*3.2. Shear Modulus (G\*)*

Figure 5 shows the 2S2P1D Cole–Cole plot of the shear complex modulus at different temperatures and frequencies for all recovered bitumen from CR, CRM, FR, FRM, and control mix. 2S2P1D was adopted to model the shear modulus of recovered bitumen. From Figure 5, it seemed that the virgin bitumen (PG64-28) was more viscous than the other bitumen.

**Figure 5.** Cole–Cole shear modulus of recovered bitumen (2S2P1D model).

Table 2 shows the seven constant values for all four mixes. As mentioned earlier, these seven constants represented the bitumen characteristics. In general, the same binder was supposed to have equal values for the constants. Table 2 shows that the constants were not the same, so it could be concluded that recovered binder from FR was not the same as CR. Virgin bitumen was expected to have higher viscous components. Aged binder lost some parts of its viscous components and became brittle, so it mixed with aged bitumen and had a lower viscosity than virgin bitumen.


**Table 2.** The 2S2P1D model constants for all recovered binder.

Figure 6 shows the master curve of shear modulus (Pa). The G\* values of FR and CR were higher than the other mixes. Asphalt production, lifetime, and presence of air impacted the aging progress. A single source of RAP was used for CR and FR. Then, since all these factors were the same for CR and FR, the recovered bitumen was supposed to have the same master curve. Figure 6 shows that, except for the mentioned factors, particle size may change the rheology of bitumen. This was because FR and CR mixes had higher aged bitumen content than CRM and FRM at intermediate and lower frequencies. FR was stiffer than CR, which meant that the finer RAP particles were covered by a stiffer bitumen. This could be explained as bitumen that surrounded fine particles aged faster than when they surrounded coarse particles; a higher surface area of the bitumen was exposed to oxidative aging. After

mixing the coarse and fine RAP with virgin materials, master curves from recovered bitumen were plotted. Here, we again saw that FRM was stiffer than CRM at intermediate and lower frequencies.

**Figure 6.** G\* master curve at 10 ◦C of recovered binder (2S2P1D model).

The Reduced G\* (RG\*) index was looked at to clarify the interaction of RAP bitumen with virgin bitumen according to RAP particles. G\* was determined for CR and FR as well as for CRM and FRM. According to CRM (FRM) mix design, CR (or FR) was added to the 2.2% virgin bitumen. The difference between CR (or FR) and CRM (FRM) showed the impact of virgin bitumen on total bitumen stiffness. (RG\*) is calculated by Equation (2) as a percentage:

$$\mathcal{R}G^\* = ((\mathcal{G}\_i^\* - \mathcal{G}\_{i\mathcal{M}}^\*)) / (\mathcal{G}\_i^\*),\tag{2}$$

where *RG*\* is the percentage of reduced G\*, G\**<sup>i</sup>* is the shear modulus of pure RAP, and G\**iM* is the shear moduli of RAP and virgin bitumen mixes. The difference of G\**<sup>i</sup>* and G\**iM* showed how well the bitumen mixed together. As the aged bitumen was stiffer than virgin bitumen, eventually G\**<sup>i</sup>* was supposed to be higher than G\**iM*. Figure 7 indicates the rheology transition before and after mixing RAP with virgin materials. Both CR and FR mixed with 2.2% virgin binder. Most of the influence of aged binder was observed at low frequency. The difference between aged bitumen and mixture bitumen changed from 0% to 90%. These differences meant rigidity was changed. FRM was 90% softer than FR; it increased rapidly and was constant over a wide frequency range. The impact of CR clearly differed from FR. The different trends in CR and FR could translate to the impact of each type of RAP on virgin bitumen. CR and CRM had the same rigidities at high frequency and gradually increased at low frequency. CR and FR bitumen recovered from a single source of recycled asphalt were supposed to have the same characteristics when blended with a specific amount of virgin bitumen, but the interactions were different. Aging rates were not the same between fine gradation and coarse gradation.
