## 6 Results
### Load Transfer
The average pile efficacy (\(Q_{head,av}\%\)) plotted against \(s\) is shown in Figure 17b and calculated as  
\[Q_{head,av}\%=Q_{head,av}/Q_{pile,av} \tag{5}\]  
where \(Q_{pile,av}\) is the average load over the tributary area (\(s^{2}\)), as seen in Figure 3. The difference in \(Q_{head,av}\) (Figure 17a) between the square and triangular pile arrangements was \(\leq\)3%, leading to the conclusion that the pile arrangement had no significant effect on pile head efficacy. For the modelled uniform embankment with a semi-floating pile group, used for comparison in the previous chapter, the difference in \(Q_{head,av}\) was \(<\)2% between the two pile arrangements. In addition, modelling the pile group as floating instead of semi-floating resulted in a \(<\)3.5% difference in \(Q_{head,av}\) (Figure 17a), and thus had no significant effect on pile head efficacy. The difference in \(Q_{head,av}\) is due to the larger relative displacement between the subsoil and pile head in the semi-floating pile group than in the floating pile group, which lead to a greater arching effect. This partly explains the observed difference in \(N_{\text{pile}}\) and \(N_{pile,max}\%\) between the floating and the semi-floating pile group in Figures 15 and 16. From the results, it can be concluded that the stress distributions shown in Figures 11 and 12 are comparable or deemed equal for the square and the triangular pile arrangements and for both the floating and semi-floating pile groups for a given value of \(s\). Figure 16: Utilisation ratio of the piles as percentage (\(N_{pile,max}\%\)) with increasing \(s\). The structural bearing capacity of 106 kN, European strength class C14 [49], is marked with a dashed line at \(N_{pile,max}\%=100\%\). As seen in Figure 17b, \(Q_{head,av}\)% decreased approximately linearly over the range of \(s\) for all pile groups by almost 25%, from about 60% at \(s\) = 0.8 m to above 35% at \(s\) = 2.0 m. When \(Q_{head,av}\)% = 100%, the sum of the embankment weight and traffic load is carried solely by the piles. When there is no arching or membrane effect, \(Q_{head,av}\)% < 5% for the present study. It should be noted that the lightly piled embankment design with no pile caps results in a small pile coverage ratio (\(\alpha\)), defined as a percentage  
\[\alpha=a^{2}/s^{2}\cdot 100 \tag{6}\]  
where \(a\) is the equivalent square side length of a circular pile head with diameter \(s_{d}\), and is calculated as  
\[a=\sqrt{\frac{(\pi d^{2})}{4}} \tag{7}\]  
As previously mentioned, \(s_{d}\) was set to 200 mm for the timber piles, resulting in a range of \(\alpha\) from 4.9% at \(s\) = 0.8 m to 0.8% at \(s\) = 2.0 m. Subsequently, \(Q_{head,av}\)% ranged from about 60% at \(\alpha\) = 4.9% to above 35% at \(\alpha\) = 0.8%. Similarly, [PERSON] et al. [35] performed DE simulations of a piled embankment with and without GR and for different values of \(\alpha\), and obtained a result of roughly 60% pile efficacy for the simulation with GR and \(\alpha\) = 4.9% (\(a\) = 100 mm and \(s\) = 0.45 m). [PERSON] and [PERSON] [54] carried out a full-scale test on a piled embankment reinforced (\(\alpha\) = 2.8%) with two layers of geogrid, similar to the load distribution layer in Figure 4, and measured 74% pile efficacy. The simulated \(Q_{head,av}\)% in this study was about 55% at \(\alpha\) = 3.1% (\(s\) = 1.0 m), which is significantly less in comparison. However, in the Kyoto Road project by [PERSON] et al. [2] on a monitored timber piled embankment (\(\alpha\) = 4.4%), the pile efficacy was about 38%. Note that the Kyoto Road embankment fill material consisted of a sludge mixture with a friction angle lower than that of the embankment material simulated in this paper. The results shown in Figure 18 are the maximum and average values of the GR tensile load (\(T_{GR,max}\) and \(T_{GR,av}\)) above the pile heads, plotted against the modelled range of \(s\). Modelling the piles in a triangular arrangement instead of a square arrangement increased \(T_{GR,max}\) by 6% and \(T_{GR,av}\) by 7% on average.