## 5 Finite Element Modelling of the Two Embarments
### Material Model Parameters
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Depth [m]** & **Soil Strata** & \(\kappa\) [\(-\)] & \(\lambda\) [\(-\)] & \(M\) [\(-\)] & \(\phi_{C}^{*}\) [\(-\)] & \(\phi_{E}^{*}\) [\(-\)] \\ \hline
0.0–1.5 & Surface clay layer & 0.025 & 0.25 & 1.6 & 39.17 \\ \hline
1.5–4.0 & & & 0.107 & 1.07 & & \\
4.0–6.0 & Soft silty clay & 0.119 & 1.19 & & & \\
6.0–8.0 & & & 0.084 & 0.84 & 1.6 & 39.17 \\
8.0–9.8 & & & 0.066 & 0.66 & & \\ \hline
9.8–12.0 & & & MC parameters: \(E=7500\) kPa \(c=20\) kPa \(\phi^{\prime}=35^{\circ}\)\(\Psi=5^{\circ}\) \\
12.0–15.0 & Clayey sand & & MC parameters: \(E=20,000\) kPa \(c=20\) kPa \(\phi^{\prime}=35^{\circ}\)\(\Psi=5^{\circ}\) \\
15.0–20.0 & & & MC parameters: \(E=37,500\) kPa \(c=20\) kPa \(\phi^{\prime}=35^{\circ}\)\(\Psi=5^{\circ}\) \\ \hline \hline \end{tabular} \({}^{*}\)Volumetric weight.  
\end{table} 
Table 3: Soil model parameters for Embankment A.  
where \(\sigma_{v}^{\prime}\) is the current value of the vertical effective stress. The used values of POP are given in Table 1 for Embankment A and in Table 2 for Embankment B. The variation of OCR with depth for both embankments is given in Figure 7.  
The values of the horizontal (\(k_{h}\)) and vertical (\(k_{v}\)) hydraulic conductivities were the same ones as used in [6,8]. The natural clayey soils exhibit permeability anisotropy--higher permeability in the horizontal direction than in the vertical direction. For Embankment A, the permeability anisotropy ratio \(r_{k}=k_{h}/k_{v}\) was set to 1.5 for all clay layers [42]. For Embankment B, the permeability anisotropy ratio was set equal to 2.0 for all soil layers [8]. The values of \(k_{h}\) and \(k_{v}\) listed in Tables 1 and 2 are the initial values for both embankments. The values of hydraulic conductivity were allowed to change during consolidation with void ratio, according to the Equation (22):  
\[k=k_{0}\cdot 10^{-(\epsilon_{0}-e)/C_{k}}, \tag{22}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Depth [m]** & **Soil Strata** & \multicolumn{3}{c}{**MCC Parameters**} & \multicolumn{3}{c}{**HASP Parameters**} \\  & & \(\kappa\) [\(-\)] & \(\lambda\) [\(-\)] & \(M\) [\(-\)] & \(\phi_{C}^{\prime}\) [\(-\)] & \(\phi_{E}^{\prime}\) [\(-\)] \\ \hline
0.0–1.0 & Surface clay layer & 0.011 & 0.078 & 1.33 & 33 & 40.29 \\ \hline
1.0–2.5 & & & & & & \\
2.5–3.5 & Soft clay & 0.02 & 0.587 & 1.07 & 27 & 29.95 \\
3.5–8.5 & & & & & & \\ \hline
8.5–11.5 & Dense sand & MC parameters: \(E=26,672\) kPa \(c=5\) kPa \(\phi^{\prime}=30^{\circ}\)\(\Psi=0^{\circ}\) \\ \hline
11.5–15.0 & & & & & & \\
15.0–20.0 & Firm clay & 0.009 & 0.134 & 1.11 & 28 & 31.41 \\
20.0–30.0 & & & & & & \\ \hline \multicolumn{5}{c}{Embankment} & MC parameters: \(E=5000\) kPa \(c=10\) kPa \(\phi^{\prime}=28^{\circ}\)\(\Psi=0^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Soil model parameters for Embankment B.  
Figure 7: Variation of OCR with depth for Embankment A [6] (**a**) and Embankment B [8] (**b**). where \(k_{0}\) is the initial hydraulic conductivity, \(e_{0}\) is the initial void ratio, \(k\) is the current hydraulic conductivity, \(e\) is the current void ratio, and \(C_{k}\) is a constant. For \(C_{k}\) a value of \(0.4e_{0}\) was adopted for all calculations, as suggested in [43]. Because of the much greater stiffness of sand layers than clay layers, the void ratio of the sand layers does not change significantly during the calculation. As a consequence, the hydraulic conductivity of the sand layers is unchanged throughout all the calculation phases for both embankments. The coefficient of earth pressure at-rest for normally consolidated soil \(K_{0}^{NC}\) for all soil layers has the same value as reported in [6; 8] for both embankments. For all layers except the clay layers in Embankment A, \(K_{0}^{NC}\) was determined by [PERSON]'s estimation [44]:  
\[K_{0}^{NC}=1-sin\phi, \tag{23}\]  
where \(\phi\) is friction angle (given in Tables 3 and 4). For the clay layers in Embankment A, \(K_{0}^{NC}\) has the same value as given in [6].