# Preparation and Properties of SBS/REOB-Modified Rejuvenated Asphalt
## 4 Results and Analysis
### Dynamic Shear Rheological Test
#### 4.2.2 Frequency Characteristic  
A frequency sweep was carried out for each original asphalt in the range of 0.1-100 Hz (about 0.628-628.319 rad/s) within the linear viscoelastic range, and the actual pavement temperature generally did not exceed 70 \({}^{\circ}\)C [12]. Accordingly, the test temperature was set at an interval of 10 \({}^{\circ}\)C, starting from 35 \({}^{\circ}\)C, with a total of 5 temperatures, 35 \({}^{\circ}\)C, 45 \({}^{\circ}\)C, 55 \({}^{\circ}\)C, 65 \({}^{\circ}\)C, and 75 \({}^{\circ}\)C. We selected 25 mm parallel plates, and the spacing of the parallel plates was 1 mm. Taking the 9\(\%\) REOB + aged asphalt reclaimed asphalt and 4.5\(\%\) SBS + 9\(\%\) REOB + aged asphalt modified rejuvenated asphalt as examples, the lgG\({}^{*}\) - lg\(f\) logarithmic curve of complex modulus and frequency were drawn, as shown in Figure 5a,b.  
We took the logarithm of the \(G^{*}\)-\(f\) test results at different temperatures and performed linear fitting. Taking the complex shear modulus as lgG\({}^{*}\) = 5 Pa, the lg\(f\) corresponding to the temperatures of 35 \({}^{\circ}\)C, 45 \({}^{\circ}\)C, 55 \({}^{\circ}\)C, 65 \({}^{\circ}\)C, and 75 \({}^{\circ}\)C were \(-\)0.581 Hz, 0.396 Hz, 0.963 Hz, 1.451 Hz, and 1.985 Hz, respectively. Based on this, the displacement factors at each temperature were determined as 1.544 Hz, 0.567 Hz, 0 Hz, \(-\)0.488 Hz, and \(-\)1.022 Hz, respectively. According to the time-temperature equivalence principle, the main curves of each asphalt material at 55 \({}^{\circ}\)C were established, as shown in Figure 5c, to evaluate the rheological properties of the SBS/REOB modification regeneration in a broader frequency domain.  
Figure 4: Rutting factor (\(G^{*}\)/sin\(\delta\))—temperature curve.  
It can also be seen from the test results of each asphalt sample that the complex modulus decreased as the temperature increased, with the highest \(G^{\star}\) value at 35 \({}^{\circ}\)C and the lowest \(G^{\star}\) value at 75 \({}^{\circ}\)C, which reflected the temperature characteristics discussed in the above section. In addition, the figure also shows that there was a linear relationship between the complex shear modulus of each asphalt material and frequency in logarithmic coordinates; the complex modulus increased with the increase in frequency, which means that the anti-deformation ability of asphalt increased with the increase in frequency. This is because under the condition of low frequency, the asphalt sample had a certain contact time with the external single load, while under the condition of high frequency, the contact time was relatively short. Therefore, the larger the deformation caused by the low-frequency load per unit time, or the greater the stress required to produce the same strain, the greater the complex modulus value, and the law under the action of the high-frequency load was just the opposite. The above research conclusions show that the test material presented a low \(G^{\star}\) value at high temperature and low frequency and a high \(G^{\star}\) value at low temperature and high frequency, which was dependent on temperature and loading frequency; the large and small loading frequency corresponded to the short and long loading time, which was  
Figure 5: (a) IgG\({}^{\star}\) - lg\(f\) double logarithmic curve of complex modulus and frequency of 4.5% SBS + 9% REOB + aged asphalt modified rejuvenated asphalt; (b) IgG\({}^{\star}\) - lg\(f\) double logarithmic curve of complex modulus and frequency of 9% REOB + aged asphalt rejuvenated asphalt; (c) main curve.  
in line with the time-temperature equivalence principle in asphalt rheology. This law is also consistent with the change law of the complex shear modulus of asphalt mixture in the actual use of asphalt pavement [13].