# Bearing Capacities and Failure Behaviors of F-Type Socket Joint in Rectangular Pipe Jacking Tunnel
## 3 Numerical Simulations
### Numerical Results and Comparisons to the Tests  
The numerical simulation on rectangular pipe jacking tunnel joint segment was firstly conducted to verify the accuracy and applicability of the numerical model, as shown in Figure 17.  
It can be seen from Figure 17 that the overall damage of the pipe joint showed that the top of the pipe was compressed, and the bottom of the pipe was separated under the action of bending moment. The plastic deformation occurred at the top of the pipe joint, resulting in the steel collar at the joint being extruded by the concrete at the socket segment, which deformed in flexure and buckled upward. The steel ring crushed concrete at the upper contact surface, and there was a large degree of concrete separation between the steel ring at the bottom of the pipe and the concrete at the socket segment. In this case, the pipe joint was deformed greatly because of the bottom of the pipe joint, resulting in structural damage and the calculation was stopped. From the deformation characteristics of the model, it was found that the deformation of the top plate, bottom plate and side wall is more significant. Therefore, the deformation of the top plate, bottom plate and side wall at the joint was analyzed in detail by setting the junction and path to extract the required junction displacement at the socket segment, the socket segment and the steel ring. The 14 units were divided spaced from left to right into equally in the jack segment, socket segment and steel ring at the joint of the top plate and bottom plate, and 15 nodes were set to extract their vertical displacements, and the deformation curves shown in Figure 18 are drawn. As shown in Figure 18 (the negative sign in the figure indicates the deformation direction downward), the vertical deformation was the largest in the center of the top plate, with a maximum value of 40 mm. As shown in Figure 18, the deformation of the jack segment, socket segment and steel ring of the top plate joint of the top pipe was basically the same under the load, the vertical deformation of the middle part of the top plate was the largest, the vertical  
Figure 17: Schematic diagram of rotational failure. Figure 18: Displacement curve of tunnel joint. (**a**) Displacement curve of roof. (**b**) Displacement curve of baseplate. (**c**) Displacement curve of side. deformation of the chamfered position gradually decreased, the maximum difference in vertical displacement between the jack segment and the socket segment was 28.84 mm and the maximum difference in vertical displacement between the socket segment and the steel ring was 29.16 mm. The deformation law of jack segment, socket segment and steel ring at the joint was approximately the same as that at the top plate, the vertical deformation was the largest at the middle of the steel ring at the bottom plate, the vertical deformation gradually decreased at the chamfered position, the maximum difference in vertical displacement between the jack segment and the socket segment was 24.28 mm, and the maximum difference in vertical displacement between socket segment and steel ring was 29.26 mm. The above shows that the joint area of the top plate is more prone to deformation than other locations under the same load, so it is necessary to focus on protection research at the top plate of the joint area, when dealing with the safety issues such as the waterproofing and uneven settlement of rectangular pipe tunnel  
The vertical load on the top plate was larger than the horizontal load on the side plate; the deformation of the side plate of the rectangular top pipe at the socket segment and the spigot segment was approximately wavy, from top to bottom, the side plate was concave and then convex, and then concave again, and returned to normal when it was close to the bottom plate. The maximum deformation of the side plate was 0.05 mm, which was much smaller than the minimum deformation of the top and bottom plates of the rectangular top pipe joint of 7.42 mm.