# Induction Heating-Assisted Compaction in Porous Asphalt Pavements: A Computational Study
## 4 Results and Main Findings  
The asphalt pavement compaction model was created by taking into account the effect of IH and its generated temperature field, which was calculated before. It was assumed that the generated heat for asphalt pavements of an initial temperature of 20 \({}^{\circ}\)C was also valid for higher initial temperatures. All the parameters of the asphalt compaction process are shown in Table 3.  
The relation of asphalt compactability or air void content to the roller passes are shown in Figure 11. Four cases were considered. Figure 10: Schematic flow diagram of the overall coupling methodology. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Values** \\ \hline _Pavement model_ & \\ model size & 50 cm (length) \(\times\) 50 cm (width) \(\times\) 8 cm (thickness) \\ particles size & 2–22.4 mm (PA 0/16) \\ _Roller Parameters_ & \\ wheel size & 100 cm (diameter) \(\times\) 200 cm (width) \\ wheel weight & 5 tons (one wheel) \\ _Mortar parameters_ & \\ air void content estimated & \(n=-2.8706+28.765\overline{n}_{c}\) \\ dynamic modulus (MPa) & \(E^{*}\) = 13664.0e\({}^{-0.135\overline{T}}\) \\ critical strain & \(\overline{\epsilon}_{r}=0.017\)e\({}^{-0.018\overline{T}}\) \\ effective strength (MPa) & \(\overline{\sigma}_{c}=232.29\)e\({}^{-0.153\overline{T}}\) \\ initial bond radius ratio & \(\zeta_{0}=0.06\) \\ enlargement multiplier of bond radius & \(\varepsilon=\sqrt{1+0.06n_{c}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters used in the discrete element method (DEM) analysis. Low temperature group:  
Case 1: Mix temperature \(T_{0}\) = 60 \({}^{\circ}\)C  without IH. Case 2: Mix temperature \(T_{0}\) = 60 \({}^{\circ}\)C  with IH (surface temperature of \(T_{f}\) = \(\sim\)90 \({}^{\circ}\)C). High temperature group:  
Case 3: Mix temperature \(T_{0}\) = 120 \({}^{\circ}\)C  without IH. Case 4: Mix temperature \(T_{0}\) = 120 \({}^{\circ}\)C  with IH (surface temperature of \(T_{f}\) = \(\sim\)142 \({}^{\circ}\)C). Figure 11: _Cont._  
In Figure 11a, it was found that during the first pass (initial compaction), the air void content fluctuated dramatically and the mix was easily flown. If taking the studied point (the midpoint of the model) as a reference, when the compactor came close to it, the mix air void content declined because of the aggregates' pushing movement. When the roller moved to the right above the point, many bonds were broken, caused by tensile stress, and the air void content showed a slight increase. When the roller moved off this point, the air void content went down again and the mix recompacted. With passes increased, the air void content continually declined, whereas fluctuation started to be stable and the variation amplitude of porosity reduced. Figure 11b shows that the entire compaction process could be divided into two distinct stages, the early stage (passes \(<\) 3) and the late stage (passes \(>\) 3). In the early stage, the mix density during compaction could be sorted in descending order as Case 1 \(>\) Case 2 \(>\) Case 3 \(>\) Case 4. That is to say, (i) relative to the high temperature group (Case 3 and Case 4), the low temperature group (Case 1 and Case 2) showed much higher density in the early stage, and (ii) regardless of the high temperature group or low temperature group, the density of the mix without IH was higher than that with IH in the early stage (i.e., Case 1 \(>\) Case 2, Case 3 \(>\) Case 4). In the late stage of compaction, the mix density at higher temperatures eventually exceeded the density at low temperatures (i.e., Case 2 \(>\) Case 1). The phenomenon happened mainly due to the fact that higher temperatures do not always increase the mix density, but they can increase the mobility of particles, leading to bad mix compactability. Further, IH operated efficiently in the late compaction stage when the mix density reached a certain value, rather than at the very beginning. Also, the effect of IH on the asphalt compaction process was not obvious at higher temperatures.