Study on the Characteristics of Coal Ultrasonic Response during Loading and Its Influence Mechanism

Abstract

The prediction and prevention· of mine disasters are crucial to identifying the stress and strain state of coal using ultrasonic response characteristics. In this study, ultrasonic testing experiments of primary structure coal samples under uniaxial loading were conducted using a low-frequency rock physics measuring device. Based on the experimental results, the study focused on analyzing the relationship of the stress–strain state of coal samples with the ultrasonic velocity and quality factor of coal samples during stress loading, and exploring the influence mechanism of ultrasonic propagation in coal during stress loading. The results demonstrated that the stress-loading process of coal samples falls into the elastic deformation stage and the plastic deformation stage. In the elastic deformation stage, the ultrasonic velocity and the quality factor of the coal sample increased with the increase in the coal axial strain. In the plastic deformation stage, the ultrasonic velocity and quality factor of coal samples decreased as the axial strain of coal samples increased. Coal porosity was the fundamental factor affecting the coal wave velocity variation and the coal quality factor variation. In the elastic deformation stage, increased coal axial stress was accompanied by decreased coal porosity, contributing to the increase in coal wave velocity and coal quality factor. In the plastic deformation stage, the increase in the coal axial strain increased coal porosity and thus curtailed the wave velocity and quality factor of coal. Significant differences were observed in ultrasonic response characteristics of coal under various stress and strain states. The research results can lay a theoretical foundation for the safe and efficient development of coal resources and the prevention and control of mine disasters.

1. Introduction

Coal stress and its change are one of the main causes of accidents such as rib spalling, roof fall, rock burst, and coal and gas outbursts. Obtaining the stress–strain state and its variation law of coal can greatly help to reduce various mine disasters in the process of coal mining and realize safe and efficient coal mining.

The ultrasonic detection method mainly focuses on the exploration of geophysical properties. This method mainly emits ultrasonic waves into a coal medium and uses the parameters such as wave velocity, amplitude, and waveform collected after the ultrasonic wave passes through the medium to reversely infer the physical properties of the coal medium [1]. Much research has been done on the relationship between ultrasonic waves and physical properties of coal. Mahmood Karimaei et al. [2] established an exponential relationship between compressive strength and ultrasonic pulse velocity. The research results of Wang Bo et al. [3] show that the ultrasonic velocity is negatively and linearly related to the gas pressure. Kim Wonchang [4] obtained the correlation coefficient between ultrasonic pulse velocity and residual elastic modulus through an ultrasonic pulse experiment. Marta Krzesin’ska [5] applied the ultrasonic velocity measurement method to their study and found that the log (density/velocity) value of bituminous coals is closely related to elastic properties. The above research results provide theoretical support for obtaining the physical properties of coal and play an active role in ensuring coal mining. However, with the increase of coal mining depth, the influence of stress on the physical characteristics of coal is more and more significant, and the influence on coal mining is more and more serious.

Under stress loading, the stress and its changes have a significant effect on the physical properties exhibited by coal and rock mass, affecting the ultrasonic propagation law of the coal. Therefore, investigating the ultrasonic response characteristics of coal can help to identify the coal stress state [6,7], laying a foundation for the prevention and control of mine disasters.

Researchers have conducted many studies to explore the correlation between ultrasonic response characteristics and coal stress [8]. In 1988, Shea and Hanson [9] studied the structural failure law of loaded coal samples in different stages through the test of elastic wave velocity of coal samples. Through a uniaxial loading test, Tiedemann et al. [10], Zhai Xiaojie [11], and Zhao Mingjie et al. [12] revealed that the coal elastic modulus, the density of coal samples, and the compressive strength were obviously and linearly related to their longitudinal wave velocity (LWV) and transverse wave velocity (TWV). They believed that the closing of micro-cracks was the major factor that impacted the axial acoustic characteristics of rocks. Guo Deyong [13], Zhou Feng [14], and Tong Jiqiang et al. [15] suggested that increasing the confining pressure boosted coals’ LWV and TWV through ultrasonic detection experiments. Yan Lihong [16] and Wu Jiwen [17] analyzed the relevance of wave velocity to mechanical parameters under tensile conditions through experiments, revealing a good power function correlation between the wave velocity and the tensile strength. Li Qiong et al. [18] paid attention to the impact of pressure on LWV and TWV through experiments, demonstrating that coal samples’ LWV and TWV increased with the increase in pressure, and there was a quadratic correlation between them. During loading, rock or coal samples’ internal strain exhibited relaxation properties, and the ultrasonic velocity variation could indicate the rock stress relaxation [19]. Engelder and Plumb [20] investigated the changing law of ultrasonic wave velocity under uniaxial loading and performed wave tests for describing the wave velocity–stress relationship. Nur [21] researched the response characteristics presented by ultrasonic wave velocity to the loading stress level. Zheng Guiping et al. [22] confirmed a correspondence relationship of the wave velocity with rock damage variable under uniaxial compression. Liu Xiaofei [23] investigated the laws by which ultrasonic signals propagated through a coal material under different loading conditions, as well as analyzed the changes in ultrasonic parameters such as amplitude, dominant frequency, and velocity. Chen Zhuo [24] explored the response characteristics of coal stress–strain and ultrasonic waves under different confining pressure conditions through triaxial loading of the coal in the laboratory, discovering that the variations of LWV can more accurately reflect the change characteristics of coal pore fissure under different confining pressure conditions compared to TWV.

In conclusion, many studies have focused on the relevance of ultrasonic velocity to the stress of coal, while few paid attention to the relationship between the coals’ stress–strain state and their ultrasonic response characteristics during the stress-loading process. Additionally, most of the coal ultrasonic experimental studies only consider the characteristics of acoustic kinematics and only use the acoustic velocity to reflect the coal properties while ignoring the characteristics of its dynamics. Moreover, there are few studies on acoustic attenuation under different loading stress conditions. The stress of underground coal is in different stress and strain states, and the mine disaster is closely associated with the coal stress and strain state. It is particularly critical to obtain the stress and strain state of coal as well as its change trend for predicting and preventing mine disasters. Therefore, the ultrasonic response characteristic experiment under uniaxial loading was performed with the primary structure coal as the research object to obtain the ultrasonic response characteristic law of coal under different stress states. Besides, the ultrasonic velocity variation law and energy attenuation law of coal under uniaxial loading were analyzed considering the experimental results. The study demonstrates the association between ultrasonic kinematics (LWV and TWV), dynamic characteristics (attenuation), and stress and strain under the consideration of the coal anisotropy and lays a theoretical foundation for back calculating the stress–strain state and its changes in coal.

