## 3 Finite Element Model  
### Numerical Model  
Finite element analyses using the CEL approach were performed using Abaqus/Explicit [25] to simulate penetrations of spudcan foundations with conical shapes with extruded spigots, the dimensions of which are reported in [PERSON] et al. [12]. A 3D finite element model with an axisymmetric quarter domain was used for both the spudcan and soil, as shown in Figure 2. The spudcan was discretized with Lagrangian mesh using hexahedron elements (C3D8R). A rigid body constraint was assigned to prohibit relative deformation of the spudcan. The soil was modelled using the Eulerian domain hexahedron elements with reduced integration and hourglass control (EC3D8R). In the analyses, the soil  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Reference** & \(D\) **(m)** & \(H_{s}\)/\(D\) & \(I_{D}\) **(\%)** & \(\phi_{cv}\) **(°)** & \(s_{u}\) **(kPa)** & **\(k\) (kPa/m)** \\ \hline [PERSON] et al. [22] & 6.0–16 & 0.21–1.12 & 92 & 31 & 16.3–19.1 & 2.1 \\ [PERSON] et al. [12] & 6.0–20 & 0.16–1.0 & 43 & 31 & 11.01–12.96 & 1.55 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of sand and clay strength parameters used in centrifuge experiments.  
Figure 1: Failure mechanisms: (**a**) stress-dependent model of [PERSON] et al. [11], (**b**) modified stress model [PERSON] et al. [12].  
mesh remained intact, whereas the soil materials were allowed to flow into or out of the Eulerian element. A layer of void elements above the top surface of sand layer was used to allow heaving of soil. The bottom of the soil domain was fixed in all translational degrees of freedom. The horizontal displacement constraints were applied at the lateral boundaries. The size of the computational domain is consistent with the [PERSON] et al. [17] model. A uniform fine mesh for 1\(D\) around spudcan periphery was used, whereas a gradually increasing coarser mesh was extended to edges of the domain. The size of the smallest element used was 0.025\(D\), which was selected from a sensitivity study, as displayed in Figure 2(a).  
The interface between the spudcan foundation and soil was set to follow the Coulomb friction law. The friction coefficient was defined as \(\alpha tan\phi^{\prime}\), where \(\alpha\) is the roughness factor of the footing. The reported value of \(\alpha\) ranges from 0.3 to 0.6 [1,14,15,26]. \(\alpha\) was set to 0.5, following the recommendation of [PERSON] et al. [16]. A sensitivity study was performed to quantify the influence of the penetration rate. The response was shown to converge at rates lower than 0.3 m/s, as shown in Figure 2(b). The penetration rate used was 0.2 m/s, which is consistent with the value applied in previous studies [16,17]. Linear elastic-perfectly plastic models following the Mohr-Coulomb and Tresca failure criteria were used for sands and clays, respectively. A drained behavior was assumed for the sand layer, whereas clay was assumed to deform in an undrained condition. The computational process is composed of two steps. In the first step, the gravity load is applied to the model to induce geostatic stresses. In the second step, a constant penetration velocity is applied at the load reference point (RP) of the spudcan. The penetration resistance is calculated by dividing the vertical reaction force at RP with the cross-section area of the spudcan.