Study on Damage Evolution and Resistivity Variation Regularities of Coal Mass Under Multi-Stage Loading

Featured Application

It is more comprehensive and precise to understand the evolution process of coal-rock dynamic disasters and understand the evolution process of coal-rock dynamic disasters.

Abstract

In order to describe resistivity variation regularities during the process of damage evolution of loading coal mass more comprehensively and accurately, electrical resistivity and acoustic emission (AE) characteristics of coal mass were tested by 3532-50 LCR tester and AMSY-6 AE data acquisition system under the condition of multi-stage loading, and resistivity variation characteristics were analyzed with stress changing. The damage evolution process of coal mass was studied by the measurement of the AE parameters, and the resistivity curve was obtained in the damage conditions based on the relationship between the AE damage variable and the resistivity. The results show that resistivity and stress curves of coal mass have a good correspondence during the multi-stage loading, and the resistivity shows a trend of fluctuating downward with the increasing of stress. The resistivity increases sharply to the maximum value when the load increases to the ultimate compressive strength of specimens. AE information can reveal effectively damage evolution process of microcracks formation, expansion and fracture in coal mass under external force, and during multi-stage loading, the cumulative AE ringing counts curve of coal mass have three different types of growth trends: stable stage, sudden change stage, gradual increasing stage. Meanwhile, the relationship between resistivity and AE damage variable is established based on the formula of damage variable under uniaxial compression and combined with continuous damage mechanics, and its rationality is verified.

1. Introduction

The coal mass is affected by long-term geological processes, which is a complex mechanical medium. In the process of underground mining, the coal mass is affected by the interaction of original rock stress field and mining stress field, and the distribution state of primary cracks and mining cracks in coal mass will change with the stress state, resulting in internal damage and failure of coal mass [1,2]. The resistivity is an important parameter reflecting the change of microfractures in coal mass, and it will change abnormally in abnormal geological structure areas and stress concentration zones [3]. Therefore, studying the damage and failure characteristics under different loading stages and further revealing internal relation between resistivity and damage variable can be able to monitor the stability of surrounding rock and the occurrence of coal-rock dynamic disasters in practical engineering [4,5].