2. Materials and Methods

2.1. Ultrasonic Propagation Theory of Coal during Stress Loading

The physical characteristics exhibited by coal determined the propagation law of ultrasonic waves in coals. The stress and loading process of coal can change their physical properties, thereby affecting the above mentioned propagation. Therefore, the change in the ultrasonic propagation law is the result of the response to the change in the physical properties of coal.

Close et al. believed that coal is a dual structural medium constituted of matrix pores and fractures [25]. Pores in coal include micropores, small pores, mesopores, and macropores, according to their pore size [26]. Following its genesis, the fractures in coal include endogenous, exogenous, and inherited fractures. Generally, the wave velocity and its attenuation characteristics of coal exhibit a close association with the development degree of coal pore fissures. That is to say, the more developed the pores and fissures of coal, the lower the coal wave velocity, and the greater the attenuation coefficient.

The stress–strain relationship of coal during stress loading involves four stages: pore compaction(OA stage), linear deformation(AB stage), micro-fracture propagation(BC stage), and coal failure(CD stage) (Figure 1) [27]. Among them, the coal in the pore compaction and linear deformation stage belongs to elastic deformation, and the coal in the micro-fracture propagation and coal failure stage belongs to plastic deformation. The law and mechanism of the change in pore and fissure in coal caused by elastic deformation and plastic deformation are different, and so is the mechanism of wave velocity change and attenuation characteristics of coal. Therefore, the study analyzed the coal wave velocity change and its attenuation characteristics during stress loading from the perspective of elastic deformation and plastic deformation.

2.1.1. Theory of Ultrasonic Velocity Change

Coal is a dual structure system composed of matrix pores and fractures which are usually regarded as pores to facilitate the study. Experiments revealed that the relationship between LWV and porosity of coal conforms to the following laws [28,29]:

$$\phi =b{e}^{a{V}_p}$$

(1)

where φ denotes porosity; a and b are constants; V_p refers to the LWV, i.e., the wave velocity in Equation (1). Since the longitudinal wave and transverse wave had similar propagation laws during stress loading, Equation (1) was also applicable to the transverse wave.

In the elastic deformation stage, the porosity equation expressed in volume strain can be obtained from the definition of porosity [30]:

$$\phi =1-\frac{(1-{\phi }_0)}{1+{\epsilon }_V}$$

(2)

where φ₀ represents the initial porosity, and ε_V indicates the volume strain (negative for volume compression and positive for volume expansion).

Additionally, the volumetric strain–stress relationship of coal is based on the volumetric compressibility coefficient and defined according to the definition of volumetric compressibility coefficient [31]:

$$1+{\epsilon }_V=\exp (-C_f\Delta {\sigma }^{\prime })$$

(3)

where Δσ’ indicates the change of effective stress, C_f denotes the volumetric compressibility coefficient of coal, C_f = 3(1 − 2v)/E, v represents the Poisson’s ratio, and E represents the elastic modulus.

By substituting Equation (3) into Equation (2), the relation between porosity and stress can be obtained:

$$\phi =1-\frac{1-{\phi }_0}{\exp (-C_f\Delta {\sigma }^{\prime })}$$

(4)

It can be obtained by substituting Equation (4) into Equation (1) to calculate V_p that

$$V_P=\frac{1}{a}\ln \left\{\frac{1}{b}[1-\frac{1-{\phi }_0}{\exp (-C_f\Delta {\sigma }^{\prime })}]\right\}$$

(5)

Then,

$$V_P=\frac{1}{a}\ln \left\{\frac{1}{b}[1-\frac{1-{\phi }_0}{\exp [-\frac{3(1-2v)}{E}\Delta {\sigma }^{\prime }]}]\right\}$$

(6)

Considering that the experiment in this paper was a uniaxial loading test, the change in effective stress during stress loading is $\Delta {\sigma }^{\prime }=\frac{1}{3}\Delta {\sigma }_x$ and $\Delta {\sigma }_x={\sigma }_1-{\sigma }_0$; then:

$$V_P=\frac{1}{a}\ln \left\{\frac{1-(1-{\phi }_0)\exp [\frac{1-2v}{E}({\sigma }_1-{\sigma }_0)]}{b}\right\}$$

(7)

where σ₀ and σ₁ respectively denote the initial stress and the current stress.

In the plastic deformation stage, the change in coal porosity is related to coal damage. The equation below describes the relationship between coal porosity and the coal damage variable [32]:

$$\phi ={\phi }_1{e}^{\beta D}$$

(8)

where φ₁ represents the porosity at the beginning of coal damage, φ indicates the porosity, β denotes the damage parameter of coal which can be obtained by parameter fitting, and D signifies the damage variable.

The plastic variable is defined as the damage variable [33]:

$$D=\frac{{\epsilon }^p-{\epsilon }_0^p}{{\epsilon }_f^p-{\epsilon }_0^p}$$

(9)

where ${\epsilon }_0^p$ denotes the threshold value of damage strain, that is, the plastic strain when the coal starts to damage; ${\epsilon }^p$ represents the current plastic strain; ${\epsilon }_f^p$ stands for the plastic strain at the residual strength of coal. ${\epsilon }_0^p$, ${\epsilon }^p$, and ${\epsilon }_f^p$ are positive. Considering that the experiment in this paper was a uniaxial stress loading test, various plastic strains were replaced by various axial strains. Specifically, ${\epsilon }_0^p$, ${\epsilon }^p$, and ${\epsilon }_f^p$ are the axial strains at the beginning of plastic deformation, during plastic deformation, and after the failure of coal, respectively.

