## 3 Results Analysis
### Classification of Crack Types
There are some empirical factors that impact the determination of the split line equation by the RA-AF method due to the considerable inaccuracies in the T1 and T51 conditions. The diagonal split line method is recommended in engineering for convenience. Still, it essentially reflects the concept of clustering, in which data points with the same characteristics are grouped into one category, and the split line should be determined based on the distribution characteristics of the actual RA-AF value data points. [PERSON] et al. [28], for example, employed machine learning to discover the splitting equation that is not over the origin, as illustrated in Figure 9a. Similarly, the fraction of shear cracks in the T1 condition can vary greatly when alternative splitting line formulae are used, as illustrated in Figure 9b. The dense distribution of data points near the diagonal line in Figure 8a and the forced diagonal division will undoubtedly lead to misjudgment of crack types in the T1 condition, whereas the blue splitting line in Figure 9b is certainly more reasonable, and the percentage of shear cracks identified based on this splitting line is 25.1%, which is close to the 21.5% obtained using the amplitude-PF method. Despite the absence of horizontal shear stress, the number of shear cracks in the direct tensile test is greater than in compressive-shear and tensile-shear failure tests. This is mainly because, due to material heterogeneity, the path of crack initiation may not be perpendicular to the direction of tensile stress, resulting in shear cracking, as observed in the direct tensile tests conducted by [PERSON]  
Figure 7: The classification principle of crack types. (**a**) The calculation method of RA and AF value; (**b**) crack classification based on RA–AF values. oulis [9]. In summary, peak frequencies during specimen failure exhibit a \"three-band\" distribution, with medium- and high-frequency bands corresponding to tensile cracks and the low-frequency band containing both tensile and shear cracks, which can be roughly judged based on amplitude, i.e., AE signals with amplitudes larger than 55 dB correspond to shear cracks, and the rest correspond to tensile cracks. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test Type** & **Specimen** & **Classification** & **Tensile Crack** & **Shear Crack** & **Shear Crack’** \\  & **Number** & **Method** & **Percentage** & **Percentage** & **Percentage Error** \\ \hline \multirow{3}{*}{Tensile test} & T1 & _RA–AF_ & 48.0\% & 52.0\% & \(-\)30.5\% \\  & T1 & _Amplitude–PF_ & 78.5\% & 21.5\% & \(-\)30.5\% \\  & T2 & _RA–AF_ & 82.5\% & 17.5\% & \(-\)0.6\% \\  & T2 & _Amplitude–PF_ & 83.1\% & 16.9\% & \(-\)0.6\% \\ \hline \multirow{3}{*}{Compressive- shear test} & CS1 & _RA–AF_ & 100\% & 0.0\% & \(3.2\%\) \\  & CS1 & _Amplitude–PF_ & 96.8\% & 3.2\% & \(3.2\%\) \\  & CS2 & _RA–AF_ & 91.9\% & 8.1\% & \(8.1\%\) \\  & CS2 & _Amplitude–PF_ & 91.1\% & 8.9\% & \(0.8\%\) \\ \hline \multirow{3}{*}{Tensile-shear test} & TS1 & _RA–AF_ & 93.0\% & 7.0\% & \(9.8\%\) \\  & TS1 & _Amplitude–PF_ & 83.2\% & 16.8\% & \(9.8\%\) \\ \cline{1-1}  & & _RA–AF_ & 87.9\% & 12.1\% & \(4.4\%\) \\ \cline{1-1}  & TS2 & _Amplitude–PF_ & 83.5\% & 16.5\% & \(4.4\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of crack classification results between the _RA–AF_ and _amplitude–PF_ methods. Figure 8: Crack classification based on the RA–AF values at the peak strength time. (**a**) Specimen T1; (**b**) specimen CS1; (**c**) specimen TS1; (**d**) specimen T2; (**e**) specimen CS2; (**f**) specimen TS2.