# Stability Analysis of Soil Flow Protector and Design Method for Estimating Optimal Length
## 2 Scaled Model Experiment
### Experimental Setup  
#### 2.2.1.  
It is necessary to consider the similitude ratio when fabricating an experimental model. The analogy law represents the relationship between an actual prototype and a scaled model. This law is based on dimensional analysis, which is a mathematical technique for inferring the theoretical relationship between variables to explain physical phenomena. Model-based experiments that do not consider the similitude ratio yield incorrect predictions of quantitative behaviors. Therefore, before conducting a model experiment, it is necessary to define a prototype that can meet the research objectives and to identify and apply a similitude ratio that conforms with the behavior of the prototype. These are performed to review the model behavior [10].  
To solve the aforenoted problems, many researchers have proposed various methods for model ground construction and verification. [PERSON] [11] studied the similitude laws of ground structures subjected to dynamic loads that use force ratios. [PERSON] and [PERSON] [12] studied the similitude laws of the nonlinear dynamic responses of soils using [PERSON]'s \(\pi\) theorem. [PERSON] [13] proposed the overall analogy of a saturated soil-fluid-structure system based on the geometrical similitude ratio (\(\uplambda\)) and the similitude ratio with respect to the density (\(\uplambda_{\rho}\)) and strain (\(\uplambda_{\epsilon}\)). [PERSON] and [PERSON] [14] classified the similitude law introduced by [PERSON] [13] into three types, using the concepts of cyclic mobility and strain softening. They also conducted a 1-G shaking table model reduction experiment on a quay wall structure by applying the similitude law.  
In this study, we used the similitude law and dimensional analysis suggested by [PERSON] [13] (Table 2) and applied a similitude ratio (\(\uplambda\)) of 18. We applied this similitude ratio of 18 to consider the size of the field and scaled model tests. For the tests presented in this paper, we used type 3 similitude because it is a strain-softening type with constant deformation even after the vibration stops, and a size-strain relationship cannot be introduced owing to the large deformation. We applied the value calculated using the relational expression of each parameter to the scaled model experiment using the applied similitude ratio.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multicolumn{2}{c}{**Length of Upper**} & **Length of Lower** & **Total Length of** \\  & **Part of SFP (mm)** & **Part of SFP (mm)** & **SFP (mm)** \\ \hline Non\_SFP & - & - & - \\ U50\_L50 & 50 & 50 & 100 \\ U100\_L50 & 100 & 50 & 150 \\ U150\_L50 & 150 & 50 & 200 \\ U100\_L150 & 100 & 150 & 250 \\ U150\_L150 & 150 & 150 & 300 \\ U200\_L150 & 200 & 150 & 350 \\ U50\_L250 & 50 & 250 & 300 \\ U100\_L250 & 100 & 250 & 350 \\ \hline \hline \end{tabular} Notes: Non: non-reinforcement; U: length of the upper part of the SFP with reference to the edge of the box structure; L: length of the lower part of the SFP with reference to the edge of the box structure; the numbers 50, 100, 150, 200, and 250 indicate the lengths of the upper and lower parts of the SFP..  
\end{table}
Table 1: Test cases.