## 3 Numerical Simulation
### Influence of Burial Depth on Mechanical Response of Buried Pipeline  
(1) Comparison of the soil arch rate and soil pressure calculated using the Chinese code with finite-element analysis. The ratio of the earth pressure value to the self-weight stress of the soil at the measuring point is defined as the soil arch rate (VAF) [32]. The formula is as follows:  
\[VAF=\frac{q}{\gamma H} \tag{10}\]  
where \(q\) is the earth pressure value at the top of the pipe, \(\gamma\) is the unit weight of soil, and \(H\) is the filling height at the top of the pipe. Figure 12 provides the VAF calculated using the Chinese code method [24] and the finite-element analysis at the pipe top under soil pressure. The values of soil pressure on the pipe roof obtained by finite-element analysis and the Chinese code method are shown in Figure 13. It is observed from the figures that the VAF under each buried depth calculated by the finite-element model is less than 1, indicating that the soil arch effect occurs during backfill application during pipeline construction. In addition, with increasing buried depth, the VAF shows a decreasing trend, and the soil arch effect at the top of the pipeline is more obvious. The Chinese code [24] did not consider the influence of soil arching effect on the soil pressure on the pipe top, so the formula solution of the code was quite different from the finite-element analysis, and the difference between them further increased with  
Figure 11: The circumferential strain of pipeline obtained by finite-element analysis and field tests: (**a**) Condition 1, (**b**) Condition 2, and (**c**) Condition 3.  
the increase of the buried depth of the pipe. When the buried depth reached 2.0 m, the calculated value of the standard formula was 1.58 times the finite element calculation value. (2) Influence of buried depth on the mechanical response of pipeline  
Figures 14 and 15 show the deformation of the pipeline and the displacement of the pipe top under strong and weak vibrations (vibration frequencies of loads are 28 Hz and 33 Hz, respectively). Figures 16 and 17 represent the deformation and displacement of the pipeline under earth pressure. It can be seen from these four figures that, under the earth pressure, the deeper the pipeline is buried, the greater the deformation of the pipeline and the displacement of the pipe top. The vertical deformation of the pipeline increased more rapidly than the horizontal deformation. When the buried depth increased from 0.8 m to 2 m, the lateral deformation increased by 1.02 mm, which was less than the 1.3 mm increase in vertical deformation. During backfilling, the compaction degree of the soil on the sides of the pipeline was higher than that on the top of the pipeline, which made the pipe less likely to deform to both sides. With increasing burial depth, the pipeline experiences horizontal deformation, which tends to compact the soil on the side of the pipeline. At the same time, the pressure from the top-filling soil will further compress the soil on the side of the pipeline. The compaction degree of the bottom-filling soil will also increase with the increasing pressure from the top-filling soil. Therefore, the increased rate of pipe top displacement decreases with the increase of buried depth. Figure 12: The VAF calculated using the Chinese code method and finite-element analysis. Figure 13: The soil pressure on the pipe roof. Figure 16: Deformation of the pipe under earth pressure. Figure 14: Deformation of the pipeline under different vibration modes. Figure 15: Displacement of the pipe top under different vibration modes. With an increase in filling height for both strong and weak vibration states, the deformation of the pipeline had a decreasing trend. This shows that with increasing buried depth, the speed of vibration load attenuation is greater than the growth rate of soil pressure.