## 4 Numerical Modelling: Validation  
The numerical model of earth slopes based on the finite element method is developed to ascertain the accuracy of laboratory model results. The PLAXIS-2D code is used to develop computational model of nailed soil slope considering plane strain conditions of soil slope. Four types of elements are used to model the sand, steel and Perspex glass material. A nonlinear elastic (Hyperbolic) model is used to simulate the sand material. In this model, the stress-strain curve is hyperbolic, and the soil modulus is a function of  
Figure 31: Influence of footing position on horizontal stresses behind the nailed soil mass at mid-height of slope. Figure 32: Influence of footing position on vertical stresses behind the nailed soil mass at mid-height of slope. confining stress and the shear stress that a soil is experiencing. Depending on the stress state and stress path, three soil moduli are required, namely, the initial modulus, the tangential modulus and the unloading-reloading modulus. The geometry of the model is taken as 850 mm in height and 1760 mm in length, the inner dimensions of the sand bed used in the experimental model. The other nailed soil slope geometry parameters used in the model are taken from Figure 3. The geometry of the model is divided to meet the requirement of the construction stages and loading phases. The construction sequence is modeled in stages, as explained in Section 2.3.2 above. The 5 mm diameter steel bars with a length of 700 mm are modeled as the reinforcement, and a rigid steel plate of dimensions 840 mm \(\times\) 150 mm \(\times\) 22 mm is used to simulate the footing. Perspex plate with a thickness of 5.0 mm is selected to simulate the facing material, which is flexible enough to withstand the ground displacement during excavation. The strength parameters of nails, facing and footing materials are taken from Tables 2 and 3. The soil parameter used in the material model is given in Table 4. The discretized nailed soil slope model with boundary conditions is shown in Figure 33.  
To verify the accuracy of the laboratory results, a numerical model of nailed soil slope of height (\(H\)) 700 mm is developed with a length of horizontal nails as \(H\) and vertical spacing of nails as 0.4 \(H\). The footing settlements (S/\(H\), %) at different soil densities are computed using the developed numerical model. The plots of computational and experimental results of sand having three different relative densities (i.e., 35%--Fine sand, 48%--Medium sand and 68%--Dense sand) at different surcharge pressure, i.e., at the excavation stage and loading stage, are depicted in Figure 34. It is clear from the figure that the maximum footing \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Soil Type**} & \multirow{2}{*}{**Density** (kN/m3)**} & \multicolumn{3}{c}{**Mohr-Coulomb**} & \multirow{2}{*}{**Plastic Straining Due to Model**} & \multirow{2}{*}{**Plastic Straining Due to Primary Comp./Deviator**} & \multirow{2}{*}{**Elastic Unloading/Reloading**} & \multirow{2}{*}{**Stress-Dependent Stiffness (m)**} \\  & & & & & & & & & \\ \cline{3-10}  & \multirow{2}{*}{**\(\mathbf{\varphi}\)**} & \multicolumn{1}{c}{**C**} & \multirow{2}{*}{\(\mathbf{\psi}\)} & \multirow{2}{*}{\(\mathbf{\upsilon}\)} & \multirow{2}{*}{**Loading (E\({}_{\text{ood}}\))ref (kPa)**} & \multirow{2}{*}{**(E\({}_{\text{ur}}\))ref**} & \multirow{2}{*}{**\(\mathbf{\upsilon_{\text{ur}}}\)**} & \\  & & & & & & & & & \\ \hline Loose sand (RD = 34\%, \(\text{e}\) = 0.631) & 16.06 & 30 & 0.2 & 0 & 0.33 & 1327 & 3981 & 0.2 & 0.5 \\ Medium sand (RD = 48\%, \(\text{e}\) = 0.597) & 16.41 & 34 & 0.2 & 4 & 0.31 & 1959 & 5877 & 0.2 & 0.5 \\ Dense sand (RD = 68\%, \(\text{e}\) = 0.549) & 16.92 & 40 & 0.2 & 10 & 0.26 & 2632 & 7896 & 0.2 & 0.5 \\ \hline \hline \end{tabular} \(\mathbf{\varphi}\)—friction angle; C—cohesion; \(\mathbf{\psi}\)—dilatancy angle; \(\mathbf{\upsilon}\)—Poisson’s ratio; e—void ratio.  
\end{table} 
Table 4: Soil parameters of sand used in material model.