## 3 Two-Dimension Dynamic Numerical Analysis
### Design Parameters
#### 3.2.2 H-pile Parameters  
The dimensions of the H-pile were \(300\times 300\times 10\times 15\) mm, which are the same as those used in the field test. During the analysis, the support was applied as a linear elastic model, and the axial stiffness (EA) and bending stiffness (EI) were calculated using Equations (1) and (2), where the elastic modulus of the H-pile (\(E_{\mathrm{s}}\)) was 210,000 MPa. These equations were derived with reference to the Plaxis manual [26]. Table 5 shows the H-pile parameters according to the installation interval (_c.t.c._). \[\mathrm{EA}=E_{\mathrm{s}}\times A/c.t.c, \tag{1}\]  
\[\mathrm{EI}=E_{\mathrm{s}}\times I_{\mathrm{X}}/c.t.c, \tag{2}\]  
where \(E_{\mathrm{s}}\) is the elastic modulus of the H-pile (kPa), \(A\) is the area of the H-pile (m\({}^{2}\)), \(I_{\mathrm{X}}\) is the moment of the second order of the H-pile (m\({}^{4}\)), and _c.t.c._ is the installation interval of the H-pile (m). _Appl. Sci._**2019**, 9, 2213  
Figure 8: Vertical displacement at the top for each type: D-F2-B2-10 (type A), S-F1-10 (type B), D-F4-B4-5 (type C), S-F2-5 (type D), D-F4-B2-7.5 (type E), and D-F2-B4-7.5 (type F). Figure 7: Lateral displacement at the top for each type: D-F2-B2-10 (type A), S-F1-10 (type B), D-F4-B4-5 (type C), S-F2-5 (type D), D-F4-B2-7.5 (type E), and D-F2-B4-7.5 (type F). Figure 10: Vertical displacement at the bottom for each type: D-F2-B2-10 (type A), S-F1-10 (type B), D-F4-B4-5 (type C), S-F2-5 (type D), D-F4-B2-7.5 (type E), and D-F2-B4-7.5 (type F). Figure 9: Lateral displacement at the bottom for each type: D-F2-B2-10 (type A), S-F1-10 (type B), D-F4-B4-5 (type C), S-F2-5 (type D), D-F4-B2-7.5 (type E), and D-F2-B4-7.5 (type F). Figure 7 shows the results of the lateral displacement at the top of the retaining wall. As shown, types B and D, which are single supports, have a much larger lateral displacement than a dual support. This result indicates that a dual support has a greater load resistance than a single support. This is because the effects of the front and back supports are combined to transfer the support effect, increasing the efficiency. Comparing the results for the single supports, it is evident that type D, with a smaller number of H-beams, has a larger displacement than type B. Comparing the results for the dual supports, the largest lateral displacement occurred in type C, and the smallest lateral displacement occurred in type A. The larger the number of H-beams, the greater the load resistance. Types E and F were compared with the same number of H-beams but for different numbers in the front and back. It was determined that the lateral displacement of type F was approximately 2 mm larger than that of type E, but no other significant differences were shown. The results indicate that if the support has the same number of H-beams, the distribution of beams, when relatively large in number at the front or back, did not have a significant effect. Combined with the results for the lateral displacement, it can be determined that the most significant influence on the lateral displacement is the support type, namely, single or dual support, during dynamic loading. The next most influential factor is the number of H-beams, whereas the least influential factor is their arrangement, i.e., their distribution between the front and back for the same number of H-beams. Figure 8 shows the vertical displacements at the top of the retaining wall. According to the results of the support type, a greater amount of vertical displacement occurred with the single support than with the dual support. This result indicates that a dual support has greater resistance to a vertical displacement under a dynamic load than a single support. To analyze the effect of the number of H-beams, the results for dual support types A and C were compared along with single support types B and D. For the single support, the vertical displacement was larger for type D with fewer H-beams than that of type B.