Determination of P-AM Composition

The influence of steel slag powder content on the penetration, softening point and ductility of P-AM was firstly analyzed according to (JTG E20-2011). The results were then analyzed to figure out the optimum content of steel slag powder.

In addition, it is necessary to characterize the effect of PF on adhesion between asphalt and limestone, since phosphogypsum is acidic and shows poor moisture stability. How steel slag powder affects the moisture stability of asphalt mixture can hence be investigated. A boiling test investigating the adhesion between P-AM and aggregate was introduced. Limestone aggregate with the size of 26.5 to 31.5 mm was selected. Aggregates were heated at 150 ◦C and then put in P-AM at 135 ◦C for 10 s so that they could be fully covered with P-AM. They were then put in boiling water for 30 min after cooling for 24 h at 25 ◦C. Afterwards, the boiled aggregate was put in a drying box at 80 ◦C for 5 h to remove moisture. Finally, the mass loss ratio of P-AM on aggregate can be described as Equation (1) [25].

$$\text{MLR} = \frac{\mathbf{m}\_1 - \mathbf{m}\_2}{\mathbf{m}\_1 - \mathbf{m}\_0} \times 100\% \tag{1}$$

where: MLR = mass loss ratio of P-AM on aggregate, (%);

m<sup>0</sup> = mass of original aggregate, (g);

m<sup>1</sup> = mass of aggregate covered by P-AM;

m<sup>2</sup> = mass of the boiled aggregate.

Determination of PL-AM

The penetration, ductility and softening point of different PL-AM mixes were characterized. The penetration index (PI) and equivalent softening point T<sup>800</sup> were also included to indicate their mechanical properties. Equation (2) is a unary linear equation which was used to fit the functional relationship between penetration and temperature. Equations (3) and (4) were used to calculate PI and T<sup>800</sup> [26]. The equations used are as follows and all indexes are dimensionless:

$$\mathbf{d}\_{\mathbf{g}}\mathbf{P} = \mathbf{K} + \mathbf{A}\_{\mathbf{l}\_{\mathbf{g}}\mathbf{P}\mathbf{en}} \times \mathbf{T} \tag{2}$$

$$\text{PI} = \frac{20 - 500 \text{A}\_{\text{l}\_{\text{g}} \text{Pen}}}{1 + 50 \text{A}\_{\text{l}\_{\text{g}} \text{Pen}}} \tag{3}$$

$$\text{T}\_{800} = \frac{\text{l\_g}800 - \text{K}}{\text{A}\_{\text{l\_g}\text{Pen}}} = \frac{2.9031 - \text{K}}{\text{A}\_{\text{l\_g}\text{Pen}}} \tag{4}$$

where: lgP = Penetration logarithm at different temperatures;

K = Constant of the linear equation;

AlgPen = Slope of the linear equation;

T = Testing temperature of penetration;

PI = Penetration index;

T<sup>800</sup> = Equivalent softening point.

This study adopted the overall desirability method which can combine comprehensive indicators and express the final effect by overall desirability. Introduction of comprehensive indicators in the overall desirability method facilitates the integration of indicators with different data ranges into desirability data; thus, the optimum value of asphalt mortar considering each factor control range can be calculated. Using the overall desirability method, dimensional indicators such as penetration, softening point, and ductility are standardized and converted into corresponding dimensionless desirability values between 0 and 1 through linear transformation. The geometric mean of desirability for each indicator can be calculated. Consequently, the desirability of overall evaluation can be obtained. The closer the desirability of the general evaluation to "1", the better the comprehensive performance of the asphalt mortar will be.

