# A Theoretical Method and Model for TBM Tunnelling Trajectory Adjustment
###### Abstract  
TBM tunnelling trajectory adjustment is a significant issue in guaranteeing a tunnel project. This paper proposes a theoretical method of trajectory adjustment aimed at synchronously reducing bias angle and distance. The proposed method can be divided into three steps. First, the need for manual intervention in the tunnelling trajectory is determined based on the current bias angle and distance. Next, if manual intervention is required, a theoretical relationship is established using the current bias angle and distance as an input and the rotated angle of the TBM main beam as an output. Finally, a series of constraints according to the normal working conditions of the TBM are incorporated into the method. These constraints ensure that the method remains within the acceptable range of TBM operation. Using mechanical parameters such as the cutterhead diameter and cutter spacing of the TBM used in the sixth section of the Qingdao Metro Project, a model suitable for the project is established, and the model is modified by the tunnelling trajectory data collected in the field. This method provides a reference for TBM drivers to use to correct the tunnelling trajectory while considering the specific conditions of the project. t 202330  
and this model can be used to predict the TBM tunnelling direction [7]. In addition, many researchers, such as [PERSON] et al., [PERSON] et al., and [PERSON] et al., made efforts with great reference value [3; 8; 9; 10; 11; 12]. These research studies provide valuable insights and references for TBM trajectory adjustment. In contrast, the second category focuses on macroscopically designing the tunnelling trajectory in order to make it close to the expected route. For example, [PERSON] et al. established an LSTM real-time tunnelling deviation prediction model. Compared with the model only based on theoretical analysis, the analyzing process of this model includes the geological factors [13]. [PERSON] et al. incorporated the Grey prediction (PID) strategy into the TBM trajectory adjustment and built a trajectory adjustment dynamic model which can optimize the tunnelling trajectory in real time by analyzing the difference between the current and expected tunnelling direction [14]. [PERSON] et al. proposed a strategy for controlling the TBM tunnelling trajectory using the hydraulic thrust system principle and hydraulic load simulation test, and the tunnelling direction and position were well controlled using this method [15]. [PERSON] et al. conducted kinematic analysis of the thrust system of the TBM and developed a control system for the multiple thrust cylinder system of the TBM, and this is useful for controlling the TBM attitude [16]. In addition, other studies conducted by researchers are helpful with this problem [7; 17; 18; 19; 20; 21; 22; 23; 24]. This research belongs to the second category, aiming to optimize the tunnelling trajectory to closely match the expected route and simultaneously eliminate deviations in distance and direction. The proposed method can obtain a feasible region of the rotated angle of the main beam used to adjust the tunnelling trajectory according to the current bias angle and distance. The method consists of three steps. First, the need for manual intervention in the tunnelling trajectory is determined based on the mode of tunnelling attitude. Then, in cases requiring manual intervention, a theoretical relationship between the current bias condition (bias angle and distance) and the rotated angle of the main beam used for controlling the tunnelling trajectory is established. Finally, several constraints are established based on the requirements for the normal operation of the TBM, and a feasible region for selecting the rotated angle is obtained. This feasible region serves as a reference for the TBM driver to adjust the tunnelling trajectory, allowing them to select a suitable rotated angle within the obtained feasible region. This paper is organized as follows: Section 2 introduces the TBM tunnelling trajectory adjustment method.