## 3 Result and Discussion
### Relationship between CT Number and Soil Settlement  
In order to obtain the 3D distribution characteristics of pores in the clay, the software \"Aviso\" was used to realize the 3D reconstruction of CT image. In order to reduce the error, we selected the region in the red ring as the basis of soil structure remodeling in every CT image, as in Figure 12. The 3D reconstruction results are shown in Figure 13.  
Figure 11: Dry density obtained by cutting ring method. Figure 12: Image cutting. Figure 13: Pore 3D reconstruction results. As can be seen from Figure 14, the distribution of CT numbers along the height can be divided into three areas:  
1 The average value of CT number in 0-125 mm area is higher than other areas, the CT number near the freezing front is the largest, and the soil is the densest. There is a linear relationship between CT number CT (H) and height \(h\):  
\[\text{CT}(\text{H})=0.341\times h+1199.9 \tag{1}\]  
2 In the 125-150 mm section, the CT number decreases rapidly with the increase of height. After melting, the final position of the freezing front is 150 mm from the centerline of the freezing pipe. The water in the unfrozen area above the freezing front migrates to the freezing area below the freezing front. The water in the freezing area is continuously enriched during freezing, and the clay drainage consolidation in the melting stage. The relationship between CT number CT (H) and height h in this section is as follows:  
\[\text{CT}(\text{H})=-6.1318\times h+2010.6 \tag{2}\]  
3 In the 150-485 mm section, the CT number in this section decreases slowly with the increase of height. During the freezing process, the moisture in the unfrozen area near the front decreases continuously, the soil loses water and compresses, and the soil layer becomes dense. The CT number in this interval is negatively correlated with the distance from the freezing front:  
\[\text{CT}(\text{H})=-0.261\times h+1125.8 \tag{3}\]  
Actually, the CT number reflects the density of the object. The CT numbers collected from each layer were connect with the dry density and obtained the fitting curve shown in Figure 15.  
It can be seen from Figure 15 that there is a good linear relationship between CT number and dry density:  
\[\rho_{\text{dry}}=0.0012\text{CT}(\text{H})-0.0341 \tag{4}\]  
In the above formula, the correlation coefficient \(R^{2}=0.9483\), so the dry density value can be calculated according to the CT number. It should be noted that in Figure 15, the experimental data at the point near CT (H) = 1150 are missing because the CT number decreases rapidly in the 125-150 mm section away from the freezing pipe, and the interval range is only 25 mm, while the height of the ring knife sample for measuring the dry density is 20 mm, and the dry density is not measured in this interval. Figure 13.0 Distribution of CT number along height. The void ratio \(e(h)\) of soil can be calculated according to the relationship between dry density and height \(h\):  
Figure 13.1  
The calculated void ratio distribution along the height is shown in Figure 13.2  
Without considering the lateral deformation, the thawing settlement of soil belongs to a one-dimensional compression problem:  
Figure 13.3  
where \(e_{1}\) and \(e_{2}\) is the void ratio of soil before and after freezing and thawing, and H is the thickness of soil layer. According to the CT test results, the spatial distribution \(e(h)\) of void ratio along the vertical direction after melting has been obtained, and the melting settlement can be obtained by integration:  
Figure 13.4  
where \(h_{1}\) and \(h_{2}\) are the upper and lower limit height of the frozen area. Figure 13.5 Void ratio along height. Figure 13.6 The relationship between CT number and dry density. The void ratio at the height of \(h=485\) mm (at the surface) is taken as the initial value \(e_{1}\) before freezing and thawing. According to the settlement calculated by the void ratio, the settlement of the soil layer (0-485 mm) from the freezing pipe to the surface is 41.2 mm.