## 3 Experimental Results and Analysis  
### Analysis on Failure Process  
Macroscopic failure modes of the fractured red sandstone specimens can be determined by observing their failure results (Figure 4). Even though physical and mechanical information, including initial location, morphology, and the opening of macro-cracks, was obtained, it is still not convincing enough to investigate the expansion process of cracks and the evolution law of red sandstone failure only by this information. Therefore, the DIC method and the AE technology were adopted for more in-depth research and analysis of the strain field on the specimen's surface and the expansion characteristics and evolution law of the internal micro-cracks [19; 20; 21]. Uniaxial compression experiments were performed on red sandstone specimens with 30\({}^{\circ}\) and 60\({}^{\circ}\) prefabricated cracks, and the DIC-AE information obtained during the experiments is illustrated from Figures 5-8. Taking the specimen with a 30\({}^{\circ}\) prefabricated crack as an example, the deformation and failure process can be analyzed in four stages, namely, the crack closure stage I, the linear elastic deformation stage II, the crack expansion stage III, and the post-peak failure stage IV. Figure 4: Failure results of the fractured rock specimens: (**a**) 0\({}^{\circ}\); (**b**) 30\({}^{\circ}\); (**c**) 60\({}^{\circ}\); (**d**) 90\({}^{\circ}\). Figure 3: Schematic diagram of the DIC method. In crack closure stage I, the stress curve of the specimen is relatively gentle and concave upward, which is mainly caused by the compaction and closure of the micro-cracks and pores in the rock (Point a is a typical location). Meanwhile, the AE count is of a low frequency and a low intensity, the cumulative AE count increases slowly, and only a small number of low RA-high AF signals appear. A relatively concentrated area of strain can be observed at the right end of the prefabricated crack (Region 1 in the cloud image). In linear elastic deformation stage II, the stress curve is approximately linear. In this stage, new micro-cracks emerge and develop, local elastic deformation occurs, and internal elastic energy accumulates rapidly. Due to the interaction and friction between micro-cracks in the rock mass, the AE count becomes more frequent, the cumulative AE count is more frequent. Figure 5: Stress curves and DIC information of sandstone with a prefabricated 30\({}^{\circ}\) crack: (**a**) Point a; (**b**) Point b; (**c**) Point c; (**d**) Point d.  
Figure 6: Rupture modes of sandstone with a prefabricated 30\({}^{\circ}\) crack based on the KDE method: (**a**) Point a; (**b**) Point b; (**c**) Point c; (**d**) Point d.  
count begins to rise at a higher rate, and a small number of low RA-high AF AE signals and a tiny number of high RA-low AF AE signals appear. At Point b, no obvious cracks or strain changes appear in the digital image or the strain cloud image. At this moment, the specimen contains few internal cracks and is accumulating elastic energy. In crack expansion stage III, the stress curve fluctuates violently, lasts for a short period, and eventually reaches the specimen's peak stress. Massive micro-cracks emerge, develop, and expand continuously in the specimen, finally forming penetrating cracks until macro-cracks can be observed. Meanwhile, the AE count becomes frequent with several extremely large values, the cumulative AE count sur  
Figure 8: Rupture modes of sandstone with a prefabricated 60\({}^{\circ}\) crack based on the KDE method: (a) Point a; (b) Point b; (c) Point c; (d) Point d.  
Figure 7: Stress curves and DIC information of sandstone with a prefabricated 60\({}^{\circ}\) crack: (a) Point a; (b) Point b; (c) Point c; (d) Point d.  
low RA-high AF AE signals and some high RA-low AF AE signals are detected. At Point c, obvious macroscopic cracks have formed on the surface of the specimen, which expand upward and downward from the upper and lower ends of the prefabricated crack, respectively.