Experimental Study on Spectral Response Characteristics and Mechanical State of Coal Based on Artificial Acoustic Signals

Abstract

With the increase in coal mining depth, the stress and strain state of coal and rock mass affects the formation of dangerous zones of dynamic phenomena. In order to study the relationship between the frequency spectrum characteristics of artificial acoustic signals and the stress state of coal and gas pressure, a test device and system that can generate acoustic signals by mechanical vibration excitation are developed by using the design idea of the unit module. Firstly, the basic mechanical parameters of coal under uniaxial compression are analyzed. On this basis, we use the test device to study the qualitative and quantitative relationships between the relative stress coefficient K value of the coal body and the axial loading stress, whether it contains gas, and the mechanical vibration force. The test results show that when the gas-containing coal and the gas-free coal are subjected to the same external mechanical vibration knocking force to stimulate the artificial acoustic signal test, the relative stress coefficient K value increases first and then decreases with the increase in axial loading stress. The relationship between the relative stress coefficient K and the axial loading stress σ can be expressed in the form of exponential function $K=e^{-{\displaystyle \frac{C}{\sigma }}}$. When the axial loading stress and the external mechanical vibration force are both fixed values, the relative stress coefficient K value of the coal body with gas is smaller than that without gas. When the axial loading stress and gas-bearing pressure of the coal body are both fixed values, the relative stress coefficient K value decreases with the increase in the impact force of the external mechanical vibration. This experimental study can provide a reference for the identification and prediction of dynamic disasters based on artificial acoustic signals.

1. Introduction

With the development of the mine to the deep, the characteristics of strong adsorption and low permeability are more obvious. The coupling effect of high stress, high gas pressure, and low-permeability coal under mining disturbance is more obvious, which leads to an increase in coal and gas outburst accidents [1,2,3,4]. External vibration, such as coal cutter operation, roadheader excavation, artificial blasting construction, etc., induces frequent coal and gas outburst accidents. The dynamic change in ground stress and the characteristics of gas migration near the working face in the process of coal falling, blasting, and tunneling of shearers and coal cutters are very important for predicting coal and gas outburst and timely warning of the danger of dynamic phenomena.

In recent years, the detection and early warning technology of geological disasters, such as microseism, electromagnetic radiation, and acoustic emission, has developed rapidly [5,6,7]. Years of field application show that there is no single-value correspondence between the acoustic emission activity intensity of the coal body and the stress and strain state of the space near the working face, which leads to the low reliability of the seismic acoustic prediction method [8]. In the 1980s, Russia began to study the artificial acoustic prediction method for coal seam outburst risk. The artificial acoustic signal prediction method can realize the continuous online monitoring and early warning of the danger of various dynamic phenomena, geological damage, and stress change dynamics near the working face [9]. For the first time, Professor М.С. Анциферoв [10] proposed a prediction method for outburst risk based on the number of acoustic emission pulses and their increase to evaluate the stress and strain state of coal seams. С.В. Мирер [11] was the first to study the artificial acoustic prediction method for outburst risk. He developed a method for predicting outburst hazard based on the analysis of amplitude-frequency characteristics of acoustic signals formed in the formation during the operation of process equipment. This lays the foundation for the artificial acoustic method to become the standard method of prominent risk prediction. Кoлчин et al. [12,13,14,15] solved a series of mine production problems, including the prediction of gas dynamic phenomena, the prediction of geological damage in front of the moving face, and the monitoring of the effect of anti-outburst measures. The developed method has been successfully applied in the prediction of mine dynamic phenomena. In 2015, the Russian company МНТЛ РИВАС developed the intelligent system of mine dynamic phenomenon prediction and rock mass status monitoring [16]. In China, in order to realize continuous automatic prediction of the stress and strain state of rock masses near working faces, Wei Fengqing et al. [17] conducted relevant research: Based on the roof deformation delay theory formed by the risk of dynamic phenomena and the elastic resonance spectrum characteristics of artificial acoustic signals, they developed CAKCM, an automated system for rock mass acoustic monitoring and prediction of dynamic phenomena, according to the results of many years of research and testing in Russia and the latest requirements of safety regulations. It has been tested and applied in a production mine.

