# Induction Heating-Assisted Compaction in Porous Asphalt Pavements: A Computational Study
## 3 Simulation of Induction Heating-Assisted Compaction in Porous Asphalt
### Modeling of Asphalt Mix
#### 3.2.2 Micromechanical Modeling of Asphalt Mix  
To simplify the micromechanical modeling of LTPAs, the mix was divided into three different individual constituents: (i) Coarse aggregate particles larger than 2.0 mm, (ii) asphalt mortar, and (iii) air voids. Considering that the shape of the coarse aggregates, which formed the aggregate skeleton in the mix, has a major impact on mix compaction and performance [22; 23; 24], five different particles with complex geometries (Figure 3) were developed to compose the PA 0/16 material. The shape of each aggregate particle was randomly chosen from these five shapes. The values of _L:W:H_ denoted the ratio of the particle's length, width, and height, respectively, and they were used to control the flatness and elongation of particles (Figure 3).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Sieving Size (mm)** & **22.4–16.0** & **16.0–11.2** & **11.2–8.0** & **8.0–5.6** & **5.6–2.0** & **2.0–0.063** & **<0.063** \\ \hline Cum. ret. (\%) & 4 & 25 & 57 & 80 & 85 & 95.5 & 100 \\ \% ret. by weight & 4 & 21 & 32 & 23 & 5 & 10.5 & 4.5 \\ \hline \end{tabular}
\end{table}
Table 1: Aggregate gradation of porous asphalt (PA) 0/16 mix based on the Dutch standard (RAW 2005).  
Figure 2: Finite element method (FEM) results of induction heating on pavement: (**a**) thermal field distribution on the pavement surface, (**b**) surface temperature development of the pavement, and (**c**) temperature distribution in the pavement after 120 s of induction.  
For the DEM modeling, asphalt mortar (i.e., asphalt binder, mineral filler, and fine sand), which was added as the bond between the generated coarse aggregate particles in the analyses, was considered to be a continuum and homogeneous. The bond was envisioned as a pie made by many elastic springs and viscous dashpots lying on the contact plane and centered at the contact point of two particles, as seen in Figure 3. When the pie was bonded, it could resist the tensile force and the relative rotation moment until the tensile strength or shear strength limit of the spring was exceeded. After the break of contact bonds, only compressive forces were active.  
Due to the fact that when two aggregates are covered by mortar, they are easily glued together during movement, the broken bond may be refolued again when the particles are close enough. This is the biggest different between compaction simulation and the common mechanical analysis for asphalt mix. This mechanism could be realized through continually judging and generating new bonds when necessary but keeping the state of old bonds unchanged during the cycle.  
The pie-shaped bond model was determined by five key parameters related to asphalt mortar. These parameters were (i) the normal stiffness, (ii) the shear stiffness \(\overline{k}_{s}\), (iii) the tensile strength \(\overline{\sigma}_{c}\), (iv) the shear strength \(\overline{\tau}_{c}\) (calculated by cohesion \(c\) and angle of internal friction \(\varphi\)), and (v) the pie radius \(r_{c}\). Parameters such as the gap between the particles \(g_{s}\), the viscosity of contact \(\eta_{n}\), and the friction of contact \(\mu\) should also be taken into account in the model development, as seen in Figure 4. The particle contact behavior was governed by Kelvin-Voigt constitutive laws, and tension was determined through the Mohr-Coulomb failure criterion.  
Figure 4: Schematic of contact conditions between the coarse aggregate particles: (**a**) asphalt mortar, (b) pie-shaped bond, and (**c**) physical model of the bond.  
Figure 3: Generated coarse aggregate particles: (**a,b**) \(L\):\(W\):\(H\) = 1:1:1, (**c,d**) \(L\):\(W\):\(H\) = 1:0.8:0.6, and (**e**) \(L\):\(W\):\(H\) = 1:0.5:0.25.