# Experimental and Theoretical Study of One-Way Cyclic Lateral Responses of Piles in Sloping Ground
## 2 Experimental Setup and Procedure
### Experimental Setup  
The model experiments were performed in a custom-made steel test tank (1.6 \(\times\) 1 \(\times\) 1.2 m), one side of which was made of strengthened glass for observing the deformations of pile and slope (Figure 1). To eliminate the boundary effect, the minimum distance between the model pile and four sides of the test tank was designed to be about 15 times the pile diameter, much greater than the pile influence zone [28; 29; 39]. The model pile was made of a polypropylene random pipe (PPR pipe) with an outer diameter and wall thickness of 32 mm and 4.4 mm, respectively, and the pile was pre-installed with an embedded length of 1 m. PPR pipe was used mainly because of its toughness and creep resistance, high strength, machinability, and economic efficiency, allowing a greater selection of the other geometry parameters in the model experiment design. The model pile can be classified as a flexible pile as per the pile deformation coefficient \(\alpha\)[38], derived by Equation (7). In addition, a steel cylinder was welded at the bottom of the test tank to enclose and fix the pile tip, whereas a cylindrical iron mass (80 N) near the pile head was used to model the self-weight of superstructures and consider the second-order effect (\(P\)-\(\Delta\) effect). \[\alpha=\sqrt[3]{\frac{mb}{EI}} \tag{7}\]  
As illustrated in Figure 2, several pairs of strain gauges (BFH120-5 AA-D150, electrical resistance type) and earth pressure cells (DMTY, vibrating wire type, range of 100 kPa) \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Prototype** & **Model** & **Similarity Constant** \\ \hline Calculating width of piles (m) [38] & 2.70 & 0.0657 & 41.10 \\ Pile embedded length (m) & 25.00 & 1.00 & 25.00 \\ Flexural rigidity (kN\(\cdot\)m\({}^{2}\)) & 2.43 \(\times\) 10\({}^{7}\) & 4.31 \(\times\) 10\({}^{-2}\) & 5.56 \(\times\) 10\({}^{8}\) \\ Proportional coefficient of subgrade & 35.42 & 26.24 & 1.35 \\ reaction coefficient (MN/m\({}^{4}\)) [38] & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physicochemical parameters of prototype and model tests. were symmetrically placed along the pile [11; 13]. These sensors were further protected by the thin and low-strength tape [15] to avoid the possible damage resulting from the soil around the pile and infiltrated water [10]. The displacement gauges (DMWY-100, range of 100 mm) were also installed to measure the pile head deflections \(y_{0}\). The model slope was first constructed in lifts with unsaturated river sand (containing clay components and hydrophilic minerals) at a uniform density (constructed in lifts with six sand layers; each layer is 0.2 m thick with a prescribed mass of 480 kg) and then graded for cases of different slopes. The internal friction angle (\(\varphi\) = 13.26\({}^{\circ}\)) and apparent cohesion (\(c\) = 10.66 kPa) were determined by direct shear tests; apparent cohesion can guarantee sufficient slope stability even for a slope of 60\({}^{\circ}\). Some laboratory geotechnical tests were also carried out to obtain the physicochemical parameters, such as moisture content \(\omega\) = 3.84%, modulus of compression \(E_{\mathrm{s}}\) = 4.43 MPa, void ratio \(e\) = 0.42, unit weight \(\gamma\) = 18.83 kN/m\({}^{3}\), specific gravity \(G_{\mathrm{s}}\) = 2.62, and proportion coefficient of subgrade reaction \(m\) = 26.24 MN/m\({}^{4}\). The relative density was not given because the maximum and minimum void ratios are easy to access only in the absence of clay components and hydrophilic minerals. As demonstrated in Figure 3, the coefficient of uniformity \(C_{\mathrm{u}}\) and coefficient of curvature \(C_{\mathrm{c}}\) were 5.74 (<6.0) and 0.94 (<6.0), respectively, and thus the soil classification is given as SP. The ratio of pile diameter to grain diameter \(d_{50}\) is approximately 100, comfortably greater than the minimum requirement of 40 [25]. Figure 1: Experimental setup. (**a**) model pile and slope; (**b**) geometric dimension. Figure 2: Installations of strain gauges and earth pressure cells.