Empirical models for estimating penetration rate of tunnel boring machines in rock mass

Tunnel boring machines (TBMs) are one of the most widely used means of excavating tunnels in rock masses in a more economical, faster, and safer manner. Despite the recent technological advances in tunneling, a reliable estimation of the TBM rate of penetration (ROP) still remains a challenging task. This study aims to develop empirical models for predicting the ROP, which can be applied to a variety of rock mass conditions. A large database with 557 instances of TBM performance parameters including the rock mass properties such as rock strength and frequency of discontinuity, machine specifications and ROP, was established. To account for the effect of the discontinuity on the ROP a rock mass fracture index is introduced via a weighting method and used in the model formulation. Numerous linear and nonlinear multiple regression models were developed; the five most accurate models were selected, and their performances were compared using the values of performance indices and the total ranking method. The results indicate that the best model is the non-linear multiple regression models that has fewer input variables and the best estimation result (total score ranking of 42, Eq. 9) in comparison with others. It was concluded that the proposed models relating the intact rock strength, the weighted fracture index in rock mass, and TBM specifications including cutter force, rotation speed and cutterhead diameter could be confidently used for TBM tunneling.