## 5 Validation Methodology
### Validation of the Scaling Methodology
The proposed scaling and validation technique suggests that reducing the model flexural stiffness to simulate the correct prototype flexural stiffness may provide even more accurate results. However, considering a rational reduction factor is important and requires further research to provide reasonable guidelines. In this scaling and validation technique, the static and/or dynamic pile response, including the pile head loads, deflections, and maximum moments, is considered on the basis of a constant bending stiffness (\(EI\)) along the pile length. Many studies revealed that the bending moment along the pile length did not significantly depend on the characteristics of the structure (e.g., [40]). Therefore, a small deviation between the numerical modelling according to prototype properties and the scaled physical test can be justified due to the 5% difference in \(EI\) values. Moreover, the pile/soil compressibility ratio \(K\) can be expressed as follows (see Equations (21)-(23)):  
Figure 16:2  
The lateral pile/soil stiffness ration \(K_{r}\) is given as:  
Figure 16:3  
\(K_{r}\) can be written as a function of \(K\) as in the following equation:  
Figure 16:4  
According to geotechnical codes such as AASHTO [41] and Eurocode 7, [42], the pile design phenomena depend mostly on the ultimate and serviceability limit states in which the load-deflection behaviour of the pile under lateral loads should be considered appropriately. The pile slenderness ratio and the pile-soil stiffness ratio are crucial factors that control the dynamic response of the pile-soil system. Realistic scaling and analysis of such these interactions should consider the nonlinear response of the system and the homogeneity of soil properties. In pile design practice, the \(L/D\) ratio reflects the effect of the embedded length of the pile on the pile stiffness associated with the pile and the soil [43]. Increasing the \(L/D\) ratio results in an accumulative decline in the relative pile-soil stiffness \(K_{r}\) ([PERSON] and [PERSON] 1980). These consequences are significantly influenced by the pile head conditions. The value of the degradation factor indicates that there is less reduction in the soil-pile interactive performance for arrangements with a relatively high \(L/D\) value. Low degradation factors induce a significant decline in the axial capacity of the pile due to the lower degradation factor values. For comparable dynamic loading properties and pile geometry parameters, a review of the literature shows that the degradation of the free headed pile is less significant compared to that of the fixed headed pile. The \(L/D\) ratio limitation must be identified carefully before starting the scaling process. Moreover, an accurate \(L/D\) ratio must be determined to produce the correct scale-model-to-prototype system behaviour associated with this significant scaling parameter. The minimum wall thickness of the pile based on the \(D/\)/ ratio is one of the principal parameters that must be considered to produce a scale model. According to [PERSON] (2007), [PERSON] (2007) the \(D/\)/ ratio along the pile length must be small enough to prevent local buckling developing at stresses up to the yield strength of the pile material. The loading circumstances occur during the installation, so loading periods of the service life of the piling must be considered, and standard limitations of wall thickness \(t\) should be applied as a minimum requirement. Accordingly, the minimum pile wall thickness \(t\) should not be less than the value given in Equation (24):  
Figure 16:5  
where \(t\) and \(D\) are the wall thickness and diameter of pile in mm, respectively. This condition did not exist in the targeted and scale model properties. The minimum \(t\) required is 6.8 mm, and the actual values of \(t\) were 1.586 and 0.711 mm for the target and scale model, respectively.