# Experimental Investigation on Damage Characteristics and Early Warning of Frozen Coal under Uniaxial Compression

Authors: Xiang Sun; Bin Liu; Qi Dong; Feng Shi
Journal: Advances in Materials Science and Engineering
 (2023)

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## Abstract

This article conducted acoustic emission tests of natural coal, natural frozen coal, and saturated frozen coal to explore the damage characteristics of frozen coal and in view of the frozen coal damage early warning problems and explored the strength deformation and acoustic emission characteristics of coal samples. The test results showed that the compressive strength of the frozen coal samples decreased significantly, and the strength of the saturated frozen coal samples was the lowest; more acoustic emissions were generated at the initial loading stage. The damage parameters were defined using the acoustic emission parameters. The damage characteristics of the coal samples were analyzed. The damage model of the coal samples was established based on the power function. The early warning parameterVAEi to analyze the evolution characteristics of the variance curve was proposed; the sudden jump point b of VAEi from the stable development stage to the rapid growth stage was defined as a general early warning point; the endpoint point c of the parameter rapid growth stage was defined as a key early warning point; a zonal and hierarchical early warning was finally proposed.


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## Body

## 1. Introduction

The demand for coal is increasing, and the mining depth is increasing with the world economy’s continuous development; the coal seam gas content and ground stress are increasing; the coal seam permeability is decreasing; and the difficulty of gas drainage is increasing [1–3]. The existing coal seam antireflection technologies include deep hole blasting [4], hydraulic fracturing [5, 6], and low-temperature freezing, mainly. The low-temperature frozen antireflection technology is widely concerned due to the advantages of low energy consumption and no pollution [7]. It is urgent to research the physical and mechanical properties of coal mass under low-temperature frozen conditions to provide a theoretical basis for gas drainage of high-gas coal seams in deep mining areas.Many scholars have carried out a lot of research studies on the physical and mechanical properties of low-temperature frozen coal and rock under different test conditions and have made certain research results in recent years. Wang et al. [8] studied the influence of a low-temperature gradient on the dynamic mechanical properties of coal through the Split-Hopkinson Pressure Bar (SHPB) Dynamic Impact Experiment, and the coal-rock stress-strain curve characteristics subject to the low-temperature load coupling effect were discussed. Xiao et al. [9] carried out experiments under cyclic loading of rocks after heating at different temperatures to explore the permeability characteristics of rocks in different temperature regions permeability. Yang et al. [10] studied the meso-damage propagation mechanism and mechanical properties of rocks under different frozen temperatures by using computed tomography (CT) scanning technology. Liu et al. [11] studied the influence of frozen temperature on the mechanical properties of red sandstone and discussed the influence mechanism of ground stress on its freezing process preliminarily. Wang et al. [12] studied the influence of temperature on the mechanical properties and fracture modes of two types of saturated rocks and proposed a theoretical model to predict the change in rock strength with temperature. Ren et al. [13] studied the influence of liquid nitrogen cold shock on the mechanical properties of coal and rock and explored the mechanism of coal and rock cold shock. Shi et al. [14] analyzed the effects of freeze-thaw cycles and confining pressure on the mechanical properties of red sandstone. Yang et al. [15] studied the influence of temperature and water content on coal permeability under low-temperature freezing. Zhang et al. [16] studied the anisotropy of coal seam permeability under the conditions of a high dip angle. Most of the above achievements focused on rock or coal, but the research on the physical and mechanical properties of frozen coal is relatively few.The increasing difficulty of gas drainage with the mining depth of the mine continues to increase, and the possibility of rock bursts and other disasters increases [17]. Therefore, it is important to study the damage characteristics of frozen coal samples and give early warning before damage particularly. A lot of research studies have been done on rock fracture instability and early warning in recent years [18, 19]. Acoustic emission monitoring can study the damage and failure processes of rocks, reveal the rock failure process, explore the internal relationship between rock failure and acoustic emission changes, and facilitate understanding of the rock failure mechanism [20, 21]. In terms of acoustic emission research on coal or rock damage and early warning, Xiao et al. [22] conducted uniaxial compression tests on coal samples with different water contents based on acoustic emission and infrared thermal imaging technology, analyzed the evolution characteristics of overall damage and surface damage of coal samples, and screened out warning signals. Zhang et al. [23] conducted experiments on flawed sandstone to investigate the infrared radiation characteristics during the failure process. Mu et al. [24] conducted uniaxial compression tests and analyzed the mechanical and acoustic emission (abbreviated as AE) response characteristics and damage evolution characteristics of rock samples with different fracture angles. Lai et al. [25] studied the energy release characteristic of damage evolution in the whole process of uniaxial compression of coal and rock samples with different water contents and picked up the key hazards of acoustic emission signals based on the common criteria of energy contribution rate and ring counting contribution rate. Sun et al. [26] defined the rock damage variable through acoustic emission parameters and analyzed the stress-strain curve under uniaxial conditions. The above research focuses on the damage characteristics and early warnings of the failure process of ordinary coal samples under different moisture content conditions, while there are few research studies on the damage process and early warnings of frozen coal samples under saturated conditions. In addition, most of the previous studies were qualitative analyses of rock failure and instability, and there is a lack of zonal and time-sharing early warnings of coal sample failure and instability.The coal samples from a coal mine in western China were taken as the research object in this article, and the natural state and saturated coal samples were frozen at low temperatures, respectively. Uniaxial compression acoustic emission tests were carried out on two groups of coal samples after frozen treatment and one group of coal samples without frozen treatment.The strength and deformation characteristics of coal samples under three different conditions were analyzed, as were the acoustic emission evolution and damage characteristics of coal samples during the processes of deformation and failure. The variance parameters representing the damage of coal samples were proposed based on the acoustic emission parameters, and the damage warning of coal samples was studied. The research results in this article can provide a theoretical basis for the application of low-temperature frozen and antipermeability technology in the high gas coal seam and provide a new idea for the research on early warning and control of rock bursts and other disasters during the mining process of high gas coal seams, to ensure the safe production.


