# Experimental Research on Acoustic Emission Characteristics and Felicity Effects during Coal Fatigue Failure under Cyclic Loading

Authors: Yongjie Yang; Luyi Xing
Journal: Advances in Materials Science and Engineering
 (2020)

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## Abstract

In order to study the acoustic emission characteristics and Felicity effect in the process of coal fatigue failure and reveal the internal relationship between the fatigue damage evolution law and the acoustic emission activity, with the help of MTS815.02 electrohydraulic servo rock mechanics test system and PCI-2 acoustic emission detection and analysis system, a triaxial cycling loading acoustic emission test was carried out on the coal samples. The results show that the higher the upper limit stress is, the more obvious the degree of fatigue damage will be caused by coal samples. At the same time, the more active acoustic emission signal will appear. The coal samples under linear loading are on the initial damage state, and slight fatigue, moderate fatigue, deep fatigue, and ultimate fatigue failure under cyclic loading. The acoustic emission shows the “L-” type development evolution law in any previous stress level range, while at the last stress level, it shows the obvious “U-” type development evolution law. The higher the frequency of the cyclic loading is, the higher the rate of initiation and expansion of the microcrack will be, while the more obvious acoustic emission phenomenon will appear. Furthermore, the ringing counting rate is basically the same as that of the energy counting rate. Under triaxial cyclic loading, a shear failure mode that extends along different directions of fracture surface will be presented. The acoustic emission in the range of different stress levels shows a different degree of Felicity effect. In contrast, it is more reasonable to use the principal stress difference as a parameter to study the Felicity effect of coal under cyclic loading.


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## Body

## 1. Introduction

Damage failure mechanisms and mechanical properties of rocks and coal under monotonic loading (uniaxial and conventional triaxial compression) have been extensively studied [1–6]. Pervasive microcracking occurs in the interior of rocks and coal under external loading, which ultimately leads to fatigue and failure. The compaction and closure of primary cracks is known to occur simultaneously with the gradual initiation, propagation, cracking, and penetration of new cracks. This process is accompanied by the release of strain energy in the form of transient elastic waves or stress waves called acoustic emission (AE), which is frequently called “stress wave emission” [7–9].Acoustic emission techniques have been widely used in the field of rock mechanics and mine engineering [10–17] as a dynamic nondestructive test for measuring the crack propagation characteristics of brittle materials such as rock, coal, and concrete. However, research and application of coal fatigue damage tests under cyclic loading remain scarce. Liu et al. [18] studied the damage evolution and acoustic emission characteristics of coal under uniaxial compression. Acoustic emission information is believed to be closely related to the formation, expansion, and penetration of primary fractures in coal and can provide insight into its deformation and damage evolution behavior. Ji and Lu [19] performed acoustic emission tests on granite under different confining pressures, obtained the mechanical parameters of the entire rock fracture process, and analyzed the acoustic emission characteristics of granite from triaxial compression tests. Song et al. [20] carried out uniaxial compression tests on red sandstone. The evolution of rock deformation in the field during loading was observed using the digital speckle correlation method and AE signals were collected using an acoustic emission detection system. They also systematically studied the corresponding acoustic emission characteristics, extension, dislocation, and overall evolution of the localized deformation zone during deformation in the field. Shahidan et al. [14] studied the acoustic emission behavior of reinforced concrete beams under cyclic loading, classified tensile-shear cracks on the basis of the acoustic emission amplitude, rise time, average frequency, and signal strength, and determined the damage level and crack propagation law. Zou et al. [21] systematically studied the damage evolution characteristics of raw coal under uniaxial and triaxial cyclic loading using acoustic emission technology. They concluded that acoustic emission phenomena during the initial stage of loading is more significant under graded cyclic loading conditions and that raw coal exhibits different damage evolution characteristics at different cyclic stages. Xiao et al. [22] studied the law of energy conversion and acoustic emission characteristics of coal under cyclic loading. They proposed that coal instability can be predicted by the abrupt rise of AE energy and abrupt drop of AE amplitude. Zhang et al. [23] observed accelerated energy release during loading, which is closely related to the occurrence of larger cracks in rocks and can be used as a precursor of rock macro-failure through analysis of acoustic emission test data of three types of rocks. Kong et al. [24–26] determined the relationship between acoustic emission parameters and stress–strain of coal samples under uniaxial compression and derived qualitative and quantitative expressions of coal damage variables. Although many studies have contributed important achievements in understanding the acoustic emission characteristics of rock deformation and failure, these features during different loading paths remain scarcely reported, especially for the fatigue damage failure evolution of coal under cyclic loading. A more comprehensive and systematic study of the acoustic emission characteristics of coal fatigue damage failure is therefore required.We performed acoustic emission tests on coal samples under triaxial cyclic loading using a MTS815.02 electrohydraulic servo rock mechanics test system and PCI-2 acoustic emission detection analysis system. We use the results to better understand the characteristics of acoustic emission and the Felicity effect under different stress levels and cyclic loading frequencies during coal fatigue failure.


