# Shear Band Characterization of Clayey Soils with Particle Image Velocimetry
## 3 Digital Image Analysis  
The particle image velocimetry (PIV) technique was first developed in the field of fluid dynamics by [PERSON] [29] and uses digital images to measure displacement and deformation in soil specimens in the field of geotechnics [20; 23; 27; 30]. The PIV technique was used to measure the displacement and deformation in a target specimen as follows: (1) Digital images were captured before and after the deformation of the target specimen. (2) Cross-correlation was performed on the pixel subsets in the images before and after deformation, as shown in Figure 4. (3) The correlation coefficients found by the cross-correlation were interpolated to find the points with the correlation. (4) The location of the pixel subset with the highest correlation was used to calculate the relative displacement for each location in the specimen [15]. The commercial software GeoPIV [31] was used for the PIV analysis. The displacement for each of the target specimen's locations was measured, and the strain was calculated to analyze the deformation behavior within the specimens during the experiments [15].  
Figure 3: Flowchart of the experiments conducted in this study.  
The accuracy of the PIV technique is primarily influenced by the strain interval and size of the pixel subset. Therefore, these factors need to be considered when determining the optimal conditions. The accuracy of the PIV technique improves as the strain interval decreases [32]. However, if the strain interval is overly small, the analysis time increases, and it becomes difficult to examine the deformation characteristics. Therefore, a suitable strain interval must be found. [PERSON] et al. [27] found that a random pattern must be created by sprinkling black ink because there is no unique texture for each particle in clayey soil, unlike in sandy soil. This method showed a satisfactory accuracy of 0.37% for the strain. In this study, random patterns were created by a black spray as well, and the vertical strain interval was set at 0.25% to ensure the reliability of the study results.  
As the size of the pixel subset that is used with the PIV technique increases, the pixel subset's uniqueness increases, and it commonly becomes possible to obtain highly accurate analysis results [32]. However, to calculate the displacement at various locations, the size of the pixel subset needed to be small. Therefore, calculating an appropriate pixel subset size is also important. In this study, DIA was performed on the specimen's original image and images in which the rigid body had been moved by 1 pixel at various pixel subset sizes. The results verified the accuracy of the GeoPIV program. As shown in Figure 5, the accuracy and precision increased with the size of the pixel subset. After \(80\times 80\) pixels, the increment of the improvement in accuracy became smaller. A maximum error of around 1.5% (0.015 mm) was observed at \(80\times 80\) pixels. This error was determined to be sufficiently small, thus the optimal pixel subset size for DIA was set to \(80\times 80\) pixels.  
To exclude the boundary effect (i.e., the effect of the friction between the specimen and the upper and lower caps) as much as possible, DIA was performed on the area shown in Figure 6 at 720 (\(16\times 45\)) locations, and the displacement was calculated.  
Figure 4: Cross-correlation with the Particle image velocimetry (PIV) technique.  
Figure 5: Accuracy and precision of the GeoPIV program: accuracy (left) and precision (right).