# Optimization Study on Longitudinal Joints in Quasi-Rectangular Shield Tunnels
## 1 Introduction  
The mechanized shield tunneling method has the advantage of a smaller environmental influence when compared with conventional tunneling methods (e.g., open cut method and blasting), and it has been widely used in urban underground space construction, from drainage tunnels to subway tunnels [1, 2]. Longitudinal joints between segments divide the cross-section of a lining structure into several parts. For a certain lining shape and a given lining thickness, the joint configuration is the main factor affecting the overall lining stiffness and its deformations [3, 4, 5, 6, 7]. Moreover, the longitudinal joint is also the most critical part, as the lining failure is initiated by joint damage, which causes water leakage and other detrimental distress [8, 9, 10, 11]. Therefore, the choice of the joint type is of great importance when a shield tunnel is designed. There are two types of longitudinal joints for concrete segments connected by bolts, i.e., joints with or without preinstalled panels. In conventional circular shield tunnels, joints without panels are commonly used, as shown in Figure 1a. In order to avoid damage of the concrete near the joint, the bolt installing hole cannot be very deep in the direction to the outer segment side or very close to the joint section. This means that the possibilities of adjusting the bolt installing hole are very limited. Studies about this joint type have been conducted through experiments, simulations, and theoretical analyses [10; 12; 13; 14]. In the joint type shown in Figure 1b, the joint panels are embedded into the concrete of the segments with connecting reinforcement. The panels are commonly made from ductile iron [15], and the ductile iron joint panels (DIJPs) can be cast into different shapes to achieve a more flexible bolt positioning. Joints with DIJPs have been adopted in water conveyance tunnels [16; 17; 18]. As small circumferential stresses might occur in water conveyance tunnels due to the changes of the inside water level, more bolts are needed to prevent the joints from opening [19; 20; 21]. However, fewer studies have been conducted for this joint type. Another important aspect is the fact that when a shield tunnel crosses a city center, the choice of the cross-section for the tunnel affects the extent of environmental influences and building or foundation settings related to tunnel construction. Quasi-rectangular shield tunnels, which have a narrow excavation width by accommodating two tracks in one tube, were introduced to reduce the environmental impact and to increase the underground space efficiency when crossing beneath a crowded urban area, as shown in Figure 2[22; 23]. Quasi-rectangular shield tunnels also have advantages such as easier control of the surface subsidence and lower cost of the segment linings when compared to other special-section shield tunnels [24; 25; 26]. However, unlike the circular lining ring, the quasi-rectangular lining shape has a reduced arching effect due to its small height-to-width ratio [27], and as a result, the bending moments in the lining are significantly larger when compared to circular linings with the same buried depth. The quasi-rectangular tunnels considered in this paper adopt joints with DIJPs to resist joint opening and rotation. As water tightness from the inner segment side is not necessary and the circumferential stresses are not reduced by the inner water pressure in quasi-rectangular tunnels, the joint section design is different from that in water conveyance tunnels. Although, as mentioned before, the joint type has an important influence on the lining's structural deformation and bearing capacity, there are few studies on the mechanical behavior of this new joint type. Moreover, behavioral insight for this joint is necessary for its further application in quasi-rectangular shield tunnels or other special-section shield tunnels with large bending moments.