## 3 Test Process  
### Model Piles, Test Apparatus, and Test Site  
There were six single-plate helical piles (see Figure 4) used in model test. In order to connect these model piles with relevant test apparatus used in the model test, there was a flange on the top of each helical pile. All the helical piles were manufactured by steel with one steel helix with thickness, \(t\) = 0.003 m, welded on a steel central shaft, which was steel pipe pile with the outside diameter of shaft, \(D_{\text{S-out}}\) = 0.06 m, the inside diameter of shaft, \(D_{\text{S-in}}\) = 0.052 m, and the length of shaft, \(L\) = 1 m. The outer diameters, \(D_{\text{H-out}}\) = 0.12 m, 0.16 m, and 0.20 m, and pitches of helixes, \(p\) = 0.03 m, 0.06 m, 0.10 m, and 0.16 m, used in each model pile were different. The details about the dimensions of model piles are shown in Table 1.  
All tests were conducted in a reinforced concrete tank with dimensions of 4 m internal length, 4 m internal width, and 2 m internal depth (see Figure 5) in Tianjin University. The test apparatus, which was fixed with a hold and placed on the tank, consisted of three parts: (a) The servo motor which controlled the vertical motion of model piles; (b) a servo motor which controlled the rotational motion of model piles; (c). the monitoring part which consisted of one tension and compression load cell (measuring range: \(-\)2-2 t; accuracy: 10 N) and a torque sensor (measuring range: \(-\)500\(\sim\)500 N-m; accuracy: 0.25 N-m). For the tension and compression load cell, its bottom was connected with a steel plate, and the model pile was connected with this plate through its flange. In order to avoid  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Name of Model Piles**} & \(\begin{array}{c}D_{\text{S-in}}\\ \text{(m)}\end{array}\) & \(\begin{array}{c}D_{\text{S-out}}\\ \text{(m)}\end{array}\) & \(\begin{array}{c}D_{\text{H-out}}\text{(m)}\end{array}\) & \(\begin{array}{c}p\text{(m)}\end{array}\) & \(\begin{array}{c}L\text{(m)}\end{array}\) & \(\begin{array}{c}I\text{(m)}\end{array}\) & \(\begin{array}{c}t\text{(m)}\end{array}\) \\ \hline H-1 & 0.052 & 0.06 & 0.12 & 0.03 & 1 & 0.06 & 0.003 \\ H-2 & 0.052 & 0.06 & 0.16 & 0.03 & 1 & 0.06 & 0.003 \\ H-3 & 0.052 & 0.06 & 0.20 & 0.03 & 1 & 0.06 & 0.003 \\ H-4 & 0.052 & 0.06 & 0.16 & 0.06 & 1 & 0.06 & 0.003 \\ H-5 & 0.052 & 0.06 & 0.16 & 0.10 & 1 & 0.06 & 0.003 \\ H-6 & 0.052 & 0.06 & 0.16 & 0.16 & 1 & 0.06 & 0.003 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters for the model piles used in test.  
Figure 4: Photograph of the model piles. (**a**) Pipe pile and helical piles with different outer diameters (\(D_{\text{H-out}}\)). (**b**) Pipe pile and helical piles with different \(p\).  
the influence of torque on the tension and compression load cell, there were four linear bearings fixed on the steel plate. For the torque sensor, there were four fixed bars around it to prevent the influence of compression or tension. With the help of device mentioned above, two sensors could work independently and monitor the vertical force and installation torque of helical pile at the same time. The test apparatus could control the vertical motion and the rotational motion of helical piles at the same time. In order to provide enough counter-force (2.5 t), two concrete blocks, each with 500 kg weight, were put on the both ends of the hold. The test apparatus had contacts with the panel box and the data acquisition system.