## 4 Fatigue Damage of Cement-Stabilized Macadam Base
### Fatigue Damage of Cement-stabilized Base under Actual Engineering Conditions
#### 4.3.2 Analysis of Actual Stress in Practical Engineering  
During the actual construction process, the working conditions of cement-stabilized macadam subbase are different when different structural layers are paved during the construction period. The following working conditions model is put forward (Figure 12), where \(\delta\) represents the equivalent circle radius. The maximum bottom tensile stress of each pavement layer under different axle loads was calculated after 7 days of curing under different working conditions (Figure 13). Working condition 1 indicates that when the subbase was maintained for 7 days, the condition of the base course construction was carried out. Working condition 2 indicates that after 7 days of subbase maintenance, 7 days of base maintenance was completed, and the condition of the construction of the lower pavement layer was carried out. Working condition 3 indicates construction of the upper layer after construction of the lower layer was finished in 7 days. Working condition 4 indicates that the road surface was formally opened to traffic after the construction of the upper layer within 7 days. When the axle load was 100 kN, the stress ratio was less than 0.3, and when the axle load was 220 kN, the stress ratio was close to 0.5, which could easily cause irreversible fatigue damage (Figure 13). In case 2, when the axle load was less than 160 kN, the stress ratio was less than 0.3,  
Figure 11: The maximum bottom tensile stress calculated under different conditions: (**a**) Relationship between different loads and the maximum bottom tensile stress; (**b**) relationship between different curing times and the maximum bottom tensile stress. and when the maximum axle load was 250 kN, the stress ratio was 0.38. In case 3, when the axle load was less than 220 kN, the stress ratio was less than 0.3, and when the maximum axle load was 250 kN, the stress ratio was 0.32. In case 4, when the load was less than 250 kN, the stress ratio was less than 0.3, showing that stress ratio decreased gradually with increasing curing time, and damage to the pavement decreased. Condition 1 produced the worst pavement conditions. The number of repeated actions under different working conditions and loads was calculated and compared to that of the construction vehicles. Working condition 4 represents the operational period of the pavement, and hence there was no construction load. Fatigue damage easily occurred under working condition 1, and the fatigue damage caused by axle loads less than 160 kN was negligible (Figure 14). When the axle load was 190 kN, fatigue damage was 0.11. When axle load increased to 220 kN, fatigue damage was as high as 0.74. When axle load was 250 kN, the fatigue damage in the water-stabilized macadam appeared. Using Miner linear damage theory \(\mathrm{D}=\sum_{i=1}^{m}\frac{n_{i}}{N}\), \(N\) could be obtained by combining Figure 13 with Equation (10): The look-up Table 5 gives \(n\), and \(i\) indicates different working conditions. The fatigue damage values of pavement under different loads were calculated as follows in Table 7.  
Figure 12: Pavement conditions model for different construction periods. Figure 13: Maximum tensile stress under different working conditions. With the gradual completion of pavement structure, damage to the subbase decreased rapidly. Therefore, in the design of pavement structure, the damage to the subbase caused by construction loads should be fully considered. The subbase thickness should be properly increased, and the overloaded construction vehicles should be tightly restricted. Vehicle axle load had a significant influence on subbase damage. When the load increased from 160 kN to 190 kN, the damage increased by 10.5%. When the load increased from 190 kN to 220 kN, the damage increased by 66.1%. On the other hand, the ability of subbase to bear loads would be enhanced if the number of base curing days was increased, and the damage under the same axle load would drop dramatically. Therefore, the number of basement maintenance days should be increased.