The loading deformation process of coal mass is accompanied by the phenomenon of internal microfractures in generating, expanding and fracturing and the evolution of AE energy, which can reflect the damage and failure of coal mass effectively [6]. Yang et al. compared the AE experiments of intact sandstone to that of sandstone with a single fracture under different loading stages, and found that experiments could help to analyze the damage and deformation characteristics of rock mass that comparing [7]. Cao et al. conducted studies on response regularities of AE parameters and damage evolution regularities of rock mass at different loading rates under uniaxial compression and derived the corresponding damage evolution equation based on the equivalent strain assumption and AE accumulative ringing count [8]. Wang et al. found that the variation characteristics of AE energy are closely related to the deformation and failure of coal mass under uniaxial compression [9]. Kong et al. discovered the relationship between AE parameters and stress-strain of coal samples under uniaxial compression, and derived the qualitative and quantitative expressions of coal samples damage variable [10]. Zhang et al. conducted a detailed study of AE under cyclic loading conditions and found there was a great positive correlation between the AE parameters and stress of coal mass [11]. As we all known, it will be occurring the damage and deformation during the process of loading coal mass, which will lead to changing in its conductive properties. Besides, Chen et al. carried out uniaxial compression tests on different types of coal and rock mass, analyzed and discovered the resistivity variation regularities with stress and strain, and fitted the resistivity variation curve with the formula [12]. Wang et al. investigated variation regularities of electrical parameters and stress under uniaxial compression and found both of them had obvious consistency [13]. Li et al. conducted a further study of resistivity variation regularities of sandstone during the damage and failure process under uniaxial compression. They found that AE response information had strong regularity and complementarity with resistivity variation regularities, and calculated the damage evolution equation of typical rock samples on the basis of experiments [14]. Qi et al. put into effect on a detailed study of resistivity, AE parameters, stress and strain in coal gangue under uniaxial compression. They proposed a theory that AE parameters could reflect the initiation and propagation of cracks, and further explained the resistivity variation regularities [15]. Li et al.’s work pointed out that AE parameters and surface potential of coal and rock mass had obvious response characteristics to the formation, expansion and transfixion of internal cracks under uniaxial compression [16]. Wang et al. calculated and regressed the relational expression between resistivity and damage variable of coal mass by using the joint test method of uniaxial compression and AE parameters, which verified the feasibility of its variation regularities [17]. Xu et al. conducted Brazilian Split tests for limestone samples that further corrected the variable of resistivity and AE characteristics, which obtained the response regularities of resistivity and AE parameters in different bedding directions and discovered evolution regularities of damage variables [18]. Recently, it was found that the resistivity of coal mass is affected by temperature, frequency, applied electric field and its properties. Lyu et al. conducted studies on and discovered the resistivity variation regularity decreased linearly at temperatures above 45 °C for raw coal, while the resistivity of briquettes showed a linear decline in the temperature range of 15b °C~65 °C [19]. Zheng et al. carried out a series of experiments on fly ash and found that resistivity increased at first and then gets worse with the increase of temperature, and discovered there is peaking in the range of 373–473 K [20]. Guo et al. pointed out that resistivity decreased exponentially with increase in test frequency, and appeared different characteristics in different test directions [21]. In summary, most of researches on damage evolution regularity and resistivity variation regularity had been carried out independently, or more reflected the inherent relation between the two by data fitting, and it was not took into account inherent relation between resistivity and damage evolution of coal-rock mass. And that the majority of researches had been carried out under uniaxial compression conditions, and the coal and rock mass were usually under constant load loading conditions before the disaster, so that the complex stress environment of the actual coal and rock mass was not adequately considered [22]. Besides, the electrical resistivity is more susceptible to temperature, frequency, applied electric field and its properties, and the change of loading environment can easily cause abrupt change of resistivity, so that it will affect the instantaneous determination of damage of coal-rock mass. But acoustic emission is an intrinsic property during deformation and failure process of coal-rock mass, and it has strong sensitivity to the deformation and failure, which can determine the time of failure of the coal-rock mass exactly. And AE parameters have strong scale effects on the process of coal sample damage, which can cause not only in terms of specimen peak stress changes with the different size and slenderness, but also in terms of AE signals cumulative counting changes significantly [23]. To this end, it is important to adopt the simultaneous test method of resistivity and acoustic emission to establish the relationship between the AE damage variable and resistivity of coal mass under multi-stage loading without considering the scale effects in this paper, and calculate the resistivity by using cumulative AE ringing count, so as to provide a basis for the application of resistivity and AE monitoring and forecasting technology, and further improve theoretical basis of electric prospecting technology for predicting coal-rock dynamic disasters.

2. Experiment Test

2.1. Sample Preparation

In this paper, coal samples of loading experiments were taken from the Sihe Coal Mine in Jincheng City, Shanxi Province. In mining areas, the geological structure of the coal mass is simple, and it is hard and mainly bases on horizontal bedding. When coring, we should avoid the area of primary cracks as far as possible and arrange the core position reasonably so as to ensure that coal samples are similar in layered joint structure. Then the on-site collecting cores of coal mass were cut into standard specimens with a length of 100 mm and a diameter of 50 mm by cutting machine along vertical bedding direction in the laboratory and polished by polishing machine to keep the parallelism error of end face less than 0.05 mm and the smoothness error of end face less than 0.02 mm. Besides, the reserved position of AE probes on all specimens should be polished smoothly so as to make contact between probes and sample more suitable before the experiments. In addition, in order to ensure the accuracy of the experimental results and free from moisture and other factors, it was necessary to put coal samples into a vacuum drying oven for dehydration and drying, and then put them into a drying bottle for experimental using. At the same time, in order to prevent the coal samples from being affected by other factors, they were wrapped in plastic wrap. Coal samples are shown in Figure 1.

