## 2 Materials and Experimental Method
### Multiple Stress Creep and Recovery (MSCR) Test  
The Multiple Stress Creep and Recovery (MSCR) test is designed to simulate the high-stress conditions encountered by pavement structures, particularly during the early stages of their service life when nutting is most prevalent. This test uses Rolling Thin Film Oven Test (RTFOT)-aged asphalt to more accurately reflect the binder's resistance to nutting, as this aging process replicates the initial aging that occurs in the field. By evaluating the binder under these conditions, the MSCR test provides a realistic assessment of its performance in resisting permanent deformation.  
Two critical parameters are derived from the MSCR test data: non-recoverable creep compliance (\(J_{nr}\)) and percent recovery (\(rec\%\)). The non-recoverable creep compliance (\(J_{nr}\)) is calculated as the ratio of unrecoverable shear strain to the applied stress, reflecting the binder's susceptibility to permanent deformation under sustained loading and is shown below as Equation (1). And the percent recovery (\(rec\%\)) is determined as the percentage difference between peak strain and unrecovered strain relative to the peak strain, which indicates the binder's ability to recover after loading and is shown below as Equation (2) [24].  
\[J_{nr}=\frac{\textit{Unrecoverable shear strain}}{\textit{Applied Stress}} \tag{1}\]  
\[rec\left(\%\right)=100\ \times\ \frac{\textit{Peak strain}-\textit{Unrecovered strain}}{\textit{Peak strain}} \tag{2}\]  
The MSCR test involves applying 20 cycles of stress at 0.1 kPa, followed by 10 cycles at 3.2 kPa, with each cycle consisting of 1 s of shear creep loading and a subsequent 9 s recovery period. The 0.1 kPa stress level evaluates the binder's behavior in the linear viscoelastic region, while the 3.2 kPa stress level assesses performance in the non-linear region. This approach ensures a comprehensive understanding of the binder's performance across different stress levels, which is crucial for predicting long-term pavement durability.  
The average values of \(J_{nr}\) and \(rec\%\) are calculated using the following Formulas (3)-(6) [24].  
\[J_{nr(0,1)} = \frac{\sum_{n=11}^{20}\left[J_{nr}\,0,1n\right]}{10} \tag{3}\] \[J_{nr(3,2)} = \frac{\sum_{n=21}^{30}\left[J_{nr}\,3,2n\right]}{10}\] (4) \[rec_{0,1} = \frac{\sum_{n=11}^{20}\left[rec_{0,1}\ n\right]}{10}\] (5) \[rec_{3,2} = \frac{\sum_{n=21}^{30}\left[rec_{3,2}\ n\right]}{10} \tag{6}\]  
These parameters are essential for determining the appropriate high-temperature performance grade (PG) of asphalt binders according to traffic loading conditions. The PG classification--Standard (S), Heavy (H), Very Heavy (V), and Extremely Heavy (E)--is based on \(J_{nr}\)3.2 values, with specific thresholds set at 4.5 kPa\({}^{-1}\), 2.0 kPa\({}^{-1}\), 1.0 kPa\({}^{-1}\), and 0.5 kPa\({}^{-1}\), respectively. Additionally, the difference in non-recoverable creep compliance (\(J_{nr}\) diff) between the 0.1 kPa and 3.2 kPa stress levels must not exceed 75%, ensuring the binder's stress sensitivity remains within acceptable limits. This stringent evaluation ensures that only binders with sufficient resilience and stability under varying stress conditions are selected, thereby enhancing the durability and longevity of pavement structures [24].