## 4 Results and Analyses
### Mean and SD of Thermodynamic Properties  
Analyzing the evolution of average temperature and average thickness of soft clay rock in underground space engineering is crucial for several reasons. Firstly, it provides insights into the thermal behavior of the surrounding soft clay rock and the effectiveness of the soft clay rock in controlling ground temperatures. Understanding how the average temperature changes over time helps in optimizing freeze designs and operational parameters to ensure adequate ground freezing and prevent soil settlement during tunnel construction. Secondly, monitoring the average thickness evolution allows engineers to assess the progression of the freezing front within the soil. By tracking changes in thickness, they can identify potential areas of inadequate freezing and take corrective measures to enhance freeze-soft clay rock performance. Moreover, analyzing the evolution of both temperature and thickness provides valuable data for validating analytical models and simulation tools used in underground space engineering. Comparing model predictions with observed data enhances the accuracy and reliability of these tools, ultimately improving decision-making and risk management during underground space engineering. Furthermore, understanding the long-term evolution of average temperature and thickness helps in assessing the stability and durability of underground space engineering over time. By predicting how these parameters will evolve under different conditions, engineers can implement preventive maintenance measures and ensure the long-term integrity of underground space engineering. In summary, analyzing the evolution of average temperature and thickness of soft clay rock is essential for optimizing design, validating models, ensuring construction safety, and maintaining the long-term stability of underground infrastructure. Sections A, B, C, D,  
Figure 4: Experimental temperatures and numerical temperatures of soft clay rock: (**a**) measured data and calculated data of Points A, B, and C; (**b**) measured data and calculated data of Points D, E, and F.  
and E represent five sections through the center of the inner ring of freezing pipes, with azimuth angles of \(0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\), \(135^{\circ}\), and \(180^{\circ}\), respectively. Figure 5 shows the variability of temperature characteristic value of soft clay rock. From Figure 5a, the overall trend of the average thickness of the soft clay rock increases with the increase of freezing time. From the second month to the 10 th month, it increases at a faster rate, and there are differences in the thickness of different sections, with the largest difference being 1.35 m, which is due to the fact that the frozen curtain has not formed a stable form. When the freezing time reaches 12 months, the average thickness stabilizes, indicating that the stable formation of the frozen curtain is essentially achieved at this point. From Figure 5c, the overall trend of the average temperature of the frozen curtain decreases with the increase of freezing time. From the second month to the 10 th month, it decreases at a relatively fast rate, and there are differences in the temperature of different sections, with the largest difference being 0.58 \({}^{\circ}\)C, which is due to the fact that the frozen curtain has not formed a stable form. When the freezing time reaches 12 months, the average temperature stabilizes, indicating that the stable formation of the frozen curtain is essentially achieved at this point. From Figure 5b,c, the overall trend of SD of the freeze curtain increases with time. When the freezing time reaches 12 months, the SD of the average thickness and temperature stabilizes.