Research on Rock Crack Classification Based on Acoustic Emission Waveform Feature Extraction Technology

Rock fracture mode has practical significance for the prediction and prevention of engineering disasters, and the inversion of fracture mode by the waveform signal not only reduces the experimental error of the mechanical strength measurement but also simplifies the type and quantity of disaster prediction source data. For the relationship between crack mode and mechanical strength, the acoustic emission (AE) waveform signal is studied. Six coarse-grained sandstone samples were tested by uniaxial compression, AE, and scanning electron microscopy. The results show that the number of microhole cracks in rock is positively correlated with tensile-shear cracks and negatively correlated with mechanical strength. The quadratic function regression curve of the proportion of shear cracks and mechanical strength is more realistic. When crack ratio is less than 0.31, the number of shear cracks is positively correlated with the mechanical strength and vice versa. The waveform mutation coefficient k is defined as the overall change description. It is found that the increase of signal mutation has a positive impact on the mechanical strength of rock. The fitting function of crack and the signal mutation near the peak of rock can be divided into six risk zones in a two-dimensional plane. In addition to these exciting results and discoveries, the determination of the number of tensile-shear cracks and its relationship with mechanical strength provide innovative methods and ideas for crack pattern discrimination and rock burst risk assessment of roadway surrounding rock.


Introduction
The crack mode of rock will directly affect the performance of roadway support and the stability of surrounding rock. The failure of support will induce the deformation [1], which will seriously cause dynamic disasters such as rock burst and greatly threaten the safety of staff [2,3]. As for the porous material of roadway surrounding rock, it shows the characteristic of brittleness, and researchers have generally agreed to explain this phenomenon from the macroscopic and microscopic perspectives [4,5]. There are many microstructures such as pores and cracks in the rock, and the distribution is chaotic [6]. The changes of these microstructures have a vital impact on the stability of rock. When the rock is disturbed by the external force, the closure, dislocation and sliding of the pore stress concentration of the rock itself, and the combination of the crack initiation and propagation mechanism are the inevitable reasons for the deformation and failure of the macroscopic structure. The interaction mechanism between rock instability failure and cracks has been a hot research topic [7,8]. It is very important to explore and reveal the mutual feedback mechanism of crack mode and failure mode characteristics for mastering the mechanical problems of rock mass disasters, especially in the damage analysis of materials and disaster risk zoning of rock mass engineering [9].
Many valuable research results have been obtained to characterize rock mass cracks' development direction, locate crack propagation paths, identify crack types, and evaluate rock mass cracks and safety [10][11][12][13]. Acoustic emission is a nondestructive testing technology. In terms of crack classification and identification, the parameter data of AE can be calculated through mathematical calculations to obtain new parameter characteristics. Researchers mainly use two characteristic parameters of RA and AF to distinguish the types of cracks. When the RA value is smaller and the AF value is immense, it shows a shear crack and vice versa. For example, the trend line ratios which distinguish the two types of crack characteristic parameter values are slightly different. For composite beams, when the trend line ratio of crack classification is 1 : 25, the effect is best [14]. At the same time, the trend line with a ratio of 1 : 1 shows that the number and strength of bedding planes have a more significant impact on the fracture and crack distribution of the sample [8], and when the strain rate increases, tensile cracking becomes the primary fracture mode [15]. In addition, when the inclination angle of the prefabricated cracks in the cracked sandstone increases, it is difficult for the rock to develop tensile cracks, but it is easy to produce shear cracks [16]. The trend line with a ratio of 1 : 80 shows that the primary crack mode of reinforced concrete is shear crack [17]. The ratio of 1 : 10 verifies the effectiveness of the crack and damage characteristics under the three different failure modes of shear, mixing, and bending [18]. According to Zhang and Deng [4], the uniaxial compression condition of brittle rock applies a trend line with a ratio of 1 : 100-1 : 500, and with a ratio of 1 : 1500, the shear cracks dominated under uniaxial compression [19].
In terms of AE waveform signal extraction, since the AE waveform data contains about 9 million data points in just 3.0 s, the tremendous amount of data is not conducive for further calculation and application of various research contents. Therefore, before applying the collected waveform signal, it is necessary to perform data preprocessing and feature extraction on the signal. For example, Siracusano et al. and Zhang et al. adopted advanced Hilbert-Huang signal processing technology to significantly improve the systematic research of crack phenomena based on AE data [20,21]. Moreover, in unsupervised learning, rock fracture types are generally distinguished by AE events. Feature extraction of waveform signal in coal rock failure process using Mel frequency cepstrum coefficient (MFCC) method can be seen in [22]. In addition, Tirumala et al. reviewed 160 papers related to speech signal feature extraction from 2011 to 2016 [23]. They confirmed that the cepstral coefficient method based on pure Mel frequency is the most popular. Furthermore, Randall found that real cepstrum can edit nonstationary sample data amplitude spectrum [24]. The time signal can obtain by combining it with the original phase. Mantena et al. believed that the frequency domain linear prediction cepstrum coefficients could capture the time dynamics of the speech signal, and a simplified feature vector can achieve fast search [25]. The parameter includes arrival time, amplitude, duration, rise time, number of ringing, number of rises, energy, practical voltage value, average signal level, number of impacts, impact rate, the center of mass frequency, and peak frequency. In summary, there are research accumulations on related topics and experiments in terms of the parameter data and waveform data obtained from the AE monitoring experiment.
The deformation and failure of rocks are closely related to the initiation and propagation of cracks. The cracks in a mechanical test need to be classified by the RA-AF method to classify the rock surface cracks. However, the waveform signals monitored at the same time also have abundant data characteristics and illustrativeness. After consulting the literature, it is found that the research on the correlation between crack mode and waveform signal is still blank, and the content seems to be relatively independent. The prediction of crack mode through waveform change can provide important reference for the stability control of engineering rock mass. It is found that there are few studies on waveform signal in the field of crack prediction. In this paper, many meaningful phenomena can be found by analyzing and summarizing the crack mode, mechanical strength, and waveform characteristics. The waveform data generated by the rock mass under external force disturbance will automatically classify the types of cracks. Moreover, according to the cracks, the interaction within the rock mass can be used to divide the risk zonation of rock mass stability. It will provide necessary reference for the determination of rock mass quality, stability, and rock burst disaster in laboratory and engineering site.