By substituting Equation (8) into Equation (1), LWV V_p at the plastic deformation stage is calculated as:

$$V_P=\frac{1}{a}\ln [\frac{{\phi }_1{e}^{\beta D}}{b}]$$

(10)

2.1.2. Ultrasonic Wave Propagation Energy Attenuation Theory

The main forms of energy attenuation included diffusion attenuation, absorption attenuation, and scattering attenuation when the ultrasonic wave propagated in the medium. Among them, diffusion attenuation is correlated with the distance of ultrasonic propagation [34], and absorption attenuation mainly comprises heat conduction attenuation and viscous absorption attenuation [35]. In the experiment of this study, the coal samples have the same length and same structure type. Meanwhile, the influence of diffusion attenuation and absorption attenuation on ultrasonic is small and thus can be ignored. Hence, the energy attenuation of ultrasonic wave propagation in coal is primarily reflected in scattering attenuation. According to the research results of Urick R J, the scattering attenuation coefficient of ultrasonic wave propagation in coal is [36]:

$${\alpha }_s=\phi \frac{1}{6}{(\frac{2\pi f}{v})}^4{\overline{r}}^3$$

(11)

where α_s denotes the scattering attenuation coefficient of ultrasonic, φ is the coal porosity, $\overline{r}$ indicates the effective radius of pores and fractures in coal, f represents ultrasonic frequency, and v refers to ultrasonic velocity.

According to Equation (11), the scattering attenuation coefficient α_s is majorly associated with the porosity of coal, the effective radius of pores and fractures, and the ultrasonic velocity. During the experiment, the ultrasonic velocity of coal has been measured, the porosity of coal has been obtained in the elastic deformation stage and plastic deformation stage, and the effective radius of pores and fractures in coal is difficult to be directly obtained. The existing research confirms that the porosity and effective radius of coal have the following relationship [37]:

$$\phi =\frac{12}{\pi }\xi \overline{r}N$$

(12)

where ζ denotes the linear density exhibited by cracks in the coal sample, and N represents a coefficient related to the shape of the crack.

Substituting Equation (12) into Equation (11) yields:

$${\alpha }_s={\phi }^4\frac{1}{6}{(\frac{2\pi f}{v})}^4{(\frac{\pi }{12\xi N})}^3$$

(13)

Considering that the energy attenuation regarding ultrasonic wave propagation in coal is mainly scattering attenuation, the attenuation coefficient can be obtained as:

$$\alpha ={\alpha }_s={\phi }^4\frac{1}{6}{(\frac{2\pi f}{v})}^4{(\frac{\pi }{12\xi N})}^3$$

(14)

Thus, the quality factor of coal during ultrasonic propagation is:

$$Q=1/\alpha =\frac{1}{{\phi }^4\frac{1}{6}{(\frac{2\pi f}{v})}^4{(\frac{\pi }{12\xi N})}^3}$$

(15)

The parameters ξ and N in Equation (15) are not easy to measure and cannot be effectively verified directly through the laboratory data. Hence, the comparison method is used for verification. During comparison and verification, the ratio of a quality factor at different stages to that at the initial stage is expressed as M with the ultrasonic attenuation coefficient at the beginning of this stage as the standard. The calculation method of M is:

$$M=\frac{Q_b}{Q_a}=\frac{v_b^4{\phi }_a^4}{{\phi }_b^4{v}_a^4}$$

(16)

where M is the ratio of quality factor, Q_b indicates the quality factor of the current state, Q_a denotes the quality factor in the initial state, and v_b and v_a represent the wave velocity in the current state and in the initial state, respectively. φ_b and φ_a denote the porosity in the current state and in the initial state, respectively.

In the elastic deformation stage, substituting Equation (4) into Equation (16) yields:

$$M_1=\frac{v_{}^4{\phi }_0^4}{{\left\{1-(1-{\phi }_0)\exp [\frac{1-2v}{E}({\sigma }_1-{\sigma }_0)]\right\}}^4{v}_0^4}$$

(17)

where M₁ indicates the ratio of quality factor in the elastic deformation stage.

In the plastic deformation stage, substituting Equation (8) into Equation (16) yields:

$$M_2=\frac{v_{}^4{\phi }_1^4}{{\phi }_{}^4{v}_1^4}=\frac{v_{}^4{\phi }_1^4}{({\phi }_1{e}^{\beta D}{)}^4{v}_1^4}$$

(18)

where M₂ denotes the ratio of quality factor in the plastic deformation stage.

2.2. Experiment

2.2.1. Experimental Equipment

The ultrasonic experiment adopted a rock physics measurement device under low frequency during the stress loading process. Its working principle is illustrated in Figure 2. The device is equipped with a core sample testing system (System 1) and a data acquisition system (System 2).

System 1, as an essential part of the device, has a semiconductor strain gauge, ultrasonic transducer, standard aluminum sample, servo vibrator, and epoxy resin sheet. System 1 can transmit and receive ultrasonic waves through ultrasonic transducers to realize the ultrasonic measurement of coal media. The frequency range of the ultrasonic measurement is 5 Hz–1 MHz. The axial pressure measurement is realized by applying stress to the test coal sample through a servo vibrator.

System 2, taking charge of recording the change in coal strain and ultrasonic velocity during the experiment, is adopted mainly to achieve high-precision data acquisition, which consists of a control software, signal generator, 12-channel high-precision differential amplifier, servo vibration amplifier, pulse generator receiver, digital oscilloscope, digital acquisition board, embedded computer, and analog-to-digital input board.

Additionally, auxiliary tools such as balances and vernier calipers are also needed during the experiment.

2.2.2. Measurement Principle

The measurement of ultrasonic wave velocity in low-frequency rock physics measurement systems primarily adopted the pulse transmission method [38,39]. Specifically, the measurement was conducted using the polarization filtering method to pick up the initial transverse wave, and then its wave velocity was calculated. Due to the constraints of experimental conditions, the propagation of the ultrasonic transverse wave in the anisotropic thin layer is accompanied by the propagation of fast and slow transverse waves in the medium in the way of orthogonal polarization, so as to weaken the time difference between them reaching the receiver. The detector can only identify the time point of receipt of the transverse wave fast wave, and it is difficult to identify the time point of arrival of the transverse wave slow wave. Therefore, this experiment only focuses on the shear wave velocity given the influence of realistic conditions.

(1)

Measurement of wave velocity.

