## 4 Discussion
### Comprehensive Service Life Based on Analytic Hierarchy Process
#### 4.2.5 Calculating the Comprehensive Service Life of RABs  
The comprehensive service life was calculated by Equation (2) and is listed in Table 7 for each sample. This is a very common equation in AHP. It combines the specific contributions of different factors (here, they are the service years and material composition) with engineering experience (the weights and artificial amendment coefficients) to determine the goal (comprehensive service life) of the system (aging). However, this a repeated trial calculation process just like a study system where the goal will tend to what we expect it to be by repeated adjustment of the weights and artificial amendment coefficients.  
\[P=(w_{1}\times P_{1}\times Q_{1}+w_{2}\times P_{2}\times Q_{2}+w_{3}\times P_{3 }\times Q_{3})\times\text{n} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Combination** & **Upper + Middle + Lower** & **Upper + Middle** & **Middle + Lower** & **Upper** & **Middle** & **Lower** \\ \hline Coefficient & 1.1 & 1.3 & 0.8 & 1.5 & 1.2 & 0.7 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Layer combination coefficients.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Numeric Scale** & **Significance** \\ \hline
2.0 & Extremely important \\
1.5 & Clearly important \\
1.0 & Important \\ (1.0, 1.5), (1.5, 2.0) & Interval of importance \\ Reciprocal & If \(b_{ij}\) is the importance ratio of factor \(i\) and factor \(j\), \(1/b_{ij}\) \\  & will be the importance ratio of factor \(j\) and factor \(i\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Significance of the Numeric Scales.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**RABs** & **Upper Surface Layer** & **Middle Surface Layer** & **Lower Surface Layer** & **Weights** \\ \hline Upper Surface Layer & 1.0 & 1.5 & 1.7 & 0.45 \\ Middle Surface Layer & 0.7 & 1.0 & 1.1 & 0.28 \\ Lower Surface Layer & 0.6 & 0.9 & 1.0 & 0.27 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Judgment Matrix and Weights.  
In Equation (2), \(P\) is the comprehensive service life. \(w_{1}\), \(w_{2}\), \(w_{3}\) are the weights of the upper, middle and lower surface layers, respectively. \(P_{1}\), \(P_{2}\), \(P_{3}\) are the service years of the upper, middle and lower surface layers, respectively. \(Q_{1}\), \(Q_{2}\), \(Q_{3}\) are the material coefficients (If 100% Reclaimed SBS modified asphalt, \(Q=1\); If Reclaimed base asphalt included, \(Q=0.65\)) and n is the layer combination coefficient.  
The data in Table 7 indicated that consistency exists between aging grades and comprehensive service life. That is to say, it would be useful to assess the aging grades of RABs directly by calculating their comprehensive service life.  
Anyway, results in Table 7 is based on the field data of reclaimed asphalt pavement collected in this study from the same climatic zone in southern China. Thus, the service years and structural layer levels can be the key influencing factors on the aging grade. This made the comprehensive service life considering structural layer levels possible and feasible. For complicated situations, more factors should be taken into account to determine the comprehensive service life using the AHP.  
Based on the results in terms of binder classification and aging grades in this paper, methods to determine the contents of rejuvenation agents and new asphalt in the design of RAP mixtures need further study, which is also the next topic of research of the current project.