## 7 Concluding Remarks
In the GRPSE design, the embankments are in general assumed to be uniform when calculating the arching and membrane effect, and the spreading effect is only considered when calculating the tensile force in the GR. Thus, assuming a uniform embankment in GRPSE design may neglect asymmetrical arch formation caused by the spreading effect of the embankment slopes. The simulations show that the pile arrangement, square or triangular, has no significant influence on the settlements of a lightly piled embankment, nor does the type of pile arrangement have any significant influence on the arching and the membrane effect. These results indicate that the maximum allowable value of \(s\) in TK Geo 13 can increase from 1.2 to 1.6 m without reaching the characteristic bearing capacity of the timber piles. The structural bearing capacity of the GR was far from being exceeded for any value of \(s\). Furthermore, the settlements did not exceed the serviceability limits in TK Geo 13 for the modelled range of \(s\). The settlements of embankments with a floating pile group remained almost constant for \(0.8\leq s\leq 1.2\) m. In contrast, the settlements increased by roughly 30% on average for the semi-floating pile groups when increasing \(s\) from 0.8 to 1.2 m. Thus, it might only be beneficial in terms of settlement reduction to install piles with \(s<1.2\) m if the piles can be driven down to a firm soil layer or bedrock. By increasing \(s\) from 1.2 to 1.4 m, the resource efficiency in terms of settlement reduction per pile increased by 30% for both the floating and semi-floating piles, and the number of piles was reduced by almost one third. Increasing \(s\) above 1.4 m resulted in significantly less gain in resource efficiency. Based on the results, it is recommended to consider setting the TK Geo 13 design criterion of \(s\) to \(0.8\leq s\leq 1.4\) m for lightly piled embankments. It should be noted that the geometry of the FE simulations is exact, which is not the case in reality. There are variations in pile head diameter, pile position and pile curvature, for example. No probabilistic model was used to take these variations into account. The piles can be expected to be driven within \(\pm 5\) cm accuracy of the suggested design criterion of \(s\). In the future, our research group is planning to examine the arching and membrane effect in lightly piled embankments for different embankment heights and locations of the GR, as well as to test the hypothesis of increased allowable \(s\) to 1.4 m. A newly built three-lane motorway is currently being monitored. The monitoring results will be used to calibrate a physical model and an FE model of the motorway embankment. Conceptualization, P.G. and H.M.; methodology, P.G. ; software, P.G. ; validation, P.G. and H.M.; formal analysis, P.G. ; investigation, P.G. ; resources, H.M.; data curation, P.G. ; writing--original draft preparation, P.G. ; writing--review and editing, P.G., H.M. and J.L. ; visualization, P.G. ; supervision, H.M. and J.L. ; project administration, H.M. and J.L. ; funding acquisition, H.M. All authors have read and agreed to the published version of the manuscript. This work was funded by the Swedish Transport Administration (STA) and the Swedish joint research program for road and railway geotechnology, Branschsamverkan i grunden (BIG) [grant number B2015-21]. Not applicable. The data that support the findings of this study are available from the corresponding author upon reasonable request. The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.