## 4 The Influence of Different Factors on the Development of Temperature Field Patterns
### Effect of Initial Ground Temperature  
In order to investigate the influence of different initial ground temperatures on the new pipe curtain freezing method under seepage conditions, the initial ground temperature is set as the only variable under typical parameters. Different models with varying initial ground temperatures are numerically obtained to analyze their respective outcomes. Six different initial ground temperatures ranging from 10 \({}^{\circ}\)C to 35 \({}^{\circ}\)C are set at intervals of 5\({}^{\circ}\) C to study the effects of different initial temperatures on the new pipe curtain freezing method. Based on the previously set temperature measurement paths DGJ-3 and DGJ-4, two temperature measurement points are selected along the paths: one located directly between the freezing pipes and the other positioned 1 m away. Figure 8 shows the cooling curves of the different temperature measurement points on the two different paths. From Figure 8, it can be observed that with the increase in the initial ground temperature, the time required for the new pipe curtain freezing method to form a frozen soil curtain under seepage conditions is prolonged, and the final temperature of the frozen soil curtain also increases. The time taken for each point on the path to reach \(-1\)\({}^{\circ}\)C (freezing temperature) is also extended with the increase in the original ground temperature. Moreover, the cooling curve of the temperature measurement point becomes more susceptible to the influence of the increase in the initial temperature as the distance from the freezing pipe increases. Taking point DGJ-3-5 as an example, when the original ground temperature is 10 \({}^{\circ}\)C, the time required for point DGJ-3-5 to reach \(-1\)\({}^{\circ}\)C is 28 days. When the original ground temperature increases to 25 \({}^{\circ}\)C, the time required for point DGJ-3-5 to reach \(-1\)\({}^{\circ}\)C is 46 days, extending the freezing time by 18 days. When the original ground temperature increases to 35 \({}^{\circ}\)C, the time required for point DGJ-3-5 to reach \(-1\)\({}^{\circ}\)C is 58 days, extending the freezing time by 30 days. At the same time, the final freezing temperature of temperature measurement point DGJ-3-5 also increases with the rise in the initial temperature. When the initial temperature increases from 10 \({}^{\circ}\)C to 35 \({}^{\circ}\)C, the final freezing temperature increases from \(-16.77\)\({}^{\circ}\)C to \(-8.66\)\({}^{\circ}\)C, with a rise of 8.11 \({}^{\circ}\)C. The frozen soil engineering design stipulates that the final frozen soil curtain temperature should not exceed \(-10\)\({}^{\circ}\)C, which is not met when the initial ground temperature is 35 \({}^{\circ}\)C.  
Figure 7: _Cont._Figure 7: Cont. temperature measurement points at the same position on the two paths are both affected by the increase in the initial ground temperature. However, the temperature decrease at point 2 on DGJ-4, located on the upstream side, is slower than that at point 4 on temperature measurement path DGJ-3 on the downstream side of the curtain due to the influence of the groundwater flow. Similarly, due to the partial removal of cold energy by the groundwater flow, the cooling curve at point 5 on path DGJ-3 differs from that at point 3 on path DGJ-4. According to the engineering design requirements, in order to meet the construction excavation requirements, the thickness of the frozen soil curtain should be greater than 2 m and the average temperature should be less than \(-10\)\({}^{\circ}\)C. Based on the final freezing temperature calculation at the temperature measurement point DGJ-3-5, located 1 m away from the freezing pipe, for every 5 \({}^{\circ}\)C increase in the original ground temperature, the final freezing temperature increases by 1.62 \({}^{\circ}\)C. When the initial ground temperature is greater than 35 \({}^{\circ}\)C, it significantly affects the formation of the frozen soil curtain in permeable conditions.