## 2 Establishment of Three-Dimensional Pipeline-Sooil Thermo-Mechanical Coupling Model
### Establishment of the Pipeline-Soil Solid Model  
The pipeline-soil thermo-mechanical coupling model in this paper used sequential coupling analysis (that is, from the initial temperature field to the cyclic temperature field and then to the stress field). The Mohr-Coulomb elastic-plastic constitutive model was adopted for soil, as shown in Formulas (2) and (3). The failure envelope of Mohr-Coulomb constitutive model combines the shear failure criterion and tensile failure criterion. As shown in Figure 3a the elements of the soil within the range of 5 m near the junction of the soil transition section and the frost having section and the soil near the axial direction of the pipeline should be grid refined, with a total of 28,431 elements. In addition, the insulation layer and the non-corroded pipeline were also divided by hexahedron with 2000 and 8000 elements.  
\[\sigma_{1}-\sigma_{3}\mathrm{N}_{\varphi}-2c\sqrt{\mathrm{N}_{\varphi}}=0 \tag{2}\]  
\[\mathrm{N}_{\varphi}=\tan^{2}\left(\frac{\pi}{4}+\frac{\varphi}{2}\right) \tag{3}\]  
where \(\sigma_{1}\) and \(\sigma_{3}\) are first principal stress and third principal stress, respectively; c and \(\varphi\) are the cohesion and internal friction angle of frozen soil, respectively.  
In order to improve the calculation accuracy and efficiency of the study area, the non-corrosion pit area of the corroded pipeline was roughly meshed along the axis of the pipeline, and the corrosion pit area was densified by fine grid size; in the direction along the wall thickness of the corrosion area, when the corrosion depth was 15% to 80%, the appropriate grid division method was obtained by comparing the variation curve of Mises equivalent stress on the inner wall of the pipeline with internal pressure when dividing  
Figure 3: (**a**) Three-dimensional pipe-soil thermal-mechanical coupling model for non-corroded and internally corroded defective pipelines; (**b**) Trend of equivalent stresses with a different number of grid layers.  
Figure 2: The Ramberg-Osgood model curve of X65 pipeline.  
grids with different layers. For example, when the corrosion depth was 25%, the Mises equivalent stress curves obtained by the simulation analysis of the hexahedral mesh with different numbers of layers were compared, as shown in Figure 3b. It can be found that four layers in the corrosion area and two layers in other areas will be able to obtain more accurate results. At this time, there were 24,716 hexahedral elements in corroded pipelines.  
The boundary conditions are shown in Figure 4. Symmetric constraints were applied to the \(Z=-50\) m and X = 0 sections of the pipeline-soil coupling model. Setting a single displacement constraint on \(Z=0\), Y = \(-20\) m and X = \(-20\) m sections; the ground at Y = 0 is free constraint. The contact surface between the insulation layer and the pipeline was bound. The contact property between the insulation layer and the soil was set as surface-surface contact, the vertical direction was set as hard contact, when the horizontal friction coefficient was 0.3, the real tangential behavior between pipeline and soil can be well reflected. When the temperature field and stress field were analyzed, the hexahedral heat transfer DC3D8 element and the three-dimensional stress C3D8 element were selected respectively. In this paper, a three-dimensional pipeline-soil thermo-mechanical coupling model of a 1/4 symmetrical non-corroded pipeline was established to determine the location of the maximum Mises equivalent stress on the inner wall of the buried pipeline. Furthermore, on this basis, a three-dimensional pipeline-soil thermo-mechanical coupling model of a 1/4 symmetrical pipeline with internal corrosion defects was established.