# Shear Band Characterization of Clayey Soils with Particle Image Velocimetry
## 1 Introduction  
Generally, soil failure occurs with the formation and development of one or more shear bands [1]. Applying a load to a soil element causes spatially non-uniform deformation that gradually focuses on a specific shear band [2]. When the load exceeds the soil element's shear strength, progressive failure (i.e., shear failure) occurs along the shear band where the deformation is concentrated. The soil behavior during this shear failure greatly influences the stability of nearby geotechnical structures. Therefore, it is important to identify the spatial distribution of deformation and the shear band characteristics from the initial state to the post-failure state (i.e., throughout the shearing process). This allows geotechnical engineers to accurately model the ground and evaluate the behavior of nearby geotechnical structures. With conventional shear test methods (e.g., triaxial, direct shear, and plane strain test), many researchers have adopted special experimental techniques, such as X-ray computed tomography(CT), scanning electron microscopy (SEM), and digital image analysis (DIA), to evaluate the spatial deformation and shear band characteristics within test specimens. For the triaxial test, X-ray CT [3; 4; 5; 6] or thin-section analysis with epoxy impregnation [7; 8; 9] is used to obtain the density variation of specimens, which is used to evaluate the spatial deformation. [PERSON] et al. [10; 11], [PERSON] et al. [12], and [PERSON] et al. [13] carried out biaxial direct shear tests of clay-rich fault rocks and applied SEM and X-ray texture goniometry (XTG) to analyze the microstructures of the sheared samples. However, these techniques are limited because they require expensive equipment and it is impossible to continuously observe deformation behavior during the entire experimental process from the beginning to the end. To overcome these limitations, the use of DIA techniques has recently become more widespread because they can take continuous direct measurements of spatial deformation [6; 14; 15; 16; 17]. DIA techniques are mainly applied to plane strain tests that use flat specimens because the internal state of a plane strain test specimen can be represented by images through a transparent side wall (i.e., the external state of the specimen). The spatial distribution of deformation can be continuously computed by tracing reference markers or grid points painted on a membrane enclosing a specimen. In addition, automated DIA techniques, which can accurately obtain a large amount of displacement data for a two-dimensional surface, have also been utilized in soil mechanics [15; 16; 17]. Unlike granular soil, there has been very little research on the spatial distribution of deformation and the shear band characteristics of clayey soil during shearing. Studies on assessing the shearing behavior of clayey soil have mainly focused on the overall stress-strain response of specimens during triaxial tests [18; 19; 20]. Some studies [8; 21] have used DIA in triaxial tests to evaluate the spatial distribution of deformation; however, triaxial test specimens, which have axial symmetry, have limited applicability because their surface and internal behaviors do not match [2]. [PERSON] [22] and [PERSON] and [PERSON] [23] used plane strain tests to evaluate the shear band characteristics (e.g., angle and thickness) of clayey soils during shear failure. However, even though such shear band characteristics change from the initial state to the post-failure state [17], the authors only observed the shear band during the experiment's final stage and were not able to continuously observe the spatial distribution of deformation and shear band characteristics. The main objective of this study was to evaluate the spatial distribution and evolution of deformation in clayey soil from the initial to the post-failure state, and to determine the shear band characteristics.