## 5 Conclusions  
In this study, numerical analyses were performed to compare the behavior of the soil and a buried pipeline through frost heave and thaw settlement with thermosiphon application. For that, the frost-heave and thaw-settlement scenarios were established, and finite  
Figure 19: Axial stress of pipeline: (**a**) CASE_T (top side), (**b**) CASE_T (bottom side), and (**c**) results for all cases.  
Figure 18: Displacement of pipeline: (**a**) results of CASE_T at different times and (**b**) results for all cases.  
element analysis was conducted using the frost-heave model [23] and the thermosiphon model [20], which were applied via user subroutines in ABAQUS. The main numerical analysis results and conclusions of this study are as follows:  
In the case of the frost-heave scenario, it was confirmed that as the number of thermosiphons increased, the displacement of soil and the pipeline and the axial stresses of the pipeline decreased. Compared to CASE_H, the maximum reduction rates of pipeline displacement in CASE_HC were 62.71%. Furthermore, the maximum reduction rate of the axial stress (tension) in CASE_HC was 63.75%; the maximum reduction rate of the axial stress (compression) was 61.92%. Similar to the frost-heave scenario, it was confirmed that the ground-stabilization performance increased as the number of thermosiphons increased in the thaw-settlement scenario. As the number of applied thermosiphons was increased, the pipeline displacement decreased accordingly. Compared to CASE_T, the maximum displacement reduction rate of CASE_TC was 82.36%. In addition, the maximum axial stress reduction rate was 83.61% (axial compression) and 85.25% (axial tension) for CASE_TC.  
The results of this study verified that as the number of thermosiphons was increased, the frost-heave and thaw-settlement behaviors of pipelines and soil were effectively suppressed. Specifically, thermosiphons verifiably and significantly improved the ground-stabilization performance for these two behavioral conditions of the soil. However, in order to simulate the relationship between pipelines and thermosiphons used in the real environment, environmental conditions such as air temperature and multi-layered soil, and various installation variables such as the placement distance between the thermosiphons and the pipeline and the buried depth should be reflected, and these conditions and installation variables offer various avenues for future research directions.  
Conceptualization, D.-S.P.; Methodology, D.-S.P. and M.-B.S.; Software, D.-S.P., M.-B.S. and W.-J.P.; Formal analysis, D.-S.P., M.-B.S. and W.-J.P.; Validation, D.-S.P.; Writing--Original draft preparation: D.-S.P.; Investigation, M.-B.S. and W.-J.P.; Project administration, Y.-K.S.; Supervision, Y.-K.S.; Writing--Review and editing: Y.-K.S. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Research Foundation of Korea (NRF) through a grant funded by the Korea government (MSIT, No 2021R1F1A1051104). The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.