# High-Temperature Rheological Properties of Asphalt Mortar Modified with Spent FCC Catalysts
## 2 Experimental
### Test Method  
The characterization of the high-temperature rheological properties of asphalt mastics was conducted using a dynamic shear rheometer (DSR) for both the temperature scan test and the multiple stress creep recovery (MSCR) test. The instrument used for these tests was the Bohlin Gemini2 dynamic shear rheometer from Malvern Instruments. The experimental procedure is presented in Figure 3. All the tests were repeated three times, and the average values were obtained.  
In the temperature scanning mode, the DSR provided data such as the phase angle (8) and rutting factor (G\({}^{\star}\)/sin8) to assess the high-temperature rheological properties of asphalt mastics. The phase angle (8) serves as a relative indicator of the hysteresis behavior between the stress response and strain response of the asphalt slurry under oscillation. A larger phase angle indicates a more viscous asphalt slurry with a more pronounced hysteresis phenomenon. The rutting factor (G\({}^{\star}\)/sin8) characterizes the resistance of the asphalt material to permanent deformation and reflects the high-temperature performance of the asphalt mastic. A higher rutting factor indicates greater elasticity of the asphalt slurry and stronger resistance to permanent deformation. The tests were conducted using a parallel plate with a 25 mm diameter and a 1 mm gap, spanning a temperature range of 30-80 \({}^{\circ}\)C; strain control mode was employed with an oscillation frequency of 10 rad/s and a strain amplitude of 12%. Results at 58 \({}^{\circ}\)C, 64 \({}^{\circ}\)C, 70 \({}^{\circ}\)C, and 76 \({}^{\circ}\)C were used to evaluate the high-temperature rheological properties of asphalt mastics.  
Figure 2: Preparation process of S-FCC-C-modified asphalt slurry. **1**, **2**, **3**: the hot base asphalt was added to the MP/S-FCC in three separate batches.  
The MSCR test enabled the determination of the initial strain, residual strain, and total strain of each creep-recovery cycle at different stress levels. From these values, the irrecoverable creep flexibility (Jnr), irrecoverable creep flexibility difference (Jnr-diff), and deformation recovery rate (R) were calculated. R indicates the ability of asphalt to recover from deformation during creep, while Jnr represents irrecoverable deformation, and Jnr-diff reflects the stress sensitivity of irrecoverable creep flexibility. A higher R value and a lower Jnr value signify easier recovery of asphalt deformation at high temperatures and better performance under such conditions. The tests were performed under stress levels of 0.1 and 3.2 kPa. Each creep-recovery cycle consists of 1 s of creep and 9 s of recovery, with the results of the last ten cycles being used for analysis. The test temperature chosen for this study was 60 \({}^{\circ}\)C. The calculations for R, Jnr, and Jnr-diff are as follows [35]:  
\[R=\frac{\epsilon_{c}-\epsilon_{r}}{\epsilon_{c}-\epsilon_{o}} \tag{1}\]  
\[J_{nr}=\frac{\epsilon_{r}-\epsilon_{o}}{\tau} \tag{2}\]  
\[J_{nr-diff}=\frac{(J_{nr3.2}-J_{nr0.1})}{J_{nr0.1}}\times 100\% \tag{3}\]  
where \(\epsilon_{c},\epsilon_{r},\epsilon_{o}\), and \(\tau\) are peak strain, residual deformation, initial strain, and stress levels during each loading cycle, respectively.