## 3 Results and Discussion
### Failure Characteristics  
Figure 9 shows the axial stress-strain curves and acoustic emission (AE) accumulation of the nonpersistent fractured rock specimens with different inclinations. The green histogram exhibits the AE counts over axial strain, the red scatters represent the green histogram exhibits the AE counts over axial strain, and the red scatters represent the accumulation of AE counts. Based on the accumulation trend of AE counts, the failure process can be classified into four stages: the first stage is the linear elastic stage (before point a), in which the microcrack behaviour is very limited and almost no AE signal is generated. After the longer linear elastic stage, the specimen enters the second stage (stable crack growth stage-from point a to b). In this stage, obvious acoustic emission signals are generated, and macroscopic cracks appear and expand inside the specimen. For the third stage (unstable crack growth from point b to c), the AE counts increase significantly with increasing axial load. As the slope of the cumulative AE counts increased rapidly, it also indicated crack growth and coalescence at this stage. The last stage can be called the post-destruction stage (after point c), in which the acoustic emission count is still increasing, the microcracks expand and develop into through-cracks, and the specimen exhibits obvious macroscopic failure. Figure 8: The experimental and simulated stress-strain curves. Figure 9: \(Cont.\)The particle flow simulation can monitor and count the damage evolution of microcracks in the fracture process. Figures 10-12 show the damage evolution process of the nonpersistent jointed rock mass with different inclinations. For each specimen, four points a, b, c, and d (which correspond with Figure 9) were recorded to analyse the microcrack accumulation and macrocrack growth during loading. For the specimen in the splitting failure mode (specimen S-0-K1), the damage evolution process is shown in Figure 9a-d. As shown in Figure 10a,b, before peak stress, crack initiation occurs randomly inside the specimen. Although there are many internal microcracks, no visible macroscopic fracture surface is found. When loading reaches point c, as the crack further develops, the cracks are densely generated on the outer edge of the joint, forming a damage zone (Figure 10c). As the loading continues, at point d, many microcracks gather inside several rock bridges, which indicates that these rock bridges are fractured. Additionally, the splitting failure surface is derived from the boundary position of the rock bridge. Figure 10: Microcrack development in specimen S-0-K1. Figure 9: Evolution of the load, AE count rate and cumulative AE count of sandstone over time. For the specimen with an inclination of 30\({}^{\circ}\) (S-30-K1), microcracks first concentrate near the joint surface (Figure 10(a)). With continuous loading, more microcracks gather in the rock bridge (Figure 10(b)). This indicates that the failure starts from the damage of the rock bridge, and the derivative development of microcracks is also located near the rock bridge. With the rapid increase in the number of cracks under axial loading, at point c, a potential shear fracture surface appears near the joint surface. At the same time, many microcracks are derived in the direction parallel to the loading direction, which means that a tensile fracture surface appears at the boundary of some rock bridges (Figure 10(c)). The mixed failure mode can be clearly seen in Figure 10(d). A large number of contact failures occurred near the top and bottom of the joint, and a splitting failure surface composed of microcracks appeared on the lower side. Unlike the specimen above, the microcracks first appeared in the interior of the rock bridge on the joint plane, and no microcracks appeared in the rest of the model (Figure 11(a)). As the loading continues, the microcracks accumulate in the rock bridge, leading to the continuous damage of the rock bridge (Figure 11(b)).