# Stability Analysis of Soil Flow Protector and Design Method for Estimating Optimal Length
## 2 Scaled Model Experiment
### Experimental Method  
The model test procedures consisted of five steps: ground composition, small-scale box structure and SFP installation, vibration generation, image acquisition, and settlement measurement.  
First, to create a loose sandy ground with a constant density, we dropped the sand from a drop height of 0.1 m. We installed the SFP model in advance while considering the horizontal position of the box structure, and applied grease between the wall surfaces of the PSST and the SFP models. As the SFP model (408 mm) was narrower than the PSST model (410 mm), the applied grease prevented the sand from the constructed ground from flowing toward the SFP model.  
Second, we conducted the experiment by applying air pluviation to the lower level where the SFP model was installed. Thereafter, we dropped sand onto the bottom level where the box structure was installed to ensure that no differences occurred in the earth pressure between the front and back surfaces of the SFP model. To prevent penetration and minimize the friction of the sand, we applied grease to the contact surface between the box structure and the SFP model when installing the box structure.  
Third, to analyze the effect of the SFP settlement reduction, we forcibly generated the settlement of the soil in the PSST using a vibration motor installed under the PSST. The settlement was the highest after a vibration time of 1440 s.  
Fourth, for the visual analysis, we monitored the variations in the ground behavior and the SFP model from the front of the PSST.  
Fifth, after applying the vibration for 1440 s, we measured the settlement at each point from 0.1 \(B\) to 3.0 \(B\) on the model structure based on the width of the box structure (\(B=350\) mm). The settlement was measured at the front, middle, and rear of the wall surface of the PSST and the obtained values from the three locations were averaged. Figure 6 presents the installed ground, box structure, and SFP model. We applied the experimental conditions of the structure and ground at half sections to evaluate the settlement behavior up to a certain distance from the box structure during the scaled model experiment. This allowed the observation of the settlement reduction due to wall friction on the left side of the PSST; however, settlement reduction only appeared on a small section along the wall, which had little effect on the overall settlement beneath the box structure. In addition, the rightmost end of the model soil was located at a distance of more than three times the width of the box structure \(B\), which helped to minimize the impact on the settlement behavior due to the wall friction.  
Figure 5: Mechanical properties of the Jumunjin standard sand: (**a**) dry density of the Jumunjin standard sand, relative to the drop height; (**b**) internal friction angle, relative to the dry density; and (**c**) relative density, relative to the dry density.  
Finally, the experimental results were summarized in terms of the ratio between the distance from the end of the box structure and the width of the box structure. We compared the results and analyzed them based on the surface settlement at the corresponding point when the SFP was not installed.