*3.3. Rheological Properties*

#### 3.3.1. Frequency Sweep Tests

Asphalt binder is a viscoelastic material whose stress–strain characteristics depend on temperature and time. The mechanical and viscoelastic behavior of asphalt binder varies with loading frequency. Thus, the effects of compound modification of APAO and PPA on the rheological behavior of base binder were investigated by frequency sweep tests.

Figure 5 shows the master curves of complex modulus (G\*) and phase angle (δ) for the composite modified binders. Increases in the G\* values and decreases in the δ values can be observed for all the tested binders. The complex modulus curve is elevated over the whole frequency range and the phase angle curve is lowered correspondingly. The increasing content of APAO and PPA causes an increase in G\* values and a decrease in δ values, which indicates an increase in the elastic behavior of the asphalt binder. Moreover, G\* values increase significantly at lower frequencies (higher temperatures) and increase slightly at higher frequencies (lower temperatures). This indicates that the incorporation of APAO and PPA improves the asphalt binder's high-temperature performance.

It can be noted that the values of G and G vary with the concentration of APAO and PPA. As can be seen, both G and G increase significantly as the contents of APAO or PPA increase. Remarkably, the increment in G is much greater than that of G, showing that G has a strong dependence on the APAO or PPA concentration. As mentioned above, APAO or PPA are contributing factors to the enhancement of the elastic component, which further strengthens the elastic behavior. Moreover, the value of G increases significantly when the APAO concentration is 2 wt.% and the PPA concentration exceeds 1.0 wt.%. Therefore, the PPA proportion should be optimized to enhance the synergistic modification effect of APAO.

From Figure 6, it is obvious that the shear storage modulus G and shear loss modulus G increase as the frequency increases. This phenomenon signifies that asphalt binder exhibits more stiff and elastic characteristics with increases in vehicle travel speed. The increases in frequency accelerate the rate of increase of G , indicating that G is highly sensitive to frequency. The compound modification of APAO and PPA markedly enhances G and G in comparison to that of virgin binder.

#### 3.3.2. Temperature Sweep Tests

Temperature is the main factor that affects the rheological behavior of asphalt binders [46]. The temperature dependence of G and G of the compound modified binders is shown in Figure 7. Clearly, the parameters G and G show a decreasing trend with increasing temperature. Moreover, the reduced level of G is higher than that in G with increasing temperature, indicating that higher temperatures promote the transition of asphalt binder from an elastic to viscoelastic state. G always has a greater value than G , revealing that the viscous component is more dominant. Thus, the elastic component in asphalt binder should be enriched to enhance its high-temperature resistance.

The increasing concentration of APAO and PPA contributes to a marked enhancement of G and G. When the PPA content remains at 1.5 wt.%, increasing the concentration of APAO leads to an increment in G and G, with the former experiencing a higher growth rate. This suggests that APAO strengthens the elastic behavior which represents a stronger high-temperature deformation resistance. Similarly, when the APAO proportion is 2 wt.%, an increase in PPA concentration also enhances the G and G values. The G value increases significantly when the content of PPA exceeds 1.0 wt.%, providing evidence that an appropriate amount of PPA benefits the reinforcement of anti-rutting performance of composite modified asphalt binder. Therefore, the enhancement of viscoelastic performances of asphalt binder is based on the interaction of APAO and PPA.

**Figure 5.** Complex modulus and phase angle master curves of composite modified binders: (**a**) composite modified binders with various contents of APAO; (**b**) composite modified binders with various contents of PPA.

**Figure 6.** G and G variations with frequency for composite modified binders: (**a**) composite modified binders with various contents of APAO; (**b**) composite modified binders with various contents of PPA.

**Figure 7.** G and G variations with temperature for composite modified binders: (**a**) composite modified binders with various contents of APAO; (**b**) composite modified binders with various contents of PPA.

The rutting resistance index G\*/sinδ is utilized to characterize the anti-rutting property of asphalt binders. Higher G\*/sinδ signifies better resistance to permanent deformation. The calculated rutting index G\*/sinδ values of all samples are displayed in Figure 8. As shown, G\*/sinδ increases with increasing content of APAO, indicating that APAO benefits the anti-rutting property of the binder. Similarly, the rising concentration of PPA also leads to an increasing trend of G\*/sinδ. It is worth noting that PPA has a greater contribution to the increment in G\*/sinδ. Moreover, the failure temperatures of asphalt binders are acquired through calculation when the G\*/sinδ value is 1.0 kPa. Failure temperatures of all tested samples are given in Table 7. Obviously, the failure temperatures increase with the addition of APAO and PPA. The incorporation of APAO markedly improves the failure temperature, with an increase of 9.38 ◦C for A6P1.5 compared to A0P1.5. However, PPA has a greater contribution to the increase in failure temperature. This result can be demonstrated by the fact that the failure temperature of A2P2.0 is 19.66 ◦C higher than that of A2P0. The failure temperature of modified binder A2P2.0 is 91.15 ◦C, which is 23.67 ◦C higher than that of virgin binder. Therefore, the combined effect of APAO and PPA can significantly improve the high-temperature properties of composite modified binder, with PPA contributing more to this improvement.

