# Three-Dimensional Numerical Modeling of Artificially Freezing Ground in Metro Station Construction
## 2 Site Description
### Design Scheme  
A schematic diagram showing the layout of the freezing holes is given in Figures 1-3. The left-line tunnel was addressed, and the freezing holes were arranged on one side. As indicated in Figure 2, there were 27 freezing holes in total, which were arranged at three angles: horizontal, pitched up, and pitched down. The total length of the freezing holes was 300 m. Two penetration holes were provided in the middle of the channel for the freezing pipe arrangement of the opposite channel in any emergency. Seven temperature measuring holes, C1-C7, were set and their main purpose was to measure the temperature development condition of the freezing curtain range, so as to adopt comprehensive corresponding control measures to ensure construction safety. A pressure relief hole, X1, was arranged in the closed area of the freezing curtain.  
Figure 3: Contralateral freezing hole layout.  
Figure 2: Layout of freezing holes on the machine room side.  
The main parameters of the freezing construction are shown in Table 2. It is necessary to combine the temperature monitored by the temperature monitoring hole, the hole detection condition, the pressure relief hole pressure, and other factors to determine the timing of opening the pipe. It is necessary to meet the design requirement conditions shown in Table 3 before the excavation.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Unit** & **Value** & **Remarks** \\ \hline Frozen soil curtain design thickness & m & 2 & / \\ \hline Frozen soil curtain average & \({}^{\circ}\)C & \(\leq\)\(-10\) & The average temperature of the interface between frozen soil curtain and pipeline sheet \(\leq\)\(-5\,{}^{\circ}\)C \\ \hline Frozen soil curtain closure time & Day & 22–25 & / \\ \hline Active freezing time & Day & 35 & / \\ \hline Number of freezing holes & & 27 & / \\ \hline Freezing hole control spacing & m & 1.5 & / \\ \hline Freezing hole allowable verticality & mm & 300 & When the deflection exceeds the standard, it is decided whether to fill the hole according to the comprehensive situation of the deflection. \\ \hline Designed minimum brine temperature & \({}^{\circ}\)C & \(-25\)—\(-28\) & The saltwater temperature gets below \(-20\,{}^{\circ}\)C after freezing for 7 days \\ \hline Maintain freezing brine temperature & \({}^{\circ}\)C & \(\leq\)\(-25\) & / \\ \hline Single-hole brine flow & m\({}^{3}\)/h & 3–5 & / \\ \hline Freezing pipe specification & mm & \(\Phi 89\times 8\) & Low carbon steel seamless steel pipe \\ \hline Number of temperature-measuring holes & & 7 & \(\Phi 89\times 8\) or \(\Phi 32\times 2.5\) \\ \hline Number of pressure relief holes & & 1 & / \\ \hline Total length of freezing pipe & mm & 297.516 & / \\ \hline Total cooling capacity of freezing & \(104\) kcal/h & 3.5 & According to specific working conditions \\ \hline \hline \end{tabular}
\end{table}
Table 2: Operational parameters during ground freezing.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Projects** & **Value** & **Remarks** \\ \hline Installation of tunnel support and protective doors & / & Emergency materials are fully equipped \\ \hline Remote monitoring facilities for connecting passages & / & / \\ and tunnels are all ready & / & / \\ \hline Frozen curtain average temperature & \(-10\,{}^{\circ}\)C & Calculated by the icing prediction formula \\ \hline Brine temperature & Active period & \(-25\,{}^{\circ}\)C or less & Monitoring with a thermometer \\ \hline The temperature & Maintenance period & \(<\)\(-25\,{}^{\circ}\)C & Decrease the temperature to design value \\ \hline \multirow{2}{*}{Pressure relief hole} & \multirow{2}{*}{Before closure} & \multirow{2}{*}{Hydrostatic pressure} & Observed by a pressure gauge, and no water, mud flowing out. \\ \cline{1-1}  & & & \\ \end{tabular}
\end{table}
Table 3: Technical indices in the excavation of cross-passage.