## 3 Results and Discussion
### Dynamic Shear Rheometer
#### 3.4.2 Strain Sweep Test  
The DSR test stress-strain control mode at medium- and high temperatures ranging from 58 to 88 \({}^{\circ}\)C were conducted on the modified and unmodified bitumen binders. The stress-strain relationship curves of unmodified and modified bitumen at medium- and high-temperatures is illustrated in Figure 8a-c. The results show that the CRM has a more extensive linear viscoelasticity areas than PP- and TPS-modified binders.  
Figure 8a-c shows that the stress-strain relationship of the modified bitumen binders demonstrates a significant difference. The relationship increased with the addition of CRM, PP, and TPS modifiers. Therefore, the dosage of the additive has vital importance in medium- and high-temperature properties.  
The elevated-temperature features (stress) were increased when CRM content increased for all concentrations. However, in the case of PP and TPS, the properties increased at 2%, 3%, and 3.5%, respectively, in the PP contents, and then decreased considerably at 4% PP. Then, the properties increased at concentrations 2% and 3% of TPS; then, the stress significantly reduced at 3.5% and 4% of TPS contents (Figure 8b,c). Thus, the 3.5% of PP and 3% of TPS concentrations are considered as ideal percentages for PP and TPS, respectively.  
Figure 7: G*; temperature curves of modified and unmodified asphalt binders.  
The rutting resistance features of the bitumen were remarkably enhanced by adding 2 to 4% CRM, 2 to 3.5% of PP, and 2 to 3% of TPS modifiers. The medium- and high-temperature characteristics obtained from the ideal percentages were substantially higher in the 4% of CRM modified bitumen than the 3.5% of PP and 3% of TPS modified bitumen binders. At temperatures above 76 \({}^{\circ}\)C, the 3.5% of CRM- and 3.5% of PP-modified binders are close to each other and showed a very slight variation. The medium- and high-temperature properties of the 2% of PP-, 3.5%, and 4% of TPS-modified asphalt are also close to each other and displayed only minor differences at temperatures less than 76 \({}^{\circ}\)C.  
The complex shear modulus (G*) and the phase angle (\(\delta\)) serve as a function of temperature for modified and unmodified bitumen binders at medium- and high-temperatures (Figure 9a-c). The complex shear modulus and phase angle temperature relationship further demonstrate that CRM has more extensive linear viscoelasticity areas. Figure 9a-c show the complex shear modulus and phase angle temperature relationship that is obtained by the same behaviors as the stress-strain relationship. It is observed that when the G* values increased, the \(\delta\) magnitudes decreased with increasing concentrations of CRM, PP, and TPS modifiers. This increase in G* increases the asphalt's resistance to permanent deformation. Meanwhile, a decrease in \(\delta\) improves the elastic response of the binder and mixture flexibility. Overall, the results of all the modified binders prove that CRM-modified binders have the highest rutting resistance. Therefore, CRM is the most preferable for enhancing medium and high-temperature performance.  
Figure 8: The stress-strain relationship at medium- and high-temperatures: (**a**) CRM; (**b**) PP; and (**c**) TPS.