The traditional contact discontinuous borehole index prediction method cannot meet the needs of complex geological conditions, complex dynamic phenomena, or high-yield, high-efficiency, and intelligent mines in many mining areas. The artificial acoustic signal prediction method can realize continuous, automatic, and quantitative prediction and early warning of the coal state and dynamic phenomena in the working face and in front of the working face. It can establish the functional relationship between the prediction index and the stress state of coal rock mass, and improve the reliability of the prediction results. However, the research on the spectral characteristics of artificial acoustic signals in China is still not perfect. How to use the amplitude-frequency characteristics of artificial acoustic signals to directly reflect the deformation and failure of coal and the gas content in coal has not been solved. The quantitative relationship between the amplitude-frequency characteristics of artificial acoustic signals and mechanical parameters such as the coal stress state and gas pressure is still not clear enough. Therefore, we need to carry out basic theoretical research based on artificial acoustic signals to reflect the stress state of coal and rock and the prediction of gas outburst risk. In view of the previous research experience, we have independently designed an experimental device and experimental method for mechanical vibration excitation of artificial acoustic signals. We have carried out qualitative and quantitative research on the spectral response characteristics of artificial acoustic signals generated by mechanical vibration excitation of coal and the stress and gas content of coal. We hope to provide a new direction and technical means for the identification of the front stress anomaly area and the risk identification and prediction of dynamic disasters such as coal outbursts in the mining process.

2. Artificial Acoustic Signal Test of Mechanical Vibration Excitation

2.1. Design Principle of Test Device

“Artificial acoustic signal” refers to the wide-band artificial acoustic vibration or artificial sound source excited by running mining equipment (such as shearers, cutting mechanisms of coal ploughs, drill bits, etc.) in the rock mass near the working face (by hammering the side wall of the roadway) to detect the rock mass. According to the amplitude-frequency characteristics of artificial acoustic signals, the stress state of rock masses near the working face can be analyzed. The risk of coal and gas outbursts in the mining face can be predicted, and the state of rock masses can be monitored (such as the geological damage in front of the working face and the stress state near the working face) [18]. The artificial acoustic signals of external vibration feedback carry plenty of important information, such as details about the rock stress, mechanical properties, structural changes, deformation and failure characteristics, and gas pressure. The artificially excited acoustic signal in coal rock is the superposition of inherent elastic vibration (hereinafter referred to as resonance). Resonance occurs in each rock layer from the free surface to the weakened contact surface [19]. Therefore, the acoustic signal excited in the layered coal-rock mass is the superposition of its own (resonant) elastic vibration in each individual layer. In the process of coal mining, the cutting mechanism of the running mining equipment is used as the source of acoustic vibration [20]. Taking the working face as an example, the acoustic vibration excites near the working face, with propagation to the deep coal body and the sound wave passing through the medium with variable parameters. The change in stress in the medium corresponds to the parameters of the stress diagram. Its length corresponds to the strike length of the increased mine pressure area. The propagation process of acoustic vibration is shown in Figure 1.

Affected by external forces, resonance occurs in the coal seam. There is the following relationship between the thickness of the rock layer (h) that generates resonance in the coal seam and the resonance frequency ($f_p$):

$$f_P={\displaystyle \frac{v}{h}}$$

(1)

where “v” is the phase velocity of the shear wave, m/s. The value of this speed is based on experience. The variable “h” is the thickness of the rock layer that generates resonance, m. The variable “h” can also be understood as the distance from the oscillation excitation point to the weakened mechanical (interlayer) contact surface in the rock mass.

According to the formula, the frequency of the natural resonance recorded during the monitoring process can determine the location of these weakened mechanical (interlayer) contact surfaces at the pulse action site of the rock mass relative to the coal seam. By analyzing the resonance frequency and amplitude, a conclusion can be drawn about the change in the stress and strain state of the rock mass in the section of the vibration excitation point. Considering that harmonic signals can be obtained only when the oscillating system is acted upon, an experimental device and a measurement method are designed for rock masses affected by mining operations on a small scale in the laboratory. In this method, the pulse effect of a small hammer on coal is used as the source of an artificial acoustic signal, and a seismometer is used to record it. Based on the elastic vibration pulse excitation in coal and rock masses, the seismometer converts the elastic vibration into an acoustic signal. On the spectrum of the recorded acoustic signal is the superposition of the elastic vibration, and the resonance frequency is distinguished by high amplitude. The obtained artificial acoustic signal spectrum reflects the stress–strain state of coal under loading stress and external mechanical vibration force.

