# Stability Analysis of Soil Flow Protector and Design Method for Estimating Optimal Length
## 1 Introduction
Therefore, it is extremely important to analyze the influence of SFP installation on the trends and behavior of a ground settlement under various conditions through scaled model experiments. Prior to performing the experimental investigation, we performed a literature review to analyze and verify the results of existing scaled model experiments, verified the reliability of the study results, and performed additional research to complement existing results. [PERSON] et al. [9] experimented by classifying the material stiffness of SFPs in terms of their flexibility and rigidity in sandy soil. They divided the SFPs into upper and lower sections based on the lower edge of the box structure and varied the installation length from 0 to 300 mm. The installation of the SFP reduced settlement, particularly for rigid SFP materials. Settlement also decreased with the increase in the installation length of the SFP, and the ratio of the settlement gradually decreased over a certain installation length. In summary, they proposed the optimum length ratios of 1.38 and 0.73 for flexible and rigid SFPs, respectively. Here, the length ratio is the length of the SFP divided by the height of the box structure. In previous studies, experiments were conducted by increasing the upper and lower installation lengths of the SFP at the same ratio, and the optimum length ratio between the overall length of the SFP and the height of the box structure was proposed for calculating the optimal length. However, the settlement of the ground and the change trend in the upper and lower section lengths of the SFP should also be considered. Moreover, in applying the results of a prior scaled model experiment in a field test, the SFP length was determined without considering the ground settlement and the earth pressure. Therefore, the overall length of the installed SFPs was too short. Subsequently, the lengths of the upper and lower SFPs were set differently, considering the stability of the earth pressure, and the results differed from those under the installation conditions reported in the previous study. To consider the effects of SFPs with different lengths and ground conditions, additional field tests should be executed. However, field tests are expensive and time-consuming. Therefore, in this study, we conducted a scaled model experiment to analyze the ground surface settlement reduction effect and suggest an optimal installation length based on the influencing factors with the SFP installed. We achieved this by analyzing the effects of changes in the installation lengths of the upper and lower sections of the SFP in sandy soil, as well as the interactions between the SFP and the ground. Furthermore, we varied the installation lengths of the upper and lower sections of the SFP to determine the relationship between the settlement volume based on changes in the installation length of the SFP, and we confirmed the behavior of the SFP and the adjoining ground through visual analyses. Finally, we determined the optimal installation length, while considering economic feasibility and stability by aggregating the results of existing research and those of the scaled model experiments performed in this study.