## 2 Test Program
### Test Procedures
The pore pressure, accumulated strain, and other data were automatically recorded during the test, and the tests were terminated once the failure standard was met. Dynamic Response of the Silt Containing Fine Particles under Conventional  
Triaxial Stress Path  
Undrained Cyclic Tests  
The development of permanent axial strain versus number of cycles was obtained through long-term cyclic tests on silt with different fine particle contents, as shown in Figure 2a-e. Although the failure axial strain was 5%, the upper limit of the strain in the figures was set to 2% to show the strain development of all loading cycles clearly. The permanent axial strain curve can be divided into stable and failure modes based on different dynamic stress amplitudes. The permanent axial strain of the stable mode increases rapidly in the first few cycles, indicating that the soil sample is significantly compacted. The growth rate of the accumulated strain gradually decreases as the number of cycles increases, and the strain tends to a stable value, indicating that the specimen exhibits an elastic response. In the early stages of cyclic loading, the permanent axial strain of the failure mode is nearly identical to that of the stable mode. The structure of the soil samples is damaged when a certain number of cycles is reached, and the strain increases dramatically in a short period of time. The permanent axial strain curves change from stable to failure mode as dynamic stress amplitude increases, with the threshold stress amplitude serving as the demarcation point. The number of vibration cycles required to reach the failure strain decreases significantly as the dynamic stress amplitude exceeds the threshold value. Figure 3a,b are the stress paths at \(\sigma_{\text{d}}\) = 40 kPa (stable mode) and \(\sigma_{\text{d}}\) = 48 kPa (failure mode) with the fine particle content of 7%. With the increase in the number of cycles, \(p^{\prime}\) and \(q\) remain almost unchanged when \(\sigma_{\text{d}}\) = 40 kPa. When \(\sigma_{\text{d}}\) = 48 kPa, \(p^{\prime}\) continues to decrease and \(q\) remains stable at the initial stage. As the number of cycles approaches the critical value, the excess pore water pressure accumulates rapidly, and the sample has difficulty bearing the cyclic dynamic stress. The lower limit of \(q\) increases and the upper limit decreases, and the soil sample reaches failure condition. Figure 4 shows the accumulative axial strain development under stable and destructive modes, and the permanent axial strain is the lower envelope of accumulative axial strain. Figure 5 shows the influence of different fine particle contents on the threshold dynamic stress amplitude and failure cycles at 5% axial strain. The threshold dynamic stress amplitude and failure cycles both decrease at first, then increase. At 10% fine particle content, the stress amplitude and number of cycles reach a minimum of 39 kPa and 5495, respectively, indicating that the silt is more vulnerable to long-term traffic load. When the fine particle content is less than 10%, the fine particles act as a lubricant and allow the coarse particles to slide, which causes the threshold dynamic stress amplitude to decrease. When fine particle content exceeds 10%, its viscous effect becomes noticeable to stabilize the soil skeleton, resulting in an increase in the threshold dynamic stress amplitude. Figure 2: Permanent axial strain of the saturated silt with different fine particle contents under undrained conditions. (**a**) 7% fine particle content; (**b**) 8% fine particle content; (**c**) 10% fine particle content; (**d**) 12% fine particle content; (**e**) 14% fine particle content. Under undrained conditions, Figure 6 shows the excess pore water pressure (EPWP) versus the number of cycles of silt with different fine particle contents. The development of pore water pressure and permanent axial strain is similar and can be divided into two modes: stable mode and failure mode.