2.2. Introduction of Experimental Device

Considering the complex disaster-pregnant environment of deep coal seams and the influence of mechanical vibration force in the process of coal seam mining, and based on the shortcomings of existing instruments and equipment, the design idea of the unitized module is adopted to develop a test device and system that can realize mechanical vibration force to stimulate the gas-bearing coal body to produce acoustic signals. The test device system includes inflatable and exhaust units, a mechanical vibration unit, an axial compression unit, a mechanical vibration force monitoring unit, and an artificial acoustic signal monitoring and collecting unit. Each unit module cooperates with the others to realize the coupling effect of gas pressure, a high-stress environment, and mechanical vibration force. The overall design is shown in Figure 2.

Considering that the harmonic signal can be obtained only when acting on the oscillating system, for the coal body affected by the mining operation, the pulse effect on the coal body is used as the source of the artificial acoustic signal, and the seismic geophone is used to record it. Based on the pulse excitation of elastic vibration in coal and rock masses, the seismic geophone converts the elastic vibration into an acoustic signal. Under laboratory conditions, using a portable artificial acoustic probe to collect the artificial acoustic signal excited by the mechanical vibration force of the coal body to the portable seismic geophone can be considered, and the spectrum characteristics and information parameters of the artificial acoustic signal can be analyzed. The overall structure of the experimental device for mechanical vibration excitation of artificial acoustic signals is shown in Figure 3.

Inflatable and exhaust units can realize coal with different gas pressures. Through the mechanical vibration unit and the mechanical vibration force monitoring unit, different mechanical vibration knocking forces can be realized. Axial compression with different degrees of pressure can be achieved by applying axial compression elements. The artificial acoustic signal monitoring and collection unit monitors and collects the artificial acoustic signal generated by the coal sample in the pendulum mechanical vibration excitation chamber. With the cooperation of each unit, the gas content, different stress and different mechanical vibration and knocking force can be set. The artificial acoustic signals generated by coal excitation under mechanical vibration are collected to study the dynamic response characteristics of coal under mechanical vibration. By analyzing and processing the data, the quantitative relationship between the amplitude-frequency characteristics of artificial acoustic signals and mechanical parameters such as coal stress state and gas pressure is established. The specific experimental device diagram is shown in Figure 4.

2.3. Experimental Scheme

The coal samples used in the test were taken from No.8 Mine of Pingdingshan. In order to reduce the possible influence of the primary cracks of coal rock samples on the test results, the wave velocity and density of the specimens were measured before the test. The specimens with similar wave velocity and density were selected for the test. The coal sample selected in the test was a cylinder with a diameter × length of 50 mm × 100 mm. The average mass of the coal sample was 249.95 g, and the average density of the coal sample was 1.147 g/m³. After measurement, the wave velocity of the selected coal sample was between 1930 m/s and 2013 m/s, and the texture was relatively uniform. The sample used in this test is shown in Figure 5.

The fixed pointer points to the dial at 15°, 20°, 25°, 30°, 35°, and 40°—six scales. Let the hammer strike the coal body freely, and ensure that the hammer strikes each time in each group of experiments are almost the same. The bottom swing of the small hammer strikes the middle and lower part of the coal body, and the instantaneous force of the knock can be recorded by the pressure sensor of the mechanical vibration force monitoring unit. Through the mechanical control system, the axial pressure controller is set to the axial pressure, loading rate, sample size, and other related parameters, so as to control the RMT-301 rock direct shear/triaxial compression composite testing machine to apply axial pressure to the indenter of the machining chamber. When each scale (percussion force) is tested, the control axial pressure is 10 kN, 15 kN, 20 kN, 25 kN, 30 kN, 35 kN, and 40 kN. When each axial pressure is set, the axial pressure is controlled to be stable, knocking once every 10 s, knocking about 6–10 times.