## 2. Materials and Methods

### 2.1. Starting Material and Test Equipment

In order to minimize dispersion of the test results owing to individual differences of natural coal samples and avoid the obvious difference of stress history and stress state caused by different horizons and depths as far as possible, the slotting method was adopted to carve coal blocks in relatively complete coal bodies with undeveloped joints. Coal samples were extracted using a drill coring machine and processed into cylindrical specimens with approximate dimensions of 100 mm in height and 50 mm in diameter. The parallelism of the two ends was controlled within 0.01 mm. After being formed, a natural drying state was maintained and a fresh film was used. The sealing is shown in Figure1(a). In order to reduce the influence of the discreteness of the coal samples on the test results, the acoustic velocity test was performed on all the samples that were processed. Finally, the samples with the greater dispersion of the acoustic velocity were removed, and the samples with the most similar acoustic velocity were used for testing and numbered sequentially [16].Figure 1
Standard coal samples and test equipment. (a) Standard coal samples, (b) MTS815.02 electrohydraulic servo rock mechanics test system, and (c) PCI-2 acoustic emission detection and analysis system.
(a)(b)(c)Conventional triaxial cyclic loading tests were performed using an MTS815.02 electrohydraulic servo rock mechanics test system developed by American Mechanical Testing and Simulation (MTS) Corporation, as shown in Figure1(b). The maximum axial load of the equipment is 1700 kN, the maximum confining pressure is 50 MPa, and the maximum pore pressure is 50 MPa. The system provides a highly accurate and stable performance, can obtain high- and low-speed data, and allows uniaxial or triaxial compression tests, cyclic loading tests, permeability tests, and creep tests using force, displacement, axial strain, transverse strain, and other control modes. We used a six-channel PCI-2 acoustic emission detection and analysis system produced by the American Physical Acoustic Corporation, as shown in Figure 1(c). The system uses a PCI-2 board (i.e., contains only two channels), which effectively reduces acquisition noise and ensures the authenticity of AE signals. Because the PCI-2 acoustic emission detection and analysis system is digital, it offers ultra-fast processing speed, low noise, low threshold, and reliable stability.


### 2.2. Acoustic Emission Test Method

As a matter of fact, the AE detector at the previous triaxial compression acoustic emission tests was usually placed outside the triaxial chamber or on the coal sample, as shown in Figures2 and 3. In this way, it is very difficult to obtain the comprehensive and reliable acoustic emission detection signals [17].Figure 2
AE detector placed outside the triaxial chamber.Figure 3
AE detector placed on the coal sample.In order to solve the problem that the AE detector could not withstand the pressure of the hydraulic oil in the triaxial chamber, the test head that can seal the AE detector inside the triaxial chamber was developed [17], as shown in Figure 4. Therefore, the triaxial cyclic loading acoustic emission test method for coal samples can be optimized, which is convenient to use a more reasonable acoustic emission test method to carry out the acoustic emission test of different loading paths, especially cyclic loading, under the triaxial condition.Figure 4
AE detector placed in a test head.As shown in Figure5, taking a confining pressure 3 MPa as an example, the left and right sides represent the acoustic emission parameter curves with AE detector outside and inside the triaxial chamber, respectively. We can find that more accurate acoustic emission information can be detected when the AE detector is inside the triaxial chamber. The maximum ringing count of coal sample is 8,326 with AE detector inside the triaxial chamber, while 5,230 outside the triaxial chamber. The maximum AE energy is 30,036 mV with AE detector inside the triaxial chamber, while being 24,198 mV outside the triaxial chamber. The maximum number of ringing counts with AE detector inside the triaxial chamber is 59.2% higher than that with AE detector outside the triaxial chamber, and the energy is 24.1% higher than that outside the triaxial chamber.Figure 5
Acoustic emission parameter curves of coal sample. (a) AE ringing count and (b) AE energy.
(a)(b)Through this method, it is easy to find that the triaxial chamber fluid will not have any effect on the performance of the AE signals, and the accuracy of experimental results will be improved effectively.


### 2.3. Experimental Procedure

To compare and analyze the acoustic emission characteristics of coal samples under different stress levels and cyclic loading frequencies, the control variables of the servo test system were controlled by stress, and the loading waveforms were uniformly selected as sinusoidal waves (Figure6). During testing, cyclic fatigue tests were performed on one hundred standard coal samples under two loading frequencies of 0.25 and 0.5 Hz, fixed lower limit stress (30% of the average compressive strength of the conventional triaxial), and variable upper limit stress. The loading of the coal samples was increased to the next stress level until fatigue failure occurred. In order to obtain the average compressive strength, conventional triaxial compression tests were carried out on samples from the same coal block. Since the acoustic emission characteristics of coal samples under the same loading frequency are roughly the same, only two coal samples are used for comparative analysis on each loading frequency. The mechanical parameters of each coal sample are listed in Table 1. Because the test results under the same conditions are essentially the same, only two cyclic loading tests are selected for further analysis in this paper. The threshold value, gain multiple, and data acquisition parameters of the acoustic emission tests are determined according to pre-test analyses. The acoustic emission characterization parameters can be selected as ringing counting rate, impact counting rate, energy counting rate, amplitude, and others, as discussed later.Figure 6
Diagram of cyclic loading wave.Table 1
Coal sample size and test conditions.
Coal samples numberConventional triaxial compression testTriaxial cyclic loading testMA-1MA-2MA-3MB-1MB-2MB-3MB-4Coal samples sizeDiameter (mm)50.0250.0050.0150.0150.0250.0150.00Height (mm)100.01100.01100.02100.00100.02100.01100.01Loading frequency (Hz)———0.250.50.250.5Confining pressure (MPa)1010Conventional triaxial compressive strengthσcMPa56.8455.3760.21————Average compressive strengthσ¯cMPa57.47————


