## 1 Introduction  
The drill-expanded concrete pile is a new type of variable cross-section cast-in-place pile based on the expanded pile and which has one or more expanded bodies at the appropriate positions based on the ordinary straight-hole cast-in-place pile created by drilling and expanding equipment. Compared with regular expanded piles, drill-expanded concrete piles have better pile quality and less disturbance of the soil around the pile due to the difference in construction technology. The process of creating a drill-expanded concrete pile is shown in Figure 1. First, the forward rotation is used to start drilling (Figure 1a). When drilling to the specified position, the equipment is reversed to start the diameter expansion, and the drilling-expanding arm gradually expands to cut the soil around the hole wall (Figure 1b). When the diameter is expanded, the drill stops rotating and becomes a reliable support for the diameter expansion operation until the diameter expansion is completed (Figure 1c). Then, the equipment is switched to drilling mode, after which the next diameter expansion is carried out. Finally, the steel cage is placed, and the concrete is poured (Figure 1d). A photo of a real drill-expanded concrete pile is shown in Figure 1e. For drill-expanded concrete piles, the expanded body and the soil are mutually embedded, which can result in the complicated behavior of the interface between pile and soil. Studying the process of soil displacement around the drill-expanded concrete pile is important for improving the interaction between the soil and the pile and to ensuring the long-term safety and stability of the drill-expanded concrete piles used in high buildings, power transmission lines, highways, and large bridges. Improving our understanding of the entire process of soil deformation around the pile is an important step forward for the field. The problem of the mechanics and deformation characteristics of the soil around the pile has been studied and discussed by many scholars using numerical simulation [1; 2; 3; 4], theoretical model [5; 6], and indoor physical test [7; 8; 9; 10; 11]. Due to better control of conditions and being more economically viable than in situ tests, physical model studies are being widely used in the study of the interaction between soil and expanded pile. [PERSON] et al. [12; 13] used indoor and on-site half-face pile models to obtain the load-bearing performance of a drill-expanded concrete pile under vertical and horizontal loads and analyzed the failure mode of the soil around the expanded pile. [PERSON] et al. [14] simulated variable cross-section piles with extra-large diameters and assessed the effect of several factors on soil deformation characteristics through indoor model tests. [PERSON] et al. [15] analyzed the soil deformation caused by expanded-base pile jacking with casing by particle image velocimetry (PIV). [PERSON] and [PERSON] [16] found that the compressive strength of concrete, the height-to-width ratio of the expanded plate, and the disc diameter ratio of the expanded plate were the major factors affecting the expanded plate's bearing capacity by using the small-scale model test. However, the displacement value of the soil around the pile cannot be obtained in the traditional indoor physical test, and in the transparent soil test, the transparent soil cannot simulate types of soil. Therefore, it is necessary to find a test method that can not only use the real soil but also reflect the displacement of the soil around the pile. The development of digital camera and computer analysis technologies enabled the subsequent development and improvement of digital image correlation (DIC) technology. DIC compares two images in order to determine the magnitude and direction of soil displacement. When two images undergo a displacement, the location of the peak of the correlation function determines the location of the best match between the two images, which corresponds to the magnitude and direction of the movement.