## 2 Establishment of the Seasonally Frozen Ground-Pipeline System Model  
### Overview of the Study Area  
Xinjiang is the largest agricultural province in China, where agricultural water use accounts for over 90% of total water consumption, reaching as high as 95% in the southern regions. Due to the issue of low agricultural water efficiency, there is an urgent need to develop water-saving technologies to address the conflict between water resource supply and demand and to promote efficient water use. Currently, irrigation in Xinjiang primarily relies on canal systems. However, during long-distance water transport, significant evaporation and leakage occur, leading to resource wastage, rising groundwater levels, and soil salinization. Moreover, the design of canals is constrained by strict topographic requirements, increasing construction costs and limiting affordable irrigation options in certain areas, thus hindering agricultural development. Research has shown that converting the entire canal system in Xinjiang to a pipeline water transport system could save approximately 9.488 billion tons of water. Therefore, the development of a pipeline water transport system is crucial for improving agricultural water use efficiency. However, the safety of long-distance pipeline transport is significantly influenced by soil and geological conditions, particularly in frozen soil regions. The effects of freeze-thaw cycles on pipelines primarily manifest as frost heave and thaw settlement, which can damage, fail, or cause leaks in pipelines, posing a serious threat to the safety of the water supply system. In the cold winter climate of Xinjiang, especially on the northern slopes of the Tianshan Mountains, pipelines traversing seasonal frozen soil regions face freeze-thaw damage as a major challenge to safe operation. This study focuses on the typical soil structure of the cold region in northern Xinjiang, where the soil consists of mixed fill, silty clay, and gravelly sandy soil, with the water transport pipeline buried in the silty clay layer. A structural schematic diagram is shown in Figure 1.  
Frozen soil is a porous and heterogeneous medium, and its thermophysical properties are highly sensitive to moisture content and temperature variations. The interaction between pipes and soil during the freeze-thaw process in frozen soil is a THM coupling issue, where the coupling relationships between various physical fields are illustrated in Figure 2. Hydrothermal coupling primarily involves the influence of water state changes (such as freezing and thawing) on heat conduction and the temperature field. During freezing, water affects the soil's thermal conductivity and thermal capacity. The formation and thawing of ice alter the soil's pore structure, further influencing its thermal conductivity. Thermal coupling is reflected in how temperature changes affect the mechanical properties and stress state of the soil. Variations in temperature can lead to changes in pore water pressure, which directly impact the soil's physical properties, such as shear strength and compressibility. Elevated temperatures may cause plastic deformation in the soil, while lower temperatures can result in brittle failure. Hydraulic coupling focuses on the influence of water flow on the mechanical behavior of the soil. In frozen regions, water flow is suppressed, but in thawed areas, water can flow freely. This results in changes in pore water pressure, which in turn affect the effective stress in the soil. It is evident that temperature field variations lead to phase transitions between water and ice in frozen soil, facilitating moisture migration. Meanwhile, the latent heat generated during phase changes also regulates the temperature field of the soil. The deformation caused by the water-ice phase transition leads to changes in soil parameters and stress-strain relationships, while changes in stress and strain further influence the soil's moisture and temperature fields.