Experiment Equipment and Sample Preparation
2.1.1. Experiment Instrument. The rock mechanics loading equipment and AE monitoring instruments in Figure 1 are used for the current study. The rock mechanics loading equipment, HCT-605A manufactured by Shenzhen Wance Test Equipment Co., Ltd, is a hydraulically servocontrolled testing machine. The AE monitoring instrument DS5-16B full-information AE signal analyzer was produced by Beijing Softland Times Science & Technology Co., Ltd.

Sample Preparation.
The sandstone tested in this paper was taken from a rock burst mine in Xianyang City, Shaanxi Province, China. The core was coarse-grained sandstone at 15 m above the roadway roof. The cementation form is argillaceous cementation, and the bedding is uniform. After sampling, the sample was cut and polished in the laboratory, and after finishing treatment, it was made into a cylindrical standard specimen with a diameter of 50 mm and a height of 100 mm, numbered as R1-R6. The rock mechanics test was carried out in the laboratory mechanical loading system.

Experiment Program and Postprocessing of AE
The test steps are as follows: (a) the AE sensors were adhered to the surface of sandstone sample by coupling agent; (b) the AE signal amplifier was connected to the AE signal analyzer equipment; (c) the uniaxial compression test was adopted by the force loading control method, and the loading speed was set to 0.2 KN/s. The experimental sequences are as follows: (a) fixing specimens, connecting sensors, and installing equipment; (b) the electrohydraulic servo pressure testing machine and AE signal acquisition system were opened simultaneously to ensure data synchronization. If the data results are not synchronized, the nonsignal segment can be truncated according to the location of the initial signal.
Eight sensors were used in the AE test, a total of two groups, and the circumference distance between any two sensors in the two groups of sensors is 12.5π mm. The axial 2 Lithosphere distance between the first group of sensors and the upper surface of the rock specimen is 20 mm, the axial distance between the second group of sensors and the lower surface of the rock specimen is 20 mm, and the axial distance between the two sets of sensors is 60 mm. The schematic diagram of the sensor adhesion position in the threedimensional space is shown in Figure 2.