2.2. Sample System

The experimental system was mainly consisting of loading control system, AE testing system and resistivity testing system. The loading control system adopted the test system of Tianchen electro-hydraulic servo pressure testing machine (Tianchen Testing Machine Manufacturing Co., Ltd., Jinan, China), which was mainly consisting of press and automatic control program named TensonTest. On top of that the control program was used to modify such as stress, strain, control modes and record experimental data in real time, which could switch the observation mode at any time for efficient sampling. Thus, it could achieve the high-precision constant load testing experiment during the process of deformation and failure in coal mass. Moreover, the resistivity testing system was mainly composing of 3532-50 LCR tester (Dongfang Zhongke Integrated Technology Co., Ltd., Beijing, China) with a measuring accuracy of 0.01 Ω·m. And it was worth noting that a layer of conductive coupling agent should be coated between coal samples and copper electrodes before the experiment. In addition, in order to avoid the effect of experimental equipment on the resistivity measurement results, a piece of insulating paper was laid under the electrode, and then the electrode was fixed and connected with LCR tester. In general, the electrical resistivity decreases with the increase of test frequency during the process of loading, and it is extremely significantly that the resistivity variation range changes in process under low frequency conditions and can eliminate the resistivity polarization phenomenon effectively under low frequency conditions. Therefore, a certain frequency (usually 10 kHz) was generally used to measure electrical resistivity of coal mass in low frequency range [24,25]. To the end, the AE-measurement system adopted data acquisition system of AMSY-6 AE tester (Vallen Systeme, German), and there were six AE data acquisition channels in system and collecting AE parameters by data processing software Vallen in real time during the loading and deformation process of coal mass. Even more important, in order to analyze the damage evolution process of coal samples in real time during the loading process, and realize the visual analysis in damage and deformation process of coal samples simultaneously, a low-speed camera was used to record the process of deformation and failure during loading. The loading control system, AE testing system and resistivity testing system is shown in Figure 2.

In this paper, the experiment of multi-stage loading was carried out on standard coal samples of Sihe Mine, which was loading at a rate of 0.5 MPa in steps with displacement loading control mode. On top of that axial stress increased gradually from 0 MPa to 11 MPa step by step until the coal samples are completely destroyed. In the meantime, the electrical resistivity was collected in real time by using the 3532-50 LCR tester during the loading process, and the cumulative AE ringing counts were collected and sorted out by the AE testing system. It was worth noting that the reserved position of AE probe needed to be polished smoothly and put on Vaseline evenly between AE probes and coal sample so that the probes fitted well on the coal sample. Furthermore, the upper three probes were placed separately at 120 degrees in a cross section, and the lower probes were arranged in a cross section that was misalignment with the upper portion, the schematic diagram of AE probes is shown in Figure 3.

3. Experimental Results and Analysis.

The coal samples were loading at a rate of 0.5 MPa/s in steps of 1 MPa, 3 MPa, 5 MPa, 7 MPa, 9 MPa and 11 MPa, and conducted a detailed research on measuring resistivity variation characteristics and the AE response regularities. In this paper, a total of three sets of coal sample loading experiments were carried out, and a typical group of experimental results was used to analyze as one of my priorities in this paper due to the limitation of layout. The experimental results are shown in Figure 4 and Figure 5.

3.1. Electrical Resistivity Variation Characteristics

The coal mass is one of solid conductor material, and the separation of internal charges and directional movement of free charges in coal mass is the basis and premise for conductivity [26,27]. When the external force is applied to coal mass, the conductivity of coal mass will increase with directional movement of internal charges between macromolecular structure in coal mass [28]. It can be seen that the trend of the change of resistivity fluctuates slightly in steps of 1 MPa, 3 MPa, 5 MPa, 7 MPa, 9 MPa and 11 MPa from the above figure. It shows a trend of fluctuating downward with the increasing of inter-stage stress, but there is a good correspondence relationship between the resistivity curve and stress curve in the mass. The deformation and failure of internal microstructures in the coal sample are inapparent due to lower load at the initial stage of loading, while the value of electrical resistivity is relatively large. However, it is obvious that the resistivity almost maintains a constant value during the stage of constant loading. In addition, the electrical resistivity will decrease with the increase of loading not only as a result of the internal microstructures of coal sample are gradually compacted, but also because of conductive channels are better with each other. When the loading continues to increase and reach the ultimate compressive strength of coal mass, the internal microstructure of coal sample will be completely destroyed, and it is generating a large number of cracks during the process of loading, which greatly cuts off the conductive channels of coal mass. In this moment, the sample is completely destroyed because of the generation of main fracture, the electrical resistivity is abruptly increasing to a maximum.

