## 2 Experimental Test
### Experimental Results
#### 2.5.2 Load-Displacement Curve  
The load-displacement (_F-u_) curves of different test cases are illustrated in Figure 7. The hollow symbols denote the _F-u_ curves obtained from experimental tests. Taking the _F-u_ curve of H63-Push as an example, the characteristic points (_o_, \(a\), \(b\), and _c_) of the curve are marked with solid circles. The \(u\) corresponding to each characteristic point are \(u_{\text{a}}\), \(u_{\text{b}}\), and \(u_{\text{c}}\), respectively, and the corresponding \(F\) are \(F_{\text{a}}\), \(F_{\text{b}}\), and \(F_{\text{u}}\), respectively. With an \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **H** \\ **(cm)** \\ \end{tabular} } & \multirow{2}{*}{**Loading** \\ \multirow{2}{*}{**Direction**} & & & \(a\) & & \(b\) & & \(c\) & & \(k\) & \(l\) \\ \cline{3-10}  & & & _u\({}_{\text{m}}\)_ & _F\({}_{\text{a}}\)_ & _u\({}_{\text{b}}\)_ & _F\({}_{\text{b}}\)_ & _u\({}_{\text{c}}\)_ & _F\({}_{\text{u}}\)_ & **(kN/mm)** & **(kN/mm)** \\ \hline
0 & & H0-Push & 0.52 & 4.81 & 1.52 & 5 & 50 & 5.85 & 9.25 & 0.02 \\
21 & & H21-Push & 0.61 & 6.36 & 3.38 & 7.2 & 50 & 9.51 & 10.43 & 0.05 \\
31.5 & & H31.5-Push & 0.75 & 8.43 & 6.42 & 15.3 & 50 & 17.71 & 11.24 & 0.06 \\
63 & & H63-Push & 1.42 & 26.41 & 8.74 & 35.5 & 50 & 35.62 & 18.60 & 0.00 \\ \hline
0 & & H0-Pull & \(-0.45\) & \(-2.73\) & \(-2.45\) & \(-5.1\) & \(-50\) & \(-6.75\) & 6.07 & 0.03 \\
21 & & H21-Pull & \(-0.56\) & \(-3.84\) & \(-2.58\) & \(-7\) & \(-50\) & \(-7.82\) & 6.86 & 0.02 \\
31.5 & & H31.5-Pull & \(-1.21\) & \(-8.74\) & \(-3.66\) & \(-10.3\) & \(-50\) & \(-13.35\) & 7.22 & 0.07 \\
63 & & H63-Pull & \(-1.41\) & \(-18.12\) & \(-5.27\) & \(-18.6\) & \(-50\) & \(-31.7\) & 12.85 & 0.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristic points in _F-u_ curves. increase in \(u\), the \(F\)-\(u\) curves under push or pull \(u_{\rm t}\) exhibit similar characteristics, which can be divided into three stages. * Elastic stage \(\alpha\): when \(u\) is less than \(u_{\rm a}\), \(F\) and \(u\) exhibit a linear relationship. The sand is in an elastic state, and the stiffness of the curve is \(k\). * Elastoplastic stage \(ab\): when \(u\) is between \(u_{\rm a}\) and \(u_{\rm b}\), the internal stress of the sand is redistributed, and some soil particles slip relatively. The sand enters a plastic state, and the \(k\) gradually decreases. * Failure stage \(bc\): when \(u\) is larger than \(u_{\rm b}\), the sand in the plastic state gradually forms a slip surface. With a rapid increase in \(u,F\) increases slightly. The stiffness of the curve decreases to \(l\). The value of \(F_{\rm u}\) at point \(c\) is the ultimate load. The characteristic points of the \(F\)-\(u\) curves in different test cases and corresponding \(k\) and \(l\) are listed in Table 1. It can be found that with an increase in \(H\), \(F_{\rm a}\), \(F_{\rm b}\), \(F_{\rm u}\), and \(k\) increase, while \(l\) is very small. This is because, in the elastic stage, the movement of the FAS specimen is affected by the friction between the top and bottom surfaces of the FAS specimen and the sand above and below it, as well as the earth pressure at the distal end of the FAS specimen. With an increase in \(H\), the mass of the sand above the FAS specimen increases, resulting in an increment in the friction force between the FAS specimen and the sand, and the earth pressure at the distal end of the FAS specimen. In the failure stage, after the slip surface of the sand is formed, \(F\), the friction force, and the earth pressure on the FAS specimen reach a state of mechanical equilibrium. Therefore, \(F\) largely stops increasing and \(l\) is nearly zero. Under push \(u_{\rm t}\), the increments in \(H\) changing from H0-Push to H31.5-Push and from H31.5-Push to H63-Push are both 31.5 cm and the corresponding \(F_{\rm u}\) values increase by 11.9 kN and 17.9 kN, respectively.