## 4 Results and Discussion  
### Deformation Field Evolution  
The image captured at the beginning of an experiment was taken as the reference image, and the other images captured during the experiment were the deformed images. The second-order STS-DIC algorithm was used to calculate the displacement fields, and then the strain fields (i.e., maximum shear strain fields) could be obtained. For the DIC process, the size of the spatial-temporal subset is 13 \(\times\) 13 \(\times\) 5 pixels. As shown in Figure 3, six points (A-F) were marked on the stress-time curve, and the corresponding strain fields were determined. Points A and B belonged to the initial loading stage, where the strain values were small, and the strain distribution was uniform. With increasing stress, some small strain concentration regions occurred in the strain field, as shown by point C, but the strain values were still small. At point D, an obvious deformation concentration region occurred in the lower part of the strain field, and this was defined as the starting point of the deformation localization. Point E corresponded to the first peak stress, and a distinct deformation concentration region with a band shape was formed that was called a deformation localization band (DLB). At the peak stress (point F), another DLB formed. After an abrupt drop in stress, the specimen failed because of the rapid growth of macro-cracks (point G). The deformation fields shown by the images at point F and point G indicate that the final failure of the rock specimen resulted from the evolution of the deformation localization. Figure 2: Experiment setup: (**a**) schematic of the experiment system and (**b**) specimen and AE sensors, (1–6) are the number of sensors. According to the above analysis, the evolution of the deformation localization plays a decisive role in rock deformation and failure. To analyze the evolution of the deformation field in the deformation localization stage in detail, the strain fields corresponding to points 1-6 in Figure 4 were selected, as shown in Figure 5. Point 1 had a stress of 18.44 MPa (84.9% of \(\sigma_{\text{c}}\)) and was after the start of the deformation localization. Several obvious deformation concentration areas were observed that were independent of each other (regions 1-3 in Figure 5a). Point 2 had a stress of 20.21 MPa (93.1% of \(\sigma_{\text{c}}\)); because of the further development of micro-cracks in region 2, some deformation concentration areas connected to form a DLB (Figure 5b). Point 3 had a stress of 20.94 MPa (96.5% of \(\sigma_{\text{c}}\)) and was after the first stress drop; because of the greater connection between regions 2 and 3, an obvious DLB formed throughout the specimen (Figure 5c) and was defined as DLB1. Meanwhile, region 1 did not continue to develop. This indicates that the development of the deformation concentration areas is unbalanced during the evolution of the deformation localization, and some areas may not develop into the final DLB. Point 4 was the minimum of the first stress drop; the strain in DLB1 continued to increase, and a new deformation concentration area (region 4) appeared in the upper right part of the specimen, as shown in Figure 5d. At Point 5, the stress began to increase again, and region 4 developed into a new DLB (Figure 5e) that was defined as DLB2. Point 6 had a stress of 21.28 MPa (98.1% of \(\sigma_{\text{c}}\)); the strain in DLB1 and length of DLB2 continued to increase, as shown in Figure 5f. Figure 4: Marked points at different stress levels during the deformation localization stage. Figure 3: Stress–time curve and deformation field for the entire loading process, (A–G) are the marker points on the stress–time curve. In summary, when the DLB first started to form, its influence on the global mechanical properties of the rock specimen was small, and the rock specimen still bore the load as a whole. However, as the DLB evolved, the mechanical behavior of the rock specimen changed dramatically.