# Optimization Study on Longitudinal Joints in Quasi-Rectangular Shield Tunnels
## 6 Conclusions  
In this paper, for the joints equipped with DIJP components, joint tests and FEM joint simulations were both conducted to investigate the joint behavior before and after the bolt position improvements. The joint model provides an efficient approach for exploring the influence of the internal forces in the joint's vicinity and the effect of other optimizing methods, such as concrete strength class, bolt diameters, and the number of bolts. From the analysis of the joints with DIJPs, the following conclusions can be drawn:  
Figure 24: Evolution of the rotations and bolt stresses with different concrete classes: (**a**) rotation curves; (**b**) bolt stress curves. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Concrete Class**} & \multicolumn{2}{c}{**Rotational Stiffness in Positive Cases**} & \multicolumn{2}{c}{**Rotational Stiffness in Negative Cases**} \\ \cline{2-5}  & **Type-BPos** & **Increase Rate** & **Type-BNeg** & **Increase Rate** \\ \hline C50 & 37,404 & - & 32,598 & - \\ C70 & 38,431 & 3\% & 35,406 & 9\% \\ C90 & 39,602 & 6\% & 37,342 & 15\% \\ \hline \end{tabular}
\end{table} 
Table 9: Summary of the rotational stiffnesses during the third stage with different concrete classes (stiffness unit: kN\(\cdot\)m/m/rad, modulus unit: GPa). The failure of the joints is initiated by concrete cracking at the core section and is terminated by concrete crushing. At that stage, the bolts do not yield, and thus provide an additional safety margin. This type of joint failure mode is similar to that of a column cross-section with small eccentricity. For the joints under positive bending moments, the joint stiffness increases once the outer edges of the segments touch each other. 2. The joint's resistance to cracking and the ultimate bearing capacity after bolt position improvements are both enhanced. The resistance to cracking increases by 33.6% for positive cases and by 18.0% for negative cases. The resistance to crack penetration increases by 13.8% for positive cases and 18.4% for negative cases. 3. The connecting reinforcements between DIJPs and concrete can guarantee the DIJPs' anchorage in the concrete. The components of the DIJPs and their connections in this new joint type are proven to be reliable. 4. For a given axial force, the joint behavior can be divided into three stages. At the first stage, the whole joint core section is under compression, and bolts do not contribute to the rotation resistance. The joint behavior is governed by the structural details of the core section. At the second stage, the bolts start being tensioned. The bolt stress increases fairly quickly while the rotational stiffness decreases gradually. At the third stage, the lever arm exceeds the distance from the edge of the outer section to the joint central axis. The evolutions of the joint rotation and the bolt stress appear to be almost linear. 5. When compared to an increase of the concrete strength class, an increase of the bolt diameter, or an increase in the number of bolts, a change of the joint section to increase the lever arm between the bolts and the compression zone can most effectively improve the joint behavior, resulting in a decrease of the bolt stresses, as well as an increase of the joint rotation stiffness and of the joint bearing capacity. This optimization direction should be preferably considered when designing a joint section. Conceptualization, methodology, writing--original draft preparation, W.Z. ; formal analysis, validation, software, W.Z. and W.D.C. ; writing--review and editing, supervision, W.D.C. and L.T. ; project administration, funding acquisition, X.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (grant number 51578409) and the China Scholarship Council. The financial support is gratefully acknowledged. Not applicable. Data Availability Statement: Data is contained within the article.