# Stability Analysis of Soil Flow Protector and Design Method for Estimating Optimal Length
## 3 Results and Analysis
### Stability  
Practically applying the SFP requires the establishment of relevant standards and design methods. To apply a relevant design method, the stability of the SFP should be reviewed. For this purpose, we examined the behavior of the SFP and the deformation in the ground for stability against the soil pressure using visual analyses. As shown in Figure 11a, the settlement increases with the distance from the box structure and proceeds in the downward direction of the structure. As shown in Figure 11b, movements of the upper part of the SFP wall in the opposite direction to the structure and of the lower part in the direction of the structure have occurred.  
Figure 10: Relationship between the settlement ratio and the ratio of the lower length of the SFP to the box structure height.  
The upper and lower parts of the SFP can be classified based on the lower edge of the structure; the surrounding ground and the structure were considered to be the front and rear sides, respectively. During the initial stage, the earth pressure acting on the SFP penetrated the ground and generated an active earth pressure at the front of the SFP and a passive earth pressure at the rear; the state of the static earth pressure resulted in a settlement. However, the direction of the ground's behavior at the front surface of the SFP was not clearly shown in this study. If the ground movement and the movement of the upper part of the SFP occur in opposite directions, a passive earth pressure is generated, and no earth pressure acts on the SFP wall in the same direction. [PERSON] et al. [26] performed an inverse analysis based on the numerical analyses of the results of inclinometer tests (Figure 12a) performed during field experiments. As shown in Figure 12b, the upper part of the SFP moves toward the outside of the structure. Therefore, it was confirmed that the displacement occurred in the lower front part of the structure; thus, the earth pressure occurred at the upper front of the SFP at rest, whereas the active and passive earth pressures occurred at the lower front and the rear side, respectively.  
Based on the results obtained by [PERSON] et al. [26], we considered the earth pressure acting on the upper part of the SFP conservatively to be zero during the safety assessment of the structure. Figure 13 presents a schematic for analyzing the stability of the SFP against  
Figure 11: Visual analysis: (**a**) ground behavior; (**b**) SFP movement.  
Figure 12: Displacement behavior of the ground: (**a**) inclinometer results; (**b**) finite element method results [26].  
the soil pressure. The safety factor (\(F_{s}\)) was calculated by considering the active earth pressure on the lower front surface of the SFP, the passive earth pressure on the rear surface, and the ground load on the upper front surface of the SFP. A standard safety factor of 1.2 was used for the retaining wall. The temporary earth retaining wall design standard gives a standard safety factor of 1.2 [27]. As a result, the safety factor was 1.690 when the optimum length ratio was 0.34 and the surface settlement ratio was 0.45; even with a settlement of 82.3 mm, the safety factor was 1.2 or higher. However, the surface settlement ratio did not increase significantly with an increase in the lower length of the SFP.