3.2. Damage Evolution Analysis of Coal Sample

AE technology is a method that can effectively monitor perform energy release during the loading of coal and rock materials, and cumulative AE ringing counts as an effective index of damage evolution during the loading of coal and rock mass, which can be used to reveal effectively damage evolution process of microcracks formation, expansion and fracture in coal-rock mass under external force [29,30,31]. During the loading of coal mass, AE energies are released in the form of stress wave and received by AE probes, which can accurately reflect internal morphological changes of particle motion, fracture and microcrack propagation in process [32,33]. The experimental results of the cumulative AE ringing counts of loading coal sample are shown in Figure 5.

It can be seen from the analysis in Figure 4 that the curves of cumulative AE ringing counts and stress have the same growth trend during the multi-stage loading process, and the curve of cumulative AE ringing counts has three different types of growth trends, i.e., stable stage, sudden change stage, gradual increasing stage, during the compression process. In order to realize the visual analysis of damage and deformation process of coal sample simultaneously, a low-speed camera was used to record the process of deformation and failure during loading. It can be seen in the fracture process of coal mass in Figure 6.

The values of AE accumulative ringing count are extremely small at the initial stage of loading, which are basically maintaining near zero and the curve of AE accumulative ringing count shows a stage of stable change. It indicates that the internal microfracture structures of coal sample are gradually compressed and closed during the constant loading process, and producing small amounts of elastic deformations to some extent in the process. There are no new fracture structures in coal sample, its internal integrity is quite good and it is merely occurring minor amounts of slip phenomenon of the structural plane. That is why the conductive channels of coal sample are good contact with each other and the resistivity decreases slightly compared with the initial loading stage, but the resistivity fluctuates around a fixed value due to the stable and unchanged internal microfracture and porosity under constant loading.

The values of AE accumulative ringing count increase suddenly during the stress increases to the second stage loading, and the curve of AE accumulative ringing count shows a stage of sudden change. It makes clear that new cracks begin to form in the coal sample and the damage and destruction begin to emerge at this stage. However, the values of AE accumulative ringing count are tending to be stable under the constant loading. It shows that the curve of AE accumulative ringing count shows a stage of stable change and internal microfracture structures of coal sample are not further expanding, not causing further aggravation of damage. The resistivity variation curve has a slight downward trend owing to damage and failure of coal samples in this stage, and internal microfracture structures of coal sample are gradually further compressed and closed during the constant loading process, creating resistivity fluctuates around a fixed value and appears small increment.

The trend of AE accumulative ringing count curve is similar to the curve of the upper level during the stress increases to the third stage loading. In this stage, it is merely occurring tiny quantity of increasing in counts, causing further expansion of microfractures and aggravation of damage and failure, which creating the resistivity variation curve shows a further downward trend.

The values of AE accumulative ringing count increase suddenly and substantially during the stress increases to the fourth stage loading, and the curve of AE accumulative ringing count shows a stage of sudden change. It makes clear that coal sample is in plastic deformation stage and the interaction between internal microfracture structures is obvious. Consequently, the microfracture structures extend and penetrate with each other gradually lead to the destruction of the coal sample. Nevertheless, the values of AE accumulative ringing count are increasing slowly under the constant loading, and it indicates that the curve of AE accumulative ringing count shows a stage of gradual increasing. In other words, the internal microfracture structures of coal samples are still expanding even in constant loading, and coal sample further damage and destruction in this process.

The trend of AE accumulative ringing count curve is similar to the curve of the upper level during stress increases to the fifth stage loading. In this process, it is increasing significantly in AE accumulative ringing count, and the interaction between internal microfracture structures is more obvious. Therefore, the microfracture structures extend and penetrate with each other gradually lead to the destruction of coal samples. When the coal sample is completely destroyed, the curve of AE accumulative ringing count shows a state of stable change with time. That is to say the compression capacity of the coal sample has reached the ultimate load-bearing limit in this continuous stable stage.

From the fourth stage of loading, the damage and failure of the coal sample are further aggravated, which causing the resistivity variation curve has a fluctuating downward trend. When the stress is gradually increasing the ultimate compressive strength, the values of AE accumulative ringing count increase to the peak at the same time. Meanwhile, formation, expansion and fracture of internal microfracture structures in coal mass reach the final stage to an end, and coal sample completely damage and destroy in this process. It is obvious that the value of resistivity increases to a peak abruptly at this time.