Postprocessing of AE Test
Data. This AE test uses continuous monitoring to collect data, and the technical parameters are shown in Table 1. The collected data were divided with the parameters and waveforms. The parameter includes arrival time, amplitude, duration, rise time, ring count, rise count, energy, practical voltage value, average signal level, hits, impact rate, the center of mass frequency, and peak frequency. In contrast, waveform data is a two-dimensional kind of data composed of time and amplitude. The traditional AE data analysis mainly adopts AE ringing count, energy, hits, and peak frequency parameters. In Reference [4], the number and distribution characteristics of cracks in rock failure process can be obtained by using the rising angle (RA) and the average frequency (AF). Combined with the optimal transition line, the classification of secondary cracks and the determination of crack mode can be realized. In order to realize the classification of rock secondary cracks in uniaxial compression test and the proportion analysis of different crack modes, two characteristic parameters, rising angle and average frequency, were selected and the calculation formula is expressed as Equations (1) and (2).
Many researchers have obtained the discrimination of rock failure mode by the changes of these two types of characteristic parameters. This paper selects RA as the independent variable and AF as the dependent variable. When the independent variable value (RA) is lower and the dependent variable (AF) is higher, there are fewer shear cracks, and the sample mainly presents I-type tensile failure. When the RA value is higher and the AF value is lower, there are fewer tensile cracks, and the sample mainly exhibits type II shear cracks. Some researchers have proposed that mixed damage and destruction occur when the RA value is close to the AF value [26][27][28].
2.3. Data Feature Extraction Technology. The AE waveform was selected as the data sample, and the characteristics of the waveform signal were extracted by the MFCC method using the automatic speech recognition technology. The processing of this method mainly includes the following four steps: data preprocessing, fast Fourier transform, Mel filter, and discrete cosine transform. The specific processes are shown in Figure 3. Figure 3 illustrates how to deal with the waveform obtained by acoustic emission. In the data preprocessing part, the increase of high-frequency signal and the suppression of low frequency signal are realized by preemphasis. The Fast Fourier transform was used to transform the audio information from time domain to frequency domain. The next Mel filter was used to eliminate the influence of harmonics, highlight the resonance peak of the original signal, and reduce the calculation amount. The last step of the discrete cosine transform was used to eliminate the correlation between the Mel filters, so that the low frequency information of the spectrum can be expressed by the Mel frequency. The above four steps calculate the MFCC of the AE waveform signal. The slope factor will construct the analysis

Rock Failure Modes and AE Parameter Characteristics
They are taking the peak period before the failure of the rock specimen as the research object of the AE waveform data. The crack type characteristics were obtained by calculating the AE parameters. The waveform feature extraction and calculation can obtain the waveform characteristics that describe the near-failure of the specimen. It uses to establish the relationship of the rock strength and the two types of AE data characteristics, exploring the primary influence of the sudden change of the waveform during the AE monitoring process on the rock failure mode through the mechanical properties of an intermediate variable.

