## 5 Validation Methodology
### Numerical Modelling Characteristics  
A three-dimensional (3D) FEA simulation was carried out using the sequential analysis method for considering the effects of soil-structure interaction (SSI) during static and dynamic loading conditions. The sequential analysis method is commonly employed in numerical analysis for considering the consequences of the (1) geostatic, (2) static, and (3) seismic loads on a system. The first step (1) is the geostatic step, and only the soil body force is employed. Consequently, the considerable force and initial stresses should be precisely equilibrated and established for minimal soil displacement. Abaqus/Standard [34] offers two methods for establishing the initial equilibrium. The first procedure is appropriate for applications in which the initial stress state is identified approximately. The second, somewhat improved method is applicable for circumstances wherein the initial stresses are unidentified but only for a limited number of elements and materials. In this respect, the second procedure was followed in the current study, in which the pore water  
Figure 13: Flowchart describing the validation methodology. pressures varied linearly with depth and the initial effective stresses were appropriately stated according to the total stresses. The second (2) step was the static step, which comprised two substeps in the analysis. Firstly, to create stability between the two interacting parts (namely, the soil and the pile) and to prevent negative shear stress between them, the static-frictionless step must be employed. This represents the piles' installation stage during model construction. Secondly, the static-friction loading step must be applied; this comprises the application of gravity loads, which are assumed to be static and uniform, and the mass loading according to the loading condition of the physical test was also applied. In the current analysis, four pile head masses were employed as a superstructure--a set of single pile models with head masses of 3.0, 11.40, 45.4, and 72.70 kg were used in accordance with the reference physical test (Test 1.15) after applying the corresponding scaling factors as given in Table 2.  
The third step (3) was the dynamic analysis step. The time history input data from the Loma Prieta earthquake, as mentioned and described previously, were applied to the bottom of the clay soil at the base of the shaking table [35]. The displacements were restrained in the horizontal direction for the geostatic and static step and changed to the vertical direction for this dynamic analysis step, allowing free movement in the horizontal direction. The base of the model was restrained with roller supports in the vertical direction. In contrast, the other two direction boundary conditions, which were perpendicular to the shaking direction, were constrained [36]. Both the soil and the superstructure were modelled using 3D solid elements (C3D8R in the Abaqus library) that were eight-node linear brick elements with reduced integration. For the piles, linear shell elements (S4R) were used; these were a four-node doubly curved shell elements [34]. As this was a cylindrical application, a radial mesh was employed in accordance with the approach of other researchers [37]. In addition, a mesh sensitivity study was conducted to achieve accurate and reliable results, resulting in elements that were 400 mm in each dimension at the boundary of the model and refined to 80 mm near and at the pile. Given the similarity between the approach of using the combination system of flexible wall material properties, which was chosen in the reference case study, and the alternative method of using the soil sample properties directly, the combination system was not adopted further in the numerical analysis. Alternatively, the soil boundary was constrained in accordance with the physical test conditions. In the numerical model, the soil/pile contact was considered to be a discontinuous constraint, which can occur when loads transfer between contacting elements under contact conditions.