## 6 Results
### Settlements  
The main reason for reinforcing a road or railway with piles, apart from stabilising the embankment, is to avoid excessive settlements (downward vertical displacements). The numerically simulated settlements on the road in this study were analysed and compared with the criteria for serviceability limit states set by the Swedish Transport Administration in TK Geo 13 [16]. The criteria of interest are the total settlements and the drainage gradient of the road pavement. The total settlement of the pavement is limited to 35 cm for the type of road studied in order to avoid seasonal flooding. The drainage gradient is defined as the inclination of the pavement between the crest and the side of the road. For the studied road, the design drainage gradient is 3.6%. The decrease in design drainage gradient due to settlements is limited to 1.1%, i.e., the final drainage gradient must be at least 2.5% to maintain sufficient water drainage of the pavement surface. The settlements analysed were numerically computed on the crest of the road (point A), at the side of the road (point B), and at the embankment toe (point C), as shown in Figure 1. The differential settlement between points A and B gives a measurement of the change in drainage gradient. Heaving at point C could indicate a potential problem with the stability of the embankment. Differential settlements between point C and points A and B might lead to damage to the geosynthetic reinforcement due to large strains. In Figure 9, the settlements \(u_{v}\) at points A, B and C were plotted against increasing centre-to-centre pile spacing (\(s\)) from 0.8 to 2.0 m for floating and semi-floating pile groups with square and triangular pile arrangements. No significant difference in \(u_{v}\) was found between the modelled square and triangular pile arrangements. Furthermore, \(u_{v}\) in the pavement (points A and B) remained within the serviceability limit state of 35 cm. The maximum values of \(u_{v}\) for floating and semi-floating pile groups were obtained on the crest (point A) of the embankment. As expected, the floating pile groups settled more than the semi-floating pile groups. The magnitude of the differential settlements in Figure 9 between the three points A, B and C did not vary much with the pile spacing \(s\). The largest changes in the differential settlements were observed when increasing the value of \(s\) from 1.4 to 1.5 m and from 1.8 to 2.0 m. In both cases, \(u_{v}\) increased less at point C than at points A and B. The reason is an unchanged number of piles in the two cases at the same time as \(s\) increased (see Table 1), bringing the outermost pile closer to the embankment toe. The differential settlement between points A and B was approximately the same (about 1.5 cm) for both types of pile group and for all values of \(s\). The decrease in drainage gradient was thus  
Figure 9: Settlement (\(u_{v}\)) computed in points A, B and C (Figure 1) with increasing centre-to-centre spacing (\(s\)) for a square (Sq) and triangular (Tri) pile arrangements. Both floating and semi-floating pile groups. approximately 0.3% for all models, which is within the serviceability limit state of 1.1%. No local differential settlements (depressions) between the piles were observed in the pavement in the simulations. For the semi-floating pile group, the differential settlements between points B and C increased from 1.3 cm when \(s\) = 0.8 m to 2.0 cm when \(s\) = 2.0 m. For the floating pile group, it remained almost constant at 1.9 cm for the full range of \(s\). The differential settlements observed in Figure 9 are not of a magnitude that could damage the GR by plastic strains. No heaving was observed at point C, which is good from a stability point of view. The results for \(u_{\
u}\) shown in Figure 9 were compared with \(u_{\
u}\) for the case of no piles in order to quantify the reduction in \(u_{\
u}\) from pile-reinforcing the embankment.