## 4 Conclusions  
With the revised SMP, Mohr-Coulomb and Druck-Prage models, the strains of UGM layer were analyzed and compared. The following summaries and conclusions were obtained from the numerical simulation:  
1. Using the three models, the maximum horizontal and vertical plastic strains of UGM are at the bottom of the loading areas centerline. At the position of 5-10 cm of the UGM layer, the plastic strains change sharply for the Mohr-Coulomb model but smooth for the revised SMP and Druck-Prage models. The horizontal plastic tensile and compressive strains exist in the top surface of UGM in the revised SMP model, and the tensile strain is obvious in the middle and lower part of UGM layer and the compressive strain distributes on the both sides for the loading areas. However, there are no vertical plastic tensile strains in the Mohr-Coulomb and Druck-Prage models. With the revised SMP model, vertical plastic tensile strains appear on both sides of the loading area. This phenomenon is closely related to the dilatancy of the material, proving the reasons for the rutting caused by the UGM layer.
2. Compared with the Mohr-Coulomb and Druck-Prage models, the revised SMP model can better represent the accumulated process of plastic strain under repeated loads. There is an obvious increment in the first several loading cycle by the Mohr-Coulomb and Druck-Prage models, but little changes in the subsequent loading cycles. This indicates that the revised SMP model can better describe the process of the plastic strain accumulation in the actual loading condition. In addition, the rutting is over-predicted by the Mohr-Coulomb model and underestimated by the Druck-Prage model during the early loading, which may result in the ahead or delay of maintenance.
3. With the three models, the compressive strains of subgrade on top surface and the tensile strains of asphalt layer on the bottom are similar. The Mohr-Coulomb model has the greatest average plastic and elastic strains, and the Druck-Prage model produces the smallest plastic and elastic strains during the first 100 loading cycles. This result is related to the hardening law used in the revised SMP model, which will be a long process until it reaches the elastic shakedown state.  
Based on the validation of the laboratory tests, the finite element analyses were conducted using the revised SMP model in this study. The results show that this model has the advantage in describing the calculation process of plastic strain under repeated loads. There are still some shortcomings and limitations, such as stress-dependence and anisotropy, which are not included in the model. The completely continuous of contact relationship between UGM and other layers seems unsatisfactory after the use of the revised SMP model. In the next step, our plan is to apply the revised SMP model in the real pavement structure which will consider the plasticity of the HMA and subgrade layers. Moreover, the calculations will be compared with the actual monitoring data. These aspects will be the main directions for the future study.  
N.L.: Conceptualization, Methodology, Formal analysis, Investigation, Writing--original draft; B.M.: Conceptualization, Methodology, Resources; H.W.: Conceptualization, Writing--review & editing. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The supports from the Talent Technology Foundation in Xi'an University of Architecture and Technology (No RC1907) and Project funded by China Postdoctoral Science Foundation (No 2019M663649) are greatly appreciated.  
The authors declare no conflict of interest.