## 3 Experimental Setup and Procedure
### Model Pile  
The model piles (40 \(\times\) 40 \(\times\) 800 mm) were made of cement mortar and steel bars, and the elasticity modulus and inertia moment were \(E_{\mathrm{P}}\) = 34.25 GPa (the simply-supported beam method) and \(I_{\mathrm{P}}\) = 2.13 \(\times\) 10\({}^{-7}\) m\({}^{4}\), respectively. The model piles can be assorted as a rigid pile (\(\alpha L\) = 1.93 \(\leq\) 2.5) as per the deformation coefficient of piles \(\alpha\), obtained by \(\alpha\) = (\(mb/E_{\mathrm{P}}I_{\mathrm{P}}\))\({}^{0.2}\) (unit: m\({}^{-1}\)), where \(b\) is the pile width, \(E_{\mathrm{P}}I_{\mathrm{P}}\) is the flexural rigidity of the piles, and \(m\) is the proportional coefficient of the subgrade reaction coefficient [39]. In addition, the proportion of the pile diameter to the median particle diameter \(d_{50}\) is approximately 100, far greater than the minimum requirement of 40 [40]. As shown in Figure 4b, a positive battered pile has embankment-induced horizontal thrusts acting in the same direction as the batter. In contrast, a negative battered pile has horizontal thrusts acting in the opposite direction to the batter [41]. The piles were embedded about 760 mm, leaving a segment of 40 mm above ground under different pile inclinations (\(\beta\) = \(-\)20\({}^{\circ}\), \(-\)10\({}^{\circ}\), 0\({}^{\circ}\), +10\({}^{\circ}\), and +20\({}^{\circ}\)), and the free tip boundary conditions were considered in these cases (namely, friction piles). Moreover, the fixed tip boundary condition was further considered in the cases of \(\beta\) = \(-\)20\({}^{\circ}\) by inserting the pile tip into the cast-in-place concrete block fixed in the bottom of the test tank (namely, end-bearing piles). Considering that there are two cases with the same pile inclination, \(\beta\) = \(-\)20\({}^{\circ}\), but different constraint conditions at the pile tip, the case of \(\beta\) = \(-\)20\({}^{\circ}\) in the following investigation mainly refers to the one with a free tip unless otherwise stated to avoid possible confusion. The model pile was installed by a  
Figure 6: Grading curve of the soil with \(C_{\mathrm{u}}\) and \(C_{\mathrm{c}}\) (classified as well–graded sand).  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameters** & **Values** & **Parameters** & **Values** \\ \hline Unit weight \(\gamma\) (kN/m\({}^{3}\)) & 17.7 & Moisture content \(\omega\) (\%) & 2 \\ Void ratio \(e\) & 0.536 & Relative density \(D_{\mathrm{r}}\) (\%) & 65.8 \\ Maximum void ratio \(e_{\mathrm{max}}\) & 0.718 & Internal friction angle \(\varphi\) (\({}^{\circ}\)) & 40 \\ Minimum void ratio \(e_{\mathrm{min}}\) & 0.441 & Specific gravity \(G_{\mathrm{s}}\) & 2.68 \\ Maximum unit weights \(\gamma_{\mathrm{dmax}}\) (kn/m\({}^{3}\)) & 18.2 & Coefficient of uniformity \(C_{\mathrm{u}}\) & 5.5 \\ Minimum unit weights \(\gamma_{\mathrm{dmax}}\) (kn/m\({}^{3}\)) & 15.3 & Coefficient of curvature \(C_{\mathrm{c}}\) & 2.7 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Physical and mechanical parameters of sand.  
batten framing scheme while filling sand in lifts. The battens of the front and back sides are used to locate the position perpendicular to the paper, and the ones in the same plane with PVC pipes are used to adjust the pile inclination. The position and inclination of the model pile will be checked after it is completely fixed.  
Note that the concrete blocks at the pile tips do not necessarily mean pouring concrete blocks in the field. To avoid possible problems of test design, it is a simplification method for a model test to quantitatively evaluate the maximum benefit of driving the pile into a harder soil layer on the pile-bearing capacity.