## 6 Results
### Comparison with Analytical Models
Hence, the analytical models primarily estimate the load distribution below the pavement of the embankment. Thus, the numerical results shown in Figure 19 are based on the average embankment height below the pavement. The weight of the soil beneath the arches (\(W_{sub}\)) is excluded from the calculation results shown in Figure 19 for the Extended Carlsson, SINTEF, and H&R models. Note that this underestimates the values of \(Q_{head}\) for these three models, since \(Q_{head}\) is normally set equal to the tributary load, defined as \((\gamma H+q)\cdot s^{2}\), according to the respective guideline in Table 3. For the Zaeske and CA models, \(Q_{head}\) in Figure 19 is the sum of the arched load (\(Q_{archal}\)) and the vertical component of \(T_{GR,max}\) (\(T_{V}\)) along the pile head perimeter. Unlike in CUR226, \(T_{V}\) is not explicitly calculated in EBGEO. Thus, the Zaeske model results of \(T_{V}\) were calculated using the methods in CUR226, combined with [PERSON] (2001). As shown in Figure 19, the analytical results of \(Q_{head}\) for the Extended Carlsson, SINTEF, and CA models were larger than the numerical results for all values of \(s\). The results of the CA model almost followed the same trend as the numerical results, with an approximately 55% to 30% larger value of \(Q_{head}\) at \(s\) = 0.8 to 2.0 m. The results of the Extended Carlsson and SINTEF models followed a similar trend as the numerical results, although the difference increased more than the CA results with increasing value of \(s\). The results of the SINTEF model were constant for \(s\geq 1.6\) m due to the calculated arch becoming taller than the embankment. The results of the H&R and Zaeske(Sq) models showed a similar trend, and were the closest to the numerical results for the full range of \(s\). The results of the Zaeske(Tri) model of \(Q_{head}\) were the closest to the numerical results for \(s\leq 1.3\) m. Contrary to the numerical results, the results of the Zaeske model showed much smaller values of \(Q_{head}\) in the triangular pile arrangement than in the square pile arrangement. In general, both of the numerical results of \(Q_{head}\) were lower than the analytical results for \(s<1.6\) m. In the simulations, full arching or fully mobilised soil shear strength was not achieved, as the differential settlements between the pile heads and the subsoil were too small. In comparison, the analytical models assume full arching to be on the safe side with regard to the design axial load per pile. Thus, the numerical results were closer to the analytical results for \(s\geq 1.6\) m, as the differential settlements between the pile heads and the subsoil became larger. Figure 20 shows the resulting values of \(T_{GR,max}\) for the modelled range of \(s\). In the numerical results, \(T_{GR,max}\) is taken as the average value of the quantity above those pile heads that are located below the pavement. As seen in Figure 20, the Extended Carlsson, SINTEF, and H&R models give a much greater increase in \(T_{GR,max}\) than the numerical results for an increasing value of \(s\), which is due to the exclusion of subsoil support in these models. The results of the Zaeske(Sq) and CA models show a similar trend to the numerical results for the range of \(s\), with the results of the CA model being closer in magnitude to the numerical results. The values of \(T_{GR,max}\) were lower for Zaeske(Tri) than for Zaeske(Sq), since the sum of \(T_{GR,M}\) and \(T_{GR,S}\) in the transversal direction of the road was lower than \(T_{GR,M}\) in the longitudinal direction with the triangular pile arrangement. The Zaeske(Tri) results of \(T_{GR,max}\) decreased for \(s>1.5\) m as the long diagonal of the rhombus-shaped arch base (length of \(2s\)) became too great in relation to the embankment height to support a stable arch. However, the numerical results showed no arch instability for any value of \(s\) with the triangular pile arrangement.