## 5 Conclusions  
In order to evaluate the long-term deformation of the silt around the existing tunnel under the unloading of the above foundation pit and the cyclic loading of metro trains, a series of dynamic triaxial tests using the silt with different fine particle content and unloading intensities were carried out. The following conclusions are drawn:  
1. In cyclic loading tests, there is a dynamic stress amplitude threshold. The permanent axial strain and excess pore water pressure of the silt tend to be stable as the number of cycles increases when the dynamic stress amplitude is less than this value. When the dynamic stress amplitude exceeds this value, the silt will liquefy and fail as the number of cycles increases. With increasing fine particle content, the threshold dynamic stress and failure cycles in silt decrease and then increase, reaching a minimum of 39 kPa and 5495, respectively, at 10% fine particle content.
2. For the same fine particle content, the permanent axial strain under drained conditions is greater than that under undrained conditions (when the sample does not fail at 10,000 cycles) because the excess pore pressure under drained conditions is dissipated in time, resulting in the consolidation deformation of soil samples. At the same time, due to higher permeability and lower fine particles of silt, the difference between undrained and drained permanent axial strain is more significant.  
Figure 12: Excess pore water pressure under unloading stress path. (a) BU\(-1\) (unloading intensity = 10 kPa); (b) BU\(-2\) (unloading intensity = 20 kPa); (c) BU\(-3\) (unloading intensity = 40 kPa).  
Figure 13: Excess pore water pressure under unloading and reloading stress path. (a) CU\(-1\) (unloading intensity = 10 kPa); (b) CU\(-2\) (unloading intensity = 20 kPa); (c) CU\(-3\) (unloading intensity = 40 kPa).  
3. The threshold dynamic stress amplitude and failure cycles of the silt are significantly reduced by axial unloading. The silt is disturbed during the unloading and reloading path, resulting in a slight reduction in the critical dynamic stress amplitude and failure period. The dynamic stress threshold amplitude of a soil sample decreases slightly as unloading strength increases. As a result, the impact of fine particle content and foundation pit unloading on the dynamic characteristics of silt under long-term cyclic loading should be considered.  
Conceptualization, F.M. and C.X.; methodology, F.M. and C.X.; software, F.M. and C.X.; validation, F.M. and M.Z.; formal analysis, M.Z.; investigation, Z.T., C.L. and M.Z.; resources, F.M. and C.X.; data curation, Z.T.; writing--original draft preparation, F.M.; writing--review and editing, F.M., C.X. and M.Z.; visualization, F.M. and C.X.; supervision, F.M. and M.Z.; project administration, F.M., C.X. and M.Z.; funding acquisition, F.M., C.X. and M.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the China Postdoctoral Science Foundation, grant number 2021T140475; the National Natural Science Foundation of China, grant number 52008263, grant number 52108329, grant number 52090084; Zhejiang science and technology planning project, grant number 2013C31034; and Shenzhen Science and Technology Program, grant number KQTD20200909113951005.  
Not applicable.  
Data Availability Statement: Data is contained in the article.  
The authors declare no conflict of interest.