## 5 Capacities of Tetrapod Bucket Foundations
### Horizontal Capacities  
#### 5.2.1 Effects of Foundation Separation Distance Ratio on Horizontal Capacities  
If the uniaxial horizontal capacity of tetrapod bucket foundations is denoted as \(H_{ult}\), the horizontal capacity factor of tetrapod bucket foundations can be defined as \(N_{H}=H_{ult}/As_{u0}\). Take \(\varphi=0\) as an example: the horizontal capacities of tetrapod bucket foundations at \(\kappa=10\) are shown in Figure 11.  
It can be observed from Figure 11a that \(N_{H}\) is visibly dependent on the foundation separation distance ratio (\(s/D\)). With the increase in \(s/D\), \(N_{H}\) shows an enhancement trend at first and finally converges into the maximum horizontal capacity factor of the single bucket foundation (\(N_{Hmax,s}=H_{maxs}/A_{s}s_{u0}\)) corresponding to the motion mode of pure horizontal displacement without a rotation angle. \(H_{max,s}\) is the maximum horizontal capacity of the single bucket foundation. Take \(\varphi=0\) for instance: the rotation angles of tetrapod bucket foundations (\(\theta\)) under uniaxial horizontal loading are listed in Table 2. The results show that \(\theta\) decreases with the increase in \(s/D\) because of the increase in the anti-tipping moment, which is mainly caused by the increase in the moment arm. When \(s/D\) is large enough, \(\theta\) is close to 0. Therefore, \(N_{H}\) becomes closer to \(N_{Hmax,s}\) as \(s/D\) increases. The horizontal group  
Figure 10: The magnitude of displacement contours of tetrapod bucket foundations and soils under ultimate vertical loading at \(s/D=1.5\) and \(d/D=0.25\) when (**a**) \(\kappa=0\), (**b**) \(\kappa=1\), (**c**) \(\kappa=2\) and (**d**) \(\kappa=10\).  
effect factor of tetrapod bucket foundations (\(E_{H}=N_{H}/N_{H,s}\)) is shown in Figure 11b. It indicates that \(E_{H}\) increases notably with the increase in \(s/D\) and most of \(E_{H}\) are greater than 1.0. Meanwhile, it can be observed from Figure 11b that the maximum value of \(N_{H}\) is about 2.3 times of \(N_{H,s}\), manifesting that the horizontal capacity of tetrapod bucket foundations greatly enhances with large \(s/D\), compared to that of the single bucket foundation. In order to produce simplified formulas to evaluate the horizontal capacity of tetrapod bucket foundations, the normalized horizontal group effect factor of tetrapod bucket foundations (\(F_{H}=N_{H}/N_{Hmax,s}\)) is defined, as shown in Figure 11c. F\({}_{H}\) firstly increases with the increase in \(s/D\), and finally converges into 1.0.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{s/\(D\)} & \multirow{2}{*}{\(\kappa\)} & \multicolumn{4}{c}{\(\theta\) (\({}^{\circ}\))} \\ \cline{3-6}  & & _d/D_ = **0.25** & _d/D_ = **0.5** & _d/D_ = **0.75** & _d/D_ = **1.0** \\ \hline \multirow{3}{*}{0.75} & 0 & 0.06 & 0.18 & 0.68 & 8.50 \\  & 2 & 0.03 & 0.10 & 0.32 & 2.27 \\  & 10 & 0.02 & 0.08 & 0.26 & 1.87 \\ \hline \multirow{3}{*}{1.0} & 0 & 0.04 & 0.13 & 0.37 & 1.93 \\  & 2 & 0.02 & 0.07 & 0.18 & 1.09 \\ \cline{1-1}  & 10 & 0.02 & 0.06 & 0.15 & 0.90 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Rotation angles of tetrapod bucket foundations under uniaxial horizontal loading.  
Figure 11: Horizontal capacities of tetrapod bucket foundations at \(\kappa=10\): (**a**) horizontal capacity factor, (**b**) horizontal group effect factor and (**c**) normalized horizontal group effect factor.