# Optimization Study on Longitudinal Joints in Quasi-Rectangular Shield Tunnels
## 4 Bearing Capacity of the Joint with DIJPs
### Damage Process
It is worth comparing the performance of a joint with DJJPs to that of the joints commonly used in conventional circular shield tunnels (see Figure 1a). From the test results for joints in a conventional circular shield tunnel [14], the bending moments when cracks appeared and cracks penetrated are compared to those from the tests for the joints with DJJPs mentioned above (see Tables 4 and 5). In addition, the corresponding rotation and deflection values are added. It should be noted that no direct comparison is possible, since the segmental thickness is not equal in both tests. Rather, the ratio between the thickness of the segments with DJJPs (450 mm) and that of the conventional joints (350 mm) is 1.29, and correspondingly, the ratio between the moments of inertia is 2.13. In the case of a comparison to the Type-A configuration, the bending moment resistances to cracking and crack penetration of the DJJP joint are more than twice those from the conventional one, which is generally consistent with the inertia moment ratio. After the bolt position improvements (Type-BPos and Type-BNeg), the resistances to cracking and crack penetration are clearly higher, and even under these large bending moments, the improved joints have smaller deflections. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Phenomenon**} & \multicolumn{3}{c}{**Bending Moment**} & \multicolumn{3}{c}{**Rotation**} & \multicolumn{3}{c}{**Deflection**} \\  & \multicolumn{3}{c}{**(kN\(\cdot\)m/m)**} & \multicolumn{3}{c}{**(rad)**} & \multicolumn{3}{c}{**(mm)**} \\ \cline{2-10}  & \begin{tabular}{c} **Circular** \\ **Tunnel** \\ \end{tabular} & **Type-A** & \begin{tabular}{c} **Type-** \\ **BPos** \\ \end{tabular} & \begin{tabular}{c} **Circular** \\ **Tunnel** \\ \end{tabular} & **Type-A** & \begin{tabular}{c} **Type-** \\ **BPos** \\ \end{tabular} & \
\begin{tabular}{c} **Circular** \\ **Tunnel** \\ \end{tabular} & **Type-A** &
\begin{tabular}{c} **Type-** \\ **BPos** \\ \end{tabular} \\ \hline core concrete cracking & 155.0 & 406.7 & 543.3 & 0.030 & 0.023 & 0.026 & 18 & 16.0 & 14.9 \\ \hline crack penetration & 200.0 & 506.7 & 576.7 & 0.045 & 0.035 & 0.030 & 28 & 21.5 & 16.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison between the joints with DJJPs and joints in a conventional circular tunnel in positive cases. Figure 15: Type-A joint under a negative bending moment: (**a**) core section cracking; (**b**) quickly developing cracks; (**c**) crack penetration; (**d**) concrete crushing. In Figures 12 and 13, the slopes of the moment-rotation curves represent the joint rotational stiffness, showing that after bolt position improvements, the rotational stiffness is also increased. These observations mean that the improvements not only contribute to a larger bearing capacity, but also to a better structural deformation control. Hence, joints adapted to the sign of the bending moment are preferable in quasi-rectangular shield tunnels, as they can sustain larger bending moments and also reduce overall lining deformations when compared to a single-joint type. In addition, in Figures 12 and 13, the curves of joint rotations and deflections obtained from the 3D joint model are consistent with those from the tests. The bending moments in the joints of quasi-rectangular tunnels are normally within 300 kN\(\cdot\)m under service conditions, or 250 kN\(\cdot\)m/m after normalization [30; 31; 32]. The calculation results from the proposed joint model can cover this bending moment range well, and therefore, the developed joint model provides an effective and economical approach for studying the joint behavior within the moment range at the normal service level. The related aspects are discussed in Section 5.