Diameter-independent indices for TBM rock-mass classification

The rock mass classification index for TBM tunneling serves as a critical basis for machine selection and construction control. Existing methods predominantly rely on empirical stability grading of rock masses, lacking explicit mechanical basis, while in-situ testing incurs high costs and exhibits limited applicability across tunnel conditions. Addressing these issues, this paper establishes a force model for the cutterhead rock-breaking process based on the rock-TBM interaction mechanism. Building upon existing thrust- and torque-related indicators, this study unifies and refines their penetration characterization methods, introducing the Diameter-independent Force Penetration Index (DFPI) and the Diameter-independent Torque Penetration Index (DTPI). These metrics mitigate the influence of equipment variations and human manipulation, enabling stable characterization of rock-cutting difficulty under diverse ground conditions based on actual TBM operational response. Based on data analysis from five typical projects, including ZX, ABH, KS-Ⅶ, XE-VIII and GLGS, quantitative analysis of the statistical characteristics of DFPI and DTPI in different rock mass categories. Results demonstrate that both indices exhibit good stability, monotonicity, and inter-class separability across tunnel conditions. Within the same rock-mass class, the CV ranges of DTPI and DFPI are 0.13–0.35 and 0.14–0.26, respectively, confirming their cross-diameter comparability. Building on this, a two-dimensional Bayesian rock-mass classification model was developed using DFPI and DTPI data from four projects (ZX, ABH, KS-Ⅶ, GLGS), and its applicability was validated using independent data from the YCJL and XE-VIII projects. To further meet rapid on-site identification needs, this study constructed a one-dimensional composite index χ U based on Bayesian posterior probability weighting and normalization. Combined with kernel density estimation to extract rock mass classification thresholds, this formed directly applicable discrimination rules. Results indicate that rock mass Class IV corresponds to χ U values between 0.651 and 1.270, while Class III corresponds to χ U values between 1.270 and 1.661, enabling rapid classification. Overall, the study delivers a cross-diameter rock-mass identification workflow that links rock–machine interaction modeling to transferable classification boundaries and field-deployable threshold rules, providing a practical basis for TBM design/selection and real-time parameter decision-making.