The pulse transmission ultrasonic system was adopted in the experiment. The computer can directly read out the sound wave velocity. The principle of test is expressed as:

$$\{\begin{array}{c}{V}_p=L/(t_p-t_0)\\ V_s=L/(t_s-t_0)\end{array}$$

(19)

where V_p and V_s denote the LWV and TWV, respectively. L represents the distance between the transmitting and receiving transducers, t_p stands for the longitudinal wave propagation time, t_s is the transverse wave propagation time, and t₀ signifies the zero delay of the instrument system.

(2)

Measurement of quality factor.

Due to the existence of pores and fissures in coal, ultrasonic waves will inevitably undergo attenuation in coal. The distribution law and structural characteristics of coals’ internal microstructure and the ground stress state in the coal can be effectively obtained by studying the attenuation law of ultrasonic waves after passing through the coal sample. Their attenuation characteristics are generally measured by quality factors. A larger quality factor indicates smaller pore and crack size in coal, and slower attenuation. The quality factor is calculated by 2π times the ratio of the energy consumed by ultrasonic propagation attenuation to its own energy within a wavelength [40]:

$$Q=\frac{2\pi E}{\Delta E}$$

(20)

where Q denotes the quality factor, E represents the energy it has, and ΔE indicates the decayed energy.

The main methods for determining the quality factor are the time domain method and the frequency domain method. The study employed the amplitude decay method in the time domain to determine the quality factor. The key to this method was the determination of the main frequency and the initial arrival time. The specific steps were detailed as follows. Firstly, the ultrasonic wavelet waveform of the failed coal sample and the ultrasonic waveform passing through the coal sample obtained by the experiment were derived. Then, the more complete transmission wave waveform was intercepted by the first arrival pickup and was subjected to broadband filtering to remove other clutter. Afterward, the frequency point corresponding to the maximum amplitude in the first arrival pickup intercepted waveform was picked up as the main frequency. Next, the root mean square amplitude of the ultrasonic wavelet of failed coal samples and the ultrasonic wavelet passing through coal samples were calculated, respectively. Finally, the obtained main frequency, first arrival time, amplitude, and other parameters were substituted into the formula to obtain the corresponding quality factor value.

The process of determining quality factors by amplitude attenuation method is:

$$A(x)=A_0\cdot e^{-\alpha x}$$

(21)

where A₀ denotes the wavelet amplitude without passing through the coal sample, A(x) indicates the ultrasonic amplitude passing through the coal sample, α represents the attenuation coefficient, and x refers to the length of the medium.

Among them, the attenuation coefficient α can be expressed as:

$$\alpha =\frac{\pi f}{QV}$$

(22)

where f and V denote the main frequency and the wave velocity, respectively.

Substituting Equation (22) into Equation (21) yields:

$$A(x)=A_0{e}^{\frac{-\pi fx}{QV}}$$

(23)

From the first arrival time of ultrasonic wave t = x/V, it can be obtained that

$$A(x)=A_0{e}^{\frac{-\pi ft}{Q}}$$

(24)

After taking logarithms on both sides, Q can be obtained as:

$$Q=-\pi ft/\ln [\frac{A(x)}{A_0}]$$

(25)

2.2.3. Coal Sample Collection and Preparation

With the underground raw coal as the research object in the experiment, coal samples were collected per the provisions of Methods for Taking Coal Rock Samples [41] and Classification of Coal Structure [42]. The collected raw coal was primary structural coal. The strike orientations of the fractures in the coal seam are different, suggesting the influence of the anisotropy of the coal seam on the transmission of ultrasonic waves. Hence, attention should be paid to indicating coal samples’ strike, tendency, and vertical bedding direction in the coal seam upon the collection of the coal samples on site.

The sampling site was located at 31004 working face of Shanxi Xinyuan Coal Co., Ltd. of Yangmei Group (Jinzhong, China). The working face was located in the Hanzhuang sub-district and mainly mined 3# coal seam. Its coal quality was high-quality lean coal with medium ash and low sulfur. The coal seam was majorly bright coal with developed endogenous fractures. The coal seam contained 1–2 layers of argillaceous gangue, and the thickness was in the range of 0.01–0.04 m (0.02 m on average). The 3# coal seam mined in this working face had steady occurrence and simple structure, and the coal firmness coefficient was 0.51–0.82, meeting the requirements of coal sample collection in this experiment.

The coal with a large volume and relatively complete structure preservation should be picked up as the master sample when coal samples are collected. After picking up the master sample, it should be put into the pre-prepared woven bag. Concurrently, the structure type and direction of the collected coal samples should be indicated on the bag surface. After the master sample was collected, it was transferred to the laboratory and processed into a 100 mm-high cylindrical standard coal sample (50 mm in diameter) by drilling equipment. Additionally, the coal core obtained by drilling was polished to make its flatness less than 0.02% to enable the transducer of the ultrasonic tester to form better contact with the coal core.

The total processing completed three experimental coal samples, including one in the strike, inclination, and vertical bedding direction. The coal sample number is specified as follows for contributing to the statistics and analysis. The direction of the parallel plane cleat, vertical plane cleat, and vertical bedding is defined as the X, Y, and Z direction, respectively, as shown in Figure 3. According to the classification standard of coal structure type, the primary structure coal is class I coal. Hence, experimenters name the three coal samples IX1, IY1, and IZ1 in turn.

The coal sample obtained after processing is exhibited in Figure 4. The specific parameters of the coal sample are presented in

Table 1. Statistics of parameters of processed coal samples.

Coal Sample Number	Coal Structure Type	Length (mm)	Diameter (mm)	Fracture Development	Ro,max	Vdaf (%)	Bulk Density (t/m3)	Porosity (%)	Modulus of Elasticity (MPa)	Poisson’s Ratio
IX1	Primary structural coal	100.0	50.1	The bedding is clear without obvious cracks.	1.86	15.7	1.43	3.5	1500	0.3
IY1		99.9	49.9
IZ1		100.1	50.1

.

2.2.4. Experimental Scheme and Steps

In this experiment, there were three coal samples; stress loading was in the form of uniaxial compression; pressure was maintained 5 min after every certain value until the end of the coal failure experiment. Each coal sample experiment’s specific steps are described as follows.

