# Performance Analysis of Tunnel Boring Machines for
## 1 Introduction
The main goal of the CSM model is to estimate the total thrust, the torque and the power of the TBM; these values are then compared with the machine design parameters; through iterative calculation, assuming each time a different value of p, the maximum penetration p achievable in a given rock mass with a given TBM can be evaluated. All the references above belong to research that can differ from each other, but that are commonly based on a direct approach to the problem (information about the productivity of the machine is provided taking into account the parameters of both the machine and the rock). However, it is worth mentioning another type of approach, which could be defined indirect, capable of deriving predictive models based on the statistical analysis of real excavation cases [30; 36; 37; 38; 39; 40; 41], developed predicting models based on that approach. The equations obtained, resulting from the statistical treatment of real data, also take into account the characteristic parameters of the TBMs, such as diameter, thrust, torque, and power. The equations are useful for leading engineers to choose the best machine in a given geological context. Unfortunately, the weakness of the indirect approach cannot be overlooked, databases must be constantly updated according to new construction sites. Ref. [42] conducted a statistical analysis on a database consisting of design parameters of 262 TBMs (72 open, 24 single shield, 41 double shield, 86 Earth Pressure Balance EPB, and 39 slurry TBM) that refer to projects implemented since 1985 around the world. The study analyzes potential correlations between TBM diameter, thrust, torque, total machine weight, head rotation speed, and number of tools on the cutterhead. Some parameters are well correlated, then forecasts for design purposes could be made. To this end, the authors validated their models by comparing the estimated parameters with the TBM data used to carry out 30 projects in Turkey in different geological contexts. The statistical treatment of the data was carried out, and different regression functions were evaluated to find the best fitting. The function with the highest correlation value was selected and chosen as the forecast equation. [PERSON]. [43] conducted a study whose goal was to evaluate the correlations between TBM diameter and design parameters (thrust, torque, power, rotational speed) to obtain prediction equations for different types of TBM and in different geological conditions. Studies by [42; 43] are the most recent but still not updated to the present day. In addition to this drawback, the need for tools capable of guiding tunnel construction companies to the choice of the right machine for a given excavation work becomes crucial, since a wrong choice could lead to a reduction in excavation performance and consequently an increase in time and construction costs. In light of these needs, this paper analyzes a larger and more updated database. In total, 270 TBM data, with a diameter greater than 6 m, used to carry out tunnel projects in various parts of the world were analyzed. Regression analysis was also done in cases where less than 10 data were available, although being understood that the significance of the model needs to be refined with further research. A total of three different geological conditions were also considered: soft ground, mixed ground, and rock. As for the correlation between diameter and thrust, 90 data were analyzed. Open and single shield machines were not part of the analysis due to lack of data. The results show a strong link between diameter and thrust, mainly for soft ground conditions. The studies by [42; 43] were adopted for comparison purposes while the validation of the study was proposed in a real case, represented by the Moncerisio base tunnel. Finally, the authors want to underline that this research is not intended for the final choice of a TBM in the execution phase of a project, but it can be a valid tool in the design phase.