## 4 Results and Analyses
### Effect of ACD on Hydrothermal Parameter  
Analyzing the autocorrelation distance of thermal parameters in soft clay rock is essential for assessing its impact on freeze curtain temperatures. The autocorrelation distance delineates how thermal properties fluctuate spatially, directly influencing temperature distribution. Understanding this distance aids in optimizing freeze curtain designs to ensure uniform ground freezing and mitigate soil settlement risks during underground space engineering. Incorporating autocorrelation distance into analytical models enhances accuracy, enabling precise predictions of temperature variations along the freeze curtain. This information is vital for informed decision-making in underground space engineering, ensuring the safety, stability, and effectiveness of freeze curtain systems. By considering the autocorrelation distance, engineers can strategically deploy freeze curtain elements, minimizing temperature differentials and promoting reliable ground stabilization. Overall, analyzing the autocorrelation distance of thermal parameters is imperative for comprehens  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Case ID**} & \multicolumn{2}{c}{**Thermal Conductivity**} & \multicolumn{2}{c}{**Heat Capacity**} & \multicolumn{2}{c}{**Hydraulic Conductivity**} \\ \cline{2-7}  & \(\lambda_{u}\) **(W/m/\({}^{\circ}\)C)** & \(\lambda_{f}\) **(W/m/\({}^{\circ}\)C)** & \(C_{u}\)**(10\({}^{6}\) J/m\({}^{3}\)/C)** & \(C_{f}\) **(10\({}^{6}\) J/m\({}^{3}\)/C)** & \(K_{x}^{u}\) **(10\({}^{-6}\) m/s)** & \(K_{y}^{u}\) **(10\({}^{-6}\) m/s)** \\ \hline Reference case & 0.15 & 0.15 & 0.15 & 0.15 & 0.15 & 0.15 \\ \hline \multirow{4}{*}{COV of thermal conductivity} & 0.05 & 0.05 & 0.15 & 0.15 & 0.15 & 0.15 \\  & 0.10 & 0.10 & 0.15 & 0.15 & 0.15 & 0.15 \\  & 0.15 & 0.15 & 0.15 & 0.15 & 0.15 & 0.15 \\  & 0.20 & 0.20 & 0.15 & 0.15 & 0.15 & 0.15 \\  & 0.25 & 0.25 & 0.15 & 0.15 & 0.15 & 0.15 \\ \hline \multirow{4}{*}{COV of heat capacity} & 0.15 & 0.15 & 0.05 & 0.05 & 0.15 & 0.15 \\  & 0.15 & 0.15 & 0.10 & 0.10 & 0.15 & 0.15 \\  & 0.15 & 0.15 & 0.15 & 0.15 & 0.15 & 0.15 \\  & 0.15 & 0.15 & 0.20 & 0.20 & 0.15 & 0.15 \\ \hline \multirow{4}{*}{COV of hydraulic conductivity} & 0.15 & 0.15 & 0.15 & 0.15 & 0.05 & 0.05 \\  & 0.15 & 0.15 & 0.15 & 0.15 & 0.10 & 0.10 \\ \cline{1-1}  & 0.15 & 0.15 & 0.15 & 0.15 & 0.15 & 0.15 \\ \cline{1-1}  & 0.15 & 0.15 & 0.15 & 0.15 & 0.20 & 0.20 \\ \cline{1-1} \cline{2-7}  & 0.15 & 0.15 & 0.15 & 0.15 & 0.25 & 0.25 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parametric influence of different COVs of hydrothermal properties.  
Figure 7: Effects of different COV of variable hydrothermal parameters on uncertain thermodynamic properties: **(a)** Thermal conductivity; **(b)** heat capacity; **(c)** hydraulic conductivity.  
freezing curtain temperature is the smallest. When the ACD is 0.8 m, the SD of the freezing curtain temperature is in the middle. When the ACD is 1.2 m, the SD of the freezing curtain temperature is the largest. The maximum and minimum SD of freezing curtain temperature during the freezing process are 2.40 \({}^{\circ}\)C and 0.87 \({}^{\circ}\)C, respectively. Different variations of hydrothermal parameters have different effects on the standard deviation of freezing curtain temperatures. Different ACDs of parameters have varying impacts on the temperature of the freeze curtain. The biggest influence is the thermal conductivity, the second is the permeability coefficient, and the least influence is the specific heat capacity. Additionally, the larger the ACD of the hydrothermal parameter, the smaller the SD of the freezing curtain temperature.