• Clean the sticking position of the coal sample’s strain gauge, firmly stick the strain gauge on the coal sample surface with glue, and press it hard to ensure full contact. After the glue is dry and firmly connected, the resistance value is checked with a strain gauge to ensure no open circuit or short circuit.
• In order to improve the measurement accuracy, the coupling agent is applied to the coal sample and the ultrasonic transducer probe, and put the coal sample into the loading test system. Thus, the coal sample is consistent with the central axis of the transducer probe to ensure stable placement.
• Connect the outgoing line of the strain gauge with the strain measurement instrument, and obtain the strain of the coal through the output of the strain measurement instrument.
• Connect the ultrasonic testing instrument following the experimental setting, turn on the computer control terminal and digital oscilloscope power, and debug to assure the normal use of the instrument.
• Adjust the loading system for controlling axial pressure change, and load the coal sample by stages until it breaks. Stabilize the voltage for 5 min after each new stress value is loaded, read out the corresponding ultrasonic wave velocity, record the first wave amplitude, and export the waveform data on the oscilloscope.
• Record the loading stress value, axial strain, and ultrasonic response characteristic parameters, and repeat step 5 until the coal sample is broken and the experiment is completed.

3. Results

3.1. Experimental Results

Table 2. Test results of ultrasonic velocity, axial strain, and quality factor of coal samples under uniaxial stress loading.

Loading Step	Axial Stress (MPa)		P-Wave Velocity (m·s−1)			S-Wave Velocity (m·s−1)			Axial Strain (10−4)			Quality Factor Qp			Quality Factor Qs
	X, Y	Z	X	Y	Z	X	Y	Z	X	Y	Z	X	Y	Z	X	Y	Z
1	0	0	1925	1886	1623	1056	959	807	0	0	0	0.2954	0.2846	0.2541	0.2541	0.2489	0.2182
2	0.4	0.5	2114	2013	1785	1129	1131	1056	8.5621	8.1562	10.3216	0.4823	0.4124	0.4015	0.4765	0.4795	0.3695
3	0.9	1	2236	2205	1973	1150	1262	1174	10.5689	9.1564	13.1684	0.6569	0.6386	0.5912	0.6071	0.6025	0.6128
4	1.5	1.5	2280	2342	2003	1296	1364	1203	13.6415	12.6156	14.1235	0.7614	0.7783	0.6962	0.7215	0.7054	0.7218
5	2.2	2.1	2312	2341	2016	1304	1352	1222	15.9501	14.8204	16.2605	0.7962	0.7893	0.7316	0.7428	0.7199	0.7356
6	2.9	2.8	2356	2364	2053	1356	1379	1218	16.7851	16.6925	17.3694	0.8124	0.8201	0.7356	0.7594	0.7259	0.7398
7	3.6	3.7	2392	2368	2123	1375	1378	1230	18.9654	17.1651	18.2068	0.8238	0.8158	0.7465	0.7816	0.7467	0.7695
8	4.2	4.1	2385	2395	2073	1362	1396	1201	19.6258	16.2609	19.2654	0.8417	0.8196	0.7256	0.8119	0.7692	0.7512
9	4.9	4.2	2399	2384	2048	1396	1403	1182	20.6041	17.1656	24.3654	0.8514	0.8214	0.7026	0.8364	0.7697	0.7435
10	5.8	4.3	2416	2399	2046	1381	1399	1174	22.2354	18.1561	27.3691	0.8632	0.8309	0.5865	0.8516	0.7927	0.5216
11	6.6	1.7	2434	2412	1508	1408	1416	765	23.6351	20.1656	35.3614	0.8863	0.8218	0.1369	0.8632	0.7983	0.1689
12	6.8	—	2415	2356	—	1327	1375	—	27.6248	20.2518	—	0.7312	0.7269	—	0.7415	0.6662	—
13	6.9	—	2387	2310	—	1305	1343	—	28.0695	23.6325	—	0.6124	0.6214	—	0.6589	0.5918	—
14	7.2	—	2347	2296	—	1321	1300	—	28.9562	25.1659	—	0.5164	0.514	—	0.5321	0.5238	—
15	1.5	—	1743	1695	—	893	864	—	35.8601	34.8661	—	0.1984	0.1541	—	0.1631	0.1578	—

lists the experimental results of coal samples in terms of the ultrasonic velocity, quality factor, and axial strain during uniaxial stress loading.

3.2. Relationship between the Ultrasonic Velocity and Axial Strain of Coal Sample during Stress Loading

Table 2 explains the ultrasonic velocity–axial strain relationship of the coal sample during stress loading (Figure 5).

With Figure 5, the analysis on the above relationship assists in drawing the following conclusions:

