## 4 Numerical Modeling
### Pile Capacities and Horizontal Subgrade Modulus of Piles  
The bearing capacity of the piles in soils has been calculated based on in-situ SPT test results. The piles have been designed as frictional piles; this means that only the side \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameters** & **Fill** & **S1-Laterite** & **S2-Sand 1** & **S3-Sand 2** & **S4-Clay** & **Units** \\ \hline \(\gamma_{\text{Vunsat}}\), Unsaturated unit weight & 19 & 19 & 19 & 19 & 19 & kN/m\({}^{3}\) \\ \(\gamma_{\text{sat}}\), Saturated unit weight & 20 & 20 & 20 & 20 & 20 & kN/m\({}^{3}\) \\ \(\text{E}_{\text{S}}\text{{}^{0}}\text{ref}\), Secant stiffness & 50,000 & 13,000 & 16,000 & 19,500 & 30,000 & kN/m\({}^{2}\) \\ \(\text{E}_{\text{o}}\text{ref}\), Tangent stiffness & 50,000 & 13,000 & 16,000 & 19,500 & 30,000 & kN/m\({}^{2}\) \\ \(\text{E}_{\text{u}}\text{ref}\), Unloading/reloading stiffness & 150,000 & 39,000 & 48,000 & 58,500 & 90,000 & kN/m\({}^{2}\) \\ m, Power for stress-level & 0.5 & 0.5 & 0.5 & 0.5 & 0.7 & - \\ \(c^{\prime}\), Cohesion & 1 & 5 & 5 & 5 & 8 & kN/m\({}^{2}\) \\ \(\phi^{\prime}\), Angle of internal friction & 34 & 30 & 30 & 33 & 28 & \({}^{\circ}\) \\ \(\psi\), Angle of dilatancy & 4 & 0 & 0 & 3 & 0 & \({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Soil parameters. resistance has been taken into account while the base resistance has been ignored. By doing this, bearing capacity values have been conservatively obtained. The natural and saturated unit weights of the soil have been taken as 19 kN/m\({}^{3}\) and 20 kN/m\({}^{3}\), respectively. The saturated unit weight of the rockfill was taken as 22 kN/m\({}^{3}\). The unit weight of the pile material was taken as 25 kN/m\({}^{3}\). The groundwater level was taken as 3 m from the surface. Since the piles are bored piles, the difference of the pile weight and the excavated soil was finally subtracted from the allowable pile bearing capacity. The submerged unit weight of the pile was used since most of it is below groundwater, i.e., the unit weight of the pile material was subtracted from the unit weight of water. Piles are frequently applied in cohesionless soils. In cohesionless layers, the individual nominal resistance of each shaft in a group should be reduced by applying an adjustment factor \(\eta\) taken as shown in Table 2. For intermediate spacing, the value of \(\eta\) may be determined by linear interpolation. For adjustment factor \(\eta\) to be taken as 1, the center-to-center spacing of the piles must be 4D or more, i.e., 4 \(\times\) 0.65 = 2.6 m. The center-to-center spacing of all the piles is greater than 2.6 m except for A-axis where the spacing is 1.75 m; due to this the factor, \(\eta\) is taken as 0.72. The layout of the piles on the A-, B-, and C-axes is shown in Figure 6. Pile bearing capacities were calculated as indicated in Table 3.  
The geotechnical axial capacities of the piles calculated using the soil properties do not exceed the allowable structural capacity of the piles that are calculated by considering the pile material (usually in pile standards, this value is in the order of 0.4-0.5 times the characteristic concrete compressive strength. Concrete class is C30/37). Considering the soil profile and recommended parameters given in Section 4.2, the horizontal subgrade modulus of the piles was calculated using Bowles [20] and CGS [21] recommendations. The values have been conservatively selected as given in Table 4. These values have been used in the 3D analysis. \begin{table}
\begin{tabular}{c c c} \hline
**Group Configuration** & **Shaft Center-to-Center** & **Reduction Factor for Group** \\  & **Spacing** & **Effects, \(\eta\)** \\ \hline Single Row & 2D & 0.90 \\  & 3D or more & 1.00 \\ \hline  & 2.5D & 0.67 \\ Multiple Row & 3D & 0.80 \\  & 4D or more & 1.00 \\ \hline \end{tabular}
\end{table} 
Table 2: Design group reduction factors for bearing resistance of shafts.