## 4 Related International Guidelines and Research
In accordance with the Nordic guidelines, the Norwegian Public Roads Administration (NPRA) prescribes the Extended Carlsson model in the Norwegian guidelines, Handbok V221 [28]. Among the other European national standards and recommendations for geotechnical engineering, there exist several limit equilibrium (LE) models for the design of GRPSE. To the best of the authors' knowledge, aside from the Extended Carlsson model the three most commonly used models for GRPSE design are: (1) The H&R model by [PERSON] [29], used in the British BS8006 [22] and the French ASIRI [30]; (2) the Zaeske [31] model, used in the German EBGEO [32]; and (3) the Concentric Arches (CA) model by [PERSON] [8], implemented in the Dutch CUR226 [33; 34]. All three models consider the transfer of the load through the arch in limit equilibrium, with the difference being the formation of the arch. The H&R model assumes a single semi-circular arch between the piles, the [PERSON] model assumes nonconcentric semielliptical arches, and the CA model assumes concentric semicircular arches. The H&R model considers no subsoil support, whereas the Zaeske and CA models take subsoil support into consideration. Numerical analyses of GRPSE have been performed more often in recent years, both in the design of single cases and in the verification of new analytical models. [PERSON] and [PERSON] [6] coupled discrete element (DE) and FE (DE modelled soil particles and FE modelled GR), with an emphasis on the membrane effect. [PERSON] [31] and [PERSON] [8] used the FE method to verify the shape of the arches assumed in the [PERSON] and CA models. [PERSON] et al. [35] studied the formation of soil arching in GRPSE using DE method simulations. [PERSON] and [PERSON] [36] observed in their FE analysis that the arching effect is not instantaneous, and that the arches fully develop during the consolidation process after final construction. All of these studies show that it is possible to clearly visualise the formation of arches with numerical simulations. The effective major principal stress (\(\sigma_{1}^{\prime}\)) vectors will align tangentially to the arch [8; 31; 36] and the effective vertical stress (\(\sigma_{v}^{\prime}\)) will reduce underneath the arches and concentrate around the piles [37], as illustrated in Figure 5.  
[PERSON] et al. [38] observed a triangular arch in an unreinforced piled embankment, i.e., no GR, by geotechnical centrifuge trapdoor tests and DE analysis and assuming uniform displacement between the piles. Under similar conditions, [PERSON] et al. [39] also observed triangular arch formation. [PERSON] et al. [40] also used centrifuge trapdoor tests, and showed that the arch in an unreinforced piled embankment changes from curved to triangular, with increasing settlement of the soil beneath the arch. With one layer of GR lying directly on the pile heads, [PERSON] and [PERSON] [41] observed the formation of arches in relation to the shear stresses in the load distribution layer in their FE analysis. They observed formation of triangular arches prior to reaching the maximum shear strength, i.e., at ultimate limit state (ULS). Concentric semi-elliptical arches were observed when the subsoil support was removed and the mobilised shear stress reached the maximum shear strength (ULS was reached). In practice, road and railway construction design aims to not reach ULS in order to avoid differential settlements at the surface of the embankment. Semi-elliptical concentric arches were also observed by [PERSON] et al. [39] in their geotechnical centrifuge trapdoor tests when placing one layer of GR at the base of the embankment and removing the subsoil support (by lowering the trapdoor). Nevertheless, no differential settlement developed at the surface. [PERSON] et al. [37] concluded that the height of a geosynthetic-reinforced embankment needs to be at least 1.5 times the clear spacing between pile caps to avoid differential settlements at the surface. From the combined results of [PERSON] and [PERSON] [41] and [PERSON] et al.