## 2 Materials and Methods
### Materials
#### 2.1.6 Proportion Optimization of RAMB  
The orthogonal design method of four factors at three different levels was used to determine the mass ratio of water and bio-oil in RAMB and the optimal content of each material. The influence of bio-oil content, the mass ratio of water and bio-oil and the content of rock asphalt and montmorillonite on penetration, ductility, softening point and rotational viscosity of asphalt was considered. Three levels were set for each factor, as shown in Table 5. According to the orthogonal design table of L9(34) (as shown in Table 6), nine asphalts with different content combinations were prepared and tested. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Level**} & \multicolumn{4}{c}{**Factor**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Mass Ratio of Water**} & \multirow{2}{*}{**Content of Bio-Oil (\%)**} & **Content of Rock** & **Content of** \\  & \multicolumn{2}{c}{**and Bio-Oil**} & & **Asphalt (\%)** & **Montmorillonite (\%)** \\ \hline
1 & 1:1 & 5 & 20 & 3 \\
2 & 2:1 & 7 & 30 & 5 \\
3 & 3:1 & 9 & 40 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Factors and levels. Figure 2: Pretreatment of bio-oil. (**a**) Mixing of water and oil; (**b**) Bio-oil before and after treatment. Table 7 lists the orthogonal test results. The penetration of the matrix asphalt was 67.6 (0.1 mm) and the softening point was 48.5 \({}^{\circ}\)C in this paper. The penetration values of No.6, No.8 and No.9 were far larger than matrix asphalt. Additionally, the softening point was slightly lower than that of matrix asphalt. This indicates that the high-temperature performance of these three combinations was poor. Improving the high-temperature performance of bio-asphalt was the main purpose of this paper but these three combinations could not meet the requirements. After these three combinations were eliminated, the remaining six combinations were selected by Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) in multi-objective decision-making. The decision matrix was a 6 \(\times\) 4 matrix [29; 30]. Table 8 lists the ranking results of TOPSIS. According to the table, the second combination was a suitable preparation method for RAMB. In this method, the mass ratio of water and bio-oil was 1:1, the content of bio-oil was 7%, the content of rock asphalt was 30% and the content of montmorillonite was 5%. Note: Di\({}^{+}\) presents the distance between each combination and positive ideal solution; Di\({}^{-}\) presents the distance between each combination and negative ideal solution; CI presents approaching index. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number**} & **Mass Ratio of** & **Content of** & **Content of Rock** & **Content of** & **Orthogonal** \\  & **Water and Bio-Oil** & **Bio-Oil (\%)** & **Asphalt (\%)** & **Montmorillonite (\%)** & **Combinations** \\ \hline
1 & 1:1 & 5 & 20 & 3 & A\({}_{1}\)B\({}_{1}\)C\({}_{1}\) D\({}_{1}\) \\
2 & 1:1 & 7 & 30 & 5 & A\({}_{1}\)B\({}_{2}\)C\({}_{2}\) D\({}_{2}\) \\
3 & 1:1 & 9 & 40 & 7 & A\({}_{1}\)B\({}_{3}\)C\({}_{3}\) D\({}_{3}\) \\
4 & 2:1 & 5 & 30 & 7 & A\({}_{2}\)B\({}_{1}\)C\({}_{2}\) D\({}_{3}\) \\
5 & 2:1 & 7 & 40 & 3 & A\({}_{2}\)B\({}_{2}\)C\({}_{3}\) D\({}_{1}\) \\
6 & 2:1 & 9 & 20 & 5 & A\({}_{2}\)B\({}_{3}\)C\({}_{1}\) D\({}_{2}\) \\
7 & 3:1 & 5 & 40 & 5 & A\({}_{3}\)B\({}_{1}\)C\({}_{3}\) D\({}_{2}\) \\
8 & 3:1 & 7 & 20 & 7 & A\({}_{3}\)B\({}_{2}\)C\({}_{1}\) D\({}_{3}\) \\
9 & 3:1 & 9 & 30 & 3 & A\({}_{3}\)B\({}_{3}\)C\({}_{2}\) D\({}_{1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Combinations of orthogonal test L9(34).