Penetration, penetration index (PI), ductility, and softening point were taken as the calculation indexes of the overall desirability method. Firstly, for each performance indicator (γ), the maximum and minimum value obtained in this study were noted. Then, the desirability (γ ∗ n ) was calculated by linear transformation of performance indicators, using Equations (5) and (6). The equations specify the calculation of desirability based on γ whose values positively or negatively determine the performance of asphalt mortar. Finally, the desirabilities of each performance indicator were used to calculate their geometric mean value by Equation (7), which was the overall desirability. The calculation method of overall desirability is shown below [27,28]:

$$
\gamma\_{\text{max}}^\* = \frac{\gamma - \gamma\_{\text{min}}}{\gamma\_{\text{max}} - \gamma\_{\text{min}}} \tag{5}
$$

$$
\gamma\_{\rm min}^\* = \frac{\gamma\_{\rm max} - \gamma}{\gamma\_{\rm max} - \gamma\_{\rm min}} \tag{6}
$$

$$\text{OD} = \left(\gamma\_1^\* \gamma\_2^\* \gamma\_3^\* \dots \gamma\_n^\*\right)^{\frac{1}{n}} \tag{7}$$

where: OD = overall desirability, dimensionless;

γ ∗ <sup>n</sup> = desirability index after linear transformation, dimensionless;

γ = performance indicator value, dimensionless;

n = number of performance indicators used in overall desirability, dimensionless;

γmax = maximum value of corresponding performance indicator in this study, dimensionless;

γmin = minimum value of corresponding performance indicator in this study, dimensionless; γ ∗ max = desirability based on the γ whose value positively determined performance of asphalt mortar, dimensionless; *Materials* **2023**, *16*, x FOR PEER REVIEW 7 of 21

> γ ∗ min = desirability based on the γ whose value negatively determined performance of asphalt mortar, dimensionless. Rheological Performance

#### Rheological Performance Rheological performance of PL-AM and limestone filler were also characterized by

Rheological performance of PL-AM and limestone filler were also characterized by using a dynamic shear rheometer (DSR) after PF's content and composition were determined. A limestone filler-based asphalt mortar with filler-asphalt mass ratio of 1:1 was prepared as control group. Table 4 shows the setting table of DSR high-temperature scanning parameters. using a dynamic shear rheometer (DSR) after PF's content and composition were determined. A limestone filler-based asphalt mortar with filler-asphalt mass ratio of 1:1 was prepared as control group. Table 4 shows the setting table of DSR high-temperature scanning parameters.

**Table 4.** DSR high-temperature scanning parameter setting table.

**Table 4.** DSR high-temperature scanning parameter setting table.


#### 2.2.4. Pavement Performance of PF Based Asphalt Mixture 2.2.4. Pavement Performance of PF Based Asphalt Mixture

Mixed filler containing PF was also used to prepared asphalt mixture to indicate its effect on pavement performance. AC-20 was used as the gradation of asphalt mixture which was specified in JTG E40-2005, and its gradation curve is shown in Figure 3. Limestone filler-based AC-20 asphalt mixture was firstly fabricated. Afterwards, PF based asphalt mixture using the mixed filler containing PF can be prepared. The mass ratio of asphalt to aggregate was 4.25% for both the limestone filler and PF based asphalt mixture. Volumetric performance, high-temperature performance, low temperature performance and moisture stability were tested. Volumetric property refers to void volume (VV) and void in mineral aggregate (VMA). Mixed filler containing PF was also used to prepared asphalt mixture to indicate its effect on pavement performance. AC-20 was used as the gradation of asphalt mixture which was specified in JTG E40-2005, and its gradation curve is shown in Figure 3. Limestone filler-based AC-20 asphalt mixture was firstly fabricated. Afterwards, PF based asphalt mixture using the mixed filler containing PF can be prepared. The mass ratio of asphalt to aggregate was 4.25% for both the limestone filler and PF based asphalt mixture. Volumetric performance, high-temperature performance, low temperature performance and moisture stability were tested. Volumetric property refers to void volume (VV) and void in mineral aggregate (VMA).