• As the loading step increases, the axial strain of the coal sample will be on a rise, while the LWV and TWV will present an increase-to-decrease trend.
• The wave velocity exhibits strong anisotropy. The coal sample possesses higher LWV than TWV, and the LWV in the Z direction is lower than that in the X and Y directions. Through numerical analysis, the Pearson correlation coefficient of the TWV in the X and Y directions is 0.96501, indicating that the TWV in the X and Y directions is similar. During the whole process of stress loading, the TWV in the X and Y directions of the coal sample showed a change trend of “increase-slow increase-slow decrease-sharply decrease”. The TWV in the X direction increases from 1056 m/s to 1296 m/s in the stress range of 0–1.5 MPa. Then, with the increase of axial stress to 6.6 MPa, the TWV in X direction increases slowly from 1296 m/s to 1408 m/s. Then, it slowly decreases to 1321 m/s, and the axial stress is 7.2 MPa. After the coal sample is damaged, the stress value drops sharply to 1.5 Mpa, and the TWV in the X direction decreases sharply to 893 m/s. The TWV in the Y direction increases from 959 m/s to 1364 m/s in the stress range of 0–1.5 Mpa. Then, with the increase of axial stress to 6.6 MPa, the TWV in Y direction increases slowly from 1364 m/s to 1416 m/s. Subsequently, it slowly begins to decrease to 1300 m/s, and the axial stress is 7.2 MPa. After the failure of the coal sample, the stress value drops sharply to 1.5 MPa, and the TWV in the Y direction decreases sharply to 864 m/s. The Pearson correlation coefficient of the LWV in the X and Y directions is 0.98241, indicating that the LWV in the X and Y directions is similar. In the whole process of stress loading, the LWV of coal samples in X and Y directions showed the change trend of “increase-slow increase-slow decrease-sharply decrease”. The LWV in the X direction increases from 1925 m/s to 2280 m/s in the stress range of 0–1.5 MPa; then, as the axial stress increases to 6.6 MPa, the LWV in the X direction slowly increases from 2280 m/s to 2434 m/s, and then slowly decreases to 2347 m/s, and the axial stress is 7.2 Mpa. After the coal sample is destroyed, the stress value drops sharply to 1.5 Mpa, and the LWV in the X direction decreases sharply to 1743 m/s. The LWV in the Y direction increases from 1886 m/s to 2342 m/s in the stress range of 0–1.5 Mpa. Then, with the increase of axial stress to 6.6 Mpa, the LWV in the Y direction increases slowly from 2342 m/s to 2412 m/s, and then decreases slowly to 2296 m/s, and the axial stress is 7.2 Mpa. After the coal sample is destroyed, the stress value drops sharply to 1.5 Mpa, and the LWV in the Y direction decreases sharply to 1695 m/s.
• According to the stress loading process of coal samples, the changes in axial strain, LWV, and TWV fall into the initial stage, the middle stage, the late stage, and end stage of stress loading.
• In the early stage of stress loading, the LWV, TWV, and axial strain of coal samples increase. In the middle stage of stress loading, the LWV, TWV, and axial strain of coal samples increase slowly. In the late stage of stress loading, the axial strain of coal samples showed a significant increase trend, and the LWV and TWV of coal samples began to decrease slowly. At the end of the stress loading, the coal sample is broken, the axial strain of the coal sample increases sharply, and the LWV and TWV of the coal sample decreases sharply. The reasons for these trends are as follows: in the early stage of stress loading, the coal structure is compressed, the size of pores and cracks in the coal decreases, the axial strain increases, and the acoustic wave velocity of the coal increases. In the middle of stress loading, with the increase of axial pressure, the compression amplitude of coal structure decreases, so the LWV, TWV, and axial strain of coal sample increase slowly. In the late stage of stress loading, the coal enters the plastic stage, the internal cracks of the coal sample begin to increase, the size of the pores and cracks increases, the axial strain of the coal sample increases, and the LWV and TWV of the coal sample begin to decrease slowly. At the end of the stress loading, because the load of the coal sample exceeds its maximum bearing capacity, a large number of cracks appear in the coal, the axial strain increases sharply, and the wave velocity decreases abruptly.
• In the initial and middle stages, the ultrasonic velocity and axial strain of coal samples present an uptrend and have a good positive correlation. In the late stage and at the end of stress loading, the axial strain continues to increase, while the wave velocity significantly decreases. The ultrasonic velocity of coal samples shows a negative correlation with the axial strain.

3.3. Relationship between the Axial Strain and Quality Factor of Coal Sample during Stress Loading

Similarly, the relationship between the coal sample quality factor and axial strain during stress loading can be obtained according to Table 2 (Figure 6).

Analysis on the above relationship assists in drawing the following conclusions, as shown in Figure 6:

• The quality factors of coal samples also demonstrate strong anisotropy. The quality factors of coal samples in the Z direction are less than those in the X and Y directions. The quality factors of coal samples in the two directions are similar, and the variation law is the same. In other words, coal samples present a higher wave velocity attenuation amplitude in the Z direction relative to the X and Y directions.
• The variation trend of coal sample quality factors during stress loading also falls into the initial stage, the middle stage, the late stage, and the end stage of stress loading. In the initial stage, the coal sample quality factor significantly increases. In the middle stage, the quality factor slowly increases. In the late stage, the quality factor significantly decreases. At the end of stress loading, the quality factor sharply decreases.
• In the initial and middle stage of stress loading, the coal sample quality factor increases as the axial strain increases, indicating that the attenuation amplitude of energy during ultrasonic propagation decreases as the axial strain increases. In the late stage and at the end of stress loading, the axial strain of coal samples keeps increasing, while the quality factor of coal samples sharply decreases, implying that the attenuation range of energy during ultrasonic propagation increases as the axial strain increases.

3.4. Relationship between Coal Sample Wave Velocity and Quality Factor during Stress Loading

Based on Table 2, the coal sample quality factor-wave velocity relationship of coal sample during stress loading can be obtained (Figure 7).

As revealed in Figure 7, the quality factor-wave velocity relationship of the coal sample during the stress loading process can be concluded as follows. The two parameters have significant stage characteristics, and their variation laws are the same.

4. Discussion

4.1. Analysis of Influencing Factors of Coal Ultrasonic Velocity Change during Stress Loading

Equations (7) and (10) are used to calculate ultrasonic wave velocity in the elastic deformation stage and plastic deformation stage, respectively. Whether Equations (7) and (10) are reliable is further verified with the longitudinal wave data in the X direction as an example.

According to the longitudinal wave data in the X direction in Table 2, Equation (26) can be obtained by fitting according to Equation (1):

$$\phi =0.044741915{{\displaystyle e}}^{-0.000126133V_P}$$

(26)

where a = −0.000126133, and b = 0.044741915; V_p refers to the LWV, m/s.

The coefficient of Equation (26) is fitted based on the measurement results of this experiment. However, due to the limitation of test conditions, the number of coal samples in this experiment is small, which may lead to a certain error of the coefficient. Therefore, we will focus on improving this problem in subsequent research. The variation data of LWV with stress can be obtained by substituting coal mechanical parameters and fitting parameters a and b into Equation (7). Figure 8 displays the comparison diagram between the calculated value of LWV in the X direction and the experimental value in the elastic deformation stage in combination with the experimental data in Table 2. In Figure 9, the LWV in the X direction demonstrates a linear increase with stress during the elastic deformation phase of the stress loading process, revealing the increase in stress in the elastic deformation stage, the decrease in coal porosity, and the increase in wave velocity. This conclusion is consistent with Yale’s research results. Yale [43] also proposed in the research results that the porosity of rock decreases with the increase of stress, which leads to the increase of wave velocity transmitted in rock mass. Therefore, the internal factor affecting the change of coal wave velocity in the elastic deformation stage is porosity, which theoretically explains the root cause of the change of coal wave velocity.

