## 4 Results and Discussion
### DSR Test Results  
The temperature sweep tests of BA, CBMA and NHSSMA under the F-T aging process were carried out, and the complex shear modulus (G*), phase angle (8), rutting factor and G*/sin \(\delta\) were analyzed.  
It can be seen from Figure 11, with the increase of temperature, the complex shear modulus of BA, CBMA and NHSSMA gradually decreases, but the phase angle shows an upward trend with the increase of temperature. This is because the increase in temperature causes the volume of free asphalt to increase, and the elastic state of asphalt at low temperature gradually shifts to the flow state at high temperature. The maximum shear stress of asphalt samples decreases, and the maximum shear strain increases gradually with increasing temperature in the dynamic shear test, so the complex shear modulus of BA, CBMA and NHSSMA gradually decreases with increasing temperature. Meanwhile, as the temperature increases, the viscous component in the asphalt increases and the elastic component decreases, so the phase angle increases with increasing temperature.  
Figure 11: Complex shear modulus and rutting factor of BA, CBMA and NHSSMA without F-T aging process. (**a**) complex shear modulus; (**b**) rutting factor.  
Figure 10: Rotational viscosity test results of modified and unmodified asphalt at different F-T cycles. (**a**) 135 \({}^{\circ}\)C rotational viscosity; (**b**) aging index.  
The complex modulus and the rutting factor variation tendency of BA, CBMA and NHSSMA with temperature is basically the same, which indicates that the addition of carbon black and NHSS does not change the viscoelastic properties of asphalt. However, the addition of carbon black and NHSS changes the value of complex shear modulus and rutting factor. The complex shear modulus of CBMA and NHSSMA is increased by 22-27% and 82-92% compared with BA respectively, while the increase in rutting factor of CBMA and NHSSMA is 21-28% and 45-48%. The results show that the addition of NHSS provided a certain rheological resistance of asphalt, and NHSS could better increase the viscosity of asphalt binder relative to carbon black due to the NHSS particles having higher affinity with asphalt binder functional groups through surface attraction, which is consistent with the conclusions of the basic properties test. The rutting factor of NHSSMA has a certain improvement compared with BA and CBMA, which manifested that the incorporation of NHSS improves the high temperature stability and resistance to high temperature permanent deformation of asphalt.  
Figures 12 and 13 show the relationship between DSR parameters of BA and NHSSMA and F-T cycles. The changes of the rutting factor of BA and NHSSMA were relatively consistent with the changes of complex shear modulus. The rutting factor and complex shear modulus have increased under the F-T aging process. After 10 F-T cycles, the rutting factor of BA increased by 13-21% at different temperature, and the increase range was 31-34% after 20 F-T cycles. After 30 cycles, the improvement rate reached 43-54%. This is because the F-T aging progress makes the asphalt harder, reduces the fluidity, and improves the rutting factor of asphalt. After 10, 20 and 30 F-T cycles, the rutting factor of NHSSMA increased by 8-30%, 13-30% and 18-53%, indicating that