## 4 Results and Discussion  
### The Effect of Bern Geometry on the Lateral Pile Deflection  
Figure 7 illustrates the influence of the earth berm's geometric parameters (height, top width, and bottom width) on the lateral deformation of the supporting piles. As presented in Figure 7a, the lateral deflection of the supporting pile decreases significantly with the increasing height of the berm. Such an effect occurs mainly in the middle of the pile and gradually diminishes along the top and bottom of the pile. Moreover, the reduction in lateral pile deflection decreases as the berm height increases, indicating a non-linear relationship between the two of them. A similar relationship exists between the lateral pile displacement and the top width of the earth berm (see Figure 7b). However, it appears that for soil types and retaining walls analyzed in this research, a top berm width of approximately 0.3 \(h\) is equivalent to reducing the excavation depth to the height of berm. That is to say, berm top widths greater than 0.3 \(h\) have little effect on pile deflection reduction. Figure 7c illustrates the correlation between the lateral pile deflection and the bottom width of the earth berm. The bottom width of the earth berm exhibits a similar impact on the lateral pile deflection as the top width and height of the berm. The lateral pile deflection increases with the width of the bottom width of the berm. Moreover, as the bottom width of the berm exceeds 0.55 \(h\), its increase has little effect on the lateral pile deflection. It closely approximates the passive zone, which is given by the intersection with the excavation level of a line drawn from the bottom of the supporting pile at an angle of (45\({}^{\circ}-\varphi^{\prime}/2\)) to the horizon, as depicted in Figure 6.  
Figure 8 presents the relationship between various geometric parameters of the earth berm and the maximum lateral pile deflections, as well as their corresponding locations. In terms of the height, top width, and bottom width of the berm, their increase results in a non-linear decrease in the maximum lateral deflection and an upward shift in the location of the maximum lateral deflection. Over the same range, the height of the berm has a more pronounced effect on the reduction in the maximum lateral deflections compared to the top and bottom widths of the berm. As the top and bottom widths of the berm reach the critical values of 0.3 \(h\) and 0.45 \(h\), respectively, meaning that the total width of the berm extends beyond the passive zone, their increase has an essentially negligible effect on the reduction in the maximum lateral deflection and its positional change. It implies that the earth berm's impact on the retaining wall arises from both its lateral resistance and the vertical pressure it exerts on the passive zone. As the height of the berm decreases from 0.35 \(h\) to 0.15 \(h\), the location of the maximum lateral pile deflection shifts downward from 0.45 \(h\) to 0.70 \(h\). Additionally, with a decrease in the top width of the berm from 0.00 \(h\) to 0.30 \(h\), the location of the maximum lateral pile deflection moves downward from 0.50 \(h\) to 0.61 \(h\). Similarly, a decrease in the top width of the berm from 0.15 \(h\) to 0.45  
Figure 6: Geometry of the earth berms.  
results in the location of the maximum lateral pile deflection shifting downward from 0.52 \(h\) to 0.61 \(h\). Furthermore, when the top and bottom widths of the berm exceed 0.30 \(h\) and 0.45 \(h\), respectively, the locations of the maximum lateral pile deflections do not change significantly with their variations.