## 5 Conclusions  
In this study, a double-walled corrugated pipe was simplified into a straight-walled pipe on the basis of hoop stiffness, and a three-dimensional finite element model was established. The changes in the Von-Mises stress of the pipe under a real traffic load and loose backfill were analyzed. For the tested conditions, the following conclusions could be drawn.  
1. In the numerical simulation, the Von-Mises stress of the straight-walled pipe can be used to predict the deformation response of the interior wall of the corrugated pipe under an external load, and the method for simulating the real traffic load by combining the Vdload subroutine with the half sinusoid is credible.
2. In the backfilling process, the maximum Von-Mises stress of the pipe is several times that of the stable state, the time during which the pipe is in this high-stress state is very short, and the influence on the pipe is very limited. The Von-Mises stress of the pipe is mainly determined by the earth's pressure at the crown. The increase in the buried depth of the pipe increases the deformation of the pipe and reduces the influence of the traffic load on the pipe.
3. Reducing the compaction degree of the backfill in contact with the pipe causes greater deformation of the pipe. Loose L1 has a negative effect on the pipe; the decrease in the compactness of L2 leads to an increase in the invert stress and a decrease in the stresses of the crown and the springline, and a decrease in the compactness of L3 results in an increase in stresses at the crown and the springline and decreases in the stress at the invert.
4. Compared with the earth pressure, the impact of the traffic load on the pipe is very limited. Pipes are more sensitive to traffic loads when the compaction degree of the backfill in contact with the pipe decreases. The response of the Von-Mises stress of the pipe to traffic loads is determined by the magnitude and the speed of the load, and the maximum Von-Mises stress is proportional to the traffic load magnitude and independent of the load speed.
5. The diameter and the hoop stiffness of the pipe affect the response of the pipe to the compactness of the backfill and the traffic load. The compactness of the backfill soil around the pipe needs to be higher when the diameter of the pipe is small; the variation in the hoop stiffness has a limited effect on the Von-Mises stress of the pipe, and there is no obvious law.  
Figure 27: Comparison of measurement and numerical simulation of pipe Von-Mises stress under traffic load: (**a**) the crown; (**b**) the springline; (**c**) invert.  
If the compactness of the backfill on the left and right sides of the pipe is not consistent, then the Von-Mises stress concentrates near the region of the pipe in contact with the loose backfill. The Von-Mises stress fluctuation caused by the traffic load is more significant than the stress under standard conditions, but it can still be negligible.  
Conceptualization, H.F.; Data curation, P.T., B.L., K.Y., and Y.Z.; Funding acquisition, H.F.; Investigation, P.T., B.L., K.Y., and Y.Z.; Methodology, P.T.; Software, P.T.; Writing--original draft, P.T.; Writing--review and editing, X.D. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Research and Development Program of China (No. 2016 YFC0802400), the National Natural Science Foundation of China (No. 51678536), the Scientific and Technological Research Program of Henan Province (No. 152102310066), and the Outstanding Young Talent Research Fund of Zhengzhou University (1621323001), for which the authors are grateful.  
The authors would like to thank the anonymous reviewers for their constructive suggestions to improve the quality of the paper. We thank MDPI for its linguistic assistance during the preparation of this manuscript.  
The authors declare no conflict of interest.