## 4 Overall Stability of Insulated Cold Transfer pipes
### Overall Structural Stability of Long-Distance Insulated Cold Transmission Pipes  
The overall stability of the structure of the insulated cold transmission pipe directly affects the safety and stability of the operation of the insulated cold pipe in passing through the deep strata for the ground cooling system. Therefore, analyzing the displacement, stress, and plasticity zones is particularly important. The vertical displacement contour of the pipe under different ground stress conditions shows that the displacement of the pipe mainly occurs at the upper and lower walls of the pipe and decreases outwards layer by layer. At the same time, there is almost no vertical displacement on both sides of the pipe. Figure 12 shows that when the ground stress is 3 MPa and 6 MPa, there is almost no vertical displacement between the inner steel pipe and the cement, and the deformation of the whole pipe is minimal. When the ground stress exceeds 6 MPa, the vertical displacement of the inner steel pipe is significantly higher than that of the outer steel pipe and the layer of cement. Under high-ground stress, the deformation of the unit thickness of the FCM is much higher than that of the OCM. Meanwhile, there is almost no deformation of the steel pipe, and the deformation of the insulated pipe mainly comes from the deformation of the cement material. As the ground stress increases, the vertical displacement of the steel pipe, OCM, and FCM all increase linearly. The change in vertical displacement of the inner steel pipe is mostly influenced by the ground stress, and the OCM is least influenced by the ground stress. The axial stress distribution of the insulated cold transmission pipe under different ground stress conditions is shown in Figure 13, from which it can be seen that the largest zone of the insulated cold transmission pipe subjected to axial stress is the left and right sides, and the two layers of steel pipe bear more stress concentration, relieving the stress concentration in the OCM and FCM. Under high-ground stress conditions, the stress distribution of the insulated cold transmission pipe is as follows: the left and right inner walls of the pipe are the largest, the inner walls of the four corners are the second largest, and the upper and lower inner walls are the smallest. Figure 14 shows the different parts of the insulated cold transmission pipes with the distance from the inner steel pipe wall and the change in ground stress. As can be seen from the figure, the distance from the inner steel pipe wall and ground stress has the smallest impact on the axial direction of the inner steel pipe, and with the increase in ground stress, the axial stress of the inner steel pipe almost has no change, which is about  
Figure 12: Variation of vertical displacement of insulated cold transmission pipe at measurement points with distance from the inner pipe wall. 0 MPa, indicating that the inner steel pipe is almost not subject to axial stress. At this time, the inner part of insulated pipe can operate normally. When the distance from the inner wall of the steel pipe exceeds 9 mm, the axial stress of the insulation pipe increases linearly with the distance, and the OCM and FCM have the essential roles in the attenuation and dissipation of the axial stress. As the ground stress increases, the OCM is most affected by the axial stress and the inner steel pipe is least affected by the axial stress. Figure 15 shows the distribution of the plastic zone in different parts of the insulated cold transmission pipe under different ground stress conditions. The figure shows no  
Figure 14: Variation of the axial stress at the measurement point of an insulated cold pipe with distance from the inner pipe wall. Figure 13: Axial stress distribution of insulated cold transmission pipes under different ground stress conditions. yielding in the plastic zones of the insulated cold transmission pipe when the ground stress ranges from 3 MPa to 12 MPa.