## 4 Analysis Results and Discussion  
### Digital Image Correlation Analysis  
When conducting digital speckle analysis, it was found that the variation trend of the deformation field was more pronounced than that of the strain field at different loading stages. Additionally, the variation patterns of the strain field and deformation field differed  
Figure 3: The failure conditions of the specimen at each stage of the loading process during the goat failure test. (**a**) Initial state, \(t=0\) s; (**b**) upper left corner fracture, \(t\approx 1420\) s; (**c**) bottom fracture, \(t\approx 1421\) s; (**d**) overall instability, \(t>1421\) s. The yellow circles indicate the locations of the cracks during the loading process. Figure 2: The curves of the loading process in the goat failure test: (**a**) the force–time curve and the corresponding stress–time curve; (**b**) the stress–strain curve. in both the horizontal and vertical directions. For comparative analysis, the moments with significant horizontal deformation were selected for a slicing analysis of the horizontal deformation patterns, followed by analyzing the horizontal strain changes at the same time points. Similarly, the moments with obvious vertical deformation were selected as time points to slice and analyze the vertical deformation patterns, followed by analyzing the vertical strain changes at the same time points. The horizontal displacement evolution results of the specimen during the loading process are shown in Figure 4, corresponding to the results of the X direction in the specimen coordinate system. It can be seen from the figure that during the process from the beginning of loading to 654 s, the overall horizontal deformation of the specimen is relatively small, approximately distributed between \(-0.06\) mm and \(-0.07\) mm, indicating that the horizontal deformation occurs along the negative direction of the X-axis (to the left in the figure). Meanwhile, two deformation difference zones are formed on the left and right sides of the roof and floor of the goat, respectively. The horizontal deformation of the surrounding rock on the left side of the goat is obviously greater than that on the right side, indicating that two tensile stress regions have formed. Figure 4: Displacement evolution in the X direction of the goat instability experiment. The white square indicates the excavated goat in the specimen. During the continued loading process, the deformation difference between the left and right sides of the goaf becomes increasingly significant, and the tensile stress in the surrounding rocks above and below the goaf also increases. When loaded to about 830 s, a sudden change in horizontal deformation occurs above the goaf, indicating the formation of a crack. As the loading continues to around 848 s, a crack also occurs in the surrounding rock below the goaf, with another sudden mutation region appearing. During the further loading processes, the deformation difference between the left and right sides continues to increase. When loading to 1167 s, a region with a significant deformation difference appears in the inclined direction of the upper left corner of the goaf, and the surrounding rock of the floor exhibits a horizontal deformation stratification phenomenon. When the loading reaches 1236 s, the horizontal deformation difference at the upper left corner of the goaf and the horizontal deformation stratification in the floor surrounding rock become more pronounced, indicating the potential formation of a crack. As the loading process continued to 1332 s, a horizontal deformation difference area appeared in the lower left corner of the goaf, along an inclined left direction. Additionally, an abnormal horizontal deformation area was observed at the horizontal deformation stratification position, indicating that cracks had begun to initiate and develop in the floor rocks. After 2 more seconds of loading, the difference in the lower left corner of the goaf became increasingly noticeable, clearly indicating the presence of cracks.