## 2. Test Introduction

The test introduction is explained in the following sections.


### 2.1. Test Samples and Methods

The samples for this test were taken from a coal mine in western China. The area of the sampled coal mine is 192.6 km2, and the recoverable reserves are 2 billion tons. The geological structure of the minefield is simple. There are 10 minable coal seams in total, which are mined in 3 levels. The average thickness of the coal seam was 3.5 m, the average burial depth was 400 m, and the apparent density of the coal sample was 1.3 g/cm3. The moisture content of the coal sample was 9.97%, the volatile content was 26.43%, the ash content was 1.2%, and the fixed carbon content was 62.39%, all belonging to bituminous coal, according to the industrial analysis results.When selecting coal samples, we try to overcome the coal samples with many defects and structures and take samples from the same coal sample for processing to improve the accuracy of test data and reduce the dispersion of test results. The coal blocks were made into cylindrical coal samples with a diameter of 25 mm and a height of 50 mm according to the recommendations of the International Society for Rock Mechanics. The two end faces of the coal sample were perpendicular to the cylindrical axis, the maximum deviation was not more than 0.25°, and the unevenness of the end faces was not more than 0.1 mm. The processed coal samples were divided into three groups: natural state (marked as N), natural frozen state (marked as NF), and saturated frozen state (marked as SF). There were three coal samples in each group, and they were numbered in turn; the natural state was the control group. Then, the height, diameter, and weight of the coal samples were measured, and the specific measurement results are shown in Table1.Table 1
Physical and mechanical parameters of coal samples.
Coal sampleHeight (mm)Diameter (mm)Weight (g)AE impact rateCompressive strength (MPa)Average (MPa)N150.3425.0229.88346123.2422.31N250.2524.8629.68227322.34N350.5824.9029.12279321.37NF150.1824.9429.45119420.2019.54NF250.1424.9629.62273620.37NF350.2824.8229.38284918.04SF150.0224.3429.38308716.6116.76SF250.0624.2429.54329815.83SF350.2225.1629.23289317.85We saturate the coal sample with the mark of SF, soak the coal sample in water completely, take out the sample every 2 hours within 72 hours, wipe off the surface moisture, weigh it with a balance, and record it. The coal sample water absorption weight-time curve is shown in Figure1. It can be seen from the figure that when the water absorption time is 40 h, the coal sample reaches the saturation state. After the coal sample was saturated with water completely, it was warped with fresh film and sealed. We put it in the freezer with another group of natural coal samples marked NF immediately for treatment. The frozen temperature is −20°C, and the frozen time is 48 h.Figure 1
Coal sample water absorption weight-time curve.


### 2.2. Test Equipment

The uniaxial compression test system is shown in Figure2, including the WDW-100E universal testing machine test system and PCI-II acoustic emission monitoring system produced by American Physical Acoustics Corporation (PAC). The maximum test force of the WDW-100E universal testing machine is 100 kN, the accurate measurement range is 2 kN–100 kN, the measurement accuracy is ±1%, the displacement resolution is 0.01 mm, the displacement speed control range is 0.1 mm/min∼500 mm/min, the tensile test space is 0–600 mm, the compression test space is 0–600 mm, and the test space width is 0–420 mm. The PCI-II acoustic emission monitoring system is 18 bit A/D, and the frequency range is 1 kHz–3 MHz. PCI-II has a unique waveform stream data storage function, which can store the acoustic emission waveform into the hard disk at the rate of 10 megabits per second.Figure 2
Test equipment layout.The axial displacement control loading mode was adopted during the test, and the loading rate was set to be constant at 0.1 mm/min to obtain the full stress-strain curve of the coal samples effectively under different processing conditions and analyze the change rule of their mechanical properties. Two acoustic emission sensors were arranged on both sides of the test coal sample, and the signal threshold and sampling rate of the acoustic emission system were set to 40 dB and 1 MHz, respectively. The acoustic emission sensor was fixed on the coal sample surface with couplant and adhesive tape to ensure full contact and no falling off.We ensure that the acoustic emission system is consistent with the universal testing machine system in time, and then, start loading the coal samples during the test. The acoustic emission system started to collect acoustic emission signals until the coal samples were damaged, stopped loading synchronously, and stored relevant data. For the coal samples treated with low-temperature freezing, they will not be taken out of the frozen chamber until before the test to ensure the freezing effect, and then, the test will be carried out immediately, and the impact of ambient temperature on them will be ignored during the test.