4. The Influence of Damage Evolution on Electrical Resistivity

4.1. The Establishment of AE Damage Model

In order to further analyze the damage evolution process of coal sample, AE accumulative ringing count is used as a characteristic parameter to describe the damage characteristics of the coal sample. It was used to describe the process from microscopic damage to macroscopic fracture of materials with the concept of continuous factor and define the damage variable by L. M. Kachanov and Rabotnov [34,35].

$$D=A_d/A$$

(1)

where A_d is the damage cross-sectional area of loading coal sample and A is the cross section area in the initial undamaged state.

The counts of AE rings per unit area when the coal sample is destroyed as follows:

$${\mathrm{C}}_{\mathrm{w}}=\frac{C_0}{A}$$

(2)

where C₀ is ringing counts of the whole section of coal sample in complete failure.

When the damage area reaches A_d, the AE accumulative ringing count of the A_d area destruction is defined as follows:

$$C_d=C_w{A}_d=\frac{C_0}{A}{A}_d$$

(3)

Hence,

$$D=\frac{C_d}{C_0}$$

(4)

The damage variable can be modified to Equation (4) due to the different failure conditions of coal mass.

$$D=D_U\frac{C_d}{C_0}$$

(5)

where D_u is the critical damage value.

For convenience of calculation, the critical damage value can be expresses as follows:

$$D_U=1-\frac{{\sigma }_c}{{\sigma }_p}$$

(6)

Baoxian Liu and Xue Sun conducted a detailed study of uniaxial and triaxial compression in coal and rock mass, and the analytical expressions of damage variable were deduced on this foundation of AE accumulative ringing count. In this paper, the theoretical analysis was carried out with the analytic formula of damage variable of coal-rock mass under uniaxial compression only as follows [10,36,37]:

$${\mathrm{D}}_{\mathrm{c}}=D_u\frac{C_d}{C_0}=\left(1-\frac{{\sigma }_c}{{\sigma }_p}\right)\frac{C_d}{C_0}$$

(7)

where D_u is the critical damage value of sample; C_d is the AE accumulative ringing count of coal and rock mass at any time under the loading; C₀ is the AE accumulative ringing count of completely destroyed coal and rock mass; σ_c is the residual strength and σ_p is the ultimate strength.

Consequently, the damage of coal and rock mass is analyzed basing on the AE parameters and the results of stress strain, and combining with the damage variable expression of AE accumulative ringing count, and the damage curve of uniaxial compression in coal sample is shown in Figure 7.

It can be seen from the Figure 7 that there is a good correspondence relationship between damage variable and resistivity variation curve of coal mass, and the curve of damage variable has a stepladder upward trend, while the resistivity curve shows a stepladder downward trend with time. Besides, the curve of damage variable is consistent with the curve of cumulative AE ringing counts, and there are three different types of growth trends, i.e., smooth change, abrupt rise, muted growth. In addition, it is clear that the values of damage variable are relatively small in the initial stage of loading, which indicates the damage degree of loading coal sample increases slowly at the initial stage of loading. It is precisely because of the compaction of internal microfracture structures that new conductive channels are generated, resulting in a decrease in resistivity at the initial stage of loading [38]. When the stress increases gradually to 9 MPa, the curve of damage variable is still increasing constantly during the constant loading stage even, and it shows that new cracks constantly form in coal sample and the interaction, extension and penetration between internal microcracks with each other lead to the destruction of coal sample to the end.. Meanwhile, all of conductive channels are destroyed, and thus electrical resistivity increases to a peak suddenly along with the movement circuits of electrons are cut off or blocked. Moreover, it can be seen from picture that jump point of resistivity is slightly lagged behind damage variable, and it shows that the sensitivity of resistivity to the fracture is lower than that of acoustic emission, and the sensitivity of resistivity to microstructures change is better than that of acoustic emission in the initial stage of loading. Therefore, in order to accurately calculate electrical resistivity by using AE accumulative ringing count, the mathematical relationship between resistivity and cumulative AE ringing was established combining advantages with both for predicting and forecasting the occurrence time of coal-rock dynamic disasters.

4.2. The Relationship between AE Damage Variable and Electrical Resistivity

According to the working principle of LCR tester, the electrical resistivity of the sample is calculated by the following formula [39].

$$\rho =R\cdot S/L$$

(8)

where $\rho$ is the electrical resistivity of coal mass; R is the real-time resistance value of loading coal in Ω; L is the length of the coal sample in m and S is the cross-sectional area of sample in m².

