## 3 Results and Discussions
### Dynamic Shear Rheological Properties  
Dynamic shear rheometer test was performed to check the rheological properties of asphalt binder at intermediate to high temperatures for different frequencies. Figure 11 shows that an increase in failure temperature of the bitumen was observed when increasing percentages of MWCNTs were introduced. Failure temperature of the bitumen for unaged samples was determined as per superpave method. Temperature at which G*/Sin\(\delta\) becomes less than 1 kPa is failure temperature for unaged asphalt binder [45]. The failure temperature of original bitumen was about 61 \({}^{\circ}\)C, so the upper performance grade of original asphalt binder was 58\({}^{\circ}\)C. By increasing the CNT dosage, the failure temperature of samples was also increased, which is an indication of the reduction in temperature susceptibility. At 0.5% dosage, high PG grade of bitumen was 64, while the PG grades for 1% and 3% CNTs modified bitumens were 70 and 76, respectively. It means that a 3% dosage of CNTs resulted in three grade bumps. The climate in most of Pakistan is hot and summer air temperature rises up to 50 \({}^{\circ}\)C and in winter it hardy drops below 0 \({}^{\circ}\)C. PG 70 is recommended for most regions of the country [46]. This study aimed at achieving a PG 76 after a great bump in the required PG 70 to accommodate the overloading on the highways of the country. Figure 12 shows master curve of Complex Shear Modulus (G*) at 58 \({}^{\circ}\)C for unmodified and CNT-modified bitumen. The G* value increased from 3132 Pa to 14,264 Pa at 10 Hz frequency with the addition of 3% of CNTs. By increasing the content of MWCNTs in the original asphalt binder, the  
Figure 11: Putting parameter (G*/Sin\(\delta\)) versus temperature for unaged asphalt binder at 10 rad/s. Figure 10: Ductility of bitumen with different contents of CNTs. G* value increased, which is an indication of increase in bitumen stiffness and its resistance against permanent deformation at higher temperature. Bitumen is a viscoelastic material that shows viscous behavior at higher temperature and elastic behavior at low temperature. Phase angle is used to describe the bitumen elastic or viscous behavior. In Figure 13, it can be seen that, with the increase of CNTs in bitumen, phase angle of binder decreased, which is an indication of the increase in elastic behavior of bitumen [33]. The smaller is the phase angle, the higher is the elastic recovery when bitumen pavements are subjected to traffic at high temperatures. Thus, for MWCNT-modified bitumen, the chances of permanent deformation at higher temperatures are low. One of the most important problems for asphaltic pavement is the deformation of the pavement in the wheel path due to heavy traffic at high temperature, which is called rutting. The parameter G*/Sin\(\delta\) is called rut factor and predicts the failure of binder at high temperature. Figure 14 shows that, with the modification of bitumen with MWCNTs, this parameter improved, which means the materials resistance against the rutting is enhanced at higher temperatures. The same effect was observed by [PERSON] et al. (2016) [33]. Figure 12: Master curve of G* for CNT-modified and unmodified bitumen at 58 \({}^{\circ}\)C.  
Figure 13: Master curve of \(\delta\) for CNT-modified and unmodified bitumen at 58 \({}^{\circ}\)C.  
Complex shear modulus (G*) and phase angle (\(\delta\)) obtained by frequency sweep test are represented in the form of black diagram in Figure 15. Black diagram is free of frequency and temperature. It allows all the data to be presented in a single graph. As shown in Figure 15, the viscoelastic properties of bitumen were very sensitive to CNTs content, as there was a significant change in the curves obtained for unmodified binder in comparison to the binder modified with different dosages of CNTs. It was observed that, with increase in temperature, phase angle of bitumen increased and G* value decreased.