## 2 Training Data Acquisition Based on Virtual Compacted Particle Mixtures
### Virtual Compacted Model Design  
In this study, Particle Flow Code (PFC) was applied to carry out the virtual compaction test. Static compaction, as a commonly used compaction method in road material's DEM modelling, was chosen, considering both compacting effect and computing efficiency. In addition, in order to determine a suitable static compaction pressure, the influence of static pressure applied for the compaction was tested in detail. It should be noted that all particles are ball shaped in order to control a single variable in this stage. Three gradations were selected randomly and their passing rates are shown in Table 3.  
Since all the particle combinations were a coarse part of an entire gradation, the total mass of different mixtures may also be different. All elements were generated in accordance with passing rate and total volume of design specimen. The boundary condition for the container is simulated by a wall, which is similar to its counterpart steel container in the laboratory test. The compaction pressure only applied on top and bottom wall. The height of design cylindrical specimen is 100 mm and the diameter of the container is also 100 mm.  
For each specimen, the virtual test mainly follows three steps:  
1. The ball elements were generated without overlap in a random position in a cylindrical area;
2. Seven levels of hydrostatic pressure were applied to compact seven specimens, including 100 kPa, 200 kPa, 300 kPa, 400 kPa, 500 kPa, 600 kPa and 700 kPa;
3. Compression was performed until all elements become stable as shown in Figure 3. At that time, mixtures are considered to be in the most compact state.  
Because there are only coarse aggregates in this model, linear contact model was applied to all particles. The density of aggregates was set as 2650 g/cm\({}^{3}\) and effective modulus and friction coefficient were 50 GPa and 0.4, respectively. The results are shown in Table 4.  
Figure 3: Virtual compression model.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sieving Sizes (mm)** & **19.0** & **16.0** & **13.2** & **9.5** & **4.75** & **2.36** \\ \hline \multirow{3}{*}{**Passing Rate (\%)**} & Gradation\#1 & 100 & 91 & 72 & 69 & 56 & 39 \\  & Gradation\#2 & 100 & 92 & 62 & 57 & 30 & 22 \\  & Gradation\#3 & 100 & 93 & 91 & 77 & 20 & 19 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Passing rates of three gradations for static pressure test.  
It can be observed that compaction pressure caused little effect on final porosity for same gradation mixture. Taking Gradation#1 as an example, the range of mixture porosity is from 0.328 to 0.334, which indicates the mixture with sphere particles can be well compacted at all above pressures. Meanwhile, a compaction pressure of 600 kPa is commonly used in laboratory tests in many countries' specification, for instance, Superior Performing Asphalt Pavement (SUPERPAVE) specification. Therefore, a fixed compaction pressure of 600 kPa was chosen to carry out virtual compaction tests in this study. The particle number in each specimen varies from about 1000 to 17,000 for different gradations, and computing time changes from 10 min to nearly 2 h.