## 6 Results
### Comparison with Analytical Models
In the Extended Carlsson, SINTEF and H&R model, \(T_{GR,\ S}\) is calculated as  
\[T_{GR,S}=K_{a}H\bigg{(}\frac{1}{2}\gamma H+q\bigg{)} \tag{8}\]  
where \(K_{a}\) is the coefficient of active earth pressure, \(H\) is the embankment height of 2.5 m, \(\gamma\) is the unit weight of the embankment material (calculated as 21.7 kN/m\({}^{3}\) for the partially saturated embankment), and \(q\) is the surcharge (traffic) load of 15 kPa, resulting in \(T_{GR,S}=18.1\) kN/m. In the [PERSON] and CA models, \(z\) is subtracted from \(H\), which resulted to \(T_{GR,S}=13.1\) kN/m. The Extended Carlsson, SINTEF, and H&R models, and their corresponding standards or recommendations consider no subsoil support. A void is assumed to form underneath the GR due to soil consolidation and creep strains. That means that the entire embankment weight and surcharge load are transferred onto the pile heads, directly through the arching effect and indirectly through the membrane effect. Thus, \(Q_{head}\)% = 100% for the Extended Carlsson, SINTEF and H&R models. \(T_{GR,M}\) is based on the geometry, load on the GR, GR stiffness, and maximum GR strain (\(\epsilon_{GR,max}\)). The value of \(\epsilon_{GR,max}\) is chosen based on the allowed short- and long-term strains. \(\epsilon_{GR,max}\) was set to 6% for the calculations with the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Guideline** & **Type** & **Pile Arrangement** & **Arch Shape** & **Subsoil Support** \\ \hline Extended Carlsson [26] & TR Geo 13 [24] & Rigid & Square & Triangular & None \\ SINTEF [27] & & Rigid & Square & Triangular & None \\ Hewlett \& Randolph (H&R) [29] & BS8006 [22] \& ASIRI [30] & LE & Square & Semi-circle & None \\ Zaeske [31] & EBGEO [32] & LE & Square/ & Non-concentriclubin & \\  & & & liubinTriangular a  & semi-ellipses & Subgrade modulus, \(k_{s}\) \\ \multirow{2}{*}{Concentric Arches (CA) [8]} & CUR226 [34] & LE & Square & Concentric & \\  & & & semi-circles & \\ \hline \hline \end{tabular} Note: a represents a 45\({}^{\circ}\) rotated square grid. LE = Limit equilibrium.  
\end{table} 
Table 3: Summary of the analytical models used for comparison and the guidelines (or standards) they are incorporated in. Extended Carlsson, SINTEF, and H&R model, in accordance with the long-term criteria in TR Geo 13, the Nordic guidelines, BS8006, and ASIRI. For the H&R model calculations, the load on the GR was set to the minimum load prescribed in BS8006, which is equivalent to 15% of the embankment weight and the surcharge load. Both the Zaeske and the CA models take subsoil support into consideration. \(T_{GR,M}\), is calculated in a fashion similar to the Extended Carlsson, SINTEF, and H&R models, except that \(\varepsilon_{GR,max}\) is calculated instead of selected. The value of \(\varepsilon_{GR,max}\) is determined at vertical equilibrium between the loads acting on the GR and the sum of the GR reaction force and the subsoil support. The subsoil support is based on the modulus of subgrade reaction (\(k_{s}\)) of the subsoil, which can be set to zero if a void is expected to form below the GR. Based on oedometer tests with a constant rate of strain, \(k_{s}\) was set to 304 kN/m\({}^{3}\) for the Zaeske model and 151 kN/m\({}^{3}\) for the CA model. \(k_{s}\) was greater for the Zaeske model, as the model considers the stiffness and thickness of the embankment fill under the elevated GR. Figure 19 shows the analytically and numerically determined values of \(Q_{head}\) plotted against the pile centre-to-centre distance (\(s\)). The numerical results are the average values of \(Q_{head}\) below the pavement for the square and triangular pile arrangements. The analytical results of the Zaeske model for the square and triangular pile arrangement are denoted as \"Zaeske(Sq)\" and \"Zaeske(Tri)\", respectively. As previously mentioned, the analytical models included in this paper assume a uniform embankment height equal to the embankment crest height.