## 1 Introduction  
In the underground space resources development within highly permeable and weakly consolidated formations, sustainable hazards often arise. These include groundwater inundation, leading to tunnel flooding and potential structural instability, soil subsidence due to water seepage, risking tunnel collapse, and environmental impacts like land settlement and groundwater contamination [1; 2; 3]. Addressing these challenges requires comprehensive engineering solutions, including artificial ground freezing, soil stabilization techniques, and effective groundwater management strategies, to ensure the sustainable and safe development of underground space in such geological conditions [4; 5; 6]. Artificial ground freezing (AGF) is a sophisticated engineering method extensively employed in underground space resources development. The freezing tube temperature can be reduced to \(-\)30 \({}^{\circ}\)C. The soil temperature can be lowered to \(-15\)\({}^{\circ}\)C. The permeability can be reduced by about three times. The strength can be increased by about three times. By manipulating groundwater levels and soil temperatures, AGF creates a protective frozen barrier underground, effectively shielding underground space excavation sites from water and soil infiltration [7; 8]. This technique is particularly invaluable in areas with complex geological compositions and high groundwater levels, where traditional construction methods are prone to safety hazards like ground settlement and underground space collapse due to water seepage. AGF involves a series of meticulously executed steps, including pre-freezing to lower groundwater temperatures, primary freezing utilizing freezing pipes, and subsequent underground space excavation within the frozen support layer. Post-freezing curing is then carried out to ensure the long-term stability and integrity of the frozen barrier [9]. AGF not only guarantees high safety standards by mitigating the risks associated with groundwater ingress but also enhances construction efficiency by enabling uninterrupted excavation processes. Furthermore, its minimal environmental impact compared to conventional support structures underscores its significance in sustainable urban development initiatives. The temperature of underground space construction is crucial for ensuring the effectiveness and safety of AGF techniques [10]. It directly influences the formation and stability of the frozen barrier underground, which is essential for controlling groundwater inflow and stabilizing surrounding soil during excavation. By studying the optimal freezing temperature, engineers can enhance the efficiency of this method, minimize construction risks such as underground space collapse and ground settlement, and ultimately ensure the long-term structural integrity and safety of underground space [11; 12]. The temperature field of the soft clay rock in underground space resources development is influenced by several factors. Firstly, the properties of the surrounding soft clay rock, such as thermal conductivity and moisture content, impact heat transfer rates and the extent of freezing. Secondly, the type and temperature of the refrigerant used for ground freezing play a critical role in controlling the temperature distribution within the soft clay rock. Additionally, environmental factors like ambient temperature and groundwater flow rates can affect the effectiveness of the freezing process. Furthermore, the geometry and design of the freezing system, including the spacing and arrangement of freezing pipes, also influence the temperature field [13; 14; 15]. Soft clay rock thermal conductivity determines the rate of heat transfer within the ground, impacting the freezing process's efficiency and the uniformity of temperature distribution in the underground space. Additionally, the moisture content of soft clay rock affects thermal conductivity and heat capacity, influencing the heat absorption and release capabilities.