## 4 Results
### Microscopic Fracture Evolution and Macroscopic Failure Characteristics
#### 4.3.2 Characteristic Analysis of AE \(b\)-Value  
The \(b\)-value of AE is an important indicator for analyzing material fracture and microcrack activity. A high \(b\)-value indicates a higher proportion of small-scale microfracture events, suggesting that the rock material predominantly experienced the development and expansion of small-scale cracks with relatively low damage to the sample. A low \(b\)-value, on the other hand, reflects a higher proportion of large-scale microfracture events, indicating that small-scale cracks further coalesce into microscopic or even macroscopic fractures, leading to a higher level of damage in the rock sample [38]. The relationship for the \(b\)-value is given by:  
\[\log_{10}N=a-bM \tag{4}\]  
where \(N\) is the number of events observed within a specific time and region; \(M\) is the amplitude or energy of the AE events; and a and b are constants.  
Based on Equation (4), the evolution of the b-value during the loading and unloading processes was calculated. To avoid large errors due to the limited number of AE events, a 50 s time interval was chosen, with a 10 s time step for sliding sampling. The amplitude interval was set to 5 dB.  
As Figure 23 shows, although the b-value fluctuated with increasing deviatoric stress owing to inherent natural defects in the samples, the overall evolution trend exhibited a high degree of similarity. By combining the triaxial test results from the four loading paths, it was observed that the decreasing trends of the initiation, closure, and damage stresses were closely related to changes in the AE counts and \(b\)-value. As the water content increased, the initiation and damage stresses of the rock decreased significantly, indicating that microcracks began to initiate and propagate at lower stress levels. In particular, under high-water-content conditions, the AE counts increased significantly, indicating that  
Figure 22: Relationship between acoustic emission (AE) count, cumulative count, and strain.  
microcracks formed and expanded more frequently at earlier stages. This is consistent with the rapid decrease in the \(b\)-value, which indicates that not only did the number of cracks increase, but their scale also progressively increased, ultimately leading to a significant reduction in rock strength. The sharp decline in the \(b\)-value reveals the intensity and instability of crack propagation, especially under the complex stress conditions of Paths III and IV, where this change was more pronounced.  
Macroscale failure images further validated these findings. Under high-water-content conditions, the failure mode was characterized by more pervasive cracks, leading to the eventual disintegration of the rock. The increase in the AE counts and decrease in the \(b\)-value, as indicated by the AE results, reflect the continuous initiation and propagation of microcracks, which eventually coalesced into macrocracks. Once these cracks reached a certain scale, they ultimately led to macroscale instability and rock failure. Combining the stress-strain curve, AE counts, cumulative energy, and evolution of the \(b\)-value with the macroscopic failure mode showed that under high-water-content conditions, the rock exhibited lower initiation stress, more frequent crack activity (higher AE counts), more intense crack propagation (rapid decline in \(b\)-value), and faster energy accumulation, ultimately resulting in a failure mode characterized by pervasive cracks.  
Figure 23: Relationship between AE \(b\)-value and offsetting force.