# A Theoretical Method and Model for TBM Tunnelling Trajectory Adjustment
## 6 Conclusions  
This study introduces a theoretical method for adjusting the tunnelling trajectory of a TBM. It calculates a feasible region for the rotated angle of the main beam, which controls the tunnelling trajectory based on the current bias angle and distance. The model is developed using the mechanical parameters of the TBM used in the sixth section of the Qingdao Metro Project and is validated and refined using field trajectory data from the same project. The main conclusions of this study are as follows.  
A method for adjusting the TBM tunnelling trajectory is proposed, and it takes the current bias angle and distance as an input and determines the rotated angle of the main beam as an output. Through theoretical calculations, the relationship between the input and output is established. Additionally, a set of constraints is proposed based on the normal working conditions of the TBM, limiting the feasible solutions to a specific region known as the feasible region. The calculated feasible region can serve as a reference for TBM drivers to control the tunnelling trajectory, thereby eliminating deviations in distance and direction.  
The proposed method involves several unknown variables that represent the TBM's mechanical parameters, such as the cutterhead diameter and cutter spacing. These unknown variables are determined based on the TBM used in the sixth section of the Qingdao Metro Project, and a trajectory adjustment model is developed accordingly. To test this model, an example with an assumed bias angle and distance is presented, and the corresponding feasible region is calculated.  
Furthermore, trajectory data are collected from the same project in order to test and refine the proposed model. The results indicate that the constraints on the total tunnelling distance used in the original model are too strict, resulting in the rotated angle of the main beam in the field falling outside the feasible region. Therefore, a modified model with looser constraints is proposed, incorporating multiple levels of feasible regions based on the difference in total tunnelling distance.  
These findings contribute to the understanding and practical application of TBM tunnelling trajectory adjustment, providing valuable insights for future projects.  
Methodology, R.W.; validation, R.W. and L.Z.; formal analysis, R.W. and L.Z.; field investigation, R.W. and L.Z.; data collection, R.W. and L.Z.; writing--original draft preparation, R.W. and L.Z.; writing--review and editing, R.W. and L.Z.; writing--figures and tables, L.Z.; funding acquisition, R.W.. All authors have read and agreed to the published version of the manuscript.  
The research was funded by the Natural Science Foundation of Shandong Province (No. ZR202103010903) and the doctoral fund of Shandong Jianzhu University (No. X21101Z).  
Not applicable.  
Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the requirements of the third party, also the partner of this paper.  
The authors declare no conflict of interest.