# Investigation of the Fatigue Life of Bottom-Up Cracking in Asphalt Concrete Pavements
## 4 Prediction of Fatigue Crack Life of Asphalt Pavements
### Fatigue Crack Life  
In view of the above study, fatigue cracking life and crack propagation life should be considered in the whole life of any crack formed. Therefore, the entire fatigue crack life \(N\) can be obtained by adding the fatigue cracking life \(N_{i}\) and fatigue propagation life \(N_{p}\), as shown in Tables 11 and 12. From Table 11, it can be seen that, for the flexible base of the asphalt pavement surface, the surface thickness of structure B increased by 30 mm relative to structure A at 25 \({}^{\circ}\)C, and the fatigue crack life of the pavement structure increased by 9 \(\times\) 10\({}^{7}\) times. Compared with structure A, the surface thickness of structure C increased by 90 mm, and the fatigue crack life of the pavement structure increased by 1.5 \(\times\) 10\({}^{8}\) times. We can thus know that the fatigue crack life of the pavement structure only increased by less than 2.0 times when the surface thickness increased by 3.0 times. When the room temperature was 25 \({}^{\circ}\)C, the crack propagation life of structures A, B, and C accounted for about 97.4%, 76.3%, and 87.3% of the entire fatigue life, respectively. Therefore, the crack propagation life of the pavement structure at 25 \({}^{\circ}\)C may be much longer than the fatigue cracking life. When the room temperature was \(-\)10 \({}^{\circ}\)C, the fatigue cracking life of structures A, B, and C accounted for 99.8% of the entire fatigue life. Therefore, the crack propagation life of the pavement structure at low temperatures (\(-\)10 \({}^{\circ}\)C) was far less than the fatigue cracking life. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pavement Structure** & **Temperature (\({}^{\circ}\)C)** & \(N_{i}\)**(time)** & \(N_{p}\)**(time)** & \(N\) \\ \hline \multirow{4}{*}{A} & 25 & 391,312 & 14,628,099 & \(1.5\times 10^{8}\) \\  & 0 & 208,632 & 47,998 & \(2.6\times 10^{6}\) \\  & \(-\)10 & 54,454 & 78 & \(5.5\times 10^{5}\) \\  & 25 & 5,766,217 & 1,860,0394 & \(2.4\times 10^{8}\) \\ \multirow{2}{*}{B} & 0 & 1,068,115 & 58,390 & \(1.1\times 10^{6}\) \\  & \(-\)10 & 492,909 & 97 & \(4.9\times 10^{6}\) \\  & 25 & 3,898,008 & 26,937,407 & \(3\times 10^{8}\) \\ \multirow{2}{*}{C} & 0 & 1,947,968 & 80,363 & \(2\times 10^{7}\) \\  & \(-\)10 & 1,068,115 & 134 & \(1\times 10^{7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Entire fatigue crack life of flexible base asphalt pavement surface. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Pavement Structure** & **Temperature (\({}^{\circ}\)C)** & \(N_{i}\)**(time)** & \(N_{p}\)**(time)** & \(N\) \\ \hline \multirow{4}{*}{A} & 25 & 1,947,968 & 14,628,099 & \(1.7\times 10^{8}\) \\  & 0 & 628,683 & 47,998 & \(6.8\times 10^{6}\) \\  & \(-\)10 & 492,909 & 78 & \(4.9\times 10^{6}\) \\ \multirow{4}{*}{B} & 25 & 5,766,216 & 18,600,394 & \(2.4\times 10^{8}\) \\  & 0 & 2,719,023 & 58,390 & \(2.8\times 10^{7}\) \\ \multirow{4}{*}{C} & \(-\)10 & 1,428,062 & 97 & \(1.4\times 10^{7}\) \\  & 25 & 24,168,688 & 26,937,407 & \(5.1\times 10^{8}\) \\ \multirow{4}{*}{C} & 0 & 8,854,377 & 80,363 & \(8.9\times 10^{7}\) \\  & \(-\)10 & 1,947,968 & 134 & \(1.9\times 10^{7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Entire fatigue crack life of semirigid base asphalt pavement surface. It can be seen from Table 12, for the semirigid base of the asphalt pavement surface, the surface thickness of structure B increased by 30 mm relative to structure A at 25 \({}^{\circ}\)C, and the fatigue crack life of the pavement structure increased by 7 \(\times\) 10\({}^{7}\) times. Compared with structure A, the surface thickness of structure C increased by 90 mm, and the fatigue crack life of the pavement structure increased by 3.4 \(\times\) 10\({}^{8}\) times. We know that the fatigue crack life of the pavement structure only increased by less than 4.8 times when the surface thickness increased by 3.0 times.