# Durability-Aimed Design Criteria of Cement-Stabilized Loess Subgrade for Railway
## 3 Results and Discussion
### Strength Reduction under Wet-Dry Cycling  
The 28-day compressive strength test results of cement-stabilized loess under wet-dry cycling are shown in Table 6. The wet-dry reduction coefficient is used to represent the reduction characteristics of compressive strength of specimens after wet-dry cycling, which was calculated according to Equation (9). The greater the wet-dry reduction coefficient, the smaller the strength reduction of stabilized loess after wet-dry cycling. \[\eta_{\text{G}}=q_{\text{G}}/q_{\text{u}} \tag{9}\]  
where  
\(\eta_{\text{G}}\) is the strength reduction coefficient under wet-dry cycling;  
\(q_{\text{G}}\) is the compressive strength of specimens after \(N\) times of wet-dry cycling;  
\(q_{\text{u}}\) is the compressive strength of specimens before wet-dry cycling. Assuming that there is a strength reduction coefficient equation for cement-stabilized loess under wet-dry cycling, and it is satisfied the following three boundary conditions:  
\[\text{when}\ N=0,\ \eta_{\text{GN}}=\eta_{\text{G0}}\]  
\[\text{when}\ N=\infty,\ \eta_{\text{GN}}=\eta_{\text{G\infty}}\]  
\[\eta_{\text{G0}}>\eta_{\text{G\infty}}\] \begin{table}
\begin{tabular}{c c c c 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} } & \multicolumn{2}{c}{**The Compressive Strength (MPa) of Cement-stabilized Loess under the Following Cycling \(N\) (Time)**} \\ \cline{3-11}  & & & **0** & **1** & **3** & **5** & **7** & **9** & **12** & **15** & **20** & **25** \\ \hline \multirow{3}{*}{2} & 0.92 & 1.03 & 0.73 & 0.68 & 0.58 & 0.53 & 0.48 & 0.44 & 0.43 & 0.43 & 0.43 \\  & 0.95 & 1.34 & 1.06 & 0.91 & 0.80 & 0.72 & 0.66 & 0.60 & 0.58 & 0.58 & 0.56 \\  & 0.97 & 1.65 & 1.32 & 1.14 & 1.01 & 0.91 & 0.83 & 0.76 & 0.73 & 0.73 & 0.71 \\ \hline \multirow{3}{*}{3} & 0.92 & 1.30 & 1.03 & 0.88 & 0.75 & 0.69 & 0.64 & 0.57 & 0.55 & 0.55 & 0.55 \\  & 0.95 & 1.60 & 1.28 & 1.10 & 0.99 & 0.86 & 0.82 & 0.74 & 0.70 & 0.69 & 0.69 \\  & 0.97 & 2.03 & 1.68 & 1.44 & 1.28 & 1.12 & 1.08 & 0.95 & 0.89 & 0.89 & 0.89 \\ \hline \multirow{3}{*}{4} & 0.92 & 1.49 & 1.21 & 1.04 & 0.94 & 0.83 & 0.76 & 0.69 & 0.64 & 0.64 & 0.63 \\  & 0.95 & 1.90 & 1.58 & 1.39 & 1.24 & 1.08 & 0.99 & 0.91 & 0.84 & 0.84 & 0.84 \\  & 0.97 & 2.26 & 1.90 & 1.74 & 1.56 & 1.29 & 1.24 & 1.11 & 1.02 & 1.01 & 1.01 \\ \hline \multirow{3}{*}{6} & 0.92 & 2.03 & 1.68 & 1.42 & 1.30 & 1.14 & 1.04 & 0.95 & 0.87 & 0.87 & 0.87 \\  & 0.95 & 2.44 & 2.03 & 1.78 & 1.63 & 1.39 & 1.27 & 1.17 & 1.07 & 1.06 & 1.05 \\ \cline{1-1}  & 0.97 & 2.80 & 2.38 & 2.18 & 1.96 & 1.62 & 1.60 & 1.34 & 1.26 & 1.25 & 1.25 \\ \hline \end{tabular}
\end{table} 
Table 6: The 28-day compressive strength test results of cement-stabilized loess under wet–dry cycling. where  
\(N\) is the time of wet-dry cycling of cement-stabilized loess;  
\(\eta_{\text{GN}}\) is the strength reduction coefficient of cement-stabilized loess after \(N\) times of wet-dry cycling;  
\(\eta_{\text{G0}}\) is the strength reduction coefficient of cement-stabilized loess before wet-dry cycling, which is equal to \(1\);  
\(\eta_{\text{G0}}\) is the limit of strength reduction coefficient of cement-stabilized loess under wet-dry cycling. According to the above boundary conditions, the strength reduction coefficient equation of cement-stabilized loess after wet-dry cycling was established:  
\[\eta_{\text{GN}}=\eta_{\text{G0}}-(\eta_{\text{G0}}-1)/(\xi\!\cdot\!N^{2}+1) \tag{10}\]  
where  
\(\xi\) is the regression parameter of equation. The strength reduction coefficient equations of cement-stabilized loess after wet-dry cycling were obtained by fitting with Equation (10), which are shown in Figure 2. As can be seen from Figure 2, the strength reduction of cement-stabilized loess gradually increases with the increase of the number of wet-dry cycling, and the reduction coefficient is stable between 0.41 and 0.48 after more than 15 times of wet-dry cycling.