## 7 Concluding Remarks  
The objective of the presented study was to evaluate the current design criteria in the Swedish national standards, TK Geo 13 [16], in terms of optimal pile arrangement (square or triangular) and centre-to-centre distance pile spacing (\(s\)), in order to reduce the amount of timber piles used in light embankment piling. The hypothesis was that a triangular pile arrangement would result in the most stable arches and that the value of \(s\) could be greater than the upper limit of the TK Geo 13 design criteria of \(0.8\leq s\leq 1.2\) m. The evaluation of the design criteria was done by three-dimensional FE simulations of a typical lightly piled road embankment. The parameters used in the evaluation included the differential and total settlements, axial pile load, GR tensile load, and formation of arches, with a focus on resource efficiency. The modelled value of \(s\) ranged from 0.8 to 2.0 m, including the \begin{table}
\begin{tabular}{c c c} \hline \hline  & \(\mathbf{H}\) & \(\mathbf{s_{max}}\) [m] \\ \hline TR Geo 13 [24] & \(H\geq 1.2(s-a)\) & 2.26 \\ BS8006 [22] & \(H\geq 0.7(s-a)\) & 3.75 \\ EBGEO [32] & \(H\geq 0.8(sd-d)\) & 2.35 \\ CUR226 [34] & \(H\geq 0.66(sd-d)\) & 1.66  \\ \multicolumn{3}{c}{Note: \({}^{\ast}\) represents a triangular pile arrangement, for which \(s_{d}=2s\).} \\ \end{tabular}
\end{table} 
Table 4: Maximum value of \(s\) (\(s_{max}\)) for \(H\) = 2.5 m, calculated using geometrical limits in the guidelines studied. Figure 20: Comparison of the maximum tensile load in the GR (\(T_{GR,max}\)) from the numerical and analytical results, plotted against \(s\). TK Geo 13 design criterion of \(0.8\leq s\leq 1.2\) m. Both floating and semi-floating pile groups were modelled, with either square or triangular pile arrangements, resulting in 38 different cases in total. The limiting states were set as the maximum allowed total and differential settlements in TK Geo 13 as well as the structural bearing capacity of the piles and GR. A state-of-the-art study was carried out on the mechanisms of load transfer in GRPSE, as well as the GRPSE guidelines and analytical models used in practice. The numerical results from FE simulations were compared and validated against results from five analytical models implemented in European national standards or recommendations, namely, the Extended Carlsson model by [PERSON] et al. [26] and the Concentric Arches (CA) model by [PERSON] [8], the former being the prescribed analytical model in TR Geo 13 [24] for the design of lightly piled embankments. The results of the comparison show that the numerical simulations are reliable in terms of load distribution in the embankment. The numerical results of the GR tensile load were low in magnitude in comparison with the analytical results, but deemed reasonable. Overall, the Extended Carlsson model greatly overestimated the numerical results. Thus, it is recommended to use the CA model primarily instead of the Extended Carlsson model for the design of lightly piled embankments. However, the simpler Extended Carlsson model could still be used for a first estimation when designing them. Mostly triangular arches were observed between the piles, due to lack of differential settlements between the piles and subsoil for semi-circular arches to form. Stable arches should in the present study form for \(s\leq 1.6\) m, following the geometrical limits of the studied national standards and recommendations. The simulations showed no significant arch instabilities for the modelled range of \(s\), i.e., \(0.8\leq s\leq 2.0\) m. However, the slopes of the embankment had a significant influence on the overall arch formation. Due to the spreading effect of the embankment slopes arch formation was asymmetrical, with arches primarily forming in the longitudinal road direction. By modelling an embankment with uniform height instead, the arch formation was symmetrical in the transversal and the longitudinal road directions. The overall arching effect was also greater compared with the sloped embankment.