# Effect of Gradation Segregation on Mechanical Properties of an Asphalt Mixture
## 2 DEM Model Development
### Contact Model and Model Parameters  
In order to describe the interaction amongst the aggregates in asphalt mixture, two bonding models are available in PFC2D, contact-bond model and parallel-bond model. The main difference  
Figure 1: Development of 2D DEM Model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Gradation** & **HC** & **MC** & **LC** & **D** & **LF** & **MF** & **HF** \\ \hline VMA/\% & 13.77 & 12.03 & 11.01 & 10.45 & 9.98 & 9.56 & 9.17 \\ Model height/mm & 100.2 & 100.5 & 100.3 & 100.9 & 100.4 & 100.7 & 100.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: VMA of the mixture and height of the model. between these two bond models is that the contact-bond model can only transmit force through the contact point, whereas the parallel-bond provides possibility for both transmitting force and moment. In addition, the parallel-bond model also adds the effect of binding materials [25]. Thus, the parallel-bond model was employed in this study to simulate the mechanical response of the aggregate skeleton in asphalt mixtures. The parallel-bond model can be viewed as the combination of serval springs with normal and tangential stiffness. The micro-parameters for developing the asphalt mixture model were collected from laboratory test, i.e. uniaxial compression test. The test was performed by the US MTS810 material test system with the test temperature and load speed of 20 \({}^{\circ}\)C and 1 mm/s, respectively. Vertical loadings were conducted on the DEM model and laboratory prepared asphalt samples. When the vertical deformation of asphalt mixture sample arrives at \(\Delta h\), the corresponding vertical load in the laboratory and DEM model is recorded and labelled as \(P_{i}\) and \(P_{i}\)', respectively. The difference between \(P_{i}\) and \(Pi^{\prime}\) is defined by \(\beta_{i}=|P_{i}-P_{i}\)/\(|P_{i}\). Micro-parameters were adjusted for minimizing \(\beta\). The obtained micro-parameters used in the DEM model are presented in Table 4. The mechanical response of asphalt mixture samples and the corresponding DEM models under vertical load are presented in Table 5. As can be seen, the difference in loading between the DEM model and laboratory test is less than 8%, indicating that the microscopic parameters obtained by this method are appropriate. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model Component** & **Microscopic Parameters** & **Value** \\ \hline \multirow{8}{*}{Spheres} & Density \(\rho\)/(kg\(\cdot\)m\({}^{-3}\)) & 2600 \\  & Friction coefficient \(\mu\) & 0.5 \\  & Normal stiffness \(K_{nl}\)/(N\(\cdot\)m\({}^{-1}\)) & \(5.2\times 10^{8}\) \\  & Shear stiffness \(K_{s}\)/(N\(\cdot\)m\({}^{-1}\)) & \(5.2\times 10^{8}\) \\  & Normal parallel-bond stiffness \(pb\_k_{nl}\)/(N\(\cdot\)m\({}^{-1}\)) & \(1.1\times 10^{5}\) \\  & Shear parallel-bond stiffness \(pb\_k_{s}\)/(N\(\cdot\)m\({}^{-1}\)) & \(1.1\times 10^{5}\) \\  & Bond radius \(r\) & 0.5 \\ \hline \multirow{4}{*}{Boundary wall} & Friction coefficient \(\mu_{w}\) & 0 \\  & Normal stiffness \(K_{un}\)/(N\(\cdot\)m\({}^{-1}\)) & \(2.3\times 10^{8}\) \\  & Shear stiffness \(K_{us}\)/(N\(\cdot\)m\({}^{-1}\)) & \(2.3\times 10^{8}\) \\ \hline Other & Local damping D & 0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Microscopic parameters for contact of the skeleton model.