## 5 Conclusions  
Numerical calculations explored soil loss and development processes following the rupture of unpressurized pipelines below the water table. Factors considered were particle friction coefficient, groundwater level, and particle size distribution, with a focus on their impact on stratum subsidence. The conclusions are summarized below:  
(1) A higher particle friction coefficient results in slower soil loss around unpressurized pipelines below the groundwater level, ensuring greater stability. In practical engineering, the particle friction coefficient equals the tangent of the soil's internal friction angle. Adjusting the internal friction angle during underground pipeline installation, through methods such as soil replacement or compaction changes, is recommended in areas with high groundwater levels.  
(2) The influence of groundwater level on particle loss and stratum subsidence is significant. Higher groundwater levels create increased pressure differentials, making soil particle loss into unpressurized pipelines more likely. To address this, selecting suitable dewatering methods during pipeline installation becomes crucial. Additionally, implementing effective waterproofing measures for the pipelines during later use is essential to prevent potential issues.  
(3) The particle size distribution also significantly affects particle transport. According to Stokes' law, particle movement speed in a fluid depends on their radius. Hence, fine and continuous particle size distributions promote soil particle loss. During pipeline installation and backfilling, considering materials with larger particles for backfilling can help reduce soil loss.  
In this study, only a small portion of factors contributing to soil erosion resulting from unpressurized pipeline rupture below the groundwater level were examined, primarily focusing on particle displacement and stratum subsidence. In future research, the analysis could be extended to include other factors such as pipeline materials and broader environmental conditions. Moreover, a more detailed exploration of particle interactions, including aspects such as particle aggregation and settling dynamics, could provide a more comprehensive and systematic understanding of this complex issue. Finally, the lack of actual engineering data for comparison with our research results is a limitation of this study, which restricts the direct applicability of the research findings in real-world engineering projects.  
[PERSON] organized the textual work of the entire paper, participated in the establishment of the computational model, and summarized and analyzed the computational results. [PERSON] initially proposed this idea, modified the computational model, and provided theoretical support during the analysis process. [PERSON] contributed to the establishment of the computational model and collected the computational results. [PERSON] provided technical guidance during the model construction. [PERSON] offered more reasonable suggestions for the entire paper. All authors made contributions to the writing of this paper. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This study was funded by the National Natural Science Foundation of China (No. 12072260 and No. 51679198) and the State Key Laboratory of Eco-hydraulics in Northwest Arid Region of China (QNZX-2019-07).  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.  
**Conflicts of Interest:** The authors declare no conflict of interest.