3.1.1. Master Curves and Black Diagrams of Rheological Properties
The complex modulus (G*) and phase angle (δ) were obtained from the DSR frequency sweep tests at various temperatures. A master curve was constructed for each type of hydraulic bitumen based on the time–temperature superposition. In this study, the reference temperature was selected as 20 °C. Frequency sweep test data at other temperatures were shifted horizontally to obtain a smooth master curve of the complex modulus as well as the phase angle [
28]. The shift factors at various temperatures were usually described by using the Arrhenius equation [
29].
where:
αT = Temperature shift factor;
T = Test temperature, K;
ΔEa = Apparent activation energy, kJ/mol;
R = Universal gas constant, R = 8.314 J/(K·mol).
The master curve of the complex modulus and the phase angle constructed at a reference temperature is usually a function of the reduced frequency. In general, the master curve can be mathematically modelled by a sigmoidal-shape function, described as follows [
30,
31]:
where:
= , equilibrium complex modulus, ;
= , glass complex modulus, Pa;
fc = Location parameter with dimensions of frequency, Hz;
= Reduced frequency, function of temperature, Hz;
k, me = Shape parameters, dimensionless.
The reduced frequency is determined by multiplying the test frequency by the shift factor, α
T:
The equation for the master curve of the phase angle is as follows:
where:
= Phase angle constant at fd, the maximum value for asphalt mixtures and the value at the inflexion for asphalt binders;
= Reduced frequency;
fd = Location parameters with dimensions of frequency, at which occurs, Hz;
, = Shape parameters; .
The experimental data obtained from the DSR testing were then fitted to the sigmoidal-shape functions given by Equations (5) and (7), respectively. All of the model parameters or constants can be automatically obtained by minimizing the mean relative error using the Solver function in the Excel spreadsheet. The determination of the model parameters for the master curves are listed in
Table 3. As indicated by the value of R
2, good fit was obtained for the prediction of the master curves as well as the shift factor. However, it should be noted that the Arrhenius equation has its limit to fit at a wide temperature range between −10 °C and 70 °C. In particular, a slight deviation between the model prediction and the actual value was found at −10 °C [
29].
As can be seen in
Table 3, the Jurong SG90 bitumen had the maximum value of the glass complex modulus, followed by Karamay SG70, Jingbo SG70 and Liaohe SG90 bitumen; Jingbo PMB showed the minimum value. This indicated that the SBS polymer modification had a positive effect to reduce the bitumen’s brittleness at extreme low temperature.
With respect to the phase angle constant δ
m, it reflected the ratio between the viscosity and elasticity of bitumen at low reduced frequency, which corresponded to high temperature. The lower value of δ
m indicates a higher fraction of elasticity, which was desired for thermal stability and creep resistance. Among these five hydraulic bitumen binders, Jingbo PMB showed the minimum value, following by Liaohe SG90, Jurong SG90 and Jingbo SG70; Karamay SG70 bitumen had the maximum value of δ
m. This also indicated that the SBS polymer modification had a positive effect to improve the bitumen’s performance at high temperature. The apparent activation energy Δea usually relates to the temperature sensitivity of bitumen. The data listed in
Table 3 showed that the value of Δ
ea had a narrow range between 173 and 178 kJ/mol, indicating a similar temperature sensitivity for all of the five bitumen binders.
Figure 2a shows the master curve of the complex modulus and the phase angle of the five hydraulic bitumen binders. In this figure, it can be observed that the complex modulus increased as the frequency increased for all of the hydraulic bitumen binders. Because high frequency corresponded to low temperature, it was found that the descending ranking of the complex modulus at low temperature was as follows: Jurong SG90 hydraulic bitumen, Karamay hydraulic bitumen, Liaohe SG90 hydraulic bitumen, Jingbo SG70 hydraulic bitumen and Jingbo PMB. With respect to high temperature, which corresponded to low frequency, the descending ranking of complex modulus at high temperature was as follows: Jingbo PMB, Karamay SG70 hydraulic bitumen, Liaohe SG90 hydraulic bitumen, Jingbo SG70 hydraulic bitumen and Jurong SG90 hydraulic bitumen.
Similar to the complex modulus, it can be observed that the phase angle decreased as the frequency increased for all of the hydraulic bitumen binders. Among these five bitumen binders, the Jingbo SG70 hydraulic bitumen, Jurong SG90 hydraulic bitumen and Liaohe SG90 hydraulic bitumen exhibited an obvious change when compared with Karamay SG70. A remarkable plateau was seen for Jingbo PMB. The change of the phase angle master curve, especially the plateau, usually indicated the existence of the polymer. Because the degree of change strongly depends on the polymer content, it can be inferred that the Jingbo SG70 hydraulic bitumen, Jurong SG90 hydraulic bitumen and Liaohe SG90 hydraulic bitumen were slightly modified by a relatively small amount of polymer when compared with Jingbo PMB, which usually has a polymer content of around 4%.
Figure 2b shows the black diagrams based on the complex modulus and the phase angle. The curves exhibited the relationship between the measured complex modulus and the phase angle on a semi-logarithmic scale. It can be observed that the complex modulus decreased as the phase angle increased for all of the hydraulic bitumen binders. Karamay SG70 bitumen exhibited a smooth decline tendency over a wide range of phase angles. However, the Jingbo SG70 hydraulic bitumen, Jurong SG90 hydraulic bitumen and Liaohe SG90 hydraulic bitumen exhibited a slight deviation from the smooth trend. A distinct deviation can be found for Jingbo PMB. The complex modulus dropped dramatically as the phase angle remained in a plateau between 60° and 70°. It should be noted that the existence of the phase angle plateau is believed to be attributed to the addition of polymer into bitumen. Again, the degree of the plateau demonstrated that the Jingbo SG70 hydraulic bitumen, Jurong SG90 hydraulic bitumen and Liaohe SG90 hydraulic bitumen were slightly modified by a smaller amount of polymer when compared with real Jingbo PMB.
