# Key Issues in Using the Freezing Method in Power Tunnel Rehabilitation Projects
## 4 Analysis of Numerical Simulation Results
#### 4.1.2 Z-Section Considering Seepage Flow  
The impact of groundwater seepage on the development of permafrost barriers is a critical consideration. Under typical construction scenarios, the flow of groundwater through the porous medium is characterized by laminar flow, adhering to [PERSON]'s law. For the purposes of this analysis, the discussion in this study is limited to unidirectional seepage, assuming that seepage occurs exclusively at the upper and lower boundaries of the model. To elucidate the effects of varying seepage velocities on the freezing temperature field under seepage conditions, the time intervals between frozen soil curtain circles and the final thickness of the frozen soil curtain were investigated for different seepage rates. Through numerical simulations, the head differences at the upstream and downstream boundaries of the model were set to 1 m, 2 m, 3 m, 4 m, and 5 m to investigate the effect of seepage velocity changes on the freezing temperature field. Figure 6: Schematic representation of the location of the profiles in different directions. Figure 7: _Cont._  
Figure 8 illustrates the changes in the freezing temperature field under various seepage velocities. For comparative analysis, temperature field cloud diagrams at 1 d, 20 d, 30 d, and 60 d were selected to examine the impact of seepage velocity on the freezing temperature field. Initially, at 1 d, the freezing tube began to generate a minimal amount of cold for different seepage velocities, which was not yet transferred to the surrounding area but was confined to the immediate vicinity of the freezing tube. At this stage, groundwater flow was horizontal and uniform, moving from high to low heads across the frozen area. By 20 d, with a head difference of 1 m, the initial outline of the frozen soil curtain started to form, and as freezing progressed, the curtain developed steadily. However, with a head difference of 2 m, the development of the frozen soil curtain was somewhat hindered, showing non-uniform growth upstream and downstream, indicating that the curtain was not yet fully closed and did not completely prevent groundwater inflow. As the freezing pipe continued to apply cold, a more stable frozen soil curtain eventually formed. A head difference of 3 m revealed that the groundwater flow influenced the freezing method's temperature field, with the curtain's development slowing down, particularly at the waterfront. By the 30 th day, the curtain had not yet closed, and there was still a small amount of water flow within the freezing area. By the end of freezing (60 d), a very weak frozen soil curtain had formed. With head differences of 4 m and 5 m, the impact of groundwater flow on the formation of the frozen soil curtain was evident, with the curtain remaining unstable throughout the freezing period. Water flow was present in the freezing gap and through the excavation area surrounding the freezing pipe, posing a significant risk for subsequent construction excavation in actual projects. The cold produced by the freezing pipe was gradually carried downstream by the groundwater flow, leading to uneven development of the frozen soil curtain. As the seepage velocity increased, the unevenness of the curtain's development grew, expanding the frozen area's scope but weakening the overall freezing effect, and the curtain's thickness gradually decreased, making it impossible to form a stable frozen soil curtain. The engineering construction of permafrost curtains involves a well-developed method for measuring freezing, primarily based on two indicators: the intersection time and the specific thickness of the permafrost curtain. Figure 9 illustrates the variation in the intersection times of the \(-1\)\({}^{\circ}\)C and \(-10\)\({}^{\circ}\)C isotherms under different seepage velocities. As Figure 8 indicates, the intersection times of the \(-1\)\({}^{\circ}\)C and \(-10\)\({}^{\circ}\)C isotherms increased with an increase in seepage velocity.