Firstly, the axial loading rate is set to 0.01 mm/s, and the mechanical parameters of the uniaxial compression of the coal are analyzed. Next, the experimental study of artificial acoustic signals stimulated by mechanical vibration is carried out under two conditions of no gas and 0.3 MPa gas pressure. Finally, combined with uniaxial compression parameters of the coal body, the mechanical state of the coal body under different axial loading stress and different mechanical vibration and knocking force is analyzed.

The control axial loading stress is divided into 5–30 MPa, with 2.5 MPa as a class, and the control axial loading stress does not change in each class. The hammer is located at 15°, 20°, 25°, 30°, 35°, and 40° of the dial, and freely falls to hit the coal body. Make sure that the small hammer strikes the coal body 6–10 times at each dial. The interval between each knock is 10 s.

Table 1. Artificial acoustic signal test of gas-free coal body mechanical vibration excitation.

Number	Knock Scale/°	Axial Loading Stress/MPa	Interval Time/s	Number of Knocks
1	15	5 MPa, 7.5 MPa	10	6–10
2	20	10 MPa, 12.5 MPa
3	25	15 MPa, 17.5 Mpa
4	30	20 MPa, 22.5 Mpa
5	35	25 MPa, 27.5 Mpa
6	40	30 MPa

shows the test of artificial acoustic signals stimulated by mechanical vibration in coal without gas.

Table 2. Artificial acoustic signal test of coal mechanical vibration excitation when gas pressure is 0.3 MPa.

Number	Knock Scale/°	Axial Loading Stress/MPa	Gas Pressure/MPa	Interval Time/s	Number of Knocks
1	15	5 MPa, 7.5 MPa	0.3	10	6–10
2	20	10 MPa, 12.5 MPa
3	25	15 MPa, 17.5 MPa
4	30	20 MPa, 22.5 MPa
5	35	25 MPa, 27.5 MPa
6	40	30 MPa

shows the test of the artificial acoustic signal stimulated by mechanical vibration when the gas pressure in the coal is 0.3 MPa.

3. The Spectrum Parameters of Artificial Acoustic Signals

3.1. Principle of Artificial Acoustic Signal Acquisition

The system converts the rock mass vibration (artificial acoustic signal) caused by the action of mining equipment into audio electrical signals. Based on the results of spectrum analysis, the prediction parameters based on the frequency and amplitude of the artificial acoustic signals were constructed [21].

By analyzing the frequency spectrum characteristics of the elastic vibration waves generated in coal and rock masses, the frequency spectrum parameters of artificial acoustic signals can be used for daily prediction of the dynamic phenomenon risk of mining faces in coal and gas outburst mines and rock burst mines, daily monitoring of the rock mass state of working faces, and monitoring of the safety and effectiveness of working face anti-outburst measures for relief drilling. According to the research results of C.B. Merpep in Russia [11], the artificial acoustic signal prediction method is based on the fact that the attenuation coefficient of sound waves decreases with the increase in spatial stress near the working face, and this reduction is more obvious at high frequency than at low frequency. Thus, the ratio of harmonic amplitudes of acoustic signals measured at high and low frequencies increases with increasing stress. The increase in the relative stress coefficient K corresponds to the increase in stress, potential energy accumulation, and dynamic phenomenon risk in the surrounding rock of the roadway.

In order to evaluate the relative stress dynamics of coal during the test, we calculated a third of the spectrum of the artificial acoustic signal. Based on this, the low-frequency component and high-frequency component of the spectrum corresponding to the sum of the amplitudes of the low-frequency and high-frequency parts of the spectrum were determined. Based on these, the relative stress coefficient K was calculated, as shown in Formula (2). The relative stress coefficient K value is equal to the ratio of the sum of the amplitudes of the high-frequency part of the spectrum to the sum of the amplitudes of the low-frequency part of the spectrum [22], as shown in Figure 6.

$$K={\displaystyle \frac{A_B}{A_H}}$$

(2)

where “$A_B$” is the sum of the amplitudes of the high-frequency part of the acoustic signal spectrum, and “$A_H$” is the sum of the amplitude of the low-frequency part of the acoustic signal spectrum.

