# Performance Analysis of Tunnel Boring Machines for
## 2 Data Collection for Performing Statistical Analysis
### Analysis of the Correlations Identified on the Basis of the TBM Type
In general, these two parameters are not very well correlated, as the thrust depends only in part on the diameter, whereas it is mainly conditioned by the geomechanical characteristics of the rock mass. On the other hand, the correlation (R\({}^{2}\) < 0.5) in the single shield TBM is poor. Considering the intersection of the domains of the three functions and examining, therefore, a range of diameters between 2 and 12.5 m, the trend represented by single shield TBMs is always above the other two functions. As for the double shield TBMs, also in this case the correlation is low. However, a model consisting of a power function was considered, with R\({}^{2}\) = 0.4089. The processed data (\(n\) = 77), are correctly distributed along the function up to a diameter of 5 m; in the range 2 to 6 m, the trends of the open and double shield TBMs are very similar. Over 6 m, with the same diameter, the thrust exerted by the double shield TBM is greater than that exerted by the open TBM; however, starting from these values, the dispersion of the experimental points increases considerably. Ref. [43] stated that the trend of the thrust vs. the diameter is linear for double shield machines. This difference, compared to the model described in Figure 3, is linked to the small number of data processed (8) by [43], in addition to the probable difference in geomechanical characteristics of the rock masses analyzed. Figure 2: Correlation between diameter and torque. Red: open TBM; blue: single shield TBM; green: double shield TBM. Thrust and torque in the open TBM are linked by a relationship described by a power function with a high R\({}^{2}\) coefficient, equal to 0.8682. The range of thrust values is 4-28 MN, while the torque is in the range 0-10 MNm. Figure 4 shows that most thrust data are between 4 and 13 MN, distributed with a very small deviation along the regression function. As for the single shield TBM, the data fitting was done with a linear function; in this case R\({}^{2}\) is slightly greater than 0.5, as the available cases were limited to 14. In the double shield TBM, on the contrary, a good correlation is observed. The experimental points (37) are mainly distributed in a thrust range between 3500 and 34,000 kN, with a maximum peak torque of 5200 kNm. In total, two isolated points with thrusts equal to 82,500 and 93,000 kN can be identified, which correspond to torques of 18,700 and 41,000 kNm, respectively. The linear regression function, with R\({}^{2}\) = 0.838, could be more precise if more data were available for thrusts greater than 34,000 kN. The comparison between the three regression functions can only be carried out for thrusts lower than 20 MN. In this range, with the same thrust, it can be noticed that single shield TBMs require a higher torque than the other two types of machines, whose trends overlap. From the study of [42], the correlation between thrust and torque is linear for single and double shield TBM and is instead expressed by a power for open TBM. Figure 5 provides the power-torque trends. The correlation is expressed by a power function for open TBM and single shield TBM and by an exponential for double shield TBM. Open TBMs exhibit a strong correlation between power and torque. A total of 44 data were analyzed, and R\({}^{2}\) is 0.8809. It is also noticeable that single shield TBMs operate with higher torques than the other two. The model approximates the experimental data very well, especially up to 2000 kW. For higher values, the dispersion partially increases, and the torque variation interval increases too. Furthermore, in the power range between 400 and 3000 kW, the curves referring to the open TBM and double shield TBM overlap. In this interval, the power being the same, the gap between single shield TBM and open and double shield TBM increases in terms of torque. Figure 4: Correlation between thrust and torque. Red: open TBM; blue: single shield TBM; green: double shield TBM. Figure 3: Correlation between diameter and thrust. Red: open TBM; blue: single shield TBM; green: double shield TBM.