Macroscopic Failure Characteristic/Morphology of Rock
Surface. The stress-strain curve of the sandstone uniaxial compression obtained by the servo pressure testing machine is shown in Figure 4, and the uniaxial compression test results are shown in Table 2.
It can be seen from Figure 4 that even if the same loading speed is selected for the compression test of the samples, the initial pore compaction stage of the stress-strain curve of the rock is slightly different. It is caused by the difference and anisotropy of the internal structure of rocks, and the difference in the number, size, and location of micropore defects is the reason for different performance behaviors in the pore compaction stage. In addition to the rock sample R4, the stress of the rock sample is almost unchanged with the increase of strain. The stress does not begin to increase until the strain increases to 1%. The reason for this phenomenon is that the selected rock is coarse-grained sandstone, and the cementation form is argillaceous cementation, containing carbon chips. Therefore, the sandstone has high particle size, and a large number of holes and other microstructure make the loading to a large deformation to produce force changes. However, when the rock samples R4 and R5 were loaded to the peak stress, although the samples were damaged, the stress gradually increased again with the continuous loading, which was related to the hard structure inside the rock. It means that with the uniaxial compression, whether this crack became the key crack leading to rock failure during the pore compaction to crack propagation stage was the reason for the increase of stress again.
It is shown in Table 2 that the uniaxial compressive strengths of R1-R3 are relatively lower than that of R4-R6. The axial strain is the ratio of the rock deformation variable to the height of the specimen. The stress-strain curve of the specimen in Figure 5 shows that all specimens reach the peak stress when the strain is 0.02, and most of them will break. It shows that when the size effect could not consider, the standard rock specimen obtained in this mine can resist the deformation of the maximum 2 mm at the height of itself, and then, it will be destroyed.
It can be seen from Figure 5 that after the uniaxial compression test, the sandstone samples have different degrees of splitting and fragmentation. The samples with lower uniaxial compressive strength have large block fractures, such as R1-R3. According to the fracture form in Figure 5, the specimen R6 is a "Y-type" fracture and has not developed into an "Xtype" fracture, so it can be considered that R6 still has a certain bearing capacity, and the strength of this sample is also the largest. However, the failure of the three samples of specimen R1, R2, and R3 is relatively serious. The failure of specimen R1 reasonably confirms the "X-type" fracture of rock failure in the rock mechanics textbook, indicating that the failure is sufficient and the bearing capacity is almost lost, while the surface rupture and block appear in specimen R2 and R3. The failure crack of sample R4 is more developed than that of sample R5, so its compressive strength is also less than that of sample R5. Under the controlled compression of 0.2 KN/s, each sample forms a shear failure pattern mainly along the rock structure surface, all of which were mainly shear cracks accompanied by a few tensile cracks. In this way, it is better to explain that in the uniaxial compression test, the more the number of cracks, the greater the probability of rock failure, and the smaller the mechanical strength.
3.2. Mesostructure Morphology of Rock Surface. After the test, rubber bands spliced and fixed the fractured rock fragments or rock blocks according to the fracture surface, as shown in Figure 5. The microstructure of SEM pores and fractures of the rock after the test is shown in Figure 6.  During the diagenesis process, sedimentary rocks are affected by the interaction of biological, chemical, and physical movements, resulting in many microporous fissure structures of different sizes, shapes, and disorderly distributions [6]. Sedimentary rock produced many different shapes and chaotic distribution of microporous fracture structure during diagenesis. It shows the distribution of such micro-structures in sandstone in Figure 6. The observation of Figures 6(a)-6(e) shows that the sandstone after compression has high particle size, but holes and cracks produced by compression can still be observed. Among them, the yellow ellipse represents the concentrated area of the microcracks in the scanned image, and the yellow rectangle represents the hole and pore structure. Microporous fissures  Combined with Figure 6 and Table 2, it can be seen that the hole exists in the rock as a primary structure, and its direct relationship with the mechanical strength is not obvious, but the effect on mechanical strength can be intuitively observed in the spherical accumulation model of sandstone at mesoscale. The rock sample R6 has the largest mechanical strength but only one crack was found. The rock sample R1 has the smallest mechanical strength but contains a large number of large cracks. Therefore, there is a negative correlation between the number of cracks and mechanical strength, that is, with the increase of loading degree, the primary and secondary cracks in the rock increase. It is worth noting that, taking the results of rock fragments as an example, the more cracks in the rock fragments, the greater the degree of loading, and the more significant the damage. In electron microscope scanning under 200 times magnification, R1-R3 have more pores and cracks than R4-R6. The increase of micropore cracks is the main factor in decreasing rock mechanical strength. Figure 4 and Table 2 show that R1-R3 samples have serious spalling and low mechanical strength. In contrast, the macroscopic surface morphology of R4-R6 samples is relatively complete. Since the rock is susceptible to tensile cracks, the more shear cracks are, the fewer internal tensile cracks are. Therefore, the comprehensive strength test results indicate that more shear cracks can maintain the higher strength of the rock. What cannot be ignored is that the number of shear cracks increases with the increasing degree of compression. No matter the number of shear cracks is large, rock can only maintain the strength of tensile-shear cracks in a critical state before failure.

