## 3 Model Test Verification
### Analysis of Test Results  
(1) Displacement analysis of pile top  
The relationship between the horizontal load of the pile top and the horizontal displacement of the ZK pile, ZPJ-35 pile, and ZPW-25 pile is shown in Figure 5.  
As can be seen from Figure 5, under different pile top horizontal loads, the horizontal displacements of ZPJ-35 and ZPW-25 piles measured by tests are always smaller than ZK piles. Under the eighth level load of 50 N, the measured pile top displacements of the ZPJ-35 pile, ZPW-25 pile, and ZK pile are 5.32 mm, 5.42 mm, and 6.09 mm, respectively. The pile top displacements of the squeezed branch pile are reduced by 14% and 12% compared with those of the straight pile, indicating that the existence of the squeezed branch pile effectively improves the horizontal bearing stiffness of the pile. Through the fitting analysis of the test data, the load-displacement relationship of the ZK pile and ZPW-25 pile conforms to the quadratic parabola relationship, while the curve of the ZPJ-35 pile has good linearity. Figure 5 shows that the load-displacement data points of the ZPJ-35 pile obtained by the test are scattered around the load-displacement curve of the ZPJ-35 pile obtained by using the calculation theory in this paper. And the two have a good coincidence. Under the eighth-order load, the theoretical calculation result of the pile top displacement of the ZPJ-35 pile is 5.03 mm, which has a relative error of 5.45% compared with the measured result of 5.32 mm. Under the same load, the theoretical calculation result of the pile top displacement of the ZPW-25 pile is 4.45 mm, which has a 17.90% relative error from the measured result of 5.42 mm. The error between the calculation results and the measured results of the pile top horizontal displacement of the two squeezed branch piles is less than 20%, which is ideal in the model test with a small scale. And the theoretical calculation of the pile top horizontal displacement can be considered credible. (2) Analysis of pile top rotation angle  
The relationship between the pile top horizontal load and pile top angle of the ZK pile, ZPJ-35 pile, and ZPW-25 pile is shown in Figure 6.  
As shown in Figure 6, the existence of a bearing plate makes the pile top rotation angle of ZPJ-35 and ZPW-25 piles always smaller than that of ZK piles under different pile top horizontal loads. Under the eighth level load with a size of 50 N, the measured pile top rotation angle of ZPJ-35 pile, ZPW-25 pile, and ZK pile is 3.750\({}^{\circ}\), 3.434\({}^{\circ}\), and 4.542\({}^{\circ}\), respectively. The pile top rotation angle of the squeezed branch pile is reduced by 21% and 32% compared with that of the straight pile. Obviously, the existence of the bearing plate effectively limits the pile top angle displacement. The fitting of the test data shows that  
Figure 5: Ground displacement between ZK pile and ZPJ-35 pile, ZPW-25 pile. (**a**) Comparison between the ZK pile and the ZPJ-35 pile by testing, theory and fitting curves about ground displacement. (**b**) Comparison between the ZK pile and the ZPW-25 pile by testing, theory and fitting curves about ground displacement. the load-top angle of the pile conforms to the quadratic parabola relationship between the straight pile and the squeezed branch pile. As can be seen from Figure 6, the load-top rotation angle data points of the ZPJ-35 pile obtained by the test are scattered around the load-top angle curve of the ZPJ-35 pile obtained by using the calculation theory in the paper, and the two are in good agreement. Under the eighth-order load, the theoretical calculation result of the pile top rotation angle of ZPJ-35 is 3.314\({}^{\circ}\), which has a relative error of 11.63% compared with the measured result of 3.750\({}^{\circ}\). Under the same load, the theoretical calculation result of the pile top rotation angle of the ZPW-25 pile is 3.047\({}^{\circ}\), which has a 11.27% relative error from the measured result of 3.434\({}^{\circ}\).