## 6 Results
### Comparison with Analytical Models  
The numerical results were compared with results from analytical calculations, as no field measurements were conducted on the studied lightly piled embankment. Although the Extended Carlsson model [23] is the analytical model recommended in TR Geo 13 [16] for the design of lightly piled embankments, more advanced models were also included in the comparison in order to investigate their suitability for this type of GRPSE. Several analytical models for the design of GRPSE exist, and several of them represent national standards or recommendations. The analytical models considered most interesting for the present study are presented in Table 3. The Swedish guidelines TR Geo 13 [24] in combination with the Nordic guidelines [23] were used for the calculations with the Extended Carlsson model [26] and the SINTEF model [27]. The British standards BS8006 [22] were used for calculations with the H&R model [29]. The French guidelines ASIRI [30] were taken into consideration as a complement to BS8006, as the H&R model is also incorporated into ASIRI. The German recommendations EBGEO [32] were used for the calculations with the Zaeske model [32]. The calculations with the Concentric Arches (CA) model were done according to the Dutch guidelines CUR226 [34]. The analytical models are ordered in Table 3 according to their complexity, with the Extended Carlsson model being the simplest and the CA model the most advanced. The results of the analytical calculations were  
Figure 18: The maximum GR tensile load (\(T_{GR,max}\)) and average GR tensile load (\(T_{GR,av}\)) plotted against \(s\). compared to the numerical results on pile head load (\(Q_{head}\)), pile efficacy (\(Q_{head}\)%), and maximum GR tensile load (\(T_{GR,max}\)). Among the analytical models included in the comparison with the numerical model, the [PERSON] model is the only one that supports a triangular pile arrangement. However, the only triangular pile arrangement supported in EBGEO is a square pile arrangement rotated 45 degrees. Thus, the formulas in Zaeske [31] for a triangular pile arrangement were used, as they support the geometry of the TK Geo 13 triangular pile arrangement utilised in this study. Note that ASIRI presents geometrical recommendations but no analytical models for triangular pile arrangements. Furthermore, the Zaeske model is the only one of the included analytical models that takes into consideration an elevated GR, i.e., a vertical distance \(z\) between the pile head and the GR layer, when calculating the vertical stresses on the GR. The EBGEO [32] contains recommendations for GR elevations; however, no elevation is included as a variable when calculating the vertical stress on the GR. Thus, the vertical stresses on the GR were calculated using the formulas derived by [PERSON] [31] for vertical stresses underneath the arch at \(z\) metres above the pile heads (where \(z=0\) m is in level with the pile heads), which are based on the same mechanical principles as the formulas prescribed in EBGEO. As previously mentioned, \(z=0.45\) m for the numerically modelled lightly piled embankment. According to the analytical models included in the comparison and the corresponding guidelines (Table 3), the calculated value of \(T_{GR,max}\) is the sum of the tensile load in the GR due to the membrane effect (\(T_{GR,M}\)) and the added tensile load in the GR due to the spreading effect (\(T_{GR,S}\)) in the transversal road direction. The calculation of \(T_{GR,\ M}\) differs between the included analytical models, and each method is briefly described further below. \(T_{GR,\ S}\) is calculated similarly for all of the analytical models.