After calculation, the error rate between the experimental value and the calculated value of the LWV in the X direction of the elastic deformation stage is 1.14% (loading step 1), and the maximum is 10.75% (loading step 4), which shows that it is feasible to calculate the LWV in the elastic deformation stage by this formula.

With the longitudinal wave data in the X direction in Table 2, β = 0.05 can be obtained by fitting according to Equation (8). Then, the coal mechanical parameters are substituted, and parameters a and b are fitted into Equation (10), so as to acquire the variation data of LWV with strain. With respect to the experimental data in Table 2, the comparison diagram between the calculated value of LWV in the X direction in the plastic deformation stage and the experimental value can be depicted (Figure 9). As observed in Figure 9, the LWV in the X direction decreases exponentially with the strain in the plastic deformation stage during stress loading. Thus, in the plastic deformation stage, the coal axial strain, the damage variable, and the porosity increase, leading to weakened wave velocity. After calculation, the error rate between the experimental value and the calculated value of the LWV in the X direction of the plastic deformation stage is 7.36% (loading step 13), and the maximum is 11.9% (loading step 15), which shows that it is feasible to calculate the LWV in the plastic deformation stage by this formula.

Equation (7) illuminates that the main factor affecting the change of coal wave velocity in the elastic deformation stage is stress, and the wave velocity increases linearly with the increasing stress. This research result is in line with the research results of Meng Zhaoping [44], Zhou Feng [14], and Li Qiong [45]. In addition, Dong Shouhua et al. [46] focused on the measurement of the ultrasonic wave velocity of anthracite samples under triaxial stress. The research found that the confining pressure increase was accompanied by the increase in ultrasonic wave velocity, and the wave velocity increased slowly and became stable when it exceeded the critical value of confining pressure. Sun Xiaoyuan [47] found that the P-wave velocity of briquettes was positively correlated with its pressure; Zhang Long [48] and others found a logarithmic relationship between ultrasonic LWV and stress. Yu Hongyan [49] and others found that effective stress increase resulted in obviously increased P-wave and S-wave velocities of fractured shale. Cao Anye et al. [50] found that the P-wave velocity was exponentially positively correlated with the applied stress through laboratory experiments. The research results of these scholars show that the change of wave velocity is related to stress, but the influence of stress on wave velocity is different, which shows that there are different variation rules of wave velocity in different stress change stages. Therefore, according to the stress–strain characteristics of coal, the stress loading process is divided into the elastic stage and plastic stage. In these two stages, the variation law of wave velocity is studied respectively, which can reflect the response characteristics of the ultrasonic wave more truly.

Equation (10) suggests that the primary factor that impacts the change of coal wave velocity in the plastic deformation stage is strain. As the strain is on a rise, the wave velocity exhibits an exponential decrease, consistent with the research results of Zhao Mingjie [51]. Zhao Mingjie established an exponential relationship between rock strength and ultrasonic velocity based on damage mechanics. In addition, the results of Yang Sen [52] and Li Jian [53] show that the LWV decreases with the development of coal and rock damage. Zhang Zhibo et al. [54] also found through experimental research that the wave velocity decreases with the increase of stress, and the important factor affecting the change of UTV is the change of microcrack structure. This shows that the wave velocity of coal decreases in the propagation stage of micro-cracks, and the reason for the decrease of wave velocity can be caused by damage or stress increase. In this paper, the reason for the decrease of wave velocity is summarized as strain, which is due to the fact that the increase of coal damage and the propagation of micro-cracks are two expressions of the same result in the plastic deformation stage. Using strain can describe the change of wave velocity more realistically, and it is also easy to quantify the change of wave velocity.

According to Equations (7) and (10), the main influencing factors of wave velocity change of coal in the elastic deformation stage and plastic deformation stage are different. However, further analysis by combining Equations (7) and (10) unveils that porosity is still the fundamental factor influencing the wave velocity change of coal in the process of stress loading. Moreover, a good mathematical relationship exists between the change in coal porosity and the coal stress in the elastic deformation stage, confirming the stress as the primary factor that impacts wave velocity change in the elastic deformation stage. However, a relationship can be hardly established between the coal porosity change and stress in the plastic deformation stage, while a strain can establish a good relationship with the coal porosity change. Hence, the primary factor influencing coal wave velocity change in the plastic deformation stage is strain. This is the influence mechanism of the ultrasonic wave velocity change during the stress loading process. Equations (7) and (10) reveal the variations of ultrasonic velocity during coal stress loading more deeply and comprehensively, with better accuracy and applicability.

4.2. Analysis of Influencing Factors of Ultrasonic Propagation Energy Attenuation

Equations (17) and (18) describe the change in coal quality factor in the elastic deformation stage and plastic deformation stage, respectively. The calculated value of the quality factor is compared with the experimental value in Table 2 with the X-direction longitudinal wave as an example to verify the reliability of Equations (17) and (18). Meanwhile, the changing trend of the ratio of the quality factor in the process of stress loading is obtained (Figure 10 and Figure 11).

As observed in Figure 10, the ratio of the coal quality factor increases in the form of a power function with the increase in stress in the elastic deformation stage. At the end of the elastic stage, the coal quality factor ratio is about three times the initial time, and the calculated value meets the experimental value, reflecting the changing trend of the quality factor. Equation (17) reveals that the quality factor ratio shows relevance to the porosity and coal wave velocity. In the elastic deformation stage of stress loading, the wave velocity of coal increases, together with the decrease in porosity.

In Figure 11, the coal quality factor ratio decreases as the parabola forms with increasing loading steps during the plastic deformation phase. The coal quality factor ratio at the time of rupture is about 20% of that at the beginning of the plastic deformation phase. The calculated value conforms to the experimental value, implying the changing trend of the quality factor. Equation (18) illuminates that the quality factor ratio of coal is correlated with the coal porosity and wave velocity. In the plastic deformation stage of stress loading, the coal wave velocity decreases, and the porosity increases. Consequently, the quality factor ratio of coal decreases in the form of the parabola function.

