## 2 Test Program
### Parameters of the Cyclic Loading  
1. Wave form and frequency of the cyclic loading  
It is critical to determine the reasonable wave form of cyclic loading. [PERSON] et al. (2008) discovered that the wave form of the dynamic stress in the surrounding soil has obvious harmonic characteristics based on measurements taken along the Shanghai Metro Line. The frequency of cyclic loading was divided into two types, 2.4-2.6 Hz and 0.4-0.6 Hz, due to the different intervals between adjacent train wheels [1]. Based on a large number of tests, [PERSON] et al. (2015) concluded that sine waves can be used to represent a variety of dynamic loading in situ in laboratory tests, including traffic load, seismic load, and wave load [23]. The peak displacement of the soil surrounding the metro tunnel induced by the train vibration load, according to [PERSON] et al. (2005), occurs near 1 Hz and 3 Hz (especially near 1 Hz) [24]. As a result, the cyclic loading in the test is determined to be a sine wave with a frequency of 1 Hz.  
2. Amplitude of the cyclic loading  
From the field measurements of the Guangzhou-Shenzhen railway and the Beijing circular railway, an empirical formula was made to predict the dynamic stress amplitude on the railroad subgrade surface [4]:  
\[\sigma_{\text{d}}=0.26P(1+0.004V) \tag{1}\]  
where \(\sigma_{\text{d}}\) is the dynamic vertical stress amplitude; \(P\) is the axle load of the train; and \(V\) is the train speed. The parameters of 0.26 and 0.004 are the axle load coefficient and speed coefficient, respectively. The axle load of Hangzhou Metro Line is 8 t under no load and 14 t under full load, with a train speed of 15 km/h to 80 km/h. The dynamic stress amplitude range of the soil can be calculated to be 22-48 kPa.  
3. The number of cycles and the failure criterion  
The number of cycles is set at 10,000. Liquefaction and strain failure criteria are currently the most common failure criteria for soil cyclic tests. The failure standard for liquefaction in sand is \"initial liquefaction\" (\(u_{\text{d}}=\sigma_{3}\), where \(u_{\text{d}}\) is the dynamic pore water pressure, \(\sigma_{3}\) is the confining pressure) [25], but the relatively low permeability of silt causes  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline _w/\%_ & \(\rho\)/g/cm\({}^{3}\) & \(\rho\)/g/cm\({}^{3}\) & \(G_{\text{s}}\) & \(e\) & \(w_{\text{L}}\)/\% & \(w_{\text{P}}\)/\% & \(I_{\text{P}}\) \\ \hline
28.91 & 1.49 & 1.94 & 2.69 & 0.79 & 31.3 & 24.70 & 6.74 \\ \hline \hline \end{tabular} Note: \(w\) = water content; \(\rho_{\text{d}}\) = dry density; \(\rho\) = natural density; \(G_{\text{s}}\) = specific gravity; \(e\) = void ratio; \(w_{\text{L}}\) = liquid limit; \(w_{\text{P}}\) = plastic limit; \(I_{\text{P}}\) = plastic index.  
\end{table}
Table 1: Physical properties of the silt.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Particle Size** & **Silt** & **Kaolin Clay** \\ \hline Fine sand (0.25–0.075 mm) (\%) & 2.48 & 0 \\ Silt (0.075–0.005 mm) (\%) & 90.54 & 49.80 \\ Clay (<0.005 mm) (\%) & 6.98 & 50.20 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Particle size distribution of soil.  
a delay in the pore water pressure measurement. As a result, the strain failure criterion is used, with the permanent axial strain set to 5%.