## 2.1. Starting Material and Test Equipment

In order to minimize dispersion of the test results owing to individual differences of natural coal samples and avoid the obvious difference of stress history and stress state caused by different horizons and depths as far as possible, the slotting method was adopted to carve coal blocks in relatively complete coal bodies with undeveloped joints. Coal samples were extracted using a drill coring machine and processed into cylindrical specimens with approximate dimensions of 100 mm in height and 50 mm in diameter. The parallelism of the two ends was controlled within 0.01 mm. After being formed, a natural drying state was maintained and a fresh film was used. The sealing is shown in Figure1(a). In order to reduce the influence of the discreteness of the coal samples on the test results, the acoustic velocity test was performed on all the samples that were processed. Finally, the samples with the greater dispersion of the acoustic velocity were removed, and the samples with the most similar acoustic velocity were used for testing and numbered sequentially [16].Figure 1
Standard coal samples and test equipment. (a) Standard coal samples, (b) MTS815.02 electrohydraulic servo rock mechanics test system, and (c) PCI-2 acoustic emission detection and analysis system.
(a)(b)(c)Conventional triaxial cyclic loading tests were performed using an MTS815.02 electrohydraulic servo rock mechanics test system developed by American Mechanical Testing and Simulation (MTS) Corporation, as shown in Figure1(b). The maximum axial load of the equipment is 1700 kN, the maximum confining pressure is 50 MPa, and the maximum pore pressure is 50 MPa. The system provides a highly accurate and stable performance, can obtain high- and low-speed data, and allows uniaxial or triaxial compression tests, cyclic loading tests, permeability tests, and creep tests using force, displacement, axial strain, transverse strain, and other control modes. We used a six-channel PCI-2 acoustic emission detection and analysis system produced by the American Physical Acoustic Corporation, as shown in Figure 1(c). The system uses a PCI-2 board (i.e., contains only two channels), which effectively reduces acquisition noise and ensures the authenticity of AE signals. Because the PCI-2 acoustic emission detection and analysis system is digital, it offers ultra-fast processing speed, low noise, low threshold, and reliable stability.


## 2.2. Acoustic Emission Test Method

As a matter of fact, the AE detector at the previous triaxial compression acoustic emission tests was usually placed outside the triaxial chamber or on the coal sample, as shown in Figures2 and 3. In this way, it is very difficult to obtain the comprehensive and reliable acoustic emission detection signals [17].Figure 2
AE detector placed outside the triaxial chamber.Figure 3
AE detector placed on the coal sample.In order to solve the problem that the AE detector could not withstand the pressure of the hydraulic oil in the triaxial chamber, the test head that can seal the AE detector inside the triaxial chamber was developed [17], as shown in Figure 4. Therefore, the triaxial cyclic loading acoustic emission test method for coal samples can be optimized, which is convenient to use a more reasonable acoustic emission test method to carry out the acoustic emission test of different loading paths, especially cyclic loading, under the triaxial condition.Figure 4
AE detector placed in a test head.As shown in Figure5, taking a confining pressure 3 MPa as an example, the left and right sides represent the acoustic emission parameter curves with AE detector outside and inside the triaxial chamber, respectively. We can find that more accurate acoustic emission information can be detected when the AE detector is inside the triaxial chamber. The maximum ringing count of coal sample is 8,326 with AE detector inside the triaxial chamber, while 5,230 outside the triaxial chamber. The maximum AE energy is 30,036 mV with AE detector inside the triaxial chamber, while being 24,198 mV outside the triaxial chamber. The maximum number of ringing counts with AE detector inside the triaxial chamber is 59.2% higher than that with AE detector outside the triaxial chamber, and the energy is 24.1% higher than that outside the triaxial chamber.Figure 5
Acoustic emission parameter curves of coal sample. (a) AE ringing count and (b) AE energy.
(a)(b)Through this method, it is easy to find that the triaxial chamber fluid will not have any effect on the performance of the AE signals, and the accuracy of experimental results will be improved effectively.


## 2.3. Experimental Procedure

To compare and analyze the acoustic emission characteristics of coal samples under different stress levels and cyclic loading frequencies, the control variables of the servo test system were controlled by stress, and the loading waveforms were uniformly selected as sinusoidal waves (Figure6). During testing, cyclic fatigue tests were performed on one hundred standard coal samples under two loading frequencies of 0.25 and 0.5 Hz, fixed lower limit stress (30% of the average compressive strength of the conventional triaxial), and variable upper limit stress. The loading of the coal samples was increased to the next stress level until fatigue failure occurred. In order to obtain the average compressive strength, conventional triaxial compression tests were carried out on samples from the same coal block. Since the acoustic emission characteristics of coal samples under the same loading frequency are roughly the same, only two coal samples are used for comparative analysis on each loading frequency. The mechanical parameters of each coal sample are listed in Table 1. Because the test results under the same conditions are essentially the same, only two cyclic loading tests are selected for further analysis in this paper. The threshold value, gain multiple, and data acquisition parameters of the acoustic emission tests are determined according to pre-test analyses. The acoustic emission characterization parameters can be selected as ringing counting rate, impact counting rate, energy counting rate, amplitude, and others, as discussed later.Figure 6
Diagram of cyclic loading wave.Table 1
Coal sample size and test conditions.
Coal samples numberConventional triaxial compression testTriaxial cyclic loading testMA-1MA-2MA-3MB-1MB-2MB-3MB-4Coal samples sizeDiameter (mm)50.0250.0050.0150.0150.0250.0150.00Height (mm)100.01100.01100.02100.00100.02100.01100.01Loading frequency (Hz)———0.250.50.250.5Confining pressure (MPa)1010Conventional triaxial compressive strengthσcMPa56.8455.3760.21————Average compressive strengthσ¯cMPa57.47————


