## 2 Materials and Methods
### GeoPIV Analysis  
GeoPIV-RG application was used for the analysis of the images obtained from the experimental studies. GeoPIV-RG is designed for geotechnical research applications and is used in the analysis of problems involving large displacements and deformations. It is capable of sub-pixel measurement resolution. At least a 10-fold improvement in measurement accuracy was achieved over the most widely used particle image velocimetry (PIV) approach for all deformation modes including rigid body displacements, rotations, and strains (compression and share) [44].  
In our study, GeoPIV-RG software was used to analyze the settlement formed as a result of loading under model strip footing for each of the unreinforced and reinforced soil groups. GeoPIV-RG: It is an image analysis module designed for geotechnical research applications, running under the MATLAB R2019B program. To perform the analysis, a fixed camera was placed in front of the test tank and pictures were taken at regular intervals from the moment the soil was loaded. The basic principle of PIV is to look for changes in the analysis points of images taken at different times. The cross-correlation function can be calculated using the Fast Fourier Transform (FFT) to match the analysis points and obtain the motion states. The normalized cross-correlation function can be expressed as  
\[R(m,n)=\frac{\sum_{i}\sum_{j}u(i,j)\cdot v(i+m,j+n)}{\sqrt{\sum_{i}\sum_{j}u^{2 }(i,j)\sum_{i}\sum_{j}v^{2}(i+m,j+n)}} \tag{1}\]  
Here, \(m\), given in Equation 1 represents displacements in the horizontal direction, \(n\) represents the displacements in the vertical direction, \(u(l,j)\) and \(v(l,j)\) represent the gray distribution functions of the image before and after deformation [45]. The pictures taken during the tests were analyzed with the GeoPIV-RG software and the displacements in the soil were obtained. In the program, certain points are selected in the first picture. The program has divided the first image entered as data into very small areas. FFT was then used to compare each area with subsequent images in sequence. As a result of the subsequent analyses, the program obtained image processing results such as vector displacement, horizontal displacement, vertical displacement, general displacement, and stress distributions of the soil from the movement of soil particles (Figure 4).  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & & \multicolumn{2}{c}{**Fl = 24 mm**} & \multicolumn{2}{c}{**Fl = 48 mm**} & \\ \hline \multirow{6}{*}{Dr = 30\%} & \multirow{3}{*}{Fc = 1\%} & \multirow{3}{*}{7 group} & B & B & (24 mm 7 group; \\ \cline{3-5}  & & & 2B & 3 group & 2B & 1-glass \\ \cline{3-5}  & & & 3B & & 3B & 2-macromesh \\ \cline{3-5}  & & & & 2B & & 3-basalt \\ \cline{3-5}  & & & 2B & 3 group & 2B & 4-glass + macromesh \\ \cline{3-5}  & & & 3B & & 3B & 5-glass + basalt \\ \hline \multirow{6}{*}{Dr = 50\%} & \multirow{3}{*}{Fc = 1\%} & \multirow{3}{*}{7 group} & B & B & 6-macromesh + basalt \\ \cline{3-5}  & & & 2B & 3 group & 2B & 7-glass + macromesh + basalt \\ \cline{3-5}  & & & 3B & & 3B & 48 mm 3 group; \\ \cline{3-5}  & & & & & & 1-glass \\ \cline{3-5}  & & & 2B & 3 group & 2B & 2-macromesh \\ \cline{3-5}  & & & 3B & & 3B & 3-glass + macromesh) \\ \hline Total & \multicolumn{2}{c}{84 group} & \multicolumn{2}{c}{36 group} & \multicolumn{2}{c}{120 group} \\ \hline \end{tabular}
\end{table}
Table 4: Test program.  
Figure 4: PIV results: (**a**) Vectorial displacements; (**b**) horizontal contours; (**c**) vertical contours; (**d**) resultant contours; (**e**) incremental strain.