## 3 Discussions  
### Estimations of Failure Size  
The b-value is statistical data for quantifying the crack behavior and failure severity and reflecting the development trend of cracks at different scales [36]. The concept of parameter b originated from earthquake research is first proposed by [PERSON] and [PERSON] [37], which describes the size distribution scaling and is often referred to as the b-value. As a technical parameter within AE, the b-value can reflect the changes in the scale of microcracks within rock mass, and its sudden change can also serve as a precursor to the macroscopic failure of rock mass [38; 39; 40; 41]. Based on the discussions of the effect of both size distribution and attenuation on the b-value, [PERSON] et al. [42] have proposed a new method to estimate the b-value for rock AE testing and its application confirms that the b-value depends on material heterogeneity and stress. [PERSON] et al. [43] have made an effort to rectify the inherent shortcomings of the b-value estimation method, which has been verified to be lightly implemented and better improved by some experimental datasets.  
The corresponding calculation formula is as follows:  
\[\lg N=a-b\ (A/20) \tag{1}\]  
Figure 7: AE events locating results of all samples: (a) AE events occurred before peak stress and (b) AE events occurred during peak stress.  
where \(b\) is a physical quantity that characterizes the level of acoustic emission activity; \(A\) is the signal amplitude (dB); \(N\) is the statistical cumulative frequency of acoustic emissions at magnitude intervals; \(a\) is an empirical constant.  
### Estimations of Failure Size  
Because the b-value is derived from statistical analysis (only related to AE event time and magnitude), the data window width (abbreviated as \"w\" in the following figures), moving step length (abbreviated as \"m\" in the following figures), and bin width of magnitude (abbreviated as \"b\" in the following figures) are thus important factors influencing the speed and accuracy of calculations. Based on the previous works [42], the suggested minimum AE event number for severity estimation is 200; we thus set the data window width to 200 and 250 and set the moving step length to 100 and 150.  
Figure 8a,c,e show the estimation results of three types of samples via different w and m values. The first finding is that the curves with the same data window width present similar changing times, trends, and ranges before the largest macroscopic destructions (earth tones and blue-green background colors). In addition, four groups of curves show the almost same changing characteristics during and after the largest macroscopic destructions (pink background). Therefore, when microscopic and macroscopic damage develops rapidly in the samples, the two influencing factors (w and m) have little impact on the evaluation results due to the instantaneous occurrence of massive AE signals.  
Figure 8: _Cont._  
When the b (bin widths of magnitude are set as 0.1, 0.5, 1.0, and 3.0 in Figure 8b,d,f) is the unique variable, the increase in the value of b will result in an overall decrease in the calculation result of b-values; the results obtained by group w250-m150-b3.0 are much lower than those of other three groups of data. Accordingly, to obtain more stable statistical results, it is recommended to set the bin width of magnitude to 0.5 or 1 in future post-processing calculations.