High-temperature performance was evaluated by testing the asphalt mixture's Marshall stability and dynamic stability according to JTG F20-2011. The dynamic stability test should be applied at 60 °C. Track plate specimens and a dynamic stability instrument

× cଵ × cଶ (8)

DS = (tଶ − tଵ) × 42 dଶ − dଵ

**Figure 3.** Aggregate gradation curve of AC-20. **Figure 3.** Aggregate gradation curve of AC-20.

High-Temperature Performance

tଵ, tଶ = test time, usually 45 min and 60 min;

where: DS = dynamic stability of the asphalt mixture, (cycle/mm);

High-Temperature Performance

High-temperature performance was evaluated by testing the asphalt mixture's Marshall stability and dynamic stability according to JTG F20-2011. The dynamic stability test should be applied at 60 ◦C. Track plate specimens and a dynamic stability instrument were used. Stability can be calculated by Equation (8) [29].

$$\text{DS} = \frac{\left(\mathbf{t}\_2 - \mathbf{t}\_1\right) \times 4\mathbf{2}}{\mathbf{d}\_2 - \mathbf{d}\_1} \times \mathbf{c}\_1 \times \mathbf{c}\_2 \tag{8}$$

where: DS = dynamic stability of the asphalt mixture, (cycle/mm);

t1, t<sup>2</sup> = test time, usually 45 min and 60 min;

d1, d<sup>2</sup> = deformation of specimen surface corresponding to the test specimens t<sup>1</sup> and t2, (mm).

c1, c<sup>2</sup> = correction factor of testing machine or specimen, dimensionless.

#### Low-Temperature Flexural Performance

Low-temperature flexural performance of the asphalt mixtures was evaluated by a three-point bending test. Track plate specimens were cut into beam specimens with a size of 250 mm × 30 mm × 35 mm, according to JTG E20-2011. A Universal Testing Machine (UTM-100) was used for the three-point bending test at −10 ◦C. The distance between supporting fulcrums was 200 mm. The loading rate of the principal axis was 50 mm/s. Corresponding indictors can be calculated using the following equations [30]:

$$\mathbf{R\_B} = \frac{\mathbf{3 \times L \times P\_B}}{2 \times \mathbf{b \times h^2}} \tag{9}$$

$$
\varepsilon\_{\mathbf{B}} = \frac{6 \times \mathbf{h} \times \mathbf{d}}{\mathbf{L}^2} \tag{10}
$$

$$\mathbf{S\_B} = \frac{\mathbf{R\_B}}{\varepsilon\_\mathbf{B}} \tag{11}$$

where: R<sup>B</sup> = flexural tensile strength (MPa);

ε<sup>B</sup> = tensile strain (µε);

S<sup>B</sup> = tensile stiffness modulus (MPa);

P<sup>B</sup> = loading peak (kN);

L = span length of beam (mm);

h = height of midspan section (mm);

b = width of midspan section (mm);

d = midspan deflection at failure (mm).

## Moisture Stability

It is important to characterize the moisture stability of the asphalt mixtures as phosphogypsum's high hydrophilicity may lead to poor adhesion between asphalt and aggregate. The immersion Marshall stability ratio (IMS) and freeze-thaw tensile strength ratio (TSR) were used to comprehensively evaluate the moisture stability of asphalt mixture according to (JTG E20-2011). IMS can be calculated by Equation (12) [29].

$$\text{IMS} = \frac{\text{MSR}\_1}{\text{MSR}} \times 100\% \tag{12}$$

where: MSR: the average stability of specimen in moisture at 60 ◦C for 30 min (kN);

MSR1: the average stability of specimen in moisture at 60 ◦C for 48 h (kN);

IMS: the average residual stability of specimen in moisture.

On the other hand, TSR can be calculated by Equation (13) [29].

$$\text{TSR} = \frac{\text{R}\_{\text{T2}}}{\text{R}\_{\text{T1}}} \times 100 \tag{13}$$

where: TSR: the average strength ratio of the freeze-thaw splitting test;

RT1: splitting tensile strength of the specimens without freeze-thaw cycle (the unconditional);

RT2: splitting tensile strength of specimens after freeze-thaw cycle (the conditional).

#### **3. Results and Discussions**
