## 3 Numerical Simulation
### Effect of Backfill Properties on Mechanical Response of Buried Pipeline  
The numerical model was used for the numerical simulation of buried pipelines under the condition of 1.7 m buried depth. To control the influence of secondary factors on the analysis, the elastic modulus of the backfill at the top of the pipeline was changed to simulate different types of backfill, and the other parameters remained unchanged. (1) Influence of backfill properties on pipeline mechanical response under earth pressure. Figure 18: Equivalent stress of the pipeline under (**a**) weak vibration state, (**b**) strong vibration state, and (**c**) earth pressure. The displacement and soil pressure at the top of the pipeline change with the elastic modulus of backfill soil under the earth pressure, as shown in Figure 19. It can be seen that the displacement and earth pressure of the pipe top shows a downward trend with an increasing elastic modulus of the backfill soil. When the elastic modulus increases to 5 times the initial value, the displacement and the earth pressure of the pipe top decrease by about 10.0 and 15.3%, respectively. However, with a further increase in elastic modulus, the decreasing trend gradually diminishes. When the elastic modulus increases to 15 times the initial value, the pipe top displacement and the pipe top earth pressure decrease by 16.2 and 23.5%, respectively. According to the definition of soil arching rate, the increase of elastic modulus of the filling material causes the soil arching rate to decrease, demonstrating that the elastic modulus of the filling has a significant influence on the soil arching effect and that there is a positive correlation between them. The possible reason is that when the elastic modulus of backfill soil is large, its own resistance to deformation is strong, and the integrity is strong, so it can reduce the stress deformation of the pipeline under static force to a certain extent. Figure 20 shows the Mises equivalent stress and circumferential strain of the pipeline when backfilled with different properties. From Figure 20a, it can be seen that with the increase of elastic modulus of backfill, the equivalent stress on the middle ring section of the pipeline decreases gradually. Additionally, the maximum equivalent stress occurs at the centerline of the sidewall of the pipeline, and the equivalent stress at other positions does not decrease significantly with an increase in the elastic modulus of the fill. It can also be observed from Figure 20b that the variation law of circumferential strain is similar to that of equivalent stress, but the position where the maximum value of circumferential strain appears is slightly lower than that of equivalent stress. In summary, under the earth pressure, the increase of elastic modulus of backfill soil makes the soil arching effect more apparent, and more of the pipe top load is borne by the soil to the side of the pipe, which is also the reason for the decrease of pipe stress and strain. Therefore, the increase of elastic modulus of fill is conducive to the protection of pipelines. Figure 19: The displacement and soil pressure at the top of the pipeline. Effect of backfill properties on the mechanical response of pipeline under vibration. The mechanical response of the pipeline under the strong vibration mode is simulated by applying a vibration load on the filling surface. The results are shown in Figures 21 and 22. Compared with the static backfill state, the displacement amplitude at the top of the pipeline, soil pressure amplitude, and circumferential strain under the action of vibration compaction show different rules. With an increasing elastic modulus of the backfill, the displacement amplitude first decreases and then increases. When the elastic modulus of the filled soil increases to 25 MPa, the displacement amplitude of the pipe top and the soil pressure reach the minimum and then increase rapidly with the increase of the elastic modulus.