**5. Conclusions**

The heavy-duty vehicle road coupling model not only adopts the vibration coupling relationship under the condition of displacement compatibility between vehicle and road but also tries to adopt the vibration coupling relationship under the condition of contact

force between vehicle and road. Further research is conducted on the coupling relationship, which provides a new idea for the future development of a vehicle–road coupling vibration model. This paper studies the vehicle–road coupling dynamic analysis model and vehicle–road interaction analysis under heavy load conditions, which will play a significant role in the whole design method and theory of vehicles and roads and will also have very important application value to future engineering practice.

In this paper, the subgrade is regarded as part of the vehicle road dynamic system, and the vehicle road coupling dynamic model under heavy load is established. The results show that the equation can better reflect the dynamic performance of a vehicle–road system; Additionally, it better reflects the coupling vibration relationship and interaction between the vehicle and the road. The model will provide a theoretical basis for a more accurate analysis of the interaction between heavy-duty vehicles and roads and then provide a theoretical basis for important parameters in heavy-duty vehicle design and road durability design. The coupling dynamic equation established in this paper can analyze the instantaneous dynamic performance of the coupling system by the finite element method.

The two-dimensional finite element model is used in the analysis of road coupled dynamic load in this paper, and the three-dimensional finite element model can be used to simulate the spatial dynamic response of the road. This will be the focus of future research.

**Author Contributions:** J.X. wrote the manuscript, B.L. designed the proposed control strategy and conceived the structure of the paper, S.S. completed theoretical derivation and numerical simulation. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Chongqing Science and technology research project under Grant No. CSTC2010AC6078.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
