## 6 Results
### Load Transfer  
The piles in a GRPSE construction need to be able to carry the load that is transferred onto the piled heads by the arching and membrane effects (\(Q_{head}\)), as well as any load from negative shaft friction along the pile shaft. Thus, it is important to analyse at which value of \(s\) the total axial pile load (\(N_{pile}\)) exceeds the structural bearing capacity of the timber piles; it is also of interest to analyse \(Q_{head}\) in order to quantify the arching and membrane effect. The average distribution of \(N_{pile}\) in the three modelled pile rows (Figure 3) is summarised in Figure 15 for both the floating and semi-floating pile groups, with \(0.8\leq s\leq 0. 2.0 m. The difference in \(N_{pile}\) between the square and triangular pile arrangements was insignificant (<3%) for the range of \(s\). Thus, the values of \(N_{pile}\) shown in Figure 15 are the average results of the square and triangular pile arrangements. The difference in the value of \(N_{pile}\) between the floating and semi-floating pile groups is mostly due to a difference in maximum pile toe resistance, set to 0 kN for the floating pile group and 14 kN for the semi-floating pile group. In addition, due to the slope of the embankment the maximum value of \(N_{pile}\) in a pile row (\(N_{pile,max}\)) was observed underneath the crest of the embankment, with the exception of \(s=0.8\) m and \(s=1.0\) m for the floating pile group. The distribution of \(N_{pile}\) along a pile row was irregular, with a larger force acting on the outermost piles than on the second-outermost piles, \(s\leq 1.4\) m for the floating pile group and \(s\leq 1.0\) m for the semi-floating pile group. As previously shown, the resource efficiency in terms of settlement reduction (\(u_{v,red}\%/n_{piles,m}\)) was almost linear (Figure 10b) for \(s\leq 1.4\) m, both for the floating and the semi-floating pile groups. Along with the distribution of \(N_{pile}\) in Figure 15, this suggests that the load bearing characteristics of the pile group were those of a combined unit for \(s\leq 1.4\) m and those of single piles for \(s>1.4\) m.  
The pile utilisation ratio as percentage (\(N_{pile,max}\%\)), defined as \(N_{pile,max}\) divided by the structural bearing capacity of 106 kN, is plotted against s in Figure 16. \(N_{pile,max}\%\) changed almost linearly for \(0.8\leq s\leq 2.0\) m, increasing from approximately 33% at \(s=0.8\) m for all pile groups to approximately 114 and 120% at \(s=2.0\) m for the floating and semi-floating pile groups, respectively. The structural bearing capacity was reached (\(N_{pile,max}\%\geq 100\%\)) in one or more piles, for \(s>1.6\) m in the case of semi-floating piles and for \(s>1.7\) m in the case of floating piles. The maximum allowable value of \(s\), in terms of structural bearing capacity, depends on the chosen factor of safety (\(F_{S}\)) defined as the ratio of the structural bearing capacity to \(N_{pile,max}\). Setting \(F_{S}\) equal to 1.2 or 1.3, for example, results in a maximum allowed \(N_{pile}\) of roughly 88 kN or 81 kN (\(N_{pile,max}\%=83\%\) or 76%), respectively. This corresponds to an \(s\) equal to 1.5 m (\(F_{S}=1.2\)) or 1.4 m (\(F_{S}=1.3\)). Figure 15: Axial pile load (\(N_{pile}\)) across a pile row (as an average of the three pile rows modelled) in the modelled floating and semi-floating pile groups, showing the results of the left and right half of each respective pile group. The horizontal axis denotes the horizontal distance from the embankment longitudinal centre line. The structural pile capacity of 106 kN, European strength class C14 [49], is marked with a dashed horizontal line. The average load transferred onto the pile heads from arching and membrane effects (\(Q_{head,av}\)) is plotted against \(s\) in Figure 17a. The proportion of embankment weight and traffic load carried by the piles is often referred to as pile efficacy in the literature ([PERSON] and [PERSON], 2020). Pile efficacy can be seen as an efficiency of the GRPSE design.