## 5 Analysis and Discussion of Calculation Results
### Distribution Law of Ground Surface Frost Heave Displacement  
Figure 10 depicts the ground surface's vertical frost heave displacement distribution curve. The tunnel centerline (x = 0 m) serves as the symmetry axis for all the curves. The vertical displacement of each point rises with freezing duration, and the effect is particularly noticeable in the \(-\)30 m \(\leq\) x \(\leq\) 30 m. range. The highest vertical uplift value of the surface at any moment in time is found at the center line, and the farther the location is from the center line, the lower the value is and ultimately approaches zero.  
Within 32 days to 70 days, there is a considerable rise, with maximum values of 68.96 mm and 122.4 mm at 45 and 70 days, respectively, and 10.71 mm and 19.38 mm at \(\pm\)30 m from the centerline. From 70 d to 90 d, the range of variation was rather minimal, with a maximum value of 155.67 mm at 90 d and 25.36 mm at 30 \(\pm\)m from the center line.  
The ground surface's horizontal frost heave displacement distribution curve is shown in Figure 10, with the tunnel centerline (x = 0 m) as the axis of symmetry--indicating an anti-symmetric distribution--and the displacement at the centerline being zero at all times. The displacement values on both sides of the centerline first gradually increase with distance, reaching the extreme value at x = \(\pm\)15.74 m, and then gradually decreasing to zero.  
The horizontal displacement of the ground surface changes relatively little from 0 d to 32 d, with an average increase of 0.26 mm/d and an extreme value of 8.17 mm at 32 d. It quickly increases from 32 to 45 days, with an average rate of 1.25 mm/d and an extreme value of 24.47 mm at 45 days. It slows down from 45 d to 70 d, with an average rate of 0.88 mm/d and an extreme value of 46.44 mm at 70 d; from 70 d to 90 d, with an average rate of 0.66 mm/d and an extreme value of 59.63 mm at 90 d.  
Comparing the numerical calculation results of vertical frost heave displacement at the surface midpoint of the selected model cross-section with the field-measured values, as shown in Figure 11, the variation patterns of the two are basically consistent, with some points having deviations less than 15 mm. The displacement value fluctuates relatively  
Figure 10: Frost heave displacement distribution curve of ground surface: (**a**) Vertical displacement curve; (**b**) Horizontal displacement curve.  
little from 0 d to 10 d, with an average increase rate of 0.07 mm/d. The displacement value varied relatively little from 0 to 10 d, with an average growth rate of 0.07 mm/d, then gradually increased to 0.93 mm/d from 10 d to 32 d. The displacement curve changes significantly from 32 d to 45 d, with an average increase rate of 3.47 mm/d, which then decreases to 2.14 mm/d from 45 d to 70 d, and further decreases to 1.54 mm/d from 70 d to 90 d. The numerical calculation result was 155.67 mm at 90 d, whereas the measured datum was 157.41 mm, showing that the calculation results are acceptable.  
The findings of the foregoing study show that the distribution and change of frost heave displacement during the freezing period are directly connected to the engineering geological circumstances, freezing scheme, forming process of frozen soil curtain, and pipe curtain structure.