## 3 Two-Dimension Dynamic Numerical Analysis  
PLAXIS (ver. 2018, PLAXIS, Delft, Netherlands) [11] was used for the 2D dynamic numerical analysis. For the analysis site, the earth retaining method was applied for a high-speed double-line railway line through an embankment. An embankment generally uses a retaining wall structure, for which many static and dynamic studies are currently being conducted. Although a retaining wall is structurally different from an IER structure, many studies have been carried out on a dynamic numerical analysis of an embankment ground. In particular, among the retaining wall structures, a reinforced earth retaining wall reduces the load acting on the front wall by increasing the strength of the embankment ground using a grid. To take advantage of the structural characteristics of the back support of an IER structure, studies applying a reinforced earth retaining wall have been further referenced. [PERSON] et al. [12] analyzed a reinforced earth retaining wall applied to an embankment ground and used special three-node elements for each block and the boundary surface of the retaining \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Measurement Location** & **Displacement** & **Lateral Displacement (mm)** & **Lateral Displacement Ratio** \\ \hline \multirow{3}{*}{Height from bottom of embankment (m)} & 4.5 & 79.1 & 61.60 & 0.78 \\  & 4.0 & 70.0 & 56.40 & 0.81 \\ \cline{1-1}  & 3.0 & 57.1 & 45.20 & 0.79 \\ \cline{1-1}  & 2.0 & 42.8 & 35.90 & 0.84 \\ \cline{1-1}  & 1.0 & 29.4 & 25.30 & 0.86 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Lateral displacement and lateral displacement ratio after completion of embankment [10]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Case Name \({}^{*}\)** & \
\begin{tabular}{c} **Maximum Lateral Displacement** \\ **from Surcharge \(\Delta u\) (mm)** \\ \end{tabular} &
\begin{tabular}{c} **Number of H-piles** \\ **Per 10 m** \\ \end{tabular} \\ \hline
1 & D-F2-B2-10 & 7.11 & 10 \\
2 & S-F2-5 & Failure & 5 \\
3 & S-F1-10 & 17.99 & 10 \\
4 & D-F4-B4-5 & 13.06 & 5 \\
5 & D-F4-B2-7-5 & 9.83 & 7.5 \\
6 & D-F2-B1-15 & 5.4 & 15 \\ \hline \hline \end{tabular} \({}^{*}\)Description of case names: S(Single support)-F(Front support)2(Interval of front support(m))-(Number of H-piles per 10 m), D(Dual support)-F(Front support)2(Interval of front support(m))-B(Back support)2(Interval of back support(m))-10(Number of H-piles per 10 m).  
\end{table} 
Table 2: Lateral displacement from a surcharge based on numerical analysis [10]. Figure 3: Field test: (**a**) IER structure and (**b**) completion of surcharge load. wall front plate. In general, a constraint method has been adopted to achieve a more stable numerical analysis of the interface than that of a Goodman element used in FLAC. [PERSON] and [PERSON] [13] applied an analysis method and included a stiffener between the blocks. In the analysis described in [13], the stiffener was treated with a beam element. [PERSON] et al. [14] presented a 2D numerical analysis of a well-monitored pile-slab-supported embankment for the Beijing-Tianjin high-speed railway in China. The piles, which are arranged in a square shape, are a three-dimensional (3D) problem. To convert a 3D problem into a 2D problem, the equivalent elastic modulus of the pile wall was calculated as follows: \(\mathrm{E_{eq}}=E_{\mathrm{p}}a_{\mathrm{s}}+E_{\mathrm{s}}\) (\(1-a_{\mathrm{s}}\)), where \(E_{\mathrm{p}}\) and \(E_{\mathrm{s}}\) are the moduli of the pile and soil, respectively; and \(a_{\mathrm{s}}\) is the area replacement ratio, defined as the ratio of the pile cross-sectional area to the total area. In this study, an analytical approach that considers the wall area was used, and a retaining wall without a reinforcement was applied as an elastic model. For the 2D analysis, the wall was modeled by calculating the area of the H-beam constituting the retaining wall. The backfill can be simulated by assuming an elastoplastic material or an elastic material similar to that used in a general geotechnical structure problem.