# Investigation of the Fatigue Life of Bottom-Up Cracking in Asphalt Concrete Pavements
## 2 Experimental Study of the Dynamic Modulus and OT of Asphalt Pavements
### Overlay Test  
The asphalt mixture was mixed according to the asphalt/stone ratio determined by the Superpave test method, and a cylindrical specimen with a height of 62 mm and a diameter of 150 mm was formed by a SGC rotary compacting instrument Then, a cylindrical specimen with a thickness of 38 mm and a diameter of 150 mm was cut with a double-sided cutting saw. Finally, the specimen was cut (76 mm wide, 38 mm thick, and 150 mm long). The specimen processing used for the OT was shown in Figure 2. The target porosity of the specimen was 7 \(\pm\) 1%. In this study, a UTM-100 multifunctional servo-hydraulic material testing machine was used for the OT. The equipment can carry out different module tests by replacing different types of sensors. The front and side of the test are shown in Figure 2c,d. The temperatures for the OT were 25 \({}^{\circ}\)C, 0 \({}^{\circ}\)C, and \(-\)10 \({}^{\circ}\)C, respectively. The test was terminated when the maximum load attenuation of the first cycle was 93 % or the maximum number of cycles before the test was 1000. The OT results are shown in Table 4.  
Figure 1: Experimental equipment; (**a**) asphalt mixture mixing pot; (**b**) rotary compactor; (**c**) indoor core machine; (**d**) grinding of specimen. Figure 2: Fabrication of the OT specimen: (**a**) OT specimen; (**b**) paste OT specimen; (**c**) the front view OT; (**d**) the side view OT. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Gradation** & \multicolumn{2}{c}{**AC-13**} & \multicolumn{2}{c}{**AC-20**} & \multicolumn{2}{c}{**AC-25**} \\ \hline
**Temperature (\({}^{\circ}\)C)** & **25** & **0** & \(-\)**10** & **25** & **0** & \(-\)**10** & **25** & **0** & \(-\)**10** \\ \hline Dynamic Modulus (MPa) & 832 & 14,690 & 25,149 & 1497 & 13,009 & 21,916 & 1850 & 15,813 & 15,813 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Dynamic modulus at different gradations and temperatures. The relationship between the maximum load of a single circle and the number of load cycles can be obtained through the OT data, as shown in Figure 3.  
The following could be found from the OTs:  
1. When the temperature dropped from 25 \({}^{\circ}\)C to \(-\)10 \({}^{\circ}\)C, the load cycles of the AC-20 and AC-13 asphalt mixtures decreased sharply. With a decrease in temperature, the crack resistance of both the AC-20 and AC-13 asphalt mixture gradually deteriorated, which was consistent with the fact that the asphalt pavement was prone to cracking in a low-temperature environment; \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Gradation** & \multicolumn{3}{c}{**AC-13**} & \multicolumn{3}{c}{**AC-20**} \\ \hline
**Temperature** & **25 \({}^{\circ}\)C** & **0 \({}^{\circ}\)C** & \(-\)10 \({}^{\circ}\)C** & **25 \({}^{\circ}\)C** & **0 \({}^{\circ}\)C** & \(-\)10 \({}^{\circ}\)C** \\ \hline OT results & 1000 & 97 & 10 & 1000 & 72 & 42 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: OT results at different gradations and temperatures. 2. In the early stages of the OT, the test load decreased rapidly with the increase in the number of load cycles. When the number of cycles continued to increase, the decline rate of the maximum load in a single circle gradually slowed down, and the curve gradually tended to level; that is, the attenuation rate of the load slowed down. The reason was that the stress transferred to the crack tip decreased with the increase in crack length at the same maximum tensile displacement before the instability failure of the structure, so the crack propagation became more and more difficult. It can be observed that there is an abrupt change in the curves in Figure 3c,d at 0 \({}^{\circ}\)C, which is not a sudden phenomenon. When the temperature was \(-10\)\({}^{\circ}\)C, the test load decreased rapidly to find stability within fewer cycle numbers, and several data points were actually very discrete.