## 3. Acoustic Emission Characteristics of Coal under Cyclic Loading

### 3.1. Effect of Stress Level on Acoustic Emission Characteristics

The mechanical energy absorbed by coal is transformed into other kinds (e.g., acoustic, electromagnetic, and thermal) under an external load, and most of the strain energy is used for deformation. The stress–strain curve of coal under cyclic loading consists of a series of plastic hysteresis loops, and the area of each plastic hysteresis loop represents the energy consumed by each cycle.(1)ΔE=∮Δσdε.The deformation of coal sampleε in each cycle includes elastic deformation εe and plastic deformation εp.(2)ΔE=∮Δσdεe+∮Δσdεp.In a closed hysteresis loop, the elastic strain energy can be regarded as zero, so the energy consumption of each cycle is almost entirely caused by plastic strain.(3)ΔE=∮Δσdεp.The stress in each cycle can be approximated by a power function.(4)Δσ=kΔεpn.Equations (3) and (4) are simultaneously available.(5)ΔE=kn+1Δεpn+1=Δεpn+1kΔεpn=ΔεpΔσn+1.The strain energy of coal sample deformationΔE is clearly proportional to the difference of stress level Δσ. When the lower stress limit is fixed, ΔE increases with increasing upper stress limit. Because strain energy stored in coal is released instantaneously in the form of elastic or stress waves, increased strain energy inevitably leads to the gradual increase of AE energy. When using acoustic emission technology to detect the fatigue damage evolution process, what is mainly reflected is the evolution of internal cracks. The characteristics of different deformation stages can be observed from the changing behavior of acoustic emission characterization parameters with time, which allows objective evaluation of coal stability.Figure7 shows the variation characteristics of the acoustic emission ringing counting rate, impact counting rate, and energy counting rate of the MB-1 coal sample under different stress levels. In view of the long-time fatigue test of coal under cyclic loading, and the large energy consumption of rock mechanics test system, the number of cyclic loadings under different stress levels in the process of cyclic load test is set to 3000. In view of the smooth sinusoidal loading waveform and high dynamic stress response, the sinusoidal loading waveform is proposed to be used. In addition, considering the large space of the triaxial chamber of the MTS815.02 electrohydraulic servo rock mechanics test system, if the confining pressure and the loading frequency used in the test are too high, the servo response is poor. According to the test results, the response degree of the confining pressure of 10 MPa and the loading frequency of 0.25 Hz is better. Therefore, each stress level is loaded 3000 times at 10 MPa with a loading frequency of 0.25 Hz.Figure 7
Acoustic emission characteristics of coal from triaxial tests under cyclic loading and different stress levels. (a) Ringing counting rate, (b) impact counting rate, and (c) energy counting rate.
(a)(b)(c)The ringing counting rate and impact counting rate mainly reflect the acoustic emission frequency, whereas the energy counting rate mainly reflects the acoustic emission intensity. All three show different behaviors over the full loading process and can be used to evaluate acoustic emission activity from different angles. During the linear loading period to the limit of the first stress level, a small number of primary cracks in coal body are compressed and closed, which leads to the occurrence of acoustic emission phenomena. This indicates that the linear loading process causes initial damage to the samples. Within the first stress level, the acoustic emission is relatively quiet in the initial stage of loading. With increasing loading time, the cracks in the coal body appear periodically closed, the AE signal gradually becomes active, and the coal sample can be considered in a slight fatigue state. Within the second stress level, increasing the upper stress limit increases the rate of initiation, propagation, and accumulation of new cracks in the coal body. More strain energy is released and the active degree of AE signal is more apparent. At this time, the coal sample is in a moderate fatigue state. Within the third stress level, further increase of the upper stress limit causes new cracks to sprout from the coal body and further extend and converge in deeper part. The AE signal is abnormally active with the appearance of the ringing counting rate and energy counting rate. With increasing number of AE impacts, the accumulated strain energy is more clearly released with additional loading time, and the coal samples enter the deep fatigue state. Within the fourth stress level, the upper stress limit is close to the average compressive strength of the coal samples under triaxial compression. At this time, the cumulative damage caused by the combination of linear loading and cyclic loading makes the coal sample gradually lose its support capacity, and the internal energy is released completely. Particularly in the dozens of cycles before the failure point, the AE signal is extremely active, and the ringing counting rate, impact counting, and energy counting all increase sharply. Finally, the fatigue failure of coal samples occurs after 154 loading times.Compared with other loading tests, this test shows different development and change rules under cyclic loading. The acoustic emission shows the “L-” type development evolution law in any previous stress level range, while at the last stress level, it shows the obvious “U-” type development evolution law.


### 3.2. Effect of Cyclic Loading Frequency on Acoustic Emission Characteristics

At the same stress level, the effect of loading frequency on acoustic emission is mainly reflected in the change of AE ringing counting rate. The increase of loading frequency accelerates the damage process of coal, that is to say, increases the rate of initiation and propagation of microcracks and also increases the AE ringing counting rate. Figures8(a) and 8(b) show the distribution characteristics of AE ring counts of coal samples MB-3 and MB-4 under the same confining pressure (10 MPa), stress level (upper limit stress is 90% of the average compressive strength of the conventional triaxial), and two different cyclic loading frequencies (0.25 and 0.5 Hz), respectively, which are close to the first 20 cycles of fatigue failure. Emphasis is placed on the study of acoustic emission precursory characteristics of coal fatigue failure. As crack propagation under cyclic loading is a process of continuous closure and opening, the increase of cyclic loading frequency causes many cracks to have new energy injection when they are not closed, reducing the resistance needed in the opening process and accelerating crack propagation and energy release, which is reflected in the change of ringing counting rate. As shown in Figures 8(a) and 8(b), the coal samples show distinct characteristics in each cycle of cyclic loading. The counting rates of acoustic emission rings at different loading frequencies under the same confining pressure and stress level also vary substantially. Particularly in the damage stage of the formation and propagation of the main cracks, the counting rates of acoustic emission rings clearly increase with increasing load frequency, which also increases the coal fatigue failure process.Figure 8
Acoustic emission ringing counting rate under the same confining pressure and stress level and different cyclic loading frequency. (a) MB-3, 0.25 Hz and (b) MB-4, 0.5 Hz.
(a)(b)Similarly, Figures9(a), 9(b), 10(a), and 10(b) show the behavior of the AE impact counting rate and energy counting rate with time under the same conditions in the 20 cycles prior to fatigue failure of the coal samples. Through comparing and analyzing the graphs, we can see that the AE rate is higher when the frequency is 0.5 Hz regardless of ring count, impact count, or energy count. At the same time, variation of the AE ringing counting rate and energy counting rate is similar, which is consistent with the acoustic emission characteristics of coal under monotonic loading conditions [27]. During the tests, the propagation rate of new cracks differs owing to the different loading frequencies. Higher loading frequencies inevitably lead to faster crack growth rates and the detected AE energy will also increase. This further illustrates that the fatigue damage process of coal reflects the process of energy release.Figure 9
Acoustic emission impact counting rate under the same confining pressure and stress level and different cyclic loading frequency. (a) MB-3, 0.25 Hz and (b) MB-4, 0.5 Hz.
(a)(b)Figure 10
Acoustic emission energy counting rate under the same confining pressure and stress level and different cyclic loading frequency. (a) MB-3, 0.25 Hz and (b) MB-4, 0.5 Hz.
(a)(b)


