## 2 Materials and HMAC Pavement Model
### HMAC Pavement Model  
A finite element model based on the software ABAQUS(TM) V6.13 (2013) by Dassault Systemes(r) (Rhode Island, RI, USA) was established (ABAQUS is one of the most powerful numerical simulation tools in the world. It can simulate the performance of most typical engineering materials and can be used to solve the problems in the field of road engineering) [26; 27]. The assumptions about the road model were made as follows [28; 29]. (1) The asphalt pavement surface was made of viscoelastic materials, and the remaining layers were made of linear elastic materials. (2) Structural layers were of uniform thickness, as well as isotropic and continuous without considering the influence of gravity. (3) The surface of the road was considered to be a horizontal plane, regardless of its roughness and the influence of the horizontal and vertical slopes. (4) The structural layers were completely continuous, and the displacement was continuous in the vertical direction.  
In order to accurately simulate the viscoelasticity of asphalt materials, the viscoelastic parameters based on the Burgers model that were measured in the actual experiment were converted to Prony series [30]. These parameters, which were used in ABAQUS software, are shown in Table 5.  
The three-dimensional structure of the asphalt pavement was established by using ABAQUS. Due to the symmetry of the pavement structure and load, the 1/2 model was taken for analysis, and the following dimensions of the pavement model were established: length (z-direction) was eight meters, width (x-direction) was six meters, and thickness (y-direction) was three meters. The C3D8R element was used in the grid-drawing process. The gridding of the mobile zone was refined across a section of the width and along the length and thickness of the model. Gradual refinement of the grid structure was made from the base to the surface of the pavement model, as shown in Figure 1.  
The boundary conditions were set as follows: (1) the fully fixed constraint was applied to the subgrade of the road; (2) displacement of the four sides of the model was constrained; and (3) symmetrical constraints were applied to the symmetrical planes.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Structural Layer** & \begin{tabular}{c} **Thick-Ness** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Density** \\ **(kg-m\({}^{-3}\))** \\ \end{tabular} & \begin{tabular}{c} **Compressive Resilient** \\ **Modulus (MPa)** \\ \end{tabular} & \
\begin{tabular}{c} **Poisson’s** \\ **Ratio** \\ \end{tabular} &
\begin{tabular}{c} **Damping** \\ **Coefficient \(\alpha\)** \\ \end{tabular} \\ \hline AC-13 & 4 & 2500 & 1 200 & 0.35 & 0.8 \\ HMAC-20 & 6 & 2500 & 2 000 & 0.30 & 0.8 \\ ATB-25 & 8 & 2450 & 800 & 0.30 & 0.8 \\ Cement treated base (CTB) & 34 & 2400 & 1 400 & 0.25 & 0.8 \\ Lime fly ash treated base (LFTB) & 20 & 1800 & 600 & 0.25 & 0.8 \\ Soil & - & 1850 & 40 & 0.40 & 0.8 \\ \hline \hline \end{tabular} Note: 1. The compressive resilient moduli are from the uniaxial compressive test based on the standard JTG D50-2006 at 20 \({}^{\circ}\)C. 2. ATB-25 means Asphalt-Stabilized Macadam.  
\end{table}
Table 4: Material parameters of HMAC pavement.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Structural Layer**} & \multicolumn{4}{c}{**Prony Series**} \\ \cline{2-5}  & \(g_{1}\) & \(g_{2}\) & \(\tau_{1}\) & \(\tau_{2}\) \\ \hline AC-13 & 0.38 & 0.62 & 1 596.17 & 36.78 \\ HMAC-20 & 0.18 & 0.82 & 24 526.03 & 170.58 \\ ATB-25 & 0.39 & 0.61 & 1 015.55 & 43.04 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Prony parameters in the Burgers model.