###### Abstract  
In this study, the digital image correlation (DIC) method and acoustic emission (AE) technology were combined to study the evolution of rock deformation localization in detail. The second-order spatial-temporal subset DIC (STS-DIC) algorithm was proposed and used for measuring strongly heterogeneous deformation fields of red sandstone specimens under uniaxial compression. The evolution of the deformation field was analyzed with a focus on the deformation localization stage. The length and width of the deformation localization band (DLB) were measured, and the relationships between the relative sliding rate of the DLB, the relative opening rate of the DLB, and the AE counts were identified. Deformation localization was found to result from the rapid evolution of the strain concentration before the peak stress. The complete development of the DLB is an inducing factor for catastrophic rock failure, and the failure modes of the rock specimens were consistent with the final state of the DLB. A good correlation was identified between the AE counts and the relative displacement rate of the DLB, and the sliding rate was found to have a significant influence on the AE counts. digital image correlation; rock mechanics; deformation localization; acoustic emission +
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the characteristics of rock deformation localization has been focused on qualitative analysis. Few in-depth and quantitative studies have been conducted. [PERSON] [PERSON] and [PERSON] and [PERSON] (2018) explored the possible application of the AE technique to identify the favorable or unfavorable state of rock salt and quantitatively analyzed the relationship between the AE signal and the fracture factors of rock salt. The results show that tensile microcracks release 85% of the AE energy. [PERSON] et al. [PERSON] et al. (2018) analyzed the degree of damage during the rock deformation process by using the deformation field value. Digital image correlation (DIC) ([PERSON], 1975; [PERSON], 1976; [PERSON], 1977; [PERSON], 1978; [PERSON], 1979; D  
The shape function of the subset \(g_{t}\) in the traditional, subset-based DIC can be written as follows:  
\[\mathbf{U}(\mathbf{X},t)=\mathbf{U}(\mathbf{X},t;\mathbf{a})=\left. \begin{bmatrix} u\\ v\end{bmatrix} \right|\left. \begin{array}{l}t=t_{i}\\ \mathbf{x}=\mathbf{x}_{c}\end{array} \right.\quad+\left. \begin{bmatrix}\frac{ \partial u}{\partial x}&\frac{\partial u}{\partial y}\\ \frac{\partial v}{\partial x}&\frac{\partial v}{\partial y}\end{bmatrix}  \right|\left. \begin{array}{l}t=t_{i}\\ \mathbf{x}=\mathbf{x}_{c}\end{array} \right[ \begin{array}{l}\Delta x\\ \Delta y\end{array} \right] \tag{2}\]  
where \(u\) and \(v\) are the horizontal and vertical components of displacement \(\mathbf{U}(\mathbf{X},t)\), \(\Delta x\) and \(\Delta y\) are the coordinate differences between the center point and any point in the subset, and \(\mathbf{a}\) is the unknown matrix to be solved. In the traditional subset-based DIC, the deformation mode of the subset (i.e., shape function) is generally assumed to be first-order [38; 39; 49]. However, the complexity of the deformation field evolution in the deformation localization process of rock is mainly reflected by a heterogeneous distribution in space and a nonlinear change over time. The first-order shape function cannot accurately describe strongly heterogeneous deformation. In fact, the deformation of solid materials is continuous over time. If deformed speckle images are captured continuously within a short time interval during an experiment, then the characteristic of continuous deformation over time can be introduced into an image analysis [50]. In this study, the subsets of the deformed image series captured in a short period were considered. According to the characteristics of rock deformation, a scheme termed second-order spatial-temporal subset (with the second-order shape function in spatial and a short period) was proposed, as shown in Figure 1b.