# Determining the Compaction Temperature of Warm-Mix Anti-Rutting Asphal Mixture
## 4 Compaction Characterization of Warm-Mix Anti-Rutting Asphal Mixture
### Compaction Analysis Based on the Saturated Surface-Dry Method  
The variable temperature compaction test can determine the compaction temperature of warm-mix anti-rutting asphalt mixture by studying the relationship between temperature change and the voids of the asphalt mixture specimen, so as to further study the effect of warm-mix agent on the compaction characteristics of anti-rutting asphalt mixture. The Marshall test determined that when the anti-rutting agent content is 6%, and the warm-mix agent content is 0%, 1%, 2%, and 3%, the optimal asphalt-aggregate ratios for the warm-mix anti-rutting asphalt mixtures are 4.46%, 4.39%, 4.36%, and 4.34%. Based on the determined the optimal asphalt-aggregate ratios, the continuous variable temperature compaction test was conducted. After the specimens were compacted, they were demolded after standing for 24 h, and all standard Marshall specimens conducted at different temperatures were placed in a storage box for subsequent tests, as shown in Figure 6.  
The saturated surface-dry method calculates the bulk density of an asphalt mixture by measuring the mass of the specimen in air, the mass in water, and the surface-dry mass. The asphalt-mixture voids are then calculated in conjunction with the maximum theoretical density of the asphalt mixture. The voids fraction, VV, is calculated according to the following formula:  
\[\gamma_{\rm f}=\frac{m_{a}}{m_{\rm f}-m_{w}} \tag{5}\]  
\[\gamma_{\rm t}=\frac{100+P_{ai}}{\frac{100}{\gamma_{\rm se}}+\frac{P_{ai}}{ \gamma_{\rm b}}} \tag{6}\]  
\[\rm VV=\left(1-\frac{\gamma_{\rm f}}{\gamma_{t}}\right)\times 100 \tag{7}\]  
where \(\gamma_{f}\) is the bulk specific gravity of the Marshall specimen at 25 \({}^{\circ}\)C, \(m_{a}\) is the mass of the dry Marshall specimen in air, \(m_{f}\) is the surface-dry mass of the Marshall specimen, \(m_{w}\) is the mass of the Marshall specimen in water, \(\gamma_{t}\) is the maximum theoretical specific gravity of the Marshall specimen, \(P_{ai}\) is the asphalt-to-aggregate ratio used, \(\gamma_{se}\) is the effective specific gravity of the aggregate used for forming the specimen, and \(\gamma_{b}\) is the specific gravity of the asphalt used. Through experiments and calculations, the final voids data of the anti-rutting asphalt mixture with different Sasobit warm-mix-agent contents were obtained, as shown in Table 7.  
Figure 6: Molded Marshall specimens. Based on the data from Table 7, the measured voids of the warm-mix anti-rutting asphalt mixture are fitted, as shown in Figure 7.  
Using the 4% voids of hot-mixed asphalt mixture Marshall specimens as a standard, when the target voids for anti-rutting asphalt mixture is set to 4%, based on the principle of equal voids, the 4% target voids is substituted into the fitting equation of the measured voids-compaction temperature for the warm-mix anti-rutting asphalt mixture with different warm-mix agent contents:  
\[0\mathrm{s}:\mathrm{y}=61.4903*\mathrm{exp}(-0.01992*\mathrm{x})+2.0494( \mathrm{R2}=0.99932) \tag{8}\]  
\[1\mathrm{s}:\mathrm{y}=54.0865*\mathrm{exp}(-0.02160*\mathrm{x})+1.6987( \mathrm{R2}=0.99994) \tag{9}\]  
\[2\mathrm{s}:\mathrm{y}=37.4936*\mathrm{exp}(-0.01902*\mathrm{x})+1.3488( \mathrm{R2}=0.99497) \tag{10}\]  
\[\gamma_{\rm f}=\frac{m_{a}}{m_{\rm f}-m_{w}} \tag{5}\]0  
The compaction temperatures for the warm-mix anti-rutting asphalt mixture with 0%, 1%, 2%, and 3% warm-mix-agent contents are 173.23 \({}^{\circ}\)C, 146.16 \({}^{\circ}\)C, 139.28 \({}^{\circ}\)C, and 133.84 \({}^{\circ}\)C. Compared with the anti-rutting asphalt mixture without the addition of warm-mix agent, the compaction temperatures decreased by 27.04 \({}^{\circ}\)C, 33.92 \({}^{\circ}\)C, and 39.36 \({}^{\circ}\)C. The percentage decreases are 15.6%, 19.6%, and 22.7%. It is evident that the warm-mix agent has a significant improving effect on the compaction characteristics of the anti-rutting asphalt mixture.