## 2.1. Test Samples and Methods

The samples for this test were taken from a coal mine in western China. The area of the sampled coal mine is 192.6 km2, and the recoverable reserves are 2 billion tons. The geological structure of the minefield is simple. There are 10 minable coal seams in total, which are mined in 3 levels. The average thickness of the coal seam was 3.5 m, the average burial depth was 400 m, and the apparent density of the coal sample was 1.3 g/cm3. The moisture content of the coal sample was 9.97%, the volatile content was 26.43%, the ash content was 1.2%, and the fixed carbon content was 62.39%, all belonging to bituminous coal, according to the industrial analysis results.When selecting coal samples, we try to overcome the coal samples with many defects and structures and take samples from the same coal sample for processing to improve the accuracy of test data and reduce the dispersion of test results. The coal blocks were made into cylindrical coal samples with a diameter of 25 mm and a height of 50 mm according to the recommendations of the International Society for Rock Mechanics. The two end faces of the coal sample were perpendicular to the cylindrical axis, the maximum deviation was not more than 0.25°, and the unevenness of the end faces was not more than 0.1 mm. The processed coal samples were divided into three groups: natural state (marked as N), natural frozen state (marked as NF), and saturated frozen state (marked as SF). There were three coal samples in each group, and they were numbered in turn; the natural state was the control group. Then, the height, diameter, and weight of the coal samples were measured, and the specific measurement results are shown in Table1.Table 1
Physical and mechanical parameters of coal samples.
Coal sampleHeight (mm)Diameter (mm)Weight (g)AE impact rateCompressive strength (MPa)Average (MPa)N150.3425.0229.88346123.2422.31N250.2524.8629.68227322.34N350.5824.9029.12279321.37NF150.1824.9429.45119420.2019.54NF250.1424.9629.62273620.37NF350.2824.8229.38284918.04SF150.0224.3429.38308716.6116.76SF250.0624.2429.54329815.83SF350.2225.1629.23289317.85We saturate the coal sample with the mark of SF, soak the coal sample in water completely, take out the sample every 2 hours within 72 hours, wipe off the surface moisture, weigh it with a balance, and record it. The coal sample water absorption weight-time curve is shown in Figure1. It can be seen from the figure that when the water absorption time is 40 h, the coal sample reaches the saturation state. After the coal sample was saturated with water completely, it was warped with fresh film and sealed. We put it in the freezer with another group of natural coal samples marked NF immediately for treatment. The frozen temperature is −20°C, and the frozen time is 48 h.Figure 1
Coal sample water absorption weight-time curve.


## 2.2. Test Equipment

The uniaxial compression test system is shown in Figure2, including the WDW-100E universal testing machine test system and PCI-II acoustic emission monitoring system produced by American Physical Acoustics Corporation (PAC). The maximum test force of the WDW-100E universal testing machine is 100 kN, the accurate measurement range is 2 kN–100 kN, the measurement accuracy is ±1%, the displacement resolution is 0.01 mm, the displacement speed control range is 0.1 mm/min∼500 mm/min, the tensile test space is 0–600 mm, the compression test space is 0–600 mm, and the test space width is 0–420 mm. The PCI-II acoustic emission monitoring system is 18 bit A/D, and the frequency range is 1 kHz–3 MHz. PCI-II has a unique waveform stream data storage function, which can store the acoustic emission waveform into the hard disk at the rate of 10 megabits per second.Figure 2
Test equipment layout.The axial displacement control loading mode was adopted during the test, and the loading rate was set to be constant at 0.1 mm/min to obtain the full stress-strain curve of the coal samples effectively under different processing conditions and analyze the change rule of their mechanical properties. Two acoustic emission sensors were arranged on both sides of the test coal sample, and the signal threshold and sampling rate of the acoustic emission system were set to 40 dB and 1 MHz, respectively. The acoustic emission sensor was fixed on the coal sample surface with couplant and adhesive tape to ensure full contact and no falling off.We ensure that the acoustic emission system is consistent with the universal testing machine system in time, and then, start loading the coal samples during the test. The acoustic emission system started to collect acoustic emission signals until the coal samples were damaged, stopped loading synchronously, and stored relevant data. For the coal samples treated with low-temperature freezing, they will not be taken out of the frozen chamber until before the test to ensure the freezing effect, and then, the test will be carried out immediately, and the impact of ambient temperature on them will be ignored during the test.


## 3. Experiment Result Analysis

The experiment result analysis is explained in the following sections.


### 3.1. Strength, Deformation, and Failure Characteristics of Coal Samples

The uniaxial compressive strength of each group of coal samples was calculated based on the test results; the calculation results are shown in Table1. The natural coal sample has the largest compressive strength, and the uniaxial compressive strength was 22.31 MPa. The average compressive strength of the natural frozen coal sample was 19.54 MPa, and the strength decreased by 12.42%, indicating that the compressive strength of the coal sample after low-temperature frozen treatment decreases significantly. The average compressive strength of the saturated frozen coal sample was the lowest, at 16.76 MPa, which is 24.88% lower than that of the natural coal sample. The main reason is that the water inside the coal sample freezes slowly under the low-temperature frozen condition, the internal fissure volume of the coal sample becomes larger, and more damage occurs in the original coal sample, leading to a decrease in the integrity of the coal sample and its strength. The moisture content of the frozen coal samples under saturated conditions is higher, and the compressive strength decreases more accordingly under the same frozen conditions.We take one coal sample under different test conditions as a typical coal sample for analysis and take N1, NF1, and SF1. Figure3 shows the stress-strain curve of the coal sample, with the same trend of stress-strain curve basically, which conforms to the stress-strain curve of rock under typical uniaxial compression conditions and can be divided into the compaction stage, elastic deformation stage, plastic deformation stage, and post-peak failure stage. At the initial stage of loading, the primary defects such as pores and cracks in the coal sample began to close under the external load, resulting in a rapid increase in deformation at this stage. The primary defects were closed and began to enter the elastic stage as the load continued to increase, where the stress and strain are linear. The curve started to deviate from the original straight line as the load continued to increase and entered the plastic stage, and microcracks began to appear inside. As the load increased to the peak load, the coal sample entered the failure stage. The internal microcracks of the coal sample penetrated quickly, forming macrocracks, and the coal sample was damaged.Figure 3
Stress-strain curves under different conditions.The slope of the compression stage curve of the coal samples after frozen treatment decreases compared with the coal samples in the natural state, and the saturated frozen state is the smallest. By comparing the postpeak stage of coal samples in different states, it can be seen that the postpeak curve of the coal samples in the natural state is the longest, showing a ladder drop and a certain degree of brittleness. The postpeak curve of the saturated frozen coal sample is the shortest, showing a direct drop. The coal sample was damaged directly, and its brittleness is obviously enhanced. The main reason for the above phenomenon is that the water inside the coal sample freezes slowly under the low-temperature frozen condition. The volume of the water increases due to the reverse expansion, leading to a decrease in the integrity of the coal sample; a crack closure occurred in the sample under a low load, resulting in large deformation. When the saturated coal sample was frozen, it was greatly damaged; the integrity of the coal sample was poor, and the brittleness increased with the increase in water content. Therefore, the postpeak curve shows a rapid drop. It can be seen that the lower the integrity of the coal sample, the stronger its brittleness.Figure4 shows the final failure patterns of typical coal samples under different test conditions. It can be seen that the fragmentation of coal samples under natural conditions is relatively large, and the fragmentation degree of coal samples after low-temperature frozen treatment is increased significantly, and the fragmentation degree is the highest under saturated frozen conditions. The reason is that the damage caused by the expansion of the water-bearing coal sample during the low-temperature freezing process reduced the integrity of the coal sample, and the internal cracks were more developed. The coal sample is more easily broken, and the integrity is lower after reaching the peak load.Figure 4
Coal sample failure patterns under different conditions.


