure 20b shows a strength of 80-120 MPa for hard rock, the maximum depth of wear reached 25.8 mm, the theoretical value and the actual value of the error is about 15.4%, and, considering the thermal effect of the wear, the prediction error is 3.7%. Figure 20c shows hard rock with a strength higher than 120 MPa, the maximum wear depth is 34.1 mm, the theoretical error is about 13.7%, and the error of the prediction model considering the thermal effect is about 5.1% of the theoretical. The cutter wear of hard-rock cutting is a power function relationship with the increase in rock strength. The prediction model considering the thermal effect is closer to the actual value, and the error is within a reasonable range. Scholars [PERSON] et al. showed that the cutter ring wear is directly proportional to the rolling distance [12]. [PERSON], [PERSON] et al. counted the variation in cutter wear with the rolling distance in the Mumbai tunnel [15] and found that radial wear is not strictly linear with its rolling distance. The comparative study is shown in Figure 21, where the cutter moves in a spiral motion with the same installation radius, and the radial wear of the cutter is the same. The shield distance of the cutter with the same installation radius is the same for each rotation of the cutter, and \(L=3\) km is selected for analysis. \(R=1650\) mm, the  
Figure 20: Distribution of wear depth with installation radius. (**a**) Radial wear fitted and comparative study of [PERSON] 2008 [12] and [PERSON]. D 2021 [1], UCS = 40–80 MPa. (**b**) Radial wear fitted and comparative study of [PERSON]. H 2021 [15], UCS = 80–120 MPa. (**c**) Radial wear fitted and comparative study of [PERSON] 2016 [2], UCS \(\geqeq\) 120 MPa.