As can be seen from the foregoing description, the damage and failure of coal mass are a process of deformation and fracture, and the formation, expansion and fracture of microcracks in coal mass can have a great impact on electrical resistivity [40]. Moreover, it is believed that the conductivity of coal mass is mainly formed by the free movement of the charge on account of conductivity theory of solid electrolyte, while the effective bearing area of free charge changes during the damage evolution of coal mass [41]. Consequently, based on the damage variable in continuum damage mechanics and the AE damage variable under uniaxial compression, the relationship between AE damage variable and electrical resistivity is established by plugging Equations (1) and (7) into Equation (8) as follows:

$$\rho =\frac{\mathrm{R}}{L}\left[\left(C_d\cdot \left({\sigma }_{\mathrm{c}}-{\sigma }_p\right)/\left(C_0\cdot {\sigma }_p\right)\right)+1\right]S$$

(9)

In order to verify the effectiveness and rationality of expression, the theoretical and experimental curves of electrical resistivity with time are calculated according to the above relational expression as shown in Figure 8. The above results show that the resistivity theoretical curve is basically consistent with the experimental curve, and it makes clear that the relationship between AE damage variable and electrical resistivity is accurate and reliable for forecasting the occurrence time of coal-rock mass. Also, it can avoid the influence of other factors such as temperature, frequency on results as well as it obtains the failure time of coal-rock mass without delaying. In addition, both of resistivity test results and theoretical calculation results decrease step by step with the gradual increasing of damage variable. When the damage variable increases to a peak abruptly, that is to say, the damage and failure of the coal sample reaches the maximum, and electrical resistivity suddenly increases to a peak in a short time as the main fracture occurring. The relationship expression between AE damage variable and electrical resistivity is compared with the previous methods of using a single test to describe resistivity variation regularities, it is more comprehensive and accurate to describe the resistivity variation regularities during the process of damage evolution of loading coal mass adopting the joint test method of resistivity and AE technique. Therefore, it is helpful to understand the evolution process of coal-rock dynamic disasters and promote the application and development of electrical prospecting technology.

5. Discussion

To summarize, it is more comprehensive and precise to describe resistivity variation regularities adopting the joint test method of resistivity and AE technique during the process of damage evolution of loading coal mass. Thus, it is conducive to understand the evolution process of coal-rock dynamic disasters and provide an important theoretical basis for the application of coal and rock dynamic disasters prediction. Moreover, there is a good correspondence relationship between the trend of resistivity and damage variable in coal mass, and the curve of damage variable has a stepladder upward trend, while the resistivity curve shows a stepladder downward trend with time. And AE characteristic parameters can mirror the damage and failure process of coal mass, which can be used to further describe resistivity variation regularities in each loading stage with establishing the relationship between the AE damage variable and electrical resistivity. And then improving the theoretical basis of electrical prospecting technology for predicting coal-rock dynamic disasters.