### 3.2. Acoustic Emission Characteristics of Coal Samples

Elastic waves will be sent out and received by the acoustic emission monitoring system during the destruction of coal samples, and then, the internal destruction characteristics of the coal samples during the destruction process will be inverted [27, 28]. The representative impact rate among acoustic emission parameters is selected as the analysis parameter to analyze the failure characteristics of coal samples. Figure 5 shows the relationship between the load and impact rate of the coal samples with time evolution. It can be seen that the characteristics of the change in the acoustic emission impact rate of coal samples after natural freezing treatment are consistent with those of coal samples in their natural state. At the initial stage of loading, a small amount of acoustic emission was generated due to the compression closure of the internal primary crack, and the impact rate was small. In the elastic stage, only a small amount of acoustic emission was generated due to the small change in internal damage of the coal samples. The coal sample enters the plastic deformation stage, the internal cracks begin to expand, and new cracks are generated at the same time. With the continuous increase in load, acoustic emission became active, and the impact ratio value increased accordingly. A large amount of acoustic emission was generated, and the impact rate reached the maximum value when approaching the peak load, which can be used as the precursor information of coal sample destruction. At the postpeak stage, certain acoustic emission signals will also be generated due to the large-scale propagation and penetration of cracks.Figure 5
Evolution of coal sample AE impact rate: (a) N1; (b) NF1; (c) SF1.
(a)(b)(c)The acoustic emission characteristics of coal samples under saturated frozen conditions are different from the former two. It is shown that more acoustic emissions were generated at the initial stage of loading and that the impact rate was high. The main reason is that more cracks are formed in the internal frozen expansion of saturated frozen coal samples, and more acoustic emissions will be generated due to the frozen expansion cracks and the closure of primary defects under external loads. In the plastic deformation stage, especially in the early stage of rock failure, more acoustic emissions were also generated, and several sudden increases occurred, indicating that more new cracks were generated in the saturated frozen coal sample at this time and the internal damage was more serious. The main reason is that the expansion cracks were generated inside the coal sample due to the low-temperature freezing, and the internal cracks were generated and expanded more frequently with the external load. Therefore, the acoustic emission before the rock failure is more than that under the natural state, and the impact rate value is relatively large.


## 3.1. Strength, Deformation, and Failure Characteristics of Coal Samples

The uniaxial compressive strength of each group of coal samples was calculated based on the test results; the calculation results are shown in Table1. The natural coal sample has the largest compressive strength, and the uniaxial compressive strength was 22.31 MPa. The average compressive strength of the natural frozen coal sample was 19.54 MPa, and the strength decreased by 12.42%, indicating that the compressive strength of the coal sample after low-temperature frozen treatment decreases significantly. The average compressive strength of the saturated frozen coal sample was the lowest, at 16.76 MPa, which is 24.88% lower than that of the natural coal sample. The main reason is that the water inside the coal sample freezes slowly under the low-temperature frozen condition, the internal fissure volume of the coal sample becomes larger, and more damage occurs in the original coal sample, leading to a decrease in the integrity of the coal sample and its strength. The moisture content of the frozen coal samples under saturated conditions is higher, and the compressive strength decreases more accordingly under the same frozen conditions.We take one coal sample under different test conditions as a typical coal sample for analysis and take N1, NF1, and SF1. Figure3 shows the stress-strain curve of the coal sample, with the same trend of stress-strain curve basically, which conforms to the stress-strain curve of rock under typical uniaxial compression conditions and can be divided into the compaction stage, elastic deformation stage, plastic deformation stage, and post-peak failure stage. At the initial stage of loading, the primary defects such as pores and cracks in the coal sample began to close under the external load, resulting in a rapid increase in deformation at this stage. The primary defects were closed and began to enter the elastic stage as the load continued to increase, where the stress and strain are linear. The curve started to deviate from the original straight line as the load continued to increase and entered the plastic stage, and microcracks began to appear inside. As the load increased to the peak load, the coal sample entered the failure stage. The internal microcracks of the coal sample penetrated quickly, forming macrocracks, and the coal sample was damaged.Figure 3
Stress-strain curves under different conditions.The slope of the compression stage curve of the coal samples after frozen treatment decreases compared with the coal samples in the natural state, and the saturated frozen state is the smallest. By comparing the postpeak stage of coal samples in different states, it can be seen that the postpeak curve of the coal samples in the natural state is the longest, showing a ladder drop and a certain degree of brittleness. The postpeak curve of the saturated frozen coal sample is the shortest, showing a direct drop. The coal sample was damaged directly, and its brittleness is obviously enhanced. The main reason for the above phenomenon is that the water inside the coal sample freezes slowly under the low-temperature frozen condition. The volume of the water increases due to the reverse expansion, leading to a decrease in the integrity of the coal sample; a crack closure occurred in the sample under a low load, resulting in large deformation. When the saturated coal sample was frozen, it was greatly damaged; the integrity of the coal sample was poor, and the brittleness increased with the increase in water content. Therefore, the postpeak curve shows a rapid drop. It can be seen that the lower the integrity of the coal sample, the stronger its brittleness.Figure4 shows the final failure patterns of typical coal samples under different test conditions. It can be seen that the fragmentation of coal samples under natural conditions is relatively large, and the fragmentation degree of coal samples after low-temperature frozen treatment is increased significantly, and the fragmentation degree is the highest under saturated frozen conditions. The reason is that the damage caused by the expansion of the water-bearing coal sample during the low-temperature freezing process reduced the integrity of the coal sample, and the internal cracks were more developed. The coal sample is more easily broken, and the integrity is lower after reaching the peak load.Figure 4
Coal sample failure patterns under different conditions.


