3.2.4. PI and T<sup>800</sup>

Penetration at 15 ◦C, 25 ◦C and 30 ◦C was used to calculate the penetration index (PI) and equivalent softening point (T800) of asphalt mortar. The logarithmic values of penetration (log P) and temperature (T) were used to calculate PI according to the fitting curves of Equation (2). The linear regression correlation coefficient R<sup>2</sup> in Equation (2) must not be less than 0.997. Equation (3) shows the calculation of PI, which was negatively correlated to asphalt mortar's temperature sensitivity. T<sup>800</sup> can be calculated based on Equation (4) and illustrated the high-temperature stability of asphalt mortar. Table 7 shows the results for penetration index PI, T800, regression equation and R<sup>2</sup> according to their dependence on PF content and filler-asphalt ratio; PF content 0% is the limestone asphalt mortar that was used as control group. Higher values of PI and T<sup>800</sup> suggested a stronger ability of asphalt mortar in resisting high-temperature deformation.



Both PI and T<sup>800</sup> values of PL-AM were larger than that of L-AM regardless of fillerasphalt ratio. Thus, PF reduced the temperature sensitivity of PL-AM. On the other hand, either PI and T<sup>800</sup> first increased and then decreased with increase of PF content. Additionally, PI and T<sup>800</sup> also showed an increasing trend as the filler-asphalt ratio was increased. PL-AM with 75% PF achieved the highest PI and T800, optimally improving the high-temperature performance. It is speculated that these properties were also related to a coupling effect of PF and phosphogypsum because they did not show a monotonic tendency as PF content was increased. This result was consistent with the penetration and softening point of PL-AM, showing that 75% could be the optimum content of PF in replacing limestone filler.

#### *3.3. Determination of PF Content*

Table 8 shows the results of the overall desirability calculation. It can be concluded that the total evaluation desirability value of PL-AM had achieved its maximum when PF content was 75%. This proved that its high-temperature performance was optimally enhanced as 75% PF was introduced. PL-AM's penetration and ductility decreased, while its softening point and PI were the highest at 75% PF, independent of the filler-asphalt ratio. Thus, 75% PF is suggested especially concerning high-temperature performance, consistent with the results for penetration, softening point, PI and T800. Therefore, it is suggested that the overall desirability method is a feasible approach to finding the optimum PF content.


**Table 8.** Overall desirability.

#### *3.4. Rheological Properties*

Figures 12–14 shows the results of the DSR high-temperature scanning test for PL-AM with 75% PF at filler-asphalt ratios of 0.8, 1.0 and 1.2, respectively. The complex shear modulus G\* of asphalt mortars showed a decreasing trend, while the phase angle showed a rising tendency with increase of temperature. G\* of PL-AM was higher than that of L-AM. PL-AM showed higher δ than that of L-AM from 30 to 60 ◦C, while the contrary result was found from 60 to 80 ◦C. A higher filler-asphalt ratio resulted in higher G\* of PL-AM, while δ was negatively affected by the filler-asphalt ratio from 65 to 80 ◦C.

PL-AM had a greater rutting factor (G\*/sinδ) compared with L-AM when their fillerasphalt ratio was 1.0. This proved that PF was able to increase the hardness of asphalt mortar, so that the ability to resist deformation in high temperatures, namely high-temperature performance, was improved. On the other hand, the fatigue factor (G\*sinδ) of PL-AM was also higher than that of L-AM at the same filler-asphalt ratio. Both rutting and fatigue factors were improved by a higher filler-asphalt ratio. Thus, use of a mixed filler containing

PF could help to enhance the rutting and fatigue resistance of PL-AM. The corresponding PF based asphalt mixture's high-temperature and fatigue performance should be higher than a limestone filler based asphalt mixture. *Materials* **2023**, *16*, x FOR PEER REVIEW 16 of 21 *Materials* **2023**, *16*, x FOR PEER REVIEW 16 of 21

δ (°)

**Figure 12.** G\* and δ of PL-AM and L-AM. **Figure 12.** G\* and δ of PL-AM and L-AM. **Figure 12.** G\* and δ of PL-AM and L-AM.

**Figure 13.** Rutting factor G\*/sinδ of PL-AM and L-AM. **Figure 13.** Rutting factor G\*/sinδ of PL-AM and L-AM.

**Figure 14.** Fatigue factor G\*sinδ of PL-AM. **Figure 14.** Fatigue factor G\*sinδ of PL-AM.
