## 6 Results
### Settlements
Two reference simulations were done without piles for the corresponding soil profiles of a floating and a semi-floating pile group; \(u_{v,red}\)% is the average value of the settlement reduction in points A, B and C defined as a percentage  
\[u_{v,red}\%=\frac{1}{3}\bigg{(}\bigg{(}1-\frac{u_{\
u}(A)}{u_{\
u}(A_{0})} \bigg{)}+\bigg{(}1-\frac{u_{\
u}(B)}{u_{\
u}(B_{0})}\bigg{)}+\bigg{(}1-\frac{u _{\
u}(C)}{u_{\
u}(C_{0})}\bigg{)}\bigg{)}\cdot 100 \tag{4}\]  
where \(u_{\
u}(A)\) is \(u_{\
u}\) at point A on the crest of a piled embankment, and \(u_{\
u}(A_{0})\) is \(u_{\
u}\) at point A on the crest of an embankment without pile reinforcement. The quantities \(u_{\
u}(B)\), \(u_{\
u}(B_{0})\), \(u_{\
u}(C)\), and \(u_{\
u}(C_{0})\) follow the same notation for points B and C. For an embankment with no pile group support, \(u_{\
u}\) at points A, B and C was 19, 18 and 12 cm, respectively, for the case of floating piles. The respective values were 17, 15 and 9 cm for the case of semi-floating piles. In Figure 10a, \(u_{v,red}\)% was plotted against \(s\) for floating and semi-floating pile groups with square and triangular pile arrangements. As expected, a semi-floating pile group reduced settlements more than a floating pile group did. However, increasing the value of \(s\) from 0.8 to 2.0 m had twice as large an influence on \(u_{v,red}\)% for semi-floating piles as compared to floating piles. For \(s\) = 0.8 to 1.2 m, \(u_{v,red}\)% remained nearly constant at 43% for the floating piles. Furthermore, for the floating piles, an increase in \(s\) from 1.2 to 2.0 m reduced \(u_{v,red}\)% almost linearly from 43% to 28%. For the semi-floating pile groups, \(u_{v,red}\)% changed almost linearly over the range of modelled values of \(s\), decreasing from 79% at \(s\) = 0.8 m to 45% at \(s\) = 2.0 m.  
The resource efficiency of each installed pile can be quantified by dividing \(u_{v,red}\)% with the number of piles per metre of road \(n_{piles,m}\) (see Table 1). The resulting ratio, \(u_{v,red}\)%/\(n_{piles,m}\), gives an indication of how much each installed pile contributes to the  
Figure 10: (**a**) average settlement reduction as percentage (\(u_{v,red}\)%) with increasing \(s\) and (**b**) ratio of \(u_{v,red}\)% to the number of piles per metre of road (\(n_{piles,m}\)) with increasing \(s\), as well as \(n_{piles,m}\) with increasing \(s\). Square (Sq) and triangular (Tri) pile arrangements. settlement reduction for a given value of \(s\). In Figure 10b, \(n_{piles,m}\) and \(u_{v,red}\%/n_{piles,m}\) were plotted on separate vertical axes against \(s\) for floating and semi-floating pile groups with square and triangular pile arrangements. \(u_{v,red}\%/n_{piles,m}\) increased with the increasing value of \(s\), meaning that each individual pile contributed more to reducing the settlements as \(n_{piles,m}\) was reduced. For both the floating and semi-floating piles, \(u_{v,red}\%/n_{piles,m}\) increased almost linearly from \(s=0.8\) to \(1.4\) m. For \(s>1.4\) m, \(u_{v,red}\%/n_{piles,m}\) still increased, although more slowly than between the simulated values of \(s\). The gain in resource efficiency when increasing the value of \(s\) was less for \(s>1.4\) m compared to what was achieved in the interval \(0.8\leq s\leq 1.4\) m. Thus, the pile spacing where \(s=1.4\) m is interesting as a design value. As previously mentioned, the pile spacing criterion in TK Geo 13 [16] is \(0.8\leq s\leq 1.2\) m. By increasing \(s\) above the maximum value, from \(1.2\) to \(1.4\) m, the simulated value of \(u_{v,red}\%/n_{piles,m}\) increased by almost \(1.3\) times for both the floating and semi-floating piles. The value of \(n_{piles,m}\) decreased from \(9.2\) to \(6.4\) when increasing \(s\) from \(1.2\) to \(1.4\) m, reducing the number of piles by almost one third. Based on these results, it can be concluded that the pile arrangement, square or triangular, has no significant influence on the settlements in the road pavement or embankment toe of a lightly piled embankment.