## 3.2. Acoustic Emission Characteristics of Coal Samples

Elastic waves will be sent out and received by the acoustic emission monitoring system during the destruction of coal samples, and then, the internal destruction characteristics of the coal samples during the destruction process will be inverted [27, 28]. The representative impact rate among acoustic emission parameters is selected as the analysis parameter to analyze the failure characteristics of coal samples. Figure 5 shows the relationship between the load and impact rate of the coal samples with time evolution. It can be seen that the characteristics of the change in the acoustic emission impact rate of coal samples after natural freezing treatment are consistent with those of coal samples in their natural state. At the initial stage of loading, a small amount of acoustic emission was generated due to the compression closure of the internal primary crack, and the impact rate was small. In the elastic stage, only a small amount of acoustic emission was generated due to the small change in internal damage of the coal samples. The coal sample enters the plastic deformation stage, the internal cracks begin to expand, and new cracks are generated at the same time. With the continuous increase in load, acoustic emission became active, and the impact ratio value increased accordingly. A large amount of acoustic emission was generated, and the impact rate reached the maximum value when approaching the peak load, which can be used as the precursor information of coal sample destruction. At the postpeak stage, certain acoustic emission signals will also be generated due to the large-scale propagation and penetration of cracks.Figure 5
Evolution of coal sample AE impact rate: (a) N1; (b) NF1; (c) SF1.
(a)(b)(c)The acoustic emission characteristics of coal samples under saturated frozen conditions are different from the former two. It is shown that more acoustic emissions were generated at the initial stage of loading and that the impact rate was high. The main reason is that more cracks are formed in the internal frozen expansion of saturated frozen coal samples, and more acoustic emissions will be generated due to the frozen expansion cracks and the closure of primary defects under external loads. In the plastic deformation stage, especially in the early stage of rock failure, more acoustic emissions were also generated, and several sudden increases occurred, indicating that more new cracks were generated in the saturated frozen coal sample at this time and the internal damage was more serious. The main reason is that the expansion cracks were generated inside the coal sample due to the low-temperature freezing, and the internal cracks were generated and expanded more frequently with the external load. Therefore, the acoustic emission before the rock failure is more than that under the natural state, and the impact rate value is relatively large.


## 4. Analysis of Damage Evolution Characteristics of Coal Samples

The analysis of damage evolution characteristics of coal samples is described in the following sections.


### 4.1. Damage Theoretical Basis

The acoustic emission evolution characteristics reflect the damage process of the coal samples better based on the above analysis. Therefore, the acoustic emission parameters can be used to define the damage variables and further analyze the initiation and expansion through the failure of internal cracks during the damage process of coal samples [29, 30]. The coal sample damage is defined by the impact number parameter in this article.The damage evolution process of rock can be seen as a nonequilibrium statistical process, so the damage parameterD of rock obeys a statistical distribution.The Weibull statistical distribution of the two parameters is as follows:(1)ϕF=mF0FF0m−1exp−FF0m,where F is the random distribution variable of the Weibull distribution of microelements, m and F0 are the distribution parameters of Weibull, where m is the parameter reflecting the brittleness of rock and F0 represents the macroaverage strength of rock, and ϕF is a measure of microelement damage of rock samples during loading.DamageD is a measure of the damage degree of the coal sample, and the damage degree is related to the flaw fissures contained in each microelement, which affect the strength of the microelement directly. The relationship between damage and the probability density of element failure is as follows:(2)dDdF=ϕF.Then, there are(3)D=∫0FϕFdF=1−exp−FF0m.As the acoustic emission activity is a statistical characteristic, it must be consistent with the statistical distribution law of internal defects in coal samples. Therefore, the acoustic emission impact number can reflect the damage distribution. If the acoustic emission accumulation is Ωm when the coal sample is damaged completely, the acoustic emission accumulation during rock sample fracture can be expressed as follows:(4)Ω=Ωm∫0Fϕxdx.When Φ (x) is (1), the integral of the above equation is as follows:(5)ΩΩm=1−exp−FF0m.By comparing (3) and (5), it can be concluded that the damage caused by the load is as follows:(6)D=ΩΩm.Equation (6) can define the acoustic emission damage value.


