## 3 FEM Modelling
### Validation of Finite Element Model  
The results obtained by the described finite element models for specimens CS1-CS4 are compared to test results. The top end of the CFT column had pinned support with released movement in the vertical direction. The stiffness at the bottom end of the CFT column was modelled by assigning the corresponding stiffness resulting from the soil-pile analysis from the PLAXIS 3D model. The buckling analysis was performed to obtain numerical values of critical buckling forces P\({}_{\rm cr,num}\) and the effective buckling length of the column L\({}_{\rm eff}\). Accordingly, the effective buckling length was measured as the distance between two consecutive points of contra flexure (points of zero moments) in the CFT column. The median value of the effective column length is 0.799 L. The median value of the ratio between experimentally and numerically obtained buckling force P\({}_{\rm cr}/\)P\({}_{\rm cr,num}\) is 1.054. As shown in Table 5, there is a good agreement between the numerically obtained results and the experimental results. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Property** & **Parameter** & **Unit** & **Fill (Light Blue)** & \
\begin{tabular}{c} **Muddy Clay** \\ **(Green)** \\ \end{tabular} &
\begin{tabular}{c} **Refuelled Sand** \\ **(Yellow)** \\ \end{tabular} \\ \hline The thickness of the soil layer & d & m & 6.40 & 3.20 & 11.40 \\ Unsaturated weight & \(\gamma_{\rm unsat}\) & kN/m\({}^{3}\) & 20.00 & 19.00 & 19.00 \\  & E\({}_{\rm 50}\)\({}^{\rm ref}\) & kN/m\({}^{2}\) & 8000.00 & 3000.00 & 30,000.00 \\ Stiffness & E\({}_{\rm 0 ed}\)\({}^{\rm ref}\) & kN/m\({}^{2}\) & 8000.00 & 3000.00 & 30,000.00 \\  & O\({}_{\rm ur}\)\({}^{\rm ref}\) & kN/m\({}^{2}\) & 24,000.00 & 9000.00 & 90,000.00 \\ Poisson ratio & \(\
u_{\rm ur}\) & - & 0.30 & 0.30 & 0.30 \\ Power & m & - & 0.50 & 0.50 & 0.50 \\ Reference pressure & p\({}^{\rm ref}\) & kN/m\({}^{2}\) & 100.00 & 100.00 & 100.00 \\ Cohesion & c\({}^{\prime}\) & kN/m\({}^{2}\) & 5.00 & 15.00 & 5.00 \\ Friction angle & \(\varphi^{\prime}\) & \({}^{\circ}\) & 30.00 & 20.00 & 31.00 \\ Dilatancy angle & \(\Psi\) & \({}^{\circ}\) & 15.00 & 17.50 & 18.50 \\ Lateral pressure coefficient & K\({}_{0}\) & - & & 1-sin\(\varphi^{\prime}\) & \\ Failure ratio & R\({}_{\rm f}\) & - & & 0.9 & \\ \hline \end{tabular}
\end{table} 
Table 4: Soil properties. The critical buckling forces obtained by the experimental tests are slightly higher than the same forces obtained by the numerical model. These differences are within the range of 3% to 8%. In addition, Figure 11 shows the numerical results of the deformed shape at failure and horizontal displacements for specimens CS1-CS4. It can be seen that the proposed numerical model can accurately simulate the behaviour of the CFT column supported on the jacked pile. It should be noted that the experimentally obtained critical buckling force is also compared with the Euler buckling force later in the study, in Section 4. In these comparisons, the effective column stiffness is determined by the proposals from the design codes, and the effective buckling length is taken as 0.8 L.  
Furthermore, the validated numerical model was used to investigate the impact of the CFT column--jacked pile connection stiffness on global column stability. The preliminary parametric analysis included three different pile diameters, usually applied during top-down construction: \(\mathcal{O}\)350 mm, \(\mathcal{O}\)450 mm and \(\mathcal{O}\)600 mm were used in the model. The  
Figure 11: Horizontal displacements in the deformed models: (**a**) CS1; (**b**) CS2; (**c**) CS3; (**d**) CS4; \begin{table}
\begin{tabular}{c c c c} \hline
**Specimen** & **Leff, num/L** & **Pc,num [kN]** & **Pc/Pc,num** \\ \hline CS1 & 0.789 & 251.6 & 1.060 \\ CS2 & 0.795 & 327.3 & 1.048 \\ CS3 & 0.802 & 373.6 & 1.078 \\ CS4 & 0.811 & 483.7 & 1.042 \\ Median & 0.799 & - & 1.054 \\ \hline \end{tabular}
\end{table} 
Table 5: Comparison of numerical and experimental results for the effective buckling length and buckling force.