## 3.1. Effect of Stress Level on Acoustic Emission Characteristics

The mechanical energy absorbed by coal is transformed into other kinds (e.g., acoustic, electromagnetic, and thermal) under an external load, and most of the strain energy is used for deformation. The stress–strain curve of coal under cyclic loading consists of a series of plastic hysteresis loops, and the area of each plastic hysteresis loop represents the energy consumed by each cycle.(1)ΔE=∮Δσdε.The deformation of coal sampleε in each cycle includes elastic deformation εe and plastic deformation εp.(2)ΔE=∮Δσdεe+∮Δσdεp.In a closed hysteresis loop, the elastic strain energy can be regarded as zero, so the energy consumption of each cycle is almost entirely caused by plastic strain.(3)ΔE=∮Δσdεp.The stress in each cycle can be approximated by a power function.(4)Δσ=kΔεpn.Equations (3) and (4) are simultaneously available.(5)ΔE=kn+1Δεpn+1=Δεpn+1kΔεpn=ΔεpΔσn+1.The strain energy of coal sample deformationΔE is clearly proportional to the difference of stress level Δσ. When the lower stress limit is fixed, ΔE increases with increasing upper stress limit. Because strain energy stored in coal is released instantaneously in the form of elastic or stress waves, increased strain energy inevitably leads to the gradual increase of AE energy. When using acoustic emission technology to detect the fatigue damage evolution process, what is mainly reflected is the evolution of internal cracks. The characteristics of different deformation stages can be observed from the changing behavior of acoustic emission characterization parameters with time, which allows objective evaluation of coal stability.Figure7 shows the variation characteristics of the acoustic emission ringing counting rate, impact counting rate, and energy counting rate of the MB-1 coal sample under different stress levels. In view of the long-time fatigue test of coal under cyclic loading, and the large energy consumption of rock mechanics test system, the number of cyclic loadings under different stress levels in the process of cyclic load test is set to 3000. In view of the smooth sinusoidal loading waveform and high dynamic stress response, the sinusoidal loading waveform is proposed to be used. In addition, considering the large space of the triaxial chamber of the MTS815.02 electrohydraulic servo rock mechanics test system, if the confining pressure and the loading frequency used in the test are too high, the servo response is poor. According to the test results, the response degree of the confining pressure of 10 MPa and the loading frequency of 0.25 Hz is better. Therefore, each stress level is loaded 3000 times at 10 MPa with a loading frequency of 0.25 Hz.Figure 7
Acoustic emission characteristics of coal from triaxial tests under cyclic loading and different stress levels. (a) Ringing counting rate, (b) impact counting rate, and (c) energy counting rate.
(a)(b)(c)The ringing counting rate and impact counting rate mainly reflect the acoustic emission frequency, whereas the energy counting rate mainly reflects the acoustic emission intensity. All three show different behaviors over the full loading process and can be used to evaluate acoustic emission activity from different angles. During the linear loading period to the limit of the first stress level, a small number of primary cracks in coal body are compressed and closed, which leads to the occurrence of acoustic emission phenomena. This indicates that the linear loading process causes initial damage to the samples. Within the first stress level, the acoustic emission is relatively quiet in the initial stage of loading. With increasing loading time, the cracks in the coal body appear periodically closed, the AE signal gradually becomes active, and the coal sample can be considered in a slight fatigue state. Within the second stress level, increasing the upper stress limit increases the rate of initiation, propagation, and accumulation of new cracks in the coal body. More strain energy is released and the active degree of AE signal is more apparent. At this time, the coal sample is in a moderate fatigue state. Within the third stress level, further increase of the upper stress limit causes new cracks to sprout from the coal body and further extend and converge in deeper part. The AE signal is abnormally active with the appearance of the ringing counting rate and energy counting rate. With increasing number of AE impacts, the accumulated strain energy is more clearly released with additional loading time, and the coal samples enter the deep fatigue state. Within the fourth stress level, the upper stress limit is close to the average compressive strength of the coal samples under triaxial compression. At this time, the cumulative damage caused by the combination of linear loading and cyclic loading makes the coal sample gradually lose its support capacity, and the internal energy is released completely. Particularly in the dozens of cycles before the failure point, the AE signal is extremely active, and the ringing counting rate, impact counting, and energy counting all increase sharply. Finally, the fatigue failure of coal samples occurs after 154 loading times.Compared with other loading tests, this test shows different development and change rules under cyclic loading. The acoustic emission shows the “L-” type development evolution law in any previous stress level range, while at the last stress level, it shows the obvious “U-” type development evolution law.


