## 3 Strength Test
### Establishing the Fatigue Equation Based on the Weibull Distribution of Point Parameters
Compared to the conventional S-N fatigue curve, the logarithm equivalent fatigue life of cement-treated aggregate base materials also monotonously decreased with stress ratio, the difference of the fatigue curves under different stress states based on the new method of fatigue analysis has been greatly reduced, and it was hard to point out the fatigue tests results of one stress state from those of the other stress states. The data points were very close to each other. It was difficult to distinguish the fatigue data points under different stress states as a whole, standardization was realized. 2. In the single logarithmic standardization fatigue equation, the difference in the fatigue equation parameters under different stress states based on the new method of fatigue analysis has been  
Figure 14: Standardization equations for fatigue properties with a cement content of 5% at a curing time of 90 days and a guaranteed rate of 95% under different stress states. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cement Content (\%)** & **Curing Times (days)** & **Standardized Fatigue Equation** & \(\mathbf{R^{2}}\) \\ \hline \multirow{2}{*}{3} & 28 & \(lgN_{i}=10.3342-9.5423(\sigma/S_{i})\) & 0.8472 \\  & 90 & \(lgN_{i}=10.4075-9.2115(\sigma/S_{i})\) & 0.9257 \\ \hline \multirow{2}{*}{4} & 28 & \(lgN_{i}=11.4540-10.4689(\sigma/S_{i})\) & 0.9615 \\  & 90 & \(lgN_{i}=10.8184-9.8136(\sigma/S_{i})\) & 0.8956 \\ \hline \multirow{2}{*}{5} & 28 & \(lgN_{i}=11.7037-10.7645(\sigma/S_{i})\) & 0.9134 \\  & 90 & \(lgN_{i}=10.8485-9.5517(\sigma/S_{i})\) & 0.9321 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Summary of the fitting results obtained for the standardization equation with different stress states at a guaranteed rate of 95%. greatly also reduced. The value of parameter a determines the steepness of the fatigue curve, representing the mechanical sensitivity. The smaller the slope of the curve, the lower the mechanical sensitivity, the greater the overloading of the road surface, and the better the over-limit capability. The parameter b value reflects the height of the curve. The higher the intercept, the better the fatigue resistance of cement-treated aggregate base materials. The highest parameter b value was observed at a curing time of 28 days and a cement content of 5%; that is, the fatigue resistance was the best. This result revealed that the higher the cement content, and the better the fatigue resistance of cement-treated aggregate base materials. From the results obtained from the fatigue tests of the existing cement-treated aggregate base materials [3; 7; 38; 39; 40], the range of parameter a was typically considered to be 7-28, and the parameter a obtained by the test ranges from 9.2 to 10.8 meet the range of parameter a. 3. The average of the parameters for the standardized fatigue equation at a curing time of 28 days and a cement content of 3-5% was expressed as follows: \[\text{a: }(9.5423+10.4689+10.7645)/3=10.2584\] (6) \[\text{b: }(10.3342+11.4540+11.7037)/3=11.1637\] (7) According to the obtained parameter average of (6) and (7), the unified expression for the standardized fatigue equation at a curing time of 28 days with different cement content can be expressed as \(lgN_{i}=11.1637-10.2584(\sigma/\text{S}_{\text{f}})\). 4. The average parameters for the standardized fatigue equation at a curing time of 90 days and a cement content of 3-5% were expressed as follows: \[\text{a: }(9.2115+9.8136+9.5517)/3=9.5256\] (8) \[\text{b: }(10.4075+10.8184+10.8485)/3=10.6914\] (9) According to the obtained parameter average of (8) and (9), a unified expression for the standardized fatigue equation at a curing time of 90 days with different cement content can be expressed as \(lgN_{i}=10.6914-9.5256(\sigma/\text{S}_{\text{f}})\). 5.