## 5 Numerical Modelling of Light Embankment Piling
### The Finite Element Model
#### 5.1.2 The Material Parameters  
Field and laboratory test results from the site showed three main soil layers, as seen in Figure 6: a top layer of sulphide-bearing silt (\(St_{top}\)) at a depth of 0 to 5 m, a middle layer of silty sulphide clay (\(St_{bottom}\)) from 5 m, and a bottom layer of silty glacial till (\(siTi\)), typically from 13 m downwards. The semi-floating pile group was assumed to be driven 30 cm into the \(siTi\)-layer, resulting in a modelled pile length (\(siTi\)) of 13 m. For the floating pile group the same pile length was used, while the layer of \(St_{bottom}\) was extended to a depth of 26 m.  
The sulphide soil (\(St_{top}\) and \(St_{bottom}\)) was modelled using the Soft Soil (SS) model, as this model was developed for soft soils under large compression. Most of the deformations were expected to take place within the soft soil layers; thus, both the \(siTi\) and the granular embankment material (_Granular_) were modelled with the simpler Mohr-Coulomb (M-C) model. The values of the soil material parameters are shown in Table 2. Soil materials \(St_{top}\), \(St_{bottom}\) and \(siTi\) were modelled taking excess pore pressure into account (\"Undrained (A)\"). For soil material _Granular_ the excess pore pressure was assumed as zero (\"Drained\"). The shear strength of all soil materials was based on effective strength parameters. How each parameter value was evaluated is denoted in Table 2. The layers of \(Su_{top}\), \(St_{bottom}\) and \(siTi\) were assumed to be fully saturated due to the shallow groundwater level. Thus, the unsaturated unit weight was set to equal the saturated unit weight for the three soil materials. The preconsolidation pressure of the sulphide soil layers was almost constant over the examined depth. Thus, pre-overburden pressures were assigned to the sulphide soils instead of overconsolidation ratios. Figure 8: Resulting pile head load (\(Q_{head}\)) and \(\sigma_{1}^{\prime}\) -vectors (red lines) in the embankment above the pile head for a pile modelled as (**a**) an embedded beam (EB), (**b**) an EB with extension, (**c**) an EB with plate, and (**d**) a volume pile. Vertical cross-section halfway between two adjacent piles in a corresponding square pile arrangement (\(s\) = 1.4 m). The direction of the \(\sigma_{1}^{\prime}\)-vectors is outlined with dashed lines. The embankment in the case study was reinforced with two biaxial geotextiles as GR, the bottom layer being stiffer in the transversal direction, and the upper one being stiffer in the longitudinal direction. The vertical distance between the two layers was too narrow in relation to the overall model size to maintain sufficient mesh quality. Thus, the two layers of GRs were combined in the numerical model to a single layer of linearly elastic GR and placed in the middle between the existing layers (0.45 m above the pile heads), with an equivalent stiffness of 2200 kN/m and 112 kN/m tensile strength. The stiffness and strength of the GR matched the material properties of the geotextile used in the case study. A 0.15 m thick interface was added to both sides of the modelled GR. Timber piles have a naturally tapered shape; however, because the tool of embedded beams is limited to constant cross sections, the simulated timber piles were modelled with a constant diameter (\(s_{d}\)). \(s_{d}\) was set to 200 mm based on the minimum allowed toe diameter of 150 mm [16] and on the natural tapering of the Swedish timber piles. According to the survey in [PERSON] et al. [21], the natural tapering of Swedish spruce and pine is equal to 8 mm difference in diameter per metre. The ultimate bearing capacity of the modelled piles was chosen as the smallest value of the geotechnical bearing capacity and the structural bearing capacity. The geotechnical bearing capacity of a pile is defined as the load that can be transferred from the pile onto the adjacent soil, i.e., the sum of the shaft and toe bearing capacity. The structural bearing capacity is the load at which the pile itself goes to failure.