## 3.2. Effect of Cyclic Loading Frequency on Acoustic Emission Characteristics

At the same stress level, the effect of loading frequency on acoustic emission is mainly reflected in the change of AE ringing counting rate. The increase of loading frequency accelerates the damage process of coal, that is to say, increases the rate of initiation and propagation of microcracks and also increases the AE ringing counting rate. Figures8(a) and 8(b) show the distribution characteristics of AE ring counts of coal samples MB-3 and MB-4 under the same confining pressure (10 MPa), stress level (upper limit stress is 90% of the average compressive strength of the conventional triaxial), and two different cyclic loading frequencies (0.25 and 0.5 Hz), respectively, which are close to the first 20 cycles of fatigue failure. Emphasis is placed on the study of acoustic emission precursory characteristics of coal fatigue failure. As crack propagation under cyclic loading is a process of continuous closure and opening, the increase of cyclic loading frequency causes many cracks to have new energy injection when they are not closed, reducing the resistance needed in the opening process and accelerating crack propagation and energy release, which is reflected in the change of ringing counting rate. As shown in Figures 8(a) and 8(b), the coal samples show distinct characteristics in each cycle of cyclic loading. The counting rates of acoustic emission rings at different loading frequencies under the same confining pressure and stress level also vary substantially. Particularly in the damage stage of the formation and propagation of the main cracks, the counting rates of acoustic emission rings clearly increase with increasing load frequency, which also increases the coal fatigue failure process.Figure 8
Acoustic emission ringing counting rate under the same confining pressure and stress level and different cyclic loading frequency. (a) MB-3, 0.25 Hz and (b) MB-4, 0.5 Hz.
(a)(b)Similarly, Figures9(a), 9(b), 10(a), and 10(b) show the behavior of the AE impact counting rate and energy counting rate with time under the same conditions in the 20 cycles prior to fatigue failure of the coal samples. Through comparing and analyzing the graphs, we can see that the AE rate is higher when the frequency is 0.5 Hz regardless of ring count, impact count, or energy count. At the same time, variation of the AE ringing counting rate and energy counting rate is similar, which is consistent with the acoustic emission characteristics of coal under monotonic loading conditions [27]. During the tests, the propagation rate of new cracks differs owing to the different loading frequencies. Higher loading frequencies inevitably lead to faster crack growth rates and the detected AE energy will also increase. This further illustrates that the fatigue damage process of coal reflects the process of energy release.Figure 9
Acoustic emission impact counting rate under the same confining pressure and stress level and different cyclic loading frequency. (a) MB-3, 0.25 Hz and (b) MB-4, 0.5 Hz.
(a)(b)Figure 10
Acoustic emission energy counting rate under the same confining pressure and stress level and different cyclic loading frequency. (a) MB-3, 0.25 Hz and (b) MB-4, 0.5 Hz.
(a)(b)


## 4. Fracture Morphology and Acoustic Emission Felicity Effects of Coal under Triaxial Cyclic Loading

### 4.1. Comparative Analysis of Coal Sample Fracture Morphology

Because the fracture morphology of coal samples under the same loading condition is similar, the fracture morphology of coal samples MA-1 and MB-2 under conventional triaxial compression and triaxial cyclic loading was selected to carry out comparative analysis. As shown in Figure11, under conventional triaxial compression, shear or splitting failure occurs mainly along the direction of the main fracture surface, while under triaxial cyclic loading, the failure modes are relatively complex. The influence of different stress levels on the initiation and propagation rate of microcracks in the coal samples clearly differs. Initial damage under linear loading and fatigue damage under cyclic loading causes the coal samples to present shear failure modes along multiple fracture surfaces.Figure 11
Fracture morphology of coal samples. (a) MA-1 and (b) MB-2.
(a)(b)