In previous studies, it could be retrieving the damage evolution process of coal-rock mass by utilizing electrical resistivity. Liu et al. conducted studies on resistivity variation regularities and accurately retrieved the formation, expansion and failure of microcracks in concrete specimens [42]. Nevertheless, it was usually limited to a fixed sampling frequency in resistivity testing of loading coal, which could not fully reflect the change of the coal mass at any time due to polarization effect [43]. Thus, collected resistivity data could not correspond to the damage evolution process of coal mass completely, so that it was difficult to determine the point-in-time of damage and failure in coal mass by resistivity variation regularities and accurately predict the occurrence of coal-rock dynamic disasters. And it is necessary for accurately calculating electrical resistivity by establishing the relationship between electrical resistivity and damage variable. Bai et al. calculated the damage evolution expression among resistance, stress and strain, and the rationality of the evolution equation is verified by fitting the data [44]. Ji et al. calculated and fitted the elastic modulus and collected resistivity data under cyclic loading and unloading, but it was not comprehensive to describe the relationship between resistivity and damage variable [45]. As shown in Figure 5, the cumulative AE ringing counts of coal mass have a long quiet period at the initial stage of loading, and they are gradually increasing with increase of stress and loading time. But there are few AE signals at a constant loading stage, and it indicates that the damage degree of loading coal sample does not increase. After loading for a while, the cumulative AE ringing counts increases at a speed of 2~3 times, which indicates that the main fracture of loading coal will occur and coal samples will be completely destroyed. In recent years, the electrical prospecting technology plays a significant role in predicting and forecasting the occurrence time of coal-rock dynamic disasters, and we all know electrical resistivity is an important parameter of coal mass [46,47]. As shown in Figure 7, when damage variable and electrical resistivity increases suddenly, this shows that electrical resistivity and cumulative AE ringing count has the same change tendency, so it is feasible that calculating the electrical resistivity by using cumulative AE ringing count. As can be seen from the foregoing description, the coal mass is a kind of solid conductor material and there are mainly two kinds of conductive forms, ionic conduction and electronic conduction, and the electrical resistivity is sensitive to temperature, frequency, applied electric field and its properties, it will gradually decrease with the increase of temperature and frequency [48,49,50]. Although the effect of applied electric field is very limited on resistivity, it can be causing damage to coal mass and increase the temperature [51]. Moreover, other factors such as gas, moisture and degree of metamorphism have significant effect on results of electrical resistivity, but all in all, it is the result of the interaction of many factors, so there are still some shortcomings in using electrical prospecting technology to predict and predict coal-rock dynamic disasters. However, acoustic emission is an intrinsic property during deformation and failure process of coal-rock mass, and electrical resistivity is more sensitive to internal fracture than AE signal, while AE signal is more sensitive to instantaneous fracture of coal mass. Consequently, in this paper, it is necessary to establish the relationship between AE damage variable and resistivity based on the analytical formula of cumulative AE ringing, so as to sufficiently consider the influence of damage and failure on resistivity variation regularities of coal mass, and determine the point-in-time of sharp change of resistivity in coal mass, which can provide more accurate signals for the coming disaster. It can be seen from Figure 8 that the relationship is in good agreement in this paper, which makes clear that adopting the joint test method of resistivity and AE technique is accurate and reliable.

However, AE parameters depend on the slenderness and samples size and have strong scale effects on the process of coal sample damage, and it is found that not only in terms of specimen peak stress changes with the different size and slenderness, but also in terms of AE signals cumulative counting changes significantly. Invernizzi et al. conducted a series of numerical simulation tests on different size and slenderness of coal samples and found AE accumulative ringing count increased with the increase of experimental size [23]. Carpinteri et al. carried out a large number of studies found that AE fractal theory can effectively evaluate crack propagation monitoring of reinforced concrete structures and masonry buildings and found that it takes into account the multi-scale character of energy dissipation has scale effects [52,53,54,55]. In this paper, standard samples with a size of 100 mm and a diameter of 50 mm are used during the loading, and the scale effects are obviously not taken into account in the analysis of the relationship between resistivity and AE accumulative ringing count, which lead to the resistivity calculated by this model is obviously uncertain due to scale effects. Therefore, the model needs further improvement on this basis, and it is important to establish a more mathematical relationship between AE parameters and resistivity directly and combine with other monitoring techniques simultaneously next work. And in this course, it is significant for further describing the deformation and failure of coal-rock mass and monitoring and predicting coal and rock dynamic disasters without confining itself to the influence of sampling frequency, temperature and scale effects on resistivity.

6. Conclusions

On the basis of previous studies, the relationship between electrical resistivity and damage variable under multi-stage loading of Sihe Coal Mine is analyzed as well as damage evolution based on them in AE characteristic testing, the main conclusions are as follows:

(1)

There is a good correspondence relationship between the resistivity variation curve and stress variation curve in the mass under multi-stage loading. The electrical resistivity will decrease step by step with the gradual increasing of stress, and when the load continues to increase and reach the ultimate compressive strength of coal mass, the electrical resistivity is abruptly increasing to maximum.

(2)

AE messages can be used to reveal effectively damage evolution process of microcracks formation, expansion and fracture in loading coal. And the curve of AE cumulative ringing count has three different types of growth trends, i.e., table stage, sudden change stage, gradual increasing stage, during the compression process.

(3)

Combining the different sensitivity of acoustic emission and resistivity to deformation and failure of coal-rock mass, the relationship between resistivity and AE accumulative ringing count is established, and its rationality is verified. And it is more comprehensive and precise to understand the evolution process of coal-rock dynamic disasters and understand the evolution process of coal-rock dynamic disasters.