## 4 Numerical Modeling
### PLAXIS Analysis  
The Plaxis 2D finite element program was used in geotechnical analysis. The program has advanced soil constitutive models that can capture real soil behavior. The program is also used for complex soil structure interactions and to assess stability and deformations of a structure. In the analysis, 15 noted elements with plane strain conditions have been used. According to [PERSON] [25] a 15 node triangle produces high quality stress results. The mesh type preferred in the model is medium type. A total of 3477 elements and 28,627 nodes were generated. The soil parameters used in the model are determined in Section 4.2. The model for the analysis is given in Figure 7. The analysis has been conducted considering the initial groundwater level (+3.00 m) and then with reference to EAU [26], the water level difference of 0.5 m (+2.50 m) has been taken into consideration. The crane loads were computed from the crane properties given in the crane appendix. The calculated uniform loads as 270 kPa and 135 kPa were considered in the analysis together with a bollard pull load of 23 kN/m. Total horizontal displacement contours, total vertical displacement contours, and total horizontal displacements on piles obtained from analyses are presented in Figure 8 for GWL = 3.00 m. The obtained results for GWL = 2.5 m and  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Depth (m)** & **k\({}_{\text{h}}\) (kN/m\({}^{3}\))** & **Depth (m)** & **k\({}_{\text{h}}\) (kN/m\({}^{3}\))** & **Depth (m)** & **k\({}_{\text{h}}\) (kN/m\({}^{3}\))** \\ \hline
0.00–1.00 & 7500 & 0.00–1.00 & 10,000 & 0.00–1.00 & 10,000 \\
1.00–3.00 & 20,000 & 1.00–3.00 & 20,000 & 1.00–3.00 & 20,000 \\
3.00–14.00 & 17,500 & 3.00–13.00 & 17,500 & 3.00–11.00 & 17,500 \\
14.00–18.00 & 50,000 & 13.00–18.00 & 50,000 & 11.00–18.00 & 50,000 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Horizontal subgrade modulus.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Allowable Pile Bearing** & **Average Allowable Pile** \\
**Pile No.** & **Pile Length (m)** & **Capacity Values (kN)** & **Bearing Capacity Values (kN)** \\ \cline{2-4}  & & **Service Condition** & **Service Condition** \\ \hline Unreinforced Pile; D = 0.65 m, L = 8.50 & 8.5 & 420 & \\ Unreinforced Pile; D = 0.65 m, L = 5.50 & 5.5 & 247 & 304 \\ Unreinforced Pile; D = 0.65 m, L = 3.00 & 3.0 & 78 & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Average unreinforced pile bearing capacity.  
3.00 m are summarized in Table 6. Since there is no active earthquake movement in the project area, analyses under dynamic loads were not required.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Displacement**} & \multicolumn{2}{c}{**Ground Water Level**} \\ \cline{2-3}  & **+2.50 m** & **+3.00 m** \\ \hline Total displacement & 2.146 cm & 1.763 cm \\ Total horizontal displacement & 1.472 cm & 1.085 cm \\ Total vertical displacement & 1.591 cm & 1.416 cm \\ Maximum total horizontal displacement of piles & 1.424 cm & 1.044 cm \\ \hline \hline \end{tabular}
\end{table}
Table 6: Analysis results for two GWL.  
Figure 7: Geometry model. (**a**) Geometry model for initial water level at GWL = 3.00 m. (**b**) Geometry model for water level at GWL = 2.50 m.  
Figure 8: Analysis results for initial water level at GWL = +3.00 m. (**a**) Total horizontal displacements. (**b**) Total vertical displacements. (**c**) Total horizontal displacements of piles.