In the laboratory, the artificial acoustic signal probe needed to be installed on the surface of the coal body in order to be used. The metal gasket was in contact with the damping gasket on the back of the artificial acoustic signal probe and was not allowed to come into contact with the metal part of the geophone. Then, a series of external mechanical vibration shocks were carried out at a certain distance from the artificial acoustic signal probe. The acoustic pulses caused by the response of the coal body to the pulse action were recorded. In this case, in different areas of the coal body, it produced its own resonance oscillation. In the recorded acoustic signal spectrum, this is the superposition of the elastic vibration, with high amplitude to distinguish the resonance frequency. The obtained artificial acoustic signal spectrum reflects the stress and strain of the coal.

3.2. Processing of Artificial Acoustic Signals

In order to evaluate the resolution process of the artificial acoustic signal spectrum component of the relative stress dynamics of the coal body during the test, the determination of the relative stress coefficient K should follow the following order:

Firstly, a stable information spectrum of the acoustic signal is formed to exclude the “unqualified” spectrum. The acoustic detection method is used to collect enough information.

Secondly, a third of the spectrum is decomposed (the boundary of the spectrum is determined) so that the sum of the low-frequency amplitude on both sides of the spectrum is equal to the sum of the high-frequency amplitude.

Thirdly, after the above decomposition of the spectrum, the relative stress dynamics during the monitoring process can be evaluated by analyzing the relative stress coefficient K of the coal body during the test.

Before calculating the average frequency spectrum of the collected artificial acoustic signals, it is necessary to eliminate the frequency spectrum with poor quality. The artificial acoustic signal spectrum suitable for further calculation is a pulse with a clean profile, which arrives at the first order, and the amplitude of the single phase of the signal decreases gently along the pulse length. In the experiment, it is difficult to guarantee the effectiveness of the collected signal with only one knock or too few knocks. Tap 6–10 times to ensure that qualified spectrum signals can be screened for processing. The information spectrum of some artificial acoustic signals collected in the experiment is shown in Figure 7.

In the case of pulse excitation, the artificial acoustic signal can be recorded by oscillogram or linear spectrum, as shown in Figure 8. The fast Fourier transform was applied to the artificial acoustic signal excited by the coal body during the test, which can be expressed as the spectrum of the resonance frequency superposition. The resonance frequency is caused by the natural vibration generated in each layer [23]. An acceptable oscillographic image of an artificial acoustic signal has a stable sine wave form, which is represented by the truncation of the upper or lower part of the signal amplitude.

During the processing, the linear spectrum and the one-third multiple spectrum were scaled according to the amplitude maximum in the spectrum (normalization: that is, the ratio of each amplitude to the maximum value is calculated). This determined the “maximum shares” on both sides of the spectrum dividing line, which were then added together to obtain the sum of the low- and high-frequency parts of the spectrum. The calculation of one third of the spectrum of the acoustic signal reduced the number of “working” values of the discrete frequency amplitude, i.e., from 256 values in the linear spectrum to 22 values in the one third of the spectrum, thus simplifying the numerical processing of the artificial acoustic signal. Geoscan software is a data extraction and analysis software for portable artificial acoustic signal acquisition equipment. It was used to extract and screen the data collected from the experiment. The extraction and screening process of the spectrum information of the artificial acoustic signal is shown in Figure 9 below.

4. Experimental Results Analysis

4.1. Analysis of Mechanical Parameters of Coal Uniaxial Compression

The quality of the coal sample is 244.7 g. The coal sample height is 99.80 mm. The density of coal is 1.108 g/m³. The stress-strain curve of the single coal under uniaxial load is shown in Figure 10. When the single coal is loaded uniaxially until it is destroyed, the stress-strain curve of the sample undergoes the crack compression compaction stage, elastic deformation stage, plastic deformation stage, yield stage and post-peak failure stage. The stress-strain curves of each stage show different variation characteristics. There is a significant stress drop after the peak stress. According to the test results, the uniaxial compressive strength of monomer coal is 17.846 MPa, the elastic modulus is 2.288 GPa, and the deformation modulus is 1.903 GPa.

