# Stability Analysis of Soil Flow Protector and Design Method for Estimating Optimal Length
## 4 Conclusions  
In this study, we performed a scaled model experiment to propose a design method for the optimal installation length of an SFP and conducted stability analyses based on the influencing factors. We achieved this by analyzing the changes in the installation lengths of the upper and lower sections of the SFP in sandy soil, as well as the behavior of the SFP and the adjoining ground. The results were as follows. 1. We summarized the surface settlement due to the development of a cavity below the box structure as the average settlement ratio when the SFP is installed. We compared the situations with and without SFP installation, and found that the installation of the SFP could effectively reduce the surface settlement ratio in the range of 0.44-0.72. A visual analysis of the structure without the SFP showed that the soil flowed into the cavity, which caused a rapid settlement of the adjoining ground of the box structure. In comparison, by installing the SFP, the surface settlement was reduced because the inflow of soil into the cavity underneath the box structure could be blocked. 2. The settlement decreased with an increase in the lower length of the SFP, and the trend gradually converged above a certain length. The optimum length ratio of the SFP was 0.34, and the surface settlement ratio was 0.45. 3. The overall average settlement ratios were 0.71, 0.47, and 0.44, corresponding to SFP lower lengths of 50, 100, and 150 mm, respectively; the settlement decreased with an increase in the lower length. However, the effect of the settlement reduction due to the increase in the upper length was minimal when compared with that due to an increase in the lower length. Thus, we confirmed that surface settlement was dominantly affected by the change in the SFP lower length. 4. We calculated the safety factor (\(F_{s}\)) by considering the active earth pressure at the lower front surface of the SFP, the passive earth pressure on the rear surface, and the  
Figure 14: Flowchart for the SFP optimal length estimation and stability analysis. earth pressure generated at the upper front surface of the SFP, which we considered to be zero. When the optimum length ratio was 0.34 and the ground settlement ratio was 0.45, the safety factor was 1.69; even after ground settlement of 82.3 mm, the SFP remained stable with a safety factor of 1.2 or higher. 5. Our comprehensive analysis of the results showed that the lower length of the SFP is the key factor causing the reduction in the surface settlement, whereas the upper length influences the SFP stability with regard to the ground settlement. Based on these results, we proposed an equation for calculating an efficient and economical optimal length (\(L_{SFP}\)), while considering the function and role of each SFP. This calculated length has a significant settlement reduction effect, and it satisfies the safety factor (\(F_{s}\)) of 1.2. Based on this design method, we found the sum of the 85.0 mm lower length (\(l_{a}\)) (OLR of 0.34 and a ground settlement ratio of 0.45) and the 52.1 mm upper length (\(l_{\beta}\)), while using a margin factor of 1.5, to be 137.1 mm. 6. In this study, we proved the settlement reduction effect of the SFP based on the test results; we calculated the OLR and proposed a design method. Apart from the settlement analyses, further studies are required to establish a more reasonable and comprehensive design method; these studies must focus on a variety of conditions, such as the earth pressure and underground conditions, which are used to identify different properties, such as the soil viscosity, for various construction site applications. We expect the findings of this study to be beneficial for urban construction. The proposed methodology can be applied to analyze the settlement under various SFP lengths and to determine the optimal length to ensure the robustness and safety of structures. However, the scaled model experiment performed during this study only analyzed the results obtained via settlements arising from vibrations in loose sandy soil.