# Research on the Accumulated Plastic Strain of Expansive Soil under Subway Loading
## 3 Analysis of Test Results  
### Analysis of the Influence Law of Loading Methods on the Dynamic Strain of Expansive Soil  
Figure 4a shows the dynamic strain-time curve of sample S3 under continuous loading conditions, while Figure 5a shows the dynamic strain-time curve of sample S21 under intermittent loading conditions (first 800 s). It can be observed from the figures that both loading modes exhibit dynamic strains comprising elastic strain \(\varepsilon_{p}\) and accumulated plastic strain \(\varepsilon_{d}\). Unlike continuous loading, the dynamic strain-time curve under intermittent loading conditions develops in a \"step-like\" manner, including loading and intermittent phases. The strain value during the loading phase increases with time, while the strain value during the intermittent phase remains close to the strain value at the end of the loading phase, with a \"strain platform\" existing between the two phases. During each cycle, the strain experiences a period of growth followed by a period of nearly constant values. The reason for this is that under partially drained conditions, the axial strain is mainly composed of two parts: one is the volume change caused by the drainage of pore  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Sample ID**} & **Loading** & **Loading Time** & **Intermission** & **Intermittent** & **Static** & **Cyclic Stress** \\  & **Method** & **T (s)** & **Time \(\Delta\)T (s)** & **Loading Ratio** & **Deviatoric** & **Ratio \(\eta_{d}\)**water, which leads to a decrease in the total volume of the soil sample and a corresponding decrease in the pore size between soil particles; the other is the deformation of the soil sample due to external loads. However, the deformation of the soil caused by the discharge of pore water accounts for the majority of the deformation. In addition, because the intermittent period stops loading, only a small amount of pore water can flow back into the soil sample. Therefore, the plastic strain during the quiescent period cannot be recovered and remains essentially unchanged. The development curves of accumulated plastic strain under continuous and intermittent loading conditions are depicted in Figures 4b and 5b, respectively. With the increase in time, the development rate of the strain changes from fast to slow, and the dynamic strain still has an upward trend under the condition of continuous loading at the end, but the dynamic strain gradually approaches the stable value under the condition of intermittent loading. Moreover, it can be observed from the figures that the initial development rate of the plastic strain is significantly higher under intermittent loading conditions. The main reason for this phenomenon is that the accumulation of the strain under continuous  
Figure 4: Strain–time curve of dynamic strain under continuous loading conditions. (**a**) Strain development curve; (**b**) cumulative strain development curve. Figure 5: Strain–time curve of dynamic strain under intermittent loading conditions. (**a**) Strain development curve; (**b**) cumulative strain development curve. loading conditions depends on the sustained action of external loads. As the number of loading cycles increases, the strain also increases accordingly. However, when the number of loading cycles reaches a certain threshold, the growth rate of the strain begins to decrease. Nevertheless, due to the sustained action of the subway load, the strain does not tend to stabilize until the test termination condition is reached, resulting in a continued upward trend. Under intermittent loading conditions, the dynamic strain is composed of two parts: the deformation induced by the external load during the loading stage and the deformation resulting from the volume reduction caused by pore water expulsion. The volume reduction caused by the release of pore water accounts for the majority of the effect.