## 3 Test Result and Discussion
### Variation Law of Freezing Pipe Strain
#### 3.2.2 Analysis of Variation Law of Freezing Pipe Strain
As the freezing brine temperature continues to decrease, the freezing wall thickness also gradually increases, which makes the bonding force between the frozen soil and the frozen pipe greater than the freezing pipe's own temperature stress, causing the frozen soil to hold the frozen pipe and begin to expand, resulting in the frozen pipe producing tensile strain. In the later stage of freezing, because the vertical volume shrinkage of frozen soil is greater than that of frozen pipe, the frozen soil will hold the frozen pipe and shrink together, which makes the frozen pipe change  
Figure 10: Vertical strain curve of freezing pipe. from tensile strain to compressive strain, resulting in the corresponding decrease in the tensile strain of the frozen pipe. 4 The D4 freezing pipe is basically in the tensile state at the soil interface. During the whole freezing process, \(\varepsilon_{N}\) increases slightly at first and then decreases gradually, but it is basically very small. It may be because the D4 frozen pipe is mainly tensile strain in the sand layer and compressive strain in the clay layer, so these two kinds of soil layers will form a neutral strain surface at the interface of soil layer. As a result, the vertical tension and compression strain of the frozen pipe is not prominent at the interface of the soil layer. (2) Pure bending strain \(\varepsilon_{m}\)  
Figures 11 and 12 are the results \(\varepsilon_{mx}-t\) and \(\varepsilon_{my}-t\) curves from the test. From Figure 9, it can be seen that the positive direction of the \(X\)-axis is the direction away from the well center, and the positive direction of the \(Y\)-axis is the direction of counterclockwise rotation around the well center. Therefore, the \"+\" sign in \(\varepsilon_{mx}-t\) and \(\varepsilon_{my}-t\) represents the direction away from the shaft center and counterclockwise around the shaft center, while the \"\(-\)\" sign is the opposite. \"+\" and \"\(-\)\" only represent the bending direction, independent of the numerical value. It can be seen from the Figures 11 and 12 that:  
1 In the clay layer, the \(\varepsilon_{mx}\) of D3 and D4 freezing pipes increases with the increase in freezing time and tends to be stable, but the bending direction is different. The D3 freezing pipe sends away from the shaft center, while the D4 freezing pipe sends near the shaft center. The maximum \(\varepsilon_{mx}\) of D3 freezing pipe is 351 \(\mu\varepsilon\), which corresponds to the bending stress of 73.7 MPa. The maximum \(\varepsilon_{mx}\) of D4 freezing pipe is 249 \(\mu\varepsilon\), which is equivalent to the bending stress of 52.3 MPa. In the sand layer, the \(\varepsilon_{mx}\) of D3 and D4 freezing pipes first increases slightly and then decreases continuously, which is generally small, and the maximum of \(\varepsilon_{mx}\) is only 47 \(\mu\varepsilon\). The bending direction of the freezing pipe is exactly opposite to the respective bending direction in the clay layer. Figure 11: X direction bending strain curve of freezing pipe. Figure 12: Y direction bending strain curve of freezing pipe. 2 In the clay layer, the \(\varepsilon_{my}\) of the D3 and D4 freezing pipes increases with the increase in the freezing time and finally stabilizes. The bending direction is also the same, and they all bend in the direction of counterclockwise rotation around the shaft center. Among them, the \(\varepsilon_{my}\) of D3 freezing pipe is the largest, reaching 696 \(\mu\varepsilon\), which is equivalent to the bending stress of 146.2 MPa. In the sand layer, the variation trend and the \(\varepsilon_{my}\) bending direction of D3 and D4 freezing pipes are the same, but \(\varepsilon_{my}\) is very small in both. 3 At the interface of soil layers, the \(\varepsilon_{mx}\) of the D4 freezing pipe increases firstly and then decreases, while the \(\varepsilon_{my}\) is just the opposite. The bending direction of each is always the same throughout the freezing process.