Distribution Characteristics of RA-AF Parameters.
In this paper, the AE parameter characteristics of the uniaxial compression are calculated by Equations (1) and (2). In this regard, the Japanese Society for Concrete Materials (JCMS-III B5706) defined RA and AF and used the diagonal of data distribution as the transition line [29]. Other researchers obtained a reasonable proportion of transition line through SIGMA analysis [30] or a large number of experiments [19] and used it as a criterion for distinguishing tensileshear cracks. After careful reading of the references in relevant research directions [4,14,16,26,30], due to the differences in the material of the test sample, the difference in the experimental scheme and equipment, and considering Ref-erence [4], the optimal proportion of the compressed rock is determined to be between 1 : 100 and 1 : 500. In this paper, the proportion of the two optimal trend lines is determined according to the proportion range. Taking R2 in Figure 7 as an example, it is an effect drawing that divides the proportions of tensile and shear cracks according to the best trend line range (1 : 100 and 1 : 500), and it shows the distribution of the characteristic parameters (RA and AF) of the AE event.
The failure characteristic of the rock in the uniaxial compression test is mainly through the propagation of shear cracks until the instability failure. As a brittle rock under compressive but not tensile loads, the distribution of cracks is mainly shear cracks, and tensile cracks account for only a relatively small proportion. However, the expansion direction of tensile cracks is often the dangerous area that causes rock damage. In the crack classification diagram of sample R2 in Figure 7, the characteristic parameters of AE/RA are primarily concentrated in the range of 0-1 ms/V. With the increase of RA value, the probability density gradually decreases, and the characteristic parameter AF is mainly concentrated in the range of 0-500 kHz. As the AF value increases, the probability density also gradually decreases. Figure 8 shows the distribution of tensile-shear cracks according to the two types of trend lines. AF1 and AF2 are the tensile-shear crack trend lines of 1 : 500 and 1 : 100, respectively. When the ratio of RA to AF is greater than the slope of the trend line, the sample produces the shear cracks, and when the ratio is less than the slope of the trend line, it shows the tensile cracks. In Figure 8, the red scatter is the tensile crack area with the trend line ratio of 1 : 500, and the rise angle is slight, and the average frequency is high. The blue scatter is the shear crack area with the trend line ratio of 1 : 100, and the rise angle is large, and the average frequency is low. As shown in Figure 8, when the trend line ratio is 1 : 500, the green scatter points are shear cracks, and when the ratio is 1 : 100, they are tensile cracks, so the green scatter points are caused by the difference between the two types of trend lines determined. In general, a trend line ratio is selected to determine the crack mode. Therefore, the green scatter only prompts other researchers here: when the proportion of two trend lines are selected, there will be a green scatter area. If you are interested, you can explore the mode of crack in this area.
Since the conclusions of other researchers only determine the transition line, the accuracy of the two types of trend lines in the classification of the sample cracks in this article cannot be evaluated. Therefore, this paper defines the area between the trend lines as an undetermined crack area, including combined and compression cracks. The calculation results of AE parameters are shown in Table 3.
When AF1 is selected as the trend line, the shear and tensile crack number is 41.37% and 58.63% of the total number of AE event cracks, respectively, while when AF2 is selected as the trend line, the number of shear and tensile cracks is 23.66% and 76.34% of the total number of cracks in the AE event, respectively. It can be found that with the increase of the slope of the trend line, the proportion of  shear cracks is also increasing, while in the uniaxial compression test of rock, the shear crack accounts for the dominant crack [16].

The Correlation between the Proportion of Shear Cracks and Mechanical
Strength. The trend lines with two slopes are pretty different, and the accuracy is uncertain. Therefore, this paper uses the results of mechanical strength as the dependent variable and the ratio of shear to tensile crack as the independent variable to explore the accuracy and effectiveness of the two types of trend lines in dividing crack characteristics, as shown in Figure 9.
Assuming that the total number of tensile and shear cracks is 100, the ratio of the shear cracks to the total number is the independent variable, and the dependent variable is the uniaxial compressive strength. It can be seen from Figure 9 that the light blue area is the distribution area of the characteristic parameters of the AE event with a trend line of 1 : 100. The proportion of shear cracks is between 0.1 and 0.25, and the data is concentrated. A monotonically decreasing logarithmic function regression model is used to characterize the distribution of negative data correlation. The function expression is shown as Equation (3), and the goodness of fit is 0.72, while within the range of 0-0.6, the shear cracks in the data gradually increase, and the uniaxial compressive strength of the rock gradually decreases. For the sandstone specimens obtained from the mine selected in this paper, from the regression model, the maximum proportion of shear cracks can reach 0.54. The specimens will fail when the maximum number of tensile cracks is 46%.
In Figure 9, the light purple area is the characteristic parameter distribution area of the AE meter with a trend line of 1 : 500. The proportion of shear cracks is between 0.25 and 0.45, and the data are concentrated. Thus, a one-variable quadratic equation regression model is used to characterize the data distribution law. The function expression is as Equation (4), the goodness of fit is 0.84, and the fitting effect is better than Equation (3). Of course, the fitting results of the above data are only regression models that are feasible and practical in a certain range, such as in the shear crack ratio of 0.1-0.5 threshold range It is worth noting that when the proportion of shear cracks is 0.31, the regression model has the maximum value. When the proportion of shear cracks is less than 0.31, with the increase in the number of shear cracks relative to tensile cracks, the uniaxial compressive strength of the rock gradually increases. This result confirms the conclusion of Du et al. [19], which is that the shear cracks in the uniaxial compression test are the prominent cracks. When the proportion of shear cracks is more significant than 0.31, the number of shear cracks increases relative to tensile cracks, and the uniaxial compressive strength of the rock gradually decreases. It shows that the rock mechanics strength of the mine is gradually destroyed after this ratio, and the specimen itself is no longer capable of resisting the fracture damage caused by crack propagation. From the regression model, the maximum proportion of shear cracks can reach 0.45. The specimen will fail when the maximum number of tensile cracks is 55%.

