## 5 Conclusions  
This paper presents a series of numerical analyses performed using Plaxis 3D. Parametric studies are conducted to investigate the effects of earth berms on the PRSS in circular excavations. Additionally, the effective formation level considering the effects of earth berms under plane strain and axisymmetric conditions has been examined. The key findings are summarized as follows:  
1. Increasing the dimensions of the earth berms, such as height, top width, and bottom width, reduces lateral deflections of supporting piles significantly. The effect is more pronounced in the middle part of the piles, while it is less significant towards the top and bottom parts. Once the top and bottom widths of earth berms reach critical values of 0.3 \(h\) and 0.45 \(h\), respectively, further widening of the earth berms has little impact on the deformations of the supporting piles. 2. The earth berm's height has a significant effect on the bending moments of the supporting piles below the lowest waling, while its effect is less pronounced above this point. The top width of the earth berms has a greater influence on the bending moments of the supporting piles than the bottom width. When the top width is less than 0.2 \(h\), the maximum bending moment of the supporting piles decreases with an increase in top width. However, when the top and bottom widths exceed 0.2 \(h\) but remain below 0.4 \(h\), the maximum bending moment of the retaining piles slightly increases as the top width increases. As the bottom width increases, its impact on the maximum bending moment of the supporting pile tends to decrease. 3. The effect of earth berm on the ground surface settlement is similar to its effect on the lateral pile deflection. As the height, top width, and bottom width of the earth berm increase, the ground surface settlements tend to decrease. However, the reduction in ground surface settlement gradually diminishes as these geometric parameters continue to increase. Once the top and bottom widths of the earth berm reach 0.30 \(h\) and 0.45 \(h\), respectively, their impact on reducing surface settlement becomes essentially negligible. However, the range of positional variations for the maximum ground surface settlement is not as extensive as that of the maximum lateral pile deflection. 4. [PERSON]'s approach is effective in considering the impact of an earth berm on the stability of the PRSS under axisymmetric conditions. In addition, the stability of the earth berm needs to be considered when its height is high. In circular excavations, it is recommended to analyze the stability of PRSS based on axisymmetric conditions. This is because it leads to excessively conservative results under plane strain conditions. 5. Under plane strain conditions, the raised effective formation level in deformation analysis increases as the berm height increases and eventually stabilizes at a constant  
Figure 16: Relationship between berm height and REFL [59]. value of 2.5 m. On the other hand, under axisymmetric conditions, the raised effective formation level in the deformation analysis also increases with increasing berm height, but it converges to a constant value of 3.6 m.  
Conceptualization, C.G. and L.C. ; methodology, L.C. ; software, L.C. ; validation, L.C. ; formal analysis, L.C. ; investigation, L.C. ; resources, C.G. ; data curation, L.C. ; writing--original draft preparation, L.C. ; writing--review and editing, C.G., D.C. and L.C. ; visualization, L.C. ; supervision, C.G. ; project administration, C.G. ; funding acquisition, C.G. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Key Research and Development Program of China, grant number 2021 YFC3100803; Science and Technology Research and Development Program of China State Railway Group Co., Ltd., grant number N2021G056. Not applicable. The data presented in this study are available on request from the corresponding author due to restrictions on privacy.