## 3 Discussions
### Failure Intensity Estimations Based on the S Value  
The S value (used to quantify AE activity) comprehensively estimates the time, space, and intensity of secondary failures in a rock sample. It involves the event rate, average energy, and maximum energy, which help to reflect the concentration degree and energy scale of AE sources inside the rock mass [44]. The corresponding calculation formula is as follows:  
\[\mathrm{S}=0.117\mathrm{lg}(\mathrm{N}+1)+0.029\mathrm{lg}\frac{1}{\mathrm{ N}}\sum_{\mathrm{i=1}}^{\mathrm{N}}10^{0.075\mathrm{m_{\mathrm{ii}}}}+0.00075 \mathrm{m_{\mathrm{s}}} \tag{2}\]  
where m\({}_{\mathrm{si}}\) is the magnitude of each AE event, and m\({}_{\mathrm{s}}\) is the magnitude of the maximum AE event amplitude in the statistical window.  
Because the majority of AE events are captured during the final period of the test, Figures 9-11 focus on the AE results neighboring to the UCS status, and the corresponding period is marked by various colors. The main conclusions are as follows:  
1. The relatively high b-values and low S values remain for a long time (0-290 s in the Design-1 sample, 0-275 s in the Design-2 sample, and 0-478 s in the Design-3 sample), which proves that the small and micro-scale destruction continues to develop, and no macroscopic large-scale damage occurs.
2. Before the final destructions of the sample, the b-values usually decline before the AE rates sharply rise (over 400 events/0.1 s); meanwhile, the S values show the opposite characteristic (290-296 s and 314-315 s in the Design-1 sample, 275-276 s and 277-278 s in the Design-2 sample, and 478.5-479 s in the Design-3 sample). During these periods, the scale of local failure expands, the macroscopic secondary cracks gradually form, and the energy released during the fracture process gradually increases.
3. When the AE rate reaches its maximum, the b-values and S values oscillate rapidly in a short period of time; the destruction is completed instantly within 0.01 s, which can be  
Figure 8: Influence of statistical analysis parameters on the b-values: (**a**) several groups of windows and moving steps in Design-1; (**b**) several groups of bin widths in Design-1; (**c**) several groups of windows and moving steps in Design-2; (**d**) several groups of bin widths in Design-2; (**e**) several groups of windows and moving steps in Design-3; (**f**) several groups of bin widths in Design-3.  
considered as the simultaneous generation of multi-scale and multi-level destructions. The duration of this type of period shall not exceed 1 s, and it is also the fastest period of secondary damage development.
4. AE rates sharply drop after reaching the UCS status of the tests, and the b-values gradually decline in the remaining period, while the S values present the opposite trend (increase) simultaneously. The above results indicate that the size and severity of secondary failures during this period gradually rise, and the macroscale and large-scale destruction ultimately take place.  
Accordingly, the long-term accumulation of small-scale damage is observed during the majority of the test duration; there will be clear premonitory features in the b-values and S values before the formation of local failures; the final failures quickly form at various scales and energy levels, then the macroscale destruction dominates in subsequent periods.  
Figure 9: Curves of the loading stress, b-values, and S values (Design-1 sample).  
Figure 11: Curves of the loading stress, b-values, and S values (Design-3 sample).  
Figure 10: Curves of the loading stress, b-values, and S values (Design-2 sample).