## 5 Numerical Modelling of Light Embankment Piling
### The Finite Element Model
#### 5.1.2 The Material Parameters
Failure of the pile in compression was taken into consideration in this paper. The interaction of an embedded beam and the surrounding soil is described by a linear elastic behaviour with a finite strength (geotechnical bearing capacity). During elastic loading, the mobilised shaft and toe resistance are based on the shear modulus of the pile-soil-interface; in the simulated case, they are set equal to the shear modulus of the surrounding soil. At elastic loading the total axial load (\(N_{pile}\)) equals the sum of the mobilised shaft and toe resistance. At plastic loading of the pile, i.e., the geotechnical bearing capacity, the shaft bearing capacity is either a direct input value or a computed value based on the shear strength of the surrounding soil. In this study, the shaft bearing capacity (\(R_{s}\)) of each pile was calculated based on the undrained shear strength according to [PERSON] et al. [48] from CPT results. The value of (\(R_{s}\)) was assumed as linearly increasing over the pile length. The toe bearing capacity (\(R_{t}\)) was calculated based on the friction angle of the embankment material, according to [PERSON] et al. [48]. The geotechnical \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Unit** & \(\mathbf{S}_{\mathbf{top}}\) & \(\mathbf{S}_{\mathbf{bottom}}\) & _siTi_ & _Granular_ \\ \hline Material model & - & SS & SS & M-C & M-C \\ Drainage type & Undrained (A) & Undrained (A) & Undrained (A) & Drained \\ Unsaturated unit weight & kN/m\({}^{3}\) & 15 \({}^{\text{a}}\) & 13.4 \({}^{\text{a}}\) & 20 \({}^{\text{d}}\) & 20 \({}^{\text{d}}\) \\ Saturated unit weight & kN/m\({}^{3}\) & 15 \({}^{\text{a}}\) & 13.4 \({}^{\text{a}}\) & 20 \({}^{\text{d}}\) & 23 \({}^{\text{d}}\) \\ Modified compression index & - & 0.117 \({}^{\text{c}}\) & 0.136 \({}^{\text{c}}\) & - & - \\ Modified swelling index & - & 0.035 \({}^{\text{c}}\) & 0.05 \({}^{\text{c}}\) & - & - \\ Young’s modulus & MPa & - & - & 10 \({}^{\text{d}}\) & 50 \({}^{\text{d}}\) \\ Poisson’s ratio & - & - & - & 0.25 \({}^{\text{d}}\) & 0.25 \({}^{\text{d}}\) \\ Poisson’s ratio, unload-reload & - & 0.15 \({}^{\text{d}}\) & 0.15 \({}^{\text{d}}\) & - & - \\ Effective friction angle & \({}^{\text{o}}\) & 36 \({}^{\text{b}}\) & 35 \({}^{\text{b}}\) & 40 \({}^{\text{d}}\) & 45 \({}^{\text{d}}\) \\ Effective cohesion & kPa & 3 \({}^{\text{b}}\) & 3 \({}^{\text{b}}\) & 0 \({}^{\text{d}}\) & 0 \({}^{\text{d}}\) \\ Initial void ratio & - & 2.18 \({}^{\text{a}}\) & 2.18 \({}^{\text{a}}\) & 0.5 \({}^{\text{e}}\) & 0.5 \({}^{\text{e}}\) \\ Overconsolidation ratio, OCR & - & 1.0 & 1.0 & 1.0 & 1.0 \\ Pre-overburden pressure, POP & kPa & 38 \({}^{\text{c}}\) & 41 \({}^{\text{c}}\) & 0 & 0 \\ Isotropic permeability & m/day & 2.16 \(\times\) 10\({}^{-4}\) \({}^{\text{c}}\) & 3.12 \(\times\) 10\({}^{-4}\) \({}^{\text{c}}\) & 2.27 \(\times\) 10\({}^{-2}\) \({}^{\text{e}}\) & 0.6 \({}^{\text{e}}\) \\ \hline \hline \end{tabular} Note: \({}^{\text{a}}\) represents results from undisturbed piston sample tests according to [PERSON] [47]; \({}^{\text{b}}\) represents results from CPT tests; \({}^{\text{c}}\) represents results from CRS; \({}^{\text{d}}\) represents values of parameter suggested by [PERSON] [47]; \({}^{\text{e}}\) represents values of parameter suggested by [PERSON] et al. [43].  
\end{table} 
Table 2: Values of soil material parameter. bearing capacity (\(R_{pile}\)) of an embedded beam with linearly increasing shaft resistance is calculated as  
\[R_{pile}=R_{t}+\frac{1}{2}L_{pile}(R_{s,head}+R_{s,toe}) \tag{2}\]  
with \(R_{t}\) set to 14.0 kN for the semi-floating pile group and set to zero for the floating pile group. \(R_{s,head}\) is the shaft bearing capacity at the pile head, set to 14.4 kN/m, and \(R_{s,toe}\) is the shaft bearing capacity in level with the pile toe, set to 15.6 kN/m. Thus, the resulting \(R_{pile}\) becomes 209 kN for the semi-floating pile group and 195 kN for the floating pile group.