**Figure 8.** Variations in G\*/sinδ with temperature for composite modified binders: (**a**) composite modified binders with various contents of APAO; (**b**) composite modified binders with various contents of PPA.



3.3.3. Creep and Recovery Behavior

The rutting index G\*/sinδ has a disadvantage in that it cannot reflect the delayed elastic deformation and recoverability of asphalt binder and thus fails to simulate real loading conditions [47]. The Federal Highway Administration (FHWA) proposed the MSCR test to more precisely evaluate the rheological behavior of modified binders at high temperatures [48]. A good correlation has been found between the non-recoverable creep compliance of the MSCR test and the anti-rutting property of asphalt mixtures [49–51]. Therefore, the MSCR test is employed to explore the influence of APAO and PPA on the high-temperature properties of the neat binder.

The samples aged by RTFOT were subjected to the MSCR test at 60 ◦C and shear stress levels of 0.1 kPa and 3.2 kPa, respectively. For instance, Figure 9 presents the variation of strain with time for all samples at 0.1 kPa. As can be seen, one cycle includes a one-second creep stage and a nine-second recovery stage. The strain level increases with increases in loading time in the creep stage. In the stage of recovery, the strain recovers instantly when the loading stress is removed, and the recovery rate decreases with the loading time. A residual strain still exists after each cycle of creep and recovery. The above results reflect the viscoelastic–plastic performance of asphalt binder. The elastic strain recovers rapidly, while the viscous strain recovers slowly after the loading stress is eliminated. The residual strain represents the permanent deformation. It is notable that the neat binder has the maximum residual strain while the modified binder A2P2.0 has the minimum residual strain. This phenomenon demonstrates that the combined effect of APAO and PPA can lower the permanent deformation of neat binder.

**Figure 9.** A creep–recovery cycle of the composite modified binder at 0.1 kPa and 60 ◦C: (**a**) composite modified binders with various contents of APAO; (**b**) composite modified binders with various contents of PPA.

Two main parameters of average non-recoverable creep compliance (Jnr) and average percent recovery (R) were proposed by the FHWA to evaluate the high-temperature viscoelastic characteristics of the modified binder. The Jnr and R are defined as the permanent deformation and elasticity indexes of asphalt binder, respectively. The higher the R value is, the lower the Jnr value is, indicating that the anti-rutting property of asphalt binder is better. Figures 10 and 11 show the Jnr and R values of composite modified asphalt binders at different stress levels. As observed from Figures 10a and 11a, the addition of 1.5 wt.% PPA alone decreases the Jnr and increases the R in comparison to neat binder, indicating that PPA reduces the permanent deformation of neat binder. Similarly, 2 wt.% APAO alone is also capable of enhancing the anti-rutting performance of neat binder, as shown in

Figures 10b and 11b. When the concentration of PPA remains constant, increasing content of APAO leads to a marked increase in the R value and a significant reduction in the Jnr value. Asphalt binders modified with a certain amount of APAO and increasing content of PPA also exhibit a similar increasing trend of the R value and decreasing trend of the Jnr value. Moreover, the R value increases by 51.50% and the Jnr value decreases by 68.48% as the APAO increases from 0 wt.% to 6 wt.% under 0.1 kPa stress. The R value increases by 6.89 times and the Jnr value decreases by 96.06% as the PPA increases from 0 wt.% to 2 wt.%. Relative to APAO, PPA contributes more to the decrease in Jnr and the increase in R. Therefore, this suggests that PPA contributes more to the improvement of the elasticity of asphalt binder.

**Figure 10.** The Jnr of composite modified binders under 0.1 kPa and 3.2 kPa at 60 ◦C: (**a**) composite modified binders with various contents of APAO; (**b**) composite modified binders with various contents of PPA.

**Figure 11.** The R of composite modified binders under 0.1 kPa and 3.2 kPa at 60 ◦C: (**a**) composite modified binders with various contents of APAO; (**b**) composite modified binders with various contents of PPA.

The variations in Jnr and R are also affected by the applied stress level. The Jnr exhibits an increasing trend and the R presents a decreasing trend when the stress increases from 0.1 kPa to 3.2 kPa. This suggests that a higher stress level reduces the anti-rutting performance of the asphalt binder. Thus, an asphalt pavement with heavier traffic is prone to experiencing rutting stress. Furthermore, the R and Jnr values vary with APAO and PPA concentration. Taking the R value as an example, the R values of A0P1.5, A2P1.5, A4P1.5 and A6P1.5 decrease by 21.26%, 15.49%, 9.63% and 8.36%, respectively, due to the increased stress level. Similarly, the R values of A2P0, A2P1.0, A2P1.5 and A2P2.0 drop by 56.81%, 36.98%, 15.49% and 5.81%, respectively. The results of the data analysis reveal that the combined effect of APAO and PPA is helpful to mitigate the adverse impact of the increased stress level.