Equation (17) suggests that the change of coal quality factor in the elastic deformation stage of coal during stress loading is related to stress. The reason is presented as follows. The porosity decreases with the increase in stress, and there is an acceptable mathematical relationship between the change in coal porosity and coal stress. This implies that the main factor influencing the coal quality factor in the elastic deformation stage is stress. Equation (18) demonstrates that the change in the coal quality factor in the plastic deformation stage is derived from strain. The reason is that the change in stress in the plastic deformation stage is difficult to reflect the change in porosity, and a good mathematical relationship can be established between strain and coal porosity. It is revealed that the main factor affecting the coal quality factor in the plastic deformation stage is strain.

As discovered by combining Equations (15)–(18), coal quality factor Q is inversely proportional to coal porosity φ₄, and the fundamental factor affecting the coal quality factor is coal porosity. The change in coal porosity in the two stress loading stages are expressed by stress and strain, respectively. This is the influence mechanism of energy attenuation during ultrasonic propagation during stress loading.

Zhao Qiufang [55] and Zhang Pingsong [56] reported that the attenuation coefficient of the coal seam presented a logarithmical association with the porosity. Liang Yanxia et al. [57]. revealed that the quality factor presented a negative linear relationship with the porosity, while the coal quality factor (Q) is inversely proportional to the coal porosity (φ₄) in our study. In other words, different researchers have different research results on the coal quality factor–coal porosity relationship. However, the general trend is consistent. Specifically, larger coal porosity indicates a smaller coal quality factor. Generally, the model established in the study based on the ultrasonic wave propagation theory covers the whole process of coal loading and has been verified by the experimental results with high accuracy and reliability.

Since the influence mechanism of ultrasonic dynamic parameters of coal is relatively complex, the relationship model between the ultrasonic attenuation coefficient and stress under loading conditions established in this paper is not perfect. The research results only reflect the variation law of the coal quality factor somewhat. Therefore, the attenuation law of coal ultrasonic should be further investigated in the future.

4.3. Relationship between the Stress–Strain State of the Coal and Ultrasonic Response Characteristics during Stress Loading

The relationship between the coal stress–strain state and ultrasonic response characteristics (ultrasonic velocity and quality factor) can be obtained (Figure 12) by analyzing the influencing factors of coal ultrasonic propagation during stress loading. Figure 12 illustrates that the stress–strain state of coal during stress loading falls into the elastic deformation stage and the plastic deformation stage. In the elastic deformation stage, the wave velocity and coal quality factor exhibit an increasing trend. They increase faster in the pore compaction stage, but increase more slowly in the linear deformation stage. In the plastic deformation stage, the two parameters decrease. They decrease slowly in the microcrack growth stage, but decrease rapidly in the coal destruction stage. Thus, the change in ultrasonic velocity and attenuation of energy have a significant corresponding relevance to the coal stress state, laying a theoretical foundation for the inversion of the stress state and its change trend through the change and attenuation of ultrasonic velocity.

The following is an application scenario. The working face is an area that possesses a high coal and gas outburst risk in coal mine production, and the high risk is obviously associated with the coal stress state. During the production process of the working face, the ultrasonic characteristics in the coal in front of the working face can be continuously monitored by drilling. The stress state and its change trend of coal are inversed by using the change and attenuation of ultrasonic velocity following the previous research results of this paper. When the ultrasonic speed slows down, the quality factor is reduced, and the stress has not reached the peak stress. Thus, the safety production status of the working face shall be analyzed, and necessary safety protection measures shall be taken to prevent the occurrence of coal mine safety production accidents.

Although the research conclusion of this paper is obtained under the condition of coal with a primary structure, it is also applicable to coal with other structure types. The difference is that the stress and strain process for the primary structure coal is significant during stress loading, and the process is gentle for the fragmented coal and mylonitic coal. As a result, the change in ultrasonic speed and the attenuation of energy are relatively weak, leading to the increased difficulty and requirements of identification. The research in this area will be strengthened in the future. Generally, the method proposed in the paper has a relatively broad application prospect and provides a new idea for inferring the stress state and change trend of coal in the working face, contributing to a positive significance for predicting and preventing the occurrence of mine disasters. Due to the limitation of experimental conditions, the number of coal samples and the range of coal samples selected in this paper are small, which have certain limitations. The ultrasonic response characteristics of loaded coal analyzed in the experiment are only general statistical laws. It is necessary to carry out experimental analysis on more coal samples in order to reduce accidental errors and obtain more accurate general ultrasonic response laws. This is also the direction that the author needs to work hard towards in the future.

5. Conclusions

(1)

The coal stress-loading process falls into the elastic deformation stage and the plastic deformation stage. In the process of stress loading, the ultrasonic velocity and the quality factor of the coal sample have the same variation law. In the elastic deformation stage, the ultrasonic velocity and quality factor of the coal sample increase as coal axial strain elevates; in the plastic deformation stage, coal samples’ axial strain continues to increase, while the ultrasonic velocity and quality factor significantly decline.

(2)

In the process of stress loading, the ultrasonic velocity and quality factor of the coal sample demonstrate strong anisotropy, and are smaller in the Z direction than those in the X and Y directions. The ultrasonic velocity and quality factor of the coal sample in the X and Y directions are similar and present the same variation law.

(3)

Coal porosity is the fundamental factor influencing the change in the coal wave velocity and coal quality factor. In the elastic deformation stage, the coal stress increases, and the porosity decreases; the coal wave velocity and coal quality factor both increase, and the coal attenuation coefficient decreases. It is revealed that the primary factor that impacts the coal wave velocity and coal quality factor is stress. In the stage of plastic deformation, the porosity increases as the coal strain is on a rise, the coal wave velocity and coal quality factor decreases, and the coal attenuation coefficient increases, suggesting that the main factor affecting coal wave velocity and coal quality factor was strain.

(4)

The wave velocity and coal quality factor rapidly increase in the pore compaction stage and slowly increase in the linear deformation stage. The wave velocity and coal quality factor slowly decrease in the stage of microcrack propagation, while the wave velocity and coal quality factor rapidly decrease in the stage of coal destruction. The stress–strain state of coal corresponds well to the ultrasonic response characteristics during the loading process.