## 4 Mechanism Analysis of FASSI
### Sand Deformation
#### 4.3.1 Influence of Embedded Depth  
The sand strain contour plots of the cases with a 300 cm \(L\) and different \(H\) under push and pull \(u_{\text{t}}\) are shown in Figure 18. The black dashed line indicates the slip surface formed by the penetration of plastic strain, and the arrow in Figure 18f indicates the plastic strain concentration area. Points M and N are, respectively, the points on the sand surface and the upper surface of the FAS closest to the bridge, and Points E and C are, respectively, the intersections of the proximal and distal slip surfaces on the upper surface of the FAS. Points G, F, D, and B represent the longitudinal positions (\(x\)) at the sand surface, which are \(x_{\text{1a}}\), \(x_{\text{1b}}\), \(x_{\text{2a}}\), and \(x_{\text{2b}}\), respectively. \(v_{\rm s2}\) of VDM\({}_{\rm 2a}\) in the case with a 132 cm \(H\) are reduced by 5 mm and 2 mm, respectively. A displacement absorption zone \(l_{\rm GB}\) for \(u_{\rm t}\) between Points G and B in Figure 18e can be found, as shown in Figure 19c. \(u_{\rm s}\) within \(w_{2}\) and \(w_{3}\) decreases by a \(\Delta u_{\rm s3}\) of 29 mm relative to \(u_{\rm t}\), indicating that the sand within \(w_{2}\) and \(w_{3}\) has a relative movement with the FAS specimen. A displacement absorption point \(x_{\rm 2b}\) at Point B in Figure 18e can absorb the \(\Delta u_{\rm s}\) of 21 mm at \(x_{\rm 2b}\) (\(\Delta u_{\rm s2b}\)), and then \(u_{\rm t}\) decreases to zero. This kind of LDM can be set as LDM\({}_{\rm 2a}\) and expressed as \(u_{\rm t}=\Delta u_{\rm s3}+\Delta u_{\rm s2a}+\Delta u_{\rm s2b}\) (\(\Delta u_{\rm s2a}=0\)). When \(H\) changes from 100 cm to 132 cm, the LDM changes from LDM\({}_{\rm 1a}\) to LDM\({}_{\rm 2a}\), \(\Delta u_{\rm s3}\) 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 by \(\Delta u_{\rm s2b}\) relatively decreases, the deformation of the sand zone GEFCAB is reduced, leading to a decrease in \(v_{\rm s2}\). * Under pull displacement: When \(H\) is 63 cm, the sand slip surfaces under pull \(u_{\rm t}\), as illustrated in Figure 18b, are similar to those of the cases with a 63 cm or 100 cm \(H\) under push \(u_{\rm t}\), as shown in Figure 18a. For the case with a 63 cm \(H\) under pull \(u_{\rm t}\), the sand in \(w_{\rm 1}\) uplifts, with a \(v_{\rm s1}\) of 41 mm; the sand in \(w_{\rm 2}\) subsides, with a \(v_{\rm s2}\) of \(-\)36 mm; \(v_{\rm s}\) within \(w_{\rm 3}\) is essentially 0 mm. This is because the sand zone EFMN is in compression and the sand zone ABD is in tension, as shown in Figure 19b. Therefore, the VDM of the case with a 63 cm \(H\) under pull \(u_{\rm t}\) can be set as VDM\({}_{\rm 1b}\). \(u_{\rm s}\) in \(w_{3}\) equals \(u_{\rm t}\), indicating that the sand zone EFDC moves along with the FAS specimen. As shown in Figure 18b, 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 \(\Delta u_{\rm s2a}=24\) mm and \(\Delta u_{\rm s2b}=26\) 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\({}_{\rm 1b}\) and expressed as \(u_{\rm t}=\Delta u_{\rm s2a}+\Delta u_{\rm s2b}\). The sand deformation ranges of the VDM\({}_{\rm 1b}\) and LDM\({}_{\rm 1b}\) are similar to those of VDM\({}_{\rm 1a}\) and LDM\({}_{\rm 1b}\), respectively, with the opposite parameter values. The VDM and LDM of the case with a 100 cm \(H\) under pull \(u_{\rm t}\) are different from those of the case with a 63 cm \(H\), as shown in Figure 19b. The sand slip surface EF is formed at the proximal end of the FAS specimen and the sand slip surfaces CF and AB are formed at the distal end of the FAS specimen, as shown in Figure 18d.