# A Geometric Model for a Shield TBM Steering Simulator
## 2 Overview of the TBM Steering System for Curved Excavation  
Thrust and articulation jacks are used for TBM steering. For straight or almost straight excavation, only the thrust jack can be used, with the jacks being extended simultaneously at the same rate, allowing the TBM to move forward. However, if the tunnel alignment comprises a straight line with a tightly curved line, both thrust and articulation jacks are used together, depending on tunnel line conditions. In this case, the articulation jacks change according to a predetermined articulation angle before the thrust jacks are extended. Curved excavation with a TBM steering system generally includes several operations, i.e., a copy cutter, an articulation jack, and shield jack operation. The first overcutting secures adequate room for curved excavation, then the articulation jacks are extended to steer the front shield with the cutterhead in the target direction. Finally, the extension of the shield jacks moves the TBM forward. Copy cutter operation was not considered in this study, and operations in curved excavation are repeatedly executed as follows:  
1. Extension of articulation jacks to the target articulation angle;Extension of shield jacks to the segment width;
* Return of articulation jacks to the original position;
* Return of shield jacks to the original position;
* Installation of segment ring;
* Repetition of step 1. Shield jack extension differences, by one-sided extension and the use of tapered segments, are required for successful curved excavation [4]. Here, we assumed that the shield jacks are extended equally, simultaneously, and at the same rate. There are two types of articulation systems: the 'V' and 'X' types, with the main difference between them being the location of the articulation point. In the V-type system, articulation jacks are extended in the opposite direction to that of the curve, with the articulation point being located opposite the extended jack. The X-type system involves the extension and retraction of the articulation jack simultaneously during articulation, with the articulation point always being at the center of the shield (Figure 1a). In the X-type, a rotation pin is located at the articulation point to connect the front and middle shields. Because the pin is on the articulation point, it is possible to maintain the gap between both shields during articulation, with this being suitable for articulation sealing and water-resistance during articulation, although fewer articulation angles can be controlled than with the V-type. In the V-type system, the articulation point is on the shield skin plate during articulation. As there are no connected pins in the system, it is easy to rotate through any articulation angle in any direction. However, as the articulation angle increases, the gaps between shields also increase and it is difficult to prevent the inflow of much and water during articulation [7; 8; 9]. As shown in Figure 1b, there are two types of thrust system: reaction force at the front shield and reaction force at the middle and tail shields. The latter is generally more appropriate for curved excavation; it can supply a constant thrust force to the segment ring without eccentric force, regardless of the rotation of the front shield [7; 8; 9]. In three-dimensional space, at least three reference points should be used for TBM positioning systems to report TBM behavior during its advance. The front reference point is located on the plane of the shield face, and the rear left and rear right points are on the rear of both sides, on the plane of the shield face (Figure 2). TBM operators attempt to follow the planned alignment by monitoring reference points. Owing to ground properties and machine weight, pitch, yaw, and roll rotations are inevitably generated during TBM advance (Figure 3a). Pitching means that the direction of shield advance deviates up or down, causing vertical deviations (Figure 3b). Yawing means  
Figure 1: Two types of steering system (modified from [PERSON] et al.