Waveform Feature Extraction and Crack
Interaction Behavior 4.1. Feature Extraction Based on MFCC Method. In addition to using AE technology to realize the source location and destruction process, this article intercepts the 3.0 s waveform segment near the peak pressure of the R1-R6 samples and the number of the waveform data of each segment is about 9 × 10 6 . The 9 × 10 6 data points of the waveform are     Lithosphere calculated and divided into 199 frames by the Mel frequency cepstral coefficient method. Due to the first and second derivatives of the first two frames and two consecutive frames of data being 0, remove the data before and after the two frames. The signal variation and fluctuation characteristics can be described with 195 data points 9 × 10 6 data points. The obtained characteristic parameters are similar to the original signal change law from the data results, and the consistency is high. The calculation results show that this method can extract the waveform signal's main characteristics and general trend. Then, the column vector output can be used as the waveform characteristics of the test sandstone near the peak.

Correlation between the Amount of Waveform Signal
Mutation and Mechanical Strength. Define the mutation coefficient k describing the waveform signal as the ratio of the maximum amplitude change of the entire twodimensional waveform △A to the change of corresponding frame number △F, and the results are shown in Figure 10.
Here, sample R2 is selected for data demonstration, and Figure 10 shows the calculation method of the mutation coefficient k in the line graph of the waveform characteristic parameters. The maximum amplitude of the 195 frame signals extracted here is 27.61 mV, and the minimum amplitude is -44.30 mV. The corresponding maximum number of frames is 98, and the minimum number of frames is 13. The difference of amplitude is 71.91 mV, and the corre-sponding change of frame number is 85. The mutation coefficient k of R2 waveform signal of the sample is 0.846 by dividing the two. The coefficient k of the R2 waveform signal mutation of the sample is calculated to be 0.846, the mutation coefficient k of the test sandstone is calculated successively, and the correlation between it and the mechanical strength is constructed as shown in Figure 11.
A linear function is used to construct the regression model of mechanical strength and waveform signal mutation coefficients, the function expression is as Equation (5), and the goodness of fit is 0.71.

UCS = 20:405k + 32:424: ð5Þ
It can be seen from the linear regression model in Figure 10 that the uniaxial compressive strength of the mine sandstone increases with the increase of the abrupt change coefficient of the waveform signal. It means that the waveform signal in the compression process of the specimen only produces the lowest and highest amplitudes near the peak. Substitute into the model, and it can be seen that there is a 71% correct rate to judge the strength of the specimen.
Whether the signal appears as a short-frame highfrequency or long-frame low-frequency variation when the frame length between the maximum and minimum amplitudes is shorter, it will return to the sample with this type of waveform characteristics to have a higher level of mechanical strength. Conversely, it has a lower intensity level. At the same time, it can be seen from Figure 11 that with the increase of the mutation coefficient, the mechanical strength does not increase directly but focuses on the strength change of the mutation factor between 0.4 and 0.8. In addition, the uniaxial compressive strength of the sample in the regression model is almost concentrated in 35-45 MPa, and the proportion of shear cracks represented by the ordinate is less than 0.5, indicating that the failure of the selected sample is accompanied by the same number of shear and tensile cracks.
In summary, the correlation between the characteristic parameters of the extracted waveform and the mechanical strength has a high degree of credibility. The model can later be applied to the on-site roadway excavation or mining process to predict the strength of the stressed rock mass based on the waveform signals collected by the current, vibration, and hydraulic sensors attached to the shearer or tunneling equipment.

