# Durability-Aimed Design Criteria of Cement-Stabilized Loess Subgrade for Railway
## 3 Results and Discussion
### Fatigue Performance of Cement-Stabilized Loess
\begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{\begin{tabular}{c} **Cement** \\ **Dosage,** \\ **\(P_{\text{s}}\) (\%)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Compaction** \\ **Level (K)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **The Fatigue** **Life** \(N\) **of Cement-Stabilized Loess Specimens under** \\ **the Following Stress Levels \(S\) (Time)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Average** \\ **Average** \\ **\end{tabular} } \\  & & & **0.80** & **0.75** & **0.70** & **0.65** & **0.60** \\ \hline \multirow{8}{*}{6} & \multirow{8}{*}{0.92} & 541 & 1676 & 4571 & 11,259 & 82,150 \\  & & 809 & 3587 & 7033 & 18,215 & 101,583 \\  & & 1168 & 4633 & 9124 & 31,945 & 134,783 \\  & & 1382 & 5684 & 13,086 & 39,661 & 159,745 \\  & & 2033 & 7590 & 17,258 & 50,157 & 181,738 \\ \cline{2-7}  & & 763 & 4781 & 10,273 & 61,235 & 125,681 \\  & & 1256 & 6955 & 15,831 & 97,650 & 165,240 \\  & & 1864 & 9271 & 20,773 & 116,042 & 228,132 \\  & & 3295 & 11,352 & 23,896 & 158,123 & 273,185 \\  & & 4136 & 13,161 & 31,652 & 195,635 & 325,160 \\ \cline{2-7}  & & 970 & 7195 & 21,453 & 101,887 & 162,293 \\  & & 1954 & 10,862 & 32,612 & 145,064 & 230,919 \\  & & 2766 & 14,276 & 43,965 & 204,692 & 292,588 \\  & & 4081 & 21,016 & 51,432 & 287,654 & 345,067 \\  & & 4852 & 26,422 & 60,100 & 346,950 & 423,740 \\ \hline \end{tabular}
\end{table} 
Table 4: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{\
\begin{tabular}{c} **\(P_{\text{s}}\) (\%)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **3** \\ **Average** \\ **\end{tabular} } \\  & & & & & & & & & & \\ \hline \(K\) & **0.92** & **0.95** & **0.97** & **0.92** & **0.95** & **0.97** & **0.92** & **0.95** & **0.97** \\ \hline \(m\) & 0.571 & 1.062 & 0.780 & 0.823 & 1.125 & 0.890 & 0.591 & 0.679 & 0.883 & 0.823 \\ \(n\) & 14.393 & 13.667 & 17.253 & 14.543 & 15.368 & 18.426 & 17.864 & 19.806 & 19.666 & 16.776 \\ \(R^{2}\) & 0.9662 & 0.9706 & 0.9378 & 0.9356 & 0.9378 & 0.9268 & 0.9663 & 0.9540 & 0.9542 \\ \hline \end{tabular}
\end{table} 
Table 5: Prediction equation regression coefficient of fatigue life \(N\) of cement-stabilized loess. The fatigue reduction coefficient is used to represent the strength reduction characteristics of specimens after repeated load. According to the above research, the fatigue reduction coefficient \(k_{\text{f}}\) of cement-stabilized loess could be expressed as:  
\[k_{\text{f}}=\sqrt[n]{10^{m}/N_{\text{e}}} \tag{8}\]  
where  
\(N_{\text{e}}\) is the accumulated times of axle load within the design life. It was assumed that railway capacity is saturated, the daily running capacity of trains is 90, and the number of accumulated daily axle load is 2880 [59; 60]. Then, the cumulative number of axle loads in the design life \(N_{\text{e}}\) is \(1.05\times 10^{8}\) times. The fatigue reduction coefficient \(k_{\text{f}}\) of cement-stabilized loess is 0.262 when \(m_{0.95}\), \(n_{0.95}\) and \(N_{\text{e}}\) are substituted into Equation (8). This result is overall consistent with the principle that the critical strength of improved soil is 5 times the dynamic stress [25]. Therefore, the fatigue reduction factor \(k_{\text{f}}\) of cement-stabilized loess is 0.26 in this study.