## 5 Results and Discussions
### Temperature Distribution within the Freezing Wall at Two Characteristic Time Points  
As mentioned in the Section 1, problems concerning temperature distribution within freezing walls have long been of great interest. In this study, the temperature distribution within the freezing wall at two characteristic time points, i.e., the starting point of the fast-freezing stage and the finishing point of the fast-thawing stage, were investigated. These two points were selected to shed light on the identification and explanation of the beginning of the fast-freezing stage and the end of the fast-thawing stage with temperature distribution. The distribution results are presented in Figures 7 and 8. Figure 7 illustrates the temperature distribution within freezing walls of different thicknesses at the cross-section of the Y-axis right before the fast-freezing stage. Before entering the fast-freezing stage, the temperature of the area right around the cross passage would already have been below freezing temperature. This may be traced to the shrinkage of the unfrozen soil due to the drop in the temperature. The shrinkage of the soil cancels part of the frost heave. Therefore, part of the soil froze ahead of the commencement of the frost heave of the ground surface. In addition, as shown in Figure 7, the lowest temperature within the freezing wall at this time point first drops and then increases with an increase in the thickness of the freezing wall. Figure 8 demonstrates the temperature distribution within freezing walls of different thicknesses at the cross-section of the Y-axis right after the fast-thawing stage. Like its counterpart in the freezing process, when achieving a stable settlement, the temperature of some areas in the middle of the freezing wall would still have been below freezing temperature. There are several potential explanations for this. There was only a very thin layer of frozen soil within the freezing wall, and most of the soil was in a thawed state. Therefore, the displacement arising from thawing would not contribute too much to the entire thawing settlement. In addition to this, when the temperature rises during the thawing process, the unfrozen soil expands, and this also counteracts the thaw settlement of the ground surface. Therefore, part of the soil remains frozen when the settlement is about to become stable. Figure 8 also shows that the lowest temperature within the freezing wall at this time point drops with an increase in the thickness of the freezing wall in a gradual, gentle way. Apart from this, it can be seen that with an increase in the thickness of the freezing wall, the center of the temperature contour moves downward. This may arise from the setting of the temperature thermal boundary at the top of the model. The temperature at the top of the model is fixed and can be thought of as a heat source which transfers the heat downward to the freezing wall, where the temperature is much lower than the surrounding soil. This heat transfer movement makes the temperature of the upper side of the cross passage higher than that of the lower side. This effect might be more apparent as the prolongation of the fast-thawing stage with an increase in the thickness of the freezing wall. Figure 6: Changes in the time corresponding to the fast-freezing stage and the fast-thawing stage with an increase in the thickness of the freezing wall. Spatial Distribution of Frost Heave and Thaw Settlement and How the Thickness of the Freezing Wall Affected It  
Figures 9 and 10 reveal that the frost heave distribution along the X-axis is wider than that along the Y-axis. This reveals that the frost heave has a gentler variation in the transverse direction of the tunnel, yet a more marked variation in the longitudinal direction of the tunnel.