## 4 Finite Element Analysis Method and Results
### Thaw-Settlement Scenario
Therefore, as an increasing number of thermosiphons is applied, the thaw-penetration depth is rendered shallower. Therefore, as the ground stabilization method, the thermosiphon plays its role well in reducing the thawing area of the ground under the pipe, and it can be confirmed that the performance of ground stabilization increases as the number of thermosiphons increases. The thaw bulb shapes (y-z plane) with the maximum and minimum thaw-penetration depths are demonstrated in Figure 17. Notably, the shape of the thaw bulb features a large depth compared to its width direction, which is attributed to the effect of the boundary condition of the top surface and the thermosiphons. The thaw-bulb size in all cases decreases as the number of thermosiphons increases. Notably, in CASE_TA, the difference in size between the maximum and minimum thaw bulbs is remarkably large compared with that of the other cases. However, the maximum thaw bulb of CASE_TA is not significantly distinct from that of CASE_T because the thermosiphons applied to CASE_TA are located at No. 7 in the x-direction and exert a limited effect on the soil adjacent to No. 1, which is located far from the thermosiphons, thereby resulting in the large size of the thaw bulb. This tendency to form a thaw bulb induces a displacement tendency in the buried pipeline. Similar to the results of the frost-heave scenario, the trend of pipeline displacement indicates a small change as the number of thermosiphons increases. Figure 18a graphically demonstrates the time-dependent results of CASE_T. Notably, the pipeline displacement converges toward the end phase of the thaw-bulb formation (680 h). Similarly, the convergence times of the cases using the same number of applied thermosiphons are identical to those corresponding to the thaw-bulb formation tendency. The convergence time is shortened as the number of applied thermosiphons is increased. The pipeline displacement results for all the cases are illustrated in Figure 18b. The final pipeline displacement decreases as the number of applied thermosiphons increases. For CASE_TA, CASE_TB, and CASE_TC, the pipeline displacements are reduced by 42.81, 70.15, and 82.36%, respectively, compared to that of CASE_H. The axial stress demonstrates a decreasing tendency as the number of thermosiphons increases, similar to that observed in the frost-heave scenario. However, as the direction of the pipeline displacement is in the opposite direction, the top portion of the pipeline (P-7-0)  
Figure 17: Maximum and minimum thaw bulbs for all cases in the x-direction at (**a**) No. 1 and (**b**) No. 7.  
verifiably receives negative stress due to axial compression, and the bottom portion of the pipeline (P-7-180) receives positive stress due to axial tension, as indicated in Figure 19.  
The converged axial stresses for all cases decrease according to the number of thermosiphons, similar to the trend observed in the frost-heave scenario. Figure 19c shows the maximum axial stress measured at measurement points \"P-7-0\" and \"P-7-180\". In the case of reduction rate, the axial stress of CASE_TA, CASE_TB, and CASE_TC were compared based on the axial stress of CASE_T. The axial stress (axial compression) measured at the measurement point \"P-7-0\" showed a 55.52% reduction rate in the case of CASE_TA and an 83.61% reduction rate in the case of CASE_TC. The axial stress (axial tension) measured at the measurement point \"P-7-180\" also showed a similar reduction rate trend and showed a reduction rate of 85.25% in the CASE_TC.