## 4 Results and Analyses
### Effect of COV of Hydrothermal Parameter  
The COV of thermal parameters in soft clay rock plays a significant role in influencing the temperature distribution of freeze curtains. As the COV increases, it indicates greater variability or heterogeneity in thermal properties within the frozen soft clay rock. This variability directly affects the spatial distribution of temperature within the soil mass and along the freeze curtain. In regions with high COV values, there is greater uncertainty in thermal properties, leading to more pronounced temperature variations. This can result in non-uniform freezing along the freeze curtain, with some areas experiencing higher or lower temperatures than others. In contrast, lower COV values indicate more consistent thermal properties, resulting in a more uniform temperature distribution along the freeze curtain. Understanding the impact of COV on freeze curtain temperature is crucial for optimizing freeze curtain designs and ensuring effective ground stabilization during underground space engineering. Engineers can use this information to identify regions of high COV, where additional measures may be needed to achieve uniform freezing and prevent ground settlement. Additionally, incorporating COV data into thermal analysis models improves their accuracy and reliability, enabling better predictions of temperature distributions within the soft clay rock. Overall, the relationship between the COV of thermal parameters and freeze curtain temperature highlights the importance of considering spatial variability in thermal properties when designing and implementing freeze curtain systems in underground space engineering. By accounting for COV values, engineers can make informed decisions to enhance the safety, stability, and efficiency of underground infrastructure projects. To elucidate the effect of COV on the temperature characteristics of soft clay rock, this paper selects the 0.05, 0.10, 0.15, 0.20, and 0.25 to represent the COV of hydrothermal parameters and conducts sensitivity grouping (Table 4) calculations for parameter variability. The results are shown in Figure 7.  
Figure 7 shows that the five different COVs have different effects on the SD of freezing temperature. For the thermal conductivity, When the COV is 0.05, the SD of the freezing curtain temperature is the smallest. When the COV is 0.15, the SD of the freezing curtain temperature is in the middle. When the COV is 0.25, the SD of the freezing curtain temperature is the largest. The maximum and minimum SD of freezing curtain temperature during the freezing process is 3.09 \({}^{\circ}\)C and 0.73 \({}^{\circ}\)C, respectively. For the heat capacity, When the COV is 0.05, the SD of the freezing curtain temperature is the smallest. When the COV is 0.05, the SD of the freezing curtain temperature is the smallest. When the COV is 0.15, the SD of the freezing curtain temperature is the largest. The maximum and minimum SD of freezing curtain temperature during the freezing process are 2.56 \({}^{\circ}\)C and 0.79 \({}^{\circ}\)C, respectively. Different variations of hydrothermal parameters have different effects on the standard deviation of freezing curtain temperature. Different COV parameters have varying impacts on the temperature of the freeze-soft clay rock. The most significant impact comes from thermal  
conductivity, followed by permeability coefficient, with specific heat capacity having the smallest effect. Additionally, the larger the COV of the hydrothermal parameters, the greater the SD of the freezing curtain temperature.