## 3 Test Result and Discussion
### Variation Law of Freezing Pipe Strain
#### 3.2.2 Analysis of Variation Law of Freezing Pipe Strain  
Due to the large vertical displacement of soil in the process of compression and consolidation, most of the strain gauge leads are broken, and only part of the test data of the strain gauge are obtained. Based on Equations (19)-(21), to process the strain gauge test data, the change curves of \(\varepsilon_{N}\), \(\varepsilon_{mx}\), and \(\varepsilon_{my}\) of each test horizon in the different soil layers with respect to the freezing time \(t\) are obtained, as shown in Figures 7-9. (1) Pure vertical tension-compression strain \(\varepsilon_{N}\)  
It can be seen from the Figure 10 that shows the \(\varepsilon_{N}-t\) curve obtained from the experiment:  
Figure 9: Schematic diagram of freezing pipe strain direction. 1 The values of \(\varepsilon_{N}\) at the corresponding positions of the D3 and D4 freezing pipes are different, but the variation rules are similar. The different \(\varepsilon_{N}\) values may be due to the different consolidation degree of the soil around the two freezing pipes, resulting in different frost heave effects of the soil during the freezing process. 2 The D3 and D4 freezing pipes are always under the pressure in the clay layer. During the period of 0-100 h, \(\varepsilon_{N}\) decreases continuously, and the \(\varepsilon_{N}\) of the D3 freezing pipe is the smallest, which is \(-305\)\(\mu\epsilon\), corresponding to the vertical compressive stress of 64.1 MPa. There are two possible reasons for this phenomenon: first, because the development speed and stiffness of the clay layer frozen wall are smaller than those of the upper and lower sand layers frozen wall. In addition, not only is the freezing temperature of the unfrozen water in the clay layer lower than that of the sand layer, but the clay layer is also located in the middle of the two sand layers. Therefore, the frozen wall of the upper and lower sand layers is rapidly formed during the freezing process, while the frozen wall of the clay layer has not yet formed, causing the frozen wall of the upper and lower sand layers to continuously squeeze the clay layer in the vertical direction so that the vertical frost heave of the clay layer is limited, resulting in the continuous compression of the frozen pipe under the action of the clay confining force. Second, at the procedure of the compression and consolidation, due to the different consolidation characteristics of the sand and clay, the vertical compression displacement of clay layer is much larger than that of sand layer, resulting in the thickness of the clay layer after consolidation being less than that of the sand layer. As a result, the vertical frost heaving force of the clay layer is less than that of the sand layer, which results in the frozen wall of the clay layer causing the vertical compression by holding the frozen pipe. 3 The D3 and D4 freezing pipes are in the state of compression first and then tension in the sand layer. During the period of 0-10 h, \(\varepsilon_{N}\) decreases gradually, and the \(\varepsilon_{N}\) of D3 freezing pipe is the smallest, and that is \(-302\)\(\mu\epsilon\), which is equivalent to the vertical compressive stress of 63.4 MPa. During the period of 10-90 h, the frozen pipe begins to change from compressive strain to tensile strain, and \(\varepsilon_{N}\) increases gradually. D3 and D4 freezing pipes transformed into pure tensile strain at 18 h and 24 h, respectively, and reached the maximum at 90 h. The \(\varepsilon_{N}\) of D4 freezing pipe is the largest, which is 406 \(\mu\epsilon\), corresponding to the vertical tensile stress of 85.2 MPa. During the period of 90-120 h, \(\varepsilon_{N}\) decreases slowly. It is mainly because in the early stage of freezing, because the temperature of the freezing pipe drops rapidly, the temperature stress generated by itself is greater than the vertical friction provided to the freezing pipe by the frost heave of the soil, causing the shrinkage strain of the freezing pipe.