# Laboratory Evaluation of Rejuvenating Agent on Reclaimed SBS Modified Asphalt Pavement
## 2 Materials and Methods
### Semi-Circular Bending Test  
The SCB test is used as a method for evaluating asphalt mixture cracking resistance [24]. The test configuration and sample size are illustrated in Figure 1. Test samples were fabricated using SGC at 7 \(\pm\) 0.5% air void. SGC-compacted samples were 10 cm in height and 15 cm in diameter; each sample was trimmed to half-disc-shaped samples 15 cm in diameter and 5 cm thick. The notch is cut in the middle point of the lower surface of the sample to ensure that the crack will initiate at the desired point. In this study, the notch depth was 1.5 cm. The test was conducted at \(-\)20 \({}^{\circ}\)C and \(-\)10 \({}^{\circ}\)C at constant loading rate of 1 mm/min.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Type**} & \multicolumn{3}{c}{**Viscosity**} & **Flash** & **Saturates** & **Aromatic** & **Density/g-cm\({}^{-3}\)** & \multicolumn{3}{c}{**Tests on Residue from TFOT**} \\  & **(60 \({}^{\circ}\)C/10\({}^{-3}\) Pa-s** & **Point\({}^{\circ}\)C** & **Content\%** & **Content\%** & **Viscosity Ratio \({}^{\star}\)** & **Weight Change/\%** \\ \hline H & 123 & 256 & 17.07 & 62.07 & 1.002 & 2.3 & \(-\)3.34 \\ S & 1202 & 267 & 23.38 & 44.35 & 1.013 & 1.8 & \(-\)2.62 \\ G & 2607 & 278 & 25.98 & 49.81 & 1.028 & 1.4 & \(-\)2.73 \\ \hline \end{tabular}  
* Viscosity ratio = Viscosity (60 \({}^{\circ}\)C) of residue from TFOT/Virgin viscosity (60 \({}^{\circ}\)C).  
\end{table}
Table 2: Main properties of rejuvenating agent.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Sieve Size/mm**} & \multicolumn{4}{c}{**Type of Recycled Mixtures**} \\ \cline{2-5}  & **0\%** & **30\%** & **50\%** & **70\%** \\ \hline
16 & 100.0 & 100.0 & 100.0 & 100.0 \\
13.2 & 97.3 & 97.2 & 97.0 & 96.9 \\
9.5 & 75.1 & 75.0 & 73.4 & 72.6 \\
4.75 & 41.9 & 41.9 & 40.4 & 40.7 \\
2.36 & 28.1 & 29.1 & 28.2 & 28.4 \\
1.18 & 18.2 & 18.7 & 18.4 & 18.6 \\
0.6 & 13.6 & 13.8 & 13.7 & 14.0 \\
0.3 & 10.2 & 10.3 & 10.3 & 10.6 \\
0.15 & 8.0 & 7.9 & 8.0 & 8.4 \\
0.075 & 6.3 & 6.2 & 6.4 & 6.7 \\ Virgin asphalt content/\% & 0.0 & 3.7 & 3.1 & 2.4 \\ Total asphalt content/\% & 4.8 & 4.8 & 4.9 & 5.0 \\ \hline \end{tabular}  
\end{table}
Table 3: Aggregate gradation and asphalt content of recycled mixtures with different reclaimed SBS (styrene-butadiene-styrene) modified asphalt pavement (RSMAP) contents.  
In order to evaluate the crack resistance of recycled mixtures, fracture energy (\(G_{f}\)) is used, which can be obtained by dividing fracture work with ligament area [25], as provided in Equation (1). The total fracture work can be calculated by the area under the \(P\)-\(u\) curve. Figure 1d shows a typical SCB load versus displacement curve.  
\[G_{f}=\frac{W_{f}}{A_{lig}} \tag{1}\]  
where \(G_{f}\) = fracture energy (J/m\({}^{2}\)); \(A_{lig}\) = ligament area (m\({}^{2}\)) = (\(r\) - \(a\)) \(\times\) \(t\); \(r\) = specimen radius (m); \(a\) = notch depth (m); \(t\) = specimen thickness (m); and \(W_{f}\) can be calculated as follows in Equation(2).  
\[W_{f}=\int Pdu \tag{2}\]  
where \(P\) = applied load (kN); and \(u\) = load line displacement (mm).  
Fracture toughness (\(K_{c}\)) is considered as the stress intensity factor at the critical load (\(P_{c}\)), and provides a single parameter characterization that includes the effect of specimen configuration, boundary conditions, and load. In addition, \(K_{c}\) is qualified as an intrinsic material property, describing the ability to resist cracking [26]. In this paper, \(K_{c}\) is calculated using the following equation.  
\[K_{c}=Y_{I}\;\sigma_{c}\sqrt{\pi a} \tag{3}\]  
where \(\sigma_{c}\) = \(P_{c}/2 rt\); \(Y_{I}\) = \(4.782\) + \(1.219(a/r)\) + \(0.063\)exp[\(7.045(a/r)\)]; \(P_{c}\) = peak load; \(Y_{I}\) = normalized stress intensity factor.