## 2 Establishment of Three-Dimensional Pipeline-Sooil Thermo-Mechanical Coupling Model  
### Pipeline-Soil Model Parameters  
#### 2.1.1 SOIL Material Parameters  
According to the geological exploration data of the frozen soil in Northeast China [18; 19; 20; 21; 22; 23; 24], the modelled depth was selected to be 20 m below the natural ground, the modelled length was 100 m, and the modelled width was 40 m. The soil of buried pipeline was divided into non-frost heaving section (10 m) + transition section (20 m) + frost heaving section (40 m) + transition section (20 m) + non-frost heaving section (10 m) = 100 m. The simplified soil layers from top to bottom were silty clay layer with a thickness of 3 m, fine sand and gravel layer with a thickness of 7 m and weathered bedrock residue layer with a thickness of 10 m. The diameter of the pipeline was 0.762 m, the wall thickness was 0.0175 m, the thickness of the insulation layer was 8 cm, and the buried depth was 1.6 m.  
The pipeline-soil system was a spatial model. Taking into account the symmetry of the model, the finite element calculation model uses 1/4 (1/2 in both vertical and horizontal directions) for analysis. The two-dimensional plane model of the pipeline-soil model is shown in Figure 1.  
The soil thermal parameters and moisture content are shown in Table 1[12], and the soil mechanical parameters of each layer in the frozen soil area are shown in Table 2[25; 26]. Since the thermal expansion and contraction of the soil has no obvious variation, only the frost heave caused by the frozen volume expansion of the water in the soil needs to be considered in the calculation. The volume expansion of water after freezing is about 9%, and the linear expansion coefficient \(\alpha\) should be introduced in the calculation [27], and the value is obtained according to the following Formula (1):  
\[\alpha=-\frac{0.09\omega}{3\Delta T} \tag{1}\]  
where \(\omega\) is the natural moisture content (%); \(\Delta T\) is the temperature increment (\({}^{\circ}\)C).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{**Temperature/\({}^{\circ}\)C**} \\ \hline  & \(-\)**30** & \(-\)**10** & \(-\)**5** & \(-\)**2** & \(-\)**1** & \(-\)**0.5** & **0** & **15** & **30** \\ \hline  & \multicolumn{8}{c}{**Sility Clay (\(\omega\) = 29.82\%)**} \\ \hline Thermal conductivity \(\lambda\) (W/m\({}^{\circ}\)C) & 1.21 & 1.21 & 1.21 & 1.21 & 1.21 & 1.21 & 0.84 & 0.84 & 0.84 \\ Specific heat C (J/kg.\({}^{\circ}\)C) & 1490 & 1490 & 1490 & 1490 & 1490 & 1490 & 1880 & 1880 \\ Soil expansion coefficient \(\alpha\) (10\({}^{-4}\)) & 2.982 & 8.946 & 17.890 & 44.730 & 89.460 & 178.9 & 0 & 0 & 0 \\ \hline  & \multicolumn{8}{c}{**Fine Sand and Gravel (\(\omega\) = 15\%)**} \\ \hline Thermal conductivity \(\lambda\) (W/m\({}^{\circ}\)C) & 1.04 & 1.04 & 1.04 & 1.04 & 1.04 & 1.04 & 1.04 & 1.04 & 1.04 \\ Specific heat C (J/kg.\({}^{\circ}\)C) & 2540 & 2540 & 2540 & 2540 & 2540 & 2540 & 3350 & 3350 \\ Soil expansion coefficient (10\({}^{-4}\)) & 1.500 & 4.500 & 9.000 & 22.500 & 45.00 & 90.00 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Thermal parameters and moisture content of soil.  
Figure 1: Two-dimensional plane model of the pipeline–soil model without damage and with internal corrosion defects.