## 4 Mechanism Analysis of FASSI
### Load-Displacement Curve  
#### 4.2.1 Influence of Embedded Depth  
The relationships between \(H\) and \(k\), as well as \(H\) and \(F_{\text{u}}\), are demonstrated in Figure 16. With an increase in \(H\), \(k\) nonlinearly increases, as shown in Figure 16a. When \(H\) is the same, \(k\) under pull \(u_{\text{t}}\) is larger than that under push \(u_{\text{t}}\). Additionally, when the increment in \(H\) is the same, the increment in \(k\) under pull \(u_{\text{t}}\) is larger than that under push \(u_{\text{t}}\). With an increase in \(H\), \(F_{\text{u}}\) nonlinearly increases, as shown in Figure 16b. When \(H\) is the same, \(F_{\text{u}}\) under pull \(u_{\text{t}}\) is smaller than that under push \(u_{\text{t}}\). Additionally, when the increment in \(H\) is the same, the increment in \(F_{\text{u}}\) under pull \(u_{\text{t}}\) is smaller than that under push \(u_{\text{t}}\). The \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Loading** & \(\mathbf{L}\) & \(\mathbf{H}\) & **Labels** & \(\mathbf{k}\) & \(\mathbf{F_{\text{u}}}\) \\
**Direction** & **(cm)** & **(cm)** & **Labels** & **(kN/mm)** & **(kN)** \\ \hline \multirow{8}{*}{Push} & \multirow{4}{*}{180} & 0 & L180H6-Push & 5.68 & 6.65 \\  & & 63 & L180H63-Push & 15.21 & 37.17 \\  & & 100 & L180H100-Push & 20.15 & 55.06 \\  & & 132 & L180H132-Push & 27.63 & 99.71 \\ \cline{2-5}  & \multirow{4}{*}{300} & 0 & L300H6-Push & 9.29 & 24.70 \\  & & 63 & L300H63-Push & 18.37 & 56.60 \\  & & 100 & L300H100-Push & 24.51 & 76.21 \\  & & 132 & L300H132-Push & 32.80 & 129.24 \\ \cline{2-5}  & \multirow{4}{*}{400} & 0 & L400H6-Push & 11.26 & 40.09 \\  & & 63 & L400H63-Push & 20.16 & 70.88 \\  & & 100 & L400H100-Push & 27.58 & 93.25 \\  & & 132 & L400H132-Push & 36.92 & 160.77 \\ \hline \multirow{8}{*}{Pull} & \multirow{4}{*}{180} & 0 & L180H0-Pull & 7.58 & \(-\)6.45 \\  & & 63 & L180H63-Pull & 21.69 & \(-\)25.28 \\  & & 100 & L180H100-Pull & 35.58 & \(-\)45.53 \\  & & 132 & L180H132-Pull & 55.66 & \(-\)58.33 \\ \cline{2-5}  & \multirow{4}{*}{300} & 0 & L300H0-Pull & 20.41 & \(-\)28.66 \\  & & 63 & L300H63-Pull & 32.21 & \(-\)48.03 \\  & & 100 & L300H100-Pull & 45.01 & \(-\)64.62 \\  & & 132 & L300H132-Pull & 67.16 & \(-\)82.73 \\ \cline{2-5}  & \multirow{4}{*}{400} & 0 & L400H0-Pull & 30.29 & \(-\)45.82 \\  & & 63 & L400H63-Pull & 43.99 & \(-\)61.14 \\  & & 100 & L400H10-Pull & 58.29 & \(-\)78.88 \\  & & 132 & L400H132-Pull & 89.37 & \(-\)97.46 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Characteristic points of the \(F\)-\(u\) curves obtained from FEM with different parameters. influence of the displacement direction on the \(H\)-\(F_{\rm u}\) relationship is opposite to that on the \(H\)-\(k\) relationship. This is due to the following reasons. When the FAS specimen starts to move and the \(F\)-\(u\) curve is in the elastic stage, the FAS specimen is subjected to friction between its upper and lower surfaces and the corresponding sand and the earth pressure from the sand at its distal end. With an increase in \(H\), the vertical pressures on the upper and lower surfaces of the FAS specimen increase accordingly, leading to an increment in the friction between the FAS specimen and sand. Meanwhile, with an increase in \(H\), the earth pressure of the sand on the distal end of the FAS specimen increases, contributing to an increment in \(k\). As shown in Figures 10 and 14, the earth pressure distribution zone ABD at the distal end of the FAS specimen is wedge-shaped. Therefore, with an increase in \(H\), the range zone ABD nonlinearly extends, resulting in a nonlinear and rapid increment in \(k\). Under push \(u_{\rm t}\), the FAS specimen and the sand above it both move away from the front wall. The earth pressure of the sand at the distal end of the FAS specimen transforms from the static earth pressure to the passive earth pressure. The earth pressure at the distal end of the FAS specimen could restrain the movement of the sand above it. Consequently, the relative sliding between the FAS specimen and the sand could produce friction.