# Research on the Accumulated Plastic Strain of Expansive Soil under Subway Loading
## 2 Dynamic Triaxial Test Plan
### Experimental Parameter Settings
#### 2.3.1 Determination of Experimental Influencing Factors  
In general, the main influencing factors of the dynamic characteristics of expansive soil can be divided into two aspects: firstly, from the perspective of dynamic loads, factors such as the load waveform, stress amplitude, vibration frequency, and duration of action are crucial. Secondly, in relation to the experimental soil sample, factors mainly include the consolidation state of the soil (consolidation ratio, overconsolidation ratio) and the stress state of the soil (confining pressure, initial force conditions, etc.). Based on the research background and objectives of this paper, the experimental investigation focuses on three key factors as the influencing parameters: the intermittent loading ratio, the static deviatoric stress, and the cyclic stress ratio. The specific parameter settings are shown below. (1) Intermittent Loading Ratio  
Considering the intermittent nature of subway loading, the intermittent loading ratio is defined as the ratio of the intermittent loading duration \(\Delta T\) and the functioning time of the subway loading \(T\). The specific parameter settings for the intermittent loading ratio are determined as follows: since the typical subway train in Hefei City consists of six sections of Type B drum-shaped cars, with a length of approximately 120 m, and the train speed ranges from 30 to 80 km/h, the time taken for the subway to pass a specific point can be calculated as 5.4 s to 14.4 s. Taking 10 s as the time for the subway to pass a specific point, the intermittent duration is generally tens of times the running time [13]. The selected values for the intermittent loading ratio \(\Delta T/T\) are 1, 5, 10, and 50, thus corresponding to intermittent durations of 10 s, 50 s, 100 s, and 500 s. A control experiment is also included with \(\Delta T/T=0\). (2) Static Deviatoric Stress  
The real loads imposed on the soil under train loading include a static load and cyclic dynamic loads, where the static load is caused by the instantaneous bias stress applied to the soil by the passing train. Researchers such as [PERSON] et al. [14] have studied the effect of static deviatoric stress ratio on the deformation behavior of saturated clay. The loading procedure is as follows: a specific static deviator stress is first applied to a predeterminedvalue, and then sinusoidal cyclic loads are superimposed on this static deviator stress. In the experiment, the static deviatoric stress ratios are set to 0, 0.1, and 0.2, with an effective consolidated confining pressure of 100 kPa. The results show that an increase in static deviator stress is detrimental to soil stability, and higher static deviator stress results in greater soil deformation. Similar experimental results were obtained by [PERSON] et al. [15] and [PERSON] et al. [16] regarding the influence of static deviator stress. In addition, it has been found that the existence of static deviatoric stress may also cause preloading of the soil, which may increase the strength of the soil. Furthermore, the method of loading can impact the experimental outcomes, making it necessary to further study the influence of static deviator stress as a contributing factor. According to previous research results [17], the instantaneous stress produced by the tunnel surrounding soil under subway trains operation is 20\(\sim\)40 kPa. [PERSON] et al. [18] considered the static load effects of the overlying structure (ballast, track, and rail sleeper) and used a static deviatoric stress of 15 kPa. In this paper, two different static deviatoric stresses of 15 kPa and 30 kPa are selected for comparison and analysis. (3) Cyclic Stress Ratio  
As one of the most important factors affecting the dynamic characteristics of soil, cyclic stress ratio can not be ignored in triaxial dynamic tests. The cyclic stress ratio \(\eta_{d}\) is defined as the ratio of the dynamic load amplitude (the difference between the peak and trough of the load) \(\sigma_{d}\) to the confining pressure \(\sigma_{c}\).