# 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
### Dynamic Modulus Test  
The asphalt pavement is not subjected to the constant external force of practical vehicle loads, and the effect of vehicle load and temperature always work together on the road. Therefore, in order to calculate the fatigue life of a pavement structure more accurately, the dynamic modulus was substituted into the model instead of the static modulus to obtain the mechanical response inside the pavement structure. The test preparation and process are as follows:  
1. According to the mix proportion (of the asphalt mixture obtained by the Superpave test method), the temperature of the mixer was raised to 155 \({}^{\circ}\)C in advance and kept warm. The aggregate was placed in the oven at 165 \({}^{\circ}\)C and a constant temperature for 4-6 h of drying, and the asphalt was placed in the oven at 135 \({}^{\circ}\)C at a constant temperature for 2-3 h for the flow stage. Then, the aggregate was poured into the blender and stirred for 60 s, as shown in Figure 1a. Then the asphalt was added quickly and continually stirred for 60 s. At last, the mineral powder was added and continually stirred for 60 s. After mixing, the asphalt mixture was placed in the oven at 135 \(\pm\) 5 \({}^{\circ}\)C for 2 h for aging. This process was used to simulate the short-term aging phenomenon in the transportation process;
2. After the short-term aging, the required quality of the hot asphalt mixture was weighed according to the sampling method in the specification (four-point method), and then they were evenly poured into the rotary compaction test mold, which was kept warm at 165 \({}^{\circ}\)C in the oven in advance. A Superpave gyratory compact (SGC) rotary compact was used for molding, as shown in Figure 1b. After cooling for 15 min, the specimen was demolded and left at an indoor temperature for at least 8 h;
3. A \(\Phi\) 100 \(\times\) 170 mm cylinder was drilled from a cylinder specimen with dimensions of \(\Phi\) 150 \(\times\) 170 mm by a core-taking machine, as shown in Figure 1c. In the process of coring, it is essential to ensure that the drill bit of the coring machine was perpendicular to the ground. According to different types of mixture, the rotation speed, descent speed, and water spraying amount of the drill bit were reasonably adjusted to ensure that the specimen was parallel, with no grooves, a smooth surface, and being perpendicular to the two end faces;
4. A double-sided saw was used to form a test specimen with a height of 150 \(\pm\) 2.0 mm, as shown in Figure 1d;
5. After the above process was completed, the physical parameters (the diameter, height, density, and voidage) of the specimen were measured, and then the specimen was placed in a ventilated place at room temperature for at least two days to dry the specimen. Three temperatures, including \(-\)10 \({}^{\circ}\)C, 0 \({}^{\circ}\)C, and 25 \({}^{\circ}\)C, and a loading frequency of 0.1 Hz were selected for this test. It is notable that, as for the 37 \({}^{\circ}\)C and 54 \({}^{\circ}\)C in the test specification, this paper mainly studies the ability of asphalt mixture to resist fatigue cracking at a low temperature; thus, the higher temperatures are not considered in the test. The dynamic modulus test follows ASTM D3497 and AASHTO TP62-03. The selection of 0.1 Hz mainly considers the standard frequency of the OT specification. Generally, the OT is loaded by the displacement control mode and the loading period is set as 10 s. In order to keep the consistent frequency of the two tests, the frequency in the dynamic modulus test is selected as 0.1 Hz.