## 4 Mechanism Analysis of FASSI
### Sand Deformation
#### 4.3.1 Influence of Embedded Depth
Figure 19: Sand surface deformation distribution at different \(x\) in cases with a 300 cm \(L\) and different \(H\): (**a**) \(v_{\rm s}\) (push); (**b**) \(v_{\rm s}\) (pull); (**c**) \(u_{\rm s}\) (push); and (**d**) \(u_{\rm s}\) (pull). As introduced in Section 4.3.1, the VDM and LDM of the cases with a 300 cm \(L\) under push \(u_{\rm t}\) are VDM\({}_{\rm 1a}\) and LDM\({}_{\rm 1a}\), respectively. Compared with the VDM and LDM of the cases with a 180 cm \(L\), \(v_{\rm S1}\) increases by 18 mm and \(v_{\rm S2}\) decreases by 2 mm, as shown in Figure 21a; \(\Delta u_{\rm S2a}\) increases by 24 mm, \(\Delta u_{\rm S2b}\) decreases by 6 mm, and \(\Delta u_{\rm S3}\) decreases to 0 mm, as shown in Figure 21c;  
When \(L\) is 400 cm, the sand slip surfaces in the sand strain contour plot shown in Figure 20c are nearly the same as those of L300H100-Push in Figure 18c. The VDM and LDM of the case with a 400 cm \(L\) is also VDM\({}_{\rm 1a}\) and LDM\({}_{\rm 1a}\). Compared with the VDM and LDM of the cases with a 300 cm \(L\), \(v_{\rm S1}\) decreases by 3 mm and \(v_{\rm S2}\) increases by 1 mm, as shown in Figure 21a; the variations in \(\Delta u_{\rm S2a}\) and \(\Delta u_{\rm S2b}\) are less than 1 mm, as shown in Figure 21c. This is because the sand deformation of sand zones EFMN, ABD, and EFG located at the distal and proximal ends of the FAS specimen are not affected by the increment in \(L\). * Under pull displacement: When \(L\) is 180 cm, the sand slip surfaces in the sand strain contour plot shown in Figure 20b are nearly the same as those of L300H132-Pull in Figure 18f. The VDM of the case with a 180 cm \(L\) can be set as VDM\({}_{\rm 3b}\). \(v_{\rm S1}\) is \(-1\) mm and \(v_{\rm S2}\) is \(-3\) mm, as shown in Figure 21b. The LDM of the case with a 180 cm \(L\) can be set as LDM\({}_{\rm 3b}\), with a \(\Delta u_{\rm S2b}\) of 1 mm and a \(\Delta u_{\rm S4}\) of 49 mm, as shown in Figure 21d;  
As introduced in Section 4.3.1, the VDM and LDM of the cases with a 300 cm \(L\) under pull \(u_{\rm t}\) are VDM\({}_{\rm 2b}\) and LDM\({}_{\rm 2b}\), respectively. Compared with the VDM and LDM of the cases with a 180 cm \(L\), \(v_{\rm S1}\) and \(v_{\rm S2}\) increase by 22 mm and 24 mm, respectively, as shown in Figure 21b; \(\Delta u_{\rm S2a}\), \(\Delta u_{\rm S2b}\), and \(\Delta u_{\rm S3}\) increase by 6 mm, 12 mm, and 32 mm, respectively, and \(\Delta u_{\rm S4}\) decreases to 0 mm, as shown in Figure 21d;  
When \(L\) is 400 cm, the sand slip surfaces in the sand strain contour plot shown in Figure 20d are nearly the same as those of L300H100-Pull in Figure 18d. The VDM and LDM of the case with a 400 cm \(L\) are also VDM\({}_{\rm 1b}\) and LDM\({}_{\rm 1b}\). Compared with the VDM and LDM of the cases with a 300 cm \(L\), \(v_{\rm S1}\) increases by 14 mm and \(v_{\rm S2}\) decreases by 5 mm, as shown in Figure 21b; \(\Delta u_{\rm S2a}\) and \(\Delta u_{\rm S2b}\) increase by 21 mm and 11 mm, respectively, and \(\Delta u_{\rm S3}\) decreases to 0 mm, as shown in Figure 21d. The analyses conducted in Sections 4.2 and 4.3 show that with an increase in \(H\), the LDM changes from LDM\({}_{\rm 1a}\) to LDM\({}_{\rm 2a}\) under push \(u_{\rm t}\) and from LDM\({}_{\rm 1b}\) to LDM\({}_{\rm 3b}\) under pull \(u_{\rm t}\). With an increase in \(L\), the LDM changes from LDM\({}_{\rm 2a}\) to LDM\({}_{\rm 1a}\) under push \(u_{\rm t}\) and from LDM\({}_{\rm 3b}\) to LDM\({}_{\rm 1b}\) under pull \(u_{\rm t}\). It can be concluded that the influence of \(H\) on the LDM of FASSI is opposite to the influence of \(L\) on the LDM of FASSI. Consequently, with an increase in \(H\) or a decrease in \(L\), \(\Delta u_{\rm S2a}\) and \(\Delta u_{\rm S2b}\) on the sand surface decrease, which is beneficial for avoiding pavement crack risks; \(v_{\rm S1}\) and \(v_{\rm S2}\) also decrease, which can improve the pavement evenness. Furthermore, a reduction in slab length can further lower the construction cost. However, when \(L\) is too small, it cannot meet the structural requirements.