## 4 Conclusions  
1. The distribution of the freezing temperature field in different soil layers is similar, but the change rate of the freezing temperature field, the cycle time of freezing wall, and the average temperature are related to soil properties.
2. In the later stage of freezing, the freezing pipes in different soil layers are vertically subjected to pure tensile stress or pure compressive stress. However, in the initial stage of freezing, not only is the freezing pipe in the sandy soil layer subjected to the temporary vertical compression, but the freezing pipe in the clay layer is also always in the vertical compression state, which is different from the previous research results on the stress and deformation law of the freezing pipe in the freezing process of the single soil layer.
3. During the freezing process, the bending direction of different freezing pipes in different soil layers is not the same. The maximum bending strain of the frozen pipe in the clay layer can reach 779 \(\mu\varepsilon\), which is 2.6 times the vertical strain at the same position, equivalent to 163.4 MPa, while the bending stress in the sand layer is relatively small. The accumulation of strain energy induced by bending can easily lead to the fracture of the frozen pipe in the process of digging.
4. The total strain of the freezing pipe is obtained by superimposing the pure vertical strain and the pure bending strain of the freezing pipe. It is concluded that the absolute value of the total strain of the freezing pipe in the clay layer is greater than that in the sand layer. By converting the strain into stress, it can be seen that the maximum tensile stress of the freezing pipe in the clay layer is 175.5 MPa, which can reach 0.75 times the yield limit of the freezing pipe, and will pose a certain degree of threat to the safety of the freezing pipe. At this time, the effective measures can be taken to improve the mechanical performance of the frozen pipe to increase the deformation capacity of the joint of the frozen pipe and reduce the strain energy stored by the frozen pipe, which will reduce the failure rate of the frozen pipe in the digging stage.
* The model test results show that the freezing pipe in the composite stratum is in the spiral torsion shape. However, because the real stratum conditions are much more complex and changeable than the model tests, the real existing forms of freezing pipes in the actual stratum will be more diversified.
* As the test load is only 8 MPa, the test results obtained are single and not three-dimensional enough. In the future, the model tests with different consolidation pressures and different freezing temperatures will be carried out, corresponding numerical simulation verification will be carried out for each group of model tests, and more innovative conclusions will be drawn. According to the innovative conclusions obtained, combined with the specific freezing project objects, the freezing problems and characteristics that the freezing project may face are proposed.  
Conceptualization and Formal analysis, L.Q. Data curation, J.L. Methodology, Y.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (Grant no. 52074264, Grant no. 51174194), the Fundamental Research Funds for the Central Universities of China (Grant no. 2021 GJZPY15, Grant no. 2018 ZZCX04), and the National Key Research and Development Program of China (Grant no. 2016 YFC0600903).  
Not applicable.  
All the data used to support the findings of this study are included within the article. The datasets generated and analyzed during the current study are available from the corresponding author upon reasonable request.  
The authors declare that there are no conflict of interest regarding the publication of this paper.