### 4.2. Analysis of Damage Evolution Characteristics of Coal Samples

Figure6 shows the damage evolution characteristic of coal samples under different test conditions. It can be seen that the changing trend is the same. It is shown that the primary cracks in the coal sample were closed at the initial stage of loading, and little damage occurred in the coal sample. At this time, the damage curve shows a slow growth trend, which belongs to the initial damage stage. When entered the elastic stage, elastic deformation occurred inside the coal sample, a small amount of acoustic emission was generated, and the internal damage was unchanged. Basically, the damage curve was almost unchanged; NF1 and SF1 are the most obvious. After entering the plastic deformation stage, the internal cracks continue to expand and converge into larger cracks. The damage curve of each coal sample shows a sharp rise, and the damage increases sharply. At this time, the coal sample is in a rapid damage stage. Especially, near the peak load, the damage appears more obvious, which can also be used as the precursor information of coal sample failure.Figure 6
Evolution of coal sample damage: (a) N1; (b) NF1; (c) SF1.
(a)(b)(c)The damage process of saturated frozen coal is different compared with natural coal and natural frozen coal. In the compaction stage, the damage is larger and increases more. The main reason is that the more water content, the greater the frozen expansion during frozen treatment, and the corresponding greater the damage accumulation in the initial compaction stage. In addition, the postpeak damage does not increase basically, and the coal sample was damaged at the peak load. At this time, the damage has reached the maximum, indicating that the more severe the corresponding damage, the higher the degree of coal sample breakage. The natural frozen coal sample damage under the peak load does not reach the maximum value, and there is still a small increase after the peak load. The postpeak damage of the coal sample in the natural state still increased greatly, indicating that the damage degree of the coal sample was small and the integrity was high. The damage analysis results are consistent with the failure characteristics in Section 3.2.


### 4.3. Damage Model of Coal Sample

A large amount of acoustic emission will be generated, the internal damage will increase rapidly, and the damage will accelerate before the coal sample is damaged. The accelerated release of energy will also occur in the vicinity of an earthquake combined with the field of seismic research, and the cumulative energy release is a power law distribution in time sequence [31, 32]. The curve fitting of the relationship between coal sample damage and time is carried out based on the power function. The fitting results are shown in Figure 7. According to the analysis, N1 and NF1 have quite good fitting effects, and the fitting degree (R) is 0.978 and 0.972, respectively. In contrast, the fitting effect of SF1 is relatively general, and the fitting degree is 0.936. The main reason is that SF1 has more damage in the compaction stage due to freezing, and the damage curve rises like a step in the compaction stage.Figure 7
Coal sample damage fitting curve: (a) N1; (b) NF1; (c) SF1.
(a)(b)(c)The fitting degree of the fitting curve exceeds 0.9 from the curve fitting effect, and the damage shows an obvious power function relationship with time. The power function expression is shown in equation (7), and the fitting result parameters of each coal sample are shown in Table 2:(7)y=a+bxc.Table 2
Coal sample damage and time fitting parameters.
Coal sampleabcRN10.0202.14402E − 217.7280.978NF10.0051.10161E − 4316.0560.972SF10.1677.1444E − 165.5710.936The damage of the coal sample will be accelerated before failure under the condition of uniaxial compression, and the acceleration characteristic conforms to the power function. Furthermore, the analysis shows that the specific meaning of each parameter is thata is the original damage inside the coal sample, that is, the original cracks and voids inside the coal sample, and b and c are the degrees of damage increase, which are related to the physical properties of the coal sample itself. Finally, the coal sample damage model is obtained:(8)D=A+BxC,where A is the original damage of the coal sample and B and C is the damage acceleration characteristic index.


## 4.1. Damage Theoretical Basis

The acoustic emission evolution characteristics reflect the damage process of the coal samples better based on the above analysis. Therefore, the acoustic emission parameters can be used to define the damage variables and further analyze the initiation and expansion through the failure of internal cracks during the damage process of coal samples [29, 30]. The coal sample damage is defined by the impact number parameter in this article.The damage evolution process of rock can be seen as a nonequilibrium statistical process, so the damage parameterD of rock obeys a statistical distribution.The Weibull statistical distribution of the two parameters is as follows:(1)ϕF=mF0FF0m−1exp−FF0m,where F is the random distribution variable of the Weibull distribution of microelements, m and F0 are the distribution parameters of Weibull, where m is the parameter reflecting the brittleness of rock and F0 represents the macroaverage strength of rock, and ϕF is a measure of microelement damage of rock samples during loading.DamageD is a measure of the damage degree of the coal sample, and the damage degree is related to the flaw fissures contained in each microelement, which affect the strength of the microelement directly. The relationship between damage and the probability density of element failure is as follows:(2)dDdF=ϕF.Then, there are(3)D=∫0FϕFdF=1−exp−FF0m.As the acoustic emission activity is a statistical characteristic, it must be consistent with the statistical distribution law of internal defects in coal samples. Therefore, the acoustic emission impact number can reflect the damage distribution. If the acoustic emission accumulation is Ωm when the coal sample is damaged completely, the acoustic emission accumulation during rock sample fracture can be expressed as follows:(4)Ω=Ωm∫0Fϕxdx.When Φ (x) is (1), the integral of the above equation is as follows:(5)ΩΩm=1−exp−FF0m.By comparing (3) and (5), it can be concluded that the damage caused by the load is as follows:(6)D=ΩΩm.Equation (6) can define the acoustic emission damage value.


