## 3 Numerical Modeling and Validation
### Validation  
In order to assess the reliability of 3D finite element models in predicting the response of the PRSS, a comparison and discussion of the results from numerical simulations and field measurements are conducted. The numerical analysis, as shown in Figure 5, demonstrates a reasonable agreement with the field data in terms of capturing the lateral pile deflections and ground surface settlements. However, there are some discrepancies. For example, in all but the last stage, the difference in lateral pile deflections between the calculated and measured values is larger above the excavation level than below it. The observed discrepancies can be attributed to the inherent limitations of the finite element method in geotechnical problems (e.g., inevitable simplifications of the actual behavior of soils and their interaction with structures under complex field conditions), without a more sophisticated simulation of the entire construction process (e.g., neglecting the PRSS installation process before excavation, and the segmental assembly process of the walings). Nevertheless, it can generally be stated that the finite element model furnishes a reasonable refection of the observed behavior of an excavation supported by the PRSS. Consequently, it is feasible to perform a subsequent parametric analysis using this model to investigate the effect of the earth berms on the PRSS. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Stage** & **Simulation Process** & **Calculation Type** \\ \hline
0 & The initial stresses were generated by the “\(K_{0}\)” procedure & \(K_{0}\) procedure \\ \hline
1 & Installation of retaining piles, crown beams, and laggings & Plastic \\ \hline
2 &
\begin{tabular}{c} Reset displacement of soil and structures (A wished-in-place wall is \\ adopted and installation effects are ignored) \\ \end{tabular} & Plastic \\ \hline
3 & Excavation to GL-2.5 m, installation of 1 st waling & Plastic \\ \hline
4 & Dewatering to GL-6.5 m & Plastic \\ \hline
5 & Excavation to GL-5.5 m, installation of 2 nd waling & Plastic \\ \hline
6 & Dewatering to GL-12.5 m & Plastic \\ \hline
7 & Excavation to GL-8.5 m, installation of 3 rd waling & Plastic \\ \hline
8 & Excavation to GL-11.5 m, installation of 4 th waling & Plastic \\ \hline
9 & Dewatering to GL-21.5 m & Plastic \\ \hline
10 & Excavation to GL-13.5 m, installation of 5 th waling & Plastic \\ \hline
11 & Excavation to GL-20.0 m & Plastic \\ \hline
12 & Excavation to GL-20.0 m & Safety \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Numerical simulation process related to construction workflow. Parametric analyses are carried out to analyze the impact of various geometric parameters of the earth berm on the behavior of the PRSS. The parameters used to characterize the geometry of the earth berm in the study of [PERSON] and [PERSON] [PERSON] and [PERSON] (1996) included height (\(H\)), top width (\(B_{1}\)), and slope (\(S\)), as depicted in Figure 6. However, in order to facilitate the qualitative comparison of the effect of each parameter on the PRSS, the bottom width (\(B_{2}\)) is used in this paper instead of the slope (\(S\)) to characterize the geometry of the earth berm. A series of numerical models are performed to analyze the effect of the earth berms on the PRSS, as listed in Table 4. It is noteworthy that the final excavation depth (\(h\)) remains constant at 20 m for all the analyses. In groups No. 1, 2, and 3, the height, top width, and bottom width are varied from 0.1 \(h\) to 0.35 \(h\), 0 to 0.75 \(h\), and 0.15 \(h\) to 0.65 \(h\), respectively, to examine the effect of the berm's geometric parameters on the performance of the PRSS, such as the lateral deflections and bending moments of the supporting piles and the ground surface settlements. The parameter analysis is performed based on the final working conditions, where the ground water level is consistently maintained at 2 m below the excavation depth, indicating that the effects of earth berms are not influenced by the ground water.