Theoretical considerations of field penetration index model and its application in TBM performance prediction

Field penetration index (FPI) is a representative key indicator for tunnel boring machine (TBM) performance estimation, however its application in real tunneling projects is still limited because of the lack of some theoretical knowledge on the relationships between FPI, rock mass properties, and TBM specifications. This study aims to establish a theoretical FPI model by analyzing the tool–rock interaction of disc cutters from a theoretical perspective. This was first done by comparison of the tool–rock interaction of the disc cutter with that of the polycrystalline diamond compact (PDC) bit, which indicated that they share similar rock breakage mechanisms and force equilibrium. A series of cutting tests were then conducted on granite, marble, and limestone to determine the relationship between rotary torque and applied thrust during the rock cutting. Referring to the test results and tool–rock interaction features of the PDC bit and disc cutter, a theoretical FPI model of the disc cutter was derived and verified using the field TBM performance dataset. It was found that the rotary torque was linearly correlated with the thrust but independent of the rotation speed during the rock cutting. In addition to the machine specifications’ contribution, rock mass parameters and abrasiveness purely control this linear relationship. The theoretical FPI model proved that FPI shows a strong positive linear relationship with rock mass properties (uniaxial compressive strength and rock integrity), even under different drilling conditions, providing a theoretical basis for empirical FPI model establishment. Therefore, in practical engineering, it is recommended to use multi-parameter rock mass classification system values—such as rock structure rating (RSR), rock mass rating (RMR), and tunneling quality index(Q)—instead of individual rock mass properties —such as uniaxial compressive strength, to establish or update semiempirical FPI models.