## 6 Conclusions  
A considerable number of 3D finite-element analyses have been performed to investigate the uniaxial capacities and failure mechanisms of tetrapod bucket foundations in undrained clay. Systematic parametric studies were conducted to provide insights into the group effects of tetrapod bucket foundations considering the foundation separation distance ratio (\(s/D\)), embedment depth ratio (\(d/D\)), soil-strength heterogeneity index (\(\kappa\)) and load direction angle (\(\varphi\)). Generalized formulas for the uniaxial capacities of tetrapod bucket foundations considering group effects in undrained clay were proposed based on the finite-element results to provide a fast designing method for engineering designers. 1. The vertical capacity factor of the tetrapod bucket foundations (\(N_{V}\)) increases as \(d/D\) increases, decreases as \(\kappa\) increases and changes quite insignificantly as \(s/D\) increases. \(N_{V}\) almost equals \(N_{V,s}\), and the vertical group effect factor (\(E_{V}\)) is among 0.9-1.0 for all cases in this study. Buckets and soils surrounded by them can be regarded as a whole when resisting vertical loading at a small \(s/D\), while a Prandtl failure mechanism is observed for each bucket at a large enough \(s/D\). The uniaxial vertical capacity of the tetrapod bucket foundations can be calculated through multiplying 4 times of that of a single bucket foundation by \(E_{V}\), which is taken as 0.9 based on conservative estimation. 2. As \(s/D\) increases, the horizontal capacity factor of tetrapod bucket foundations (\(N_{H}\)) firstly enhances perceptibly and finally converges into the maximum horizontal capacity factor of the single bucket foundation (\(N_{Hmax,s}\)) corresponding to the motion mode  
Figure 21: Comparisons of moment capacity factors for tetrapod bucket foundations between finite-element results and fitted curves with various \(d/D\) when (**a**) \(\kappa=0\) and \(\varphi=0\), and (**b**) \(\kappa=10\) and \(\varphi=0\). of pure horizontal displacement. Meanwhile, \(N_{H}\) increases with the increase in \(d\)/\(D\) and decreases with the increase in \(\kappa\). \(N_{H}\) with higher \(d\)/\(D\) or \(\kappa\) increases more visibly, compared to that of the single bucket foundation. The effect of the load direction angle (\(\varphi\)) on \(N_{H}\) can be neglected. A tetrapod bucket foundation is more likely to move horizontally than to rotate, and its rotation angle (\(\theta\)) gradually decreases with the increase in \(s\)/\(D\) and \(\kappa\), as well as the decrease in \(d\)/\(D\) under the ultimate horizontal load. The uniaxial horizontal capacity of the tetrapod bucket foundations can be calculated through multiplying 4 times that of \(H_{max,s}\) by the normalized horizontal group effect factor (\(F_{H}\)), which is among 0.5-1.0 and is influenced by \(s\)/\(D\), \(d\)/\(D\) and \(\kappa\). 3. The moment capacity factor of the tetrapod bucket foundations (\(N_{M}\)) increases quite remarkably as \(s\)/\(D\) increases, and its enhancement is up to 27 fold when \(s\)/\(D\) = 3.5 and \(d\)/\(D\) = 0.25, compared to \(N_{M,s}\). Meanwhile, \(N_{M}\) increases with the increase in \(d\)/\(D\) and decreases with the increase in \(\kappa\). \(N_{M}\) with a smaller \(d\)/\(D\) or larger \(\kappa\) enhances more significantly, compared to that of the single bucket foundation. The tetrapod bucket foundations and soils surrounded by them can be regarded as one foundation, which rotate around a point under ultimate moment loading when \(s\)/\(D\) is small, while its failure mode evolves into a push-pull failure mode at a large enough \(s\)/\(D\). The uniaxial moment capacity of the tetrapod bucket foundations is influenced by \(s\)/\(D\), \(d\)/\(D\), \(\kappa\) and \(\varphi\), and can be calculated through multiplying the moment capacity of the tetrapod bucket foundations in the push-pull failure mode (\(M_{max,pp}\)) by the normalized moment group effect factor (\(F_{M}\)). 4.