## 4.2. Analysis of Damage Evolution Characteristics of Coal Samples

Figure6 shows the damage evolution characteristic of coal samples under different test conditions. It can be seen that the changing trend is the same. It is shown that the primary cracks in the coal sample were closed at the initial stage of loading, and little damage occurred in the coal sample. At this time, the damage curve shows a slow growth trend, which belongs to the initial damage stage. When entered the elastic stage, elastic deformation occurred inside the coal sample, a small amount of acoustic emission was generated, and the internal damage was unchanged. Basically, the damage curve was almost unchanged; NF1 and SF1 are the most obvious. After entering the plastic deformation stage, the internal cracks continue to expand and converge into larger cracks. The damage curve of each coal sample shows a sharp rise, and the damage increases sharply. At this time, the coal sample is in a rapid damage stage. Especially, near the peak load, the damage appears more obvious, which can also be used as the precursor information of coal sample failure.Figure 6
Evolution of coal sample damage: (a) N1; (b) NF1; (c) SF1.
(a)(b)(c)The damage process of saturated frozen coal is different compared with natural coal and natural frozen coal. In the compaction stage, the damage is larger and increases more. The main reason is that the more water content, the greater the frozen expansion during frozen treatment, and the corresponding greater the damage accumulation in the initial compaction stage. In addition, the postpeak damage does not increase basically, and the coal sample was damaged at the peak load. At this time, the damage has reached the maximum, indicating that the more severe the corresponding damage, the higher the degree of coal sample breakage. The natural frozen coal sample damage under the peak load does not reach the maximum value, and there is still a small increase after the peak load. The postpeak damage of the coal sample in the natural state still increased greatly, indicating that the damage degree of the coal sample was small and the integrity was high. The damage analysis results are consistent with the failure characteristics in Section 3.2.


## 4.3. Damage Model of Coal Sample

A large amount of acoustic emission will be generated, the internal damage will increase rapidly, and the damage will accelerate before the coal sample is damaged. The accelerated release of energy will also occur in the vicinity of an earthquake combined with the field of seismic research, and the cumulative energy release is a power law distribution in time sequence [31, 32]. The curve fitting of the relationship between coal sample damage and time is carried out based on the power function. The fitting results are shown in Figure 7. According to the analysis, N1 and NF1 have quite good fitting effects, and the fitting degree (R) is 0.978 and 0.972, respectively. In contrast, the fitting effect of SF1 is relatively general, and the fitting degree is 0.936. The main reason is that SF1 has more damage in the compaction stage due to freezing, and the damage curve rises like a step in the compaction stage.Figure 7
Coal sample damage fitting curve: (a) N1; (b) NF1; (c) SF1.
(a)(b)(c)The fitting degree of the fitting curve exceeds 0.9 from the curve fitting effect, and the damage shows an obvious power function relationship with time. The power function expression is shown in equation (7), and the fitting result parameters of each coal sample are shown in Table 2:(7)y=a+bxc.Table 2
Coal sample damage and time fitting parameters.
Coal sampleabcRN10.0202.14402E − 217.7280.978NF10.0051.10161E − 4316.0560.972SF10.1677.1444E − 165.5710.936The damage of the coal sample will be accelerated before failure under the condition of uniaxial compression, and the acceleration characteristic conforms to the power function. Furthermore, the analysis shows that the specific meaning of each parameter is thata is the original damage inside the coal sample, that is, the original cracks and voids inside the coal sample, and b and c are the degrees of damage increase, which are related to the physical properties of the coal sample itself. Finally, the coal sample damage model is obtained:(8)D=A+BxC,where A is the original damage of the coal sample and B and C is the damage acceleration characteristic index.


## 5. Early Warning of Frozen Coal Sample

Any signal that exceeds the threshold value and enables a channel to obtain data which have an impact. Acoustic emission impact can reflect the total amount and frequency of acoustic emission activities. It is used to evaluate acoustic emissions or rock failure activity. The change in the acoustic emission impact rate well reflects the process of rock failure. It can be seen from the above analysis that when approaching the peak load, a large amount of acoustic emission will be generated, and the impact rate will reach the maximum. These phenomena can be used as the precursors of coal sample damage. This section explores the warning method for coal sample damage based on the warning precursor information. This article takes SF1 as a typical coal sample because the damage process of coal samples under different test conditions is the same. Basically, an early warning parameterVAEi based on the variance parameter of the acoustic emission impact rate is proposed, which provides a new idea for the early warning of dynamic disasters such as rockburst in the process of gas mining.The calculation formula of the acoustic emission impact rate variance parameterVAEi is as follows:(9)VAEi=1N∑q=1NIq−1N∑q=1NIq2,where VAEi is the impact variance of acoustic emission and Iq is the number of acoustic emission impacts monitored at time q. Variance indicates the deviation degree and dispersion degree of acoustic emission activity from the average level. If the variance value is too large, it means that the number of acoustic emission events increases or decreases significantly, and the internal stress of the coal sample accumulates rapidly, which means that the internal damage is greater. This parameter index can better reflect the damage process of coal samples and can be used as an early warning parameter for rock mass damage.Figure8 shows the VAEi curve and load curve of the SF1 coal sample. It can be seen from the figure that the VAEi curve has the characteristics of stage change, showing four stages as a whole: “growth, slow decline, rapid growth, stable, and unchanged.”(1)
o-a stage is the original crack compaction stage corresponding to the stress-strain curve. At the initial stage of loading, the acoustic emission activity generated by the gradual closure of the original microcracks increases significantly, acoustic emission activity was far away from its average degree, there is a small range of stress concentration inside, and the variance curve at this stage is concave.(2)
a-b stage is the stable development stage of elastic deformation corresponding to the stress-strain curve. The acoustic emission activity was less; the impact rate was relatively average and tends to be stable gradually at this stage. At this time, the variance curve shows a slow downward trend and gradually approaches a constant. The internal damage of coal samples has almost no change, and the damage or stress distribution was uniform.(3)
b-c stage is the microcrack stage of crack propagation corresponding to the stress-strain curve. Microcracks were generated constantly in this stage, cracks expanded rapidly, and a large number of acoustic emission parameters were generated, and the acoustic emission deviates from the average value greatly. The variance curve growth is more obvious than that in the o-a stage, and the sharp degree is more obvious. Large-scale cracks have been generated in the coal sample, and local damage has converted into large-scale damage gradually. Point b is a sudden jump point of the curve from a stable development stage to a rapid growth stage, and this turning and abrupt behavior is important precursor information for the early warning of coal sample fracture instability.(4)
After the pointc stage, it is a small part of the microcracking stage of crack growth in the full stress-strain curve. The curve is no longer growing, showing a steady change. The internal stress of the coal sample exceeded the internal stress limit, and the coal sample was about to be destroyed at this stage. Point c is the end point of the rapid growth stage and also the turning point of the variance curve, the coal sample is about to be destroyed.Figure 8
Evolution of the SF1 coal sampleVAEi curve.