When the loading rate is 0.01 mm/s, the failure mode of the single coal body is the tensile shear compound failure, which is dominated by a splitting crack. Among them, the middle and top parts of the sample are seriously damaged. With the increase in axial pressure, many small cracks appear in the sample. When the axial pressure is close to its peak value, several large, vertical cracks appear from both ends to the middle part. There are large cracks running through the upper and lower parts, which lead to the fracture of the coal body. The serious damage part of the sample has a local crushing fracture.

4.2. Analysis of Test Results of Artificial Acoustic Signal Excited by Mechanical Vibration

4.2.1. Gas-Bearing Situation and Influence of Axial Stress

When the hammer was located at the 20° free hem of the dial, the instantaneous knocking force measured by the mechanical sensor in contact with the small hammer in the mechanical vibration monitoring unit was 0.2 N. The small hammer was located at 20° of the dial to strike the coal body freely (that is, the external mechanical vibration knocking force was 0.2 N), and the axial stress was set to 10 kN, 15 kN, 20 kN, 25 kN, 30 kN, 35 kN, 40 kN, 45 kN, 50 kN, 55 kN, and 60 kN. Under these eleven different conditions, the spectrum information of the collected artificial acoustic signal was analyzed, and the relationship between the relative stress coefficient K and the axial loading stress under the condition of gas pressure or not was studied. For the case of no gas pressure and a gas pressure of 0.3 MPa, the relative stress coefficient K value of the coal body obtained by the test is shown in

Table 3. Value of relative stress coefficient K without gas.

Axial Loading Stress/MPa	5	7.5	10	12.5	15	17.5	20	22.5	25	27.5	30
K	0.59	0.73	0.79	0.83	0.86	0.87	0.72	0.52	0.43	0.61	0.68

and

Table 4. The relative stress coefficient K value when the gas pressure is 0.3 MPa.

Axial Loading Stress/MPa	5	7.5	10	12.5	15	17.5	20	22.5	25	27.5	30
K	0.51	0.64	0.72	0.78	0.81	0.83	0.67	0.46	0.38	0.63	0.66

. The data results are drawn as shown in Figure 11.

Through the analysis of the data, it was found that when the gas-containing coal body and the non-gas-containing coal body are stimulated by the artificial acoustic signal test under the external mechanical vibration impact force of 0.2 N, the relative stress coefficient K value increases first with the increase in the axial loading stress, then decreases, and then increases again. In the axial loading stress range of 10–35 kN, the relative stress coefficient K value is on the rise. In the early stage of loading, the growth rate of the K value is obvious, and the growth rate tends to be gentle in the later stage of loading. In the range of 35–50 kN of axial loading stress, the relative stress coefficient K value shows a downward trend, and the decline rate gradually slows down. When the axial loading stress is 50–60 kN, the relative stress coefficient K shows a rising trend again. However, under the same axial pressure, the relative stress coefficient K of gas-bearing coal is smaller than that of gas-free coal.

The reason is that the strength of the coal sample decreases with the increase in gas pressure. The cracks inside the coal are full of free gas. The free gas expands the volume of coal and reduces the density of coal. After the coal adsorbs the gas, the cohesive force between the coal particles is significantly reduced, which reduces the force and energy required when the coal is destroyed, and reduces the peak strength and peak strain. Chemical adsorption occurs after the coal adsorbs the gas, and these chemical reactions may also reduce the strength of the coal. The uniaxial compressive strength of the coal sample used in the test is 17.846 MPa, which is about 35 kN of the axial loading stress. This is the basic mechanical parameter measured by gas-free coal. When the coal gas pressure is 0 MPa and 0.3 MPa, there is no obvious damage to the coal body before reaching the peak strength measured by the gas-free coal body test. As the axial pressure continues to increase, the stress on the coal body increases, and the relative stress coefficient K increases. The strength of the coal sample decreases with the increase in gas pressure, and the relative stress coefficient K value of the coal containing gas is smaller than that of the coal without gas. After the peak strength, as the axial loading stress increases, the coal body is destroyed. The number of internal cracks increases and the coal body is broken, and the relative stress coefficient K shows a downward trend. With the continuous increase in axial stress, the surrounding of coal body is limited by the cavity, which is equivalent to the external confining pressure support. The confining pressure limits the development of coal body deformation and cracks to some extent. At this time, the radial deformation of the coal body is obviously limited. The process of the continuous application of axial pressure is the re-compaction of the coal body after peak failure. The compressive strength of the compacted coal body increases, and the relative stress coefficient K increases again.

