# Optimization Design Study of Pipe Curtain Freezing Scheme for Sanya Estuary Submarine Channel
## 5 Optimal Design of Freezing Scheme and Analysis of Numerical Simulation Results
### Analysis of Numerical Simulation Results for Scenario 1  
Through the single control variable method, other model parameters are controlled to remain unchanged, and the number of freezing pipes is reduced only on the basis of the original scheme. The Optimized Scheme 1 reduces 25 freezing pipes on the basis of the original scheme, all of which are on the inner side of the pipe curtain steel pipe, with 21 reduced in the strong freezing zone and four in the weak freezing zone. The changes in the \(-1\)\({}^{\circ}\)C and \(-10\)\({}^{\circ}\)C isotherms at different times are shown in Figure 9. On the 1 st day of freezing, \(-1\)\({}^{\circ}\)C and \(-10\)\({}^{\circ}\)C isotherms only surrounded the freezing pipe. By the 5 th day, the freezing pipe was completely encased in ice. By the 3 rd day, the pipe curtain's outermost \(-1\)\({}^{\circ}\)C isotherm had completed its inter-circle, marking the initial formation of the frozen curtain's outline and the onset of groundwater flow around the curtain. By the  
Figure 8: Freeze Optimization Scheme Freeze Tube Layout Diagram.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multicolumn{2}{c}{**The Number of Frozen Tubes**} & \multicolumn{2}{c}{**Number of Frozen Tubes in**} \\  & **in the Strong Freeze Zone** & **Weak Freeze Zone** \\ \hline Original plan & 133 & 40 \\ Scenario 1 & 112 & 36 \\ Scenario 2 & 94 & 36 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Freezing schemes.  
15 th day, the \(-1\)\({}^{\circ}\)C isotherm had completed its inter-circle, and the entire frozen region of the pipe curtain was essentially formed. At this point, the \(-10\)\({}^{\circ}\)C isotherm had completed its inter-circle in the strong freezing area and was nearly complete in the weak freezing area, with the \(-1\)\({}^{\circ}\)C isotherm filling the gaps between the pipe curtain steel pipes. By the 23 rd day, the \(-10\)\({}^{\circ}\)C isotherm had completed its inter-circle, and there was no groundwater flow inside the permafrost curtain. There was no isotherm in the gaps between the steel pipes, indicating that the temperature in these gaps was below \(-10\)\({}^{\circ}\)C, achieving the desired freezing effect. Generally, when the soil temperature reaches \(-10\)\({}^{\circ}\)C, the thickness of the soil within the \(-10\)\({}^{\circ}\)C isotherm is considered the effective permafrost curtain thickness. After 40 days of active freezing, the permafrost curtain was well developed, with the measured thickness of the permafrost curtain in the west side wall freezing area (upstream freezing area) being 4.34 m, in the east side wall freezing area (downstream freezing area) 4.40 m, and in the top slab freezing area 4.36 m, and in the bottom plate freezing area 4.33 m. Compared with the design standard's limit value for the frozen soil curtain thickness of \(-10\)\({}^{\circ}\)C, it was found that the frozen curtain met the requirement for soil reinforcement in the calculation result of the model for Freezing Optimized Scheme 1, ensuring the safety of construction and permitting the commencement of construction.