# Optimization Study on Longitudinal Joints in Quasi-Rectangular Shield Tunnels
## 4 Bearing Capacity of the Joint with DIJPs  
### Damage Process  
The effect of the bolt repositioning on the joint bearing capacity was analyzed through joint tests and finite element analysis (FEA). The obtained evolutions of the joint rotation and deflection with increasing bending moments are depicted in Figures 12 and 13. The joint rotation \(\theta\) is calculated through \(\theta=(v_{1}-v_{2})/h\), where \(h\) is the joint height of 450 mm, and \(v_{1}\) and \(v_{2}\) are the variations of the joint opening at the inner and outer side of the segment, which can be obtained from the joint tests or from the FEM 3D joint model. Key designations (KDs) during the joint damage process (see Tables 2 and 3) are indicated with numbers 1 to 5 and 1\({}^{\prime}\) to 5\({}^{\prime}\) in Figures 12 and 13. For the positive case of the Type-A joint, after the constant axial force at the joint was attained (KD 1), the joint went through core section cracking (KD 2), outer edge contacting (KD 3), outer section cracking (KD 4), crack penetration (KD 5), and concrete crushing (KD 6). When the outer edges of the segments touched each other (KD 3), the outer part of the section started to contribute to the bending moment resistance and the speed of the joint rotation and deflection evolutions decreased. Once the crushing happened, one of the bolts snapped suddenly. Then, the tensile force in this bolt needed to be sustained by other bolts, and as a result, all bolts failed rapidly. A slightly different sequence was observed for the positive case of the Type-BPos, with the outer edges contacting each other (KD 2\({}^{\prime}\)) before core concrete cracking (KD 3\({}^{\prime}\)) appeared. For the negative cases, the progressive development  
Figure 12: Evolution of the joint rotation with increasing bending moments: (**a**) positive cases; (**b**) negative cases. Figure 13: Evolution of the joint deflection with increasing bending moments: (**a**) positive cases; (**b**) negative cases. of the joint damage included core section cracking (KD 2 and 2\({}^{\prime}\)), quickly developing cracks (KD 3 and 3\({}^{\prime}\)), crack penetration (KD 4 and 4\({}^{\prime}\)), and concrete crushing (KD 5 and 5\({}^{\prime}\)), followed by bolt failure. The corresponding bending moments in both the positive and negative cases are summarized in Tables 2 and 3, respectively. As the damage processes before and after the improvements are similar, only pictures of the Type-A joint tests are shown in Figures 14 and 15 for brevity. The failure of the DJJP-equipped joints is initiated by core section cracking and terminated by local concrete crushing. The failure mode is similar to that of a column submitted to compound bending with small eccentricity, where the concrete is crushed before the reinforcement starts yielding. The noticeable core concrete cracking affects the serviceability of the segmental joint from the long-term view, as water leakage might occur or water might penetrate into the concrete and cause corrosion of the reinforcement. With this key moment chosen as a reference situation, the bolt position improvements (A to B) increase the bending moment resistance values by 33.6% for the positive cases (from 406.7 kN\(\cdot\)m/m to 543.3 kN\(\cdot\)m/m) and by 18.0% for the negative cases (from 360.2 kN\(\cdot\)m/m to 425.0 kN\(\cdot\)m/m). As soon as the cracks penetrated the segments, the compressed concrete was crushed quickly. The appearance of such penetrating cracks means that the bearing capacity of the segment is almost reached. With this key moment as a reference, the bolt improvements (A to B) increase the bending moment values by 13.8% for the positive cases (from 506.7 kN\(\cdot\)m/m to 576.7 kN\(\cdot\)m/m) and 18.4% for the negative cases (from 443.5 kN\(\cdot\)m/m to 525.0 kN\(\cdot\)m/m). It is obvious that both the joint's resistance to cracking and the ultimate bearing capacity are enhanced due to the positional improvements.