## 3 Analysis of Temperature Field of Frozen Wall
### Numerical Results and Discussion
#### 3.3.4 Influence of Brine Temperature on Temperature Field of Frozen Wall  
The temperature of circulating cooling agent (brine) governs the formation of frozen wall. Here, \(-216\) m sandy clay layer control is taken as the research object, and based on the actual position of the freezing holes, the active freezing period under different brine temperatures as well as the variations in the characteristic parameters of the temperature field of the frozen wall (effective frozen wall average temperature, effective thickness of frozen wall) with time are examined. The brine temperature in the active freezing period is \(-20\), \(-25\), \(-30\), and \(-35\)\({}^{\circ}\)C. It is assumed that the on-site circulating brine temperature for the first 19 d is the same as that in the actual project, and the brine temperature of the freezing holes remains unchanged after the 20 th day of brine circulation. As shown in Figures 8 and 9, the variation in the brine temperature during the active freezing period affects the average temperature and thickness. Under the same freezing time, the lower the brine temperature, the lower the effective frozen wall temperature and the greater the thickness. When frozen for 130 d, the brine temperature decreases from \(-20\) and \(-35\)\({}^{\circ}\)C, and the average temperature of effective frozen wall decreases from \(-12.16\) to \(-21.09\)\({}^{\circ}\)C, corresponding to a decrease of \(73.4\%\). Under freezing for 130 d, the effective frozen wall thickness increases from \(4.05\) m to \(4.65\) m, which corresponds to an increase of \(14.8\%\). For the sandy clay layer at the control horizon of toposoil (\(-216\) m), during excavation (frozen for 130 d), the designed average temperature of effective frozen wall is \(-12\)\({}^{\circ}\)C, and the designed thickness is \(4.2\) m. If the brine temperature in the active freezing period is \(-20\)\({}^{\circ}\)C, the average temperature of the effective frozen wall just reaches \(-12\)\({}^{\circ}\)C during the excavation of this layer, but the thickness cannot reach the design requirement of \(4.2\) m. Therefore, the salt water temperature in the active freezing period is \(-20\)\({}^{\circ}\)C, which cannot meet the design requirements. If the brine temperature during the active freezing period is set to \(-25\)\({}^{\circ}\)C or below, as shown in Figures 8 and 9, the average temperature and thickness of effective frozen wall during the excavation of the control layer meet the design requirements. Therefore, the brine temperature during the active freezing period is set to \(-25\)\({}^{\circ}\)C or below. It can be seen from Figures 8 and 9 that when the brine temperature is \(-25\)\({}^{\circ}\)C and below, the average temperature of effective frozen wall reaches \(-15\) to \(-21\)\({}^{\circ}\)C and the thickness is \(4.29\)-\(4.65\) m when frozen for 130 d; under the premise of ensuring safety, this can avoid increasing the difficulty in excavation due to the entry of excessive frozen soil in the excavation section as well as save the freezing costs. Therefore, after entering the maintenance freezing period, the brine temperature in the freezing hole should be adjusted in real-time while maintaining the average temperature and thickness of the effective frozen  
Figure 7: Temperature field distribution at the main surface and interface. (**a**) The \(-120.5\) m fine sand main surface. (**b**) The \(-120.5\) m fine sand interface. (**c**) The \(-190\) m clay main surface. (**d**) The \(-190\) m clay interface. (**e**) The \(-216\) m sandy clay main surface. (**f**) The \(-216\) m sandy clay interface. wall.