### 4.2. Acoustic Emission Felicity Effect of Coal Samples

The Felicity effect, also known as the anti-Kaiser effect, means that observable acoustic emission occurs before the repetitive load reaches the original maximum load for component materials under repeated loading. This is the memory characteristic of acoustic emission information, which characterizes the irreversibility of acoustic emission. The Felicity ratio is a measure of the failure degree of the Kaiser effect, which reflects the irreversibility of acoustic emission. A Felicity ratio of 1 indicates that the Kaiser effect is valid and the coal rock memory lags behind. As the Felicity ratio approaches 1, this is indicative of higher accuracy of the memory ability of the Kaiser effect. A Felicity ratio of 1 indicates that the Felicity effect is valid and the coal rock memory is ahead of time. The Felicity ratio is a broader description of the irreversibility of the acoustic emission process on the coal. Smaller ratios are associated with more apparent Felicity effects. The Felicity ratio has been well applied in composite materials (e.g., reinforced plastics, aerospace industry materials), but is seldom used in coal materials. The Felicity ratio is often used as an important criterion for evaluating the severity of material defects in engineering and can accurately reflect the degree of original damage or structural defects.At present, the study of rock memory is mostly based on acoustic emission test results under graded cyclic loading. The common points of these results are that there are more Kaiser effects in rock but lower Felicity effects (i.e., anti-Kaiser effects), and criteria for determining Felicity effects have not been discussed in previous studies [28–30]. The guideline recommended by the US CARP is to determine the beginning of “obvious” acoustic emission [31]. This shows that when the load increases by 5%, AE counts more than 10 events. However, when the load increases by 10%, AE counts more than 20 ring counts. In this paper, the Felicity ratio of axial stress Fσ1, principal stress difference Fσ1−σ3, volumetric strain FεV, axial strain Fε1, Poisson’s ratio Fμ, and elastic modulus FE are used to study the memory characteristics of coal. Among them, Fσ1=σ1AE/σ1max, Fσ1−σ3=σ1−σ3AE/σ1−σ3max, FεV=εVAE/εVmax, Fε1=ε1AE/ε1max, Fμ=μAE/μmax, FE=EAE/Emax, initial AE axial stress σ1AE, initial principal stress difference σ1−σ3AE, initial volumetric strain εVAE, initial AE axial strain ε1AE, initial Poisson’s ratio μAE, and initial elastic modulus FE under repeated loading are used. The maximum axial stress σ1max, the maximum principal stress difference σ1−σ3max, the maximum volume strain εVmax, the maximum axial strain ε1max, the maximum Poisson ratio μmax, and the maximum modulus of elasticity Emax depend on the data of the last loading. Table 2 shows the average Felicity ratio of coal samples under different stress levels.Table 2
Average Felicity ratio of coal samples under cyclic loading.
Coal sample numberStress levelF¯σ1F¯σ1−σ3F¯εVF¯ε1F¯μF¯EMB-1First0.9410.8920.9630.9690.9880.990Second0.8720.7960.9020.8670.9050.917Third0.5110.4680.6370.7310.8570.893Fourth0.3080.2030.4020.4190.7950.809MB-2First0.9360.8990.9520.9570.9790.987Second0.8690.7520.8970.8710.9010.902Third0.5040.4240.5590.5130.8900.883Fourth0.2960.1650.3710.3190.7360.815MB-3First0.9450.8370.9560.9780.9810.995Second0.8670.7100.8990.8860.9020.912Third0.5190.4010.6370.5330.8950.894Fourth0.2930.1850.3730.3280.7310.806MB-4First0.9420.8620.9610.9580.9870.989Second0.8700.7170.8930.8670.8900.917Third0.5150.3850.5600.5250.6210.893Fourth0.3010.1920.3720.4190.5980.818Taking coal sample MB-2 as an example in the range of the first stress level, the Felicity ratio average for each parameter of coal deformation is less than 1, which indicates that there is a Felicity effect in coal under cyclic loading, but it is not very apparent. At this stage, the primary cracks in the coal gradually close, elastic deformation gradually develops, and the memory effect is not apparent. In the range of the second stress level, the ratio of Felicity to the average value of each parameter of coal deformation decreases, which indicates that the Felicity effect gradually increases with increasing upper limit stress. This stage is in the initiation period of microcrack initiation in coal samples, and some new cracks have begun to expand at depth. The coal samples show clear plastic deformation and their memory effect advances. In the range of the third stress level, the ratio of Felicity to the average value is further reduced and the effect of Felicity is clearly enhanced. At this stage, the new cracks initiated in the coal samples begin to substantially propagate until they converge and penetrate and ultimately form fracture surfaces in different directions. In the fourth stress level range, fatigue failure occurs macroscopically. At this time, the new internal cracks converge and penetrate along different fracture plane directions, the degree of damage evolution is clearly deepened, and the Felicity effect is the most apparent.We observe a clear Felicity effect in coal samples under triaxial cyclic loading and the extent varies substantially over the different stress levels. With increasing the upper limit stress, the Felicity ratio gradually decreases, and the Felicity effect gradually increases. Generally speaking, the average Felicity ratio of elastic modulus shows no observable change, the average Felicity ratio of the Poisson ratio decreases slightly, and the average Felicity ratio of axial strain and volumetric strain varies greatly. In contrast, the average Felicity ratios of axial stress and principal stress difference decrease more significantly, and the latter is more significant than the former. The principal stress difference is therefore a reasonable parameter to use for studying the Felicity effect of coal.


## 4.1. Comparative Analysis of Coal Sample Fracture Morphology

Because the fracture morphology of coal samples under the same loading condition is similar, the fracture morphology of coal samples MA-1 and MB-2 under conventional triaxial compression and triaxial cyclic loading was selected to carry out comparative analysis. As shown in Figure11, under conventional triaxial compression, shear or splitting failure occurs mainly along the direction of the main fracture surface, while under triaxial cyclic loading, the failure modes are relatively complex. The influence of different stress levels on the initiation and propagation rate of microcracks in the coal samples clearly differs. Initial damage under linear loading and fatigue damage under cyclic loading causes the coal samples to present shear failure modes along multiple fracture surfaces.Figure 11
Fracture morphology of coal samples. (a) MA-1 and (b) MB-2.
(a)(b)


