## 5 Validation Methodology
### Validation of the Scaling Methodology
Figure 16: Distribution of the acceleration response for full-scale numerical simulations of the shaking table, including those with a pile head mass of (**a**) 72.7 kg, (**b**) 45.36 kg, (**c**) 11.40 kg, and (**d**) 3.0 kg. Figure 17: Pile bending moment envelopes for arrangement with various pile head masses from the full-scale numerical model. Figure 18: Pile head acceleration time history responses from the full-scale numerical model of piles with pile head masses of (**a**) 72.7 kg, (**b**) 45.36 kg, (**c**) 11.40 kg, and (**d**) 3.0 kg. Figure 19: Fourier amplitude versus frequency (FFT) responses from the full-scale numerical model of piles with pile head masses of (**a**) 72.7 kg, (**b**) 45.36 kg, (**c**) 11.40 kg, and (**d**) 3.0 kg. Figure 20: _Cont._  
Figure 21: Comparison of the pile bending moment envelopes for piles with various pile head masses from the full-scale numerical model and the scaled models. Figure 20: Acceleration response spectra from the full-scale numerical model of piles with pile head masses of (**a**) 72.7 kg, (**b**) 45.36 kg, (**c**) 11.40 kg, and (**d**) 3.0 kg. Figure 23: _Cont._  
Figure 22: Comparison of the pile head acceleration time history responses from the physical test and the scaled numerical model for piles with pile head masses of (**a**) 72.7 kg, (**b**) 45.36 kg, (**c**) 11.40 kg, and (**d**) 3.0 kg. Pile behaviour under dynamic loading is substantially affected by the properties of the soil and pile, where pile properties represent pile material and shape properties. The nonlinear pile material modelling must be adopted to identify the pile lateral load capacity, associated bending moment, pile deflection, and pile material failure onset. The variation  
Figure 16:0 Comparison of the Fourier amplitude versus frequency (FFT) responses from the physical test and the scaled numerical model for piles with pile head masses of (**a**) 72.7 kg, (**b**) 45.36 kg, (**c**) 11.40 kg, and (**d**) 3.0 kg. Figure 16:1 Comparison of the acceleration response spectra from the physical test and the scaled numerical model for piles with pile head masses of (**a**) 72.7 kg, (**b**) 45.36 kg, (**c**) 11.40 kg, and (**d**) 3.0 kg. in the bending stiffness (\(EI\)) of a laterally loaded pile is a function of the bending moment distribution along the pile length and is represented as the moment-curvature relationship. As shown in Tables 5 and 6, the target \(EI\) of the model (2.94 kNm, where the unit is derived from E per unit length equal to kN/m\({}^{2}\)/m and I is in m\({}^{4}\)) experienced an increase of 5.0% compared with the value of the computed scale model (2.42 kNm ). This deviation was reflected in the bending moment envelope values from the numerical simulation. Owing to the small difference in flexural rigidity values of the physical and numerical models, slight deviations in the corresponding bending moment envelopes can be observed in Figure 21, indicating that the current scaling and validation method could successfully examine and validate the inertial behaviour of the seismic SSI system when the primary parameters of the system were identified and scaled correctly. The pile flexural stiffnesses along the deflected pile vary with the level of loading, pile material, moment-curvature relationship, and soil reaction, which influences the pile deflection pattern. Therefore, consistency among the primary dominated parameters of the distributions of pile deflection, bending moment, bending stiffness, and soil reaction must be maintained along with the pile. Nevertheless, based on the results presented in Figures 16-20, it was shown that the scale model that was developed to predict the SSPSI response could represent all these primary parameters correctly. It permitted the evaluation of the soil-pile modulus based on the properties of the soil and pile, which included the pile flexural stiffnesses. The assessed model was thus influenced by the accuracy of the bending stiffness (in the model-to-prototype scaling) as well as the selected pile cross-section type and dimension.