## 6. Discussion

It can be seen from Figure8 that when the coal sample entered the compaction stage, the VAEi curve increased significantly, indicating that a large number of acoustic emission activities occurred in a short period of time and a large amount of damage was added inside the coal sample. Then, entering the linear elastic stage, the VAEi curve decreases slowly and approaches a constant gradually; the coal sample will not be damaged at this time. When the VAEi curve reaches point b, the VAEi curve increases sharply, and then, the rock cracks expand, penetrate, and develop in the direction of rock failure and instability gradually. Therefore, point b is defined as a general early warning point. The identification of b is very important, and early warning points can be identified through the mutation behavior of the VAEi curve.At the stage of coal sample compaction, it increases significantly and reaches the highest point, which is 49.53 s, and then decreases steadily; the load is 0.10 kN. 49.53 s is a turning point when the damage of the coal sample increases steadily and rapidly. After this time, the damage is almost unchanged or grows slowly. As the internal cracks of the coal sample continue to develop, theVAEi value reaches point b, which is 422.55 s, and the load is 5.78 kN, about 70% of the peak load. Point b is the jumping point where the damage changes from stable to rapid growth, which is the jumping point where the rock changes from a linear elastic stage to the microcrack growth stage. Then, it reaches the highest point c, where the loading time is 476.26 s, and the value gradually tends to be stable. The loading load at point c is 7.04 kN, about 90% of the peak load. Point c is defined as a key early warning point.To give a more reasonable and accurate early warning for the destruction and instability of saturated coal samples, the general early warning point for the coal sample destruction zone shall be divided into three early warning zones, namely, Level III early warning, Level II early warning, and Level I early warning. The damage of the coal sample increases gradually with the continuous increase in the loading load. When it reaches 0.7σmax, new cracks begin to appear, and the volume of the coal sample changes from compression to expansion. At this time, the Level III early warning is conducted, which is the early stage of the early warning. The external load continues to increase. When it reaches 0.8 σmax, the damage inside the coal sample increases sharply. The Level II early warning is conducted at this time, which is expected to be a medium-term stage. When it reaches 0.9 σmax, the number of cracks inside the rock reaches a critical state. After passing the key warning point, the rock deformation speed increases rapidly, and the fracture speed accelerates until it reaches the point of failure and instability. The Level I warning is conducted, which is the late warning stage at this time.


## 7. Conclusion

The acoustic emission test of natural coal, natural frozen coal, and saturated frozen coal under uniaxial compression was carried out, and the deformation, failure, and acoustic emission characteristics of coal samples were compared and analyzed. The damage process of the coal samples was analyzed, and the early warning parameterVAEi was proposed based on the acoustic emission impact rate parameter. An early warning investigation was conducted on saturated frozen coal samples. The main conclusions are as follows:(1)
The water inside the coal sample freezes slowly under low-temperature frozen conditions, the volume of the internal cracks of the coal sample becomes larger, and more damage is generated in the original coal sample, resulting in a significant reduction in the compressive strength of the coal sample after low-temperature freezing. Natural frozen coal samples and saturated frozen coal samples decreased by 12.42% and 24.88%, respectively, compared with natural coal samples. The postpeak curve of the saturated frozen coal sample was the shortest; the coal sample was damaged directly, the brittleness was obviously enhanced, and the final failure form of the coal sample was easy to break.(2)
The change characteristics of the acoustic emission impact rate of the natural frozen coal sample were consistent with those of the natural coal sample. The difference in acoustic emission characteristics of saturated frozen coal samples was mainly shown, in which more acoustic emissions were generated at the initial stage of loading, and the impact rate was large. In the plastic deformation stage, acoustic emission has increased suddenly several times due to the more frequent occurrence and propagation of internal cracks, especially in the early stage of rock failure.(3)
The damage characteristics of coal samples were basically the same under different test conditions, among which the saturated coal samples had larger damage and more growth in the compaction stage, and the postpeak damage was not increased. Based on the precursor information of the rapid increase of damage before the destruction of coal samples, the damage model of coal samples was established:D=A+BxC.(4)
VAEi, the early warning parameter, based on the variance of the acoustic emission impact rate was proposed. The VAEi curve had the characteristics of stage change, showing four stages of “growth, slow decline, rapid growth, stable, and unchanged.” The sudden change point from the stable development stage of early warning parameters to the rapid growth stage was defined as a general early warning point, and the end point of the rapid growth stage of early warning parameters was defined as a key early warning point. A hierarchical early warning idea was proposed finally.



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*Source: 1607529-2023-01-17.xml*