2.2.4. Linear Amplitude Sweep Test
The linear amplitude sweep (LAS) test evaluates the fatigue resistance of asphalt samples by applying cyclic loads with linearly increasing amplitudes. The LAS test is conducted using a dynamic shear rheometer (DSR) apparatus, utilizing standard parallel plates with a diameter of 8 mm and a plate spacing of 2 mm. The LAS testing method consists of two steps [
25], adhering to the AASHTO TP 101-14 specification.
The LAS test allows the quick determination of parameters A and B in the traditional strain-controlled fatigue equation. Parameter A represents the initial fatigue life, which indicates the asphalt binder’s ability to resist fatigue damage before significant modulus reduction occurs. Parameter B represents the rate at which fatigue life decreases with increasing strain amplitude, reflecting the material’s sensitivity to changes in strain level.
Adhesives with strong fatigue resistance exhibit higher values of parameter A and lower absolute values of parameter B [
26]. The traditional strain-controlled fatigue equation is defined as Equation (1).
where
is the fatigue life;
is the amplitude of the applied shear strain.
Generally speaking, viscoelastic continuum damage model (VECD) mechanics [
27] is used to calculate parameters
A and
B. In VECD mechanics, the damage evolution of viscoelastic materials is characterized by Schapery’s work potential theory. There are two theoretical foundations for it [
28], the first being the VECD method based on PSE (Schapery’s elastic–viscoelastic correspondence principle) [
29]; the second method is VECD based on DE (dissipated energy density). The VECD method based on PSE has the advantage of ignoring viscoelastic effects and can effectively quantify the relationship between damage strength (S) and material integrity (C) through equations. Therefore, this study adopted the VECD mechanical method based on PSE for data analysis. Experiments were conducted at 25 °C, and fatigue parameters
A and
B were calculated using formulas.
Then, the fatigue strength calculate based on the frequency sweep results and amplitude sweep results, as shown in Equation (2) below.
where
is the accumulated damage over time t (dimensionless);
; is the complex modulus at time t;
is the initial value of the complex modulus
is the strain (%);
t is the testing time;
and m are the slope of the best-fit line on the logarithmic plot of storage modulus versus frequency.
At the given time
t, we recorded the values of
and
, which could be fitted into the following equation (Equation (3)):
where
C0 = 1, while
C1 and
C2 are curve fitting parameters.
The damage value during destruction corresponds to the maximum peak shear stress, as shown in Equation (4).
Thus, the fatigue equation can be expressed by Equation (5).
where
is the maximum expected strain;
f is the loading frequency, which is 10 Hz here;
The steps of the LAS test were as follows.
The LAS test plan consisted of two consecutive types of testing. The first test was a frequency sweep experiment, aimed at obtaining the rheological properties of asphalt materials; the second test was an amplitude sweep experiment, aimed at measuring the damage characteristics of asphalt materials.
The first step was the frequency sweep experiment. During the testing period, a strain load with an amplitude of 0.1% was applied to the emulsified asphalt residue sample. We took 12 points (30, 20, 10, 8, 6, 4, 2, 1, 0.8, 0.6, 0.4, and 0.2 Hz) in the frequency range of 0.2–30 Hz, and we recorded the dynamic shear modulus and phase angle .
Step two was the amplitude sweep experiment. We applied oscillatory shear to asphalt samples in strain control mode at 25 °C, with a frequency of 10 Hz. We applied continuous oscillatory loading cycles with strain amplitudes increasing linearly from 0% to 30% to accelerate fatigue damage. The loading scheme consisted of 10 s intervals of constant strain amplitude, followed by intervals of increased strain amplitude. We recorded the peak shear strain and peak shear stress every 10 load cycles (1 s), as well as the phase angle and dynamic shear modulus.
An LAS experiment can be used to plot the curve of damage strength (S) and integrity parameter (C). C = 1 indicates that the asphalt specimen is in good condition, while C = 0 indicates that the asphalt specimen is completely destroyed. The faster the C value decreases, the poorer the fatigue resistance. By plotting the variation curves of shear stress and shear strain, the peak values and widths of different specimen curves can be compared. The higher the peak value and the wider the width, the stronger the elastic deformation ability of emulsified asphalt residue. In addition, the predicted fatigue life , can be calculated, and the smaller it is, the poorer the fatigue resistance of the specimen.