Before the destruction of gas-free coal and gas-bearing coal, with the increase in axial loading stress, the relationship between the relative stress coefficient K value obtained by the artificial acoustic signal test of mechanical vibration excitation was fitted and analyzed. The results are shown in Figure 12. The fitting results show that both of them can be expressed in the form of exponential function, and the correlation coefficient is as high as 99%.

The results of the data fitting analysis show that the relationship between the relative stress coefficient K and the axial loading stress σ can be expressed by an exponential function.

$$K=e^{-{\displaystyle \frac{C}{\sigma }}}$$

(3)

where “C” is a constant term, which is determined by the combination of the coal sample properties, mechanical vibration force, mechanical vibration wave propagation path, axial loading stress, and gas pressure [24].

4.2.2. The Influence of Mechanical Vibration Force

The gas pressure and axial loading stress were set to be constant. The impact force of the mechanical vibration was changed to study the artificial acoustic signal generated by the external mechanical vibration excitation of gas-bearing coal. The small hammer was free to swing at different scale values, and the instantaneous knocking force could be measured by the mechanical sensor. The gas pressure was set to be 0.3 MPa. The axial loading stress was 20 kN. The external mechanical vibration knocking force was 0.15 N, 0.20 N, 0.25 N, 0.30 N, 0.35 N, and 0.40 N during the test. In other words, the hammers were placed at 15°, 20°, 25°, 30°, 35°, and 40° on the dial, respectively. Then the spectrum information of the artificial acoustic signal collected by the experiment was analyzed, and the relationship between the relative stress coefficient K and the external mechanical vibration force was summarized. The relative stress coefficient K value of the coal body obtained from the test is shown in

Table 5. Parameter table of relative stress coefficients under different mechanical vibration forces.

Mechanical vibration force/N	0.15	0.20	0.25	0.30	0.35	0.40
Relative stress coefficient K value	0.74	0.72	0.68	0.65	0.60	0.54

. The data results are shown in Figure 13.

By analyzing the data, it was found that there is a quadratic function variation trend between the mechanical vibration force and the relative stress coefficient K. When the gas pressure is fixed at 0.3 MPa and the axial loading stress is 20 kN, the relative stress coefficient K decreases with the increase in external mechanical vibration. Due to the instantaneous impact, the external mechanical vibration knocking force has an influence on the change in the internal structure of the coal body. Different mechanical vibration knocking forces have different degrees of cracks in the coal body. When the mechanical vibration knocking force is less than 0.2 N, due to the small knocking force, there are fewer cracks in the coal body. The attenuation degree of the acoustic signal from the signal source to the receiving position is small, and the difference in the relative stress coefficient K value is also small. When the mechanical vibration impact force is greater than 0.2 N, due to the limited area of the external mechanical vibration acting on the surface of the coal body, the greater the impact force, the more obvious the new cracks and fissures derived from the coal body. The more obvious the impact of the small hammer on the internal structure of the coal body, the greater the attenuation degree of the acoustic signal propagation process, resulting in a gradual increase in the difference of the relative stress coefficient K value measured by the test. When the mechanical vibration impact force is greater than 0.30 N, the relative stress coefficient K value decreases more obviously. When the external mechanical vibration knocking strength reaches a certain value, the impact force has a great influence on the internal structure of the coal body. There are many large cracks in the coal body, and even regional damage occurs in the knocked part due to the small force area. The above reasons lead to the serious attenuation of the signal source propagation process, so the relative stress coefficient K value decreases more obviously and the value is smaller.

