## 3 Strength Test
### Establishing Fatigue Equations Based on the Weibull Distribution of Interval Parameters
#### 4.3.4 Example of Calculation Analysis  
Fatigue tests were carried out on the specimen with cement content of 3-5%, and the fatigue test results and the standardized fatigue equation model were obtained. According to the fatigue equation of Table 9 obtained from the test, parameter a and b values at curing times of 28 days and 90 days with a cement content of 3-5% are summarized in Table 10, which were used to obtain the standardized fatigue equation for the prediction model with the cement content of 3.5% and 4.5%. Parameters a and b at a curing time of 28 days with a cement content of 3% and 4% were averaged, respectively, and the point parameter prediction model for the standardized fatigue equation at a curing time of 28 days with a cement content of 3.5% was obtained, followed by assigning the cement \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Curing Times (days)** & **Cement Content (\%)** & **Parameter \(a\)** & **Parameter \(b\)** \\ \hline  & 3 & 9.5423 & 10.3342 \\
28 & 4 & 10.4689 & 11.4541 \\  & 5 & 10.7642 & 11.7034 \\ \hline  & 3 & 9.2115 & 10.4075 \\
90 & 4 & 9.8136 & 10.8184 \\  & 5 & 9.5517 & 10.8485 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Parameter \(a\) and \(b\) values. content of 4% and 5%. Parameters a and b for a cement content of 4.5% were averaged, and the point parameter prediction model for the standardized fatigue equation for the cement content of 4.5% at a curing time of 28 days was also obtained. The point parameter prediction model for the standardized fatigue equation at a curing time of 90 days was also available. Table 11 summarizes specific results. Parameters a and b at a curing time of 28 days with a cement content of 3% and 4% exhibited the maximum and minimum. Now, a and b were taken as interval parameters according to Formulas (10) and (11), then a: [9.5, 10.5] and b: [10.3, 11.5], and the standardized interval parameters for the fatigue prediction model at a curing time of 28 days and a cement content of 3.5% can be obtained. Parameters a and b for the cement content of 4% and 5% were also obtained from Formulas (10) and (11). The interval parameters a: [10.5, 10.8], and b: [11.4, 11.8], which corresponded to the standardized interval parameters for the fatigue equation prediction model for a cement content of 4.5% at a curing time of 28 days. In addition, the interval parameter standardization fatigue prediction model at a curing time of 90 days was also available. Table 11 summarizes specific results obtained. The fatigue life of cement-treated aggregate base materials is an important indicator to characterize the pavement base performance. Most scholars expressed fatigue life as point numerical. However, the fatigue life is typically obtained from experiments, and issues such as inadequate sampling representation; low precision; and insufficient stability of test equipment are inevitable, and the point value form cannot completely reflect the complex nature of parameters and indicators such as variability and uncertainty. From Table 11, the interval length for parameters a and b in the interval parameter fatigue equation reached 1.2, with the minimum of only 0.1. Clearly, parameters a and b in the point parameter fatigue equation were completely within the interval of the parameter fatigue equation. The uncertainty of inadequate sampling representation; low precision; and insufficient stability of test equipment can be reduced by life interval. Therefore, the point numerical fatigue life obtained by the point parameter fatigue equation must be within the life interval estimated by the interval parameter fatigue equation, and the life interval is more representative and scientific compared to the point value life, which is more consistent with the actual situation. The fatigue equation based on the interval parameters is more rational than the fatigue equation of point value form.