2.2.6. Surface Free Energy Test
Surface free energy measures the adhesive properties of materials. The surface energy method first tests the surface energy parameters of single-phase materials, such as asphalt and aggregate, under actual temperature conditions. It then calculates the peeling energy of asphalt–aggregate two-phase materials under water conditions and the adhesion energy under water-free conditions. The absolute value of the ratio of adhesion energy to peeling energy is used as a matching index to evaluate the adhesion between the two materials [
30,
31,
32]. A higher matching index indicates stronger adhesion and better water stability.
Domestic and foreign researchers typically use the absolute value of the ratio of these two parameters as the basic indicator
ER for quantifying water stability, as shown in the following formula:
where
is the adhesion energy, mJ/m2.
is the peeling energy, mJ/m2.
The subscripts s, w, and l, respectively, represent the three material phases of aggregate, water, and asphalt.
Among them, the larger the adhesion energy, the stronger the adhesion between asphalt and aggregate; the greater the peeling energy, the higher the degree of displacement and peeling of the asphalt film by water. Therefore, the larger the compatibility index, the better the match between asphalt and aggregate, and the more ideal the water stability of asphalt mixture [
33]. Based on this, some scholars have pointed out that the composition of aggregate gradation determines its specific surface area, and changing the adhesion area between asphalt and aggregate affects adhesion [
31]. Therefore, the improved matching index
ER1 for aggregate specific surface area is considered. Some scholars have considered the wetting effect of asphalt on aggregates, that is, the prerequisite for asphalt to spread on and wet the surface of aggregates is to overcome its own cohesion [
34], and thus substitute the difference between adhesion energy and asphalt internal energy as an improved matching index
ER2. The forms of the two are shown in Formulas (9) and (10), respectively.
where
is the adhesion energy of asphalt, mJ/m2, with the same meaning as .
is the peeling energy of asphalt, mJ/m2, with the same meaning as .
is the cohesive energy of asphalt, mJ/m2.
Surface free energy, also known as surface energy, measures the adhesive properties of materials. The energy required to separate solids or liquids into new units of surface area under vacuum conditions is called surface energy. This separation can occur within the same homogeneous material, known as cohesive bonding energy (or cohesive energy), or between heterogeneous materials, known as adhesion bonding energy (or adhesion energy). According to the Good–Van Oss–Chaudhury (GVOC) theory, the surface energy component of the material is shown in Formula (11), with the commonly used unit being mJ/m
2.
where
is the surface energy of the material, abbreviated as surface energy.
is the non-polar components of the material.
is the polarity component of the material.
is the polar acid content of the material.
is the polar alkali content of the material.
From the perspective of thermodynamic theory, the relationship between the cohesive energy (
) of asphalt and its surface energy is shown in the following formula:
The meaning of each parameter in the formula is the same as described above.
The calculation method for the adhesion energy (
) between asphalt and aggregate is shown in the following formula:
where
is the adhesion energy between asphalt and aggregate.
is the non-polar component of adhesion energy.
is the polarity component of adhesion energy.
, , is the surface energy component of the aggregate.
, , is the surface energy component of asphalt.
Considering the presence of water, the adhesion energy between asphalt and aggregate is calculated using the following formula:
where
is the adhesion energy between asphalt and aggregate in the presence of water, which is the peeling energy mentioned above.
is the non-polar component of adhesion energy in the presence of water.
is the polar component of adhesion energy in the presence of water.
, , is the surface energy component of water.
The meanings of the remaining parameters are the same as in Formula (13). The plug-in method for testing the surface energy of asphalt requires selecting three or more types of chemical reagents with known surface energy parameters.
Considering availability in the laboratory and adherence to the above principles, this study selected three non-polar chemical reagents: distilled water, formamide, and glycerol, all with a purity of over 99.9%. The density and surface energy parameters of the reagents are listed in
Table 3.