## 3 Elasto-Plastic Constitutive Model
### Average Compressive Strain of UGM Layer and Compressive Strain of Subgrade  
Using the three models for the \(FE\) numerical analyses, the average plastic compressive strain and the average elastic strain of UGM layer, the compressive strains of subgrade at top surface and the tensile strains of asphalt layer at bottom were obtained in the symmetry axis with 100 loading cycles, as shown in Table 4.  
With the three models, the tensile strains at bottom of HMA layer and compressive strains on top of subgrade layer showed similar values, with little differences. It shows that the average elastic and plastic strain of UGM and compressive strain of subgrade were smaller than those from the Mohr-Coulomb model. In contrast, the average plastic compressive strain of UGM from the revised SMP model accounted for 71.3% of the Mohr-Coulomb model, and the average plastic compressive strain produced by Druck-Prage model was only 22.6% of the revised SMP one. It stated that UGM layer would produce greater vertical plastic compressive strain by the Mohr-Coulomb model and smaller plastic \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Constitutive Model**} & **Tensile Strain at Bottom** & \multicolumn{2}{c}{**Average Plastic**} & \multicolumn{2}{c}{**Average Elastic**} & \multirow{2}{*}{**Compressive Strain on**} \\  & **of HMA Layer (\(\mu\epsilon\))** & & **UGM (\(\mu\epsilon\))** & & **Top of Subgrade (\(\mu\epsilon\))** \\ \hline Mohr-Coulomb Model & 300.74 & 312.3 & 418.2 & 799.1 \\ Revised SMP Model & 300.67 & 222.8 & 278.4 & 780.1 \\ Druck-Prager Model & 298.5 & 50.3 & 107.5 & 773.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Strains in different structure layers using the three models. Figure 8: Relationship of average vertical plastic strain and loading cycle using the three models. strain from the Druck-Prage model. Using the revised SMP model, the average elastic strain was 0.6 times that of the Mohr-Coulomb model and 2.6 times that of the Druck-Prage model. This suggested that the modulus in the revised SMP model was greater than that in the Mohr-Coulomb model, but smaller than that in the Druck-Prage model. The resistance and hardening modulus of UGM in the revised SMP model increased gradually with loading cycles. However, the hardening modulus of the Mohr-Coulomb and Druck-Prage models almost maintained the same level. For the UGM layer, the average vertical deformation calculated by the revised SMP model of UGM was smaller than the Mohr-Coulomb model and greater than Druck-Prage model. Namely, the Mohr-Coulomb model would overestimate the deformation of UGM, and Druck-Prage model would underestimate the deformation of UGM. The results showed that the revised SMP model can better represent the plastic strain and its development process in UGMs under repeated loads. After 100 loading cycles, the plastic deformation of the UGM layer produced by the revised SMP model was 0.557 mm, while it was 0.78 mm and 0.155 mm using the Mohr-Coulomb and Druck-Prage models, respectively. The plastic deformation of UGM layer is an important part of putting in granular base pavements. When the Mohr-Coulomb model was used, the plastic strain of UGM layer may be over-predicted, leading to the overestimation of rutting in the earlier service period. On the contrary, the rutting depth may be underestimated by the Druck-Prage model. As for the vertical compressive strain on the top surface of subgrade, the strains are similar for the three models. This was related to the stress diffusion ability of UGM layer. When the elasto-plastic model was used, the stiffness of structure layer was smaller than that of the elastic model. It has stronger stress diffusion ability using the elastic model, so that the vertical stress was relatively small on the top of the subgrade. On the other hand, the UGM layer deformed facing to the load transmitted from the upper layer.