## 3 Results and Discussion
### Back-Calculation of K Values from Experimental Results  
The values of the lateral earth pressure coefficient, K, are also back-calculated from Equations (1) and (2) as follows, and the results listed in Table 7.  
\[K=\frac{Q_{f}}{\sigma_{\rm p}^{\prime}.\ tan\delta^{\prime}.\rm P.L} \tag{2}\]  
It can be seen that the K values are different for each material at the same relative density, and this is because each material has different surface roughness; the material with higher surface roughness has higher K values. The back-calculated K values vary from 0.52 to 14.86, and it is obvious that the K values obtained are quite high and all are greater than K\({}_{\rm A}\) and some values are even greater than K\({}_{\rm P}\), especially in high relative density for PVC, timber and FRP model piles. As reported by [37, 46], the K value can be greater than K\({}_{\rm P}\) in some situations. In addition, sand particles used in this study are of small size and angular shape, as stated by [PERSON] et al. [33]; this causes high friction resistance between the pile shaft and sand and, consequently, high K values are obtained. Another reason  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model Pile** & **D\({}_{\rm r}\) (\%)** & \(\gamma_{\rm d}\) (kN/m\({}^{3}\)) & \(Q_{f}\) (kN) & \(\sigma_{\rm p}^{\prime}\) (kN/m\({}^{3}\)) & **(s) (\({}^{\circ}\))** & **K** \\ \hline \multirow{4}{*}{T timber} & 10 & 14.6 & 0.15 & 3.650 & 35.1 & 0.74 \\  & 40 & 15.5 & 0.76 & 3.875 & 36.2 & 3.41 \\  & 65 & 16.3 & 1.90 & 4.075 & 37.9 & 7.63 \\  & 90 & 17.3 & 3.20 & 4.325 & 35.3 & 13.31 \\ \hline \multirow{4}{*}{PVC} & 10 & 14.6 & 0.10 & 3.650 & 26.1 & 0.71 \\  & 40 & 15.5 & 0.62 & 3.875 & 28.7 & 3.72 \\  & 65 & 16.3 & 1.50 & 4.075 & 31.4 & 7.68 \\  & 90 & 17.3 & 2.95 & 4.325 & 30.3 & 14.86 \\ \hline \multirow{4}{*}{FRP} & 10 & 14.6 & 0.08 & 3.650 & 23.7 & 0.67 \\  & 40 & 15.5 & 0.55 & 3.875 & 26.2 & 3.67 \\  & 65 & 16.3 & 1.40 & 4.075 & 28.3 & 8.12 \\  & 90 & 17.3 & 2.40 & 4.325 & 28.2 & 13.18 \\ \hline \multirow{4}{*}{Steel} & 10 & 14.6 & 0.05 & 3.650 & 20.0 & 0.52 \\  & 40 & 15.5 & 0.16 & 3.875 & 21.0 & 1.37 \\ \cline{1-1}  & 65 & 16.3 & 0.31 & 4.075 & 22.5 & 2.34 \\ \cline{1-1}  & 90 & 17.3 & 0.62 & 4.325 & 21.0 & 4.75 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Back-calculated K values.  
Figure 11: Variation of the maximum resistance of model shaft piles versus relative density of sand.  
is that small-scale model piles generate considerably higher shaft friction resistance than full-scale piles ([PERSON] et al., 2018). The test sand has a high internal friction angle, and all of the model pile materials, with the exception of steel, have high interface friction angles with the sand; therefore, there is a potential for sand to dilate mostly in high relative density, this, of course, makes a contribution to the K values measured ([PERSON] et al., 2018).  
From Figure 10, it can be seen that the timber model pile has the highest shaft friction resistance at 90% relative density, while the maximum K value belongs to the PVC model pile; this is because PVC is a soft material and has a lower surface hardness compared to the timber, that is why during loading, sand particles try to scratch the surface of the PVC pile and form high friction resistance. In addition, the skin friction angle (8) between sand-PVC materials is lower than sand-timber and it is inversely proportional to the tangent of the skin friction angle, as shown in Equation (2).