The above analysis demonstrated that the DSR phase angle master curves and black diagrams gave more insights than the results obtained from the traditional penetration, softening point and ductility. The DSR test can well distinguish the existence of the SBS polymer in the Jurong SG90 hydraulic bitumen, Liaohe SG90 hydraulic bitumen and Jingbo SG70 hydraulic bitumen. This indicated that the addition of the SBS polymer and the change of bitumen can be detected, and thus make the DSR test a powerful method for the purpose of the quality control of bitumen.
3.1.2. Complex Modulus (G*) and Phase Angle (δ) at 70 °C
Table 4 and
Figure 3 show the complex modulus and phase angles of five hydraulic bitumen binders at 70 °C. For an ideal bitumen binder which has good high-temperature performance, a higher complex modulus and a lower phase angle at high temperatures are needed. In the field of road paving bitumen, a rutting factor, which is defined as G*/sinδ, is widely used to evaluate bitumen’s high-temperature performance. As can be seen, G*/sinδ makes good use of a combination of G* and sinδ. Higher G* together with lower δ will result in higher G*/sinδ, and thus an improved high-temperature performance. For this reason, the data obtained from G*/sinδ were also evaluated in
Figure 3.
As can be seen in
Table 4, all the bitumen binders exhibited an increase on G* with a reduction on δ as the test frequency increased. These changes seemed to be dependent on the type of bitumen. The Karamay SG70 bitumen had a phase angle of 89.4, indicating that it is close to Newtonian fluid at 70 °C. For the ease of comparison, the Karamay SG70 bitumen was selected as the reference bitumen, since it is commonly accepted and used as a hydraulic bitumen in China. The G* and δ obtained from other bitumen binders were normalized using the Karamay SG70 bitumen as the reference value of 1 at various frequencies. To do this, the G* and δ of other bitumen binders were divided by the corresponding value of the Karamay SG70 bitumen and the obtained ratios were illustrated in
Figure 3. Similarly, the values of G*/sinδ were also normalized.
At high temperature, the slope flow is the main risk for the hydraulic asphalt concrete impermeable layer. The slope flow is a long-term behavior, and thus the rheological properties at low frequency are of interest. In this case, Jingbo PMB showed an overall higher G*, followed by Liaohe SG90 bitumen with a slight improvement on G* when the frequency was lower than 0.5 Hz. The rest of the bitumen binders exhibited lower G*. With respect to the normalized δ, all the bitumen binders showed lower values compared to the Karamay SG70 bitumen. Significant reduction can be seen on Jingbo PMB as well as the Liaohe SG90 bitumen. The normalized values of G*/sinδ were similar to those of the normalized G* for all of the bitumen binders. The analysis above indicated that Jingbo PMB was superior to the other bitumen binders with respect to high-temperature properties.
When using the complex modulus, the phase angle and G*/sinδ as the indicators for high-temperature performance, Jingbo PMB was superior to other bitumen binders, indicated by the higher complex modulus, the lower phase angle as well as the higher G*/sinδ. Some hydraulic bitumen binders that were slightly modified by the SBS polymer did not always show consistent results when the traditional Karamay hydraulic bitumen was used as a reference.
3.1.3. Complex Modulus (G*) and Phase Angle (δ) at −10 °C
Table 5 and
Figure 4 show the complex modulus and the phase angle of the five hydraulic bitumen binders at −10 °C. The large flexibility at low temperatures is related to the lower complex modulus and the higher phase angle. The rheological characteristics of the bitumen (the complex modulus and phase angle) showed a strong relationship to the fracture temperature of asphalt mixtures. It was reported that bitumen with a phase angle smaller than 15° and a complex modulus higher than 300 MPa was more likely to fracture at low temperature [
32,
33].
As can be seen in
Table 5, all the bitumen binders exhibited an increase on G* with a reduction on δ as the test frequency increased. With a frequency higher than 25 Hz, some bitumen binders tended to have a complex modulus higher than 300 MPa together with a phase angle lower than 15°. This indicates that the rapid temperature drop is decisive for thermal cracking at low temperature. Similarly, the G* and δ were normalized using Karamay SG70 bitumen as the reference, as mentioned before, and the obtained results were presented in
Figure 4.
At extreme low temperature, the thermal shrinkage cracking is the main risk for the hydraulic asphalt concrete impermeable layer. The cracking resistance strongly dependent on the degree of temperature, the drop rate as well as the bitumen flexibility. After normalization, it can be clearly seen that the other bitumen binders tended to have low G* compared to the Karamay SG70 bitumen. An exception was found on the Jurong SG90 bitumen at frequencies higher than 1 Hz. With respect to the normalized δ, all the bitumen binders tended to have higher values compared to the Karamay SG70 bitumen. An exception was found on the Jurong SG90 bitumen and the Liaohe SG90 bitumen at frequencies higher than 8 Hz. In general, Jingbo PMB showed the lowest G* combined with a relatively high δ among the five bitumen binders. In general, when using the complex modulus and the phase angle as the indicators for low temperature performance, Jingbo PMB was superior to the other bitumen binders with respect to the flexibility at low temperature. Similar to the high temperature performance, as discussed before, some hydraulic bitumen binders that were slightly modified by the SBS polymer did not always show consistent results when the traditional Karamay hydraulic bitumen was used as a reference. This indicates the complexity of the system of slightly modified bitumen, and thus the stability may become a big concern.