# Durability-Aimed Design Criteria of Cement-Stabilized Loess Subgrade for Railway
## 3 Results and Discussion
### Strength Reduction under Freeze-Thaw Cycling  
The compressive strength test results of cement-stabilized loess under freeze-thaw cycling are shown in Table 7. The specimens with 2% of dosage became loose after 10 freeze-thaw cycles, so these data were not recorded. The freeze-thaw reduction coefficient is used to represent the reduction characteristics of compressive strength of specimens after freeze-thaw cycling, which was calculated according to Equation (11). The greater the freeze-thaw reduction coefficient, the smaller the strength reduction of stabilized loess after freeze-thaw cycling.  
\[\eta_{\text{D}}=q_{\text{Du}}/q_{\text{u}} \tag{11}\]  
where  
\(\eta_{\text{D}}\) is the strength reduction coefficient under freeze-thaw cycling;  
\(q_{\text{Du}}\) is the compressive strength of specimens after \(N\) times of freeze-thaw cycling;  
\(q_{\text{u}}\) is the compressive strength of specimens before freeze-thaw cycling.  
The strength reduction coefficient equation of cement-stabilized loess after freeze-thaw cycling is established with the same method in Section 3.2.  
\[\eta_{\text{DN}}=\eta_{\text{Dos}}-(\eta_{\text{Dos}}-1)/(\xi\cdot N^{2}+1) \tag{12}\]  
where  
\(\eta_{\text{DN}}\) is the strength reduction coefficient of cement-stabilized loess after \(N\) times of freeze-thaw cycling;  
\(\eta_{\text{Dos}}\) is the limit of strength reduction coefficient of cement-stabilized loess under freeze-thaw cycling.  
\(N\) is the time of freeze-thaw cycling of cement-stabilized loess;  
\(\xi\) is the regression parameter of the equation.  
The strength reduction coefficient equations of cement-stabilized loess after freeze-thaw cycling was obtained by fitting with Equation (12), which are shown in Figure 3. As can be seen from Figure 3, the strength reduction of cement-stabilized loess gradually increases with the increase of the number of freeze-thaw cycles, and the reduction coefficient is stable between 0.33 and 0.40 after more than 12 times of freeze-thaw cycling.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Cement** \\ **Dosage,** \\ **\(P_{\text{s}}\) (\%)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Compaction** \\ **Level** \\ **(K)** \\ \end{tabular} } & \multicolumn{4}{c}{**The Compressive Strength (MPa) of Cement-stabilized Loess under the Following Cycling \(N\) (Time)**} \\ \cline{3-10}  & & 0.92 & 1.03 & 0.71 & 0.61 & 0.46 & 0.31 & 0.24 & - & - & - \\
2 & 0.95 & 1.34 & 0.96 & 0.81 & 0.62 & 0.43 & 0.29 & - & - & - \\  & 0.97 & 1.65 & 1.22 & 1.01 & 0.80 & 0.57 & 0.39 & - & - & - \\ \hline \multirow{3}{*}{3} & 0.92 & 1.30 & 0.95 & 0.81 & 0.64 & 0.49 & 0.42 & 0.39 & 0.37 & 0.37 \\  & 0.95 & 1.60 & 1.19 & 1.04 & 0.81 & 0.71 & 0.64 & 0.60 & 0.58 & 0.57 \\  & 0.97 & 2.03 & 1.53 & 1.32 & 1.05 & 0.93 & 0.84 & 0.78 & 0.75 & 0.75 \\ \hline \multirow{3}{*}{4} & 0.92 & 1.49 & 1.13 & 0.98 & 0.76 & 0.64 & 0.58 & 0.53 & 0.52 & 0.52 \\  & 0.95 & 1.90 & 1.44 & 1.28 & 1.02 & 0.90 & 0.83 & 0.77 & 0.75 & 0.74 \\  & 0.97 & 2.26 & 1.76 & 1.55 & 1.30 & 1.11 & 1.02 & 0.96 & 0.93 & 0.93 \\ \hline \multirow{3}{*}{6} & 0.92 & 2.03 & 1.56 & 1.37 & 1.05 & 0.91 & 0.83 & 0.76 & 0.74 & 0.74 \\  & 0.95 & 2.44 & 1.89 & 1.61 & 1.32 & 1.16 & 1.05 & 0.99 & 0.98 & 0.98 \\ \cline{1-1}  & 0.97 & 2.80 & 2.18 & 1.87 & 1.59 & 1.38 & 1.23 The average permafrost depth in Xi'an, Cheng Cheng and Hancheng, China, is 45 cm, 29.6 cm and 19 cm, respectively, during 28 years, and the extreme depth of permafrost in northwestern China can reach more than 80 cm [61, 62]. Therefore, the reduction coefficient of the freeze-thaw cycling is 0.3 according to the most unfavorable conditions.