Regression
Model of the Proportion of Shear Cracks. The collected stress and strain, AE parameters, and waveform   (9) and (10) to obtain a mapping relationship and construct the interactive behavior of tensile-shear cracks under different mutation coefficients based on computer modules and implicit functions [31]. Figure 12 shows the critical failure curve and risk zone of the interactive behavior of tensile-shear cracks, which is the relationship between the variation characteristics of the mutation coefficient of the waveform signal near the peak stage and the crack ratio. When the trend line is 1 : 100, the monotonic blue curve goes from Q (-1.407, 0.503) to the left (k ≤ −1:407), and the number of tensile cracks is greater than that of shear cracks. With the change as an exponential function, the increasing trend appears in the sandstone specimen, and the slope of the tensile crack equation gradually increases. Therefore, the mechanical strength of rocks in this region decreases rapidly due to tensile cracks. From Q to the right (k ≥ −1:407), the number of tensile cracks gradually becomes lower than the number of shear cracks, and the slope of the tensile crack equation gradually decreases. Therefore, the mechanical strength of rocks in this area slowly degenerates due to reducing tensile cracks. That is, the proportion of shear cracks is between 0 and 1. When the trend line is 1 : 500, the black increasing curve slowly increases with the mutation coefficient, and the black decreasing curve shows an opposite trend. The shear cracks maintain between 0.3 and 0.4, consistent with the proportion of shear cracks in Table 3. Under normal circumstances, the uniaxial compressive strength﹥shear strength﹥tensile strength of rock, and this performance follows the priority to avoid the expansion of tensile cracks in the rock. Besides reducing the development of shear cracks in rocks, different colors indicate the six possible areas that can be divided by the crack cross behavior.
(1) Static Hazard Curve. The number of tensile cracks is greater than that of shear cracks. When the trend line is 1 : 100, the blue monotonic function curve ranges from Q to the left (k ≤ −1:407), while when the trend line is 1 : 500, the entire range of the black monotonic function curve is dangerous.
(2) Static Safety Curve. The number of tensile cracks is less than the shear cracks. When the trend line is 1 : 100, the blue monotonic function curve ranges from Q to the right (k ≥ −1:407).  10 Lithosphere (4) Quasi-Dynamic Safety Zone. The number of tensile cracks is gradually reduced compared with the number of shear cracks, that is, when the trend line is 1 : 100, the sum of yellow and green areas and when the trend line is 1 : 500, the sum of blue and green areas.
(5) Absolute Safety Zone. Considering the problem between the trend lines 1 : 100 and 1 : 500, the green zone is the overlapping quasi-dynamic safety zone. Therefore, the green zone surrounded by the two trend lines is the absolute safety area.
(6) Hidden Danger Zone. Considering the problem between the trend lines 1 : 100 and 1 : 500, excluding the absolute safety zone of the green surface, the sum of the static risk curve and the quasi-dynamic risk zone is the hidden danger zone. Therefore, the present paper's risk zoning of sandstone specimens can be used to reference the stability classification and safety evaluation of engineering rock mass conditions in field construction operations.

Conclusions
In this paper, AE acquisition technology was used to monitor the whole process of the uniaxial compression mechanics test of sandstone. The influence of signal variation on the number of cracks was explored by combining AE parameter feature calculation with waveform feature extraction. For the relationship between mechanical strength, parameter characteristics, and waveform variation, the regression model of crack proportion was analyzed based on the feature extraction technology and risk partition of interactive crack behavior. The main conclusions are as follows:  11 Lithosphere strength gradually decreases with the proportion of shear cracks increasing. When the trend line is 1 : 500 and the proportion of shear cracks is less than 0.31, the strength gradually increases with the proportion of shear cracks, while when it is more significant than 0.31, the strength gradually decreases as the proportion of shear cracks increases (3) The waveform characteristics and the changed behavior extracted by the MFCC method are almost identical to the original signal. They can be used to calculate the newly defined waveform mutation amount. The short-term high-amplitude fluctuation of the waveform signal leads to a gradually increasing trend of the rock mechanical strength (4) The performance of the waveform signal of rock during the compression process can explain the determination of the proportion and the classification of tensile-shear cracks. As a sample with complex internal structure and cross-growth cracks, the regression models and risk zoning of different cracks provide important reference for rock quality, safety, and dynamic disaster assessment