# New Displacement Method for Free Embedded Cantilever Walls in Sand
### Feasibility of Cantilever Walls with Large Heights  
In this study, horizontal displacement formulae have been proposed for wall heights ranging from 1 to 8 m. The baseline configurations for each wall height, along with the relative wall rotation (WR), are presented in Table 8. It is important to note that the internal friction angle for the baseline configurations is set to 35 degrees, which corresponds to the internal friction angle of medium sand. According to the recommendations in Eurocode 7 [30], Anne H, a wall rotation (WR) of 0.002 is considered acceptable for many structures. By referring to Table 8, it can be observed that the WR values for wall heights between 1 and 6 m are safely below the maximum recommended value (MRV) of 0.002. However, for wall heights exceeding 6 m, the WR abruptly increases and approaches the MRV of 0.002. This implies that designing cantilever walls higher than 6 m requires extra caution. For walls higher than 6 m, it is crucial to have sufficiently firm soil present around the wall and ensure that the wall rotation remains significantly lower than the recommended limit. Therefore, careful consideration and additional measures may be necessary when designing and constructing cantilever walls higher than 6 m.  
Figure 15: Influence coefficients of the wall in 4 m height and 4 m embedment depth.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline No & H (m) & d (m) & \(\gamma_{1}\) (\(\mathrm{\SIUnitSymbolMicro N/m^{3}}\)) & \(\gamma_{2}\) (\(\mathrm{\SIUnitSymbolMicro N/m^{3}}\)) & \(\gamma_{3}\) (\(\mathrm{\SIUnitSymbolMicro N/m^{3}}\)) & \(\gamma_{4}\) (\(\mathrm{\SIUnitSymbolMicro N/m^{3}}\)) & E\({}_{1}\) (\(\times 10^{3}\) kPa) & E\({}_{2}\) (\(\times 10^{3}\) kPa) & E\({}_{3}\) (\(\times 10^{3}\) kPa) & E\({}_{4}\) (\(\times 10^{3}\) kPa) \\ \hline
1 & 1 & 1 & 20 & 20 & 20 & 20 & 50 & 50 & 50 & 50 \\
2 & 2 & 2 & 20 & 20 & 20 & 20 & 50 & 50 & 50 & 50 \\
3 & 3 & 3 & 20 & 20 & 20 & 20 & 50 & 50 & 50 & 50 \\
4 & 4 & 4 & 20 & 20 & 20 & 20 & 50 & 50 & 50 & 50 \\
5 & 5 & 5 & 20 & 20 & 20 & 20 & 50 & 50 & 50 & 50 \\
6 & 6 & 6 & 20 & 20 & 20 & 20 & 50 & 50 & 50 & 50 \\
7 & 7 & 7 & 20 & 20 & 20 & 20 & 50 & 50 & 50 & 50 \\
8 & 8 & 8 & 20 & 20 & 20 & 20 & 50 & 50 & 50 & 50 \\ \hline No & L (\(\mathrm{\SIUnitSymbolMicro Pa}\)) & \(\phi_{1}\) (o) & \(\phi_{2}\) (o) & \(\phi_{3}\) (o) & \(\phi_{4}\) (o) & El (\(\mathrm{\SIUnitSymbolMicro N/m^{3}}\)) & \(\mathit{disp_{wall}}\) & \(\mathit{disp_{wall}}\) & Relative Wall Rotation \\ \hline
1 & 0 & 35 & 35 & 35 & 35 & 2,500,000 & 0.0002 & 0.0002 & 0.0001 & \\
2 & 0 & 35 & 35 & 35 & 35 & 2,500,000 & 0.0013 & 0.0008 & 0.0003 & \\
3 & 0 & 35 & 35 & 35 & 35 & 2,500,000 & 0.0032 & 0.0017 & 0.0005 & \\
4 & 0 & 35 & 35 & 35 & 35 & 2,500,000 & 0.0058 & 0.0032 & 0.0007 & \\
5 & 0 & 35 & 35 & 35 & 35 & 2,500,000 & 0.0087 & 0.0047 & 0.0008 & \\
6 & 0 & 35 & 35 & 35 & 35 & 2,500,000 & 0.0133 & 0.0064 & 0.0012 & \\
7 & 0 & 35 & 35 & 35 & 35 & 2,500,000 & 0.0223 & 0.0096 & 0.0018 & \\
8 & 0 & 35 & 35 & 35 & 35 & 2,500,000 & 0.0314 & 0.0124 & 0.0024 & \\ \hline \hline \end{tabular}
\end{table}
Table 8: Baseline configurations of the walls and the corresponding wall rotations.