## 3 Simulating HMAC Pavement Deformation in Curved Ramp
### ANSYS Model  
The three-dimensional pavement model with dimensions in the longitudinal, transverse and depth direction of 2.1, 2.0 and 7.55 m respectively was constructed. This pavement unit is assumed to be located near the midpoint of the horizontal curve. The pavement structure and the thickness of each layer are shown in Table 3.  
Based on the multi-layered pavement system, two different hypotheses--i.e., the elastic and linear viscoelastic hypotheses--were introduced for various layers. The former applied to semi-rigid base, subbase and subgrade which used the Solid 45 element for analyzing, while the viscoelastic hypothesis was applied to asphaltic layers which employed the 8-node Solid 185 element in the computation. Moreover, the Surf 154 element was adopted to simulate the shear force on pavement surface. For the asphaltic layers, the aforementioned viscoelastic parameters (shown in Table 1) were employed, while for the other layers, the elastic parameters are provided in Table 3.  
Consideration of different constitutive relationships for different layers in this research can be justified as follows. In China today, asphalt pavement composed of asphaltic surface course as well as semi-rigid base and subbase is the overwhelmingly adopted structure. Numerous in-situ investigations indicate that during hot days, putting deformation in such pavement mainly derives from viscous flow of asphaltic mixtures, whereas the contribution of semi-rigid base, subbase and subgrade is relatively small, provided that the pavement was well designed and constructed. Therefore, to highlight the deformation of asphaltic layers and to raise computation efficiency, this research applied viscoelastic theory to asphaltic layers while using elastic theory for the others. The vertical load is the uni-axle-two-wheel load, which has a rectangular uniform pattern and a dual tire spacing of 31.95 cm. The wheel contact area is 20 cm long and 20 cm wide. Based on previous analysis, two shear forces (longitudinal and transverse force) were applied to the model top, which were determined through multiplying the vertical pressure by 0.6 and 0.2 respectively. In terms of loading time, since similar rutting predicting results under repeated loading-unloading cycles and single long time loading have been verified [27], in this study numerous individual loading was approximately accumulated into single long time load according to the Boltzmann Superposition principle. In this modeling, the equivalent single axle load (ESAL) number ranging from 200 to 2800 (10\({}^{4}\) times) and an operational velocity of 100 km/h were considered. The corresponding accumulated loading times were calculated as shown in Table 4. Additionally, the lateral wander factor of 0.4 was adopted in the calculation in accordance with current code [26]. Since the pavement deformation at the moment of unloading includes both elastic deformation and non-elastic, different recovering times were considered as shown in Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline
**Structural Layers** & **Thickness (cm)** & **Resilient Modulus (MPa)** & **Poisson Ratio** \\ \hline \multirow{3}{*}{Asphaltic layers} & Top layer & 3–7 & \multirow{3}{*}{using viscoelastic} & \multirow{3}{*}{using viscoelastic} \\  & Middle course & 4–8 & & parameters \\ \cline{1-1}  & Binder course & 5–9 & & \\ \hline Semi rigid base & 16–32 & 1400 & 0.25 \\ Subbase & 20 & 600 & 0.25 \\ Subgrade & 700 & 60 & 0.25 \\ \hline \end{tabular}
\end{table} 
Table 3: Structural thickness and basic parameters of the pavement model. It was found that asphaltic mixtures in the pavement surface courses under two different alignments showed slow viscous flow after prolonged loading and unloading cycles, and different locations featured quite different deformations. Overall, the deformation decreased with the distance from axle center increasing. It was observed that the greatest vertical displacement occurred right below the axle load since the vertical compressive stress herein reaches the maximum value.