## 2 Testing Apparatus and Program
### Test Method  
The corresponding dry density values for these relative densities are detailed in Table 1. The experiment was conducted based on the \"Standard for Soil Test Method\" (GB/T50123-2019) [18], using sample sizes of diameter 300 mm and height 600 mm. The process was \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Specimen** & **Maximum Particle** & **Minimum Dry** & **Maximum Dry** & & & **Dry Density/(g\(\cdot\)cm\({}^{-3}\))** & \\
**Number** & **Diameter/mm** & **Density/(g\(\cdot\)cm\({}^{-3}\))** & **Density/(g\(\cdot\)cm\({}^{-3}\))** & **\(D_{\text{r}}\) = 0.9** & **\(D_{\text{r}}\) = 0.7** & **\(D_{\text{r}}\) = 0.5** & **\(D_{\text{r}}\) = 0.3** \\ \hline S1 & 40 & 1.884 & 2.244 & 2.202 & 2.122 & 2.048 & 1.979 \\ S2 & 20 & 1.844 & 2.174 & 2.136 & 2.063 & 1.995 & 1.932 \\ S3 & 10 & 1.798 & 2.1 & 2.065 & 1.999 & 1.937 & 1.879 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dry density physical parameters. Figure 4: Surface vibratory compactor for coarse-grained soils. Figure 3: Gradation curves of experimental coarse-grained soils. divided into five steps: sample preparation, saturation, consolidation, loading, and sample removal. The specific details are as follows:  
1. Sample Preparation:  
The sample was directly placed on the instrument base. A layer of petroleum jelly was applied around the instrument base and the inside of the membrane holder to prevent water and air leakage during the experiment. After fixing the rubber membrane to the base and installing the membrane holder, a vacuum pump was used to draw air out, causing the rubber membrane to adhere to the holder. The test used air-dried material, forming the sample by controlling the compaction. The weighed test material was evenly divided into six portions, each portion was placed into the membrane holder in four layers, compacted, and roughened to achieve the predetermined dry density. After filling the sample, a vacuum was applied to maintain a negative pressure of 20 kPa, and then the membrane holder was removed. 2. Saturation:  
After sample preparation, to ensure the sealed state during the experiment, the rubber ring around the instrument base was cleaned. After cleaning, the pressure chamber was installed and filled with water. Maintain a constant water temperature to control the environmental temperature during the testing process. The sample was saturated using the water head saturation method: after the pressure chamber was filled with water, water injection was stopped, and CO2 was introduced from the bottom of the sample to replace the air in the pores. Then, air-free water was injected from the bottom, and once water emerged from the top, the water head saturation method was used to gradually saturate the sample from bottom to top. The saturation was considered complete when the pore pressure coefficient B value reached above 0.95. 3. Consolidation:  
The sample was consolidated by controlling the stress. While maintaining constant confining pressure, the sample was subjected to drained consolidation with a consolidation ratio \(K_{\text{c}}\) of 2.0. Initially, isotropic consolidation was performed, and once the sample stabilized, the axial pressure was gradually increased to avoid severe deformation due to the sudden application of excessive axial pressure. Throughout the consolidation process, the sample's drainage was continuously monitored, and consolidation was considered complete when the drainage volume did not exceed 15 mL within 30 min. 4. Loading:  
Stress-controlled loading was used in the experiment. A confining pressure of 200 kPa was selected. After consolidation, while maintaining the confining pressure constant, axial dynamic stress was applied in stages from small to large. Each level of dynamic stress was \(\sigma_{\text{d}}=\pm\) 0.3\(\sigma_{3}\), 0.4\(\sigma_{3}\), 0.5\(\sigma_{3}\), \(\ldots\), and the next level of loading could only proceed after completing the previous level.