## 5 Validation Methodology
### Validation of the Scaling Methodology  
For piles that are designed to resist lateral loads, the ultimate and serviceability design limit states must be considered, including the potential load-displacement behaviour of a single pile. The potential load-displacement behaviour of a single pile is typically determined using either theoretical or/and semiempirical methods available in the literature. However, it is noteworthy that ignoring or simplifying the three-dimensional aspects of the lateral soil reaction and the variety of primary parameters governing the pile-soil interaction leads to less accurate predictions of the pile capacity. As mentioned earlier, full-scale tests are an excellent means for an accurate determination of small pile head deflections, but the expense and challenges of conducting these tests limits their practical value. Developing a scale model that represents the primary parameters of the prototype full-scale model is an efficient alternative. A number of problems in soil mechanics and structural analysis--primarily in the SSI area--can be studied using this validation approach. This method is a combination of two research areas, i.e., geotechnical and structural engineering, and is connected between the physical and numerical modelling programmes. The physical component is from the shaking table tests, which is then combined with the development of the 3D nonlinear FEA model to reflect the full and true behaviour of the system, including all interactions. The full-scale 3D numerical model is used to validate the inertial and kinematic behaviours of the scaled physical shaking table test. In this context, the bending moment envelope, acceleration time history, acceleration Fourier amplitude, and acceleration response spectrum for the model are presented in Figures 16-20, respectively. The results for these parameters were compared with the corresponding parameters used in the scaled physical shaking table test of the reference case study, [2] using the scale factors given in Table 2.  
The bending moment parameter values of the full-scale numerical model were scaled down using a scaling factor equal to \(\lambda^{4}\). Based on the procedure of validation described in Section 3, the resultant bending moment envelope behaviour of the scaled numerical model was compared to that from the reference case study. Figure 21 represents this validation. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline Density (kg/m\({}^{3}\)) & 1505.75 \\ \hline Log bulk modulus & 0.05 \\ \hline Poisson’s ratio & 0.47 \\ \hline Tensile limit & 0.00 \\ \hline Log plasticity bulk modulus & 0.27 \\ \hline Stress ratio & 1.26 \\ \hline Wet yield surface size & 1.00 \\ \hline Flow stress ratio & 0.78 \\ \hline Initial void ratio & 1.50 \\ \hline Cyclic loading parameters \\ \hline \multirow{2}{*}{Freq. (Hz)} & Cyclic stress ratio & \(\xi_{d1}\) & \(\xi_{d2}\) \\ \cline{2-3}  & (CSR) & cyclic degradation parameters \\ \hline
0.1 & 0.6 & 4.2 & 75 \\ \hline
0.25 & 0.6 & 4.2 & 97 \\ \hline
1 & 0.6 & 4.1 & 420 \\ \hline
2 & 0.6 & 4.1 & 600 \\ \hline
5 & 0.6 & 4.2 & 825 \\ \hline
10 & 0.6 & 4.2 & 1065 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Model parameters for the soil constitutive models [38]. A similar process was conducted for the output acceleration time histories of the full-scale numerical model. As the test was performed in a 1g environment, the scaling factor corresponded to the acceleration parameter, which was taken as unity. In accordance with the data given in Table 2, the time parameter was required to be divided by a factor of \(\lambda^{\frac{1}{2}}\). To create the other two parameters related to the acceleration time history behaviour; namely, the acceleration Fourier amplitude and acceleration response spectrum of the four cases of loading, the acceleration time history data were assessed using the SeismoSignal software [39]. Figures 22-24 illustrate these comparisons for the four different types of pile head.