## 4 Comparison with Other Retaining Structures
### Results and Discussion  
#### 4.2.1 Behavior of the Retaining Wall (Vertical Piles)  
The deflection of the wall (vertical piles) when excavation is supported using the CRS approach is presented in Figure 18. Once again, the wall deflections are taken with respect to the vertical center line of the wall and the values are taken to be positive when the wall (piles) moves inwards. It can be seen from Figure 18 that the deformation of the wall (piles) increased significantly during the excavation process. The deflection forms a triangular distribution, with the maximum lateral wall deformation occurring at the top of the wall. The maximum movement is 26.6 mm when H = 5 m and this rapidly developed to 356.9 mm at the final excavation depth (i.e., 3.6% of H with H = 10 m). Therefore, appropriate measures would need to be taken to control the deformation induced by the excavation process. Figure 19 shows the evolution of the deflection of the wall (vertical piles) when HSRS-supported excavation is employed. Comparing Figure 10, Figure 18, and Figure 19, it is clear that the inclusion of batter piles or horizontal struts when H = 5 m can effectively reduce the lateral deformation occurring during subsequent excavation. Figure 16: Three-dimensional (3D) numerical models of an excavation supported using a cantilever retaining structure (CRS): (**a**) difference element mesh of the excavation supported using CRS; (**b**) expanded view of the difference element mesh. Figure 17: Three-dimensional (3D) numerical models of an excavation supported using a horizontal-strutted retaining structure (HSRS): (**a**) difference element mesh of the excavation supported using HSRS; (**b**) expanded view of the difference element mesh. Figure 19 shows that the maximum lateral wall movement developed at the top of the wall (piles), and that it rebounded outwards after the installation of the horizontal strut. The maximum deformations when H = 10 m are 16.0 and 18.9 mm in Figures 10 and 19, respectively, which are only 4.5% and 5.3% of the corresponding CRS values shown in Figure 18. It can be seen that the maximum deformation (16.0 mm) when HRS is employed is a little smaller than that of the HSRS (18.9 mm). The reason for this phenomenon is that the lower parts of the batter piles provide resistance to the soil movements below the excavation bottom, which may reduce the wall displacement. Even so, the deflections are very similar when HRS and HSRS are employed by comparing Figures 10 and 19. This suggests that the new retaining system (HRS) is very effective at reducing lateral deformation during excavation. Figure 20 presents the bending moments acting on the retaining wall (vertical piles) when CRS is used. (Again, the bending moments shown are those of the center liner of the retaining wall, and a positive value corresponds to the interior cross-section of the wall experiencing tension stress.) It can be seen that the bending moments are all negative and increase significantly during excavation. The maximum bending moment occurs at 1.5-3 m below the excavation surface. A maximum value of \(-\)216 kN-m/m is obtained when the excavation depth is 5 m, but this rapidly progresses to \(-\)1490 kN-m/m by the end of the final excavation step. Figure 21 shows the bending moments acting on the retaining wall (piles) when HSRS is used. Comparing Figures 11, 20 and 21, it is clear that installing batter piles or horizontal struts when the excavation depth is 5 m can significantly reduce the bending moment acting on the retaining wall (vertical piles). Three clear extreme values also appear in Figure 21 as they did in Figure 11. The first extreme values correspond to the maximum bending moments along the wall (piles) and have the  
Figure 19: Variation of the horizontal deflection of the wall (vertical piles) at different excavation depths when HSRS is used. Figure 18: Variation of the horizontal deflection of the wall (vertical piles) at different excavation depths when CRS is used.