## 4.2. Acoustic Emission Felicity Effect of Coal Samples

The Felicity effect, also known as the anti-Kaiser effect, means that observable acoustic emission occurs before the repetitive load reaches the original maximum load for component materials under repeated loading. This is the memory characteristic of acoustic emission information, which characterizes the irreversibility of acoustic emission. The Felicity ratio is a measure of the failure degree of the Kaiser effect, which reflects the irreversibility of acoustic emission. A Felicity ratio of 1 indicates that the Kaiser effect is valid and the coal rock memory lags behind. As the Felicity ratio approaches 1, this is indicative of higher accuracy of the memory ability of the Kaiser effect. A Felicity ratio of 1 indicates that the Felicity effect is valid and the coal rock memory is ahead of time. The Felicity ratio is a broader description of the irreversibility of the acoustic emission process on the coal. Smaller ratios are associated with more apparent Felicity effects. The Felicity ratio has been well applied in composite materials (e.g., reinforced plastics, aerospace industry materials), but is seldom used in coal materials. The Felicity ratio is often used as an important criterion for evaluating the severity of material defects in engineering and can accurately reflect the degree of original damage or structural defects.At present, the study of rock memory is mostly based on acoustic emission test results under graded cyclic loading. The common points of these results are that there are more Kaiser effects in rock but lower Felicity effects (i.e., anti-Kaiser effects), and criteria for determining Felicity effects have not been discussed in previous studies [28–30]. The guideline recommended by the US CARP is to determine the beginning of “obvious” acoustic emission [31]. This shows that when the load increases by 5%, AE counts more than 10 events. However, when the load increases by 10%, AE counts more than 20 ring counts. In this paper, the Felicity ratio of axial stress Fσ1, principal stress difference Fσ1−σ3, volumetric strain FεV, axial strain Fε1, Poisson’s ratio Fμ, and elastic modulus FE are used to study the memory characteristics of coal. Among them, Fσ1=σ1AE/σ1max, Fσ1−σ3=σ1−σ3AE/σ1−σ3max, FεV=εVAE/εVmax, Fε1=ε1AE/ε1max, Fμ=μAE/μmax, FE=EAE/Emax, initial AE axial stress σ1AE, initial principal stress difference σ1−σ3AE, initial volumetric strain εVAE, initial AE axial strain ε1AE, initial Poisson’s ratio μAE, and initial elastic modulus FE under repeated loading are used. The maximum axial stress σ1max, the maximum principal stress difference σ1−σ3max, the maximum volume strain εVmax, the maximum axial strain ε1max, the maximum Poisson ratio μmax, and the maximum modulus of elasticity Emax depend on the data of the last loading. Table 2 shows the average Felicity ratio of coal samples under different stress levels.Table 2
Average Felicity ratio of coal samples under cyclic loading.
Coal sample numberStress levelF¯σ1F¯σ1−σ3F¯εVF¯ε1F¯μF¯EMB-1First0.9410.8920.9630.9690.9880.990Second0.8720.7960.9020.8670.9050.917Third0.5110.4680.6370.7310.8570.893Fourth0.3080.2030.4020.4190.7950.809MB-2First0.9360.8990.9520.9570.9790.987Second0.8690.7520.8970.8710.9010.902Third0.5040.4240.5590.5130.8900.883Fourth0.2960.1650.3710.3190.7360.815MB-3First0.9450.8370.9560.9780.9810.995Second0.8670.7100.8990.8860.9020.912Third0.5190.4010.6370.5330.8950.894Fourth0.2930.1850.3730.3280.7310.806MB-4First0.9420.8620.9610.9580.9870.989Second0.8700.7170.8930.8670.8900.917Third0.5150.3850.5600.5250.6210.893Fourth0.3010.1920.3720.4190.5980.818Taking coal sample MB-2 as an example in the range of the first stress level, the Felicity ratio average for each parameter of coal deformation is less than 1, which indicates that there is a Felicity effect in coal under cyclic loading, but it is not very apparent. At this stage, the primary cracks in the coal gradually close, elastic deformation gradually develops, and the memory effect is not apparent. In the range of the second stress level, the ratio of Felicity to the average value of each parameter of coal deformation decreases, which indicates that the Felicity effect gradually increases with increasing upper limit stress. This stage is in the initiation period of microcrack initiation in coal samples, and some new cracks have begun to expand at depth. The coal samples show clear plastic deformation and their memory effect advances. In the range of the third stress level, the ratio of Felicity to the average value is further reduced and the effect of Felicity is clearly enhanced. At this stage, the new cracks initiated in the coal samples begin to substantially propagate until they converge and penetrate and ultimately form fracture surfaces in different directions. In the fourth stress level range, fatigue failure occurs macroscopically. At this time, the new internal cracks converge and penetrate along different fracture plane directions, the degree of damage evolution is clearly deepened, and the Felicity effect is the most apparent.We observe a clear Felicity effect in coal samples under triaxial cyclic loading and the extent varies substantially over the different stress levels. With increasing the upper limit stress, the Felicity ratio gradually decreases, and the Felicity effect gradually increases. Generally speaking, the average Felicity ratio of elastic modulus shows no observable change, the average Felicity ratio of the Poisson ratio decreases slightly, and the average Felicity ratio of axial strain and volumetric strain varies greatly. In contrast, the average Felicity ratios of axial stress and principal stress difference decrease more significantly, and the latter is more significant than the former. The principal stress difference is therefore a reasonable parameter to use for studying the Felicity effect of coal.


## 5. Conclusions

(1)
Acoustic emissions contain important information about the change of internal structure and fatigue failure of coal. The variation of acoustic emission rates reflects the evolution of coal under triaxial cyclic loading and characteristics during each stage of fatigue damage. The macroscopic appearance and acoustic emission characteristics of coal fatigue failure under cyclic loading show different development behaviors under different stress loading stages(2)
Fatigue tests of coal samples under cyclic loading mainly include the linear loading stage and cyclic loading stage. Under linear loading, the internal coal cracks are gradually compacted, which occurs in the elastic stage of crack compaction and closure, and a small amount of acoustic emission appears. This indicates that the linear loading process in the early stage of cyclic loading still produces some initial damage that enhances the fatigue damage produced in subsequent stages of the cyclic loading(3)
Stress level has an important influence on the acoustic emission characteristics of coal fatigue damage evolution. When the lower limit stress is fixed, higher upper limit stress is associated with more active AE signals. Particularly within the stress level of coal fatigue failure, the AE ringing counting rate and energy counting rate increase sharply and the number of impacts increases significantly. The subsequent stages of fatigue damage occur with increasing loading time: slight fatigue, moderate fatigue, deep fatigue, and ultimate fatigue failure. The acoustic emission shows the “L-” type development evolution law in any previous stress level range, while at the last stress level, it shows the obvious “U-” type development evolution law(4)
At the same stress level and confining pressure, if the frequency of cyclic loading increases, the propagation rate of microcracks also increases, which accelerates coal fatigue damage failure and significantly increases the impact counting, whereas the ringing counting rate and energy counting rate are essentially the same. The dynamic change of acoustic emission reflects the process of primary crack closure, crack initiation, propagation, and convergence in coal samples from side to side(5)
The fatigue failure modes of the coal samples under cyclic loading differ from those under conventional triaxial compression. In conventional triaxial compression tests, shear or splitting failure of coal samples generally occurs along the main fracture surface, whereas under cyclic loading, the coal samples show intricate shear failure along the fracture surface in different directions and is accompanied by Felicity effects in different stress levels. With the continuous increase of stress level, the Felicity effect is gradually enhanced. Compared with axial stress, axial strain, volumetric strain, Poisson’s ratio, and elastic modulus, the principal stress difference is more reliable to use to study the AE-Felicity effect of coal.



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*Source: 3453128-2020-08-27.xml*