## 3 Results and Discussions
### Critical Dynamic Stress
#### 3.3.2 Impact of Temperature and Moisture Content  
Figure 17 illustrates the variation in CDS for different temperature and moisture content conditions determined based on the plastic limit criterion. As illustrated in Figure 17a, with an initial stress ratio \(\eta_{0}\) of 0.5, an initial pressure \(\mathrm{p_{0}}\) of 0.9 MPa, and a constant moisture content of 14%, the CDS \(\sigma_{\mathrm{d,s}}\) under the plastic stability limit demonstrates a gradual increase as the temperature decreases, varying from 0.49 MPa to 4.17 MPa. In contrast, the CDS \(\sigma_{\mathrm{d,c}}\) pertaining to the plastic creep limit undergoes a gradual escalation from 3.12 MPa to 6.86 MPa within the span of temperatures considered in the experimentation. The reason should be that with the gradual decrease in temperature, the frozen soil body, the unfrozen moisture content in the void gradually decreased, the ice particle content gradually increased, the proportion of enhancement, the cementing effect of ice makes the soil particles increase the adhesion between the particles, at the same time the cementing effect between the ice particles is also enhanced, so when the other conditions are certain, the lower the temperature, the strength of the frozen powdery clay increases, the resistance to deformation ability increased, the CDS would also increase. Figure 17b shows that when the initial stress ratio \(\eta_{0}\) is 0.5, the initial pressure \(\mathrm{p_{0}}\) is 0.9 MPa, and the temperature is held at \(-5\)\({}^{\circ}\)C, the CDS \(\sigma_{\mathrm{d,s}}\) under the plastic stability limit generally decreases with increasing moisture content, experiencing a slight reversal at a moisture content of 18.5%. Specifically, it gradually decreases from 2.82 MPa to 1.24 MPa before marginally increasing to 1.62 MPa. Similarly, the CDS \(\sigma_{\mathrm{d,c}}\) for plastic creep diminishes as the moisture content rises, initially decreasing from 7.52 MPa to \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Sequence** & **Formulas \(\epsilon_{\mathrm{sub}}\) = a*eb*x** & **a** & **b** & **R2** \\ \hline S1:D51–D55 & \(\epsilon_{\mathrm{sub}}=0.15\mathrm{e^{0.85}}\)x & 0.15 & 0.85 & 0.994 \\ \hline S2:D56–D60 & \(\epsilon_{\mathrm{sub}}=0.10\mathrm{e^{0.79}}\)x & 0.10 & 0.79 & 0.998 \\ \hline S3:D61–D65 & \(\epsilon_{\mathrm{sub}}=0.05\mathrm{e^{0.79}}\)x & 0.05 & 0.79 & 0.997 \\ \hline S4:D66–D70 & \(\epsilon_{\mathrm{sub}}=0.04\mathrm{e^{0.69}}\)x & 0.04 & 0.69 & 0.999 \\ \hline S5:D71–D76 & \(\epsilon_{\mathrm{sub}}=0.56\mathrm{e^{0.71}}\)x & 0.56 & 0.71 & 0.995 \\ \hline S6:D77–D82 & \(\epsilon_{\mathrm{sub}}=0.26\mathrm{e^{0.40}}\)x & 0.26 & 0.40 & 0.626 \\ \hline S7:D83–D88 & \(\epsilon_{\mathrm{sub}}=0.10\mathrm{e^{0.97}}\)x & 0.10 & 0.97 & 0.997 \\ \hline S8: D89–D94 & \(\epsilon_{\mathrm{sub}}=0.28\mathrm{e^{0.88}}\)x & 0.15 & 1.03 & 0.996 \\ \hline S9:D95–D100 & \(\epsilon_{\mathrm{sub}}=0.25\mathrm{e^{0.92}}\)x & 0.25 & 0.92 & 0.997 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fitting curves and parameters for the relationship between cumulative strain difference and dynamic stress. Figure 17: CDS under the influence of temperature and moisture content. 3.27 MPa, followed by a slight augmentation to 3.43 MPa. In general, the higher the moisture content, the higher the proportion of ice particles in the frozen soil, and the stronger the ice cementation, the higher the corresponding triaxial strength, the CDS of frozen powdery clay under long-term reciprocal loading is different from the CDS here, there exists an extreme value under the specific condition of a particular moisture content.