5. Discussion

The artificial acoustic signal prediction method can realize the continuous online monitoring and early warning of various dynamic phenomenon risks, geological failures, and stress changes near the working face, and is one of the most promising development directions of dynamic mine phenomenon prediction. Now, a multifunctional intelligent monitoring and warning system based on amplitude-frequency characteristics of artificial acoustic signals has been developed and applied in Pingdingshan coal mine. With the help of shearers and roadboring machines in operation, the system can automatically determine the stress–strain state and relative stress dynamics of the roof by processing and analyzing the elastic wave spectrum characteristics of the roof, and issue a risk prediction conclusion, which can provide a scientific basis for the safety decision of mine dynamic phenomenon prevention and control. However, the small-scale laboratory theory based on the spectral characteristics of artificial acoustic signals needs to be studied urgently. The construction of an artificial acoustic signal monitoring test system of coal loaded with gas under mechanical vibration and the quantitative relationship between artificial acoustic signals and coal stress state and gas pressure are of great significance for guiding field engineering practice and verifying field monitoring rules.

In this study, based on artificial acoustic signals, a test device for artificial acoustic signals stimulated by mechanical vibration was independently designed to study the dynamic response characteristics of coal containing gas under mechanical vibration and collect artificial acoustic signals generated by coal excited under mechanical vibration. The stress–strain state of coal in different periods can be reflected by the relative stress coefficient K value in the basic parameters of artificial acoustic signals, so the qualitative and quantitative relationship between the relative stress coefficient K value and axial loading stress, gas content of coal, and different mechanical vibration forces is established. The experimental research can provide a theoretical basis for the prediction and early warning of dynamic disasters by artificial acoustic signals.

At present, the study on the frequency spectrum characteristics of artificial acoustic signals in China is still not perfect, and the quantitative relationship between artificial acoustic frequency spectrum signals and mechanical parameters such as the stress–strain state of coal and gas pressure is still not clear. As far as the relative stress coefficient K value is concerned, a preliminary qualitative and quantitative relationship has been obtained, but whether there is a clearer quantitative relationship between the relative stress coefficient K value and the gas pressure, gas migration, and axial loading stress of gas-containing coal remains to be studied further. Whether other parameters based on the artificial acoustic signal spectrum can be studied in a laboratory on a small scale, and what qualitative and quantitative relationship they have with the mechanical parameters of coal, remains to be studied further.

6. Conclusions

Considering the complex disaster-forming environment of deep coal seams and the influence of mechanical vibration force in the process of coal seam mining, an experimental device and system for generating acoustic signals from gas-bearing coal by mechanical vibration force are developed. Based on the analysis of mechanical parameters of coal under uniaxial compression, the effects of axial loading stress, gas content, and mechanical vibration force on the relative stress coefficient K of coal are tested. The main findings are as follows:

(1) During the uniaxial compression mechanical test of the coal sample, the stress–strain curve experienced the fracture compression compaction stage, the elastic deformation stage, the plastic deformation stage, the yield stage, and the post-peak failure stage. The uniaxial compressive strength of coal samples was 17.846 MPa and the elastic modulus was 2.288 Gpa. When the loading rate was 0.01 mm/s, the failure of single coal was mainly splitting failure and shear cracking.

(2) When the gas-bearing coal and gas-free coal were subjected to the same external mechanical vibration impact force excitation artificial acoustic signal test, the relative stress coefficient K value increased first, then decreased, and then increased with the increase in axial loading stress. Under the same axial pressure, the relative stress coefficient K value of coal containing gas was smaller than that of coal without gas.

(3) The relationship between the relative stress coefficient K value and the axial loading stress σ of the gas-containing coal body and the gas-free coal body can be expressed in the form of exponential function $K=e^{-{\displaystyle \frac{C}{\sigma }}}$. The constant term C value obtained by the test in the case of coal containing gas was larger than that without gas.

(4) When the axial loading stress of the coal body was the same as the gas pressure of the coal body, with the increase in external mechanical vibration, the relative stress coefficient K showed a downward trend. When the impact force of mechanical vibration was too large, it had a great influence on the damage to the coal body, and the relative stress coefficient K was smaller.