## 4 Mechanism Analysis of FASSI
### Sand Deformation
#### 4.3.1 Influence of Embedded Depth
The sand in \(w_{\rm 1}\) and \(w_{\rm 3}\) both uplift; and the sand in \(w_{\rm 2}\) subsides. This is because the sand zones EGMN and EFCDG in Figure 18d are in compression and the sand zone ABD is in tension. This kind of VDM can be set as VDM\({}_{\rm 2b}\). Compared with VDM\({}_{\rm 1b}\) of the case with a 63 cm \(H\), \(v_{\rm s1}\) and \(v_{\rm s2}\) of VDM\({}_{\rm 2b}\) in the case with a 100 cm \(H\) are reduced by 19 mm and 9 mm, respectively. A displacement absorption zone \(l_{\rm GB}\) for \(u_{\rm t}\) between Points G and B in Figure 18d can be found, as shown in Figure 19d. \(u_{\rm s}\) within \(w_{\rm 1}\) and \(w_{\rm 3}\) decreases by a \(\Delta u_{\rm s3}\) of 32 mm relative to \(u_{\rm t}\). Two absorption points of \(u_{\rm t}\) (\(x_{\rm 2a}\) and \(x_{\rm 2b}\)) can be found at Points D and B, and the corresponding \(\Delta u_{\rm s}\) are\(\Delta u_{\rm s2a}=21\) mm and \(\Delta u_{\rm s2b}=11\) mm, respectively. \(u_{\rm t}\) reduces to zero at \(x_{\rm 2b}\), indicating that the sand surface away from \(x_{\rm 2b}\) is not affected by \(u_{\rm t}\). This kind of LDM can be set as LDM\({}_{\rm 2b}\) and expressed as \(u_{\rm t}=\Delta u_{\rm s3}+\Delta u_{\rm s2a}+\Delta u_{\rm s2b}\). The sand deformation ranges of VDM\({}_{\rm 2b}\) are similar to those of VDM\({}_{\rm 2a}\). \(v_{\rm s1}\) and \(v_{\rm s2}\) of VDM\({}_{\rm 2b}\) are opposite to those of VDM\({}_{\rm 2a}\). \(\Delta u_{\rm s2a}\) of LDM\({}_{\rm 2b}\) is not zero due to the sand slip surface CD, which is different from \(\Delta u_{\rm s2a}\) of LDM\({}_{\rm 2a}\). When \(H\) changes from 63 cm to 100 cm, the LDM changes from LDM\({}_{\rm 1b}\) to LDM\({}_{\rm 2b}\), the volume of the sand zones EGMN, EFCDG, and ABD, and the corresponding displacement absorption increase. Moreover, \(\Delta u_{\rm s3}\) is absorbed by the displacement absorption zone \(l_{\rm GB}\), which will reduce \(u_{\rm t}\) absorbed by the sand zone EGMN and the corresponding \(v_{\rm s1}\). Simultaneously, since \(u_{\rm t}\) absorbed \(\Delta u_{\rm s2a}\) and \(\Delta u_{\rm s2b}\) relatively decreases, the deformation of the sand zone EFCDG is reduced, leading to a decrease in \(v_{\rm s2}\)The VDM and LDM of the case with a 132 cm \(H\) under pull \(u_{\rm t}\) are different from those of the cases with a 63 cm or 100 cm \(H\), as shown in Figure 19b. The sand surfaces in \(w_{1}\) and \(w_{3}\) do not change and the sand in \(w_{2}\) subsides. This kind of VDM can be set as VDM\({}_{\rm 3b}\). Compared with VDM\({}_{\rm 2b}\) of the case with a 100 cm \(H\), \(v_{\rm s1}\) and \(v_{\rm s2}\) of VDM\({}_{\rm 3b}\) in the case with a 132 cm \(H\) are reduced by 22 mm and 25 mm, respectively. \(u_{\rm s}\) decreases by a \(\Delta u_{\rm s4}\) of 50 mm relative to \(u_{\rm t}\), which nearly equals \(u_{\rm t}\), as shown in Figure 19c. Relative sliding is observed between the FAS specimen and the sand. An absorption point of \(u_{\rm t}\) (\(x_{\rm 2b}\)) can be found at Point C, and the corresponding \(\Delta u_{\rm s}\) is \(\Delta u_{\rm s2b}=1\) mm. \(u_{\rm t}\) reduces to zero at \(x_{\rm 2b}\), indicating that the sand surface away from \(x_{\rm 2b}\) is not affected by \(u_{\rm t}\). This kind of LDM can be set as LDM\({}_{\rm 3b}\) and expressed as \(u_{\rm t}=\Delta u_{\rm s4}+\Delta u_{\rm s2b}\). VDM\({}_{\rm 3b}\) and LDM\({}_{\rm 3b}\) are due to the fact that the plastic strains at Points A and C do not extend to the sand surface, as shown in Figure 18f. \(u_{\rm t}\) is reduced by \(\Delta u_{\rm s4}\) due to the relative sliding between the FAS specimen and the sand. Meanwhile, local voids generated at the end of the FAS specimen lead to the subsidence of Point B directly above it and the reduction of \(u_{\rm t}\) by \(\Delta u_{\rm s2b}\). Therefore, the \(u_{\rm s}\) reflected to the sand surface is so small that the \(v_{\rm s}\) on the sand surface is hardly noticeable.