# Seismic Response of Aeolian Sand High Embankment Slopes in Shaking Table Tests
## 2 Shaking Table Tests
### Test Cases  
Shaking table tests were conducted on three embankment slope models (i.e., embankments with slopes of 1/1.5, 1/1.2, and 1/0.8). Three models were named model 1, model 2, and model 3, respectively. Model 1 was placed in a model box separately, while model 2 and model 3 shared a model box. The dimension of the outside edge of the box is 1960 \(\times\) 1700 \(\times\) 800 mm (length \(\times\) width \(\times\) height). The internal size of the box is 1820 \(\times\) 1500 \(\times\) 800 mm (length \(\times\) width \(\times\) height) without box thickness and boundary treatment materials. The surfaces of the model box parallel to the direction of vibration are transparent. A polystyrene foam board was set behind the model to reduce the box-effect during the test. The experimental setup design is shown in Figure 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Physical Quantity** & **Similarity Law** & **Similarity Constants** & **Remark** \\ \hline Geometry (l) & \(C_{l}\) & 30 & Control variable \\ Mass density (\(\rho\)) & \(C_{p}^{\prime}\) & 1.02 & Control variable \\ Gravity acceleration (g) & \(C_{g}\) & 1.0 & Control variable \\ Stress (\(\sigma\)) & \(C_{c}=C_{p}C_{l}^{\prime}\) & 30.6 & \\ Strain (\(\epsilon\)) & \(C_{c}=C_{p}=C_{l}^{\prime}\)/\(C_{l}^{\prime 2}\)/\(C_{l}^{\prime 2}\) & 5.53 & \\ Shear modulus (G) & \(C_{G}=C_{p}C_{l}^{\prime}\) & 5.53 & \\ Displacement (u) & \(C_{a}=C_{G}=C_{c}^{\prime}\) & \(C_{c}^{\prime 3/2}\) & 165.95 & \\ Velocity (\(\
u\)) & \(C_{c}=C_{p}^{\prime}\)/\(C_{l}^{\prime 3/2}\)/\(C_{l}^{\prime 2}\) & \(C_{l}^{\prime 3/4}\) & 12.88 & \\ Input acceleration (a) & \(C_{a}\) & 1.0 & Input control \\ Time (t) & \(C_{l}=C_{l}^{\prime 4}\)/\(C_{l}^{\prime 3/4}\) & 12.88 & Input control \\ Frequency (f) & \(C_{f}=C_{p}^{\prime 1/4}\)/\(C_{l}^{\prime 3/4}\) & 1/12.88 & \\ Damping ratio (\(\lambda\)) & \(C_{c}\) & 1.0 & \\ Internal friction angle & \(C_{p}\) & 1.0 & \\ (\(\psi\)) & \(C_{p}\) & 1.0 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Similar laws of aeolian sand high embankment slope. Figure 3: Design of dynamic triaxial tests and test results. The thickness of the sand foundation was 50 mm, and the height of the model was 700 mm according to the similarity theory. The sand was compacted in layers (100 mm/layer) by controlling the compaction degree based on the similarity laws. The construction process of the models is shown in Figure 5.  
To observe the shift of the model, \(50\times 50\) mm squares were drawn at the transparent side of the model box and white trace particles were set at the intersections of the squares. The original positions of white trace particles were marked with a red point. Horizontal accelerometers were used in the shaking table test. The accelerometers set on the vibration table were numbered AC1 and AC3. The accelerometers at the top of the model box were numbered as AC2 and AC4. The accelerometers in slope surfaces were upwardly numbered as A1-A4, A8-A11, and A15-A18. Inner horizontal accelerometers were downwardly numbered as A5-A7, A12-A14, and A19-A21. The accelerometers at the boundary were downwardly numbered as AB1-AB3, AB4-AB6, and AB7-AB9 to test boundary effect, as shown in Figure 6.  
Figure 4: Experimental setup design. acceleration time-history curves of AB1-AB2, AB4-AB5, and AB7-AB8 with those of A5-A7, A12-A14, and A19-A21. The natural frequency of the box differs from that of the sand to reduce the 'box-effect'; therefore, the natural frequency of the model box was analyzed via hammering test, and results showed that the natural frequencies of the boxes were 43.97 Hz and 43.66 Hz, respectively. The natural frequency of the model was obtained via spectrum analysis of the white noise scanning, and were 17.5 Hz, 16.6 Hz, and 16.6 Hz, respectively; therefore, the 'box-effect' was negligible and the test results were accurate and reliable. Then, Lan Zhou motions and El-Centro motions were selected for the test.