# Performance Analysis of Tunnel Boring Machines for
## 2 Data Collection for Performing Statistical Analysis
### Analysis of Correlations Based on the Type of Rock Crossed
#### 2.2.1 Open TBM  
Data relating to the excavation in granite and gneiss were available for open TBMs. The diameter of the machines examined varies between 3 and 10 m. For both types of rocks, the correlation between the diameter and the power supplied to the head is linear (Figure 8). In the case of gneiss, the number of data analyzed is higher (30) and the dispersion is greater; in fact, a given diameter often corresponds to several power values, showing that engisses have mechanical properties different from each other. The regression equations identified have, in both cases, a medium-high correlation coefficient. The data available about the trend of the thrust as a function of the diameter refer to case studies carried out in granite, gneiss, and shale, and the trends obtained are shown in Figure 9. As for granite, the regression function identified is logarithmic with a very high R\({}^{2}\), greater than 0.9. The experimental data are perfectly approximated by the function, and this suggests that the geomechanical properties of the granite are very similar in the different cases analyzed (n. 13). The TBM diameter varied from 3 to 8 m, which corresponds to thrusts between 5 and 17 MN. As for the gneiss, the regression function is an exponential, with R\({}^{2}\) greater than 0.8. Additionally, in this case, the experimental data are represented very well by the function, with a very small deviation. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Granite** & **Gneiss** & **Schist** & **Limestone** & **Sandstone** \\ \hline Diameter (m)—Power (kW) & 19 & 24 & 21 & 38 & 27 \\ \hline Diameter (m)—Torque (kNm) & 20 & 12 & 33 & 23 & 22 \\ \hline Diameter (m)—Thrust (kN) & 11 & 8 & 21 & 35 & 17 \\ \hline Power (kW)—Torque (kNm) & 13 & 7 & & 17 & 14 \\ \hline Power (kW)—Thrust (kN) & & 7 & 16 & & \\ \hline \end{tabular}
\end{table} 
Table 2: Number of cases found in the literature to compare the main parameters of the TBM analyzed as a function of the rock mass crosse. Figure 7: Correlation between the diameter and the rotation speed of the head. Red: open TBM open; blue: single shield TBM; green: double shield TBM. The diameter of the machines examined varies between 3 and 10 m, with thrusts in the range between 5 and 28 MN. As for shale rocks, low correlations were almost always obtained in the case studies examined. The equation is linear and was taken from 24 pairs of parameters. R\({}^{2}\) coefficient, slightly higher than 0.5, is low compared to expectations, since almost all the data available fall within a very small diameter range, between 3 and 6 m. Therefore, several thrust values correspond to a given diameter, which implies that the excavations have been performed in rocks with variable mechanical characteristics. The diameter and the torque are also very well correlated in granites. the experimental points can be represented by an exponential function with a coefficient R\({}^{2}\) greater than 0.9 (Figure 10). The correlation is also very high in greisses, except for a diameter of about 10 m, where four different torque values can be observed. In all other cases, the torque increases linearly as the diameter increases. The equation that expresses the correlation between the diameter and the torque in the shale is logarithmic. The R\({}^{2}\) coefficient is very low compared to expectations, since almost all the available data fall within a very small range of diameters, between 3 and 5 m. Therefore, for the same diameter, more torque values are noticeable, which derive from having carried out the excavation in rock masses with variable mechanical characteristics. The last correlation analyzed in granite rocks is between the power at the excavation head and the torque (Figure 11). The 11 experimental points are approximated by an exponential function with an R\({}^{2}\) coefficient greater than 0.9. The head power varies between 700 and 4400 kW, which corresponds to torque values between 400 and 11,000 kNm.