## 4 Overall Stability of Insulated Cold Transfer pipes
### Stability of the Surrounding Rock on the Outside of the Cold Transmission Pipe  
The vertical displacement of the surrounding rock above the insulated cold pipe at different distances from the inner wall of the steel pipe is shown in Figure 9. It can be seen that when the ground stress is 3 MPa, the vertical displacement of the surrounding rock within the range of 40 mm measurement points almost does not change, which is approximately equal to 0. Due to the homogeneity of the nature of the model surrounding rock, the vertical displacement of the surrounding rock decreases linearly with the increase in the distance from the inner wall of the steel pipe. With the increasing ground stress, the vertical displacement of the surrounding rock also gradually increases. When the ground stress is 17.5 MPa, the vertical deformation of the surrounding rock around the pipe reaches about 0.12 mm, and the difference of vertical displacement within 40 mm is about 0.02 mm. Figure 10 shows the vertical stress distribution contour and the axial and tangential stress curves at the measurement points of the surrounding rock with the distance from the inner wall of the steel pipe under different ground stress conditions for the composite insulated cold transmission pipe trough deep strata. Figure 9: Variation of vertical displacement of the surrounding rock measurement points with distance from the inner steel pipe wall. Under the conditions of ground stress, the axial stress distribution of the external rock surrounding the composite insulated cold transmission pipe through deep strata is butterfly-shaped, while the stress concentration mainly occurs on the left and right sides of the pipe. The axial stress on the left and right sides is generally greater than on the upper and lower sides. The stress concentration is most obvious at the four corner positions of the upper left, lower left, upper right, and lower right, and the axial stress on the upper and lower sides is relatively small. Table 2 presents the maximum vertical stress values of the external surrounding rock under different in situ stress conditions, where the negative sign indicates compressive stress. From Table 2, it can be observed that the maximum vertical stress of the external surrounding rock gradually increases with the increase in in situ stress. This finding is similar to that of [PERSON] et al [29]. They found that with the rise of the shaft depth and stress coefficient under the different surrounding rock grades, the radial and tangential stress showed an increasing trend, but the growing trend was relatively gentle. Figure 11 shows the variation of the axial stress at the measurement point in the surrounding rock with the distance from the inner steel pipe wall. At ground stresses greater than 9 MPa, there is a slightly abrupt change in the distance from the inner steel pipe wall between 113 mm and 123 mm, and then gradual stabilization occurs. The same can be seen in the curve of tangential stresses in the surrounding rock with distance from the inner steel pipe wall, where there is an abrupt change in tangential stresses downwards as the distance from the measurement point increases from 113 mm to 123 mm. It can be \begin{table}
\begin{tabular}{c c} \hline
**In-Situ Stress/MPa** & **Maximum Vertical Stress/MPa** \\ \hline
3 & \(-\)1.49 \\
6 & \(-\)3.19 \\
9 & \(-\)4.87 \\
12 & \(-\)6.58 \\
15 & \(-\)8.22 \\
17.5 & \(-\)9.55 \\ \hline \end{tabular}
\end{table} 
Table 2: Maximum vertical stress of external surrounding rock under different in situ stress conditions. Figure 10: Distribution of vertical stresses in the external surrounding rock under different ground stress conditions: (**a**) 3 MPa; (**b**) 6 MPa; (**c**) 9 MPa; (**d**) 12 MPa; (**e**) 15 MPa; (**f**) 17.5 MPa. assumed that the effect of ground stress on the external rock is also zoned, with 113-123 mm being the critical zone.